TSTP Solution File: SEV218^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV218^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n020.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 : Thu Aug 31 19:24:31 EDT 2023
% Result : Theorem 10.70s 10.89s
% Output : Proof 10.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV218^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.16/0.34 % Computer : n020.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 02:58:15 EDT 2023
% 0.16/0.34 % CPUTime :
% 10.70/10.89 SZS status Theorem for theBenchmark.p
% 10.70/10.89 SZS output start Proof for theBenchmark.p
% 10.70/10.89 Clause #0 (by assumption #[]): Eq
% 10.70/10.89 (Not
% 10.70/10.89 ((Exists fun Xf =>
% 10.70/10.89 ∀ (Xx : a),
% 10.70/10.89 And (And (Exists fun Xz => Xf Xx Xz) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy)))
% 10.70/10.89 (Xf Xx Xx)) →
% 10.70/10.89 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx))
% 10.70/10.89 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)))
% 10.70/10.89 True
% 10.70/10.89 Clause #1 (by betaEtaReduce #[0]): Eq
% 10.70/10.89 (Not
% 10.70/10.89 ((Exists fun Xf =>
% 10.70/10.89 ∀ (Xx : a),
% 10.70/10.89 And (And (Exists (Xf Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) (Xf Xx Xx)) →
% 10.70/10.89 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx))
% 10.70/10.89 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz)))
% 10.70/10.89 True
% 10.70/10.89 Clause #2 (by clausification #[1]): Eq
% 10.70/10.89 ((Exists fun Xf =>
% 10.70/10.89 ∀ (Xx : a),
% 10.70/10.89 And (And (Exists (Xf Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) (Xf Xx Xx)) →
% 10.70/10.89 And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx))
% 10.70/10.89 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
% 10.70/10.89 False
% 10.70/10.89 Clause #3 (by clausification #[2]): Eq
% 10.70/10.89 (Exists fun Xf =>
% 10.70/10.89 ∀ (Xx : a),
% 10.70/10.89 And (And (Exists (Xf Xx)) (∀ (Xx_0 : a), Xf Xx Xx_0 → ∀ (Xy : a), Iff (Xf Xx Xy) (cQ Xx_0 Xy))) (Xf Xx Xx))
% 10.70/10.89 True
% 10.70/10.89 Clause #4 (by clausification #[2]): Eq
% 10.70/10.89 (And (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx))
% 10.70/10.89 (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz))
% 10.70/10.89 False
% 10.70/10.89 Clause #5 (by clausification #[3]): ∀ (a_1 : a → a → Prop),
% 10.70/10.89 Eq
% 10.70/10.89 (∀ (Xx : a),
% 10.70/10.89 And
% 10.70/10.89 (And (Exists (skS.0 0 a_1 Xx))
% 10.70/10.89 (∀ (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)))
% 10.70/10.89 (skS.0 0 a_1 Xx Xx))
% 10.70/10.89 True
% 10.70/10.89 Clause #6 (by clausification #[5]): ∀ (a_1 : a → a → Prop) (a_2 : a),
% 10.70/10.89 Eq
% 10.70/10.89 (And
% 10.70/10.89 (And (Exists (skS.0 0 a_1 a_2))
% 10.70/10.89 (∀ (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)))
% 10.70/10.89 (skS.0 0 a_1 a_2 a_2))
% 10.70/10.89 True
% 10.70/10.89 Clause #7 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 a_2 a_2) True
% 10.70/10.89 Clause #8 (by clausification #[6]): ∀ (a_1 : a → a → Prop) (a_2 : a),
% 10.70/10.89 Eq
% 10.70/10.89 (And (Exists (skS.0 0 a_1 a_2))
% 10.70/10.89 (∀ (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)))
% 10.70/10.89 True
% 10.70/10.89 Clause #9 (by clausification #[4]): Or (Eq (And (∀ (Xx : a), cQ Xx Xx) (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx)) False)
% 10.70/10.89 (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False)
% 10.70/10.89 Clause #10 (by clausification #[9]): Or (Eq (∀ (Xx Xy Xz : a), And (cQ Xx Xy) (cQ Xy Xz) → cQ Xx Xz) False)
% 10.70/10.89 (Or (Eq (∀ (Xx : a), cQ Xx Xx) False) (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False))
% 10.70/10.89 Clause #11 (by clausification #[10]): ∀ (a_1 : a),
% 10.70/10.89 Or (Eq (∀ (Xx : a), cQ Xx Xx) False)
% 10.70/10.89 (Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False)
% 10.70/10.89 (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz)) True))
% 10.70/10.89 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 : a),
% 10.70/10.89 Or (Eq (∀ (Xx Xy : a), cQ Xx Xy → cQ Xy Xx) False)
% 10.70/10.89 (Or (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz)) True)
% 10.70/10.89 (Eq (Not (cQ (skS.0 2 a_2) (skS.0 2 a_2))) True))
% 10.70/10.89 Clause #13 (by clausification #[12]): ∀ (a_1 a_2 a_3 : a),
% 10.70/10.89 Or (Eq (Not (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz)) True)
% 10.70/10.89 (Or (Eq (Not (cQ (skS.0 2 a_2) (skS.0 2 a_2))) True)
% 10.70/10.89 (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_3) Xy → cQ Xy (skS.0 3 a_3))) True))
