%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET974+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:00:45 PM UTC 2025 % Result : Theorem 41.68s 41.97s % Output : Proof 41.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET974+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n009.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 14:02:08 EDT 2025 % 0.13/0.34 % CPUTime : % 41.68/41.97 SZS status Theorem for theBenchmark.p % 41.68/41.97 SZS output start Proof for theBenchmark.p % 41.68/41.97 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A B) (set_intersection2 B A)) True % 41.68/41.97 Clause #8 (by assumption #[]): Eq (∀ (A B : Iota), disjoint A B → disjoint B A) True % 41.68/41.97 Clause #9 (by assumption #[]): Eq % 41.68/41.97 (∀ (A B C D E : Iota), % 41.68/41.97 Not % 41.68/41.97 (And (in A (set_intersection2 (cartesian_product2 B C) (cartesian_product2 D E))) % 41.68/41.97 (∀ (F G : Iota), % 41.68/41.97 Not (And (And (Eq A (ordered_pair F G)) (in F (set_intersection2 B D))) (in G (set_intersection2 C E)))))) % 41.68/41.97 True % 41.68/41.97 Clause #10 (by assumption #[]): Eq % 41.68/41.97 (Not % 41.68/41.97 (∀ (A B C D : Iota), Or (disjoint A B) (disjoint C D) → disjoint (cartesian_product2 A C) (cartesian_product2 B D))) % 41.68/41.97 True % 41.68/41.97 Clause #11 (by assumption #[]): Eq % 41.68/41.97 (∀ (A B : Iota), % 41.68/41.97 And (Not (And (Not (disjoint A B)) (∀ (C : Iota), Not (in C (set_intersection2 A B))))) % 41.68/41.97 (Not (And (Exists fun C => in C (set_intersection2 A B)) (disjoint A B)))) % 41.68/41.97 True % 41.68/41.97 Clause #16 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), disjoint a B → disjoint B a) True % 41.68/41.97 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (disjoint a a_1 → disjoint a_1 a) True % 41.68/41.97 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (disjoint a_1 a) True) % 41.68/41.97 Clause #32 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a B) (set_intersection2 B a)) True % 41.68/41.97 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)) True % 41.68/41.97 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (set_intersection2 a a_1) (set_intersection2 a_1 a) % 41.68/41.97 Clause #35 (by clausification #[10]): Eq (∀ (A B C D : Iota), Or (disjoint A B) (disjoint C D) → disjoint (cartesian_product2 A C) (cartesian_product2 B D)) % 41.68/41.97 False % 41.68/41.97 Clause #36 (by clausification #[35]): ∀ (a : Iota), % 41.68/41.97 Eq % 41.68/41.97 (Not % 41.68/41.97 (∀ (B C D : Iota), % 41.68/41.97 Or (disjoint (skS.0 2 a) B) (disjoint C D) → % 41.68/41.97 disjoint (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 B D))) % 41.68/41.97 True % 41.68/41.97 Clause #37 (by clausification #[36]): ∀ (a : Iota), % 41.68/41.97 Eq % 41.68/41.97 (∀ (B C D : Iota), % 41.68/41.97 Or (disjoint (skS.0 2 a) B) (disjoint C D) → disjoint (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 B D)) % 41.68/41.97 False % 41.68/41.97 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 41.68/41.97 Eq % 41.68/41.97 (Not % 41.68/41.97 (∀ (C D : Iota), % 41.68/41.97 Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint C D) → % 41.68/41.97 disjoint (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 3 a a_1) D))) % 41.68/41.97 True % 41.68/41.97 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 41.68/41.97 Eq % 41.68/41.97 (∀ (C D : Iota), % 41.68/41.97 Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint C D) → % 41.68/41.97 disjoint (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 3 a a_1) D)) % 41.68/41.97 False % 41.68/41.97 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 41.68/41.97 Eq % 41.68/41.97 (Not % 41.68/41.97 (∀ (D : Iota), % 41.68/41.97 Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) D) → % 41.68/41.97 disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 3 a a_1) D))) % 41.68/41.97 True % 41.68/41.97 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 41.68/41.97 Eq % 41.68/41.97 (∀ (D : Iota), % 41.68/41.97 Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) D) → % 41.68/41.97 disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 3 a a_1) D)) % 41.68/41.97 False % 41.68/41.97 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 41.68/41.97 Eq % 41.68/41.97 (Not % 41.68/41.97 (Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) → % 41.68/41.97 disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 41.68/41.97 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))) % 41.68/41.97 True % 41.68/41.97 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 41.68/41.97 Eq % 