%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG284^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 4.46s 4.61s % Output : Proof 4.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG284^5 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.13 % Command : duper %s % 0.14/0.34 % Computer : n009.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 09:44:23 EDT 2025 % 0.14/0.34 % CPUTime : % 4.46/4.61 SZS status Theorem for theBenchmark.p % 4.46/4.61 SZS output start Proof for theBenchmark.p % 4.46/4.61 Clause #0 (by assumption #[]): Eq % 4.46/4.61 (Not % 4.46/4.61 (And (And (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : Iota), Eq (cP cE Xx) Xx)) % 4.46/4.61 (∀ (Xy : Iota), Eq (cP (cJ Xy) Xy) cE) → % 4.46/4.61 ∀ (X Y : Iota), Eq (cJ (cP X Y)) (cP (cJ Y) (cJ X)))) % 4.46/4.61 True % 4.46/4.61 Clause #1 (by clausification #[0]): Eq % 4.46/4.61 (And (And (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : Iota), Eq (cP cE Xx) Xx)) % 4.46/4.61 (∀ (Xy : Iota), Eq (cP (cJ Xy) Xy) cE) → % 4.46/4.61 ∀ (X Y : Iota), Eq (cJ (cP X Y)) (cP (cJ Y) (cJ X))) % 4.46/4.61 False % 4.46/4.61 Clause #2 (by clausification #[1]): Eq % 4.46/4.61 (And (And (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : Iota), Eq (cP cE Xx) Xx)) % 4.46/4.61 (∀ (Xy : Iota), Eq (cP (cJ Xy) Xy) cE)) % 4.46/4.61 True % 4.46/4.61 Clause #3 (by clausification #[1]): Eq (∀ (X Y : Iota), Eq (cJ (cP X Y)) (cP (cJ Y) (cJ X))) False % 4.46/4.61 Clause #4 (by clausification #[2]): Eq (∀ (Xy : Iota), Eq (cP (cJ Xy) Xy) cE) True % 4.46/4.61 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 % 4.46/4.61 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (cP (cJ a) a) cE) True % 4.46/4.61 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (cP (cJ a) a) cE % 4.46/4.61 Clause #8 (by clausification #[3]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Eq (cJ (cP (skS.0 0 a) Y)) (cP (cJ Y) (cJ (skS.0 0 a))))) True % 4.46/4.61 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Y : Iota), Eq (cJ (cP (skS.0 0 a) Y)) (cP (cJ Y) (cJ (skS.0 0 a)))) False % 4.46/4.61 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Not (Eq (cJ (cP (skS.0 0 a) (skS.0 1 a a_1))) (cP (cJ (skS.0 1 a a_1)) (cJ (skS.0 0 a))))) True % 4.46/4.61 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Eq (cJ (cP (skS.0 0 a) (skS.0 1 a a_1))) (cP (cJ (skS.0 1 a a_1)) (cJ (skS.0 0 a)))) False % 4.46/4.61 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Ne (cJ (cP (skS.0 0 a) (skS.0 1 a a_1))) (cP (cJ (skS.0 1 a a_1)) (cJ (skS.0 0 a))) % 4.46/4.61 Clause #13 (by clausification #[5]): Eq (∀ (Xx : Iota), Eq (cP cE Xx) Xx) True % 4.46/4.61 Clause #14 (by clausification #[5]): Eq (∀ (Xx Xy Xz : Iota), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) True % 4.46/4.61 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (Eq (cP cE a) a) True % 4.46/4.61 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (cP cE a) a % 4.46/4.61 Clause #17 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), Eq (cP (cP a Xy) Xz) (cP a (cP Xy Xz))) True % 4.46/4.61 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), Eq (cP (cP a a_1) Xz) (cP a (cP a_1 Xz))) True % 4.46/4.61 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Eq (Eq (cP (cP a a_1) a_2) (cP a (cP a_1 a_2))) True % 4.46/4.61 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Eq (cP (cP a a_1) a_2) (cP a (cP a_1 a_2)) % 4.46/4.61 Clause #22 (by superposition #[20, 7]): ∀ (a a_1 : Iota), Eq (cP cE a) (cP (cJ a_1) (cP a_1 a)) % 4.46/4.61 Clause #35 (by forward demodulation #[22, 16]): ∀ (a a_1 : Iota), Eq a (cP (cJ a_1) (cP a_1 a)) % 4.46/4.61 Clause #40 (by superposition #[35, 7]): ∀ (a : Iota), Eq a (cP (cJ (cJ a)) cE) % 4.46/4.61 Clause #42 (by superposition #[35, 20]): ∀ (a a_1 a_2 : Iota), Eq a (cP (cJ (cP a_1 a_2)) (cP a_1 (cP a_2 a))) % 4.46/4.61 Clause #51 (by superposition #[40, 35]): ∀ (a : Iota), Eq cE (cP (cJ (cJ (cJ a))) a) % 4.46/4.61 Clause #109 (by superposition #[51, 35]): ∀ (a : Iota), Eq a (cP (cJ (cJ (cJ (cJ a)))) cE) % 4.46/4.61 Clause #112 (by superposition #[109, 40]): ∀ (a : Iota), Eq (cJ (cJ a)) a % 4.46/4.61 Clause #118 (by backward demodulation #[112, 40]): ∀ (a : Iota), Eq a (cP a cE) % 4.46/4.61 Clause #207 (by superposition #[42, 7]): ∀ (a a_1 : Iota), Eq a (cP (cJ (cP (cJ (cP a_1 a)) a_1)) cE) % 4.46/4.61 Clause #271 (by superposition #[207, 118]): ∀ (a a_1 : Iota), Eq (cJ (cP (cJ (cP a a_1)) a)) a_1 % 4.46/4.61 Clause #300 (by superposition #[271, 112]): ∀ (a a_1 : Iota), Eq (cJ a) (cP (cJ (cP a_1 a)) a_1) % 4.46/4.61 Clause #334 (by superposition #[300, 35]): ∀ (a a_1 : Iota), Eq (cJ (cP a a_1)) (cP (cJ a_1) (cJ a)) % 4.46/4.61 Clause #593 (by backward contextual literal cutting #[334, 12]): False % 4.46/4.61 SZS output end Proof for theBenchmark.p 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