% 10.70/10.89 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a),
% 10.70/10.89 Or (Eq (Not (cQ (skS.0 2 a_1) (skS.0 2 a_1))) True)
% 10.70/10.89 (Or (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2))) True)
% 10.70/10.89 (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_3) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_3) Xz) False))
% 10.70/10.89 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a),
% 10.70/10.89 Or (Eq (Not (∀ (Xy : a), cQ (skS.0 3 a_1) Xy → cQ Xy (skS.0 3 a_1))) True)
% 10.70/10.92 (Or (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_2) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_2) Xz) False)
% 10.70/10.92 (Eq (cQ (skS.0 2 a_3) (skS.0 2 a_3)) False))
% 10.70/10.92 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a),
% 10.70/10.92 Or (Eq (∀ (Xy Xz : a), And (cQ (skS.0 1 a_1) Xy) (cQ Xy Xz) → cQ (skS.0 1 a_1) Xz) False)
% 10.70/10.92 (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))
% 10.70/10.92 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or (Eq (∀ (Xy : a), cQ (skS.0 3 a_2) Xy → cQ Xy (skS.0 3 a_2)) False)
% 10.70/10.92 (Eq (Not (∀ (Xz : a), And (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) (cQ (skS.0 4 a_3 a_4) Xz) → cQ (skS.0 1 a_3) Xz))
% 10.70/10.92 True))
% 10.70/10.92 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or
% 10.70/10.92 (Eq (Not (∀ (Xz : a), And (cQ (skS.0 1 a_2) (skS.0 4 a_2 a_3)) (cQ (skS.0 4 a_2 a_3) Xz) → cQ (skS.0 1 a_2) Xz))
% 10.70/10.92 True)
% 10.70/10.92 (Eq (Not (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))) True))
% 10.70/10.92 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (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)
% 10.70/10.92 (Eq (∀ (Xz : a), And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) Xz) → cQ (skS.0 1 a_4) Xz) False))
% 10.70/10.92 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or
% 10.70/10.92 (Eq (∀ (Xz : a), And (cQ (skS.0 1 a_2) (skS.0 4 a_2 a_3)) (cQ (skS.0 4 a_2 a_3) Xz) → cQ (skS.0 1 a_2) Xz) False)
% 10.70/10.92 (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))
% 10.70/10.92 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (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)
% 10.70/10.92 (Eq
% 10.70/10.92 (Not
% 10.70/10.92 (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) →
% 10.70/10.92 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)))
% 10.70/10.92 True))
% 10.70/10.92 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or
% 10.70/10.92 (Eq
% 10.70/10.92 (Not
% 10.70/10.92 (And (cQ (skS.0 1 a_2) (skS.0 4 a_2 a_3)) (cQ (skS.0 4 a_2 a_3) (skS.0 6 a_2 a_3 a_4)) →
% 10.70/10.92 cQ (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4)))
% 10.70/10.92 True)
% 10.70/10.92 (Eq (cQ (skS.0 3 a_5) (skS.0 5 a_5 a_6)) True))
% 10.70/10.92 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or
% 10.70/10.92 (Eq
% 10.70/10.92 (Not
% 10.70/10.92 (And (cQ (skS.0 1 a_2) (skS.0 4 a_2 a_3)) (cQ (skS.0 4 a_2 a_3) (skS.0 6 a_2 a_3 a_4)) →
% 10.70/10.92 cQ (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4)))
% 10.70/10.92 True)
% 10.70/10.92 (Eq (cQ (skS.0 5 a_5 a_6) (skS.0 3 a_5)) False))
% 10.70/10.92 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True)
% 10.70/10.92 (Eq
% 10.70/10.92 (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) →
% 10.70/10.92 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6))
% 10.70/10.92 False))
% 10.70/10.92 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True)
% 10.70/10.92 (Eq (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6))) True))
% 10.70/10.92 Clause #26 (by clausification #[24]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)) False))
% 10.70/10.92 Clause #27 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.92 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.92 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True))
% 10.70/10.95 Clause #28 (by clausification #[25]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.70/10.95 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.95 (Or (Eq (cQ (skS.0 3 a_2) (skS.0 5 a_2 a_3)) True) (Eq (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) True))
% 10.70/10.95 Clause #29 (by clausification #[8]): ∀ (a_1 : a → a → Prop) (a_2 : a),
% 10.70/10.95 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
% 10.70/10.95 Clause #31 (by clausification #[29]): ∀ (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
