TSTP Solution File: LCL531+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL531+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n011.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 07:10:03 EDT 2023
% Result : Theorem 226.13s 226.34s
% Output : Proof 226.30s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL531+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n011.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 01:02:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 226.13/226.34 SZS status Theorem for theBenchmark.p
% 226.13/226.34 SZS output start Proof for theBenchmark.p
% 226.13/226.34 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
% 226.13/226.34 Clause #4 (by assumption #[]): Eq (Iff implies_2 (∀ (X Y : Iota), is_a_theorem (implies (implies X (implies X Y)) (implies X Y)))) True
% 226.13/226.34 Clause #8 (by assumption #[]): Eq (Iff and_3 (∀ (X Y : Iota), is_a_theorem (implies X (implies Y (and X Y))))) True
% 226.13/226.34 Clause #34 (by assumption #[]): Eq modus_ponens True
% 226.13/226.34 Clause #37 (by assumption #[]): Eq implies_2 True
% 226.13/226.34 Clause #41 (by assumption #[]): Eq and_3 True
% 226.13/226.34 Clause #49 (by assumption #[]): Eq (Iff necessitation (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X))) True
% 226.13/226.34 Clause #65 (by assumption #[]): Eq (Iff axiom_m4 (∀ (X : Iota), is_a_theorem (strict_implies X (and X X)))) True
% 226.13/226.34 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True
% 226.13/226.34 Clause #77 (by assumption #[]): Eq necessitation True
% 226.13/226.34 Clause #82 (by assumption #[]): Eq op_strict_implies True
% 226.13/226.34 Clause #84 (by assumption #[]): Eq (Not axiom_m4) True
% 226.13/226.34 Clause #86 (by clausification #[0]): Or (Eq modus_ponens False)
% 226.13/226.34 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 226.13/226.34 Clause #119 (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)
% 226.13/226.34 Clause #126 (by clausification #[84]): Eq axiom_m4 False
% 226.13/226.34 Clause #127 (by clausification #[86]): ∀ (a : Iota),
% 226.13/226.34 Or (Eq modus_ponens False)
% 226.13/226.34 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 226.13/226.34 Clause #128 (by clausification #[127]): ∀ (a a_1 : Iota),
% 226.13/226.34 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 226.13/226.34 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota),
% 226.13/226.34 Or (Eq modus_ponens False)
% 226.13/226.34 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 226.13/226.34 Clause #130 (by clausification #[129]): ∀ (a a_1 : Iota),
% 226.13/226.34 Or (Eq modus_ponens False)
% 226.13/226.34 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 226.13/226.34 Clause #131 (by forward demodulation #[130, 34]): ∀ (a a_1 : Iota),
% 226.13/226.34 Or (Eq True False)
% 226.13/226.34 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 226.13/226.34 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota),
% 226.13/226.34 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 226.13/226.34 Clause #134 (by clausification #[49]): Or (Eq necessitation False) (Eq (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X)) True)
% 226.13/226.34 Clause #140 (by clausification #[134]): ∀ (a : Iota), Or (Eq necessitation False) (Eq (is_a_theorem a → is_a_theorem (necessarily a)) True)
% 226.13/226.34 Clause #141 (by clausification #[140]): ∀ (a : Iota), Or (Eq necessitation False) (Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True))
% 226.13/226.34 Clause #142 (by forward demodulation #[141, 77]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True))
% 226.13/226.34 Clause #143 (by clausification #[142]): ∀ (a : Iota), Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True)
% 226.13/226.34 Clause #232 (by clausification #[8]): Or (Eq and_3 False) (Eq (∀ (X Y : Iota), is_a_theorem (implies X (implies Y (and X Y)))) True)
% 226.13/226.34 Clause #240 (by clausification #[65]): Or (Eq axiom_m4 True) (Eq (∀ (X : Iota), is_a_theorem (strict_implies X (and X X))) False)
