%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 11:35:54 AM UTC 2026 % Result : Theorem 8.57s 8.87s % Output : Proof 8.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0. % 0.00/0.05 % Command : duper %s % 0.11/0.37 % Computer : n029.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Sat Sep 5 13:01:40 UTC 2026 % 0.11/0.37 % CPUTime : % 8.57/8.87 SZS status Theorem for theBenchmark.p % 8.57/8.87 SZS output start Proof for theBenchmark.p % 8.57/8.87 Clause #0 (by assumption #[]): Eq % 8.57/8.87 (Not % 8.57/8.87 (Not % 8.57/8.87 (And % 8.57/8.87 (And % 8.57/8.87 (And % 8.57/8.87 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q)) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies P (implies Q P)))) % 8.57/8.87 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R))))) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies (implies (not P) (not Q)) (implies Q P)))) % 8.57/8.87 (Exists fun A => Not (a_truth (implies A A)))))) % 8.57/8.87 True % 8.57/8.87 Clause #1 (by clausification #[0]): Eq % 8.57/8.87 (Not % 8.57/8.87 (And % 8.57/8.87 (And % 8.57/8.87 (And % 8.57/8.87 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q)) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies P (implies Q P)))) % 8.57/8.87 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R))))) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies (implies (not P) (not Q)) (implies Q P)))) % 8.57/8.87 (Exists fun A => Not (a_truth (implies A A))))) % 8.57/8.87 False % 8.57/8.87 Clause #2 (by clausification #[1]): Eq % 8.57/8.87 (And % 8.57/8.87 (And % 8.57/8.87 (And % 8.57/8.87 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q)) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies P (implies Q P)))) % 8.57/8.87 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R))))) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies (implies (not P) (not Q)) (implies Q P)))) % 8.57/8.87 (Exists fun A => Not (a_truth (implies A A)))) % 8.57/8.87 True % 8.57/8.87 Clause #3 (by clausification #[2]): Eq (Exists fun A => Not (a_truth (implies A A))) True % 8.57/8.87 Clause #4 (by clausification #[2]): Eq % 8.57/8.87 (And % 8.57/8.87 (And % 8.57/8.87 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q)) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies P (implies Q P)))) % 8.57/8.87 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R))))) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies (implies (not P) (not Q)) (implies Q P)))) % 8.57/8.87 True % 8.57/8.87 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (Not (a_truth (implies (skS.0 0 a) (skS.0 0 a)))) True % 8.57/8.87 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (a_truth (implies (skS.0 0 a) (skS.0 0 a))) False % 8.57/8.87 Clause #8 (by clausification #[4]): Eq % 8.57/8.87 (And % 8.57/8.87 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q)) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies P (implies Q P)))) % 8.57/8.87 (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R))))) % 8.57/8.87 True % 8.57/8.87 Clause #11 (by clausification #[8]): Eq (∀ (P Q R : Iota), a_truth (implies (implies P (implies Q R)) (implies (implies P Q) (implies P R)))) True % 8.57/8.87 Clause #12 (by clausification #[8]): Eq % 8.57/8.87 (And (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q)) % 8.57/8.87 (∀ (P Q : Iota), a_truth (implies P (implies Q P)))) % 8.57/8.87 True % 8.57/8.87 Clause #13 (by clausification #[11]): ∀ (a : Iota), % 8.57/8.87 Eq (∀ (Q R : Iota), a_truth (implies (implies a (implies Q R)) (implies (implies a Q) (implies a R)))) True % 8.57/8.87 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 8.57/8.87 Eq (∀ (R : Iota), a_truth (implies (implies a (implies a_1 R)) (implies (implies a a_1) (implies a R)))) True % 8.57/8.87 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 8.57/8.87 Eq (a_truth (implies (implies a (implies a_1 a_2)) (implies (implies a a_1) (implies a a_2)))) True % 8.57/8.87 Clause #16 (by clausification #[12]): Eq (∀ (P Q : Iota), a_truth (implies P (implies Q P))) True % 8.57/8.87 Clause #17 (by clausification #[12]): Eq (∀ (P Q : Iota), Or (Or (Not (a_truth (implies P Q))) (Not (a_truth P))) (a_truth Q)) True % 8.57/8.87 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Q : Iota), a_truth (implies a (implies Q a))) True % 8.57/8.87 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (a_truth (implies a (implies a_1 a))) True % 8.57/8.87 Clause #20 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Q : Iota), Or (Or (Not (a_truth (implies a Q))) (Not (a_truth a))) (a_truth Q)) True % 8.57/8.89 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (a_truth (implies a a_1))) (Not (a_truth a))) (a_truth a_1)) True % 8.57/8.89 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Or (Not (a_truth (implies a a_1))) (Not (a_truth a))) True) (Eq (a_truth a_1) True) % 8.57/8.89 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (a_truth a) True) (Or (Eq (Not (a_truth (implies a_1 a))) True) (Eq (Not (a_truth a_1)) True)) % 8.57/8.89 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (a_truth a) True) (Or (Eq (Not (a_truth a_1)) True) (Eq (a_truth (implies a_1 a)) False)) % 8.57/8.89 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (a_truth a) True) (Or (Eq (a_truth (implies a_1 a)) False) (Eq (a_truth a_1) False)) % 8.57/8.89 Clause #27 (by superposition #[25, 15]): ∀ (a a_1 a_2 : Iota), % 8.57/8.89 Or (Eq (a_truth (implies (implies a a_1) (implies a a_2))) True) % 8.57/8.89 (Or (Eq (a_truth (implies a (implies a_1 a_2))) False) (Eq False True)) % 8.57/8.89 Clause #42 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 8.57/8.89 Or (Eq (a_truth (implies (implies a a_1) (implies a a_2))) True) (Eq (a_truth (implies a (implies a_1 a_2))) False) % 8.57/8.89 Clause #45 (by superposition #[42, 19]): ∀ (a a_1 : Iota), Or (Eq (a_truth (implies (implies a a_1) (implies a a))) True) (Eq False True) % 8.57/8.89 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (a_truth (implies (implies a a_1) (implies a a))) True % 8.57/8.89 Clause #49 (by superposition #[48, 25]): ∀ (a a_1 : Iota), Or (Eq (a_truth (implies a a)) True) (Or (Eq True False) (Eq (a_truth (implies a a_1)) False)) % 8.57/8.89 Clause #52 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (a_truth (implies a a)) True) (Eq (a_truth (implies a a_1)) False) % 8.57/8.89 Clause #55 (by superposition #[52, 19]): ∀ (a : Iota), Or (Eq (a_truth (implies a a)) True) (Eq False True) % 8.57/8.89 Clause #57 (by clausification #[55]): ∀ (a : Iota), Eq (a_truth (implies a a)) True % 8.57/8.89 Clause #58 (by superposition #[57, 6]): Eq True False % 8.57/8.89 Clause #63 (by clausification #[58]): False % 8.57/8.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------