%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET044^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 4.06s 4.28s % Output : Proof 4.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET044^5 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.12 % Command : duper %s % 0.12/0.32 % Computer : n025.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Thu Oct 2 14:00:23 EDT 2025 % 0.12/0.32 % CPUTime : % 4.06/4.28 SZS status Theorem for theBenchmark.p % 4.06/4.28 SZS output start Proof for theBenchmark.p % 4.06/4.28 Clause #0 (by assumption #[]): Eq % 4.06/4.28 (Not % 4.06/4.28 ((Exists fun Xy => ∀ (Xx : Iota), Iff (cF Xx Xy) (cF Xx Xx)) → % 4.06/4.28 Not (∀ (Xx : Iota), Exists fun Xy => ∀ (Xz : Iota), Iff (cF Xz Xy) (Not (cF Xz Xx))))) % 4.06/4.28 True % 4.06/4.28 Clause #1 (by clausification #[0]): Eq % 4.06/4.28 ((Exists fun Xy => ∀ (Xx : Iota), Iff (cF Xx Xy) (cF Xx Xx)) → % 4.06/4.28 Not (∀ (Xx : Iota), Exists fun Xy => ∀ (Xz : Iota), Iff (cF Xz Xy) (Not (cF Xz Xx)))) % 4.06/4.28 False % 4.06/4.28 Clause #2 (by clausification #[1]): Eq (Exists fun Xy => ∀ (Xx : Iota), Iff (cF Xx Xy) (cF Xx Xx)) True % 4.06/4.28 Clause #3 (by clausification #[1]): Eq (Not (∀ (Xx : Iota), Exists fun Xy => ∀ (Xz : Iota), Iff (cF Xz Xy) (Not (cF Xz Xx)))) False % 4.06/4.28 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Xx : Iota), Iff (cF Xx (skS.0 0 a)) (cF Xx Xx)) True % 4.06/4.28 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (Iff (cF a (skS.0 0 a_1)) (cF a a)) True % 4.06/4.28 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (cF a (skS.0 0 a_1)) True) (Eq (cF a a) False) % 4.06/4.28 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (cF a (skS.0 0 a_1)) False) (Eq (cF a a) True) % 4.06/4.28 Clause #8 (by clausification #[3]): Eq (∀ (Xx : Iota), Exists fun Xy => ∀ (Xz : Iota), Iff (cF Xz Xy) (Not (cF Xz Xx))) True % 4.06/4.28 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (Exists fun Xy => ∀ (Xz : Iota), Iff (cF Xz Xy) (Not (cF Xz a))) True % 4.06/4.28 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), Iff (cF Xz (skS.0 1 a a_1)) (Not (cF Xz a))) True % 4.06/4.28 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (Iff (cF a (skS.0 1 a_1 a_2)) (Not (cF a a_1))) True % 4.06/4.28 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 1 a_1 a_2)) True) (Eq (Not (cF a a_1)) False) % 4.06/4.28 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 1 a_1 a_2)) False) (Eq (Not (cF a a_1)) True) % 4.06/4.28 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 1 a_1 a_2)) True) (Eq (cF a a_1) True) % 4.06/4.28 Clause #15 (by superposition #[14, 6]): ∀ (a a_1 a_2 : Iota), % 4.06/4.28 Or (Eq (cF (skS.0 1 a a_1) a) True) (Or (Eq (cF (skS.0 1 a a_1) (skS.0 0 a_2)) True) (Eq True False)) % 4.06/4.28 Clause #16 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF a (skS.0 1 a_1 a_2)) False) (Eq (cF a a_1) False) % 4.06/4.28 Clause #19 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF (skS.0 1 a a_1) a) True) (Eq (cF (skS.0 1 a a_1) (skS.0 0 a_2)) True) % 4.06/4.28 Clause #23 (by equality factoring #[19]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) True) % 4.06/4.28 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 4.06/4.28 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) True) (Eq True False) % 4.06/4.28 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) True % 4.06/4.28 Clause #28 (by superposition #[27, 7]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 1 (skS.0 0 a) a_1)) True) % 4.06/4.28 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 1 (skS.0 0 a) a_1)) True % 4.06/4.28 Clause #30 (by superposition #[29, 16]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) False) % 4.06/4.28 Clause #31 (by superposition #[29, 6]): ∀ (a a_1 a_2 : Iota), Or (Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a_2)) True) (Eq True False) % 4.06/4.28 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a_2)) True % 4.06/4.28 Clause #33 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (cF (skS.0 1 (skS.0 0 a) a_1) (skS.0 0 a)) False % 4.06/4.28 Clause #34 (by superposition #[33, 32]): Eq False True % 4.06/4.28 Clause #37 (by clausification #[34]): False % 4.06/4.28 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------