TSTP Solution File: LCL544+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:10:05 EDT 2023
% Result : Theorem 217.30s 217.61s
% Output : Proof 217.55s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 01:24:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 217.30/217.61 SZS status Theorem for theBenchmark.p
% 217.30/217.61 SZS output start Proof for theBenchmark.p
% 217.30/217.61 Clause #0 (by assumption #[]): Eq (Iff modus_ponens (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y)) True
% 217.30/217.61 Clause #4 (by assumption #[]): Eq (Iff implies_2 (∀ (X Y : Iota), is_a_theorem (implies (implies X (implies X Y)) (implies X Y)))) True
% 217.30/217.61 Clause #8 (by assumption #[]): Eq (Iff and_3 (∀ (X Y : Iota), is_a_theorem (implies X (implies Y (and X Y))))) True
% 217.30/217.61 Clause #34 (by assumption #[]): Eq modus_ponens True
% 217.30/217.61 Clause #37 (by assumption #[]): Eq implies_2 True
% 217.30/217.61 Clause #41 (by assumption #[]): Eq and_3 True
% 217.30/217.61 Clause #49 (by assumption #[]): Eq (Iff necessitation (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X))) True
% 217.30/217.61 Clause #65 (by assumption #[]): Eq (Iff axiom_m4 (∀ (X : Iota), is_a_theorem (strict_implies X (and X X)))) True
% 217.30/217.61 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True
% 217.30/217.61 Clause #77 (by assumption #[]): Eq necessitation True
% 217.30/217.61 Clause #83 (by assumption #[]): Eq op_strict_implies True
% 217.30/217.61 Clause #85 (by assumption #[]): Eq (Not axiom_m4) True
% 217.30/217.61 Clause #87 (by clausification #[0]): Or (Eq modus_ponens False)
% 217.30/217.61 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 217.30/217.61 Clause #120 (by clausification #[4]): Or (Eq implies_2 False) (Eq (∀ (X Y : Iota), is_a_theorem (implies (implies X (implies X Y)) (implies X Y))) True)
% 217.30/217.61 Clause #127 (by clausification #[85]): Eq axiom_m4 False
% 217.30/217.61 Clause #128 (by clausification #[87]): ∀ (a : Iota),
% 217.30/217.61 Or (Eq modus_ponens False)
% 217.30/217.61 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 217.30/217.61 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota),
% 217.30/217.61 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 217.30/217.61 Clause #130 (by clausification #[129]): ∀ (a a_1 : Iota),
% 217.30/217.61 Or (Eq modus_ponens False)
% 217.30/217.61 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 217.30/217.61 Clause #131 (by clausification #[130]): ∀ (a a_1 : Iota),
% 217.30/217.61 Or (Eq modus_ponens False)
% 217.30/217.61 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 217.30/217.61 Clause #132 (by forward demodulation #[131, 34]): ∀ (a a_1 : Iota),
% 217.30/217.61 Or (Eq True False)
% 217.30/217.61 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 217.30/217.61 Clause #133 (by clausification #[132]): ∀ (a a_1 : Iota),
% 217.30/217.61 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 217.30/217.61 Clause #135 (by clausification #[49]): Or (Eq necessitation False) (Eq (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X)) True)
% 217.30/217.61 Clause #150 (by clausification #[135]): ∀ (a : Iota), Or (Eq necessitation False) (Eq (is_a_theorem a → is_a_theorem (necessarily a)) True)
% 217.30/217.61 Clause #151 (by clausification #[150]): ∀ (a : Iota), Or (Eq necessitation False) (Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True))
% 217.30/217.61 Clause #152 (by forward demodulation #[151, 77]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True))
% 217.30/217.61 Clause #153 (by clausification #[152]): ∀ (a : Iota), Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True)
% 217.30/217.61 Clause #195 (by clausification #[65]): Or (Eq axiom_m4 True) (Eq (∀ (X : Iota), is_a_theorem (strict_implies X (and X X))) False)
% 217.30/217.61 Clause #197 (by clausification #[195]): ∀ (a : Iota),
% 217.30/217.61 Or (Eq axiom_m4 True) (Eq (Not (is_a_theorem (strict_implies (skS.0 20 a) (and (skS.0 20 a) (skS.0 20 a))))) True)
% 217.30/217.61 Clause #198 (by clausification #[197]): ∀ (a : Iota),
