%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ITP209_2 : TPTP v9.2.0. Released v8.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 3.67s 3.87s % Output : Proof 3.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : ITP209_2 : TPTP v9.2.0. Released v8.0.0. % 0.11/0.14 % Command : duper %s % 0.15/0.35 % Computer : n025.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Thu Oct 2 23:14:38 EDT 2025 % 0.15/0.35 % CPUTime : % 3.67/3.87 SZS status Theorem for theBenchmark.p % 3.67/3.87 SZS output start Proof for theBenchmark.p % 3.67/3.87 Clause #1 (by assumption #[]): Eq (∀ (A2 B2 : a), Eq (aa a a (aa a (fun a a) f A2) B2) (aa a a (aa a (fun a a) f B2) A2)) True % 3.67/3.87 Clause #2 (by assumption #[]): Eq % 3.67/3.87 (∀ (A2 B2 C : a), % 3.67/3.87 Eq (aa a a (aa a (fun a a) f A2) (aa a a (aa a (fun a a) f B2) C)) % 3.67/3.87 (aa a a (aa a (fun a a) f B2) (aa a a (aa a (fun a a) f A2) C))) % 3.67/3.87 True % 3.67/3.87 Clause #14 (by assumption #[]): Eq % 3.67/3.87 (Not % 3.67/3.87 (Eq (aa a a (aa a (fun a a) f (aa a a (aa a (fun a a) f a2) b)) c) % 3.67/3.87 (aa a a (aa a (fun a a) f (aa a a (aa a (fun a a) f a2) c)) b))) % 3.67/3.87 True % 3.67/3.87 Clause #39 (by clausification #[1]): ∀ (a_1 : a), Eq (∀ (B2 : a), Eq (aa a a (aa a (fun a a) f a_1) B2) (aa a a (aa a (fun a a) f B2) a_1)) True % 3.67/3.87 Clause #40 (by clausification #[39]): ∀ (a_1 a_2 : a), Eq (Eq (aa a a (aa a (fun a a) f a_1) a_2) (aa a a (aa a (fun a a) f a_2) a_1)) True % 3.67/3.87 Clause #41 (by clausification #[40]): ∀ (a_1 a_2 : a), Eq (aa a a (aa a (fun a a) f a_1) a_2) (aa a a (aa a (fun a a) f a_2) a_1) % 3.67/3.87 Clause #54 (by clausification #[14]): Eq % 3.67/3.87 (Eq (aa a a (aa a (fun a a) f (aa a a (aa a (fun a a) f a2) b)) c) % 3.67/3.87 (aa a a (aa a (fun a a) f (aa a a (aa a (fun a a) f a2) c)) b)) % 3.67/3.87 False % 3.67/3.87 Clause #55 (by clausification #[54]): Ne (aa a a (aa a (fun a a) f (aa a a (aa a (fun a a) f a2) b)) c) % 3.67/3.87 (aa a a (aa a (fun a a) f (aa a a (aa a (fun a a) f a2) c)) b) % 3.67/3.87 Clause #56 (by forward demodulation #[55, 41]): Ne (aa a a (aa a (fun a a) f c) (aa a a (aa a (fun a a) f a2) b)) % 3.67/3.87 (aa a a (aa a (fun a a) f (aa a a (aa a (fun a a) f a2) c)) b) % 3.67/3.87 Clause #57 (by forward demodulation #[56, 41]): Ne (aa a a (aa a (fun a a) f c) (aa a a (aa a (fun a a) f b) a2)) % 3.67/3.87 (aa a a (aa a (fun a a) f (aa a a (aa a (fun a a) f a2) c)) b) % 3.67/3.87 Clause #58 (by forward demodulation #[57, 41]): Ne (aa a a (aa a (fun a a) f c) (aa a a (aa a (fun a a) f b) a2)) % 3.67/3.87 (aa a a (aa a (fun a a) f b) (aa a a (aa a (fun a a) f a2) c)) % 3.67/3.87 Clause #59 (by forward demodulation #[58, 41]): Ne (aa a a (aa a (fun a a) f c) (aa a a (aa a (fun a a) f b) a2)) % 3.67/3.87 (aa a a (aa a (fun a a) f b) (aa a a (aa a (fun a a) f c) a2)) % 3.67/3.87 Clause #68 (by clausification #[2]): ∀ (a_1 : a), % 3.67/3.87 Eq % 3.67/3.87 (∀ (B2 C : a), % 3.67/3.87 Eq (aa a a (aa a (fun a a) f a_1) (aa a a (aa a (fun a a) f B2) C)) % 3.67/3.87 (aa a a (aa a (fun a a) f B2) (aa a a (aa a (fun a a) f a_1) C))) % 3.67/3.87 True % 3.67/3.87 Clause #69 (by clausification #[68]): ∀ (a_1 a_2 : a), % 3.67/3.87 Eq % 3.67/3.87 (∀ (C : a), % 3.67/3.87 Eq (aa a a (aa a (fun a a) f a_1) (aa a a (aa a (fun a a) f a_2) C)) % 3.67/3.87 (aa a a (aa a (fun a a) f a_2) (aa a a (aa a (fun a a) f a_1) C))) % 3.67/3.87 True % 3.67/3.87 Clause #70 (by clausification #[69]): ∀ (a_1 a_2 a_3 : a), % 3.67/3.87 Eq % 3.67/3.87 (Eq (aa a a (aa a (fun a a) f a_1) (aa a a (aa a (fun a a) f a_2) a_3)) % 3.67/3.87 (aa a a (aa a (fun a a) f a_2) (aa a a (aa a (fun a a) f a_1) a_3))) % 3.67/3.87 True % 3.67/3.87 Clause #71 (by clausification #[70]): ∀ (a_1 a_2 a_3 : a), % 3.67/3.87 Eq (aa a a (aa a (fun a a) f a_1) (aa a a (aa a (fun a a) f a_2) a_3)) % 3.67/3.87 (aa a a (aa a (fun a a) f a_2) (aa a a (aa a (fun a a) f a_1) a_3)) % 3.67/3.87 Clause #72 (by backward contextual literal cutting #[71, 59]): False % 3.67/3.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------