0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : duper %s
0.13/0.34	% Computer : n022.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1440
0.13/0.34	% WCLimit    : 180
0.13/0.34	% DateTime   : Mon Jul  3 04:01:29 EDT 2023
0.13/0.34	% CPUTime    : 
13.26/13.43	SZS status Theorem for theBenchmark.p
13.26/13.43	SZS output start Proof for theBenchmark.p
13.26/13.43	Clause #0 (by assumption #[]): Eq
13.26/13.43	  (Not
13.26/13.43	    ((Exists fun Xf =>
13.26/13.43	        ∀ (Xx : a),
13.26/13.43	          And (And (Exists fun Xz => Xf Xx Xz) (Xf Xx Xx))
13.26/13.43	            (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) →
13.26/13.43	      And (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xy Xz) (cQ Xx Xy) → cQ Xx Xz))
13.26/13.43	        (∀ (Xx : a), cQ Xx Xx)))
13.26/13.43	  True
13.26/13.43	Clause #1 (by betaEtaReduce #[0]): Eq
13.26/13.43	  (Not
13.26/13.43	    ((Exists fun Xf =>
13.26/13.43	        ∀ (Xx : a),
13.26/13.43	          And (And (Exists (Xf Xx)) (Xf Xx Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) →
13.26/13.43	      And (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xy Xz) (cQ Xx Xy) → cQ Xx Xz))
13.26/13.43	        (∀ (Xx : a), cQ Xx Xx)))
13.26/13.43	  True
13.26/13.43	Clause #2 (by clausification #[1]): Eq
13.26/13.43	  ((Exists fun Xf =>
13.26/13.43	      ∀ (Xx : a),
13.26/13.43	        And (And (Exists (Xf Xx)) (Xf Xx Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) →
13.26/13.43	    And (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xy Xz) (cQ Xx Xy) → cQ Xx Xz))
13.26/13.43	      (∀ (Xx : a), cQ Xx Xx))
13.26/13.43	  False
13.26/13.43	Clause #3 (by clausification #[2]): Eq
13.26/13.43	  (Exists fun Xf =>
13.26/13.43	    ∀ (Xx : a),
13.26/13.43	      And (And (Exists (Xf Xx)) (Xf Xx Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy)))
13.26/13.43	  True
13.26/13.43	Clause #4 (by clausification #[2]): Eq
13.26/13.43	  (And (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xy Xz) (cQ Xx Xy) → cQ Xx Xz))
13.26/13.43	    (∀ (Xx : a), cQ Xx Xx))
13.26/13.43	  False
13.26/13.43	Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → Prop),
13.26/13.43	  Eq
13.26/13.43	    (∀ (Xx : a),
13.26/13.43	      And (And (Exists (skS.0 0 a_1 Xx)) (skS.0 0 a_1 Xx Xx))
13.26/13.43	        (∀ (Xx_0 : a), skS.0 0 a_1 Xx Xx_0 → ∀ (Xy : a), Iff (skS.0 0 a_1 Xx Xy) (cQ Xx_0 Xy)))
13.26/13.43	    True
13.26/13.43	Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : a),
13.26/13.43	  Eq
13.26/13.43	    (And (And (Exists (skS.0 0 a_1 a_2)) (skS.0 0 a_1 a_2 a_2))
13.26/13.43	      (∀ (Xx_0 : a), skS.0 0 a_1 a_2 Xx_0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx_0 Xy)))
13.26/13.43	    True
13.26/13.43	Clause #7 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a),
13.26/13.43	  Eq (∀ (Xx_0 : a), skS.0 0 a_1 a_2 Xx_0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx_0 Xy)) True
13.26/13.43	Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (And (Exists (skS.0 0 a_1 a_2)) (skS.0 0 a_1 a_2 a_2)) True
13.26/13.43	Clause #9 (by clausification #[7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 a_2 a_3 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ a_3 Xy)) True
13.26/13.43	Clause #10 (by clausification #[9]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a),
13.26/13.43	  Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ a_3 Xy)) True)
13.26/13.43	Clause #11 (by clausification #[10]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.26/13.43	  Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (Iff (skS.0 0 a_1 a_2 a_4) (cQ a_3 a_4)) True)
13.26/13.43	Clause #12 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.26/13.43	  Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Or (Eq (skS.0 0 a_1 a_2 a_4) True) (Eq (cQ a_3 a_4) False))
13.26/13.43	Clause #13 (by clausification #[11]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.26/13.43	  Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Or (Eq (skS.0 0 a_1 a_2 a_4) False) (Eq (cQ a_3 a_4) True))
13.26/13.43	Clause #14 (by clausification #[4]): Or (Eq (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xy Xz) (cQ Xx Xy) → cQ Xx Xz)) False)
13.26/13.43	  (Eq (∀ (Xx : a), cQ Xx Xx) False)
13.26/13.43	Clause #15 (by clausification #[14]): Or (Eq (∀ (Xx : a), cQ Xx Xx) False)
13.26/13.43	  (Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False)
13.26/13.43	    (Eq (∀ (Xx Xy Xz : a), And (cQ Xy Xz) (cQ Xx Xy) → cQ Xx Xz) False))
