%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG286^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 : Fri Oct 3 07:44:16 PM UTC 2025 % Result : Theorem 3.61s 3.82s % Output : Proof 3.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG286^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.14 % Command : duper %s % 0.13/0.35 % Computer : n013.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 : Fri Oct 3 09:45:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.61/3.82 SZS status Theorem for theBenchmark.p % 3.61/3.82 SZS output start Proof for theBenchmark.p % 3.61/3.82 Clause #0 (by assumption #[]): Eq % 3.61/3.82 (Not % 3.61/3.82 (And % 3.61/3.82 (And (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) % 3.61/3.82 (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0)) % 3.61/3.82 (∀ (Xt : a), Iff (Ne Xt cZ) (Eq Xt (cP (cL Xt) (cR Xt)))) → % 3.61/3.82 Eq u (cP x y) → Ne u cZ)) % 3.61/3.82 True % 3.61/3.82 Clause #1 (by clausification #[0]): Eq % 3.61/3.82 (And % 3.61/3.82 (And (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) % 3.61/3.82 (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0)) % 3.61/3.82 (∀ (Xt : a), Iff (Ne Xt cZ) (Eq Xt (cP (cL Xt) (cR Xt)))) → % 3.61/3.82 Eq u (cP x y) → Ne u cZ) % 3.61/3.82 False % 3.61/3.82 Clause #2 (by clausification #[1]): Eq % 3.61/3.82 (And % 3.61/3.82 (And (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) % 3.61/3.82 (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0)) % 3.61/3.82 (∀ (Xt : a), Iff (Ne Xt cZ) (Eq Xt (cP (cL Xt) (cR Xt))))) % 3.61/3.82 True % 3.61/3.82 Clause #3 (by clausification #[1]): Eq (Eq u (cP x y) → Ne u cZ) False % 3.61/3.82 Clause #4 (by clausification #[2]): Eq (∀ (Xt : a), Iff (Ne Xt cZ) (Eq Xt (cP (cL Xt) (cR Xt)))) True % 3.61/3.82 Clause #5 (by clausification #[2]): Eq % 3.61/3.82 (And (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) % 3.61/3.82 (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0)) % 3.61/3.82 True % 3.61/3.82 Clause #6 (by clausification #[4]): ∀ (a_1 : a), Eq (Iff (Ne a_1 cZ) (Eq a_1 (cP (cL a_1) (cR a_1)))) True % 3.61/3.82 Clause #7 (by clausification #[6]): ∀ (a_1 : a), Or (Eq (Ne a_1 cZ) True) (Eq (Eq a_1 (cP (cL a_1) (cR a_1))) False) % 3.61/3.82 Clause #9 (by clausification #[7]): ∀ (a_1 : a), Or (Eq (Eq a_1 (cP (cL a_1) (cR a_1))) False) (Ne a_1 cZ) % 3.61/3.82 Clause #10 (by clausification #[9]): ∀ (a_1 : a), Or (Ne a_1 cZ) (Ne a_1 (cP (cL a_1) (cR a_1))) % 3.61/3.82 Clause #11 (by destructive equality resolution #[10]): Ne cZ (cP (cL cZ) (cR cZ)) % 3.61/3.82 Clause #12 (by clausification #[3]): Eq (Eq u (cP x y)) True % 3.61/3.82 Clause #13 (by clausification #[3]): Eq (Ne u cZ) False % 3.61/3.82 Clause #14 (by clausification #[12]): Eq u (cP x y) % 3.61/3.82 Clause #15 (by clausification #[13]): Eq u cZ % 3.61/3.82 Clause #16 (by backward demodulation #[15, 14]): Eq cZ (cP x y) % 3.61/3.82 Clause #23 (by clausification #[5]): Eq (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0) True % 3.61/3.82 Clause #24 (by clausification #[5]): Eq (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) True % 3.61/3.82 Clause #25 (by clausification #[23]): ∀ (a_1 : a), Eq (∀ (Xy0 : a), Eq (cR (cP a_1 Xy0)) Xy0) True % 3.61/3.82 Clause #26 (by clausification #[25]): ∀ (a_1 a_2 : a), Eq (Eq (cR (cP a_1 a_2)) a_2) True % 3.61/3.82 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 : a), Eq (cR (cP a_1 a_2)) a_2 % 3.61/3.82 Clause #29 (by superposition #[27, 16]): Eq (cR cZ) y % 3.61/3.82 Clause #30 (by backward demodulation #[29, 11]): Ne cZ (cP (cL cZ) y) % 3.61/3.82 Clause #115 (by clausification #[24]): Eq (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0) True % 3.61/3.82 Clause #117 (by clausification #[115]): ∀ (a_1 : a), Eq (∀ (Xy0 : a), Eq (cL (cP a_1 Xy0)) a_1) True % 3.61/3.82 Clause #118 (by clausification #[117]): ∀ (a_1 a_2 : a), Eq (Eq (cL (cP a_1 a_2)) a_1) True % 3.61/3.82 Clause #119 (by clausification #[118]): ∀ (a_1 a_2 : a), Eq (cL (cP a_1 a_2)) a_1 % 3.61/3.82 Clause #127 (by superposition #[119, 16]): Eq (cL cZ) x % 3.61/3.82 Clause #130 (by backward demodulation #[127, 30]): Ne cZ (cP x y) % 3.61/3.82 Clause #139 (by forward demodulation #[130, 16]): Ne cZ cZ % 3.61/3.82 Clause #140 (by eliminate resolved literals #[139]): False % 3.61/3.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------