%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET985+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:00:46 PM UTC 2025 % Result : Theorem 4.48s 4.72s % Output : Proof 4.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET985+1 : TPTP v9.2.0. Released v3.2.0. % 0.08/0.13 % Command : duper %s % 0.13/0.34 % Computer : n011.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 14:55:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.48/4.72 SZS status Theorem for theBenchmark.p % 4.48/4.72 SZS output start Proof for theBenchmark.p % 4.48/4.72 Clause #0 (by assumption #[]): Eq (empty empty_set) True % 4.48/4.72 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (cartesian_product2 A B) empty_set) (Or (Eq A empty_set) (Eq B empty_set))) True % 4.48/4.72 Clause #5 (by assumption #[]): Eq % 4.48/4.72 (∀ (A B C D : Iota), % 4.48/4.72 subset (cartesian_product2 A B) (cartesian_product2 C D) → % 4.48/4.72 Or (Eq (cartesian_product2 A B) empty_set) (And (subset A C) (subset B D))) % 4.48/4.72 True % 4.48/4.72 Clause #6 (by assumption #[]): Eq % 4.48/4.72 (Not % 4.48/4.72 (∀ (A : Iota), % 4.48/4.72 Not (empty A) → % 4.48/4.72 ∀ (B C D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 A B) (cartesian_product2 C D)) % 4.48/4.72 (subset (cartesian_product2 B A) (cartesian_product2 D C)) → % 4.48/4.72 subset B D)) % 4.48/4.72 True % 4.48/4.72 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), subset empty_set A) True % 4.48/4.72 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (subset empty_set a) True % 4.48/4.72 Clause #15 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (cartesian_product2 a B) empty_set) (Or (Eq a empty_set) (Eq B empty_set))) True % 4.48/4.72 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Iff (Eq (cartesian_product2 a a_1) empty_set) (Or (Eq a empty_set) (Eq a_1 empty_set))) True % 4.48/4.72 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), % 4.48/4.72 Or (Eq (Eq (cartesian_product2 a a_1) empty_set) False) (Eq (Or (Eq a empty_set) (Eq a_1 empty_set)) True) % 4.48/4.72 Clause #26 (by clausification #[6]): Eq % 4.48/4.72 (∀ (A : Iota), % 4.48/4.72 Not (empty A) → % 4.48/4.72 ∀ (B C D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 A B) (cartesian_product2 C D)) % 4.48/4.72 (subset (cartesian_product2 B A) (cartesian_product2 D C)) → % 4.48/4.72 subset B D) % 4.48/4.72 False % 4.48/4.72 Clause #27 (by clausification #[26]): ∀ (a : Iota), % 4.48/4.72 Eq % 4.48/4.72 (Not % 4.48/4.72 (Not (empty (skS.0 2 a)) → % 4.48/4.72 ∀ (B C D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 (skS.0 2 a) B) (cartesian_product2 C D)) % 4.48/4.72 (subset (cartesian_product2 B (skS.0 2 a)) (cartesian_product2 D C)) → % 4.48/4.72 subset B D)) % 4.48/4.72 True % 4.48/4.72 Clause #28 (by clausification #[27]): ∀ (a : Iota), % 4.48/4.72 Eq % 4.48/4.72 (Not (empty (skS.0 2 a)) → % 4.48/4.72 ∀ (B C D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 (skS.0 2 a) B) (cartesian_product2 C D)) % 4.48/4.72 (subset (cartesian_product2 B (skS.0 2 a)) (cartesian_product2 D C)) → % 4.48/4.72 subset B D) % 4.48/4.72 False % 4.48/4.72 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (Not (empty (skS.0 2 a))) True % 4.48/4.72 Clause #30 (by clausification #[28]): ∀ (a : Iota), % 4.48/4.72 Eq % 4.48/4.72 (∀ (B C D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 (skS.0 2 a) B) (cartesian_product2 C D)) % 4.48/4.72 (subset (cartesian_product2 B (skS.0 2 a)) (cartesian_product2 D C)) → % 4.48/4.72 subset B D) % 4.48/4.72 False % 4.48/4.72 Clause #31 (by clausification #[29]): ∀ (a : Iota), Eq (empty (skS.0 2 a)) False % 4.48/4.72 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (Not % 4.48/4.72 (∀ (C D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 C D)) % 4.48/4.72 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D C)) → % 4.48/4.72 subset (skS.0 3 a a_1) D)) % 4.48/4.72 True % 4.48/4.72 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (∀ (C D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 C D)) % 4.48/4.72 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D C)) → % 4.48/4.72 subset (skS.0 3 a a_1) D) % 4.48/4.72 False % 4.48/4.72 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (Not % 4.48/4.72 (∀ (D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) D)) % 4.48/4.72 