%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET877+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:00:37 PM UTC 2025 % Result : Theorem 4.46s 4.62s % Output : Proof 4.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET877+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n010.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 14:45:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.46/4.62 SZS status Theorem for theBenchmark.p % 4.46/4.62 SZS output start Proof for theBenchmark.p % 4.46/4.62 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A B) (set_intersection2 B A)) True % 4.46/4.62 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 4.46/4.62 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A (singleton B)) (singleton B) → in B A) True % 4.46/4.62 Clause #7 (by assumption #[]): Eq (Not (∀ (A B : Iota), Eq (set_intersection2 (singleton A) (singleton B)) (singleton A) → Eq A B)) True % 4.46/4.62 Clause #10 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a (singleton B)) (singleton B) → in B a) True % 4.46/4.62 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a (singleton a_1)) (singleton a_1) → in a_1 a) True % 4.46/4.62 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_intersection2 a (singleton a_1)) (singleton a_1)) False) (Eq (in a_1 a) True) % 4.46/4.62 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Ne (set_intersection2 a_1 (singleton a)) (singleton a)) % 4.46/4.62 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a B) (set_intersection2 B a)) True % 4.46/4.62 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)) True % 4.46/4.62 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (set_intersection2 a a_1) (set_intersection2 a_1 a) % 4.46/4.62 Clause #27 (by superposition #[26, 13]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Ne (set_intersection2 (singleton a) a_1) (singleton a)) % 4.46/4.62 Clause #31 (by clausification #[7]): Eq (∀ (A B : Iota), Eq (set_intersection2 (singleton A) (singleton B)) (singleton A) → Eq A B) False % 4.46/4.62 Clause #32 (by clausification #[31]): ∀ (a : Iota), % 4.46/4.62 Eq % 4.46/4.62 (Not % 4.46/4.62 (∀ (B : Iota), % 4.46/4.62 Eq (set_intersection2 (singleton (skS.0 2 a)) (singleton B)) (singleton (skS.0 2 a)) → Eq (skS.0 2 a) B)) % 4.46/4.62 True % 4.46/4.62 Clause #33 (by clausification #[32]): ∀ (a : Iota), % 4.46/4.62 Eq % 4.46/4.62 (∀ (B : Iota), % 4.46/4.62 Eq (set_intersection2 (singleton (skS.0 2 a)) (singleton B)) (singleton (skS.0 2 a)) → Eq (skS.0 2 a) B) % 4.46/4.62 False % 4.46/4.62 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 4.46/4.62 Eq % 4.46/4.62 (Not % 4.46/4.62 (Eq (set_intersection2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) → % 4.46/4.62 Eq (skS.0 2 a) (skS.0 3 a a_1))) % 4.46/4.62 True % 4.46/4.62 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 4.46/4.62 Eq % 4.46/4.62 (Eq (set_intersection2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) → % 4.46/4.62 Eq (skS.0 2 a) (skS.0 3 a a_1)) % 4.46/4.62 False % 4.46/4.62 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 4.46/4.62 Eq (Eq (set_intersection2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a))) True % 4.46/4.62 Clause #37 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) False % 4.46/4.62 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (set_intersection2 (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (singleton (skS.0 2 a)) % 4.46/4.62 Clause #40 (by superposition #[27, 38]): ∀ (a a_1 : Iota), % 4.46/4.62 Or (Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) % 4.46/4.62 Clause #41 (by clausification #[37]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (skS.0 3 a a_1) % 4.46/4.62 Clause #42 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 4.46/4.62 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 4.46/4.62 Clause #45 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 4.46/4.62 Clause #52 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 4.46/4.62 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 4.46/4.62 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True)) % 4.46/4.63 Clause #58 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 4.46/4.63 Clause #59 (by destructive equality resolution #[58]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 4.46/4.63 Clause #90 (by eliminate resolved literals #[40]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (singleton (skS.0 3 a a_1))) True % 4.46/4.63 Clause #91 (by superposition #[90, 59]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 4.46/4.63 Clause #96 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1) % 4.46/4.63 Clause #97 (by forward contextual literal cutting #[96, 41]): False % 4.46/4.63 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------