% 217.30/217.61 Or (Eq axiom_m4 True) (Eq (is_a_theorem (strict_implies (skS.0 20 a) (and (skS.0 20 a) (skS.0 20 a)))) False)
% 217.30/217.61 Clause #199 (by forward demodulation #[198, 127]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (strict_implies (skS.0 20 a) (and (skS.0 20 a) (skS.0 20 a)))) False)
% 217.30/217.61 Clause #200 (by clausification #[199]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies (skS.0 20 a) (and (skS.0 20 a) (skS.0 20 a)))) False
% 217.55/217.76 Clause #234 (by clausification #[8]): Or (Eq and_3 False) (Eq (∀ (X Y : Iota), is_a_theorem (implies X (implies Y (and X Y)))) True)
% 217.55/217.76 Clause #1027 (by clausification #[74]): Or (Eq op_strict_implies False) (Eq (∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True)
% 217.55/217.76 Clause #1028 (by clausification #[1027]): ∀ (a : Iota),
% 217.55/217.76 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True)
% 217.55/217.76 Clause #1029 (by clausification #[1028]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (Eq (strict_implies a a_1) (necessarily (implies a a_1))) True)
% 217.55/217.76 Clause #1030 (by clausification #[1029]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 217.55/217.76 Clause #1031 (by forward demodulation #[1030, 83]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 217.55/217.76 Clause #1032 (by clausification #[1031]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1))
% 217.55/217.76 Clause #1193 (by clausification #[120]): ∀ (a : Iota),
% 217.55/217.76 Or (Eq implies_2 False) (Eq (∀ (Y : Iota), is_a_theorem (implies (implies a (implies a Y)) (implies a Y))) True)
% 217.55/217.76 Clause #1194 (by clausification #[1193]): ∀ (a a_1 : Iota), Or (Eq implies_2 False) (Eq (is_a_theorem (implies (implies a (implies a a_1)) (implies a a_1))) True)
% 217.55/217.76 Clause #1195 (by forward demodulation #[1194, 37]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (implies a (implies a a_1)) (implies a a_1))) True)
% 217.55/217.76 Clause #1196 (by clausification #[1195]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (implies a (implies a a_1)) (implies a a_1))) True
% 217.55/217.76 Clause #1401 (by clausification #[234]): ∀ (a : Iota), Or (Eq and_3 False) (Eq (∀ (Y : Iota), is_a_theorem (implies a (implies Y (and a Y)))) True)
% 217.55/217.76 Clause #1402 (by clausification #[1401]): ∀ (a a_1 : Iota), Or (Eq and_3 False) (Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True)
% 217.55/217.76 Clause #1403 (by forward demodulation #[1402, 41]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True)
% 217.55/217.76 Clause #1404 (by clausification #[1403]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True
% 217.55/217.76 Clause #1410 (by superposition #[1404, 133]): ∀ (a a_1 a_2 : Iota),
% 217.55/217.76 Or (Eq (is_a_theorem a) True)
% 217.55/217.76 (Or (Eq True False) (Eq (is_a_theorem (implies (implies a_1 (implies a_2 (and a_1 a_2))) a)) False))
% 217.55/217.76 Clause #21453 (by clausification #[1410]): ∀ (a a_1 a_2 : Iota),
% 217.55/217.76 Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (implies a_1 (implies a_2 (and a_1 a_2))) a)) False)
% 217.55/217.76 Clause #21458 (by superposition #[21453, 1196]): ∀ (a : Iota), Or (Eq (is_a_theorem (implies a (and a a))) True) (Eq False True)
% 217.55/217.76 Clause #21491 (by clausification #[21458]): ∀ (a : Iota), Eq (is_a_theorem (implies a (and a a))) True
% 217.55/217.76 Clause #21556 (by superposition #[21491, 153]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (necessarily (implies a (and a a)))) True)
% 217.55/217.76 Clause #21589 (by clausification #[21556]): ∀ (a : Iota), Eq (is_a_theorem (necessarily (implies a (and a a)))) True
% 217.55/217.76 Clause #21590 (by forward demodulation #[21589, 1032]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies a (and a a))) True
% 217.55/217.76 Clause #21591 (by superposition #[21590, 200]): Eq True False
% 217.55/217.76 Clause #21594 (by clausification #[21591]): False
% 217.55/217.76 SZS output end Proof for theBenchmark.p
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