%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU120+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:00:54 PM UTC 2025 % Result : Theorem 40.82s 41.01s % Output : Proof 40.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU120+2 : TPTP v9.2.0. Released v3.3.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n008.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 06:29:53 EDT 2025 % 0.14/0.36 % CPUTime : % 40.82/41.01 SZS status Theorem for theBenchmark.p % 40.82/41.01 SZS output start Proof for theBenchmark.p % 40.82/41.01 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True % 40.82/41.01 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (disjoint A B) (Eq (set_intersection2 A B) empty_set)) True % 40.82/41.01 Clause #12 (by assumption #[]): Eq % 40.82/41.01 (Not % 40.82/41.01 (∀ (A B : Iota), % 40.82/41.01 And (Not (And (Not (disjoint A B)) (∀ (C : Iota), Not (in C (set_intersection2 A B))))) % 40.82/41.01 (Not (And (Exists fun C => in C (set_intersection2 A B)) (disjoint A B))))) % 40.82/41.01 True % 40.82/41.01 Clause #30 (by clausification #[2]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True % 40.82/41.01 Clause #31 (by clausification #[30]): ∀ (a : Iota), Or (Eq (Eq a empty_set) True) (Eq (∀ (B : Iota), Not (in B a)) False) % 40.82/41.01 Clause #32 (by clausification #[30]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True) % 40.82/41.01 Clause #33 (by clausification #[31]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) False) (Eq a empty_set) % 40.82/41.01 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Eq (Not (Not (in (skS.0 2 a a_1) a))) True) % 40.82/41.01 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Eq (Not (in (skS.0 2 a a_1) a)) False) % 40.82/41.01 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Eq (in (skS.0 2 a a_1) a) True) % 40.82/41.01 Clause #40 (by clausification #[32]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set) % 40.82/41.01 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True) % 40.82/41.01 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False) % 40.82/41.01 Clause #43 (by destructive equality resolution #[42]): ∀ (a : Iota), Eq (in a empty_set) False % 40.82/41.01 Clause #45 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (disjoint a B) (Eq (set_intersection2 a B) empty_set)) True % 40.82/41.01 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Eq (set_intersection2 a a_1) empty_set)) True % 40.82/41.01 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Eq (set_intersection2 a a_1) empty_set) False) % 40.82/41.01 Clause #48 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (Eq (set_intersection2 a a_1) empty_set) True) % 40.82/41.01 Clause #49 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Ne (set_intersection2 a a_1) empty_set) % 40.82/41.01 Clause #65 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (set_intersection2 a a_1) empty_set) % 40.82/41.01 Clause #84 (by clausification #[12]): Eq % 40.82/41.01 (∀ (A B : Iota), % 40.82/41.01 And (Not (And (Not (disjoint A B)) (∀ (C : Iota), Not (in C (set_intersection2 A B))))) % 40.82/41.01 (Not (And (Exists fun C => in C (set_intersection2 A B)) (disjoint A B)))) % 40.82/41.01 False % 40.82/41.01 Clause #85 (by clausification #[84]): ∀ (a : Iota), % 40.82/41.01 Eq % 40.82/41.01 (Not % 40.82/41.01 (∀ (B : Iota), % 40.82/41.01 And (Not (And (Not (disjoint (skS.0 4 a) B)) (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) B))))) % 40.82/41.01 (Not (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) B)) (disjoint (skS.0 4 a) B))))) % 40.82/41.01 True % 40.82/41.01 Clause #86 (by clausification #[85]): ∀ (a : Iota), % 40.82/41.01 Eq % 40.82/41.01 (∀ (B : Iota), % 40.82/41.01 And (Not (And (Not (disjoint (skS.0 4 a) B)) (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) B))))) % 40.82/41.01 (Not (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) B)) (disjoint (skS.0 4 a) B)))) % 40.82/41.01 False % 40.82/41.01 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), % 40.82/41.01 Eq % 40.82/41.01 (Not % 40.82/41.01 (And % 40.82/41.01 (Not % 40.82/41.01 (And (Not (disjoint (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.01 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)))))) % 40.82/41.01 (Not % 40.82/41.01 (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.01 (disjoint (skS.0 4 a) (skS.0 5 a a_1)))))) % 40.82/41.01 True % 40.82/41.01 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), % 40.82/41.01 Eq % 40.82/41.01 (And % 40.82/41.01 (Not % 40.82/41.01 (And (Not (disjoint (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.01 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)))))) % 40.82/41.04 (Not % 40.82/41.04 (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (disjoint (skS.0 4 a) (skS.0 5 a a_1))))) % 40.82/41.04 