41.68/41.97 (Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) → % 41.68/41.97 disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 41.68/41.97 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))) % 41.77/41.99 False % 41.77/41.99 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 41.77/41.99 Eq (Or (disjoint (skS.0 2 a) (skS.0 3 a a_1)) (disjoint (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) True % 41.77/41.99 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 41.77/41.99 Eq % 41.77/41.99 (disjoint (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 41.77/41.99 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))) % 41.77/41.99 False % 41.77/41.99 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 41.77/41.99 Or (Eq (disjoint (skS.0 2 a) (skS.0 3 a a_1)) True) (Eq (disjoint (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) True) % 41.77/41.99 Clause #60 (by clausification #[9]): ∀ (a : Iota), % 41.77/41.99 Eq % 41.77/41.99 (∀ (B C D E : Iota), % 41.77/41.99 Not % 41.77/41.99 (And (in a (set_intersection2 (cartesian_product2 B C) (cartesian_product2 D E))) % 41.77/41.99 (∀ (F G : Iota), % 41.77/41.99 Not (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 B D))) (in G (set_intersection2 C E)))))) % 41.77/41.99 True % 41.77/41.99 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), % 41.77/41.99 Eq % 41.77/41.99 (∀ (C D E : Iota), % 41.77/41.99 Not % 41.77/41.99 (And (in a (set_intersection2 (cartesian_product2 a_1 C) (cartesian_product2 D E))) % 41.77/41.99 (∀ (F G : Iota), % 41.77/41.99 Not (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 D))) (in G (set_intersection2 C E)))))) % 41.77/41.99 True % 41.77/41.99 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 41.77/41.99 Eq % 41.77/41.99 (∀ (D E : Iota), % 41.77/41.99 Not % 41.77/41.99 (And (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 D E))) % 41.77/41.99 (∀ (F G : Iota), % 41.77/41.99 Not % 41.77/41.99 (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 D))) (in G (set_intersection2 a_2 E)))))) % 41.77/41.99 True % 41.77/41.99 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 41.77/41.99 Eq % 41.77/41.99 (∀ (E : Iota), % 41.77/41.99 Not % 41.77/41.99 (And (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 E))) % 41.77/41.99 (∀ (F G : Iota), % 41.77/41.99 Not % 41.77/41.99 (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 a_3))) % 41.77/41.99 (in G (set_intersection2 a_2 E)))))) % 41.77/41.99 True % 41.77/41.99 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 41.77/41.99 Eq % 41.77/41.99 (Not % 41.77/41.99 (And (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) % 41.77/41.99 (∀ (F G : Iota), % 41.77/41.99 Not % 41.77/41.99 (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 a_3))) % 41.77/41.99 (in G (set_intersection2 a_2 a_4)))))) % 41.77/41.99 True % 41.77/41.99 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 41.77/41.99 Eq % 41.77/41.99 (And (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) % 41.77/41.99 (∀ (F G : Iota), % 41.77/41.99 Not % 41.77/41.99 (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 a_3))) (in G (set_intersection2 a_2 a_4))))) % 41.77/41.99 False % 41.77/41.99 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 41.77/41.99 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.77/41.99 (Eq % 41.77/41.99 (∀ (F G : Iota), % 41.77/41.99 Not (And (And (Eq a (ordered_pair F G)) (in F (set_intersection2 a_1 a_3))) (in G (set_intersection2 a_2 a_4)))) % 41.77/41.99 False) % 41.77/41.99 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 41.77/41.99 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.77/41.99 (Eq % 41.77/41.99 (Not % 41.77/41.99 (∀ (G : Iota), % 41.77/41.99 Not % 41.77/41.99 (And % 41.77/41.99 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) G)) % 41.77/41.99 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3))) % 41.77/41.99 (in G (set_intersection2 a_2 a_4))))) % 41.77/41.99 True) % 41.77/41.99 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 41.77/41.99 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.77/41.99 (Eq % 41.77/41.99 (∀ (G : Iota), % 41.77/41.99 Not % 41.77/41.99 (And % 41.77/41.99 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) G)) % 41.77/41.99 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3))) % 41.77/41.99 (in G (set_intersection2 a_2 a_4)))) % 41.77/41.99 False) % 41.77/41.99 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 41.77/41.99 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.79/42.01 (Eq % 41.79/42.01 (Not % 41.79/42.01 (Not % 41.79/42.01 (And % 41.79/42.01 