0.09/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.09/0.11	% Command    : duper %s
0.11/0.32	% Computer : n010.cluster.edu
0.11/0.32	% Model    : x86_64 x86_64
0.11/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory   : 8042.1875MB
0.11/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1440
0.11/0.32	% WCLimit    : 180
0.11/0.32	% DateTime   : Mon Jul  3 07:13:24 EDT 2023
0.11/0.32	% CPUTime    : 
41.90/42.52	SZS status Theorem for theBenchmark.p
41.90/42.52	SZS output start Proof for theBenchmark.p
41.90/42.52	Clause #0 (by assumption #[]): Eq
41.90/42.52	  (Not
41.90/42.52	    (And (And (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) (∀ (Xx : a), Eq (cP cE Xx) Xx))
41.90/42.52	        (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) →
41.90/42.52	      And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz)))
41.90/42.52	        (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y))))
41.90/42.52	  True
41.90/42.52	Clause #1 (by clausification #[0]): Eq
41.90/42.52	  (And (And (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) (∀ (Xx : a), Eq (cP cE Xx) Xx))
41.90/42.52	      (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) →
41.90/42.52	    And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz)))
41.90/42.52	      (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)))
41.90/42.52	  False
41.90/42.52	Clause #2 (by clausification #[1]): Eq
41.90/42.52	  (And (And (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) (∀ (Xx : a), Eq (cP cE Xx) Xx))
41.90/42.52	    (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))))
41.90/42.52	  True
41.90/42.52	Clause #3 (by clausification #[1]): Eq
41.90/42.52	  (And (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz)))
41.90/42.52	    (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)))
41.90/42.52	  False
41.90/42.52	Clause #4 (by clausification #[2]): Eq (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) True
41.90/42.52	Clause #5 (by clausification #[2]): Eq (And (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) (∀ (Xx : a), Eq (cP cE Xx) Xx)) True
41.90/42.52	Clause #6 (by clausification #[4]): ∀ (a_1 : a), Eq (∀ (Xy Xz : a), Eq (cP (cP a_1 Xy) Xz) (cP a_1 (cP Xy Xz))) True
41.90/42.52	Clause #7 (by clausification #[6]): ∀ (a_1 a_2 : a), Eq (∀ (Xz : a), Eq (cP (cP a_1 a_2) Xz) (cP a_1 (cP a_2 Xz))) True
41.90/42.52	Clause #8 (by clausification #[7]): ∀ (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
41.90/42.52	Clause #9 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a), Eq (cP (cP a_1 a_2) a_3) (cP a_1 (cP a_2 a_3))
41.90/42.52	Clause #19 (by clausification #[5]): Eq (∀ (Xx : a), Eq (cP cE Xx) Xx) True
41.90/42.52	Clause #20 (by clausification #[5]): Eq (∀ (Xy : a), Eq (cP (cJ Xy) Xy) cE) True
41.90/42.52	Clause #21 (by clausification #[19]): ∀ (a_1 : a), Eq (Eq (cP cE a_1) a_1) True
41.90/42.52	Clause #22 (by clausification #[21]): ∀ (a_1 : a), Eq (cP cE a_1) a_1
41.90/42.52	Clause #26 (by clausification #[3]): Or (Eq (∀ (Xx Xy Xz : a), Eq (cP (cP Xx Xy) Xz) (cP Xx (cP Xy Xz))) False)
41.90/42.52	  (Eq (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)) False)
41.90/42.52	Clause #27 (by clausification #[26]): ∀ (a_1 : a),
41.90/42.52	  Or (Eq (∀ (X Y : a), And (Exists fun U => Eq (cP X U) Y) (Exists fun V => Eq (cP V X) Y)) False)
41.90/42.52	    (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)
41.90/42.52	Clause #28 (by clausification #[27]): ∀ (a_1 a_2 : a),
41.90/42.52	  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)
41.90/42.52	    (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)))
41.90/42.52	      True)
41.90/42.52	Clause #29 (by clausification #[28]): ∀ (a_1 a_2 : a),
41.90/42.52	  Or
41.90/42.52	    (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)))
41.90/42.52	      True)
41.90/42.52	    (Eq (∀ (Xy Xz : a), Eq (cP (cP (skS.0 0 a_2) Xy) Xz) (cP (skS.0 0 a_2) (cP Xy Xz))) False)
