%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ALG285^5 : TPTP v9.2.0. Released v4.0.0. % 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 07:44:16 PM UTC 2025 % Result : Theorem 4.71s 4.88s % Output : Proof 4.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG285^5 : TPTP v9.2.0. Released v4.0.0. % 0.13/0.13 % Command : duper %s % 0.14/0.35 % Computer : n025.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 09:20:38 EDT 2025 % 0.21/0.35 % CPUTime : % 4.71/4.88 SZS status Theorem for theBenchmark.p % 4.71/4.88 SZS output start Proof for theBenchmark.p % 4.71/4.88 Clause #0 (by assumption #[]): Eq % 4.71/4.88 (Not % 4.71/4.88 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx)) % 4.71/4.88 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) → % 4.71/4.88 And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) % 4.71/4.88 (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)))) % 4.71/4.88 True % 4.71/4.88 Clause #1 (by clausification #[0]): Eq % 4.71/4.88 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx)) % 4.71/4.88 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) → % 4.71/4.88 And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) % 4.71/4.88 (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y))) % 4.71/4.88 False % 4.71/4.88 Clause #2 (by clausification #[1]): Eq % 4.71/4.88 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx)) % 4.71/4.88 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE)) % 4.71/4.88 True % 4.71/4.88 Clause #3 (by clausification #[1]): Eq % 4.71/4.88 (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) % 4.71/4.88 (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y))) % 4.71/4.88 False % 4.71/4.88 Clause #4 (by clausification #[2]): Eq (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) True % 4.71/4.88 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 % 4.71/4.88 Clause #6 (by clausification #[4]): ∀ (a_1 : a), Eq (Eq (cP (cJ a_1) a_1) cE) True % 4.71/4.88 Clause #7 (by clausification #[6]): ∀ (a_1 : a), Eq (cP (cJ a_1) a_1) cE % 4.71/4.88 Clause #8 (by clausification #[5]): Eq (∀ (Xx : a), Eq (cP cE Xx) Xx) True % 4.71/4.88 Clause #9 (by clausification #[5]): Eq (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) True % 4.71/4.88 Clause #10 (by clausification #[8]): ∀ (a_1 : a), Eq (Eq (cP cE a_1) a_1) True % 4.71/4.88 Clause #11 (by clausification #[10]): ∀ (a_1 : a), Eq (cP cE a_1) a_1 % 4.71/4.88 Clause #12 (by clausification #[9]): ∀ (a_1 : a), Eq (∀ (Xy Xz : a), Eq (cP (cP a_1 Xy) Xz) (cP a_1 (cP Xy Xz))) True % 4.71/4.88 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a), Eq (∀ (Xz : a), Eq (cP (cP a_1 a_2) Xz) (cP a_1 (cP a_2 Xz))) True % 4.71/4.88 Clause #14 (by clausification #[13]): ∀ (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 % 4.71/4.88 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a), Eq (cP (cP a_1 a_2) a_3) (cP a_1 (cP a_2 a_3)) % 4.71/4.88 Clause #17 (by superposition #[15, 7]): ∀ (a_1 a_2 : a), Eq (cP cE a_1) (cP (cJ a_2) (cP a_2 a_1)) % 4.71/4.88 