13.26/13.43	Clause #16 (by clausification #[15]): ∀ (a_1 : a),
13.26/13.43	  Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False)
13.26/13.43	    (Or (Eq (∀ (Xx Xy Xz : a), And (cQ Xy Xz) (cQ Xx Xy) → cQ Xx Xz) False)
13.26/13.43	      (Eq (Not (cQ (skS.0 1 a_1) (skS.0 1 a_1))) True))
13.26/13.43	Clause #17 (by clausification #[16]): ∀ (a_1 a_2 : a),
13.26/13.43	  Or (Eq (∀ (Xx Xy Xz : a), And (cQ Xy Xz) (cQ Xx Xy) → cQ Xx Xz) False)
13.27/13.46	    (Or (Eq (Not (cQ (skS.0 1 a_1) (skS.0 1 a_1))) True)
13.27/13.46	      (Eq (Not (∀ (Xy : a), cQ (skS.0 2 a_2) Xy → cQ Xy (skS.0 2 a_2))) True))
13.27/13.46	Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a),
13.27/13.46	  Or (Eq (Not (cQ (skS.0 1 a_1) (skS.0 1 a_1))) True)
13.27/13.46	    (Or (Eq (Not (∀ (Xy : a), cQ (skS.0 2 a_2) Xy → cQ Xy (skS.0 2 a_2))) True)
13.27/13.46	      (Eq (Not (∀ (Xy Xz : a), And (cQ Xy Xz) (cQ (skS.0 3 a_3) Xy) → cQ (skS.0 3 a_3) Xz)) True))
13.27/13.46	Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 : a),
13.27/13.46	  Or (Eq (Not (∀ (Xy : a), cQ (skS.0 2 a_1) Xy → cQ Xy (skS.0 2 a_1))) True)
13.27/13.46	    (Or (Eq (Not (∀ (Xy Xz : a), And (cQ Xy Xz) (cQ (skS.0 3 a_2) Xy) → cQ (skS.0 3 a_2) Xz)) True)
13.27/13.46	      (Eq (cQ (skS.0 1 a_3) (skS.0 1 a_3)) False))
13.27/13.46	Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a),
13.27/13.46	  Or (Eq (Not (∀ (Xy Xz : a), And (cQ Xy Xz) (cQ (skS.0 3 a_1) Xy) → cQ (skS.0 3 a_1) Xz)) True)
13.27/13.46	    (Or (Eq (cQ (skS.0 1 a_2) (skS.0 1 a_2)) False) (Eq (∀ (Xy : a), cQ (skS.0 2 a_3) Xy → cQ Xy (skS.0 2 a_3)) False))
13.27/13.46	Clause #21 (by clausification #[20]): ∀ (a_1 a_2 a_3 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or (Eq (∀ (Xy : a), cQ (skS.0 2 a_2) Xy → cQ Xy (skS.0 2 a_2)) False)
13.27/13.46	      (Eq (∀ (Xy Xz : a), And (cQ Xy Xz) (cQ (skS.0 3 a_3) Xy) → cQ (skS.0 3 a_3) Xz) False))
13.27/13.46	Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or (Eq (∀ (Xy Xz : a), And (cQ Xy Xz) (cQ (skS.0 3 a_2) Xy) → cQ (skS.0 3 a_2) Xz) False)
13.27/13.46	      (Eq (Not (cQ (skS.0 2 a_3) (skS.0 4 a_3 a_4) → cQ (skS.0 4 a_3 a_4) (skS.0 2 a_3))) True))
13.27/13.46	Clause #23 (by clausification #[22]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or (Eq (Not (cQ (skS.0 2 a_2) (skS.0 4 a_2 a_3) → cQ (skS.0 4 a_2 a_3) (skS.0 2 a_2))) True)
13.27/13.46	      (Eq (Not (∀ (Xz : a), And (cQ (skS.0 5 a_4 a_5) Xz) (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) → cQ (skS.0 3 a_4) Xz))
13.27/13.46	        True))
13.27/13.46	Clause #24 (by clausification #[23]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or
13.27/13.46	      (Eq (Not (∀ (Xz : a), And (cQ (skS.0 5 a_2 a_3) Xz) (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) → cQ (skS.0 3 a_2) Xz))
13.27/13.46	        True)
13.27/13.46	      (Eq (cQ (skS.0 2 a_4) (skS.0 4 a_4 a_5) → cQ (skS.0 4 a_4 a_5) (skS.0 2 a_4)) False))
13.27/13.46	Clause #25 (by clausification #[24]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or (Eq (cQ (skS.0 2 a_2) (skS.0 4 a_2 a_3) → cQ (skS.0 4 a_2 a_3) (skS.0 2 a_2)) False)
13.27/13.46	      (Eq (∀ (Xz : a), And (cQ (skS.0 5 a_4 a_5) Xz) (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) → cQ (skS.0 3 a_4) Xz) False))
13.27/13.46	Clause #26 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or
13.27/13.46	      (Eq (∀ (Xz : a), And (cQ (skS.0 5 a_2 a_3) Xz) (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) → cQ (skS.0 3 a_2) Xz) False)
13.27/13.46	      (Eq (cQ (skS.0 2 a_4) (skS.0 4 a_4 a_5)) True))
13.27/13.46	Clause #27 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or
13.27/13.46	      (Eq (∀ (Xz : a), And (cQ (skS.0 5 a_2 a_3) Xz) (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) → cQ (skS.0 3 a_2) Xz) False)
13.27/13.46	      (Eq (cQ (skS.0 4 a_4 a_5) (skS.0 2 a_4)) False))
13.27/13.46	Clause #28 (by clausification #[26]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or (Eq (cQ (skS.0 2 a_2) (skS.0 4 a_2 a_3)) True)
13.27/13.46	      (Eq
13.27/13.46	        (Not
13.27/13.46	          (And (cQ (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) →
13.27/13.46	            cQ (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6)))
13.27/13.46	        True))
13.27/13.46	Clause #29 (by clausification #[28]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.46	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.46	    (Or (Eq (cQ (skS.0 2 a_2) (skS.0 4 a_2 a_3)) True)
13.27/13.46	      (Eq
