%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU932^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:02:39 PM UTC 2025 % Result : Theorem 3.73s 3.96s % Output : Proof 3.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU932^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.14 % Command : duper %s % 0.15/0.35 % Computer : n031.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Fri Oct 3 04:43:38 EDT 2025 % 0.15/0.36 % CPUTime : % 3.73/3.96 SZS status Theorem for theBenchmark.p % 3.73/3.96 SZS output start Proof for theBenchmark.p % 3.73/3.96 Clause #0 (by assumption #[]): Eq % 3.73/3.96 (Not % 3.73/3.96 (∀ (Xf : Iota → Iota), % 3.73/3.96 (Exists fun Xg => % 3.73/3.96 And (Eq (fun Xx => Xf (Xg Xx)) fun Xx => Xg (Xf Xx)) % 3.73/3.96 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) → % 3.73/3.96 Exists fun Xy => Eq (Xf Xy) Xy)) % 3.73/3.96 True % 3.73/3.96 Clause #1 (by clausification #[0]): Eq % 3.73/3.96 (∀ (Xf : Iota → Iota), % 3.73/3.96 (Exists fun Xg => % 3.73/3.96 And (Eq (fun Xx => Xf (Xg Xx)) fun Xx => Xg (Xf Xx)) % 3.73/3.96 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) → % 3.73/3.96 Exists fun Xy => Eq (Xf Xy) Xy) % 3.73/3.96 False % 3.73/3.96 Clause #2 (by clausification #[1]): ∀ (a : Iota → Iota), % 3.73/3.96 Eq % 3.73/3.96 (Not % 3.73/3.96 ((Exists fun Xg => % 3.73/3.96 And (Eq (fun Xx => skS.0 0 a (Xg Xx)) fun Xx => Xg (skS.0 0 a Xx)) % 3.73/3.96 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) → % 3.73/3.96 Exists fun Xy => Eq (skS.0 0 a Xy) Xy)) % 3.73/3.96 True % 3.73/3.96 Clause #3 (by clausification #[2]): ∀ (a : Iota → Iota), % 3.73/3.96 Eq % 3.73/3.96 ((Exists fun Xg => % 3.73/3.96 And (Eq (fun Xx => skS.0 0 a (Xg Xx)) fun Xx => Xg (skS.0 0 a Xx)) % 3.73/3.96 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) → % 3.73/3.96 Exists fun Xy => Eq (skS.0 0 a Xy) Xy) % 3.73/3.96 False % 3.73/3.96 Clause #4 (by clausification #[3]): ∀ (a : Iota → Iota), % 3.73/3.96 Eq % 3.73/3.96 (Exists fun Xg => % 3.73/3.96 And (Eq (fun Xx => skS.0 0 a (Xg Xx)) fun Xx => Xg (skS.0 0 a Xx)) % 3.73/3.96 (Exists fun Xx => And (Eq (Xg Xx) Xx) (∀ (Xz : Iota), Eq (Xg Xz) Xz → Eq Xz Xx))) % 3.73/3.96 True % 3.73/3.96 Clause #5 (by clausification #[3]): ∀ (a : Iota → Iota), Eq (Exists fun Xy => Eq (skS.0 0 a Xy) Xy) False % 3.73/3.96 Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota → Iota), % 3.73/3.96 Eq % 3.73/3.96 (And (Eq (fun Xx => skS.0 0 a (skS.0 1 a a_1 Xx)) fun Xx => skS.0 1 a a_1 (skS.0 0 a Xx)) % 3.73/3.96 (Exists fun Xx => And (Eq (skS.0 1 a a_1 Xx) Xx) (∀ (Xz : Iota), Eq (skS.0 1 a a_1 Xz) Xz → Eq Xz Xx))) % 3.73/3.96 True % 3.73/3.96 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota → Iota), % 3.73/3.96 Eq (Exists fun Xx => And (Eq (skS.0 1 a a_1 Xx) Xx) (∀ (Xz : Iota), Eq (skS.0 1 a a_1 Xz) Xz → Eq Xz Xx)) True % 3.73/3.96 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota → Iota), Eq (Eq (fun Xx => skS.0 0 a (skS.0 1 a a_1 Xx)) fun Xx => skS.0 1 a a_1 (skS.0 0 a Xx)) True % 3.73/3.96 Clause #9 (by clausification #[7]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), % 3.73/3.96 Eq % 3.73/3.96 (And (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_2)) % 3.73/3.96 (∀ (Xz : Iota), Eq (skS.0 1 a a_1 Xz) Xz → Eq Xz (skS.0 2 a a_1 a_2))) % 3.73/3.96 True % 3.73/3.96 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (∀ (Xz : Iota), Eq (skS.0 1 a a_1 Xz) Xz → Eq Xz (skS.0 2 a a_1 a_2)) True % 3.73/3.96 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_2)) True % 3.73/3.96 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Eq (Eq (skS.0 1 a a_1 a_2) a_2 → Eq a_2 (skS.0 2 a a_1 a_3)) True % 3.73/3.96 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), % 3.73/3.96 Or (Eq (Eq (skS.0 1 a a_1 a_2) a_2) False) (Eq (Eq a_2 (skS.0 2 a a_1 a_3)) True) % 3.73/3.96 Clause #14 (by clausification #[13]): ∀ (a : Iota) (a_1 a_2 : Iota → Iota) (a_3 : Iota), Or (Eq (Eq a (skS.0 2 a_1 a_2 a_3)) True) (Ne (skS.0 1 a_1 a_2 a) a) % 3.73/3.96 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Or (Ne (skS.0 1 a a_1 a_2) a_2) (Eq a_2 (skS.0 2 a a_1 a_3)) % 3.73/3.96 Clause #16 (by clausification #[5]): ∀ (a : Iota → Iota) (a_1 : Iota), Eq (Eq (skS.0 0 a a_1) a_1) False % 3.73/3.96 Clause #17 (by clausification #[16]): ∀ (a : Iota → Iota) (a_1 : Iota), Ne (skS.0 0 a a_1) a_1 % 3.73/3.96 Clause #18 (by clausification #[11]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_2) % 3.73/3.96 Clause #19 (by superposition #[18, 15]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), % 3.73/3.96 Or (Ne (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_2)) (Eq (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_3)) % 3.73/3.96 Clause #20 (by clausification #[8]): ∀ (a a_1 : Iota → Iota), Eq (fun Xx => skS.0 0 a (skS.0 1 a a_1 Xx)) fun Xx => skS.0 1 a a_1 (skS.0 0 a Xx) % 3.82/3.97 Clause #21 (by argument congruence #[20]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), % 3.82/3.97 Eq ((fun Xx => skS.0 0 a (skS.0 1 a a_1 Xx)) a_2) ((fun Xx => skS.0 1 a a_1 (skS.0 0 a Xx)) a_2) % 3.82/3.97 Clause #23 (by betaEtaReduce #[21]): ∀ (a a_1 : Iota → Iota) (a_2 : Iota), Eq (skS.0 0 a (skS.0 1 a a_1 a_2)) (skS.0 1 a a_1 (skS.0 0 a a_2)) % 3.82/3.97 Clause #24 (by superposition #[23, 15]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), % 3.82/3.97 Or (Ne (skS.0 0 a (skS.0 1 a a_1 a_2)) (skS.0 0 a a_2)) (Eq (skS.0 0 a a_2) (skS.0 2 a a_1 a_3)) % 3.82/3.97 Clause #25 (by eliminate resolved literals #[19]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Eq (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_3) % 3.82/3.97 Clause #26 (by superposition #[24, 18]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), % 3.82/3.97 Or (Ne (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 0 a (skS.0 2 a a_1 a_2))) % 3.82/3.97 (Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_3)) % 3.82/3.97 Clause #29 (by eliminate resolved literals #[26]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Eq (skS.0 0 a (skS.0 2 a a_1 a_2)) (skS.0 2 a a_1 a_3) % 3.82/3.97 Clause #30 (by superposition #[29, 17]): ∀ (a a_1 : Iota → Iota) (a_2 a_3 : Iota), Ne (skS.0 2 a a_1 a_2) (skS.0 2 a a_1 a_3) % 3.82/3.97 Clause #36 (by forward contextual literal cutting #[30, 25]): False % 3.82/3.97 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------