%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG287^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 3.55s 3.75s % Output : Proof 3.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG287^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n018.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 09:40:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.55/3.75 SZS status Theorem for theBenchmark.p % 3.55/3.75 SZS output start Proof for theBenchmark.p % 3.55/3.75 Clause #0 (by assumption #[]): Eq % 3.55/3.75 (Not % 3.55/3.75 (And % 3.55/3.75 (And (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) % 3.55/3.75 (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0)) % 3.55/3.75 (∀ (Xt : a), Iff (Ne Xt cZ) (Eq Xt (cP (cL Xt) (cR Xt)))) → % 3.55/3.75 Eq (cP x u) (cP y v) → And (Eq x y) (Eq u v))) % 3.55/3.75 True % 3.55/3.75 Clause #1 (by clausification #[0]): Eq % 3.55/3.75 (And % 3.55/3.75 (And (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) % 3.55/3.75 (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0)) % 3.55/3.75 (∀ (Xt : a), Iff (Ne Xt cZ) (Eq Xt (cP (cL Xt) (cR Xt)))) → % 3.55/3.75 Eq (cP x u) (cP y v) → And (Eq x y) (Eq u v)) % 3.55/3.75 False % 3.55/3.75 Clause #2 (by clausification #[1]): Eq % 3.55/3.75 (And % 3.55/3.75 (And (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) % 3.55/3.75 (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0)) % 3.55/3.75 (∀ (Xt : a), Iff (Ne Xt cZ) (Eq Xt (cP (cL Xt) (cR Xt))))) % 3.55/3.75 True % 3.55/3.75 Clause #3 (by clausification #[1]): Eq (Eq (cP x u) (cP y v) → And (Eq x y) (Eq u v)) False % 3.55/3.75 Clause #5 (by clausification #[2]): Eq % 3.55/3.75 (And (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) % 3.55/3.75 (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0)) % 3.55/3.75 True % 3.55/3.75 Clause #12 (by clausification #[3]): Eq (Eq (cP x u) (cP y v)) True % 3.55/3.75 Clause #13 (by clausification #[3]): Eq (And (Eq x y) (Eq u v)) False % 3.55/3.75 Clause #14 (by clausification #[12]): Eq (cP x u) (cP y v) % 3.55/3.75 Clause #15 (by clausification #[13]): Or (Eq (Eq x y) False) (Eq (Eq u v) False) % 3.55/3.75 Clause #16 (by clausification #[15]): Or (Eq (Eq u v) False) (Ne x y) % 3.55/3.75 Clause #17 (by clausification #[16]): Or (Ne x y) (Ne u v) % 3.55/3.75 Clause #24 (by clausification #[5]): Eq (∀ (Xx0 Xy0 : a), Eq (cR (cP Xx0 Xy0)) Xy0) True % 3.55/3.75 Clause #25 (by clausification #[5]): Eq (And (And (Eq (cL cZ) cZ) (Eq (cR cZ) cZ)) (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0)) True % 3.55/3.75 Clause #26 (by clausification #[24]): ∀ (a_1 : a), Eq (∀ (Xy0 : a), Eq (cR (cP a_1 Xy0)) Xy0) True % 3.55/3.75 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 : a), Eq (Eq (cR (cP a_1 a_2)) a_2) True % 3.55/3.75 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 : a), Eq (cR (cP a_1 a_2)) a_2 % 3.55/3.75 Clause #30 (by superposition #[28, 14]): Eq (cR (cP x u)) v % 3.55/3.75 Clause #31 (by superposition #[30, 28]): Eq v u % 3.55/3.75 Clause #33 (by backward demodulation #[31, 14]): Eq (cP x u) (cP y u) % 3.55/3.75 Clause #36 (by backward contextual literal cutting #[31, 17]): Ne x y % 3.55/3.75 Clause #98 (by clausification #[25]): Eq (∀ (Xx0 Xy0 : a), Eq (cL (cP Xx0 Xy0)) Xx0) True % 3.55/3.75 Clause #100 (by clausification #[98]): ∀ (a_1 : a), Eq (∀ (Xy0 : a), Eq (cL (cP a_1 Xy0)) a_1) True % 3.55/3.75 Clause #101 (by clausification #[100]): ∀ (a_1 a_2 : a), Eq (Eq (cL (cP a_1 a_2)) a_1) True % 3.55/3.75 Clause #102 (by clausification #[101]): ∀ (a_1 a_2 : a), Eq (cL (cP a_1 a_2)) a_1 % 3.55/3.75 Clause #108 (by superposition #[102, 33]): Eq (cL (cP x u)) y % 3.55/3.75 Clause #111 (by superposition #[108, 102]): Eq y x % 3.55/3.75 Clause #122 (by forward contextual literal cutting #[111, 36]): False % 3.55/3.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------