13.27/13.46	        (And (cQ (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) →
13.27/13.46	          cQ (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6))
13.27/13.46	        False))
13.27/13.46	Clause #30 (by clausification #[29]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 2 a_2) (skS.0 4 a_2 a_3)) True)
13.27/13.48	      (Eq (And (cQ (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5))) True))
13.27/13.48	Clause #31 (by clausification #[29]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 2 a_2) (skS.0 4 a_2 a_3)) True) (Eq (cQ (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6)) False))
13.27/13.48	Clause #32 (by clausification #[30]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 2 a_2) (skS.0 4 a_2 a_3)) True) (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True))
13.27/13.48	Clause #33 (by clausification #[30]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 2 a_2) (skS.0 4 a_2 a_3)) True) (Eq (cQ (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True))
13.27/13.48	Clause #34 (by clausification #[8]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 a_2 a_2) True
13.27/13.48	Clause #36 (by superposition #[34, 12]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq True False) (Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Eq (cQ a_2 a_3) False))
13.27/13.48	Clause #39 (by clausification #[36]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Eq (cQ a_2 a_3) False)
13.27/13.48	Clause #41 (by superposition #[13, 34]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq True False) (Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (cQ a_2 a_3) True))
13.27/13.48	Clause #42 (by clausification #[41]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (cQ a_2 a_3) True)
13.27/13.48	Clause #44 (by superposition #[42, 34]): ∀ (a : a), Or (Eq (cQ a a) True) (Eq False True)
13.27/13.48	Clause #45 (by clausification #[44]): ∀ (a : a), Eq (cQ a a) True
13.27/13.48	Clause #46 (by superposition #[45, 32]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.48	  Or (Eq True False) (Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True))
13.27/13.48	Clause #54 (by clausification #[27]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 4 a_2 a_3) (skS.0 2 a_2)) False)
13.27/13.48	      (Eq
13.27/13.48	        (Not
13.27/13.48	          (And (cQ (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) →
13.27/13.48	            cQ (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6)))
13.27/13.48	        True))
13.27/13.48	Clause #55 (by clausification #[54]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 4 a_2 a_3) (skS.0 2 a_2)) False)
13.27/13.48	      (Eq
13.27/13.48	        (And (cQ (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) →
13.27/13.48	          cQ (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))
13.27/13.48	        False))
13.27/13.48	Clause #56 (by clausification #[55]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 4 a_2 a_3) (skS.0 2 a_2)) False)
13.27/13.48	      (Eq (And (cQ (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5))) True))
13.27/13.48	Clause #57 (by clausification #[55]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 4 a_2 a_3) (skS.0 2 a_2)) False) (Eq (cQ (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6)) False))
13.27/13.48	Clause #58 (by clausification #[56]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 4 a_2 a_3) (skS.0 2 a_2)) False) (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True))
13.27/13.48	Clause #59 (by clausification #[56]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 1 a_1) (skS.0 1 a_1)) False)
13.27/13.48	    (Or (Eq (cQ (skS.0 4 a_2 a_3) (skS.0 2 a_2)) False) (Eq (cQ (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) True))
13.27/13.48	Clause #60 (by superposition #[58, 45]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.48	  Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 2 a_1)) False) (Or (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True) (Eq False True))
13.27/13.48	Clause #68 (by superposition #[31, 45]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.48	  Or (Eq True False)
13.27/13.48	    (Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 3 a_3) (skS.0 6 a_3 a_4 a_5)) False))
13.27/13.48	Clause #81 (by superposition #[33, 45]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.51	  Or (Eq True False)
13.27/13.51	    (Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) True))
