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 : n004.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 03:47:45 EDT 2023
0.13/0.34	% CPUTime    : 
14.18/14.36	SZS status Theorem for theBenchmark.p
14.18/14.36	SZS output start Proof for theBenchmark.p
14.18/14.36	Clause #0 (by assumption #[]): Eq
14.18/14.36	  (Not
14.18/14.36	    ((∀ (Xx : a),
14.18/14.36	        Exists fun Xp =>
14.18/14.36	          And (And (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy)) (Xp Xx)) (Exists fun Xz => Xp Xz)) →
14.18/14.36	      And (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
14.18/14.36	        (∀ (Xx : a), cQ Xx Xx)))
14.18/14.36	  True
14.18/14.36	Clause #1 (by betaEtaReduce #[0]): Eq
14.18/14.36	  (Not
14.18/14.36	    ((∀ (Xx : a),
14.18/14.36	        Exists fun Xp => And (And (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy)) (Xp Xx)) (Exists Xp)) →
14.18/14.36	      And (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
14.18/14.36	        (∀ (Xx : a), cQ Xx Xx)))
14.18/14.36	  True
14.18/14.36	Clause #2 (by clausification #[1]): Eq
14.18/14.36	  ((∀ (Xx : a),
14.18/14.36	      Exists fun Xp => And (And (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy)) (Xp Xx)) (Exists Xp)) →
14.18/14.36	    And (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
14.18/14.36	      (∀ (Xx : a), cQ Xx Xx))
14.18/14.36	  False
14.18/14.36	Clause #3 (by clausification #[2]): Eq
14.18/14.36	  (∀ (Xx : a),
14.18/14.36	    Exists fun Xp => And (And (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy)) (Xp Xx)) (Exists Xp))
14.18/14.36	  True
14.18/14.36	Clause #4 (by clausification #[2]): Eq
14.18/14.36	  (And (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
14.18/14.36	    (∀ (Xx : a), cQ Xx Xx))
14.18/14.36	  False
14.18/14.36	Clause #5 (by clausification #[3]): ∀ (a_1 : a),
14.18/14.36	  Eq (Exists fun Xp => And (And (∀ (Xx0 : a), Xp Xx0 → ∀ (Xy : a), Iff (Xp Xy) (cQ Xx0 Xy)) (Xp a_1)) (Exists Xp)) True
14.18/14.36	Clause #6 (by clausification #[5]): ∀ (a_1 : a) (a_2 : a → Prop),
14.18/14.36	  Eq
14.18/14.36	    (And
14.18/14.36	      (And (∀ (Xx0 : a), skS.0 0 a_1 a_2 Xx0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx0 Xy)) (skS.0 0 a_1 a_2 a_1))
14.18/14.36	      (Exists (skS.0 0 a_1 a_2)))
14.18/14.36	    True
14.18/14.36	Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : a → Prop),
14.18/14.36	  Eq (And (∀ (Xx0 : a), skS.0 0 a_1 a_2 Xx0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx0 Xy)) (skS.0 0 a_1 a_2 a_1))
14.18/14.36	    True
14.18/14.36	Clause #10 (by clausification #[4]): Or (Eq (And (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)) False)
14.18/14.36	  (Eq (∀ (Xx : a), cQ Xx Xx) False)
14.18/14.36	Clause #11 (by clausification #[10]): Or (Eq (∀ (Xx : a), cQ Xx Xx) False)
14.18/14.36	  (Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False)
14.18/14.36	    (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False))
14.18/14.36	Clause #12 (by clausification #[11]): ∀ (a_1 : a),
14.18/14.36	  Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False)
14.18/14.36	    (Or (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False)
14.18/14.36	      (Eq (Not (cQ (skS.0 2 a_1) (skS.0 2 a_1))) True))
14.18/14.36	Clause #13 (by clausification #[12]): ∀ (a_1 a_2 : a),
14.18/14.36	  Or (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False)
14.18/14.36	    (Or (Eq (Not (cQ (skS.0 2 a_1) (skS.0 2 a_1))) True)
14.18/14.36	      (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2))) True))
14.18/14.36	Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a),
14.18/14.36	  Or (Eq (Not (cQ (skS.0 2 a_1) (skS.0 2 a_1))) True)
14.18/14.36	    (Or (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2))) True)
14.18/14.36	      (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 4 a_3) Xy) (cQ Xy Xz) → cQ (skS.0 4 a_3) Xz)) True))
14.18/14.36	Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a),
14.18/14.36	  Or (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_1) Xy → cQ Xy (skS.0 3 a_1))) True)
14.18/14.36	    (Or (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 4 a_2) Xy) (cQ Xy Xz) → cQ (skS.0 4 a_2) Xz)) True)
14.18/14.36	      (Eq (cQ (skS.0 2 a_3) (skS.0 2 a_3)) False))
