%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 : Tue May 5 06:59:07 PM UTC 2026 % Result : Theorem 3.45s 3.67s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : duper %s % 0.17/0.34 % Computer : n007.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue May 5 09:36:23 EDT 2026 % 0.17/0.34 % CPUTime : % 3.45/3.67 SZS status Theorem for theBenchmark.p % 3.45/3.67 SZS output start Proof for theBenchmark.p % 3.45/3.67 Clause #2 (by assumption #[]): Eq (∀ (X X2 : Iota), Ne nil (cons X X2)) True % 3.45/3.67 Clause #5 (by assumption #[]): Eq (∀ (Z : Iota), Eq (drop (s Z) nil) nil) True % 3.45/3.67 Clause #6 (by assumption #[]): Eq (∀ (Z X2 X3 : Iota), Eq (drop (s Z) (cons X2 X3)) (drop Z X3)) True % 3.45/3.67 Clause #8 (by assumption #[]): Eq (Not (Exists fun N => Exists fun Xs => Exists fun Ys => Not (Eq (drop N Xs) (drop N Ys) → Eq Xs Ys))) True % 3.45/3.67 Clause #15 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (X2 : Iota), Ne nil (cons a X2)) True % 3.45/3.67 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Ne nil (cons a a_1)) True % 3.45/3.67 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Ne nil (cons a a_1) % 3.45/3.67 Clause #18 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (drop (s a) nil) nil) True % 3.45/3.67 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (drop (s a) nil) nil % 3.45/3.67 Clause #26 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (X2 X3 : Iota), Eq (drop (s a) (cons X2 X3)) (drop a X3)) True % 3.45/3.67 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (∀ (X3 : Iota), Eq (drop (s a) (cons a_1 X3)) (drop a X3)) True % 3.45/3.67 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Eq (Eq (drop (s a) (cons a_1 a_2)) (drop a a_2)) True % 3.45/3.67 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (drop (s a) (cons a_1 a_2)) (drop a a_2) % 3.45/3.67 Clause #30 (by clausification #[8]): Eq (Exists fun N => Exists fun Xs => Exists fun Ys => Not (Eq (drop N Xs) (drop N Ys) → Eq Xs Ys)) False % 3.45/3.67 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (Exists fun Xs => Exists fun Ys => Not (Eq (drop a Xs) (drop a Ys) → Eq Xs Ys)) False % 3.45/3.67 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (Exists fun Ys => Not (Eq (drop a a_1) (drop a Ys) → Eq a_1 Ys)) False % 3.45/3.67 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Eq (Not (Eq (drop a a_1) (drop a a_2) → Eq a_1 a_2)) False % 3.45/3.67 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (Eq (drop a a_1) (drop a a_2) → Eq a_1 a_2) True % 3.45/3.67 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq (drop a a_1) (drop a a_2)) False) (Eq (Eq a_1 a_2) True) % 3.45/3.67 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Ne (drop a_2 a) (drop a_2 a_1)) % 3.45/3.67 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Ne (drop a a_1) (drop a a_2)) (Eq a_1 a_2) % 3.45/3.67 Clause #39 (by superposition #[37, 19]): ∀ (a a_1 : Iota), Or (Ne nil (drop (s a) a_1)) (Eq nil a_1) % 3.45/3.67 Clause #46 (by superposition #[39, 29]): ∀ (a a_1 a_2 : Iota), Or (Ne nil (drop a a_1)) (Eq nil (cons a_2 a_1)) % 3.45/3.67 Clause #47 (by forward contextual literal cutting #[46, 17]): ∀ (a a_1 : Iota), Ne nil (drop a a_1) % 3.45/3.67 Clause #48 (by backward contextual literal cutting #[47, 19]): False % 3.45/3.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------