%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU148+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:00:58 PM UTC 2025 % Result : Theorem 3.84s 4.08s % Output : Proof 3.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU148+1 : TPTP v9.2.0. Released v3.3.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.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 : Fri Oct 3 04:19:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.84/4.08 SZS status Theorem for theBenchmark.p % 3.84/4.08 SZS output start Proof for theBenchmark.p % 3.84/4.08 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 3.84/4.08 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), Ne (singleton A) empty_set) True % 3.84/4.08 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) True % 3.84/4.08 Clause #9 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset (singleton A) (singleton B) → Eq A B)) True % 3.84/4.08 Clause #20 (by clausification #[4]): ∀ (a : Iota), Eq (Ne (singleton a) empty_set) True % 3.84/4.08 Clause #21 (by clausification #[20]): ∀ (a : Iota), Ne (singleton a) empty_set % 3.84/4.08 Clause #22 (by clausification #[9]): Eq (∀ (A B : Iota), subset (singleton A) (singleton B) → Eq A B) False % 3.84/4.08 Clause #23 (by clausification #[22]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (singleton (skS.0 2 a)) (singleton B) → Eq (skS.0 2 a) B)) True % 3.84/4.08 Clause #24 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (singleton (skS.0 2 a)) (singleton B) → Eq (skS.0 2 a) B) False % 3.84/4.08 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), % 3.84/4.08 Eq (Not (subset (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)) → Eq (skS.0 2 a) (skS.0 3 a a_1))) True % 3.84/4.08 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)) → Eq (skS.0 2 a) (skS.0 3 a a_1)) False % 3.84/4.08 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) True % 3.84/4.08 Clause #28 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) False % 3.84/4.08 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Ne (skS.0 2 a) (skS.0 3 a a_1) % 3.84/4.08 Clause #30 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 3.84/4.08 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 3.84/4.08 Clause #33 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 3.84/4.08 Clause #40 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 3.84/4.08 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 3.84/4.08 Clause #42 (by clausification #[41]): ∀ (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)) % 3.84/4.08 Clause #43 (by clausification #[41]): ∀ (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)) % 3.84/4.08 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 3.84/4.08 Clause #45 (by destructive equality resolution #[44]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 3.84/4.08 Clause #46 (by destructive equality resolution #[45]): ∀ (a : Iota), Eq (in a (singleton a)) True % 3.84/4.08 Clause #48 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a (singleton B)) (Or (Eq a empty_set) (Eq a (singleton B)))) True % 3.84/4.08 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (Iff (subset a (singleton a_1)) (Or (Eq a empty_set) (Eq a (singleton a_1)))) True % 3.84/4.08 Clause #51 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) True) % 3.84/4.08 Clause #59 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 3.84/4.08 Clause #60 (by destructive equality resolution #[59]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 3.84/4.08 Clause #63 (by clausification #[51]): ∀ (a a_1 : Iota), % 3.84/4.08 Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq a (singleton a_1)) True)) % 3.84/4.08 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a (singleton a_1)) True) (Eq a empty_set)) % 3.94/4.09 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq a empty_set) (Eq a (singleton a_1))) % 3.94/4.09 Clause #66 (by superposition #[65, 27]): ∀ (a a_1 : Iota), % 3.94/4.09 Or (Eq (singleton (skS.0 2 a)) empty_set) % 3.94/4.09 (Or (Eq (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) (Eq False True)) % 3.94/4.09 Clause #90 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Eq (singleton (skS.0 2 a)) empty_set) (Eq (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1))) % 3.94/4.09 Clause #91 (by forward contextual literal cutting #[90, 21]): ∀ (a a_1 : Iota), Eq (singleton (skS.0 2 a)) (singleton (skS.0 3 a a_1)) % 3.94/4.09 Clause #94 (by superposition #[91, 46]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a a_1) (singleton (skS.0 2 a))) True % 3.94/4.09 Clause #105 (by superposition #[94, 60]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 3 a a_1) (skS.0 2 a)) % 3.94/4.09 Clause #114 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (skS.0 3 a a_1) (skS.0 2 a) % 3.94/4.09 Clause #115 (by forward contextual literal cutting #[114, 29]): False % 3.94/4.09 SZS output end Proof for theBenchmark.p 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