False % 40.82/41.04 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), % 40.82/41.04 Or % 40.82/41.04 (Eq % 40.82/41.04 (Not % 40.82/41.04 (And (Not (disjoint (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)))))) % 40.82/41.04 False) % 40.82/41.04 (Eq % 40.82/41.04 (Not % 40.82/41.04 (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (disjoint (skS.0 4 a) (skS.0 5 a a_1)))) % 40.82/41.04 False) % 40.82/41.04 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota), % 40.82/41.04 Or % 40.82/41.04 (Eq % 40.82/41.04 (Not % 40.82/41.04 (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (disjoint (skS.0 4 a) (skS.0 5 a a_1)))) % 40.82/41.04 False) % 40.82/41.04 (Eq % 40.82/41.04 (And (Not (disjoint (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))))) % 40.82/41.04 True) % 40.82/41.04 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota), % 40.82/41.04 Or % 40.82/41.04 (Eq % 40.82/41.04 (And (Not (disjoint (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))))) % 40.82/41.04 True) % 40.82/41.04 (Eq % 40.82/41.04 (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (disjoint (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 True) % 40.82/41.04 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), % 40.82/41.04 Or % 40.82/41.04 (Eq % 40.82/41.04 (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (disjoint (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 True) % 40.82/41.04 (Eq (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)))) True) % 40.82/41.04 Clause #93 (by clausification #[91]): ∀ (a a_1 : Iota), % 40.82/41.04 Or % 40.82/41.04 (Eq % 40.82/41.04 (And (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 (disjoint (skS.0 4 a) (skS.0 5 a a_1))) % 40.82/41.04 True) % 40.82/41.04 (Eq (Not (disjoint (skS.0 4 a) (skS.0 5 a a_1))) True) % 40.82/41.04 Clause #94 (by clausification #[92]): ∀ (a a_1 : Iota), % 40.82/41.04 Or (Eq (∀ (C : Iota), Not (in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)))) True) % 40.82/41.04 (Eq (disjoint (skS.0 4 a) (skS.0 5 a a_1)) True) % 40.82/41.04 Clause #96 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), % 40.82/41.04 Or (Eq (disjoint (skS.0 4 a) (skS.0 5 a a_1)) True) % 40.82/41.04 (Eq (Not (in a_2 (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)))) True) % 40.82/41.04 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 40.82/41.04 Or (Eq (disjoint (skS.0 4 a) (skS.0 5 a a_1)) True) % 40.82/41.04 (Eq (in a_2 (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) False) % 40.82/41.04 Clause #98 (by superposition #[97, 36]): ∀ (a a_1 : Iota), % 40.82/41.04 Or (Eq (disjoint (skS.0 4 a) (skS.0 5 a a_1)) True) % 40.82/41.04 (Or (Eq (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)) empty_set) (Eq False True)) % 40.82/41.04 Clause #280 (by clausification #[93]): ∀ (a a_1 : Iota), % 40.82/41.04 Or (Eq (Not (disjoint (skS.0 4 a) (skS.0 5 a a_1))) True) % 40.82/41.04 (Eq (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) True) % 40.82/41.04 Clause #344 (by clausification #[98]): ∀ (a a_1 : Iota), % 40.82/41.04 Or (Eq (disjoint (skS.0 4 a) (skS.0 5 a a_1)) True) (Eq (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)) empty_set) % 40.82/41.04 Clause #345 (by forward contextual literal cutting #[344, 49]): ∀ (a a_1 : Iota), Eq (disjoint (skS.0 4 a) (skS.0 5 a a_1)) True % 40.82/41.04 Clause #348 (by superposition #[345, 65]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)) empty_set) % 40.82/41.04 Clause #432 (by clausification #[348]): ∀ (a a_1 : Iota), Eq (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1)) empty_set % 40.82/41.04 Clause #11568 (by clausification #[280]): ∀ (a a_1 : Iota), % 40.82/41.04 Or (Eq (Exists fun C => in C (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) True) % 40.82/41.04 (Eq (disjoint (skS.0 4 a) (skS.0 5 a a_1)) False) % 40.82/41.04 Clause #11569 (by clausification #[11568]): ∀ (a a_1 a_2 : Iota), % 40.82/41.04 Or (Eq (disjoint (skS.0 4 a) (skS.0 5 a a_1)) False) % 40.82/41.04 (Eq (in (skS.0 8 a a_1 a_2) (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) True) % 40.82/41.04 Clause #11570 (by forward demodulation #[11569, 345]): ∀ (a a_1 a_2 : Iota), % 40.82/41.04 Or (Eq True False) (Eq (in (skS.0 8 a a_1 a_2) (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) True) % 40.94/41.15 Clause #11571 (by clausification #[11570]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (set_intersection2 (skS.0 4 a) (skS.0 5 a a_1))) True % 40.94/41.15 Clause #11572 (by forward demodulation #[11571, 432]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) empty_set) True % 40.94/41.15 Clause #11573 (by superposition #[11572, 43]): Eq True False % 40.94/41.15 Clause #11611 (by clausification #[11573]): False % 40.94/41.15 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------