%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU697^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:02:14 PM UTC 2025 % Result : Theorem 3.52s 3.74s % Output : Proof 3.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU697^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n026.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 05:01:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.52/3.74 SZS status Theorem for theBenchmark.p % 3.52/3.74 SZS output start Proof for theBenchmark.p % 3.52/3.74 Clause #1 (by assumption #[]): Eq % 3.52/3.74 (Not % 3.52/3.74 (∀ (A B : Iota) (Xf : Iota → Iota), % 3.52/3.74 (∀ (Xx : Iota), in Xx A → in (Xf Xx) B) → Eq (lam A B fun Xx => Xf Xx) (lam A B fun Xx => Xf Xx))) % 3.52/3.74 True % 3.52/3.74 Clause #2 (by betaEtaReduce #[1]): Eq (Not (∀ (A B : Iota) (Xf : Iota → Iota), (∀ (Xx : Iota), in Xx A → in (Xf Xx) B) → Eq (lam A B Xf) (lam A B Xf))) % 3.52/3.74 True % 3.52/3.74 Clause #3 (by clausification #[2]): Eq (∀ (A B : Iota) (Xf : Iota → Iota), (∀ (Xx : Iota), in Xx A → in (Xf Xx) B) → Eq (lam A B Xf) (lam A B Xf)) False % 3.52/3.74 Clause #4 (by clausification #[3]): ∀ (a : Iota), % 3.52/3.74 Eq % 3.52/3.74 (Not % 3.52/3.74 (∀ (B : Iota) (Xf : Iota → Iota), % 3.52/3.74 (∀ (Xx : Iota), in Xx (skS.0 0 a) → in (Xf Xx) B) → Eq (lam (skS.0 0 a) B Xf) (lam (skS.0 0 a) B Xf))) % 3.52/3.74 True % 3.52/3.74 Clause #5 (by clausification #[4]): ∀ (a : Iota), % 3.52/3.74 Eq % 3.52/3.74 (∀ (B : Iota) (Xf : Iota → Iota), % 3.52/3.74 (∀ (Xx : Iota), in Xx (skS.0 0 a) → in (Xf Xx) B) → Eq (lam (skS.0 0 a) B Xf) (lam (skS.0 0 a) B Xf)) % 3.52/3.74 False % 3.52/3.74 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), % 3.52/3.74 Eq % 3.52/3.74 (Not % 3.52/3.74 (∀ (Xf : Iota → Iota), % 3.52/3.74 (∀ (Xx : Iota), in Xx (skS.0 0 a) → in (Xf Xx) (skS.0 1 a a_1)) → % 3.52/3.74 Eq (lam (skS.0 0 a) (skS.0 1 a a_1) Xf) (lam (skS.0 0 a) (skS.0 1 a a_1) Xf))) % 3.52/3.74 True % 3.52/3.74 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 3.52/3.74 Eq % 3.52/3.74 (∀ (Xf : Iota → Iota), % 3.52/3.74 (∀ (Xx : Iota), in Xx (skS.0 0 a) → in (Xf Xx) (skS.0 1 a a_1)) → % 3.52/3.74 Eq (lam (skS.0 0 a) (skS.0 1 a a_1) Xf) (lam (skS.0 0 a) (skS.0 1 a a_1) Xf)) % 3.52/3.74 False % 3.52/3.74 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota), % 3.52/3.74 Eq % 3.52/3.74 (Not % 3.52/3.74 ((∀ (Xx : Iota), in Xx (skS.0 0 a) → in (skS.0 2 a a_1 a_2 Xx) (skS.0 1 a a_1)) → % 3.52/3.74 Eq (lam (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (lam (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 3.52/3.74 True % 3.52/3.74 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota), % 3.52/3.74 Eq % 3.52/3.74 ((∀ (Xx : Iota), in Xx (skS.0 0 a) → in (skS.0 2 a a_1 a_2 Xx) (skS.0 1 a a_1)) → % 3.52/3.74 Eq (lam (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (lam (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.52/3.74 False % 3.52/3.74 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota), % 3.52/3.74 Eq (Eq (lam (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (lam (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.52/3.74 False % 3.52/3.74 Clause #30 (by clausification #[11]): ∀ (a a_1 : Iota) (a_2 : Iota → Iota), % 3.52/3.74 Ne (lam (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (lam (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.52/3.74 Clause #31 (by eliminate resolved literals #[30]): False % 3.52/3.74 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------