TSTP Solution File: LCL525+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL525+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n022.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 07:10:02 EDT 2023
% Result : Theorem 192.31s 192.67s
% Output : Proof 192.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL525+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 06:52:11 EDT 2023
% 0.20/0.34 % CPUTime :
% 192.31/192.67 SZS status Theorem for theBenchmark.p
% 192.31/192.67 SZS output start Proof for theBenchmark.p
% 192.31/192.67 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
% 192.31/192.67 Clause #34 (by assumption #[]): Eq modus_ponens True
% 192.31/192.67 Clause #50 (by assumption #[]): Eq
% 192.31/192.67 (Iff modus_ponens_strict_implies
% 192.31/192.67 (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (strict_implies X Y)) → is_a_theorem Y))
% 192.31/192.67 True
% 192.31/192.67 Clause #54 (by assumption #[]): Eq (Iff axiom_M (∀ (X : Iota), is_a_theorem (implies (necessarily X) X))) True
% 192.31/192.67 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True
% 192.31/192.67 Clause #79 (by assumption #[]): Eq axiom_M True
% 192.31/192.67 Clause #82 (by assumption #[]): Eq op_strict_implies True
% 192.31/192.67 Clause #84 (by assumption #[]): Eq (Not modus_ponens_strict_implies) True
% 192.31/192.67 Clause #86 (by clausification #[0]): Or (Eq modus_ponens False)
% 192.31/192.67 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (implies X Y)) → is_a_theorem Y) True)
% 192.31/192.67 Clause #126 (by clausification #[84]): Eq modus_ponens_strict_implies False
% 192.31/192.67 Clause #127 (by clausification #[86]): ∀ (a : Iota),
% 192.31/192.67 Or (Eq modus_ponens False)
% 192.31/192.67 (Eq (∀ (Y : Iota), And (is_a_theorem a) (is_a_theorem (implies a Y)) → is_a_theorem Y) True)
% 192.31/192.67 Clause #128 (by clausification #[127]): ∀ (a a_1 : Iota),
% 192.31/192.67 Or (Eq modus_ponens False) (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1)) → is_a_theorem a_1) True)
% 192.31/192.67 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota),
% 192.31/192.67 Or (Eq modus_ponens False)
% 192.31/192.67 (Or (Eq (And (is_a_theorem a) (is_a_theorem (implies a a_1))) False) (Eq (is_a_theorem a_1) True))
% 192.31/192.67 Clause #130 (by clausification #[129]): ∀ (a a_1 : Iota),
% 192.31/192.67 Or (Eq modus_ponens False)
% 192.31/192.67 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 192.31/192.67 Clause #131 (by forward demodulation #[130, 34]): ∀ (a a_1 : Iota),
% 192.31/192.67 Or (Eq True False)
% 192.31/192.67 (Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False)))
% 192.31/192.68 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota),
% 192.31/192.68 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem a_1) False) (Eq (is_a_theorem (implies a_1 a)) False))
% 192.31/192.68 Clause #153 (by clausification #[50]): Or (Eq modus_ponens_strict_implies True)
% 192.31/192.68 (Eq (∀ (X Y : Iota), And (is_a_theorem X) (is_a_theorem (strict_implies X Y)) → is_a_theorem Y) False)
% 192.31/192.68 Clause #155 (by clausification #[153]): ∀ (a : Iota),
% 192.31/192.68 Or (Eq modus_ponens_strict_implies True)
% 192.31/192.68 (Eq
% 192.31/192.68 (Not
% 192.31/192.68 (∀ (Y : Iota), And (is_a_theorem (skS.0 14 a)) (is_a_theorem (strict_implies (skS.0 14 a) Y)) → is_a_theorem Y))
% 192.31/192.68 True)
% 192.31/192.68 Clause #156 (by clausification #[155]): ∀ (a : Iota),
% 192.31/192.68 Or (Eq modus_ponens_strict_implies True)
% 192.31/192.68 (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)
% 192.31/192.68 False)
% 192.31/192.68 Clause #157 (by clausification #[156]): ∀ (a a_1 : Iota),
% 192.31/192.68 Or (Eq modus_ponens_strict_implies True)
% 192.31/192.68 (Eq
% 192.31/192.68 (Not
% 192.31/192.68 (And (is_a_theorem (skS.0 14 a)) (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) →
% 192.31/192.68 is_a_theorem (skS.0 15 a a_1)))
% 192.31/192.68 True)
% 192.31/192.68 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota),
% 192.31/192.68 Or (Eq modus_ponens_strict_implies True)
% 192.31/192.68 (Eq
% 192.31/192.68 (And (is_a_theorem (skS.0 14 a)) (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) →
% 192.31/192.68 is_a_theorem (skS.0 15 a a_1))
% 192.31/192.68 False)
% 192.31/192.68 Clause #159 (by clausification #[158]): ∀ (a a_1 : Iota),
% 192.31/192.68 Or (Eq modus_ponens_strict_implies True)
% 192.31/192.68 (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)