Clause #19 (by forward demodulation #[17, 11]): ∀ (a_1 a_2 : a), Eq a_1 (cP (cJ a_2) (cP a_2 a_1)) % 4.71/4.88 Clause #22 (by superposition #[19, 7]): ∀ (a_1 : a), Eq a_1 (cP (cJ (cJ a_1)) cE) % 4.71/4.88 Clause #25 (by clausification #[3]): Or (Eq (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) False) % 4.71/4.88 (Eq (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)) False) % 4.71/4.88 Clause #26 (by clausification #[25]): ∀ (a_1 : a), % 4.71/4.88 Or (Eq (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)) False) % 4.71/4.88 (Eq (Not (∀ (Xy Xz : a), Eq (cP (cP (skS.0 0 a_1) Xy) Xz) (cP (skS.0 0 a_1) (cP Xy Xz)))) True) % 4.71/4.88 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 : a), % 4.71/4.88 Or (Eq (Not (∀ (Xy Xz : a), Eq (cP (cP (skS.0 0 a_1) Xy) Xz) (cP (skS.0 0 a_1) (cP Xy Xz)))) True) % 4.71/4.88 (Eq (Not (∀ (Y : a), And (Exists fun U => Eq (cP (skS.0 1 a_2) U) Y) (Exists fun V => Eq (cP V (skS.0 1 a_2)) Y))) % 4.71/4.88 True) % 4.71/4.88 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 : a), % 4.71/4.88 Or % 4.71/4.88 (Eq (Not (∀ (Y : a), And (Exists fun U => Eq (cP (skS.0 1 a_1) U) Y) (Exists fun V => Eq (cP V (skS.0 1 a_1)) Y))) % 4.71/4.88 True) % 4.71/4.88 (Eq (∀ (Xy Xz : a), Eq (cP (cP (skS.0 0 a_2) Xy) Xz) (cP (skS.0 0 a_2) (cP Xy Xz))) False) % 4.71/4.88 Clause #29 (by clausification #[28]): ∀ (a_1 a_2 : a), % 4.71/4.88 Or (Eq (∀ (Xy Xz : a), Eq (cP (cP (skS.0 0 a_1) Xy) Xz) (cP (skS.0 0 a_1) (cP Xy Xz))) False) % 4.71/4.88 (Eq (∀ (Y : a), And (Exists fun U => Eq (cP (skS.0 1 a_2) U) Y) (Exists fun V => Eq (cP V (skS.0 1 a_2)) Y)) False) % 4.71/4.88 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a), % 4.75/4.91 Or (Eq (∀ (Y : a), And (Exists fun U => Eq (cP (skS.0 1 a_1) U) Y) (Exists fun V => Eq (cP V (skS.0 1 a_1)) Y)) False) % 4.75/4.91 (Eq (Not (∀ (Xz : a), Eq (cP (cP (skS.0 0 a_2) (skS.0 2 a_2 a_3)) Xz) (cP (skS.0 0 a_2) (cP (skS.0 2 a_2 a_3) Xz)))) % 4.75/4.91 True) % 4.75/4.91 Clause #31 (by clausification #[30]): ∀ (a_1 a_2 a_3 a_4 : a), % 4.75/4.91 Or % 4.75/4.91 (Eq (Not (∀ (Xz : a), Eq (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) Xz) (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) Xz)))) % 4.75/4.91 True) % 4.75/4.91 (Eq % 4.75/4.91 (Not % 4.75/4.91 (And (Exists fun U => Eq (cP (skS.0 1 a_3) U) (skS.0 3 a_3 a_4)) % 4.75/4.91 (Exists fun V => Eq (cP V (skS.0 1 a_3)) (skS.0 3 a_3 a_4)))) % 4.75/4.91 True) % 4.75/4.91 Clause #32 (by clausification #[31]): ∀ (a_1 a_2 a_3 a_4 : a), % 4.75/4.91 Or % 4.75/4.91 (Eq % 4.75/4.91 (Not % 4.75/4.91 (And (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2)) % 4.75/4.91 (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)))) % 4.75/4.91 True) % 4.75/4.91 (Eq (∀ (Xz : a), Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) Xz) (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) Xz))) % 4.75/4.91 False) % 4.75/4.91 Clause #33 (by clausification #[32]): ∀ (a_1 a_2 a_3 a_4 : a), % 4.75/4.91 Or % 4.75/4.91 (Eq (∀ (Xz : a), Eq (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) Xz) (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) Xz))) % 4.75/4.91 False) % 4.75/4.91 (Eq % 4.75/4.91 (And (Exists fun U => Eq (cP (skS.0 1 a_3) U) (skS.0 3 a_3 a_4)) % 4.75/4.91 (Exists fun V => Eq (cP V (skS.0 1 a_3)) (skS.0 3 a_3 a_4))) % 4.75/4.91 False) % 4.75/4.91 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 4.75/4.91 Or % 4.75/4.91 (Eq % 4.75/4.91 (And (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2)) % 4.75/4.91 (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2))) % 4.75/4.91 False) % 4.75/4.91 (Eq % 4.75/4.91 (Not % 4.75/4.91 (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5)) % 4.75/4.91 (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5))))) % 4.75/4.91 True) % 4.75/4.91 Clause #35 (by clausification #[34]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 4.75/4.91 Or % 4.75/4.91 (Eq % 4.75/4.91 (Not % 4.75/4.91 (Eq (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3)) % 4.75/4.91 (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3))))) % 4.75/4.91 True) % 4.75/4.91 (Or (Eq (Exists fun U => Eq (cP (skS.0 1 a_4) U) (skS.0 3 a_4 a_5)) False) % 4.75/4.91 (Eq (Exists fun V => Eq (cP V (skS.0 1 a_4)) (skS.0 3 a_4 a_5)) False)) % 4.75/4.91 Clause #36 (by clausification #[35]): ∀ (a_1 a_2 a_3 a_4 a_5 : a), % 4.75/4.91 Or (Eq (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2)) False) % 4.75/4.91 (Or (Eq (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)) False) % 4.75/4.91 (Eq % 4.75/4.91 (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5)) % 4.75/4.91 (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5)))) % 4.75/4.91 False)) % 4.75/4.91 Clause #37 (by clausification #[36]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a), % 4.75/4.91 Or (Eq (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)) False) % 4.75/4.91 (Or % 4.75/4.91 (Eq % 4.75/4.91 (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5)) % 4.75/4.91 (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5)))) % 4.75/4.91 False) % 4.75/4.91 (Eq (Eq (cP (skS.0 1 a_1) a_6) (skS.0 3 a_1 a_2)) False)) % 4.75/4.91 Clause #38 (by clausification #[37]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a), % 4.75/4.91 Or % 4.75/4.91 (Eq % 4.75/4.91 (Eq (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3)) % 4.75/4.91 (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)))) % 4.75/4.91 False) % 4.75/4.91 (Or (Eq (Eq (cP (skS.0 1 a_4) a_5) (skS.0 3 a_4 a_6)) False) % 4.75/4.91 (Eq (Eq (cP a_7 (skS.0 1 a_4)) (skS.0 3 a_4 a_6)) False)) % 4.75/4.91 Clause #39 (by clausification #[38]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a), % 4.75/4.91 Or (Eq (Eq (cP (skS.0 1 a_1) a_2) (skS.0 3 a_1 a_3)) False) % 4.75/4.91 (Or (Eq (Eq (cP a_4 (skS.0 1 a_1)) (skS.0 3 a_1 a_3)) False) % 4.75/4.91 (Ne (cP (cP (skS.0 0 a_5) (skS.0 2 a_5 a_6)) (skS.0 4 a_5 a_6 a_7)) % 4.75/4.91 (cP (skS.0 0 a_5) (cP (skS.0 2 a_5 a_6) (skS.0 4 a_5 a_6 a_7))))) % 4.75/4.91 Clause #40 (by clausification #[39]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a), % 