TSTP Solution File: ALG285^5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : ALG285^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n032.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 : Wed Aug 30 16:11:59 EDT 2023
% Result : Theorem 4.96s 5.13s
% Output : Proof 4.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG285^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : duper %s
% 0.10/0.30 % Computer : n032.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 : Mon Aug 28 05:15:15 EDT 2023
% 0.10/0.30 % CPUTime :
% 4.96/5.13 SZS status Theorem for theBenchmark.p
% 4.96/5.13 SZS output start Proof for theBenchmark.p
% 4.96/5.13 Clause #0 (by assumption #[]): Eq
% 4.96/5.13 (Not
% 4.96/5.13 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx))
% 4.96/5.13 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) →
% 4.96/5.13 And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz)))
% 4.96/5.13 (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y))))
% 4.96/5.13 True
% 4.96/5.13 Clause #1 (by clausification #[0]): Eq
% 4.96/5.13 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx))
% 4.96/5.13 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) →
% 4.96/5.13 And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz)))
% 4.96/5.13 (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)))
% 4.96/5.13 False
% 4.96/5.13 Clause #2 (by clausification #[1]): Eq
% 4.96/5.13 (And (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) (∀ (Xx : a), Eq (cP cE Xx) Xx))
% 4.96/5.13 (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE))
% 4.96/5.13 True
% 4.96/5.13 Clause #3 (by clausification #[1]): Eq
% 4.96/5.13 (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz)))
% 4.96/5.13 (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)))
% 4.96/5.13 False
% 4.96/5.13 Clause #4 (by clausification #[2]): Eq (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) True
% 4.96/5.13 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
% 4.96/5.13 Clause #6 (by clausification #[4]): ∀ (a_1 : a), Eq (Eq (cP (cJ a_1) a_1) cE) True
% 4.96/5.13 Clause #7 (by clausification #[6]): ∀ (a_1 : a), Eq (cP (cJ a_1) a_1) cE
% 4.96/5.13 Clause #8 (by clausification #[5]): Eq (∀ (Xx : a), Eq (cP cE Xx) Xx) True
% 4.96/5.13 Clause #9 (by clausification #[5]): Eq (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) True
% 4.96/5.13 Clause #10 (by clausification #[8]): ∀ (a_1 : a), Eq (Eq (cP cE a_1) a_1) True
% 4.96/5.13 Clause #11 (by clausification #[10]): ∀ (a_1 : a), Eq (cP cE a_1) a_1
% 4.96/5.13 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
% 4.96/5.13 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
% 4.96/5.13 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
% 4.96/5.13 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))
% 4.96/5.13 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))
% 4.96/5.13 Clause #19 (by forward demodulation #[17, 11]): ∀ (a_1 a_2 : a), Eq a_1 (cP (cJ a_2) (cP a_2 a_1))
% 4.96/5.13 Clause #22 (by superposition #[19, 7]): ∀ (a_1 : a), Eq a_1 (cP (cJ (cJ a_1)) cE)
% 4.96/5.13 Clause #25 (by clausification #[3]): Or (Eq (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) False)
% 4.96/5.13 (Eq (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)) False)
% 4.96/5.13 Clause #26 (by clausification #[25]): ∀ (a_1 : a),
% 4.96/5.13 Or (Eq (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)) False)
% 4.96/5.13 (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)
% 4.96/5.13 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 : a),
% 4.96/5.13 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)