% 10.70/10.95 Clause #32 (by clausification #[31]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a),
% 10.70/10.95 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)
% 10.70/10.95 Clause #33 (by clausification #[32]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.70/10.95 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)
% 10.70/10.95 Clause #34 (by clausification #[33]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.70/10.95 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))
% 10.70/10.95 Clause #35 (by clausification #[33]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.70/10.95 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))
% 10.70/10.95 Clause #36 (by superposition #[34, 7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a),
% 10.70/10.95 Or (Eq (skS.0 0 (fun x x_1 => a_1 x x_1) a_2 a_3) True) (Or (Eq (cQ a_2 a_3) False) (Eq False True))
% 10.70/10.95 Clause #39 (by betaEtaReduce #[36]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) True) (Or (Eq (cQ a_2 a_3) False) (Eq False True))
% 10.70/10.95 Clause #40 (by clausification #[39]): ∀ (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)
% 10.70/10.95 Clause #41 (by clausification #[23]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.95 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.95 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False)
% 10.70/10.95 (Eq
% 10.70/10.95 (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) →
% 10.70/10.95 cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6))
% 10.70/10.95 False))
% 10.70/10.95 Clause #42 (by clausification #[41]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.95 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.95 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False)
% 10.70/10.95 (Eq (And (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6))) True))
% 10.70/10.95 Clause #43 (by clausification #[41]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.95 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.95 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 1 a_4) (skS.0 6 a_4 a_5 a_6)) False))
% 10.70/10.95 Clause #44 (by clausification #[42]): ∀ (a_1 a_2 a_3 a_4 a_5 a_6 : a),
% 10.70/10.95 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.95 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True))
% 10.70/10.95 Clause #45 (by clausification #[42]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.70/10.95 Or (Eq (cQ (skS.0 2 a_1) (skS.0 2 a_1)) False)
% 10.70/10.95 (Or (Eq (cQ (skS.0 5 a_2 a_3) (skS.0 3 a_2)) False) (Eq (cQ (skS.0 1 a_4) (skS.0 4 a_4 a_5)) True))
% 10.70/10.95 Clause #46 (by superposition #[35, 7]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a),
% 10.70/10.95 Or (Eq (skS.0 0 (fun x x_1 => a_1 x x_1) a_2 a_3) False) (Or (Eq (cQ a_2 a_3) True) (Eq False True))
% 10.70/10.95 Clause #48 (by betaEtaReduce #[46]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 a_2 a_3) False) (Or (Eq (cQ a_2 a_3) True) (Eq False True))
% 10.70/10.95 Clause #49 (by clausification #[48]): ∀ (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)
% 10.70/10.95 Clause #51 (by superposition #[49, 7]): ∀ (a : a), Or (Eq (cQ a a) True) (Eq False True)
% 10.70/10.95 Clause #52 (by clausification #[51]): ∀ (a : a), Eq (cQ a a) True
% 10.70/10.95 Clause #53 (by superposition #[52, 27]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.70/10.95 Or (Eq True False)
% 10.70/10.95 (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 6 a_3 a_4 a_5)) True))
% 10.70/10.95 Clause #54 (by superposition #[52, 44]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.70/10.95 Or (Eq True False)
% 10.79/10.97 (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) True))
% 10.79/10.97 Clause #58 (by superposition #[26, 52]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.79/10.97 Or (Eq True False)
% 10.79/10.97 (Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 6 a_3 a_4 a_5)) False))
% 10.79/10.97 Clause #73 (by superposition #[28, 52]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/10.97 Or (Eq True False) (Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True))
% 10.79/10.97 Clause #98 (by superposition #[43, 52]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.79/10.97 Or (Eq True False)
% 10.79/10.97 (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 1 a_3) (skS.0 6 a_3 a_4 a_5)) False))
% 10.79/10.97 Clause #112 (by superposition #[45, 52]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/10.97 Or (Eq True False) (Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True))
