%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG282^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 3.72s 3.93s % Output : Proof 3.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : ALG282^5 : TPTP v9.2.0. Released v4.0.0. % 0.10/0.13 % Command : duper %s % 0.14/0.35 % Computer : n023.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 : Fri Oct 3 09:52:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.72/3.93 SZS status Theorem for theBenchmark.p % 3.72/3.93 SZS output start Proof for theBenchmark.p % 3.72/3.93 Clause #0 (by assumption #[]): Eq % 3.72/3.93 (Not % 3.72/3.93 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx)) % 3.72/3.93 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) → % 3.72/3.93 ∀ (X Y : a), Exists fun W => Eq (cP W X) Y)) % 3.72/3.93 True % 3.72/3.93 Clause #1 (by clausification #[0]): Eq % 3.72/3.93 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx)) % 3.72/3.93 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) → % 3.72/3.93 ∀ (X Y : a), Exists fun W => Eq (cP W X) Y) % 3.72/3.93 False % 3.72/3.93 Clause #2 (by clausification #[1]): Eq % 3.72/3.93 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx)) % 3.72/3.93 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE)) % 3.72/3.93 True % 3.72/3.93 Clause #3 (by clausification #[1]): Eq (∀ (X Y : a), Exists fun W => Eq (cP W X) Y) False % 3.72/3.93 Clause #4 (by clausification #[2]): Eq (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) True % 3.72/3.93 Clause #5 (by clausification #[2]): Eq (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx)) True % 3.72/3.93 Clause #6 (by clausification #[4]): ∀ (a_1 : a), Eq (Eq (cP (cJ a_1) a_1) cE) True % 3.72/3.93 Clause #7 (by clausification #[6]): ∀ (a_1 : a), Eq (cP (cJ a_1) a_1) cE % 3.72/3.93 Clause #8 (by clausification #[3]): ∀ (a_1 : a), Eq (Not (∀ (Y : a), Exists fun W => Eq (cP W (skS.0 0 a_1)) Y)) True % 3.72/3.93 Clause #9 (by clausification #[8]): ∀ (a_1 : a), Eq (∀ (Y : a), Exists fun W => Eq (cP W (skS.0 0 a_1)) Y) False % 3.72/3.93 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 : a), Eq (Not (Exists fun W => Eq (cP W (skS.0 0 a_1)) (skS.0 1 a_1 a_2))) True % 3.72/3.93 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 : a), Eq (Exists fun W => Eq (cP W (skS.0 0 a_1)) (skS.0 1 a_1 a_2)) False % 3.72/3.93 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 a_3 : a), Eq (Eq (cP a_1 (skS.0 0 a_2)) (skS.0 1 a_2 a_3)) False % 3.72/3.93 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a), Ne (cP a_1 (skS.0 0 a_2)) (skS.0 1 a_2 a_3) % 3.72/3.93 Clause #15 (by clausification #[5]): Eq (∀ (Xx : a), Eq (cP cE Xx) Xx) True % 3.72/3.93 Clause #16 (by clausification #[5]): Eq (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) True % 3.72/3.93 Clause #17 (by clausification #[15]): ∀ (a_1 : a), Eq (Eq (cP cE a_1) a_1) True % 3.72/3.93 Clause #18 (by clausification #[17]): ∀ (a_1 : a), Eq (cP cE a_1) a_1 % 3.72/3.93 Clause #19 (by clausification #[16]): ∀ (a_1 : a), Eq (∀ (Xy Xz : a), Eq (cP (cP a_1 Xy) Xz) (cP a_1 (cP Xy Xz))) True % 3.72/3.93 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 : a), Eq (∀ (Xz : a), Eq (cP (cP a_1 a_2) Xz) (cP a_1 (cP a_2 Xz))) True % 3.72/3.93 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 a_3 : a), Eq (Eq (cP (cP a_1 a_2) a_3) (cP a_1 (cP a_2 a_3))) True % 3.72/3.93 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a), Eq (cP (cP a_1 a_2) a_3) (cP a_1 (cP a_2 a_3)) % 3.72/3.93 Clause #23 (by superposition #[22, 13]): ∀ (a_1 a_2 a_3 a_4 : a), Ne (cP a_1 (cP a_2 (skS.0 0 a_3))) (skS.0 1 a_3 a_4) % 3.72/3.93 Clause #25 (by superposition #[22, 7]): ∀ (a_1 a_2 : a), Eq (cP cE a_1) (cP (cJ a_2) (cP a_2 a_1)) % 3.72/3.93 Clause #28 (by superposition #[23, 7]): ∀ (a_1 a_2 a_3 : a), Ne (cP a_1 cE) (skS.0 1 a_2 a_3) % 3.72/3.93 Clause #29 (by forward demodulation #[25, 18]): ∀ (a_1 a_2 : a), Eq a_1 (cP (cJ a_2) (cP a_2 a_1)) % 3.72/3.93 Clause #33 (by superposition #[29, 7]): ∀ (a_1 : a), Eq a_1 (cP (cJ (cJ a_1)) cE) % 3.72/3.93 Clause #40 (by superposition #[33, 29]): ∀ (a_1 : a), Eq cE (cP (cJ (cJ (cJ a_1))) a_1) % 3.72/3.93 Clause #72 (by superposition #[40, 29]): ∀ (a_1 : a), Eq a_1 (cP (cJ (cJ (cJ (cJ a_1)))) cE) % 3.72/3.93 Clause #75 (by superposition #[72, 33]): ∀ (a_1 : a), Eq (cJ (cJ a_1)) a_1 % 3.72/3.93 Clause #80 (by backward demodulation #[75, 33]): ∀ (a_1 : a), Eq a_1 (cP a_1 cE) % 3.72/3.93 Clause #85 (by backward demodulation #[80, 28]): ∀ (a_1 a_2 a_3 : a), Ne a_1 (skS.0 1 a_2 a_3) % 3.72/3.93 Clause #161 (by destructive equality resolution #[85]): False % 3.72/3.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------