TSTP Solution File: LCL538+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL538+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n005.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 186.19s 186.45s
% Output : Proof 186.40s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL538+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12 % Command : duper %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 06:50:23 EDT 2023
% 0.12/0.33 % CPUTime :
% 186.19/186.45 SZS status Theorem for theBenchmark.p
% 186.19/186.45 SZS output start Proof for theBenchmark.p
% 186.19/186.45 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
% 186.19/186.45 Clause #34 (by assumption #[]): Eq modus_ponens True
% 186.19/186.45 Clause #50 (by assumption #[]): Eq
% 186.19/186.45 (Iff modus_ponens_strict_implies
% 186.19/186.45 (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (strict_implies X Y)) → is_a_theorem Y))
% 186.19/186.45 True
% 186.19/186.45 Clause #54 (by assumption #[]): Eq (Iff axiom_M (∀ (X : Iota), is_a_theorem (implies (necessarily X) X))) True
% 186.19/186.45 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True
% 186.19/186.45 Clause #79 (by assumption #[]): Eq axiom_M True
% 186.19/186.45 Clause #83 (by assumption #[]): Eq op_strict_implies True
% 186.19/186.45 Clause #85 (by assumption #[]): Eq (Not modus_ponens_strict_implies) True
% 186.19/186.45 Clause #87 (by clausification #[0]): Or (Eq modus_ponens False)
% 186.19/186.45 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 186.19/186.45 Clause #127 (by clausification #[85]): Eq modus_ponens_strict_implies False
% 186.19/186.45 Clause #128 (by clausification #[87]): ∀ (a : Iota),
% 186.19/186.45 Or (Eq modus_ponens False)
% 186.19/186.45 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 186.19/186.45 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 186.19/186.45 Clause #130 (by clausification #[129]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq modus_ponens False)
% 186.19/186.45 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 186.19/186.45 Clause #131 (by clausification #[130]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq modus_ponens False)
% 186.19/186.45 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 186.19/186.45 Clause #132 (by forward demodulation #[131, 34]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq True False)
% 186.19/186.45 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 186.19/186.45 Clause #133 (by clausification #[132]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 186.19/186.45 Clause #154 (by clausification #[50]): Or (Eq modus_ponens_strict_implies True)
% 186.19/186.45 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (strict_implies X Y)) → is_a_theorem Y) False)
% 186.19/186.45 Clause #156 (by clausification #[154]): ∀ (a : Iota),
% 186.19/186.45 Or (Eq modus_ponens_strict_implies True)
% 186.19/186.45 (Eq
% 186.19/186.45 (Not
% 186.19/186.45 (∀ (Y : Iota), And (is_a_theorem (skS.0 14 a)) (is_a_theorem (strict_implies (skS.0 14 a) Y)) → is_a_theorem Y))
% 186.19/186.45 True)
% 186.19/186.45 Clause #157 (by clausification #[156]): ∀ (a : Iota),
% 186.19/186.45 Or (Eq modus_ponens_strict_implies True)
% 186.19/186.45 (Eq (∀ (Y : Iota), And (is_a_theorem (skS.0 14 a)) (is_a_theorem (strict_implies (skS.0 14 a) Y)) → is_a_theorem Y)
% 186.19/186.45 False)
% 186.19/186.45 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq modus_ponens_strict_implies True)
% 186.19/186.45 (Eq
% 186.19/186.45 (Not
% 186.19/186.45 (And (is_a_theorem (skS.0 14 a)) (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) →
% 186.19/186.45 is_a_theorem (skS.0 15 a a_1)))
% 186.19/186.45 True)
% 186.19/186.45 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq modus_ponens_strict_implies True)
% 186.19/186.45 (Eq
% 186.19/186.45 (And (is_a_theorem (skS.0 14 a)) (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) →
% 186.19/186.45 is_a_theorem (skS.0 15 a a_1))
% 186.19/186.45 False)
% 186.19/186.45 Clause #160 (by clausification #[159]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq modus_ponens_strict_implies True)
% 186.19/186.45 (Eq (And (is_a_theorem (skS.0 14 a)) (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1)))) True)
% 186.19/186.45 Clause #161 (by clausification #[159]): ∀ (a a_1 : Iota), Or (Eq modus_ponens_strict_implies True) (Eq (is_a_theorem (skS.0 15 a a_1)) False)