41.90/42.52	Clause #30 (by clausification #[29]): ∀ (a_1 a_2 : a),
41.90/42.52	  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)
41.90/42.52	    (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)
41.90/42.52	Clause #31 (by clausification #[30]): ∀ (a_1 a_2 a_3 : a),
41.90/42.52	  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)
41.90/42.52	    (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))))
41.90/42.52	      True)
41.90/42.52	Clause #32 (by clausification #[31]): ∀ (a_1 a_2 a_3 a_4 : a),
41.90/42.52	  Or
41.90/42.52	    (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))))
41.90/42.52	      True)
41.90/42.52	    (Eq
41.99/42.57	      (Not
41.99/42.57	        (And (Exists fun U => Eq (cP (skS.0 1 a_3) U) (skS.0 3 a_3 a_4))
41.99/42.57	          (Exists fun V => Eq (cP V (skS.0 1 a_3)) (skS.0 3 a_3 a_4))))
41.99/42.57	      True)
41.99/42.57	Clause #33 (by clausification #[32]): ∀ (a_1 a_2 a_3 a_4 : a),
41.99/42.57	  Or
41.99/42.57	    (Eq
41.99/42.57	      (Not
41.99/42.57	        (And (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2))
41.99/42.57	          (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2))))
41.99/42.57	      True)
41.99/42.57	    (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)))
41.99/42.57	      False)
41.99/42.57	Clause #34 (by clausification #[33]): ∀ (a_1 a_2 a_3 a_4 : a),
41.99/42.57	  Or
41.99/42.57	    (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)))
41.99/42.57	      False)
41.99/42.57	    (Eq
41.99/42.57	      (And (Exists fun U => Eq (cP (skS.0 1 a_3) U) (skS.0 3 a_3 a_4))
41.99/42.57	        (Exists fun V => Eq (cP V (skS.0 1 a_3)) (skS.0 3 a_3 a_4)))
41.99/42.57	      False)
41.99/42.57	Clause #35 (by clausification #[34]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
41.99/42.57	  Or
41.99/42.57	    (Eq
41.99/42.57	      (And (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2))
41.99/42.57	        (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)))
41.99/42.57	      False)
41.99/42.57	    (Eq
41.99/42.57	      (Not
41.99/42.57	        (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5))
41.99/42.57	          (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5)))))
41.99/42.57	      True)
41.99/42.57	Clause #36 (by clausification #[35]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
41.99/42.57	  Or
41.99/42.57	    (Eq
41.99/42.57	      (Not
41.99/42.57	        (Eq (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3))
41.99/42.57	          (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)))))
41.99/42.57	      True)
41.99/42.57	    (Or (Eq (Exists fun U => Eq (cP (skS.0 1 a_4) U) (skS.0 3 a_4 a_5)) False)
41.99/42.57	      (Eq (Exists fun V => Eq (cP V (skS.0 1 a_4)) (skS.0 3 a_4 a_5)) False))
41.99/42.57	Clause #37 (by clausification #[36]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
41.99/42.57	  Or (Eq (Exists fun U => Eq (cP (skS.0 1 a_1) U) (skS.0 3 a_1 a_2)) False)
41.99/42.57	    (Or (Eq (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)) False)
41.99/42.57	      (Eq
41.99/42.57	        (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5))
41.99/42.57	          (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5))))
41.99/42.57	        False))
41.99/42.57	Clause #38 (by clausification #[37]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
41.99/42.57	  Or (Eq (Exists fun V => Eq (cP V (skS.0 1 a_1)) (skS.0 3 a_1 a_2)) False)
41.99/42.57	    (Or
41.99/42.57	      (Eq
41.99/42.57	        (Eq (cP (cP (skS.0 0 a_3) (skS.0 2 a_3 a_4)) (skS.0 4 a_3 a_4 a_5))
41.99/42.57	          (cP (skS.0 0 a_3) (cP (skS.0 2 a_3 a_4) (skS.0 4 a_3 a_4 a_5))))
41.99/42.57	        False)
41.99/42.57	      (Eq (Eq (cP (skS.0 1 a_1) a_6) (skS.0 3 a_1 a_2)) False))
41.99/42.57	Clause #39 (by clausification #[38]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
