%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ITP157^1 : TPTP v9.2.0. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 07:51:20 PM UTC 2025 % Result : Theorem 6.85s 7.02s % Output : Proof 6.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP157^1 : TPTP v9.2.0. Released v7.5.0. % 0.12/0.13 % Command : duper %s % 0.12/0.34 % Computer : n015.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 : Thu Oct 2 23:39:38 EDT 2025 % 0.12/0.35 % CPUTime : % 6.85/7.02 SZS status Theorem for theBenchmark.p % 6.85/7.02 SZS output start Proof for theBenchmark.p % 6.85/7.02 Clause #0 (by assumption #[]): Eq (member_a z (prefer161218362good_a y b pr)) True % 6.85/7.02 Clause #8 (by assumption #[]): Eq % 6.85/7.02 (∀ (X Y : a) (B : set_a) (Pr : set_Product_prod_a_a), % 6.85/7.02 member_a X (prefer161218362good_a Y B Pr) → member449909584od_a_a (product_Pair_a_a X Y) Pr) % 6.85/7.02 True % 6.85/7.02 Clause #327 (by assumption #[]): Eq (Not (member449909584od_a_a (product_Pair_a_a z y) pr)) True % 6.85/7.02 Clause #711 (by clausification #[327]): Eq (member449909584od_a_a (product_Pair_a_a z y) pr) False % 6.85/7.02 Clause #1723 (by clausification #[8]): ∀ (a_1 : a), % 6.85/7.02 Eq % 6.85/7.02 (∀ (Y : a) (B : set_a) (Pr : set_Product_prod_a_a), % 6.85/7.02 member_a a_1 (prefer161218362good_a Y B Pr) → member449909584od_a_a (product_Pair_a_a a_1 Y) Pr) % 6.85/7.02 True % 6.85/7.02 Clause #1724 (by clausification #[1723]): ∀ (a_1 a : a), % 6.85/7.02 Eq % 6.85/7.02 (∀ (B : set_a) (Pr : set_Product_prod_a_a), % 6.85/7.02 member_a a_1 (prefer161218362good_a a B Pr) → member449909584od_a_a (product_Pair_a_a a_1 a) Pr) % 6.85/7.02 True % 6.85/7.02 Clause #1725 (by clausification #[1724]): ∀ (a_1 a : a) (a_2 : set_a), % 6.85/7.02 Eq % 6.85/7.02 (∀ (Pr : set_Product_prod_a_a), % 6.85/7.02 member_a a_1 (prefer161218362good_a a a_2 Pr) → member449909584od_a_a (product_Pair_a_a a_1 a) Pr) % 6.85/7.02 True % 6.85/7.02 Clause #1726 (by clausification #[1725]): ∀ (a_1 a : a) (a_2 : set_a) (a_3 : set_Product_prod_a_a), % 6.85/7.02 Eq (member_a a_1 (prefer161218362good_a a a_2 a_3) → member449909584od_a_a (product_Pair_a_a a_1 a) a_3) True % 6.85/7.02 Clause #1727 (by clausification #[1726]): ∀ (a_1 a : a) (a_2 : set_a) (a_3 : set_Product_prod_a_a), % 6.85/7.02 Or (Eq (member_a a_1 (prefer161218362good_a a a_2 a_3)) False) % 6.85/7.02 (Eq (member449909584od_a_a (product_Pair_a_a a_1 a) a_3) True) % 6.85/7.02 Clause #1728 (by superposition #[1727, 0]): Or (Eq (member449909584od_a_a (product_Pair_a_a z y) pr) True) (Eq False True) % 6.85/7.02 Clause #1740 (by clausification #[1728]): Eq (member449909584od_a_a (product_Pair_a_a z y) pr) True % 6.85/7.02 Clause #1741 (by superposition #[1740, 711]): Eq True False % 6.85/7.02 Clause #1782 (by clausification #[1741]): False % 6.85/7.02 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------