14.18/14.36	Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a),
14.18/14.36	  Or (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 4 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 4 a_1) Xz)) True)
14.18/14.36	    (Or (Eq (cQ (skS.0 2 a_2) (skS.0 2 a_2)) False) (Eq (∀ (Xy : a), cQ (skS.0 3 a_3) Xy → cQ Xy (skS.0 3 a_3)) False))
14.18/14.36	Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a),
14.18/14.36	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.18/14.36	    (Or (Eq (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2)) False)
14.22/14.39	      (Eq (∀ (Xy Xz : a), And (cQ (skS.0 4 a_3) Xy) (cQ Xy Xz) → cQ (skS.0 4 a_3) Xz) False))
14.22/14.39	Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a_3 a_4 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (∀ (Xy Xz : a), And (cQ (skS.0 4 a_2) Xy) (cQ Xy Xz) → cQ (skS.0 4 a_2) Xz) False)
14.22/14.39	      (Eq (Not (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4) → cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3))) True))
14.22/14.39	Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (Not (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3) → cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2))) True)
14.22/14.39	      (Eq (Not (∀ (Xz : a), And (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) (cQ (skS.0 6 a_4 a_5) Xz) → cQ (skS.0 4 a_4) Xz))
14.22/14.39	        True))
14.22/14.39	Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or
14.22/14.39	      (Eq (Not (∀ (Xz : a), And (cQ (skS.0 4 a_2) (skS.0 6 a_2 a_3)) (cQ (skS.0 6 a_2 a_3) Xz) → cQ (skS.0 4 a_2) Xz))
14.22/14.39	        True)
14.22/14.39	      (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5) → cQ (skS.0 5 a_4 a_5) (skS.0 3 a_4)) False))
14.22/14.39	Clause #21 (by clausification #[20]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3) → cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False)
14.22/14.39	      (Eq (∀ (Xz : a), And (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) (cQ (skS.0 6 a_4 a_5) Xz) → cQ (skS.0 4 a_4) Xz) False))
14.22/14.39	Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or
14.22/14.39	      (Eq (∀ (Xz : a), And (cQ (skS.0 4 a_2) (skS.0 6 a_2 a_3)) (cQ (skS.0 6 a_2 a_3) Xz) → cQ (skS.0 4 a_2) Xz) False)
14.22/14.39	      (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True))
14.22/14.39	Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or
14.22/14.39	      (Eq (∀ (Xz : a), And (cQ (skS.0 4 a_2) (skS.0 6 a_2 a_3)) (cQ (skS.0 6 a_2 a_3) Xz) → cQ (skS.0 4 a_2) Xz) False)
14.22/14.39	      (Eq (cQ (skS.0 5 a_4 a_5) (skS.0 3 a_4)) False))
14.22/14.39	Clause #24 (by clausification #[22]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True)
14.22/14.39	      (Eq
14.22/14.39	        (Not
14.22/14.39	          (And (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) (cQ (skS.0 6 a_4 a_5) (skS.0 7 a_4 a_5 a_6)) →
14.22/14.39	            cQ (skS.0 4 a_4) (skS.0 7 a_4 a_5 a_6)))
14.22/14.39	        True))
14.22/14.39	Clause #25 (by clausification #[24]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True)
14.22/14.39	      (Eq
14.22/14.39	        (And (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) (cQ (skS.0 6 a_4 a_5) (skS.0 7 a_4 a_5 a_6)) →
14.22/14.39	          cQ (skS.0 4 a_4) (skS.0 7 a_4 a_5 a_6))
14.22/14.39	        False))
14.22/14.39	Clause #26 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True)
14.22/14.39	      (Eq (And (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) (cQ (skS.0 6 a_4 a_5) (skS.0 7 a_4 a_5 a_6))) True))
14.22/14.39	Clause #27 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 4 a_4) (skS.0 7 a_4 a_5 a_6)) False))
14.22/14.39	Clause #28 (by clausification #[26]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 6 a_4 a_5) (skS.0 7 a_4 a_5 a_6)) True))
14.22/14.39	Clause #29 (by clausification #[26]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.39	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.39	    (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) True))
14.22/14.39	Clause #30 (by clausification #[8]): ∀ (a_1 : a) (a_2 : a → Prop), Eq (skS.0 0 a_1 a_2 a_1) True
14.22/14.39	Clause #31 (by clausification #[8]): ∀ (a_1 : a) (a_2 : a → Prop),