% 4.96/5.13 (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)))
% 4.96/5.13 True)
% 4.96/5.13 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 : a),
% 4.96/5.13 Or
% 4.96/5.13 (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)))
% 4.96/5.13 True)
% 4.96/5.13 (Eq (∀ (Xy Xz : a), Eq (cP (cP (skS.0 0 a_2) Xy) Xz) (cP (skS.0 0 a_2) (cP Xy Xz))) False)
% 4.96/5.13 Clause #29 (by clausification #[28]): ∀ (a_1 a_2 : a),
% 4.96/5.13 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)
% 4.96/5.13 (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)
% 4.96/5.13 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a),
% 4.99/5.15 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)
% 4.99/5.15 (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))))
% 4.99/5.15 True)
% 4.99/5.15 Clause #31 (by clausification #[30]): ∀ (a_1 a_2 a_3 a_4 : a),
% 4.99/5.15 Or
% 4.99/5.15 (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))))
% 4.99/5.15 True)
% 4.99/5.15 (Eq
% 4.99/5.15 (Not
% 4.99/5.15 (And (Exists fun U => Eq (cP (skS.0 1 a_3) U) (skS.0 3 a_3 a_4))
% 4.99/5.15 (Exists fun V => Eq (cP V (skS.0 1 a_3)) (skS.0 3 a_3 a_4))))
% 4.99/5.15 True)
% 4.99/5.15 Clause #32 (by clausification #[31]): ∀ (a_1 a_2 a_3 a_4 : a),
% 4.99/5.15 Or
% 4.99/5.15 (Eq
% 4.99/5.15 (Not
% 4.99/5.15 (And (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2))
% 4.99/5.15 (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2))))
% 4.99/5.15 True)
% 4.99/5.15 (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)))
% 4.99/5.15 False)
% 4.99/5.15 Clause #33 (by clausification #[32]): ∀ (a_1 a_2 a_3 a_4 : a),
% 4.99/5.15 Or
% 4.99/5.15 (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)))
% 4.99/5.15 False)
% 4.99/5.15 (Eq
% 4.99/5.15 (And (Exists fun U => Eq (cP (skS.0 1 a_3) U) (skS.0 3 a_3 a_4))
% 4.99/5.15 (Exists fun V => Eq (cP V (skS.0 1 a_3)) (skS.0 3 a_3 a_4)))
% 4.99/5.15 False)
% 4.99/5.15 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 4.99/5.15 Or
% 4.99/5.15 (Eq
% 4.99/5.15 (And (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2))
% 4.99/5.15 (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)))
% 4.99/5.15 False)
% 4.99/5.15 (Eq
% 4.99/5.15 (Not
% 4.99/5.15 (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5))
% 4.99/5.15 (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5)))))
% 4.99/5.15 True)
% 4.99/5.15 Clause #35 (by clausification #[34]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 4.99/5.15 Or
% 4.99/5.15 (Eq
% 4.99/5.15 (Not
% 4.99/5.15 (Eq (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3))
% 4.99/5.15 (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)))))
% 4.99/5.15 True)
% 4.99/5.15 (Or (Eq (Exists fun U => Eq (cP (skS.0 1 a_4) U) (skS.0 3 a_4 a_5)) False)
% 4.99/5.15 (Eq (Exists fun V => Eq (cP V (skS.0 1 a_4)) (skS.0 3 a_4 a_5)) False))
% 4.99/5.15 Clause #36 (by clausification #[35]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 4.99/5.15 Or (Eq (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2)) False)
% 4.99/5.15 (Or (Eq (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)) False)
% 4.99/5.15 (Eq
% 4.99/5.15 (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5))
% 4.99/5.15 (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5))))
% 4.99/5.15 False))
% 4.99/5.15 Clause #37 (by clausification #[36]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 4.99/5.15 Or (Eq (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)) False)
% 4.99/5.15 (Or
% 4.99/5.15 (Eq
% 4.99/5.15 (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5))
