%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU143+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 3.61s 3.77s % Output : Proof 3.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU143+1 : TPTP v9.2.0. Released v3.3.0. % 0.14/0.14 % Command : duper %s % 0.15/0.35 % Computer : n023.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 : Fri Oct 3 05:04:38 EDT 2025 % 0.15/0.35 % CPUTime : % 3.61/3.77 SZS status Theorem for theBenchmark.p % 3.61/3.77 SZS output start Proof for theBenchmark.p % 3.61/3.77 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.61/3.77 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True % 3.61/3.77 Clause #5 (by assumption #[]): Eq (Not (∀ (A : Iota), Ne (singleton A) empty_set)) True % 3.61/3.77 Clause #16 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.61/3.77 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.61/3.77 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.61/3.77 Clause #26 (by clausification #[5]): Eq (∀ (A : Iota), Ne (singleton A) empty_set) False % 3.61/3.77 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (Not (Ne (singleton (skS.0 3 a)) empty_set)) True % 3.61/3.77 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (Ne (singleton (skS.0 3 a)) empty_set) False % 3.61/3.77 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (singleton (skS.0 3 a)) empty_set % 3.61/3.77 Clause #30 (by clausification #[2]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True % 3.61/3.77 Clause #32 (by clausification #[30]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True) % 3.61/3.77 Clause #40 (by clausification #[32]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set) % 3.61/3.77 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True) % 3.61/3.77 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False) % 3.61/3.77 Clause #43 (by destructive equality resolution #[42]): ∀ (a : Iota), Eq (in a empty_set) False % 3.61/3.77 Clause #47 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.61/3.77 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.61/3.77 Clause #49 (by clausification #[48]): ∀ (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)) % 3.61/3.77 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 3.61/3.77 Clause #52 (by destructive equality resolution #[51]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 3.61/3.77 Clause #53 (by destructive equality resolution #[52]): ∀ (a : Iota), Eq (in a (singleton a)) True % 3.61/3.77 Clause #55 (by superposition #[53, 29]): ∀ (a : Iota), Eq (in (skS.0 3 a) empty_set) True % 3.61/3.77 Clause #58 (by superposition #[55, 43]): Eq True False % 3.61/3.77 Clause #61 (by clausification #[58]): False % 3.61/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------