TSTP Solution File: SEV104^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV104^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 19:24:16 EDT 2023
% Result : Theorem 9.69s 9.96s
% Output : Proof 9.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV104^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.17/0.35 % Computer : n014.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 24 03:38:34 EDT 2023
% 0.17/0.35 % CPUTime :
% 9.69/9.96 SZS status Theorem for theBenchmark.p
% 9.69/9.96 SZS output start Proof for theBenchmark.p
% 9.69/9.96 Clause #0 (by assumption #[]): Eq
% 9.69/9.96 (Not
% 9.69/9.96 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) →
% 9.69/9.96 And
% 9.69/9.96 (And (∀ (Xx : a), Exists fun Xy => f Xx Xy)
% 9.69/9.96 (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2))
% 9.69/9.96 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) →
% 9.69/9.96 ∀ (Xy : b) (Xx1 Xx2 : a),
% 9.69/9.96 And (∀ (Xw : a), Or (f Xx1 Xy) (And (Not (f Xw Xy)) (cR Xx1 z)))
% 9.69/9.96 (∀ (Xw : a), Or (f Xx2 Xy) (And (Not (f Xw Xy)) (cR Xx2 z))) →
% 9.69/9.96 cR Xx1 Xx2))
% 9.69/9.96 True
% 9.69/9.96 Clause #1 (by betaEtaReduce #[0]): Eq
% 9.69/9.96 (Not
% 9.69/9.96 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) →
% 9.69/9.96 And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2))
% 9.69/9.96 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) →
% 9.69/9.96 ∀ (Xy : b) (Xx1 Xx2 : a),
% 9.69/9.96 And (∀ (Xw : a), Or (f Xx1 Xy) (And (Not (f Xw Xy)) (cR Xx1 z)))
% 9.69/9.96 (∀ (Xw : a), Or (f Xx2 Xy) (And (Not (f Xw Xy)) (cR Xx2 z))) →
% 9.69/9.96 cR Xx1 Xx2))
% 9.69/9.96 True
% 9.69/9.96 Clause #2 (by clausification #[1]): Eq
% 9.69/9.96 (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx) →
% 9.69/9.96 And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2))
% 9.69/9.96 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) →
% 9.69/9.96 ∀ (Xy : b) (Xx1 Xx2 : a),
% 9.69/9.96 And (∀ (Xw : a), Or (f Xx1 Xy) (And (Not (f Xw Xy)) (cR Xx1 z)))
% 9.69/9.96 (∀ (Xw : a), Or (f Xx2 Xy) (And (Not (f Xw Xy)) (cR Xx2 z))) →
% 9.69/9.96 cR Xx1 Xx2)
% 9.69/9.96 False
% 9.69/9.96 Clause #3 (by clausification #[2]): Eq (And (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) (∀ (Xx : a), cR Xx Xx)) True
% 9.69/9.96 Clause #4 (by clausification #[2]): Eq
% 9.69/9.96 (And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2))
% 9.69/9.96 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) →
% 9.69/9.96 ∀ (Xy : b) (Xx1 Xx2 : a),
% 9.69/9.96 And (∀ (Xw : a), Or (f Xx1 Xy) (And (Not (f Xw Xy)) (cR Xx1 z)))
% 9.69/9.96 (∀ (Xw : a), Or (f Xx2 Xy) (And (Not (f Xw Xy)) (cR Xx2 z))) →
% 9.69/9.96 cR Xx1 Xx2)
% 9.69/9.96 False
% 9.69/9.96 Clause #5 (by clausification #[3]): Eq (∀ (Xx : a), cR Xx Xx) True
% 9.69/9.96 Clause #6 (by clausification #[3]): Eq (∀ (Xu Xv Xw : a), And (cR Xu Xv) (cR Xw Xv) → cR Xu Xw) True
% 9.69/9.96 Clause #7 (by clausification #[5]): ∀ (a : a), Eq (cR a a) True
% 9.69/9.96 Clause #8 (by clausification #[6]): ∀ (a_1 : a), Eq (∀ (Xv Xw : a), And (cR a_1 Xv) (cR Xw Xv) → cR a_1 Xw) True
