%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU143+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:00:57 PM UTC 2025 % Result : Theorem 6.96s 7.16s % Output : Proof 6.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU143+2 : TPTP v9.2.0. Released v3.3.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n003.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 04:35:08 EDT 2025 % 0.12/0.34 % CPUTime : % 6.96/7.16 SZS status Theorem for theBenchmark.p % 6.96/7.16 SZS output start Proof for theBenchmark.p % 6.96/7.16 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 6.96/7.16 Clause #16 (by assumption #[]): Eq (empty empty_set) True % 6.96/7.16 Clause #22 (by assumption #[]): Eq (Not (∀ (A : Iota), Ne (singleton A) empty_set)) True % 6.96/7.16 Clause #53 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (in A B) (empty B))) True % 6.96/7.16 Clause #90 (by clausification #[22]): Eq (∀ (A : Iota), Ne (singleton A) empty_set) False % 6.96/7.16 Clause #91 (by clausification #[90]): ∀ (a : Iota), Eq (Not (Ne (singleton (skS.0 2 a)) empty_set)) True % 6.96/7.16 Clause #92 (by clausification #[91]): ∀ (a : Iota), Eq (Ne (singleton (skS.0 2 a)) empty_set) False % 6.96/7.16 Clause #93 (by clausification #[92]): ∀ (a : Iota), Eq (singleton (skS.0 2 a)) empty_set % 6.96/7.16 Clause #175 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 6.96/7.16 Clause #176 (by clausification #[175]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 6.96/7.16 Clause #178 (by clausification #[176]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 6.96/7.16 Clause #673 (by clausification #[53]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (in a B) (empty B))) True % 6.96/7.16 Clause #674 (by clausification #[673]): ∀ (a a_1 : Iota), Eq (Not (And (in a a_1) (empty a_1))) True % 6.96/7.16 Clause #675 (by clausification #[674]): ∀ (a a_1 : Iota), Eq (And (in a a_1) (empty a_1)) False % 6.96/7.16 Clause #676 (by clausification #[675]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (empty a_1) False) % 6.96/7.16 Clause #1100 (by clausification #[178]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 6.96/7.16 Clause #1101 (by clausification #[1100]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 6.96/7.16 Clause #1102 (by clausification #[1101]): ∀ (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)) % 6.96/7.16 Clause #1104 (by clausification #[1102]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 6.96/7.16 Clause #1105 (by destructive equality resolution #[1104]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 6.96/7.16 Clause #1106 (by destructive equality resolution #[1105]): ∀ (a : Iota), Eq (in a (singleton a)) True % 6.96/7.16 Clause #1108 (by superposition #[1106, 676]): ∀ (a : Iota), Or (Eq True False) (Eq (empty (singleton a)) False) % 6.96/7.16 Clause #1113 (by clausification #[1108]): ∀ (a : Iota), Eq (empty (singleton a)) False % 6.96/7.16 Clause #1114 (by superposition #[1113, 93]): Eq (empty empty_set) False % 6.96/7.16 Clause #1117 (by superposition #[1114, 16]): Eq False True % 6.96/7.16 Clause #1122 (by clausification #[1117]): False % 6.96/7.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------