14.22/14.39	  Eq (∀ (Xx0 : a), skS.0 0 a_1 a_2 Xx0 → ∀ (Xy : a), Iff (skS.0 0 a_1 a_2 Xy) (cQ Xx0 Xy)) True
14.22/14.39	Clause #32 (by clausification #[31]): ∀ (a_1 : a) (a_2 : a → Prop) (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
14.22/14.42	Clause #33 (by clausification #[32]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a),
14.22/14.42	  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)
14.22/14.42	Clause #34 (by clausification #[33]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a),
14.22/14.42	  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)
14.22/14.42	Clause #35 (by clausification #[34]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a),
14.22/14.42	  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))
14.22/14.42	Clause #36 (by clausification #[34]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a),
14.22/14.42	  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))
14.22/14.42	Clause #38 (by superposition #[35, 30]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a),
14.22/14.42	  Or (Eq (skS.0 0 a_1 (fun x => a_2 x) a_3) True) (Or (Eq (cQ a_1 a_3) False) (Eq False True))
14.22/14.42	Clause #39 (by betaEtaReduce #[38]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Or (Eq (cQ a_1 a_3) False) (Eq False True))
14.22/14.42	Clause #40 (by clausification #[39]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Eq (cQ a_1 a_3) False)
14.22/14.42	Clause #41 (by clausification #[23]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.42	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.42	    (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False)
14.22/14.42	      (Eq
14.22/14.42	        (Not
14.22/14.42	          (And (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) (cQ (skS.0 6 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) →
14.22/14.42	            cQ (skS.0 4 a_4) (skS.0 8 a_4 a_5 a_6)))
14.22/14.42	        True))
14.22/14.42	Clause #42 (by clausification #[41]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.42	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.42	    (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False)
14.22/14.42	      (Eq
14.22/14.42	        (And (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) (cQ (skS.0 6 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) →
14.22/14.42	          cQ (skS.0 4 a_4) (skS.0 8 a_4 a_5 a_6))
14.22/14.42	        False))
14.22/14.42	Clause #43 (by clausification #[42]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.42	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.42	    (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False)
14.22/14.42	      (Eq (And (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) (cQ (skS.0 6 a_4 a_5) (skS.0 8 a_4 a_5 a_6))) True))
14.22/14.42	Clause #44 (by clausification #[42]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.42	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.42	    (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 4 a_4) (skS.0 8 a_4 a_5 a_6)) False))
14.22/14.42	Clause #45 (by clausification #[43]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
14.22/14.42	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.42	    (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 6 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) True))
14.22/14.42	Clause #46 (by clausification #[43]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.42	  Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
14.22/14.42	    (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 4 a_4) (skS.0 6 a_4 a_5)) True))
14.22/14.42	Clause #48 (by superposition #[36, 30]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a),
14.22/14.42	  Or (Eq (skS.0 0 a_1 (fun x => a_2 x) a_3) False) (Or (Eq (cQ a_1 a_3) True) (Eq False True))
14.22/14.42	Clause #49 (by betaEtaReduce #[48]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Or (Eq (cQ a_1 a_3) True) (Eq False True))
14.22/14.42	Clause #50 (by clausification #[49]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Eq (cQ a_1 a_3) True)
14.22/14.42	Clause #52 (by superposition #[50, 30]): ∀ (a : a), Or (Eq (cQ a a) True) (Eq False True)