% 192.31/192.68 Clause #160 (by clausification #[158]): ∀ (a a_1 : Iota), Or (Eq modus_ponens_strict_implies True) (Eq (is_a_theorem (skS.0 15 a a_1)) False)
% 192.31/192.68 Clause #161 (by clausification #[159]): ∀ (a a_1 : Iota),
% 192.31/192.68 Or (Eq modus_ponens_strict_implies True) (Eq (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) True)
% 192.31/192.68 Clause #162 (by clausification #[159]): ∀ (a : Iota), Or (Eq modus_ponens_strict_implies True) (Eq (is_a_theorem (skS.0 14 a)) True)
% 192.66/192.92 Clause #163 (by forward demodulation #[161, 126]): ∀ (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)
% 192.66/192.92 Clause #164 (by clausification #[163]): ∀ (a a_1 : Iota), Eq (is_a_theorem (strict_implies (skS.0 14 a) (skS.0 15 a a_1))) True
% 192.66/192.92 Clause #165 (by superposition #[164, 132]): ∀ (a a_1 a_2 : Iota),
% 192.66/192.92 Or (Eq (is_a_theorem a) True)
% 192.66/192.92 (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))
% 192.66/192.92 Clause #178 (by clausification #[54]): Or (Eq axiom_M False) (Eq (∀ (X : Iota), is_a_theorem (implies (necessarily X) X)) True)
% 192.66/192.92 Clause #189 (by clausification #[178]): ∀ (a : Iota), Or (Eq axiom_M False) (Eq (is_a_theorem (implies (necessarily a) a)) True)
% 192.66/192.92 Clause #190 (by forward demodulation #[189, 79]): ∀ (a : Iota), Or (Eq True False) (Eq (is_a_theorem (implies (necessarily a) a)) True)
% 192.66/192.92 Clause #191 (by clausification #[190]): ∀ (a : Iota), Eq (is_a_theorem (implies (necessarily a) a)) True
% 192.66/192.92 Clause #228 (by forward demodulation #[162, 126]): ∀ (a : Iota), Or (Eq False True) (Eq (is_a_theorem (skS.0 14 a)) True)
% 192.66/192.92 Clause #229 (by clausification #[228]): ∀ (a : Iota), Eq (is_a_theorem (skS.0 14 a)) True
% 192.66/192.92 Clause #230 (by superposition #[229, 132]): ∀ (a a_1 : Iota),
% 192.66/192.92 Or (Eq (is_a_theorem a) True) (Or (Eq True False) (Eq (is_a_theorem (implies (skS.0 14 a_1) a)) False))
% 192.66/192.92 Clause #522 (by forward demodulation #[160, 126]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (is_a_theorem (skS.0 15 a a_1)) False)
% 192.66/192.92 Clause #523 (by clausification #[522]): ∀ (a a_1 : Iota), Eq (is_a_theorem (skS.0 15 a a_1)) False
% 192.66/192.92 Clause #976 (by clausification #[74]): Or (Eq op_strict_implies False) (Eq (∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True)
% 192.66/192.92 Clause #977 (by clausification #[976]): ∀ (a : Iota),
% 192.66/192.92 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True)
% 192.66/192.92 Clause #978 (by clausification #[977]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (Eq (strict_implies a a_1) (necessarily (implies a a_1))) True)
% 192.66/192.92 Clause #979 (by clausification #[978]): ∀ (a a_1 : Iota), Or (Eq op_strict_implies False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 192.66/192.92 Clause #980 (by forward demodulation #[979, 82]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (strict_implies a a_1) (necessarily (implies a a_1)))
% 192.66/192.92 Clause #981 (by clausification #[980]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1))
% 192.66/192.92 Clause #1013 (by superposition #[981, 191]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (strict_implies a a_1) (implies a a_1))) True
% 192.66/192.92 Clause #1200 (by clausification #[165]): ∀ (a a_1 a_2 : Iota),
% 192.66/192.92 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)
% 192.66/192.92 Clause #1205 (by superposition #[1200, 1013]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (implies (skS.0 14 a) (skS.0 15 a a_1))) True) (Eq False True)
% 192.66/192.92 Clause #1311 (by clausification #[230]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem a) True) (Eq (is_a_theorem (implies (skS.0 14 a_1) a)) False)
% 192.66/192.92 Clause #18831 (by clausification #[1205]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (skS.0 14 a) (skS.0 15 a a_1))) True
% 192.66/192.92 Clause #18832 (by superposition #[18831, 1311]): ∀ (a a_1 : Iota), Or (Eq (is_a_theorem (skS.0 15 a a_1)) True) (Eq True False)
% 192.66/192.92 Clause #18835 (by clausification #[18832]): ∀ (a a_1 : Iota), Eq (is_a_theorem (skS.0 15 a a_1)) True
% 192.66/192.92 Clause #18836 (by superposition #[18835, 523]): Eq True False
% 192.66/192.92 Clause #18839 (by clausification #[18836]): False
% 192.66/192.92 SZS output end Proof for theBenchmark.p
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