% 4.99/5.15 (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5))))
% 4.99/5.15 False)
% 4.99/5.15 (Eq (Eq (cP (skS.0 1 a_1) a_6) (skS.0 3 a_1 a_2)) False))
% 4.99/5.15 Clause #38 (by clausification #[37]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
% 4.99/5.15 Or
% 4.99/5.15 (Eq
% 4.99/5.15 (Eq (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3))
% 4.99/5.15 (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3))))
% 4.99/5.15 False)
% 4.99/5.15 (Or (Eq (Eq (cP (skS.0 1 a_4) a_5) (skS.0 3 a_4 a_6)) False)
% 4.99/5.15 (Eq (Eq (cP a_7 (skS.0 1 a_4)) (skS.0 3 a_4 a_6)) False))
% 4.99/5.15 Clause #39 (by clausification #[38]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
% 4.99/5.15 Or (Eq (Eq (cP (skS.0 1 a_1) a_2) (skS.0 3 a_1 a_3)) False)
% 4.99/5.15 (Or (Eq (Eq (cP a_4 (skS.0 1 a_1)) (skS.0 3 a_1 a_3)) False)
% 4.99/5.15 (Ne (cP (cP (skS.0 0 a_5) (skS.0 2 a_5 a_6)) (skS.0 4 a_5 a_6 a_7))
% 4.99/5.15 (cP (skS.0 0 a_5) (cP (skS.0 2 a_5 a_6) (skS.0 4 a_5 a_6 a_7)))))
% 4.99/5.15 Clause #40 (by clausification #[39]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
% 4.99/5.15 Or (Eq (Eq (cP a_1 (skS.0 1 a_2)) (skS.0 3 a_2 a_3)) False)
% 4.99/5.15 (Or
% 4.99/5.15 (Ne (cP (cP (skS.0 0 a_4) (skS.0 2 a_4 a_5)) (skS.0 4 a_4 a_5 a_6))
% 4.99/5.15 (cP (skS.0 0 a_4) (cP (skS.0 2 a_4 a_5) (skS.0 4 a_4 a_5 a_6))))
% 4.99/5.15 (Ne (cP (skS.0 1 a_2) a_7) (skS.0 3 a_2 a_3)))
% 4.99/5.15 Clause #41 (by clausification #[40]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
% 4.99/5.17 Or
% 4.99/5.17 (Ne (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3))
% 4.99/5.17 (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3))))
% 4.99/5.17 (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)))
% 4.99/5.17 Clause #42 (by forward demodulation #[41, 15]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
% 4.99/5.17 Or
% 4.99/5.17 (Ne (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)))
% 4.99/5.17 (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3))))
% 4.99/5.17 (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)))
% 4.99/5.17 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))
% 4.99/5.17 Clause #67 (by superposition #[22, 19]): ∀ (a_1 : a), Eq cE (cP (cJ (cJ (cJ a_1))) a_1)
% 4.99/5.17 Clause #73 (by superposition #[67, 19]): ∀ (a_1 : a), Eq a_1 (cP (cJ (cJ (cJ (cJ a_1)))) cE)
% 4.99/5.17 Clause #76 (by superposition #[73, 22]): ∀ (a_1 : a), Eq (cJ (cJ a_1)) a_1
% 4.99/5.17 Clause #81 (by backward demodulation #[76, 22]): ∀ (a_1 : a), Eq a_1 (cP a_1 cE)
% 4.99/5.17 Clause #83 (by superposition #[76, 7]): ∀ (a_1 : a), Eq (cP a_1 (cJ a_1)) cE
% 4.99/5.17 Clause #84 (by superposition #[76, 19]): ∀ (a_1 a_2 : a), Eq a_1 (cP a_2 (cP (cJ a_2) a_1))
% 4.99/5.17 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))))
% 4.99/5.17 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))
% 4.99/5.17 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)
% 4.99/5.17 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)
% 4.99/5.17 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)
% 4.99/5.17 Clause #381 (by superposition #[235, 76]): ∀ (a_1 a_2 : a), Eq (cP (cP a_1 a_2) (cJ a_2)) a_1
% 4.99/5.17 Clause #398 (by superposition #[381, 76]): ∀ (a_1 a_2 : a), Eq (cP (cP a_1 (cJ a_2)) a_2) a_1
% 4.99/5.17 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)
% 4.99/5.17 Clause #705 (by superposition #[699, 398]): ∀ (a_1 a_2 a_3 : a), Ne a_1 (skS.0 3 a_2 a_3)
% 4.99/5.17 Clause #706 (by destructive equality resolution #[705]): False
% 4.99/5.17 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------