14.22/14.42	Clause #53 (by clausification #[52]): ∀ (a : a), Eq (cQ a a) True
14.22/14.42	Clause #54 (by superposition #[53, 28]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.42	  Or (Eq True False)
14.22/14.42	    (Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 6 a_3 a_4) (skS.0 7 a_3 a_4 a_5)) True))
14.22/14.42	Clause #55 (by superposition #[53, 45]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.22/14.42	  Or (Eq True False)
14.22/14.42	    (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 6 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) True))
14.28/14.45	Clause #59 (by superposition #[27, 53]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.28/14.45	  Or (Eq True False)
14.28/14.45	    (Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 4 a_3) (skS.0 7 a_3 a_4 a_5)) False))
14.28/14.45	Clause #74 (by superposition #[29, 53]): ∀ (a_1 a_2 a_3 a_4 : a),
14.28/14.45	  Or (Eq True False) (Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 4 a_3) (skS.0 6 a_3 a_4)) True))
14.28/14.45	Clause #100 (by superposition #[44, 53]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.28/14.45	  Or (Eq True False)
14.28/14.45	    (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 4 a_3) (skS.0 8 a_3 a_4 a_5)) False))
14.28/14.45	Clause #117 (by superposition #[46, 53]): ∀ (a_1 a_2 a_3 a_4 : a),
14.28/14.45	  Or (Eq True False) (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 4 a_3) (skS.0 6 a_3 a_4)) True))
14.28/14.45	Clause #125 (by clausification #[54]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 6 a_3 a_4) (skS.0 7 a_3 a_4 a_5)) True)
14.28/14.45	Clause #128 (by superposition #[125, 40]): ∀ (a_1 a_2 a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
14.28/14.45	    (Or (Eq (skS.0 0 (skS.0 6 a_3 a_4) a_5 (skS.0 7 a_3 a_4 a_6)) True) (Eq True False))
14.28/14.45	Clause #143 (by clausification #[55]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 6 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) True)
14.28/14.45	Clause #144 (by clausification #[117]): ∀ (a_1 a_2 a_3 a_4 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 4 a_3) (skS.0 6 a_3 a_4)) True)
14.28/14.45	Clause #145 (by clausification #[74]): ∀ (a_1 a_2 a_3 a_4 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 4 a_3) (skS.0 6 a_3 a_4)) True)
14.28/14.45	Clause #148 (by superposition #[145, 40]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
14.28/14.45	    (Or (Eq (skS.0 0 (skS.0 4 a_3) a_4 (skS.0 6 a_3 a_5)) True) (Eq True False))
14.28/14.45	Clause #159 (by clausification #[59]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 4 a_3) (skS.0 7 a_3 a_4 a_5)) False)
14.28/14.45	Clause #206 (by clausification #[100]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 4 a_3) (skS.0 8 a_3 a_4 a_5)) False)
14.28/14.45	Clause #222 (by clausification #[148]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (skS.0 0 (skS.0 4 a_3) a_4 (skS.0 6 a_3 a_5)) True)
14.28/14.45	Clause #227 (by superposition #[222, 36]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
14.28/14.45	    (Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 4 a_3) a_4 a_5) False) (Eq (cQ (skS.0 6 a_3 a_6) a_5) True)))
14.28/14.45	Clause #276 (by clausification #[128]): ∀ (a_1 a_2 a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (skS.0 0 (skS.0 6 a_3 a_4) a_5 (skS.0 7 a_3 a_4 a_6)) True)
14.28/14.45	Clause #401 (by clausification #[227]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
14.28/14.45	    (Or (Eq (skS.0 0 (skS.0 4 a_3) a_4 a_5) False) (Eq (cQ (skS.0 6 a_3 a_6) a_5) True))
14.28/14.45	Clause #407 (by superposition #[401, 30]): ∀ (a_1 a_2 a_3 a_4 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Or (Eq (cQ (skS.0 6 a_3 a_4) (skS.0 4 a_3)) True) (Eq False True))
14.28/14.45	Clause #408 (by clausification #[407]): ∀ (a_1 a_2 a_3 a_4 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 6 a_3 a_4) (skS.0 4 a_3)) True)
14.28/14.45	Clause #409 (by superposition #[408, 40]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True)
14.28/14.45	    (Or (Eq (skS.0 0 (skS.0 3 a_3) a_4 (skS.0 5 a_3 a_5)) True) (Eq True False))
14.28/14.45	Clause #417 (by clausification #[409]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Eq (skS.0 0 (skS.0 3 a_3) a_4 (skS.0 5 a_3 a_5)) True)