% 10.79/10.97 Clause #119 (by clausification #[53]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.79/10.97 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 6 a_3 a_4 a_5)) True)
% 10.79/10.97 Clause #122 (by superposition #[119, 40]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
% 10.79/10.97 (Or (Eq (skS.0 0 a_3 (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True) (Eq True False))
% 10.79/10.97 Clause #137 (by clausification #[54]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 4 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) True)
% 10.79/10.97 Clause #141 (by clausification #[73]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True)
% 10.79/10.97 Clause #142 (by superposition #[141, 40]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True)
% 10.79/10.97 (Or (Eq (skS.0 0 a_3 (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True) (Eq True False))
% 10.79/10.97 Clause #146 (by clausification #[112]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True)
% 10.79/10.97 Clause #151 (by clausification #[58]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 6 a_3 a_4 a_5)) False)
% 10.79/10.97 Clause #203 (by clausification #[98]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) False) (Eq (cQ (skS.0 1 a_3) (skS.0 6 a_3 a_4 a_5)) False)
% 10.79/10.97 Clause #228 (by clausification #[142]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq (skS.0 0 a_3 (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True)
% 10.79/10.97 Clause #233 (by superposition #[228, 35]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True)
% 10.79/10.97 (Or (Eq True False) (Or (Eq (skS.0 0 a_3 (skS.0 3 a_4) a_5) False) (Eq (cQ (skS.0 5 a_4 a_6) a_5) True)))
% 10.79/10.97 Clause #269 (by clausification #[122]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq (skS.0 0 a_3 (skS.0 4 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) True)
% 10.79/10.97 Clause #375 (by clausification #[233]): ∀ (a_1 a_2 : a) (a_3 : a → a → Prop) (a_4 a_5 a_6 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True)
% 10.79/10.97 (Or (Eq (skS.0 0 a_3 (skS.0 3 a_4) a_5) False) (Eq (cQ (skS.0 5 a_4 a_6) a_5) True))
% 10.79/10.97 Clause #382 (by superposition #[375, 7]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Or (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3)) True) (Eq False True))
% 10.79/10.97 Clause #388 (by clausification #[382]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 5 a_3 a_4) (skS.0 3 a_3)) True)
% 10.79/10.97 Clause #394 (by superposition #[388, 146]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Or (Eq True False) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True))
% 10.79/10.97 Clause #400 (by clausification #[394]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/10.97 Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq (cQ (skS.0 1 a_3) (skS.0 4 a_3 a_4)) True)
% 10.79/10.97 Clause #405 (by equality factoring #[400]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True)
% 10.79/11.00 Clause #406 (by clausification #[405]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Or (Eq True False) (Eq True False))
% 10.79/11.00 Clause #408 (by clausification #[406]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True) (Eq True False)
% 10.79/11.00 Clause #409 (by clausification #[408]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 1 a_1) (skS.0 4 a_1 a_2)) True
% 10.79/11.00 Clause #410 (by superposition #[409, 40]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) (skS.0 4 a_2 a_3)) True) (Eq True False)
% 10.79/11.00 Clause #414 (by clausification #[410]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 1 a_2) (skS.0 4 a_2 a_3)) True
% 10.79/11.00 Clause #415 (by superposition #[414, 34]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.79/11.00 Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) a_3) True) (Eq (cQ (skS.0 4 a_2 a_4) a_3) False))
% 10.79/11.00 Clause #416 (by superposition #[414, 35]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.79/11.00 Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) a_3) False) (Eq (cQ (skS.0 4 a_2 a_4) a_3) True))
% 10.79/11.00 Clause #428 (by clausification #[415]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.79/11.00 Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) a_3) True) (Eq (cQ (skS.0 4 a_2 a_4) a_3) False)
% 10.79/11.00 Clause #437 (by clausification #[416]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.79/11.00 Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) a_3) False) (Eq (cQ (skS.0 4 a_2 a_4) a_3) True)
