%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG270^5 : 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 07:44:15 PM UTC 2025 % Result : Theorem 3.52s 3.70s % Output : Proof 3.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : ALG270^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.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 09:14:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.52/3.70 SZS status Theorem for theBenchmark.p % 3.52/3.70 SZS output start Proof for theBenchmark.p % 3.52/3.70 Clause #0 (by assumption #[]): Eq % 3.52/3.70 (Not % 3.52/3.70 ((∀ (Xx Xy Xz : a), Eq (c_star (c_star Xx Xy) Xz) (c_star Xx (c_star Xy Xz))) → % 3.52/3.70 ∀ (W X Y Z : a), Eq (c_star (c_star (c_star W X) Y) Z) (c_star W (c_star X (c_star Y Z))))) % 3.52/3.70 True % 3.52/3.70 Clause #1 (by clausification #[0]): Eq % 3.52/3.70 ((∀ (Xx Xy Xz : a), Eq (c_star (c_star Xx Xy) Xz) (c_star Xx (c_star Xy Xz))) → % 3.52/3.70 ∀ (W X Y Z : a), Eq (c_star (c_star (c_star W X) Y) Z) (c_star W (c_star X (c_star Y Z)))) % 3.52/3.70 False % 3.52/3.70 Clause #2 (by clausification #[1]): Eq (∀ (Xx Xy Xz : a), Eq (c_star (c_star Xx Xy) Xz) (c_star Xx (c_star Xy Xz))) True % 3.52/3.70 Clause #3 (by clausification #[1]): Eq (∀ (W X Y Z : a), Eq (c_star (c_star (c_star W X) Y) Z) (c_star W (c_star X (c_star Y Z)))) False % 3.52/3.70 Clause #4 (by clausification #[2]): ∀ (a_1 : a), Eq (∀ (Xy Xz : a), Eq (c_star (c_star a_1 Xy) Xz) (c_star a_1 (c_star Xy Xz))) True % 3.52/3.70 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a), Eq (∀ (Xz : a), Eq (c_star (c_star a_1 a_2) Xz) (c_star a_1 (c_star a_2 Xz))) True % 3.52/3.70 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a), Eq (Eq (c_star (c_star a_1 a_2) a_3) (c_star a_1 (c_star a_2 a_3))) True % 3.52/3.70 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a), Eq (c_star (c_star a_1 a_2) a_3) (c_star a_1 (c_star a_2 a_3)) % 3.52/3.70 Clause #33 (by clausification #[3]): ∀ (a_1 : a), % 3.52/3.70 Eq % 3.52/3.70 (Not % 3.52/3.70 (∀ (X Y Z : a), Eq (c_star (c_star (c_star (skS.0 0 a_1) X) Y) Z) (c_star (skS.0 0 a_1) (c_star X (c_star Y Z))))) % 3.52/3.70 True % 3.52/3.70 Clause #34 (by clausification #[33]): ∀ (a_1 : a), % 3.52/3.70 Eq (∀ (X Y Z : a), Eq (c_star (c_star (c_star (skS.0 0 a_1) X) Y) Z) (c_star (skS.0 0 a_1) (c_star X (c_star Y Z)))) % 3.52/3.70 False % 3.52/3.70 Clause #35 (by clausification #[34]): ∀ (a_1 a_2 : a), % 3.52/3.70 Eq % 3.52/3.70 (Not % 3.52/3.70 (∀ (Y Z : a), % 3.52/3.70 Eq (c_star (c_star (c_star (skS.0 0 a_1) (skS.0 1 a_1 a_2)) Y) Z) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star Y Z))))) % 3.52/3.70 True % 3.52/3.70 Clause #36 (by clausification #[35]): ∀ (a_1 a_2 : a), % 3.52/3.70 Eq % 3.52/3.70 (∀ (Y Z : a), % 3.52/3.70 Eq (c_star (c_star (c_star (skS.0 0 a_1) (skS.0 1 a_1 a_2)) Y) Z) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star Y Z)))) % 3.52/3.70 False % 3.52/3.70 Clause #37 (by clausification #[36]): ∀ (a_1 a_2 a_3 : a), % 3.52/3.70 Eq % 3.52/3.70 (Not % 3.52/3.70 (∀ (Z : a), % 3.52/3.70 Eq (c_star (c_star (c_star (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (skS.0 2 a_1 a_2 a_3)) Z) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star (skS.0 2 a_1 a_2 a_3) Z))))) % 3.52/3.70 True % 3.52/3.70 Clause #38 (by clausification #[37]): ∀ (a_1 a_2 a_3 : a), % 3.52/3.70 Eq % 3.52/3.70 (∀ (Z : a), % 3.52/3.70 Eq (c_star (c_star (c_star (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (skS.0 2 a_1 a_2 a_3)) Z) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star (skS.0 2 a_1 a_2 a_3) Z)))) % 3.52/3.70 False % 3.52/3.70 Clause #39 (by clausification #[38]): ∀ (a_1 a_2 a_3 a_4 : a), % 3.52/3.70 Eq % 3.52/3.70 (Not % 3.52/3.70 (Eq (c_star (c_star (c_star (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (skS.0 2 a_1 a_2 a_3)) (skS.0 3 a_1 a_2 a_3 a_4)) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)))))) % 3.52/3.70 True % 3.52/3.70 Clause #40 (by clausification #[39]): ∀ (a_1 a_2 a_3 a_4 : a), % 3.52/3.70 Eq % 3.52/3.70 (Eq (c_star (c_star (c_star (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (skS.0 2 a_1 a_2 a_3)) (skS.0 3 a_1 a_2 a_3 a_4)) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))))) % 3.52/3.70 False % 3.52/3.70 Clause #41 (by clausification #[40]): ∀ (a_1 a_2 a_3 a_4 : a), % 3.52/3.70 Ne (c_star (c_star (c_star (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (skS.0 2 a_1 a_2 a_3)) (skS.0 3 a_1 a_2 a_3 a_4)) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)))) % 3.52/3.70 Clause #42 (by forward demodulation #[41, 7]): ∀ (a_1 a_2 a_3 a_4 : a), % 3.52/3.70 Ne (c_star (c_star (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (c_star (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4))) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)))) % 3.52/3.70 Clause #43 (by forward demodulation #[42, 7]): ∀ (a_1 a_2 a_3 a_4 : a), % 3.52/3.70 Ne (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)))) % 3.52/3.70 (c_star (skS.0 0 a_1) (c_star (skS.0 1 a_1 a_2) (c_star (skS.0 2 a_1 a_2 a_3) (skS.0 3 a_1 a_2 a_3 a_4)))) % 3.52/3.70 Clause #44 (by eliminate resolved literals #[43]): False % 3.52/3.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------