% 9.69/9.96 Clause #9 (by clausification #[8]): ∀ (a_1 a_2 : a), Eq (∀ (Xw : a), And (cR a_1 a_2) (cR Xw a_2) → cR a_1 Xw) True
% 9.69/9.96 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a : a), Eq (And (cR a_1 a_2) (cR a a_2) → cR a_1 a) True
% 9.69/9.96 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 a : a), Or (Eq (And (cR a_1 a_2) (cR a a_2)) False) (Eq (cR a_1 a) True)
% 9.69/9.96 Clause #12 (by clausification #[11]): ∀ (a_1 a_2 a : a), Or (Eq (cR a_1 a_2) True) (Or (Eq (cR a_1 a) False) (Eq (cR a_2 a) False))
% 9.69/9.96 Clause #13 (by superposition #[12, 7]): ∀ (a_1 a : a), Or (Eq (cR a_1 a) True) (Or (Eq (cR a a_1) False) (Eq False True))
% 9.69/9.96 Clause #14 (by clausification #[4]): Eq
% 9.69/9.96 (And (And (∀ (Xx : a), Exists (f Xx)) (∀ (Xx : a) (Xy1 Xy2 : b), And (f Xx Xy1) (f Xx Xy2) → cS Xy1 Xy2))
% 9.69/9.96 (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2))
% 9.69/9.96 True
% 9.69/9.96 Clause #15 (by clausification #[4]): Eq
% 9.69/9.96 (∀ (Xy : b) (Xx1 Xx2 : a),
% 9.69/9.96 And (∀ (Xw : a), Or (f Xx1 Xy) (And (Not (f Xw Xy)) (cR Xx1 z)))
% 9.69/9.96 (∀ (Xw : a), Or (f Xx2 Xy) (And (Not (f Xw Xy)) (cR Xx2 z))) →
% 9.69/9.96 cR Xx1 Xx2)
% 9.69/9.96 False
% 9.69/9.96 Clause #16 (by clausification #[14]): Eq (∀ (Xx1 Xx2 : a) (Xy : b), And (f Xx1 Xy) (f Xx2 Xy) → cR Xx1 Xx2) True
% 9.69/9.96 Clause #18 (by clausification #[16]): ∀ (a_1 : a), Eq (∀ (Xx2 : a) (Xy : b), And (f a_1 Xy) (f Xx2 Xy) → cR a_1 Xx2) True
% 9.69/9.96 Clause #19 (by clausification #[18]): ∀ (a_1 a : a), Eq (∀ (Xy : b), And (f a_1 Xy) (f a Xy) → cR a_1 a) True
% 9.69/9.99 Clause #20 (by clausification #[19]): ∀ (a_1 : a) (a_2 : b) (a : a), Eq (And (f a_1 a_2) (f a a_2) → cR a_1 a) True
% 9.69/9.99 Clause #21 (by clausification #[20]): ∀ (a_1 : a) (a_2 : b) (a : a), Or (Eq (And (f a_1 a_2) (f a a_2)) False) (Eq (cR a_1 a) True)
% 9.69/9.99 Clause #22 (by clausification #[21]): ∀ (a_1 a : a) (a_2 : b), Or (Eq (cR a_1 a) True) (Or (Eq (f a_1 a_2) False) (Eq (f a a_2) False))
% 9.69/9.99 Clause #23 (by clausification #[15]): ∀ (a_1 : b),
% 9.69/9.99 Eq
% 9.69/9.99 (Not
% 9.69/9.99 (∀ (Xx1 Xx2 : a),
% 9.69/9.99 And (∀ (Xw : a), Or (f Xx1 (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR Xx1 z)))
% 9.69/9.99 (∀ (Xw : a), Or (f Xx2 (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR Xx2 z))) →
% 9.69/9.99 cR Xx1 Xx2))
% 9.69/9.99 True
% 9.69/9.99 Clause #24 (by clausification #[23]): ∀ (a_1 : b),
% 9.69/9.99 Eq
% 9.69/9.99 (∀ (Xx1 Xx2 : a),
% 9.69/9.99 And (∀ (Xw : a), Or (f Xx1 (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR Xx1 z)))
% 9.69/9.99 (∀ (Xw : a), Or (f Xx2 (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR Xx2 z))) →
% 9.69/9.99 cR Xx1 Xx2)
% 9.69/9.99 False
% 9.69/9.99 Clause #25 (by clausification #[24]): ∀ (a_1 : b) (a_2 : a),
% 9.69/9.99 Eq
% 9.69/9.99 (Not
% 9.69/9.99 (∀ (Xx2 : a),
% 9.69/9.99 And
% 9.69/9.99 (∀ (Xw : a),
% 9.69/9.99 Or (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 1 a_1 a_2) z)))
% 9.69/9.99 (∀ (Xw : a), Or (f Xx2 (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR Xx2 z))) →
% 9.69/9.99 cR (skS.0 1 a_1 a_2) Xx2))
% 9.69/9.99 True
