%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU908^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:02:37 PM UTC 2025 % Result : Theorem 3.40s 3.58s % Output : Proof 3.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU908^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n023.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 05:56:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.40/3.58 SZS status Theorem for theBenchmark.p % 3.40/3.58 SZS output start Proof for theBenchmark.p % 3.40/3.58 Clause #0 (by assumption #[]): Eq % 3.40/3.58 (Not % 3.40/3.58 (∀ (Xx : a), % 3.40/3.58 (∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp Xx) → % 3.40/3.58 ∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp (f Xx))) % 3.40/3.58 True % 3.40/3.58 Clause #1 (by clausification #[0]): Eq % 3.40/3.58 (∀ (Xx : a), % 3.40/3.58 (∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp Xx) → % 3.40/3.58 ∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp (f Xx)) % 3.40/3.58 False % 3.40/3.58 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 3.40/3.58 Eq % 3.40/3.58 (Not % 3.40/3.58 ((∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp (skS.0 0 a_1)) → % 3.40/3.58 ∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp (f (skS.0 0 a_1)))) % 3.40/3.58 True % 3.40/3.58 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 3.40/3.58 Eq % 3.40/3.58 ((∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp (skS.0 0 a_1)) → % 3.40/3.58 ∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp (f (skS.0 0 a_1))) % 3.40/3.58 False % 3.40/3.58 Clause #4 (by clausification #[3]): ∀ (a_1 : a), Eq (∀ (Xp : a → Prop), (∀ (Xx0 : a), Xp Xx0 → Xp (f Xx0)) → Xp (skS.0 0 a_1)) True % 3.40/3.58 Clause #6 (by clausification #[4]): ∀ (a_1 : a → Prop) (a_2 : a), Eq ((∀ (Xx0 : a), a_1 Xx0 → a_1 (f Xx0)) → a_1 (skS.0 0 a_2)) True % 3.40/3.58 Clause #7 (by clausification #[6]): ∀ (a_1 : a → Prop) (a_2 : a), Or (Eq (∀ (Xx0 : a), a_1 Xx0 → a_1 (f Xx0)) False) (Eq (a_1 (skS.0 0 a_2)) True) % 3.40/3.58 Clause #8 (by clausification #[7]): ∀ (a_1 : a → Prop) (a_2 a_3 : a), % 3.40/3.58 Or (Eq (a_1 (skS.0 0 a_2)) True) (Eq (Not (a_1 (skS.0 1 a_1 a_3) → a_1 (f (skS.0 1 a_1 a_3)))) True) % 3.40/3.58 Clause #9 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 a_3 : a), % 3.40/3.58 Or (Eq (a_1 (skS.0 0 a_2)) True) (Eq (a_1 (skS.0 1 a_1 a_3) → a_1 (f (skS.0 1 a_1 a_3))) False) % 3.40/3.58 Clause #10 (by clausification #[9]): ∀ (a_1 : a → Prop) (a_2 a_3 : a), Or (Eq (a_1 (skS.0 0 a_2)) True) (Eq (a_1 (skS.0 1 a_1 a_3)) True) % 3.40/3.58 Clause #18 (by equality factoring #[10]): ∀ (a_1 : Prop) (a_2 : a), Or (Ne True True) (Eq ((fun x => a_1) (skS.0 0 a_2)) True) % 3.40/3.58 Clause #42 (by betaEtaReduce #[18]): ∀ (a : Prop), Or (Ne True True) (Eq a True) % 3.40/3.58 Clause #43 (by clausification #[42]): ∀ (a : Prop), Or (Eq a True) (Or (Eq True False) (Eq True False)) % 3.40/3.58 Clause #45 (by clausification #[43]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 3.40/3.58 Clause #46 (by clausification #[45]): ∀ (a : Prop), Eq a True % 3.40/3.58 Clause #47 (by falseElim #[46]): False % 3.40/3.58 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------