TSTP Solution File: SEU853^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU853^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 16:44:08 EDT 2023
% Result : Theorem 19.29s 19.50s
% Output : Proof 19.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU853^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : duper %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 23 16:47:54 EDT 2023
% 0.11/0.33 % CPUTime :
% 19.29/19.50 SZS status Theorem for theBenchmark.p
% 19.29/19.50 SZS output start Proof for theBenchmark.p
% 19.29/19.50 Clause #0 (by assumption #[]): Eq
% 19.29/19.50 (Not
% 19.29/19.50 (∀ (S T U : a → Prop),
% 19.29/19.50 And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) →
% 19.29/19.50 Iff (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), And (And (S Xx) (U Xx)) (Not (T Xx)) → And (U Xx) (Not (S Xx)))))
% 19.29/19.50 True
% 19.29/19.50 Clause #1 (by clausification #[0]): Eq
% 19.29/19.50 (∀ (S T U : a → Prop),
% 19.29/19.50 And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) →
% 19.29/19.50 Iff (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), And (And (S Xx) (U Xx)) (Not (T Xx)) → And (U Xx) (Not (S Xx))))
% 19.29/19.50 False
% 19.29/19.50 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop),
% 19.29/19.50 Eq
% 19.29/19.50 (Not
% 19.29/19.50 (∀ (T U : a → Prop),
% 19.29/19.50 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) →
% 19.29/19.50 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx)
% 19.29/19.50 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (T Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx)))))
% 19.29/19.50 True
% 19.29/19.50 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop),
% 19.29/19.50 Eq
% 19.29/19.50 (∀ (T U : a → Prop),
% 19.29/19.50 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) →
% 19.29/19.50 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx)
% 19.29/19.50 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (T Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx))))
% 19.29/19.50 False
% 19.29/19.50 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop),
% 19.29/19.50 Eq
% 19.29/19.50 (Not
% 19.29/19.50 (∀ (U : a → Prop),
% 19.29/19.50 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx) →
% 19.29/19.50 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 19.29/19.50 (∀ (Xx : a),
% 19.29/19.50 And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx)))))
% 19.29/19.50 True
% 19.29/19.50 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop),
% 19.29/19.50 Eq
% 19.29/19.50 (∀ (U : a → Prop),
% 19.29/19.50 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx) →
% 19.29/19.50 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 19.29/19.50 (∀ (Xx : a),
% 19.29/19.50 And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → And (U Xx) (Not (skS.0 0 a_1 Xx))))
% 19.29/19.50 False
% 19.29/19.50 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.29/19.50 Eq
% 19.29/19.50 (Not
% 19.29/19.50 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 19.29/19.50 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) →
% 19.29/19.50 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 19.29/19.50 (∀ (Xx : a),
% 19.29/19.50 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) →
% 19.29/19.50 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))))
% 19.29/19.50 True
% 19.29/19.50 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.29/19.50 Eq
% 19.29/19.50 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 19.29/19.50 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) →
% 19.29/19.50 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 19.29/19.50 (∀ (Xx : a),
% 19.29/19.50 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) →
% 19.29/19.50 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))))
% 19.29/19.50 False
% 19.29/19.50 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.29/19.50 Eq
% 19.29/19.50 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 19.29/19.50 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx))
% 19.29/19.50 True
% 19.29/19.50 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.29/19.50 Eq
% 19.29/19.50 (Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 19.29/19.50 (∀ (Xx : a),
% 19.29/19.50 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) →
% 19.29/19.50 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx))))
% 19.29/19.50 False
% 19.29/19.50 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx) True
% 19.29/19.50 Clause #14 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Eq (skS.0 0 a_1 a_2 → skS.0 2 a_1 a_3 a_4 a_2) True
% 19.29/19.50 Clause #15 (by clausification #[14]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True)
% 19.29/19.53 Clause #16 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.29/19.53 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False)
% 19.29/19.53 (Eq
% 19.29/19.53 (∀ (Xx : a),
% 19.29/19.53 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) →
% 19.29/19.53 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))
% 19.29/19.53 False)
% 19.29/19.53 Clause #17 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.29/19.53 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True)
% 19.29/19.53 (Eq
% 19.29/19.53 (∀ (Xx : a),
% 19.29/19.53 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) →
% 19.29/19.53 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))