14.28/14.45	Clause #423 (by superposition #[417, 36]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
14.28/14.45	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True)
14.31/14.47	    (Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 3 a_3) a_4 a_5) False) (Eq (cQ (skS.0 5 a_3 a_6) a_5) True)))
14.31/14.47	Clause #471 (by clausification #[423]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True)
14.31/14.47	    (Or (Eq (skS.0 0 (skS.0 3 a_3) a_4 a_5) False) (Eq (cQ (skS.0 5 a_3 a_6) a_5) True))
14.31/14.47	Clause #479 (by superposition #[471, 30]): ∀ (a_1 a_2 a_3 a_4 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Or (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3)) True) (Eq False True))
14.31/14.47	Clause #480 (by clausification #[479]): ∀ (a_1 a_2 a_3 a_4 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3)) True)
14.31/14.47	Clause #486 (by superposition #[480, 144]): ∀ (a_1 a_2 a_3 a_4 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Or (Eq True False) (Eq (cQ (skS.0 4 a_3) (skS.0 6 a_3 a_4)) True))
14.31/14.47	Clause #492 (by clausification #[486]): ∀ (a_1 a_2 a_3 a_4 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Eq (cQ (skS.0 4 a_3) (skS.0 6 a_3 a_4)) True)
14.31/14.47	Clause #497 (by superposition #[492, 40]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True)
14.31/14.47	    (Or (Eq (skS.0 0 (skS.0 4 a_3) a_4 (skS.0 6 a_3 a_5)) True) (Eq True False))
14.31/14.47	Clause #557 (by clausification #[497]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Eq (skS.0 0 (skS.0 4 a_3) a_4 (skS.0 6 a_3 a_5)) True)
14.31/14.47	Clause #563 (by superposition #[557, 36]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True)
14.31/14.47	    (Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 4 a_3) a_4 a_5) False) (Eq (cQ (skS.0 6 a_3 a_6) a_5) True)))
14.31/14.47	Clause #627 (by clausification #[563]): ∀ (a_1 a_2 a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True)
14.31/14.47	    (Or (Eq (skS.0 0 (skS.0 4 a_3) a_4 a_5) False) (Eq (cQ (skS.0 6 a_3 a_6) a_5) True))
14.31/14.47	Clause #635 (by superposition #[627, 30]): ∀ (a_1 a_2 a_3 a_4 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Or (Eq (cQ (skS.0 6 a_3 a_4) (skS.0 4 a_3)) True) (Eq False True))
14.31/14.47	Clause #636 (by clausification #[635]): ∀ (a_1 a_2 a_3 a_4 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Eq (cQ (skS.0 6 a_3 a_4) (skS.0 4 a_3)) True)
14.31/14.47	Clause #641 (by equality factoring #[636]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True)
14.31/14.47	Clause #642 (by clausification #[641]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Or (Eq True False) (Eq True False))
14.31/14.47	Clause #644 (by clausification #[642]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True) (Eq True False)
14.31/14.47	Clause #645 (by clausification #[644]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 6 a_1 a_2) (skS.0 4 a_1)) True
14.31/14.47	Clause #646 (by superposition #[645, 40]): ∀ (a_1 a_2 : a) (a_3 : a → Prop), Or (Eq (skS.0 0 (skS.0 6 a_1 a_2) a_3 (skS.0 4 a_1)) True) (Eq True False)
14.31/14.47	Clause #650 (by clausification #[646]): ∀ (a_1 a_2 : a) (a_3 : a → Prop), Eq (skS.0 0 (skS.0 6 a_1 a_2) a_3 (skS.0 4 a_1)) True
14.31/14.47	Clause #652 (by superposition #[650, 36]): ∀ (a_1 a_2 : a) (a_3 : a → Prop) (a_4 : a),
14.31/14.47	  Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 6 a_1 a_2) a_3 a_4) False) (Eq (cQ (skS.0 4 a_1) a_4) True))
14.31/14.47	Clause #659 (by clausification #[652]): ∀ (a_1 a_2 : a) (a_3 : a → Prop) (a_4 : a),
14.31/14.47	  Or (Eq (skS.0 0 (skS.0 6 a_1 a_2) a_3 a_4) False) (Eq (cQ (skS.0 4 a_1) a_4) True)
14.31/14.47	Clause #663 (by superposition #[659, 276]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.31/14.47	  Or (Eq (cQ (skS.0 4 a_1) (skS.0 7 a_1 a_2 a_3)) True)
14.31/14.47	    (Or (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True) (Eq False True))
14.31/14.47	Clause #667 (by superposition #[659, 30]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 4 a_1) (skS.0 6 a_1 a_2)) True) (Eq False True)
14.31/14.47	Clause #669 (by clausification #[667]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 4 a_1) (skS.0 6 a_1 a_2)) True
