%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ITP209^3 : TPTP v9.2.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 07:51:27 PM UTC 2025 % Result : Theorem 3.93s 4.10s % Output : Proof 3.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ITP209^3 : TPTP v9.2.0. Released v8.1.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n014.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 23:21:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.93/4.10 SZS status Theorem for theBenchmark.p % 3.93/4.10 SZS output start Proof for theBenchmark.p % 3.93/4.10 Clause #1 (by assumption #[]): Eq (∀ (A B : a), Eq (f A B) (f B A)) True % 3.93/4.10 Clause #2 (by assumption #[]): Eq (∀ (A B C : a), Eq (f A (f B C)) (f B (f A C))) True % 3.93/4.10 Clause #10 (by assumption #[]): Eq (Not (Eq (f (f a2 b) c) (f (f a2 c) b))) True % 3.93/4.10 Clause #37 (by clausification #[1]): ∀ (a_1 : a), Eq (∀ (B : a), Eq (f a_1 B) (f B a_1)) True % 3.93/4.10 Clause #38 (by clausification #[37]): ∀ (a_1 a_2 : a), Eq (Eq (f a_1 a_2) (f a_2 a_1)) True % 3.93/4.10 Clause #39 (by clausification #[38]): ∀ (a_1 a_2 : a), Eq (f a_1 a_2) (f a_2 a_1) % 3.93/4.10 Clause #57 (by clausification #[10]): Eq (Eq (f (f a2 b) c) (f (f a2 c) b)) False % 3.93/4.10 Clause #58 (by clausification #[57]): Ne (f (f a2 b) c) (f (f a2 c) b) % 3.93/4.10 Clause #59 (by forward demodulation #[58, 39]): Ne (f c (f a2 b)) (f (f a2 c) b) % 3.93/4.10 Clause #60 (by forward demodulation #[59, 39]): Ne (f c (f b a2)) (f (f a2 c) b) % 3.93/4.10 Clause #61 (by forward demodulation #[60, 39]): Ne (f c (f b a2)) (f b (f a2 c)) % 3.93/4.10 Clause #62 (by forward demodulation #[61, 39]): Ne (f c (f b a2)) (f b (f c a2)) % 3.93/4.10 Clause #63 (by clausification #[2]): ∀ (a_1 : a), Eq (∀ (B C : a), Eq (f a_1 (f B C)) (f B (f a_1 C))) True % 3.93/4.10 Clause #64 (by clausification #[63]): ∀ (a_1 a_2 : a), Eq (∀ (C : a), Eq (f a_1 (f a_2 C)) (f a_2 (f a_1 C))) True % 3.93/4.10 Clause #65 (by clausification #[64]): ∀ (a_1 a_2 a_3 : a), Eq (Eq (f a_1 (f a_2 a_3)) (f a_2 (f a_1 a_3))) True % 3.93/4.10 Clause #66 (by clausification #[65]): ∀ (a_1 a_2 a_3 : a), Eq (f a_1 (f a_2 a_3)) (f a_2 (f a_1 a_3)) % 3.93/4.10 Clause #67 (by backward contextual literal cutting #[66, 62]): False % 3.93/4.10 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------