% 19.29/19.53 True)
% 19.29/19.53 Clause #18 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 19.29/19.53 Or
% 19.29/19.53 (Eq
% 19.29/19.53 (∀ (Xx : a),
% 19.29/19.53 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) →
% 19.29/19.53 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))
% 19.29/19.53 False)
% 19.29/19.53 (Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_4))) True)
% 19.29/19.53 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.29/19.53 Or (Eq (Not (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3))) True)
% 19.29/19.53 (Eq
% 19.29/19.53 (Not
% 19.29/19.53 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5)))
% 19.29/19.53 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) →
% 19.29/19.53 And (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)))))
% 19.29/19.53 True)
% 19.29/19.53 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.29/19.53 Or
% 19.29/19.53 (Eq
% 19.29/19.53 (Not
% 19.29/19.53 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)))
% 19.29/19.53 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 19.29/19.53 And (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)))))
% 19.29/19.53 True)
% 19.29/19.53 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_5) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_5)) False)
% 19.29/19.53 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.29/19.53 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False)
% 19.29/19.53 (Eq
% 19.29/19.53 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5)))
% 19.29/19.53 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) →
% 19.29/19.53 And (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5))))
% 19.29/19.53 False)
% 19.29/19.53 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.29/19.53 Or
% 19.29/19.53 (Eq
% 19.29/19.53 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)))
% 19.29/19.53 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 19.29/19.53 And (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4))))
% 19.29/19.53 False)
% 19.29/19.53 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_5)) True)
% 19.29/19.53 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.29/19.53 Or
% 19.29/19.53 (Eq
% 19.29/19.53 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)))
% 19.29/19.53 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 19.29/19.53 And (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4))))
% 19.29/19.53 False)
% 19.29/19.53 (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_5)) False)
% 19.29/19.53 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.29/19.53 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True)
% 19.29/19.53 (Eq
% 19.29/19.53 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5)))
% 19.29/19.53 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))))
% 19.29/19.53 True)
% 19.29/19.53 Clause #26 (by clausification #[24]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.29/19.53 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) (Eq (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) True)
% 19.29/19.53 Clause #27 (by clausification #[24]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True)
% 19.35/19.56 (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5))) True)
% 19.35/19.56 Clause #28 (by clausification #[26]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)) False)
% 19.35/19.56 Clause #29 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 19.35/19.56 Or
% 19.35/19.56 (Eq
% 19.35/19.56 (∀ (Xx : a),
% 19.35/19.56 And (And (skS.0 0 a_1 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) (Not (skS.0 1 a_1 a_2 Xx)) →
% 19.35/19.56 And (skS.0 2 a_1 a_2 a_3 Xx) (Not (skS.0 0 a_1 Xx)))
% 19.35/19.56 True)
% 19.35/19.56 (Eq (skS.0 0 a_1 a_4 → skS.0 1 a_1 a_2 a_4) True)
% 19.35/19.56 Clause #30 (by clausification #[29]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 a_2 → skS.0 1 a_1 a_3 a_2) True)
% 19.35/19.56 (Eq
% 19.35/19.56 (And (And (skS.0 0 a_1 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) (Not (skS.0 1 a_1 a_3 a_4)) →
% 19.35/19.56 And (skS.0 2 a_1 a_3 a_5 a_4) (Not (skS.0 0 a_1 a_4)))
% 19.35/19.56 True)
% 19.35/19.56 Clause #31 (by clausification #[30]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop) (a_5 : a),
% 19.35/19.56 Or
% 19.35/19.56 (Eq
% 19.35/19.56 (And (And (skS.0 0 a_1 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) (Not (skS.0 1 a_1 a_3 a_2)) →
% 19.35/19.56 And (skS.0 2 a_1 a_3 a_4 a_2) (Not (skS.0 0 a_1 a_2)))
% 19.35/19.56 True)
% 19.35/19.56 (Or (Eq (skS.0 0 a_1 a_5) False) (Eq (skS.0 1 a_1 a_3 a_5) True))
% 19.35/19.56 Clause #32 (by clausification #[31]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 a_2) False)
% 19.35/19.56 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 19.35/19.56 (Or (Eq (And (And (skS.0 0 a_1 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) (Not (skS.0 1 a_1 a_3 a_4))) False)
% 19.35/19.56 (Eq (And (skS.0 2 a_1 a_3 a_5 a_4) (Not (skS.0 0 a_1 a_4))) True)))
% 19.35/19.56 Clause #33 (by clausification #[32]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop) (a_5 : a),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 a_2) False)
% 19.35/19.56 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 19.35/19.56 (Or (Eq (And (skS.0 2 a_1 a_3 a_4 a_5) (Not (skS.0 0 a_1 a_5))) True)