% 226.13/226.34 Clause #242 (by clausification #[240]): ∀ (a : Iota),
% 226.13/226.34 Or (Eq axiom_m4 True) (Eq (Not (is_a_theorem (strict_implies (skS.0 29 a) (and (skS.0 29 a) (skS.0 29 a))))) True)
% 226.13/226.34 Clause #243 (by clausification #[242]): ∀ (a : Iota),
% 226.13/226.34 Or (Eq axiom_m4 True) (Eq (is_a_theorem (strict_implies (skS.0 29 a) (and (skS.0 29 a) (skS.0 29 a)))) False)
% 226.13/226.34 Clause #244 (by forward demodulation #[243, 126]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (strict_implies (skS.0 29 a) (and (skS.0 29 a) (skS.0 29 a)))) False)
% 226.30/226.50 Clause #245 (by clausification #[244]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies (skS.0 29 a) (and (skS.0 29 a) (skS.0 29 a)))) False
% 226.30/226.50 Clause #969 (by clausification #[74]): Or (Eq op_strict_implies False) (Eq (∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True)
% 226.30/226.50 Clause #970 (by clausification #[969]): ∀ (a : Iota),
% 226.30/226.50 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True)
% 226.30/226.50 Clause #971 (by clausification #[970]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (Eq (strict_implies a a_1) (necessarily (implies a a_1))) True)
% 226.30/226.50 Clause #972 (by clausification #[971]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 226.30/226.50 Clause #973 (by forward demodulation #[972, 82]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 226.30/226.50 Clause #974 (by clausification #[973]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1))
% 226.30/226.50 Clause #1115 (by clausification #[119]): ∀ (a : Iota),
% 226.30/226.50 Or (Eq implies_2 False) (Eq (∀ (Y : Iota), is_a_theorem (implies (implies a (implies a Y)) (implies a Y))) True)
% 226.30/226.50 Clause #1116 (by clausification #[1115]): ∀ (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)
% 226.30/226.50 Clause #1117 (by forward demodulation #[1116, 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)
% 226.30/226.50 Clause #1118 (by clausification #[1117]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (implies a (implies a a_1)) (implies a a_1))) True
% 226.30/226.50 Clause #1325 (by clausification #[232]): ∀ (a : Iota), Or (Eq and_3 False) (Eq (∀ (Y : Iota), is_a_theorem (implies a (implies Y (and a Y)))) True)
% 226.30/226.50 Clause #1326 (by clausification #[1325]): ∀ (a a_1 : Iota), Or (Eq and_3 False) (Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True)
% 226.30/226.50 Clause #1327 (by forward demodulation #[1326, 41]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True)
% 226.30/226.50 Clause #1328 (by clausification #[1327]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies a (implies a_1 (and a a_1)))) True
% 226.30/226.50 Clause #1334 (by superposition #[1328, 132]): ∀ (a a_1 a_2 : Iota),
% 226.30/226.50 Or (Eq (is_a_theorem a) True)
% 226.30/226.50 (Or (Eq True False) (Eq (is_a_theorem (implies (implies a_1 (implies a_2 (and a_1 a_2))) a)) False))
% 226.30/226.50 Clause #23298 (by clausification #[1334]): ∀ (a a_1 a_2 : Iota),
% 226.30/226.50 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)
% 226.30/226.50 Clause #23302 (by superposition #[23298, 1118]): ∀ (a : Iota), Or (Eq (is_a_theorem (implies a (and a a))) True) (Eq False True)
% 226.30/226.50 Clause #23339 (by clausification #[23302]): ∀ (a : Iota), Eq (is_a_theorem (implies a (and a a))) True
% 226.30/226.50 Clause #23420 (by superposition #[23339, 143]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (necessarily (implies a (and a a)))) True)
% 226.30/226.50 Clause #23459 (by clausification #[23420]): ∀ (a : Iota), Eq (is_a_theorem (necessarily (implies a (and a a)))) True
% 226.30/226.50 Clause #23460 (by forward demodulation #[23459, 974]): ∀ (a : Iota), Eq (is_a_theorem (strict_implies a (and a a))) True
% 226.30/226.50 Clause #23461 (by superposition #[23460, 245]): Eq True False
% 226.30/226.50 Clause #23464 (by clausification #[23461]): False
% 226.30/226.50 SZS output end Proof for theBenchmark.p
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