% 9.69/9.99 Clause #26 (by clausification #[25]): ∀ (a_1 : b) (a_2 : a),
% 9.69/9.99 Eq
% 9.69/9.99 (∀ (Xx2 : a),
% 9.69/9.99 And (∀ (Xw : a), Or (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 1 a_1 a_2) z)))
% 9.69/9.99 (∀ (Xw : a), Or (f Xx2 (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR Xx2 z))) →
% 9.69/9.99 cR (skS.0 1 a_1 a_2) Xx2)
% 9.69/9.99 False
% 9.69/9.99 Clause #27 (by clausification #[26]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.69/9.99 Eq
% 9.69/9.99 (Not
% 9.69/9.99 (And
% 9.69/9.99 (∀ (Xw : a), Or (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 1 a_1 a_2) z)))
% 9.69/9.99 (∀ (Xw : a),
% 9.69/9.99 Or (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 2 a_1 a_2 a_3) z))) →
% 9.69/9.99 cR (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)))
% 9.69/9.99 True
% 9.69/9.99 Clause #28 (by clausification #[27]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.69/9.99 Eq
% 9.69/9.99 (And (∀ (Xw : a), Or (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 1 a_1 a_2) z)))
% 9.69/9.99 (∀ (Xw : a),
% 9.69/9.99 Or (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 2 a_1 a_2 a_3) z))) →
% 9.69/9.99 cR (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3))
% 9.69/9.99 False
% 9.69/9.99 Clause #29 (by clausification #[28]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.69/9.99 Eq
% 9.69/9.99 (And (∀ (Xw : a), Or (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 1 a_1 a_2) z)))
% 9.69/9.99 (∀ (Xw : a),
% 9.69/9.99 Or (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 2 a_1 a_2 a_3) z))))
% 9.69/9.99 True
% 9.69/9.99 Clause #30 (by clausification #[28]): ∀ (a_1 : b) (a_2 a_3 : a), Eq (cR (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) False
% 9.69/9.99 Clause #31 (by clausification #[29]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.69/9.99 Eq
% 9.69/9.99 (∀ (Xw : a),
% 9.69/9.99 Or (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 2 a_1 a_2 a_3) z)))
% 9.69/9.99 True
% 9.69/9.99 Clause #32 (by clausification #[29]): ∀ (a_1 : b) (a_2 : a),
% 9.69/9.99 Eq (∀ (Xw : a), Or (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) (And (Not (f Xw (skS.0 0 a_1))) (cR (skS.0 1 a_1 a_2) z))) True
% 9.69/9.99 Clause #33 (by clausification #[31]): ∀ (a_1 : b) (a_2 a_3 a_4 : a),
% 9.69/9.99 Eq (Or (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) (And (Not (f a_4 (skS.0 0 a_1))) (cR (skS.0 2 a_1 a_2 a_3) z))) True
% 9.69/9.99 Clause #34 (by clausification #[33]): ∀ (a_1 : b) (a_2 a_3 a_4 : a),
% 9.69/9.99 Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True)
% 9.69/9.99 (Eq (And (Not (f a_4 (skS.0 0 a_1))) (cR (skS.0 2 a_1 a_2 a_3) z)) True)
% 9.69/9.99 Clause #35 (by clausification #[34]): ∀ (a_1 : b) (a_2 a_3 : a), Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True) (Eq (cR (skS.0 2 a_1 a_2 a_3) z) True)
% 9.69/10.02 Clause #36 (by clausification #[34]): ∀ (a_1 : b) (a_2 a_3 a_4 : a),
% 9.69/10.02 Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True) (Eq (Not (f a_4 (skS.0 0 a_1))) True)
% 9.69/10.02 Clause #38 (by clausification #[13]): ∀ (a_1 a : a), Or (Eq (cR a_1 a) True) (Eq (cR a a_1) False)