% 10.79/11.00 Clause #443 (by superposition #[437, 7]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True) (Eq False True)
% 10.79/11.00 Clause #449 (by clausification #[443]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 4 a_1 a_2) (skS.0 1 a_1)) True
% 10.79/11.00 Clause #451 (by superposition #[449, 40]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 4 a_2 a_3) (skS.0 1 a_2)) True) (Eq True False)
% 10.79/11.00 Clause #461 (by clausification #[451]): ∀ (a_1 : a → a → Prop) (a_2 a_3 : a), Eq (skS.0 0 a_1 (skS.0 4 a_2 a_3) (skS.0 1 a_2)) True
% 10.79/11.00 Clause #463 (by superposition #[461, 35]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.79/11.00 Or (Eq True False) (Or (Eq (skS.0 0 a_1 (skS.0 4 a_2 a_3) a_4) False) (Eq (cQ (skS.0 1 a_2) a_4) True))
% 10.79/11.00 Clause #495 (by clausification #[463]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.79/11.00 Or (Eq (skS.0 0 a_1 (skS.0 4 a_2 a_3) a_4) False) (Eq (cQ (skS.0 1 a_2) a_4) True)
% 10.79/11.00 Clause #496 (by superposition #[495, 269]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.79/11.00 Or (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True)
% 10.79/11.00 (Or (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True) (Eq False True))
% 10.79/11.00 Clause #603 (by clausification #[496]): ∀ (a_1 a_2 a_3 a_4 a_5 : a),
% 10.79/11.00 Or (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True) (Eq (cQ (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True)
% 10.79/11.00 Clause #604 (by superposition #[603, 151]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/11.00 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))
% 10.79/11.00 Clause #625 (by clausification #[604]): ∀ (a_1 a_2 a_3 a_4 : a),
% 10.79/11.00 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)
% 10.79/11.00 Clause #630 (by equality factoring #[625]): ∀ (a_1 a_2 : a), Or (Ne True True) (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True)
% 10.79/11.00 Clause #631 (by clausification #[630]): ∀ (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))
% 10.79/11.00 Clause #633 (by clausification #[631]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True) (Eq True False)
% 10.79/11.00 Clause #634 (by clausification #[633]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 3 a_1) (skS.0 5 a_1 a_2)) True
% 10.79/11.00 Clause #635 (by superposition #[634, 40]): ∀ (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)
% 10.79/11.00 Clause #639 (by clausification #[635]): ∀ (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
% 10.79/11.00 Clause #641 (by superposition #[639, 35]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.79/11.00 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))
% 10.79/11.01 Clause #648 (by clausification #[641]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a),
% 10.79/11.01 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)
% 10.79/11.01 Clause #655 (by superposition #[648, 7]): ∀ (a_1 a_2 : a), Or (Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True) (Eq False True)
% 10.79/11.01 Clause #656 (by clausification #[655]): ∀ (a_1 a_2 : a), Eq (cQ (skS.0 5 a_1 a_2) (skS.0 3 a_1)) True
% 10.79/11.01 Clause #657 (by superposition #[656, 137]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 4 a_1 a_2) (skS.0 6 a_1 a_2 a_3)) True)
% 10.79/11.01 Clause #658 (by superposition #[656, 203]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) False)
% 10.79/11.01 Clause #663 (by clausification #[658]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) False
% 10.79/11.01 Clause #680 (by clausification #[657]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 4 a_1 a_2) (skS.0 6 a_1 a_2 a_3)) True
% 10.79/11.01 Clause #681 (by superposition #[680, 428]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4)) True) (Eq True False)
% 10.79/11.01 Clause #709 (by clausification #[681]): ∀ (a_1 : a → a → Prop) (a_2 a_3 a_4 : a), Eq (skS.0 0 a_1 (skS.0 1 a_2) (skS.0 6 a_2 a_3 a_4)) True
% 10.79/11.01 Clause #713 (by superposition #[709, 49]): ∀ (a_1 a_2 a_3 : a), Or (Eq True False) (Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True)
% 10.79/11.01 Clause #717 (by clausification #[713]): ∀ (a_1 a_2 a_3 : a), Eq (cQ (skS.0 1 a_1) (skS.0 6 a_1 a_2 a_3)) True
% 10.79/11.01 Clause #718 (by superposition #[717, 663]): Eq True False
% 10.79/11.01 Clause #722 (by clausification #[718]): False
% 10.79/11.01 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------