%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU922^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 08:02:38 PM UTC 2025 % Result : Theorem 3.38s 3.61s % Output : Proof 3.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.13 % Problem : SEU922^5 : TPTP v9.2.0. Released v4.0.0. % 0.05/0.15 % Command : duper %s % 0.15/0.36 % Computer : n027.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 04:50:08 EDT 2025 % 0.15/0.36 % CPUTime : % 3.38/3.61 SZS status Theorem for theBenchmark.p % 3.38/3.61 SZS output start Proof for theBenchmark.p % 3.38/3.61 Clause #0 (by assumption #[]): Eq (Not ((Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) → cP (f (f (g a))) → cP (g (f (f a))))) True % 3.38/3.61 Clause #1 (by clausification #[0]): Eq ((Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) → cP (f (f (g a))) → cP (g (f (f a)))) False % 3.38/3.61 Clause #2 (by clausification #[1]): Eq (Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx)) True % 3.38/3.61 Clause #3 (by clausification #[1]): Eq (cP (f (f (g a))) → cP (g (f (f a)))) False % 3.38/3.61 Clause #4 (by clausification #[2]): Eq (fun Xx => f (g Xx)) fun Xx => g (f Xx) % 3.38/3.61 Clause #5 (by argument congruence #[4]): ∀ (a : Iota), Eq ((fun Xx => f (g Xx)) a) ((fun Xx => g (f Xx)) a) % 3.38/3.61 Clause #6 (by clausification #[3]): Eq (cP (f (f (g a)))) True % 3.38/3.61 Clause #7 (by clausification #[3]): Eq (cP (g (f (f a)))) False % 3.38/3.61 Clause #8 (by betaEtaReduce #[5]): ∀ (a : Iota), Eq (f (g a)) (g (f a)) % 3.38/3.61 Clause #9 (by backward demodulation #[8, 7]): Eq (cP (f (g (f a)))) False % 3.38/3.61 Clause #10 (by forward demodulation #[9, 8]): Eq (cP (f (f (g a)))) False % 3.38/3.61 Clause #11 (by superposition #[10, 6]): Eq False True % 3.38/3.61 Clause #12 (by clausification #[11]): False % 3.38/3.61 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------