%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET875+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 3.73s 3.89s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET875+1 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.13 % Command : duper %s % 0.15/0.35 % Computer : n021.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Thu Oct 2 15:00:08 EDT 2025 % 0.15/0.35 % CPUTime : % 3.73/3.89 SZS status Theorem for theBenchmark.p % 3.73/3.89 SZS output start Proof for theBenchmark.p % 3.73/3.89 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.73/3.89 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (disjoint (singleton A) B) (in A B))) True % 3.73/3.89 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), Not (And (disjoint (singleton A) (singleton B)) (Eq A B)))) True % 3.73/3.89 Clause #18 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (disjoint (singleton a) B) (in a B))) True % 3.73/3.89 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Not (And (disjoint (singleton a) a_1) (in a a_1))) True % 3.73/3.89 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (And (disjoint (singleton a) a_1) (in a a_1)) False % 3.73/3.89 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (disjoint (singleton a) a_1) False) (Eq (in a a_1) False) % 3.73/3.89 Clause #22 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.73/3.89 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.73/3.89 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.73/3.89 Clause #32 (by clausification #[6]): Eq (∀ (A B : Iota), Not (And (disjoint (singleton A) (singleton B)) (Eq A B))) False % 3.73/3.89 Clause #33 (by clausification #[32]): ∀ (a : Iota), % 3.73/3.89 Eq (Not (∀ (B : Iota), Not (And (disjoint (singleton (skS.0 3 a)) (singleton B)) (Eq (skS.0 3 a) B)))) True % 3.73/3.89 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (disjoint (singleton (skS.0 3 a)) (singleton B)) (Eq (skS.0 3 a) B))) False % 3.73/3.89 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), % 3.73/3.89 Eq (Not (Not (And (disjoint (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (Eq (skS.0 3 a) (skS.0 4 a a_1))))) % 3.73/3.89 True % 3.73/3.89 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 3.73/3.89 Eq (Not (And (disjoint (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (Eq (skS.0 3 a) (skS.0 4 a a_1)))) False % 3.73/3.89 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.73/3.89 Eq (And (disjoint (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) (Eq (skS.0 3 a) (skS.0 4 a a_1))) True % 3.73/3.89 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 3 a) (skS.0 4 a a_1)) True % 3.73/3.89 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (disjoint (singleton (skS.0 3 a)) (singleton (skS.0 4 a a_1))) True % 3.73/3.89 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (skS.0 3 a) (skS.0 4 a a_1) % 3.73/3.89 Clause #41 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.73/3.89 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.73/3.89 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False)) % 3.73/3.89 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 3.73/3.89 Clause #46 (by destructive equality resolution #[45]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 3.73/3.89 Clause #47 (by destructive equality resolution #[46]): ∀ (a : Iota), Eq (in a (singleton a)) True % 3.73/3.89 Clause #64 (by forward demodulation #[39, 40]): ∀ (a : Iota), Eq (disjoint (singleton (skS.0 3 a)) (singleton (skS.0 3 a))) True % 3.73/3.89 Clause #65 (by superposition #[64, 21]): ∀ (a : Iota), Or (Eq True False) (Eq (in (skS.0 3 a) (singleton (skS.0 3 a))) False) % 3.73/3.89 Clause #67 (by clausification #[65]): ∀ (a : Iota), Eq (in (skS.0 3 a) (singleton (skS.0 3 a))) False % 3.73/3.89 Clause #68 (by superposition #[67, 47]): Eq False True % 3.73/3.89 Clause #70 (by clausification #[68]): False % 3.73/3.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------