%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU931^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 3.65s 3.88s % Output : Proof 3.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU931^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.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 06:13:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.65/3.88 SZS status Theorem for theBenchmark.p % 3.65/3.88 SZS output start Proof for theBenchmark.p % 3.65/3.88 Clause #0 (by assumption #[]): Eq % 3.65/3.88 (Not % 3.65/3.88 ((Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) → % 3.65/3.88 (Exists fun Xx => And (Eq (g Xx) Xx) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz Xx)) → Exists fun Xy => Eq (f Xy) Xy)) % 3.65/3.88 True % 3.65/3.88 Clause #1 (by clausification #[0]): Eq % 3.65/3.88 ((Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) → % 3.65/3.88 (Exists fun Xx => And (Eq (g Xx) Xx) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz Xx)) → Exists fun Xy => Eq (f Xy) Xy) % 3.65/3.88 False % 3.65/3.88 Clause #2 (by clausification #[1]): Eq (Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) True % 3.65/3.88 Clause #3 (by clausification #[1]): Eq ((Exists fun Xx => And (Eq (g Xx) Xx) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz Xx)) → Exists fun Xy => Eq (f Xy) Xy) % 3.65/3.88 False % 3.65/3.88 Clause #4 (by clausification #[2]): Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx) % 3.65/3.88 Clause #5 (by argument congruence #[4]): ∀ (a : Iota), Eq ((fun Xx => f (g Xx)) a) ((fun Xx => g (f Xx)) a) % 3.65/3.88 Clause #6 (by betaEtaReduce #[5]): ∀ (a : Iota), Eq (f (g a)) (g (f a)) % 3.65/3.88 Clause #7 (by clausification #[3]): Eq (Exists fun Xx => And (Eq (g Xx) Xx) (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz Xx)) True % 3.65/3.88 Clause #8 (by clausification #[3]): Eq (Exists fun Xy => Eq (f Xy) Xy) False % 3.65/3.88 Clause #9 (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 % 3.65/3.88 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (Xz : Iota), Eq (g Xz) Xz → Eq Xz (skS.0 0 a)) True % 3.65/3.88 Clause #11 (by clausification #[9]): ∀ (a : Iota), Eq (Eq (g (skS.0 0 a)) (skS.0 0 a)) True % 3.65/3.88 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Eq (g a) a → Eq a (skS.0 0 a_1)) True % 3.65/3.88 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) % 3.65/3.88 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (Eq a (skS.0 0 a_1)) True) (Ne (g a) a) % 3.65/3.88 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Ne (g a) a) (Eq a (skS.0 0 a_1)) % 3.65/3.88 Clause #16 (by clausification #[8]): ∀ (a : Iota), Eq (Eq (f a) a) False % 3.65/3.88 Clause #17 (by clausification #[16]): ∀ (a : Iota), Ne (f a) a % 3.65/3.88 Clause #20 (by clausification #[11]): ∀ (a : Iota), Eq (g (skS.0 0 a)) (skS.0 0 a) % 3.65/3.88 Clause #21 (by superposition #[20, 6]): ∀ (a : Iota), Eq (f (skS.0 0 a)) (g (f (skS.0 0 a))) % 3.65/3.88 Clause #22 (by superposition #[20, 15]): ∀ (a a_1 : Iota), Or (Ne (skS.0 0 a) (skS.0 0 a)) (Eq (skS.0 0 a) (skS.0 0 a_1)) % 3.65/3.88 Clause #33 (by superposition #[21, 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)) % 3.65/3.88 Clause #34 (by eliminate resolved literals #[22]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 0 a_1) % 3.65/3.88 Clause #112 (by eliminate resolved literals #[33]): ∀ (a a_1 : Iota), Eq (f (skS.0 0 a)) (skS.0 0 a_1) % 3.65/3.88 Clause #114 (by superposition #[112, 17]): ∀ (a a_1 : Iota), Ne (skS.0 0 a) (skS.0 0 a_1) % 3.65/3.88 Clause #128 (by forward contextual literal cutting #[114, 34]): False % 3.65/3.88 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------