% 186.19/186.45 Clause #162 (by clausification #[160]): ∀ (a a_1 : Iota),
% 186.19/186.45 Or (Eq modus_ponens_strict_implies True) (Eq (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) True)
% 186.19/186.45 Clause #163 (by clausification #[160]): ∀ (a : Iota), Or (Eq modus_ponens_strict_implies True) (Eq (is_a_theorem (skS.0 14 a)) True)
% 186.40/186.64 Clause #164 (by forward demodulation #[162, 127]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) True)
% 186.40/186.64 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Eq (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) True
% 186.40/186.64 Clause #166 (by superposition #[165, 133]): ∀ (a a_1 a_2 : Iota),
% 186.40/186.64 Or (Eq (is_a_theorem a) True)
% 186.40/186.64 (Or (Eq True False) (Eq (is_a_theorem (implies (strict_implies (skS.0 14 a_1) (skS.0 15 a_1 a_2)) a)) False))
% 186.40/186.64 Clause #174 (by clausification #[54]): Or (Eq axiom_M False) (Eq (∀ (X : Iota), is_a_theorem (implies (necessarily X) X)) True)
% 186.40/186.64 Clause #178 (by clausification #[174]): ∀ (a : Iota), Or (Eq axiom_M False) (Eq (is_a_theorem (implies (necessarily a) a)) True)
% 186.40/186.64 Clause #179 (by forward demodulation #[178, 79]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (necessarily a) a)) True)
% 186.40/186.64 Clause #180 (by clausification #[179]): ∀ (a : Iota), Eq (is_a_theorem (implies (necessarily a) a)) True
% 186.40/186.64 Clause #265 (by forward demodulation #[163, 127]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (skS.0 14 a)) True)
% 186.40/186.64 Clause #266 (by clausification #[265]): ∀ (a : Iota), Eq (is_a_theorem (skS.0 14 a)) True
% 186.40/186.64 Clause #267 (by superposition #[266, 133]): ∀ (a a_1 : Iota),
% 186.40/186.64 Or (Eq (is_a_theorem a) True) (Or (Eq True False) (Eq (is_a_theorem (implies (skS.0 14 a_1) a)) False))
% 186.40/186.64 Clause #623 (by forward demodulation #[161, 127]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (is_a_theorem (skS.0 15 a a_1)) False)
% 186.40/186.64 Clause #624 (by clausification #[623]): ∀ (a a_1 : Iota), Eq (is_a_theorem (skS.0 15 a a_1)) False
% 186.40/186.64 Clause #1053 (by clausification #[74]): Or (Eq op_strict_implies False) (Eq (∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True)
% 186.40/186.64 Clause #1054 (by clausification #[1053]): ∀ (a : Iota),
% 186.40/186.64 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True)
% 186.40/186.64 Clause #1055 (by clausification #[1054]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (Eq (strict_implies a a_1) (necessarily (implies a a_1))) True)
% 186.40/186.64 Clause #1056 (by clausification #[1055]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 186.40/186.64 Clause #1057 (by forward demodulation #[1056, 83]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 186.40/186.64 Clause #1058 (by clausification #[1057]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1))
% 186.40/186.64 Clause #1089 (by superposition #[1058, 180]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (strict_implies a a_1) (implies a a_1))) True
% 186.40/186.64 Clause #1276 (by clausification #[166]): ∀ (a a_1 a_2 : Iota),
% 186.40/186.64 Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (strict_implies (skS.0 14 a_1) (skS.0 15 a_1 a_2)) a)) False)
% 186.40/186.64 Clause #1283 (by superposition #[1276, 1089]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (implies (skS.0 14 a) (skS.0 15 a a_1))) True) (Eq False True)
% 186.40/186.64 Clause #1504 (by clausification #[267]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (skS.0 14 a_1) a)) False)
% 186.40/186.64 Clause #20047 (by clausification #[1283]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (skS.0 14 a) (skS.0 15 a a_1))) True
% 186.40/186.64 Clause #20048 (by superposition #[20047, 1504]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (skS.0 15 a a_1)) True) (Eq True False)
% 186.40/186.64 Clause #20133 (by clausification #[20048]): ∀ (a a_1 : Iota), Eq (is_a_theorem (skS.0 15 a a_1)) True
% 186.40/186.64 Clause #20134 (by superposition #[20133, 624]): Eq True False
% 186.40/186.64 Clause #20137 (by clausification #[20134]): False
% 186.40/186.64 SZS output end Proof for theBenchmark.p
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