13.27/13.51	Clause #94 (by clausification #[46]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True)
13.27/13.51	Clause #95 (by superposition #[94, 39]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
13.27/13.51	    (Or (Eq (skS.0 0 a_3 (skS.0 2 a_4) (skS.0 4 a_4 a_5)) True) (Eq True False))
13.27/13.51	Clause #108 (by superposition #[57, 45]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 2 a_1)) False)
13.27/13.51	    (Or (Eq (cQ (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5)) False) (Eq False True))
13.27/13.51	Clause #118 (by superposition #[59, 45]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 2 a_1)) False)
13.27/13.51	    (Or (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) True) (Eq False True))
13.27/13.51	Clause #130 (by clausification #[60]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 2 a_1)) False) (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True)
13.27/13.51	Clause #131 (by clausification #[68]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 3 a_3) (skS.0 6 a_3 a_4 a_5)) False)
13.27/13.51	Clause #155 (by clausification #[81]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) True)
13.27/13.51	Clause #159 (by superposition #[155, 39]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True)
13.27/13.51	    (Or (Eq (skS.0 0 a_3 (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True) (Eq True False))
13.27/13.51	Clause #178 (by clausification #[108]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 2 a_1)) False) (Eq (cQ (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5)) False)
13.27/13.51	Clause #179 (by clausification #[118]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 2 a_1)) False) (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) True)
13.27/13.51	Clause #204 (by clausification #[95]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (skS.0 0 a_3 (skS.0 2 a_4) (skS.0 4 a_4 a_5)) True)
13.27/13.51	Clause #209 (by superposition #[204, 13]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
13.27/13.51	    (Or (Eq True False) (Or (Eq (skS.0 0 a_3 (skS.0 2 a_4) a_5) False) (Eq (cQ (skS.0 4 a_4 a_6) a_5) True)))
13.27/13.51	Clause #328 (by clausification #[159]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq (skS.0 0 a_3 (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True)
13.27/13.51	Clause #482 (by clausification #[209]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
13.27/13.51	    (Or (Eq (skS.0 0 a_3 (skS.0 2 a_4) a_5) False) (Eq (cQ (skS.0 4 a_4 a_6) a_5) True))
13.27/13.51	Clause #490 (by superposition #[482, 34]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Or (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 2 a_3)) True) (Eq False True))
13.27/13.51	Clause #500 (by clausification #[490]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 2 a_3)) True)
13.27/13.51	Clause #506 (by superposition #[500, 130]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Or (Eq True False) (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True))
13.27/13.51	Clause #514 (by clausification #[506]): ∀ (a_1 a_2 a_3 a_4 : a),
13.27/13.51	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True)
13.27/13.51	Clause #520 (by equality factoring #[514]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
13.27/13.51	Clause #521 (by clausification #[520]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Or (Eq True False) (Eq True False))
13.27/13.51	Clause #523 (by clausification #[521]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq True False)
13.35/13.54	Clause #524 (by clausification #[523]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True
13.35/13.54	Clause #526 (by superposition #[524, 39]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq True False)
13.35/13.54	Clause #530 (by clausification #[526]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True
13.35/13.54	Clause #532 (by superposition #[530, 12]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) a_3) True) (Eq (cQ (skS.0 5 a_2 a_4) a_3) False))
13.35/13.54	Clause #533 (by superposition #[530, 13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) a_3) False) (Eq (cQ (skS.0 5 a_2 a_4) a_3) True))
13.35/13.54	Clause #540 (by clausification #[533]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) a_3) False) (Eq (cQ (skS.0 5 a_2 a_4) a_3) True)
13.35/13.54	Clause #546 (by superposition #[540, 34]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True) (Eq False True)