% 9.69/10.02 Clause #57 (by clausification #[36]): ∀ (a_1 : b) (a_2 a_3 a_4 : a), Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True) (Eq (f a_4 (skS.0 0 a_1)) False)
% 9.69/10.02 Clause #58 (by superposition #[57, 35]): ∀ (a_1 : b) (a_2 a_3 a_4 a_5 : a),
% 9.69/10.02 Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True) (Or (Eq False True) (Eq (cR (skS.0 2 a_1 a_4 a_5) z) True))
% 9.69/10.02 Clause #59 (by clausification #[58]): ∀ (a_1 : b) (a_2 a_3 a_4 a_5 : a),
% 9.69/10.02 Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True) (Eq (cR (skS.0 2 a_1 a_4 a_5) z) True)
% 9.69/10.02 Clause #65 (by superposition #[59, 38]): ∀ (a_1 : b) (a_2 a_3 a_4 a_5 : a),
% 9.69/10.02 Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True) (Or (Eq (cR z (skS.0 2 a_1 a_4 a_5)) True) (Eq True False))
% 9.69/10.02 Clause #66 (by clausification #[65]): ∀ (a_1 : b) (a_2 a_3 a_4 a_5 : a),
% 9.69/10.02 Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True) (Eq (cR z (skS.0 2 a_1 a_4 a_5)) True)
% 9.69/10.02 Clause #74 (by clausification #[32]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.69/10.02 Eq (Or (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) (And (Not (f a_3 (skS.0 0 a_1))) (cR (skS.0 1 a_1 a_2) z))) True
% 9.69/10.02 Clause #75 (by clausification #[74]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq (And (Not (f a_3 (skS.0 0 a_1))) (cR (skS.0 1 a_1 a_2) z)) True)
% 9.69/10.02 Clause #76 (by clausification #[75]): ∀ (a_1 : b) (a_2 : a), Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq (cR (skS.0 1 a_1 a_2) z) True)
% 9.69/10.02 Clause #77 (by clausification #[75]): ∀ (a_1 : b) (a_2 a_3 : a), Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq (Not (f a_3 (skS.0 0 a_1))) True)
% 9.69/10.02 Clause #82 (by clausification #[77]): ∀ (a_1 : b) (a_2 a_3 : a), Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq (f a_3 (skS.0 0 a_1)) False)
% 9.69/10.02 Clause #84 (by superposition #[82, 66]): ∀ (a_1 : b) (a_2 a_3 a_4 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Or (Eq False True) (Eq (cR z (skS.0 2 a_1 a_3 a_4)) True))
% 9.69/10.02 Clause #85 (by superposition #[82, 76]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Or (Eq False True) (Eq (cR (skS.0 1 a_1 a_3) z) True))
% 9.69/10.02 Clause #86 (by clausification #[85]): ∀ (a_1 : b) (a_2 a_3 : a), Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq (cR (skS.0 1 a_1 a_3) z) True)
% 9.69/10.02 Clause #91 (by superposition #[86, 12]): ∀ (a_1 : b) (a_2 a_3 a_4 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True)
% 9.69/10.02 (Or (Eq (cR (skS.0 1 a_1 a_3) a_4) True) (Or (Eq True False) (Eq (cR a_4 z) False)))
% 9.69/10.02 Clause #108 (by clausification #[84]): ∀ (a_1 : b) (a_2 a_3 a_4 : a), Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq (cR z (skS.0 2 a_1 a_3 a_4)) True)
% 9.69/10.02 Clause #115 (by superposition #[108, 38]): ∀ (a_1 : b) (a_2 a_3 a_4 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Or (Eq (cR (skS.0 2 a_1 a_3 a_4) z) True) (Eq True False))