14.31/14.47	Clause #670 (by superposition #[669, 40]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 (skS.0 4 a_1) a_2 (skS.0 6 a_1 a_3)) True) (Eq True False)
14.31/14.50	Clause #678 (by clausification #[670]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 (skS.0 4 a_1) a_2 (skS.0 6 a_1 a_3)) True
14.31/14.50	Clause #679 (by superposition #[678, 35]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a),
14.31/14.50	  Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 4 a_1) a_2 a_3) True) (Eq (cQ (skS.0 6 a_1 a_4) a_3) False))
14.31/14.50	Clause #724 (by clausification #[679]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a),
14.31/14.50	  Or (Eq (skS.0 0 (skS.0 4 a_1) a_2 a_3) True) (Eq (cQ (skS.0 6 a_1 a_4) a_3) False)
14.31/14.50	Clause #822 (by clausification #[663]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
14.31/14.50	  Or (Eq (cQ (skS.0 4 a_1) (skS.0 7 a_1 a_2 a_3)) True) (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True)
14.31/14.50	Clause #823 (by superposition #[822, 159]): ∀ (a_1 a_2 a_3 a_4 : a),
14.31/14.50	  Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Or (Eq (cQ (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True) (Eq True False))
14.31/14.50	Clause #833 (by clausification #[823]): ∀ (a_1 a_2 a_3 a_4 : a),
14.31/14.50	  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)
14.31/14.50	Clause #838 (by equality factoring #[833]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
14.31/14.50	Clause #839 (by clausification #[838]): ∀ (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))
14.31/14.50	Clause #841 (by clausification #[839]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq True False)
14.31/14.50	Clause #842 (by clausification #[841]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True
14.31/14.50	Clause #843 (by superposition #[842, 40]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 (skS.0 3 a_1) a_2 (skS.0 5 a_1 a_3)) True) (Eq True False)
14.31/14.50	Clause #847 (by clausification #[843]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 (skS.0 3 a_1) a_2 (skS.0 5 a_1 a_3)) True
14.31/14.50	Clause #849 (by superposition #[847, 36]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a),
14.31/14.50	  Or (Eq True False) (Or (Eq (skS.0 0 (skS.0 3 a_1) a_2 a_3) False) (Eq (cQ (skS.0 5 a_1 a_4) a_3) True))
14.31/14.50	Clause #867 (by clausification #[849]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a),
14.31/14.50	  Or (Eq (skS.0 0 (skS.0 3 a_1) a_2 a_3) False) (Eq (cQ (skS.0 5 a_1 a_4) a_3) True)
14.31/14.50	Clause #874 (by superposition #[867, 30]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True) (Eq False True)
14.31/14.50	Clause #875 (by clausification #[874]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True
14.31/14.50	Clause #876 (by superposition #[875, 143]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 6 a_1 a_2) (skS.0 8 a_1 a_2 a_3)) True)
14.31/14.50	Clause #877 (by superposition #[875, 206]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 4 a_1) (skS.0 8 a_1 a_2 a_3)) False)
14.31/14.50	Clause #887 (by clausification #[877]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 4 a_1) (skS.0 8 a_1 a_2 a_3)) False
14.31/14.50	Clause #888 (by clausification #[876]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 6 a_1 a_2) (skS.0 8 a_1 a_2 a_3)) True
14.31/14.50	Clause #889 (by superposition #[888, 724]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a),
14.31/14.50	  Or (Eq (skS.0 0 (skS.0 4 a_1) a_2 (skS.0 8 a_1 a_3 a_4)) True) (Eq True False)
14.31/14.50	Clause #921 (by clausification #[889]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 a_4 : a), Eq (skS.0 0 (skS.0 4 a_1) a_2 (skS.0 8 a_1 a_3 a_4)) True
14.31/14.50	Clause #924 (by superposition #[921, 50]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 4 a_1) (skS.0 8 a_1 a_2 a_3)) True)
14.31/14.50	Clause #929 (by clausification #[924]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 4 a_1) (skS.0 8 a_1 a_2 a_3)) True
14.31/14.50	Clause #930 (by superposition #[929, 887]): Eq True False
14.31/14.50	Clause #934 (by clausification #[930]): False
14.31/14.50	SZS output end Proof for theBenchmark.p
14.31/14.50	EOF