%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET044+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 07:59:28 PM UTC 2025 % Result : Theorem 5.05s 5.26s % Output : Proof 5.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET044+1 : TPTP v9.2.0. Released v2.0.0. % 0.04/0.13 % Command : duper %s % 0.13/0.35 % Computer : n010.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 13:54:23 EDT 2025 % 0.13/0.35 % CPUTime : % 5.05/5.26 SZS status Theorem for theBenchmark.p % 5.05/5.26 SZS output start Proof for theBenchmark.p % 5.05/5.26 Clause #0 (by assumption #[]): Eq % 5.05/5.26 (Not % 5.05/5.26 ((Exists fun Y => ∀ (X : Iota), Iff (element X Y) (element X X)) → % 5.05/5.26 Not (∀ (X1 : Iota), Exists fun Y1 => ∀ (Z : Iota), Iff (element Z Y1) (Not (element Z X1))))) % 5.05/5.26 True % 5.05/5.26 Clause #1 (by clausification #[0]): Eq % 5.05/5.26 ((Exists fun Y => ∀ (X : Iota), Iff (element X Y) (element X X)) → % 5.05/5.26 Not (∀ (X1 : Iota), Exists fun Y1 => ∀ (Z : Iota), Iff (element Z Y1) (Not (element Z X1)))) % 5.05/5.26 False % 5.05/5.26 Clause #2 (by clausification #[1]): Eq (Exists fun Y => ∀ (X : Iota), Iff (element X Y) (element X X)) True % 5.05/5.26 Clause #3 (by clausification #[1]): Eq (Not (∀ (X1 : Iota), Exists fun Y1 => ∀ (Z : Iota), Iff (element Z Y1) (Not (element Z X1)))) False % 5.05/5.26 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (X : Iota), Iff (element X (skS.0 0 a)) (element X X)) True % 5.05/5.26 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (Iff (element a (skS.0 0 a_1)) (element a a)) True % 5.05/5.26 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element a a) False) % 5.05/5.26 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Eq (element a a) True) % 5.05/5.26 Clause #8 (by clausification #[3]): Eq (∀ (X1 : Iota), Exists fun Y1 => ∀ (Z : Iota), Iff (element Z Y1) (Not (element Z X1))) True % 5.05/5.26 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (Exists fun Y1 => ∀ (Z : Iota), Iff (element Z Y1) (Not (element Z a))) True % 5.05/5.26 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), Iff (element Z (skS.0 1 a a_1)) (Not (element Z a))) True % 5.05/5.26 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (Iff (element a (skS.0 1 a_1 a_2)) (Not (element a a_1))) True % 5.05/5.26 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) True) (Eq (Not (element a a_1)) False) % 5.05/5.26 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) False) (Eq (Not (element a a_1)) True) % 5.05/5.26 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) True) (Eq (element a a_1) True) % 5.05/5.26 Clause #15 (by superposition #[14, 6]): ∀ (a a_1 a_2 : Iota), % 5.05/5.26 Or (Eq (element (skS.0 1 a a_1) a) True) (Or (Eq (element (skS.0 1 a a_1) (skS.0 0 a_2)) True) (Eq True False)) % 5.05/5.26 Clause #16 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 1 a_1 a_2)) False) (Eq (element a a_1) False) % 5.05/5.26 Clause #19 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (element (skS.0 1 a a_1) a) True) (Eq (element (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 5.05/5.26 Clause #23 (by equality factoring #[19]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) True) % 5.05/5.26 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 5.05/5.26 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) True) (Eq True False) % 5.05/5.26 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) True % 5.05/5.26 Clause #28 (by superposition #[27, 7]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 1 (skS.0 0 a) a_1)) True) % 5.05/5.26 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 1 (skS.0 0 a) a_1)) True % 5.05/5.26 Clause #30 (by superposition #[29, 16]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) False) % 5.05/5.26 Clause #31 (by superposition #[29, 6]): ∀ (a a_1 a_2 : Iota), Or (Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a_2)) True) (Eq True False) % 5.05/5.26 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a_2)) True % 5.05/5.26 Clause #33 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (element (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) False % 5.05/5.26 Clause #34 (by superposition #[33, 32]): Eq False True % 5.05/5.26 Clause #37 (by clausification #[34]): False % 5.05/5.26 SZS output end Proof for theBenchmark.p 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