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6))) % 41.79/42.01 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3))) % 41.79/42.01 (in (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6) (set_intersection2 a_2 a_4))))) % 41.79/42.01 True) % 41.79/42.01 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 41.79/42.01 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.79/42.01 (Eq % 41.79/42.01 (Not % 41.79/42.01 (And % 41.79/42.01 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6))) % 41.79/42.01 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3))) % 41.79/42.01 (in (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6) (set_intersection2 a_2 a_4)))) % 41.79/42.01 False) % 41.79/42.01 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 41.79/42.01 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.79/42.01 (Eq % 41.79/42.01 (And % 41.79/42.01 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6))) % 41.79/42.01 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3))) % 41.79/42.01 (in (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6) (set_intersection2 a_2 a_4))) % 41.79/42.01 True) % 41.79/42.01 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 41.79/42.01 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.79/42.01 (Eq (in (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6) (set_intersection2 a_2 a_4)) True) % 41.79/42.01 Clause #73 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 41.79/42.01 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.79/42.01 (Eq % 41.79/42.01 (And (Eq a (ordered_pair (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (skS.0 7 a a_1 a_3 a_2 a_4 a_5 a_6))) % 41.79/42.01 (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3))) % 41.79/42.01 True) % 41.79/42.01 Clause #87 (by clausification #[11]): ∀ (a : Iota), % 41.79/42.01 Eq % 41.79/42.01 (∀ (B : Iota), % 41.79/42.01 And (Not (And (Not (disjoint a B)) (∀ (C : Iota), Not (in C (set_intersection2 a B))))) % 41.79/42.01 (Not (And (Exists fun C => in C (set_intersection2 a B)) (disjoint a B)))) % 41.79/42.01 True % 41.79/42.01 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), % 41.79/42.01 Eq % 41.79/42.01 (And (Not (And (Not (disjoint a a_1)) (∀ (C : Iota), Not (in C (set_intersection2 a a_1))))) % 41.79/42.01 (Not (And (Exists fun C => in C (set_intersection2 a a_1)) (disjoint a a_1)))) % 41.79/42.01 True % 41.79/42.01 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (Not (And (Exists fun C => in C (set_intersection2 a a_1)) (disjoint a a_1))) True % 41.79/42.01 Clause #90 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (Not (And (Not (disjoint a a_1)) (∀ (C : Iota), Not (in C (set_intersection2 a a_1))))) True % 41.79/42.01 Clause #91 (by clausification #[89]): ∀ (a a_1 : Iota), Eq (And (Exists fun C => in C (set_intersection2 a a_1)) (disjoint a a_1)) False % 41.79/42.01 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Or (Eq (Exists fun C => in C (set_intersection2 a a_1)) False) (Eq (disjoint a a_1) False) % 41.79/42.01 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), Or (Eq (disjoint a a_1) False) (Eq (in a_2 (set_intersection2 a a_1)) False) % 41.79/42.01 Clause #94 (by superposition #[93, 46]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 41.79/42.01 Or (Eq (in a (set_intersection2 (skS.0 4 a_1 a_2 a_3) (skS.0 5 a_1 a_2 a_3 a_4))) False) % 41.79/42.01 (Or (Eq (disjoint (skS.0 2 a_1) (skS.0 3 a_1 a_2)) True) (Eq False True)) % 41.79/42.01 Clause #130 (by clausification #[90]): ∀ (a a_1 : Iota), Eq (And (Not (disjoint a a_1)) (∀ (C : Iota), Not (in C (set_intersection2 a a_1)))) False % 41.79/42.01 Clause #131 (by clausification #[130]): ∀ (a a_1 : Iota), Or (Eq (Not (disjoint a a_1)) False) (Eq (∀ (C : Iota), Not (in C (set_intersection2 a a_1))) False) % 41.79/42.01 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Not (in C (set_intersection2 a a_1))) False) (Eq (disjoint a a_1) True) % 41.79/42.01 Clause #133 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), % 41.79/42.01 Or (Eq (disjoint a a_1) True) (Eq (Not (Not (in (skS.0 8 a a_1 a_2) (set_intersection2 a a_1)))) True) % 41.82/42.03 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Not (in (skS.0 8 a a_1 a_2) (set_intersection2 a a_1))) False) % 41.82/42.03 Clause #135 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), Or (Eq (disjoint a a_1) True) (Eq (in (skS.0 8 a a_1 a_2) (set_intersection2 a a_1)) True) % 41.82/42.03 Clause #136 (by superposition #[135, 72]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 41.82/42.03 Or (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True) % 41.82/42.03 (Or (Eq True False) % 41.82/42.03 (Eq % 41.82/42.03 (in (skS.0 7 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5 a_6) % 41.82/42.03 (set_intersection2 a_1 a_3)) % 41.82/42.03 True)) % 41.82/42.03 Clause #149 (by clausification #[73]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 41.82/42.03 Or (Eq (in a (set_intersection2 (cartesian_product2 a_1 a_2) (cartesian_product2 a_3 a_4))) False) % 41.82/42.03 (Eq (in (skS.0 6 a a_1 a_3 a_2 a_4 a_5) (set_intersection2 a_1 a_3)) True) % 41.82/42.03 Clause #151 (by superposition #[149, 135]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 41.82/42.03 Or % 41.82/42.03 (Eq % 41.82/42.03 (in (skS.0 6 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5) % 41.82/42.03 (set_intersection2 a a_2)) % 41.82/42.03 True) % 41.82/42.03 (Or (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True) (Eq False True)) % 41.82/42.03 Clause #285 (by clausification #[94]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 41.82/42.03 Or (Eq (in a (set_intersection2 (skS.0 4 a_1 a_2 a_3) (skS.0 5 a_1 a_2 a_3 a_4))) False) % 41.82/42.03 (Eq (disjoint (skS.0 2 a_1) (skS.0 3 a_1 a_2)) True) % 41.82/42.03 Clause #740 (by clausification #[136]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 41.82/42.03 Or (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True) % 41.82/42.03 (Eq % 41.82/42.03 (in (skS.0 7 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5 a_6) % 41.82/42.03 (set_intersection2 a_1 a_3)) % 41.82/42.03 True) % 41.82/42.03 Clause #744 (by superposition #[740, 285]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 41.82/42.03 Or % 41.82/42.03 (Eq (disjoint (cartesian_product2 a (skS.0 4 a_1 a_2 a_3)) (cartesian_product2 a_4 (skS.0 5 a_1 a_2 a_3 a_5))) True) % 41.82/42.03 (Or (Eq True False) (Eq (disjoint (skS.0 2 a_1) (skS.0 3 a_1 a_2)) True)) % 41.82/42.03 Clause #926 (by clausification #[151]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 41.82/42.03 Or % 41.82/42.03 (Eq % 41.82/42.03 (in (skS.0 6 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5) % 41.82/42.03 (set_intersection2 a a_2)) % 41.82/42.03 True) % 41.82/42.03 (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True) % 41.82/42.03 Clause #935 (by superposition #[926, 34]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 41.82/42.03 Or % 41.82/42.03 (Eq % 41.82/42.03 (in (skS.0 6 (skS.0 8 (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3) a_4) a a_2 a_1 a_3 a_5) % 41.82/42.03 (set_intersection2 a_2 a)) % 41.82/42.03 True) % 41.82/42.03 (Eq (disjoint (cartesian_product2 a a_1) (cartesian_product2 a_2 a_3)) True) % 41.82/42.03 Clause #5203 (by clausification #[744]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 41.82/42.03 Or % 41.82/42.03 (Eq (disjoint (cartesian_product2 a (skS.0 4 a_1 a_2 a_3)) (cartesian_product2 a_4 (skS.0 5 a_1 a_2 a_3 a_5))) True) % 41.82/42.03 (Eq (disjoint (skS.0 2 a_1) (skS.0 3 a_1 a_2)) True) % 41.82/42.03 Clause #5204 (by superposition #[5203, 45]): ∀ (a a_1 : Iota), Or (Eq (disjoint (skS.0 2 a) (skS.0 3 a a_1)) True) (Eq True False) % 41.82/42.03 Clause #5207 (by clausification #[5204]): ∀ (a a_1 : Iota), Eq (disjoint (skS.0 2 a) (skS.0 3 a a_1)) True % 41.82/42.03 Clause #5213 (by superposition #[5207, 93]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in a (set_intersection2 (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False) % 41.82/42.03 Clause #5217 (by clausification #[5213]): ∀ (a a_1 a_2 : Iota), Eq (in a (set_intersection2 (skS.0 2 a_1) (skS.0 3 a_1 a_2))) False % 41.82/42.03 Clause #5224 (by superposition #[5217, 935]): ∀ (a a_1 a_2 a_3 : Iota), % 41.82/42.03 Or (Eq False True) (Eq (disjoint (cartesian_product2 (skS.0 3 a a_1) a_2) (cartesian_product2 (skS.0 2 a) a_3)) True) % 41.82/42.03 Clause #5382 (by clausification #[5224]): ∀ (a a_1 a_2 a_3 : Iota), % 41.82/42.03 Eq (disjoint (cartesian_product2 (skS.0 3 a a_1) a_2) (cartesian_product2 (skS.0 2 a) a_3)) True % 41.82/42.03 Clause #5383 (by superposition #[5382, 18]): ∀ (a a_1 a_2 a_3 : Iota), % 41.82/42.03 Or (Eq True False) (Eq (disjoint (cartesian_product2 (skS.0 2 a) a_1) (cartesian_product2 (skS.0 3 a a_2) a_3)) True) % 41.84/42.09 Clause #5385 (by clausification #[5383]): ∀ (a a_1 a_2 a_3 : Iota), % 41.84/42.09 Eq (disjoint (cartesian_product2 (skS.0 2 a) a_1) (cartesian_product2 (skS.0 3 a a_2) a_3)) True % 41.84/42.09 Clause #5386 (by superposition #[5385, 45]): Eq True False % 41.84/42.09 Clause #5489 (by clausification #[5386]): False % 41.84/42.09 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------