TSTP Solution File: LCL542+1 by Duper---1.0
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% File : Duper---1.0
% Problem : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 07:10:04 EDT 2023
% Result : Theorem 6.14s 6.37s
% Output : Proof 6.14s
% 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 : LCL542+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 18:13:18 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.14/6.37 SZS status Theorem for theBenchmark.p
% 6.14/6.37 SZS output start Proof for theBenchmark.p
% 6.14/6.37 Clause #6 (by assumption #[]): Eq (Iff and_1 (∀ (X Y : Iota), is_a_theorem (implies (and X Y) X))) True
% 6.14/6.37 Clause #39 (by assumption #[]): Eq and_1 True
% 6.14/6.37 Clause #49 (by assumption #[]): Eq (Iff necessitation (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X))) True
% 6.14/6.37 Clause #63 (by assumption #[]): Eq (Iff axiom_m2 (∀ (X Y : Iota), is_a_theorem (strict_implies (and X Y) X))) True
% 6.14/6.37 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True
% 6.14/6.37 Clause #77 (by assumption #[]): Eq necessitation True
% 6.14/6.37 Clause #83 (by assumption #[]): Eq op_strict_implies True
% 6.14/6.37 Clause #85 (by assumption #[]): Eq (Not axiom_m2) True
% 6.14/6.37 Clause #127 (by clausification #[85]): Eq axiom_m2 False
% 6.14/6.37 Clause #135 (by clausification #[49]): Or (Eq necessitation False) (Eq (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X)) True)
% 6.14/6.37 Clause #150 (by clausification #[135]): ∀ (a : Iota), Or (Eq necessitation False) (Eq (is_a_theorem a → is_a_theorem (necessarily a)) True)
% 6.14/6.37 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))
% 6.14/6.37 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))
% 6.14/6.37 Clause #153 (by clausification #[152]): ∀ (a : Iota), Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True)
% 6.14/6.37 Clause #181 (by clausification #[6]): Or (Eq and_1 False) (Eq (∀ (X Y : Iota), is_a_theorem (implies (and X Y) X)) True)
% 6.14/6.37 Clause #420 (by clausification #[63]): Or (Eq axiom_m2 True) (Eq (∀ (X Y : Iota), is_a_theorem (strict_implies (and X Y) X)) False)
% 6.14/6.37 Clause #422 (by clausification #[420]): ∀ (a : Iota),
% 6.14/6.37 Or (Eq axiom_m2 True) (Eq (Not (∀ (Y : Iota), is_a_theorem (strict_implies (and (skS.0 56 a) Y) (skS.0 56 a)))) True)
% 6.14/6.37 Clause #423 (by clausification #[422]): ∀ (a : Iota),
% 6.14/6.37 Or (Eq axiom_m2 True) (Eq (∀ (Y : Iota), is_a_theorem (strict_implies (and (skS.0 56 a) Y) (skS.0 56 a))) False)
% 6.14/6.37 Clause #424 (by clausification #[423]): ∀ (a a_1 : Iota),
% 6.14/6.37 Or (Eq axiom_m2 True) (Eq (Not (is_a_theorem (strict_implies (and (skS.0 56 a) (skS.0 57 a a_1)) (skS.0 56 a)))) True)
% 6.14/6.37 Clause #425 (by clausification #[424]): ∀ (a a_1 : Iota),
% 6.14/6.37 Or (Eq axiom_m2 True) (Eq (is_a_theorem (strict_implies (and (skS.0 56 a) (skS.0 57 a a_1)) (skS.0 56 a))) False)
% 6.14/6.37 Clause #426 (by forward demodulation #[425, 127]): ∀ (a a_1 : Iota),
% 6.14/6.37 Or (Eq False True) (Eq (is_a_theorem (strict_implies (and (skS.0 56 a) (skS.0 57 a a_1)) (skS.0 56 a))) False)
% 6.14/6.37 Clause #427 (by clausification #[426]): ∀ (a a_1 : Iota), Eq (is_a_theorem (strict_implies (and (skS.0 56 a) (skS.0 57 a a_1)) (skS.0 56 a))) False
% 6.14/6.37 Clause #473 (by clausification #[181]): ∀ (a : Iota), Or (Eq and_1 False) (Eq (∀ (Y : Iota), is_a_theorem (implies (and a Y) a)) True)
% 6.14/6.37 Clause #474 (by clausification #[473]): ∀ (a a_1 : Iota), Or (Eq and_1 False) (Eq (is_a_theorem (implies (and a a_1) a)) True)
% 6.14/6.37 Clause #475 (by forward demodulation #[474, 39]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (and a a_1) a)) True)
% 6.14/6.37 Clause #476 (by clausification #[475]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (and a a_1) a)) True
% 6.14/6.37 Clause #479 (by superposition #[476, 153]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_a_theorem (necessarily (implies (and a a_1) a))) True)
% 6.14/6.37 Clause #482 (by clausification #[479]): ∀ (a a_1 : Iota), Eq (is_a_theorem (necessarily (implies (and a a_1) a))) True
% 6.14/6.37 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)
% 6.14/6.37 Clause #1028 (by clausification #[1027]): ∀ (a : Iota),
% 6.14/6.37 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True)
% 6.14/6.37 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)
% 6.14/6.37 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)))
% 6.14/6.37 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)))
% 6.14/6.37 Clause #1032 (by clausification #[1031]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1))
% 6.14/6.37 Clause #1044 (by backward demodulation #[1032, 482]): ∀ (a a_1 : Iota), Eq (is_a_theorem (strict_implies (and a a_1) a)) True
% 6.14/6.37 Clause #1092 (by superposition #[1044, 427]): Eq True False
% 6.14/6.37 Clause #1096 (by clausification #[1092]): False
% 6.14/6.37 SZS output end Proof for theBenchmark.p
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