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D (skS.0 4 a a_1 a_2))) → % 4.48/4.72 subset (skS.0 3 a a_1) D)) % 4.48/4.72 True % 4.48/4.72 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 4.48/4.72 Eq % 4.48/4.72 (∀ (D : Iota), % 4.48/4.72 Or (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) (cartesian_product2 (skS.0 4 a a_1 a_2) D)) % 4.48/4.72 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) (cartesian_product2 D (skS.0 4 a a_1 a_2))) → % 4.58/4.74 subset (skS.0 3 a a_1) D) % 4.58/4.74 False % 4.58/4.74 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.74 Eq % 4.58/4.74 (Not % 4.58/4.74 (Or % 4.58/4.74 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) % 4.58/4.74 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.74 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) % 4.58/4.74 (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))) → % 4.58/4.74 subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.74 True % 4.58/4.74 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.74 Eq % 4.58/4.74 (Or % 4.58/4.74 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) % 4.58/4.74 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.74 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) % 4.58/4.74 (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))) → % 4.58/4.74 subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) % 4.58/4.74 False % 4.58/4.74 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.74 Eq % 4.58/4.74 (Or % 4.58/4.74 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) % 4.58/4.74 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.74 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) % 4.58/4.74 (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2)))) % 4.58/4.74 True % 4.58/4.74 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) False % 4.58/4.74 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.74 Or % 4.58/4.74 (Eq % 4.58/4.74 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) % 4.58/4.74 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.74 True) % 4.58/4.74 (Eq % 4.58/4.74 (subset (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) % 4.58/4.74 (cartesian_product2 (skS.0 5 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2))) % 4.58/4.74 True) % 4.58/4.74 Clause #41 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (Or (Eq a empty_set) (Eq a_1 empty_set)) True) (Ne (cartesian_product2 a a_1) empty_set) % 4.58/4.74 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 4.58/4.74 Or (Ne (cartesian_product2 a a_1) empty_set) (Or (Eq (Eq a empty_set) True) (Eq (Eq a_1 empty_set) True)) % 4.58/4.74 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Ne (cartesian_product2 a a_1) empty_set) (Or (Eq (Eq a_1 empty_set) True) (Eq a empty_set)) % 4.58/4.74 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Ne (cartesian_product2 a a_1) empty_set) (Or (Eq a empty_set) (Eq a_1 empty_set)) % 4.58/4.74 Clause #45 (by clausification #[5]): ∀ (a : Iota), % 4.58/4.74 Eq % 4.58/4.74 (∀ (B C D : Iota), % 4.58/4.74 subset (cartesian_product2 a B) (cartesian_product2 C D) → % 4.58/4.74 Or (Eq (cartesian_product2 a B) empty_set) (And (subset a C) (subset B D))) % 4.58/4.74 True % 4.58/4.74 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), % 4.58/4.74 Eq % 4.58/4.74 (∀ (C D : Iota), % 4.58/4.74 subset (cartesian_product2 a a_1) (cartesian_product2 C D) → % 4.58/4.74 Or (Eq (cartesian_product2 a a_1) empty_set) (And (subset a C) (subset a_1 D))) % 4.58/4.74 True % 4.58/4.74 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 4.58/4.74 Eq % 4.58/4.74 (∀ (D : Iota), % 4.58/4.74 subset (cartesian_product2 a a_1) (cartesian_product2 a_2 D) → % 4.58/4.74 Or (Eq (cartesian_product2 a a_1) empty_set) (And (subset a a_2) (subset a_1 D))) % 4.58/4.74 True % 4.58/4.74 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.74 Eq % 4.58/4.74 (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) → % 4.58/4.74 Or (Eq (cartesian_product2 a a_1) empty_set) (And (subset a a_2) (subset a_1 a_3))) % 4.58/4.74 True % 4.58/4.74 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.74 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False) % 4.58/4.74 (Eq (Or (Eq (cartesian_product2 a a_1) empty_set) (And (subset a a_2) (subset a_1 a_3))) True) % 4.58/4.74 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.74 