%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET954+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:00:44 PM UTC 2025 % Result : Theorem 64.65s 64.89s % Output : Proof 64.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET954+1 : TPTP v9.2.0. Released v3.2.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n023.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 13:46:23 EDT 2025 % 0.13/0.34 % CPUTime : % 64.65/64.89 SZS status Theorem for theBenchmark.p % 64.65/64.89 SZS output start Proof for theBenchmark.p % 64.65/64.89 Clause #4 (by assumption #[]): Eq (∀ (A B C D : Iota), Iff (in (ordered_pair A B) (cartesian_product2 C D)) (And (in A C) (in B D))) True % 64.65/64.89 Clause #7 (by assumption #[]): Eq % 64.65/64.89 (Not % 64.65/64.89 (∀ (A B C D : Iota), % 64.65/64.89 in (ordered_pair A B) (cartesian_product2 C D) → in (ordered_pair B A) (cartesian_product2 D C))) % 64.65/64.89 True % 64.65/64.89 Clause #38 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B C D : Iota), Iff (in (ordered_pair a B) (cartesian_product2 C D)) (And (in a C) (in B D))) True % 64.65/64.89 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 64.65/64.89 Eq (∀ (C D : Iota), Iff (in (ordered_pair a a_1) (cartesian_product2 C D)) (And (in a C) (in a_1 D))) True % 64.65/64.89 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 64.65/64.89 Eq (∀ (D : Iota), Iff (in (ordered_pair a a_1) (cartesian_product2 a_2 D)) (And (in a a_2) (in a_1 D))) True % 64.65/64.89 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 64.65/64.89 Eq (Iff (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) (And (in a a_2) (in a_1 a_3))) True % 64.65/64.89 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 64.65/64.89 Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) True) (Eq (And (in a a_2) (in a_1 a_3)) False) % 64.65/64.89 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 64.65/64.89 Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) False) (Eq (And (in a a_2) (in a_1 a_3)) True) % 64.65/64.89 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 64.65/64.89 Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) True) (Or (Eq (in a a_2) False) (Eq (in a_1 a_3) False)) % 64.65/64.89 Clause #55 (by clausification #[7]): Eq (∀ (A B C D : Iota), in (ordered_pair A B) (cartesian_product2 C D) → in (ordered_pair B A) (cartesian_product2 D C)) % 64.65/64.89 False % 64.65/64.89 Clause #56 (by clausification #[55]): ∀ (a : Iota), % 64.65/64.89 Eq % 64.65/64.89 (Not % 64.65/64.89 (∀ (B C D : Iota), % 64.65/64.89 in (ordered_pair (skS.0 2 a) B) (cartesian_product2 C D) → % 64.65/64.89 in (ordered_pair B (skS.0 2 a)) (cartesian_product2 D C))) % 64.65/64.89 True % 64.65/64.89 Clause #57 (by clausification #[56]): ∀ (a : Iota), % 64.65/64.89 Eq % 64.65/64.89 (∀ (B C D : Iota), % 64.65/64.89 in (ordered_pair (skS.0 2 a) B) (cartesian_product2 C D) → % 64.65/64.89 in (ordered_pair B (skS.0 2 a)) (cartesian_product2 D C)) % 64.65/64.89 False % 64.65/64.89 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), % 64.65/64.89 Eq % 64.65/64.89 (Not % 64.65/64.89 (∀ (C D : Iota), % 64.65/64.89 in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 C D) → % 64.65/64.89 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D C))) % 64.65/64.89 True % 64.65/64.89 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 64.65/64.89 Eq % 64.65/64.89 (∀ (C D : Iota), % 64.65/64.89 in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 C D) → % 64.65/64.89 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D C)) % 64.65/64.89 False % 64.65/64.89 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 64.65/64.89 Eq % 64.65/64.89 (Not % 64.65/64.89 (∀ (D : Iota), % 64.65/64.89 in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) D) → % 64.65/64.89 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D (skS.0 4 a a_1 a_2)))) % 64.65/64.89 True % 64.65/64.89 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 64.65/64.89 Eq % 64.65/64.89 (∀ (D : Iota), % 64.65/64.89 in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) D) → % 64.65/64.89 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D (skS.0 4 a a_1 a_2))) % 64.65/64.89 False % 64.65/64.89 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota), % 64.65/64.89 Eq % 64.65/64.89 (Not % 64.65/64.89 (in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) → % 64.65/64.89 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2)))) % 64.65/64.89 True % 64.65/64.89 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 64.65/64.89 Eq % 64.65/64.89 (in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) → % 64.65/64.89 in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))) % 64.65/64.89 False % 64.65/64.89 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota), % 64.83/65.00 Eq (in (ordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 64.83/65.00 True % 64.83/65.00 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota), % 64.83/65.00 Eq (in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))) % 64.83/65.00 False % 64.83/65.00 Clause #99 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) False) (Eq (in a_1 a_3) True) % 64.83/65.00 Clause #100 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (ordered_pair a a_1) (cartesian_product2 a_2 a_3)) False) (Eq (in a a_2) True) % 64.83/65.00 Clause #101 (by superposition #[99, 64]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True) (Eq False True) % 64.83/65.00 Clause #102 (by superposition #[100, 64]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq False True) % 64.83/65.00 Clause #445 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 64.83/65.00 Clause #573 (by clausification #[101]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True % 64.83/65.00 Clause #575 (by superposition #[573, 44]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 64.83/65.00 Or (Eq (in (ordered_pair (skS.0 3 a a_1) a_2) (cartesian_product2 (skS.0 5 a a_1 a_3 a_4) a_5)) True) % 64.83/65.00 (Or (Eq True False) (Eq (in a_2 a_5) False)) % 64.83/65.00 Clause #2689 (by clausification #[575]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 64.83/65.00 Or (Eq (in (ordered_pair (skS.0 3 a a_1) a_2) (cartesian_product2 (skS.0 5 a a_1 a_3 a_4) a_5)) True) % 64.83/65.00 (Eq (in a_2 a_5) False) % 64.83/65.00 Clause #2691 (by superposition #[2689, 445]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 64.83/65.00 Or % 64.83/65.00 (Eq % 64.83/65.00 (in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a_2)) % 64.83/65.00 (cartesian_product2 (skS.0 5 a a_1 a_3 a_4) (skS.0 4 a_2 a_5 a_6))) % 64.83/65.00 True) % 64.83/65.00 (Eq False True) % 64.83/65.00 Clause #8951 (by clausification #[2691]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 64.83/65.00 Eq % 64.83/65.00 (in (ordered_pair (skS.0 3 a a_1) (skS.0 2 a_2)) (cartesian_product2 (skS.0 5 a a_1 a_3 a_4) (skS.0 4 a_2 a_5 a_6))) % 64.83/65.00 True % 64.83/65.00 Clause #8952 (by superposition #[8951, 65]): Eq True False % 64.83/65.00 Clause #8958 (by clausification #[8952]): False % 64.83/65.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------