%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU930^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 4.21s 4.43s % Output : Proof 4.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SEU930^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.14 % Command : duper %s % 0.14/0.36 % Computer : n011.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 04:08:08 EDT 2025 % 0.14/0.36 % CPUTime : % 4.21/4.43 SZS status Theorem for theBenchmark.p % 4.21/4.43 SZS output start Proof for theBenchmark.p % 4.21/4.43 Clause #0 (by assumption #[]): Eq % 4.21/4.43 (Not % 4.21/4.43 ((Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) → % 4.21/4.43 ∀ (Xx : Iota), And (Eq (g Xx) Xx) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz Xx) → Eq (f Xx) Xx)) % 4.21/4.43 True % 4.21/4.43 Clause #1 (by clausification #[0]): Eq % 4.21/4.43 ((Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) → % 4.21/4.43 ∀ (Xx : Iota), And (Eq (g Xx) Xx) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz Xx) → Eq (f Xx) Xx) % 4.21/4.43 False % 4.21/4.43 Clause #2 (by clausification #[1]): Eq (Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) True % 4.21/4.43 Clause #3 (by clausification #[1]): Eq (∀ (Xx : Iota), And (Eq (g Xx) Xx) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz Xx) → Eq (f Xx) Xx) False % 4.21/4.43 Clause #4 (by clausification #[2]): Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx) % 4.21/4.43 Clause #5 (by argument congruence #[4]): ∀ (a : Iota), Eq ((fun Xx => f (g Xx)) a) ((fun Xx => g (f Xx)) a) % 4.21/4.43 Clause #6 (by clausification #[3]): ∀ (a : Iota), % 4.21/4.43 Eq % 4.21/4.43 (Not % 4.21/4.43 (And (Eq (g (skS.0 0 a)) (skS.0 0 a)) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz (skS.0 0 a)) → % 4.21/4.43 Eq (f (skS.0 0 a)) (skS.0 0 a))) % 4.21/4.43 True % 4.21/4.43 Clause #7 (by clausification #[6]): ∀ (a : Iota), % 4.21/4.43 Eq % 4.21/4.43 (And (Eq (g (skS.0 0 a)) (skS.0 0 a)) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz (skS.0 0 a)) → % 4.21/4.43 Eq (f (skS.0 0 a)) (skS.0 0 a)) % 4.21/4.43 False % 4.21/4.43 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (And (Eq (g (skS.0 0 a)) (skS.0 0 a)) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz (skS.0 0 a))) True % 4.21/4.43 Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (Eq (f (skS.0 0 a)) (skS.0 0 a)) False % 4.21/4.43 Clause #10 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz (skS.0 0 a)) True % 4.21/4.43 Clause #11 (by clausification #[8]): ∀ (a : Iota), Eq (Eq (g (skS.0 0 a)) (skS.0 0 a)) True % 4.21/4.43 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Eq (g a) a → Eq a (skS.0 0 a_1)) True % 4.21/4.43 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (Eq (g a) a) False) (Eq (Eq a (skS.0 0 a_1)) True) % 4.21/4.43 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (Eq a (skS.0 0 a_1)) True) (Ne (g a) a) % 4.21/4.43 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Ne (g a) a) (Eq a (skS.0 0 a_1)) % 4.21/4.43 Clause #16 (by betaEtaReduce #[5]): ∀ (a : Iota), Eq (f (g a)) (g (f a)) % 4.21/4.43 Clause #17 (by clausification #[11]): ∀ (a : Iota), Eq (g (skS.0 0 a)) (skS.0 0 a) % 4.21/4.43 Clause #19 (by superposition #[17, 16]): ∀ (a : Iota), Eq (f (skS.0 0 a)) (g (f (skS.0 0 a))) % 4.21/4.43 Clause #20 (by superposition #[19, 15]): ∀ (a a_1 : Iota), Or (Ne (f (skS.0 0 a)) (f (skS.0 0 a))) (Eq (f (skS.0 0 a)) (skS.0 0 a_1)) % 4.21/4.43 Clause #22 (by clausification #[9]): ∀ (a : Iota), Ne (f (skS.0 0 a)) (skS.0 0 a) % 4.21/4.43 Clause #32 (by eliminate resolved literals #[20]): ∀ (a a_1 : Iota), Eq (f (skS.0 0 a)) (skS.0 0 a_1) % 4.21/4.43 Clause #33 (by backward contextual literal cutting #[32, 22]): False % 4.21/4.43 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------