13.35/13.54	Clause #547 (by clausification #[546]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True
13.35/13.54	Clause #549 (by superposition #[547, 39]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 5 a_2 a_3) (skS.0 3 a_2)) True) (Eq True False)
13.35/13.54	Clause #563 (by clausification #[549]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 5 a_2 a_3) (skS.0 3 a_2)) True
13.35/13.54	Clause #566 (by superposition #[563, 13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 5 a_2 a_3) a_4) False) (Eq (cQ (skS.0 3 a_2) a_4) True))
13.35/13.54	Clause #598 (by clausification #[532]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) a_3) True) (Eq (cQ (skS.0 5 a_2 a_4) a_3) False)
13.35/13.54	Clause #611 (by clausification #[566]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq (skS.0 0 a_1 (skS.0 5 a_2 a_3) a_4) False) (Eq (cQ (skS.0 3 a_2) a_4) True)
13.35/13.54	Clause #612 (by superposition #[611, 328]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.35/13.54	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 6 a_1 a_2 a_3)) True)
13.35/13.54	    (Or (Eq (cQ (skS.0 2 a_4) (skS.0 4 a_4 a_5)) True) (Eq False True))
13.35/13.54	Clause #724 (by clausification #[612]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
13.35/13.54	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 6 a_1 a_2 a_3)) True) (Eq (cQ (skS.0 2 a_4) (skS.0 4 a_4 a_5)) True)
13.35/13.54	Clause #725 (by superposition #[724, 131]): ∀ (a_1 a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Or (Eq (cQ (skS.0 2 a_3) (skS.0 4 a_3 a_4)) True) (Eq True False))
13.35/13.54	Clause #735 (by clausification #[725]): ∀ (a_1 a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 2 a_3) (skS.0 4 a_3 a_4)) True)
13.35/13.54	Clause #740 (by equality factoring #[735]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True)
13.35/13.54	Clause #741 (by clausification #[740]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Or (Eq True False) (Eq True False))
13.35/13.54	Clause #743 (by clausification #[741]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True) (Eq True False)
13.35/13.54	Clause #744 (by clausification #[743]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 2 a_1) (skS.0 4 a_1 a_2)) True
13.35/13.54	Clause #745 (by superposition #[744, 39]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 2 a_2) (skS.0 4 a_2 a_3)) True) (Eq True False)
13.35/13.54	Clause #759 (by clausification #[745]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 2 a_2) (skS.0 4 a_2 a_3)) True
13.35/13.54	Clause #761 (by superposition #[759, 13]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 2 a_2) a_3) False) (Eq (cQ (skS.0 4 a_2 a_4) a_3) True))
13.35/13.54	Clause #768 (by clausification #[761]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
13.35/13.54	  Or (Eq (skS.0 0 a_1 (skS.0 2 a_2) a_3) False) (Eq (cQ (skS.0 4 a_2 a_4) a_3) True)
13.35/13.54	Clause #774 (by superposition #[768, 34]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 2 a_1)) True) (Eq False True)
13.35/13.55	Clause #776 (by clausification #[774]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 4 a_1 a_2) (skS.0 2 a_1)) True
13.35/13.55	Clause #777 (by superposition #[776, 178]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 3 a_1) (skS.0 8 a_1 a_2 a_3)) False)
13.35/13.55	Clause #778 (by superposition #[776, 179]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 8 a_1 a_2 a_3)) True)
13.35/13.55	Clause #783 (by clausification #[777]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 3 a_1) (skS.0 8 a_1 a_2 a_3)) False
13.35/13.55	Clause #789 (by clausification #[778]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 5 a_1 a_2) (skS.0 8 a_1 a_2 a_3)) True
13.35/13.55	Clause #790 (by superposition #[789, 598]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_2) (skS.0 8 a_2 a_3 a_4)) True) (Eq True False)
13.35/13.55	Clause #816 (by clausification #[790]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Eq (skS.0 0 a_1 (skS.0 3 a_2) (skS.0 8 a_2 a_3 a_4)) True
13.35/13.55	Clause #820 (by superposition #[816, 42]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 3 a_1) (skS.0 8 a_1 a_2 a_3)) True)
13.35/13.55	Clause #824 (by clausification #[820]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 3 a_1) (skS.0 8 a_1 a_2 a_3)) True
13.35/13.55	Clause #825 (by superposition #[824, 783]): Eq True False
13.35/13.55	Clause #829 (by clausification #[825]): False
13.35/13.55	SZS output end Proof for theBenchmark.p
13.35/13.55	EOF