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False) % 4.58/4.74 (Or (Eq (Eq (cartesian_product2 a a_1) empty_set) True) (Eq (And (subset a a_2) (subset a_1 a_3)) True)) % 4.58/4.74 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.74 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False) % 4.58/4.76 (Or (Eq (And (subset a a_2) (subset a_1 a_3)) True) (Eq (cartesian_product2 a a_1) empty_set)) % 4.58/4.76 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.76 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False) % 4.58/4.76 (Or (Eq (cartesian_product2 a a_1) empty_set) (Eq (subset a_1 a_3) True)) % 4.58/4.76 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.76 Or (Eq (subset (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) False) % 4.58/4.76 (Or (Eq (cartesian_product2 a a_1) empty_set) (Eq (subset a a_2) True)) % 4.58/4.76 Clause #59 (by superposition #[53, 40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set) % 4.58/4.76 (Or (Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True) % 4.58/4.76 (Or % 4.58/4.76 (Eq % 4.58/4.76 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) % 4.58/4.76 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.76 True) % 4.58/4.76 (Eq False True))) % 4.58/4.76 Clause #70 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set) % 4.58/4.76 (Or (Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True) % 4.58/4.76 (Eq % 4.58/4.76 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) % 4.58/4.76 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.76 True)) % 4.58/4.76 Clause #71 (by forward demodulation #[70, 39]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set) % 4.58/4.76 (Or (Eq False True) % 4.58/4.76 (Eq % 4.58/4.76 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) % 4.58/4.76 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.76 True)) % 4.58/4.76 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set) % 4.58/4.76 (Eq % 4.58/4.76 (subset (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) % 4.58/4.76 (cartesian_product2 (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) % 4.58/4.76 True) % 4.58/4.76 Clause #73 (by superposition #[72, 52]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set) % 4.58/4.76 (Or (Eq True False) % 4.58/4.76 (Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set) % 4.58/4.76 (Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True))) % 4.58/4.76 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set) % 4.58/4.76 (Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set) % 4.58/4.76 (Eq (subset (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)) True)) % 4.58/4.76 Clause #76 (by superposition #[75, 39]): ∀ (a a_1 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set) % 4.58/4.76 (Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set) (Eq True False)) % 4.58/4.76 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 3 a a_1) (skS.0 2 a)) empty_set) % 4.58/4.76 (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set) % 4.58/4.76 Clause #79 (by superposition #[77, 44]): ∀ (a a_1 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set) % 4.58/4.76 (Or (Ne empty_set empty_set) (Or (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 2 a) empty_set))) % 4.58/4.76 Clause #82 (by eliminate resolved literals #[79]): ∀ (a a_1 : Iota), % 4.58/4.76 Or (Eq (cartesian_product2 (skS.0 2 a) (skS.0 3 a a_1)) empty_set) % 4.58/4.76 (Or (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 2 a) empty_set)) % 4.58/4.76 Clause #83 (by forward contextual literal cutting #[82, 44]): ∀ (a a_1 : Iota), Or (Eq (skS.0 3 a a_1) empty_set) (Eq (skS.0 2 a) empty_set) % 4.58/4.76 Clause #85 (by superposition #[83, 39]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (subset empty_set (skS.0 5 a a_1 a_2 a_3)) False) % 4.58/4.76 Clause #88 (by superposition #[85, 8]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq False True) % 4.58/4.76 Clause #89 (by clausification #[88]): ∀ (a : Iota), Eq (skS.0 2 a) empty_set % 4.58/4.76 Clause #90 (by backward demodulation #[89, 31]): Eq (empty empty_set) False % 4.58/4.76 Clause #96 (by superposition #[90, 0]): Eq False True % 4.58/4.76 Clause #100 (by clausification #[96]): False % 4.58/4.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------