41.99/42.57	  Or
41.99/42.57	    (Eq
41.99/42.57	      (Eq (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3))
41.99/42.57	        (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3))))
41.99/42.57	      False)
41.99/42.57	    (Or (Eq (Eq (cP (skS.0 1 a_4) a_5) (skS.0 3 a_4 a_6)) False)
41.99/42.57	      (Eq (Eq (cP a_7 (skS.0 1 a_4)) (skS.0 3 a_4 a_6)) False))
41.99/42.57	Clause #40 (by clausification #[39]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
41.99/42.57	  Or (Eq (Eq (cP (skS.0 1 a_1) a_2) (skS.0 3 a_1 a_3)) False)
41.99/42.57	    (Or (Eq (Eq (cP a_4 (skS.0 1 a_1)) (skS.0 3 a_1 a_3)) False)
41.99/42.58	      (Ne (cP (cP (skS.0 0 a_5) (skS.0 2 a_5 a_6)) (skS.0 4 a_5 a_6 a_7))
41.99/42.58	        (cP (skS.0 0 a_5) (cP (skS.0 2 a_5 a_6) (skS.0 4 a_5 a_6 a_7)))))
41.99/42.58	Clause #41 (by clausification #[40]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
41.99/42.58	  Or (Eq (Eq (cP a_1 (skS.0 1 a_2)) (skS.0 3 a_2 a_3)) False)
41.99/42.58	    (Or
41.99/42.58	      (Ne (cP (cP (skS.0 0 a_4) (skS.0 2 a_4 a_5)) (skS.0 4 a_4 a_5 a_6))
41.99/42.58	        (cP (skS.0 0 a_4) (cP (skS.0 2 a_4 a_5) (skS.0 4 a_4 a_5 a_6))))
41.99/42.58	      (Ne (cP (skS.0 1 a_2) a_7) (skS.0 3 a_2 a_3)))
41.99/42.58	Clause #42 (by clausification #[41]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
41.99/42.58	  Or
41.99/42.58	    (Ne (cP (cP (skS.0 0 a_1) (skS.0 2 a_1 a_2)) (skS.0 4 a_1 a_2 a_3))
41.99/42.58	      (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3))))
41.99/42.58	    (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)))
41.99/42.58	Clause #43 (by forward demodulation #[42, 9]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 a_7 : a),
41.99/42.58	  Or
41.99/42.58	    (Ne (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3)))
42.04/42.63	      (cP (skS.0 0 a_1) (cP (skS.0 2 a_1 a_2) (skS.0 4 a_1 a_2 a_3))))
42.04/42.63	    (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)))
42.04/42.63	Clause #44 (by eliminate resolved literals #[43]): ∀ (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))
42.04/42.63	Clause #45 (by clausification #[20]): ∀ (a_1 : a), Eq (Eq (cP (cJ a_1) a_1) cE) True
42.04/42.63	Clause #46 (by clausification #[45]): ∀ (a_1 : a), Eq (cP (cJ a_1) a_1) cE
42.04/42.63	Clause #48 (by superposition #[46, 9]): ∀ (a_1 a_2 : a), Eq (cP cE a_1) (cP (cJ a_2) (cP a_2 a_1))
42.04/42.63	Clause #50 (by forward demodulation #[48, 22]): ∀ (a_1 a_2 : a), Eq a_1 (cP (cJ a_2) (cP a_2 a_1))
42.04/42.63	Clause #54 (by superposition #[50, 50]): ∀ (a_1 a_2 : a), Eq (cP a_1 a_2) (cP (cJ (cJ a_1)) a_2)
42.04/42.63	Clause #55 (by superposition #[50, 9]): ∀ (a_1 a_2 a_3 : a), Eq a_1 (cP (cJ (cP a_2 a_3)) (cP a_2 (cP a_3 a_1)))
42.04/42.63	Clause #58 (by superposition #[50, 46]): ∀ (a_1 : a), Eq a_1 (cP (cJ (cJ a_1)) cE)
42.04/42.63	Clause #162 (by superposition #[54, 50]): ∀ (a_1 a_2 : a), Eq a_1 (cP a_2 (cP (cJ a_2) a_1))
42.04/42.63	Clause #175 (by superposition #[54, 58]): ∀ (a_1 : a), Eq (cP a_1 cE) a_1
42.04/42.63	Clause #211 (by superposition #[162, 44]): ∀ (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))
42.04/42.63	Clause #251 (by superposition #[55, 46]): ∀ (a_1 a_2 : a), Eq a_1 (cP (cJ (cP a_2 (cJ a_1))) (cP a_2 cE))
42.04/42.63	Clause #301 (by forward demodulation #[251, 175]): ∀ (a_1 a_2 : a), Eq a_1 (cP (cJ (cP a_2 (cJ a_1))) a_2)
42.04/42.63	Clause #311 (by superposition #[301, 162]): ∀ (a_1 a_2 : a), Eq a_1 (cP (cP a_1 (cJ a_2)) a_2)
42.04/42.63	Clause #3675 (by destructive equality resolution #[211]): ∀ (a_1 a_2 a_3 : a), Ne (cP a_1 (skS.0 1 a_2)) (skS.0 3 a_2 a_3)
42.04/42.63	Clause #3681 (by superposition #[3675, 311]): ∀ (a_1 a_2 a_3 : a), Ne a_1 (skS.0 3 a_2 a_3)
42.04/42.63	Clause #3687 (by destructive equality resolution #[3681]): False
42.04/42.63	SZS output end Proof for theBenchmark.p
42.05/42.63	EOF