4.75/4.91 Or (Eq (Eq (cP a_1 (skS.0 1 a_2)) (skS.0 3 a_2 a_3)) False) % 4.75/4.91 (Or % 4.75/4.91 (Ne (cP (cP (skS.0 0 a_4) (skS.0 2 a_4 a_5)) (skS.0 4 a_4 a_5 a_6)) % 4.75/4.91 (cP (skS.0 0 a_4) (cP (skS.0 2 a_4 a_5) (skS.0 4 a_4 a_5 a_6)))) % 4.75/4.91 (Ne (cP (skS.0 1 a_2) a_7) (skS.0 3 a_2 a_3))) % 4.75/4.91 Clause #41 (by clausification #[40]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a), % 4.75/4.92 Or % 4.75/4.92 (Ne (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3)) % 4.75/4.92 (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)))) % 4.75/4.92 (Or (Ne (cP (skS.0 1 a_4) a_5) (skS.0 3 a_4 a_6)) (Ne (cP a_7 (skS.0 1 a_4)) (skS.0 3 a_4 a_6))) % 4.75/4.92 Clause #42 (by forward demodulation #[41, 15]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a), % 4.75/4.92 Or % 4.75/4.92 (Ne (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3))) % 4.75/4.92 (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)))) % 4.75/4.92 (Or (Ne (cP (skS.0 1 a_4) a_5) (skS.0 3 a_4 a_6)) (Ne (cP a_7 (skS.0 1 a_4)) (skS.0 3 a_4 a_6))) % 4.75/4.92 Clause #43 (by eliminate resolved literals #[42]): ∀ (a_1 a_2 a_3 a_4 : a), Or (Ne (cP (skS.0 1 a_1) a_2) (skS.0 3 a_1 a_3)) (Ne (cP a_4 (skS.0 1 a_1)) (skS.0 3 a_1 a_3)) % 4.75/4.92 Clause #67 (by superposition #[22, 19]): ∀ (a_1 : a), Eq cE (cP (cJ (cJ (cJ a_1))) a_1) % 4.75/4.92 Clause #73 (by superposition #[67, 19]): ∀ (a_1 : a), Eq a_1 (cP (cJ (cJ (cJ (cJ a_1)))) cE) % 4.75/4.92 Clause #76 (by superposition #[73, 22]): ∀ (a_1 : a), Eq (cJ (cJ a_1)) a_1 % 4.75/4.92 Clause #81 (by backward demodulation #[76, 22]): ∀ (a_1 : a), Eq a_1 (cP a_1 cE) % 4.75/4.92 Clause #83 (by superposition #[76, 7]): ∀ (a_1 : a), Eq (cP a_1 (cJ a_1)) cE % 4.75/4.92 Clause #84 (by superposition #[76, 19]): ∀ (a_1 a_2 : a), Eq a_1 (cP a_2 (cP (cJ a_2) a_1)) % 4.75/4.92 Clause #90 (by superposition #[83, 15]): ∀ (a_1 a_2 : a), Eq cE (cP a_1 (cP a_2 (cJ (cP a_1 a_2)))) % 4.75/4.92 Clause #99 (by superposition #[84, 43]): ∀ (a_1 a_2 a_3 a_4 : a), Or (Ne a_1 (skS.0 3 a_2 a_3)) (Ne (cP a_4 (skS.0 1 a_2)) (skS.0 3 a_2 a_3)) % 4.75/4.92 Clause #144 (by superposition #[90, 19]): ∀ (a_1 a_2 : a), Eq (cP a_1 (cJ (cP a_2 a_1))) (cP (cJ a_2) cE) % 4.75/4.92 Clause #217 (by forward demodulation #[144, 81]): ∀ (a_1 a_2 : a), Eq (cP a_1 (cJ (cP a_2 a_1))) (cJ a_2) % 4.75/4.92 Clause #235 (by superposition #[217, 84]): ∀ (a_1 a_2 : a), Eq (cP (cP (cJ a_1) a_2) (cJ a_2)) (cJ a_1) % 4.75/4.92 Clause #381 (by superposition #[235, 76]): ∀ (a_1 a_2 : a), Eq (cP (cP a_1 a_2) (cJ a_2)) a_1 % 4.75/4.92 Clause #398 (by superposition #[381, 76]): ∀ (a_1 a_2 : a), Eq (cP (cP a_1 (cJ a_2)) a_2) a_1 % 4.75/4.92 Clause #699 (by destructive equality resolution #[99]): ∀ (a_1 a_2 a_3 : a), Ne (cP a_1 (skS.0 1 a_2)) (skS.0 3 a_2 a_3) % 4.75/4.92 Clause #705 (by superposition #[699, 398]): ∀ (a_1 a_2 a_3 : a), Ne a_1 (skS.0 3 a_2 a_3) % 4.75/4.92 Clause #706 (by destructive equality resolution #[705]): False % 4.75/4.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------