% 9.69/10.02 Clause #116 (by clausification #[115]): ∀ (a_1 : b) (a_2 a_3 a_4 : a), Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq (cR (skS.0 2 a_1 a_3 a_4) z) True)
% 9.69/10.02 Clause #173 (by clausification #[91]): ∀ (a_1 : b) (a_2 a_3 a_4 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Or (Eq (cR (skS.0 1 a_1 a_3) a_4) True) (Eq (cR a_4 z) False))
% 9.69/10.02 Clause #176 (by superposition #[173, 116]): ∀ (a_1 : b) (a_2 a_3 : a) (a_4 : b) (a_5 a_6 a_7 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True)
% 9.69/10.02 (Or (Eq (cR (skS.0 1 a_1 a_3) (skS.0 2 a_4 a_5 a_6)) True)
% 9.69/10.02 (Or (Eq (f (skS.0 1 a_4 a_7) (skS.0 0 a_4)) True) (Eq False True)))
% 9.69/10.02 Clause #1251 (by clausification #[176]): ∀ (a_1 : b) (a_2 a_3 : a) (a_4 : b) (a_5 a_6 a_7 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True)
% 9.69/10.02 (Or (Eq (cR (skS.0 1 a_1 a_3) (skS.0 2 a_4 a_5 a_6)) True) (Eq (f (skS.0 1 a_4 a_7) (skS.0 0 a_4)) True))
% 9.69/10.02 Clause #1263 (by superposition #[1251, 30]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.69/10.02 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Or (Eq (f (skS.0 1 a_1 a_3) (skS.0 0 a_1)) True) (Eq True False))
% 9.87/10.04 Clause #1276 (by clausification #[1263]): ∀ (a_1 : b) (a_2 a_3 : a),
% 9.87/10.04 Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq (f (skS.0 1 a_1 a_3) (skS.0 0 a_1)) True)
% 9.87/10.04 Clause #1286 (by equality factoring #[1276]): ∀ (a_1 : b) (a_2 : a), Or (Ne True True) (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True)
% 9.87/10.04 Clause #1287 (by clausification #[1286]): ∀ (a_1 : b) (a_2 : a), Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Or (Eq True False) (Eq True False))
% 9.87/10.04 Clause #1289 (by clausification #[1287]): ∀ (a_1 : b) (a_2 : a), Or (Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True) (Eq True False)
% 9.87/10.04 Clause #1290 (by clausification #[1289]): ∀ (a_1 : b) (a_2 : a), Eq (f (skS.0 1 a_1 a_2) (skS.0 0 a_1)) True
% 9.87/10.04 Clause #1291 (by superposition #[1290, 57]): ∀ (a_1 : b) (a_2 a_3 : a), Or (Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True) (Eq True False)
% 9.87/10.04 Clause #1298 (by superposition #[1290, 22]): ∀ (a_1 : b) (a_2 a_3 : a), Or (Eq (cR (skS.0 1 a_1 a_2) a_3) True) (Or (Eq True False) (Eq (f a_3 (skS.0 0 a_1)) False))
% 9.87/10.04 Clause #1301 (by clausification #[1291]): ∀ (a_1 : b) (a_2 a_3 : a), Eq (f (skS.0 2 a_1 a_2 a_3) (skS.0 0 a_1)) True
% 9.87/10.04 Clause #1313 (by clausification #[1298]): ∀ (a_1 : b) (a_2 a_3 : a), Or (Eq (cR (skS.0 1 a_1 a_2) a_3) True) (Eq (f a_3 (skS.0 0 a_1)) False)
% 9.87/10.04 Clause #1315 (by superposition #[1313, 1301]): ∀ (a_1 : b) (a_2 a_3 a_4 : a), Or (Eq (cR (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_3 a_4)) True) (Eq False True)
% 9.87/10.04 Clause #1317 (by clausification #[1315]): ∀ (a_1 : b) (a_2 a_3 a_4 : a), Eq (cR (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_3 a_4)) True
% 9.87/10.04 Clause #1318 (by superposition #[1317, 30]): Eq True False
% 9.87/10.04 Clause #1321 (by clausification #[1318]): False
% 9.87/10.04 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------