%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG281^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 07:44:16 PM UTC 2025 % Result : Theorem 6.05s 6.29s % Output : Proof 6.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.09 % Problem : ALG281^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.10 % Command : duper %s % 0.10/0.30 % Computer : n028.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Fri Oct 3 09:09:08 EDT 2025 % 0.10/0.30 % CPUTime : % 6.05/6.29 SZS status Theorem for theBenchmark.p % 6.05/6.29 SZS output start Proof for theBenchmark.p % 6.05/6.29 Clause #0 (by assumption #[]): Eq % 6.05/6.29 (Not % 6.05/6.29 (And (And (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : Iota), Eq (cP cE Xx) Xx)) % 6.05/6.29 (∀ (Xy : Iota), Eq (cP (cJ Xy) Xy) cE) → % 6.05/6.29 ∀ (X : Iota), Eq (cP X (cJ X)) cE)) % 6.05/6.29 True % 6.05/6.29 Clause #1 (by clausification #[0]): Eq % 6.05/6.29 (And (And (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : Iota), Eq (cP cE Xx) Xx)) % 6.05/6.29 (∀ (Xy : Iota), Eq (cP (cJ Xy) Xy) cE) → % 6.05/6.29 ∀ (X : Iota), Eq (cP X (cJ X)) cE) % 6.05/6.29 False % 6.05/6.29 Clause #2 (by clausification #[1]): Eq % 6.05/6.29 (And (And (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : Iota), Eq (cP cE Xx) Xx)) % 6.05/6.29 (∀ (Xy : Iota), Eq (cP (cJ Xy) Xy) cE)) % 6.05/6.29 True % 6.05/6.29 Clause #3 (by clausification #[1]): Eq (∀ (X : Iota), Eq (cP X (cJ X)) cE) False % 6.05/6.29 Clause #4 (by clausification #[2]): Eq (∀ (Xy : Iota), Eq (cP (cJ Xy) Xy) cE) True % 6.05/6.29 Clause #5 (by clausification #[2]): Eq (And (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : Iota), Eq (cP cE Xx) Xx)) True % 6.05/6.29 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (cP (cJ a) a) cE) True % 6.05/6.29 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (cP (cJ a) a) cE % 6.05/6.29 Clause #8 (by clausification #[3]): ∀ (a : Iota), Eq (Not (Eq (cP (skS.0 0 a) (cJ (skS.0 0 a))) cE)) True % 6.05/6.29 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (Eq (cP (skS.0 0 a) (cJ (skS.0 0 a))) cE) False % 6.05/6.29 Clause #10 (by clausification #[9]): ∀ (a : Iota), Ne (cP (skS.0 0 a) (cJ (skS.0 0 a))) cE % 6.05/6.29 Clause #11 (by clausification #[5]): Eq (∀ (Xx : Iota), Eq (cP cE Xx) Xx) True % 6.05/6.29 Clause #12 (by clausification #[5]): Eq (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) True % 6.05/6.29 Clause #13 (by clausification #[11]): ∀ (a : Iota), Eq (Eq (cP cE a) a) True % 6.05/6.29 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (cP cE a) a % 6.05/6.29 Clause #15 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), Eq (cP (cP a Xy) Xz) (cP a (cP Xy Xz))) True % 6.05/6.29 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), Eq (cP (cP a a_1) Xz) (cP a (cP a_1 Xz))) True % 6.05/6.29 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (Eq (cP (cP a a_1) a_2) (cP a (cP a_1 a_2))) True % 6.05/6.29 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (cP (cP a a_1) a_2) (cP a (cP a_1 a_2)) % 6.05/6.29 Clause #20 (by superposition #[18, 7]): ∀ (a a_1 : Iota), Eq (cP cE a) (cP (cJ a_1) (cP a_1 a)) % 6.05/6.29 Clause #33 (by forward demodulation #[20, 14]): ∀ (a a_1 : Iota), Eq a (cP (cJ a_1) (cP a_1 a)) % 6.05/6.29 Clause #38 (by superposition #[33, 7]): ∀ (a : Iota), Eq a (cP (cJ (cJ a)) cE) % 6.05/6.29 Clause #49 (by superposition #[38, 33]): ∀ (a : Iota), Eq cE (cP (cJ (cJ (cJ a))) a) % 6.05/6.29 Clause #107 (by superposition #[49, 33]): ∀ (a : Iota), Eq a (cP (cJ (cJ (cJ (cJ a)))) cE) % 6.05/6.29 Clause #110 (by superposition #[107, 38]): ∀ (a : Iota), Eq (cJ (cJ a)) a % 6.05/6.29 Clause #118 (by superposition #[110, 7]): ∀ (a : Iota), Eq (cP a (cJ a)) cE % 6.05/6.29 Clause #161 (by backward contextual literal cutting #[118, 10]): False % 6.05/6.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------