%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU516^2 : TPTP v9.2.0. Released v3.7.0. % 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 08:01:48 PM UTC 2025 % Result : Theorem 4.17s 4.34s % Output : Proof 4.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU516^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n025.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 04:00:38 EDT 2025 % 0.13/0.35 % CPUTime : % 4.17/4.34 SZS status Theorem for theBenchmark.p % 4.17/4.34 SZS output start Proof for theBenchmark.p % 4.17/4.34 Clause #0 (by assumption #[]): Eq (Eq setadjoinAx (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A)))) True % 4.17/4.34 Clause #1 (by assumption #[]): Eq (Not (setadjoinAx → ∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → Or (Eq Xy Xx) (in Xy A))) True % 4.17/4.34 Clause #2 (by clausification #[1]): Eq (setadjoinAx → ∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → Or (Eq Xy Xx) (in Xy A)) False % 4.17/4.34 Clause #3 (by clausification #[2]): Eq setadjoinAx True % 4.17/4.34 Clause #4 (by clausification #[2]): Eq (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → Or (Eq Xy Xx) (in Xy A)) False % 4.17/4.34 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (A Xy : Iota), in Xy (setadjoin (skS.0 0 a) A) → Or (Eq Xy (skS.0 0 a)) (in Xy A))) True % 4.17/4.34 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), in Xy (setadjoin (skS.0 0 a) A) → Or (Eq Xy (skS.0 0 a)) (in Xy A)) False % 4.17/4.34 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.17/4.34 Eq % 4.17/4.34 (Not % 4.17/4.34 (∀ (Xy : Iota), in Xy (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) → Or (Eq Xy (skS.0 0 a)) (in Xy (skS.0 1 a a_1)))) % 4.17/4.34 True % 4.17/4.34 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.17/4.34 Eq (∀ (Xy : Iota), in Xy (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) → Or (Eq Xy (skS.0 0 a)) (in Xy (skS.0 1 a a_1))) % 4.17/4.34 False % 4.17/4.34 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.17/4.34 Eq % 4.17/4.34 (Not % 4.17/4.34 (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) → % 4.17/4.34 Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)))) % 4.17/4.34 True % 4.17/4.34 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.17/4.34 Eq % 4.17/4.34 (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1)) → % 4.17/4.34 Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) % 4.17/4.34 False % 4.17/4.34 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1))) True % 4.17/4.34 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1))) False % 4.17/4.34 Clause #13 (by clausification #[0]): Eq setadjoinAx (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A))) % 4.17/4.34 Clause #14 (by forward demodulation #[13, 3]): Eq True (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A))) % 4.17/4.34 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), Iff (in Xy (setadjoin a A)) (Or (Eq Xy a) (in Xy A))) True % 4.17/4.34 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (∀ (Xy : Iota), Iff (in Xy (setadjoin a a_1)) (Or (Eq Xy a) (in Xy a_1))) True % 4.17/4.34 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (Iff (in a (setadjoin a_1 a_2)) (Or (Eq a a_1) (in a a_2))) True % 4.17/4.34 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq (Or (Eq a a_1) (in a a_2)) True) % 4.17/4.34 Clause #28 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) False % 4.17/4.34 Clause #29 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) False % 4.17/4.34 Clause #34 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1) True) (Eq (in a a_2) True)) % 4.17/4.34 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (in a a_2) True) (Eq a a_1)) % 4.17/4.34 Clause #36 (by superposition #[35, 11]): ∀ (a a_1 a_2 : Iota), % 4.17/4.34 Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Or (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) (Eq False True)) % 4.17/4.34 Clause #55 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 2 a a_1 a_2) (skS.0 0 a) % 4.17/4.34 Clause #65 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True) (Eq (skS.0 2 a a_1 a_2) (skS.0 0 a)) % 4.17/4.34 Clause #66 (by forward contextual literal cutting #[65, 55]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 4.17/4.34 Clause #67 (by superposition #[66, 28]): Eq True False % 4.17/4.34 Clause #69 (by clausification #[67]): False % 4.17/4.34 SZS output end Proof for theBenchmark.p 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