%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:36:05 AM UTC 2026 % Result : Theorem 15.89s 16.14s % Output : Proof 15.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.05 % Command : duper %s % 0.09/0.36 % Computer : n002.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 21:52:36 UTC 2026 % 0.09/0.36 % CPUTime : % 15.89/16.14 SZS status Theorem for theBenchmark.p % 15.89/16.14 SZS output start Proof for theBenchmark.p % 15.89/16.14 Clause #6 (by assumption #[]): Eq (Iff and_1 (∀ (X Y : Iota), is_a_theorem (implies (and X Y) X))) True % 15.89/16.14 Clause #39 (by assumption #[]): Eq and_1 True % 15.89/16.14 Clause #49 (by assumption #[]): Eq (Iff necessitation (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X))) True % 15.89/16.14 Clause #63 (by assumption #[]): Eq (Iff axiom_m2 (∀ (X Y : Iota), is_a_theorem (strict_implies (and X Y) X))) True % 15.89/16.14 Clause #74 (by assumption #[]): Eq (op_strict_implies → ∀ (X Y : Iota), Eq (strict_implies X Y) (necessarily (implies X Y))) True % 15.89/16.14 Clause #77 (by assumption #[]): Eq necessitation True % 15.89/16.14 Clause #83 (by assumption #[]): Eq op_strict_implies True % 15.89/16.14 Clause #85 (by assumption #[]): Eq (Not axiom_m2) True % 15.89/16.14 Clause #127 (by clausification #[85]): Eq axiom_m2 False % 15.89/16.14 Clause #135 (by clausification #[49]): Or (Eq necessitation False) (Eq (∀ (X : Iota), is_a_theorem X → is_a_theorem (necessarily X)) True) % 15.89/16.14 Clause #150 (by clausification #[135]): ∀ (a : Iota), Or (Eq necessitation False) (Eq (is_a_theorem a → is_a_theorem (necessarily a)) True) % 15.89/16.14 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)) % 15.89/16.14 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)) % 15.89/16.14 Clause #153 (by clausification #[152]): ∀ (a : Iota), Or (Eq (is_a_theorem a) False) (Eq (is_a_theorem (necessarily a)) True) % 15.89/16.14 Clause #181 (by clausification #[6]): Or (Eq and_1 False) (Eq (∀ (X Y : Iota), is_a_theorem (implies (and X Y) X)) True) % 15.89/16.14 Clause #420 (by clausification #[63]): Or (Eq axiom_m2 True) (Eq (∀ (X Y : Iota), is_a_theorem (strict_implies (and X Y) X)) False) % 15.89/16.14 Clause #422 (by clausification #[420]): ∀ (a : Iota), % 15.89/16.14 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) % 15.89/16.14 Clause #423 (by clausification #[422]): ∀ (a : Iota), % 15.89/16.14 Or (Eq axiom_m2 True) (Eq (∀ (Y : Iota), is_a_theorem (strict_implies (and (skS.0 56 a) Y) (skS.0 56 a))) False) % 15.89/16.14 Clause #424 (by clausification #[423]): ∀ (a a_1 : Iota), % 15.89/16.14 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) % 15.89/16.14 Clause #425 (by clausification #[424]): ∀ (a a_1 : Iota), % 15.89/16.14 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) % 15.89/16.14 Clause #426 (by forward demodulation #[425, 127]): ∀ (a a_1 : Iota), % 15.89/16.14 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) % 15.89/16.14 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 % 15.89/16.14 Clause #473 (by clausification #[181]): ∀ (a : Iota), Or (Eq and_1 False) (Eq (∀ (Y : Iota), is_a_theorem (implies (and a Y) a)) True) % 15.89/16.14 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) % 15.89/16.14 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) % 15.89/16.14 Clause #476 (by clausification #[475]): ∀ (a a_1 : Iota), Eq (is_a_theorem (implies (and a a_1) a)) True % 15.89/16.14 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) % 15.89/16.14 Clause #482 (by clausification #[479]): ∀ (a a_1 : Iota), Eq (is_a_theorem (necessarily (implies (and a a_1) a))) True % 15.89/16.14 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) % 15.89/16.14 Clause #1028 (by clausification #[1027]): ∀ (a : Iota), % 15.89/16.14 Or (Eq op_strict_implies False) (Eq (∀ (Y : Iota), Eq (strict_implies a Y) (necessarily (implies a Y))) True) % 15.89/16.14 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) % 15.89/16.15 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))) % 15.89/16.15 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))) % 15.89/16.15 Clause #1032 (by clausification #[1031]): ∀ (a a_1 : Iota), Eq (strict_implies a a_1) (necessarily (implies a a_1)) % 15.89/16.15 Clause #1044 (by backward demodulation #[1032, 482]): ∀ (a a_1 : Iota), Eq (is_a_theorem (strict_implies (and a a_1) a)) True % 15.89/16.15 Clause #1092 (by superposition #[1044, 427]): Eq True False % 15.89/16.15 Clause #1096 (by clausification #[1092]): False % 15.89/16.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------