%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET813+4 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:00:31 PM UTC 2025 % Result : Theorem 6.85s 7.04s % Output : Proof 6.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET813+4 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.13 % Command : duper %s % 0.14/0.34 % Computer : n002.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 14:41:38 EDT 2025 % 0.14/0.35 % CPUTime : % 6.85/7.04 SZS status Theorem for theBenchmark.p % 6.85/7.04 SZS output start Proof for theBenchmark.p % 6.85/7.04 Clause #4 (by assumption #[]): Eq (∀ (X A B : Iota), Iff (member X (union A B)) (Or (member X A) (member X B))) True % 6.85/7.04 Clause #7 (by assumption #[]): Eq (∀ (X A : Iota), Iff (member X (singleton A)) (Eq X A)) True % 6.85/7.04 Clause #18 (by assumption #[]): Eq (∀ (A X : Iota), Iff (member X (suc A)) (member X (union A (singleton A)))) True % 6.85/7.04 Clause #19 (by assumption #[]): Eq (Not (∀ (A : Iota), member A on → member A (suc A))) True % 6.85/7.04 Clause #26 (by clausification #[19]): Eq (∀ (A : Iota), member A on → member A (suc A)) False % 6.85/7.04 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (Not (member (skS.0 0 a) on → member (skS.0 0 a) (suc (skS.0 0 a)))) True % 6.85/7.04 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (member (skS.0 0 a) on → member (skS.0 0 a) (suc (skS.0 0 a))) False % 6.85/7.04 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (member (skS.0 0 a) (suc (skS.0 0 a))) False % 6.85/7.04 Clause #80 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (A : Iota), Iff (member a (singleton A)) (Eq a A)) True % 6.85/7.04 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (Iff (member a (singleton a_1)) (Eq a a_1)) True % 6.85/7.04 Clause #82 (by clausification #[81]): ∀ (a a_1 : Iota), Or (Eq (member a (singleton a_1)) True) (Eq (Eq a a_1) False) % 6.85/7.04 Clause #84 (by clausification #[82]): ∀ (a a_1 : Iota), Or (Eq (member a (singleton a_1)) True) (Ne a a_1) % 6.85/7.04 Clause #85 (by destructive equality resolution #[84]): ∀ (a : Iota), Eq (member a (singleton a)) True % 6.85/7.04 Clause #93 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (A B : Iota), Iff (member a (union A B)) (Or (member a A) (member a B))) True % 6.85/7.04 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), Eq (∀ (B : Iota), Iff (member a (union a_1 B)) (Or (member a a_1) (member a B))) True % 6.85/7.04 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (union a_1 a_2)) (Or (member a a_1) (member a a_2))) True % 6.85/7.04 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (Or (member a a_1) (member a a_2)) False) % 6.85/7.04 Clause #98 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (member a a_2) False) % 6.85/7.04 Clause #102 (by superposition #[98, 85]): ∀ (a a_1 : Iota), Or (Eq (member a (union a_1 (singleton a))) True) (Eq False True) % 6.85/7.04 Clause #105 (by clausification #[102]): ∀ (a a_1 : Iota), Eq (member a (union a_1 (singleton a))) True % 6.85/7.04 Clause #472 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (X : Iota), Iff (member X (suc a)) (member X (union a (singleton a)))) True % 6.85/7.04 Clause #473 (by clausification #[472]): ∀ (a a_1 : Iota), Eq (Iff (member a (suc a_1)) (member a (union a_1 (singleton a_1)))) True % 6.85/7.04 Clause #474 (by clausification #[473]): ∀ (a a_1 : Iota), Or (Eq (member a (suc a_1)) True) (Eq (member a (union a_1 (singleton a_1))) False) % 6.85/7.04 Clause #479 (by superposition #[474, 105]): ∀ (a : Iota), Or (Eq (member a (suc a)) True) (Eq False True) % 6.85/7.04 Clause #490 (by clausification #[479]): ∀ (a : Iota), Eq (member a (suc a)) True % 6.85/7.04 Clause #528 (by superposition #[30, 490]): Eq True False % 6.85/7.04 Clause #529 (by clausification #[528]): False % 6.85/7.04 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------