%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU693^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:02:13 PM UTC 2025 % Result : Theorem 3.64s 3.82s % Output : Proof 3.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU693^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.14 % Command : duper %s % 0.14/0.35 % Computer : n015.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 05:25:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.64/3.82 SZS status Theorem for theBenchmark.p % 3.64/3.82 SZS output start Proof for theBenchmark.p % 3.64/3.82 Clause #0 (by assumption #[]): Eq (Not (∀ (A B Xf : Iota), in Xf (funcSet A B) → ∀ (Xx : Iota), in Xx A → Eq (ap A B Xf Xx) (ap A B Xf Xx))) True % 3.64/3.82 Clause #1 (by clausification #[0]): Eq (∀ (A B Xf : Iota), in Xf (funcSet A B) → ∀ (Xx : Iota), in Xx A → Eq (ap A B Xf Xx) (ap A B Xf Xx)) False % 3.64/3.82 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.64/3.82 Eq % 3.64/3.82 (Not % 3.64/3.82 (∀ (B Xf : Iota), % 3.64/3.82 in Xf (funcSet (skS.0 0 a) B) → % 3.64/3.82 ∀ (Xx : Iota), in Xx (skS.0 0 a) → Eq (ap (skS.0 0 a) B Xf Xx) (ap (skS.0 0 a) B Xf Xx))) % 3.64/3.82 True % 3.64/3.82 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 3.64/3.82 Eq % 3.64/3.82 (∀ (B Xf : Iota), % 3.64/3.82 in Xf (funcSet (skS.0 0 a) B) → % 3.64/3.82 ∀ (Xx : Iota), in Xx (skS.0 0 a) → Eq (ap (skS.0 0 a) B Xf Xx) (ap (skS.0 0 a) B Xf Xx)) % 3.64/3.82 False % 3.64/3.82 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.64/3.82 Eq % 3.64/3.82 (Not % 3.64/3.82 (∀ (Xf : Iota), % 3.64/3.82 in Xf (funcSet (skS.0 0 a) (skS.0 1 a a_1)) → % 3.64/3.82 ∀ (Xx : Iota), % 3.64/3.82 in Xx (skS.0 0 a) → Eq (ap (skS.0 0 a) (skS.0 1 a a_1) Xf Xx) (ap (skS.0 0 a) (skS.0 1 a a_1) Xf Xx))) % 3.64/3.82 True % 3.64/3.82 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 3.64/3.82 Eq % 3.64/3.82 (∀ (Xf : Iota), % 3.64/3.82 in Xf (funcSet (skS.0 0 a) (skS.0 1 a a_1)) → % 3.64/3.82 ∀ (Xx : Iota), % 3.64/3.82 in Xx (skS.0 0 a) → Eq (ap (skS.0 0 a) (skS.0 1 a a_1) Xf Xx) (ap (skS.0 0 a) (skS.0 1 a a_1) Xf Xx)) % 3.64/3.82 False % 3.64/3.82 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.64/3.82 Eq % 3.64/3.82 (Not % 3.64/3.82 (in (skS.0 2 a a_1 a_2) (funcSet (skS.0 0 a) (skS.0 1 a a_1)) → % 3.64/3.82 ∀ (Xx : Iota), % 3.64/3.82 in Xx (skS.0 0 a) → % 3.64/3.82 Eq (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) Xx) % 3.64/3.82 (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) Xx))) % 3.64/3.82 True % 3.64/3.82 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 3.64/3.82 Eq % 3.64/3.82 (in (skS.0 2 a a_1 a_2) (funcSet (skS.0 0 a) (skS.0 1 a a_1)) → % 3.64/3.82 ∀ (Xx : Iota), % 3.64/3.82 in Xx (skS.0 0 a) → % 3.64/3.82 Eq (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) Xx) % 3.64/3.82 (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) Xx)) % 3.64/3.82 False % 3.64/3.82 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.64/3.82 Eq % 3.64/3.82 (∀ (Xx : Iota), % 3.64/3.82 in Xx (skS.0 0 a) → % 3.64/3.82 Eq (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) Xx) % 3.64/3.82 (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) Xx)) % 3.64/3.82 False % 3.64/3.82 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.64/3.82 Eq % 3.64/3.82 (Not % 3.64/3.82 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) → % 3.64/3.82 Eq (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 3.64/3.82 (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)))) % 3.64/3.82 True % 3.64/3.82 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota), % 3.64/3.82 Eq % 3.64/3.82 (in (skS.0 3 a a_1 a_2 a_3) (skS.0 0 a) → % 3.64/3.82 Eq (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 3.64/3.82 (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 3.64/3.82 False % 3.64/3.82 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota), % 3.64/3.82 Eq % 3.64/3.82 (Eq (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 3.64/3.82 (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))) % 3.64/3.82 False % 3.64/3.82 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 3.64/3.82 Ne (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 3.64/3.82 (ap (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) % 3.64/3.82 Clause #15 (by eliminate resolved literals #[14]): False % 3.64/3.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------