% 19.35/19.56 (Or (Eq (And (skS.0 0 a_1 a_5) (skS.0 2 a_1 a_3 a_4 a_5)) False) (Eq (Not (skS.0 1 a_1 a_3 a_5)) False))))
% 19.35/19.56 Clause #34 (by clausification #[33]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 a_2) False)
% 19.35/19.56 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 19.35/19.56 (Or (Eq (And (skS.0 0 a_1 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) False)
% 19.35/19.56 (Or (Eq (Not (skS.0 1 a_1 a_3 a_4)) False) (Eq (Not (skS.0 0 a_1 a_4)) True))))
% 19.35/19.56 Clause #36 (by clausification #[34]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 a_2) False)
% 19.35/19.56 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 19.35/19.56 (Or (Eq (Not (skS.0 1 a_1 a_3 a_4)) False)
% 19.35/19.56 (Or (Eq (Not (skS.0 0 a_1 a_4)) True) (Or (Eq (skS.0 0 a_1 a_4) False) (Eq (skS.0 2 a_1 a_3 a_5 a_4) False)))))
% 19.35/19.56 Clause #37 (by clausification #[36]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 a_2) False)
% 19.35/19.56 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 19.35/19.56 (Or (Eq (Not (skS.0 0 a_1 a_4)) True)
% 19.35/19.56 (Or (Eq (skS.0 0 a_1 a_4) False) (Or (Eq (skS.0 2 a_1 a_3 a_5 a_4) False) (Eq (skS.0 1 a_1 a_3 a_4) True)))))
% 19.35/19.56 Clause #38 (by clausification #[37]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 a_2) False)
% 19.35/19.56 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 19.35/19.56 (Or (Eq (skS.0 0 a_1 a_4) False)
% 19.35/19.56 (Or (Eq (skS.0 2 a_1 a_3 a_5 a_4) False) (Or (Eq (skS.0 1 a_1 a_3 a_4) True) (Eq (skS.0 0 a_1 a_4) False)))))
% 19.35/19.56 Clause #39 (by eliminate duplicate literals #[38]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 a_2) False)
% 19.35/19.56 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 19.35/19.56 (Or (Eq (skS.0 0 a_1 a_4) False) (Or (Eq (skS.0 2 a_1 a_3 a_5 a_4) False) (Eq (skS.0 1 a_1 a_3 a_4) True))))
% 19.35/19.56 Clause #41 (by clausification #[27]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.35/19.56 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) True)
% 19.35/19.59 Clause #44 (by clausification #[23]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.35/19.59 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False)
% 19.35/19.59 (Eq
% 19.35/19.59 (And (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5)))
% 19.35/19.59 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))))
% 19.35/19.59 True)
% 19.35/19.59 Clause #46 (by clausification #[44]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.35/19.59 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) (Eq (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) True)
% 19.35/19.59 Clause #47 (by clausification #[44]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.35/19.59 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False)
% 19.35/19.59 (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) (skS.0 2 a_1 a_2 a_4 (skS.0 4 a_1 a_2 a_4 a_5))) True)
% 19.35/19.59 Clause #48 (by clausification #[46]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.35/19.59 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)) False)
% 19.35/19.59 Clause #49 (by superposition #[41, 15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.35/19.59 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3 a_4)) True)
% 19.35/19.59 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True))
% 19.35/19.59 Clause #50 (by superposition #[41, 39]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop),
% 19.35/19.59 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3 a_4)) True)
% 19.35/19.59 (Or (Eq True False)
% 19.35/19.59 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.59 (Or (Eq (skS.0 0 a_1 a_7) False) (Or (Eq (skS.0 2 a_1 a_5 a_8 a_7) False) (Eq (skS.0 1 a_1 a_5 a_7) True)))))
% 19.35/19.59 Clause #57 (by betaEtaReduce #[49]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.35/19.59 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.59 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True))
% 19.35/19.59 Clause #58 (by clausification #[57]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.35/19.59 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True)
% 19.35/19.59 Clause #70 (by clausification #[47]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.35/19.59 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4 a_5)) True)
% 19.35/19.59 Clause #87 (by betaEtaReduce #[50]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop),
% 19.35/19.59 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.59 (Or (Eq True False)
% 19.35/19.59 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.59 (Or (Eq (skS.0 0 a_1 a_7) False) (Or (Eq (skS.0 2 a_1 a_5 a_8 a_7) False) (Eq (skS.0 1 a_1 a_5 a_7) True)))))
% 19.35/19.59 Clause #88 (by clausification #[87]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop),
% 19.35/19.59 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.59 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.59 (Or (Eq (skS.0 0 a_1 a_7) False) (Or (Eq (skS.0 2 a_1 a_5 a_8 a_7) False) (Eq (skS.0 1 a_1 a_5 a_7) True))))
% 19.35/19.59 Clause #89 (by superposition #[88, 41]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 a_8 : a → Prop) (a_9 : a) (a_10 : a → Prop)
% 19.35/19.59 (a_11 : a),
% 19.35/19.59 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3 a_4)) True)
% 19.35/19.59 (Or (Eq (skS.0 1 (fun x => a_1 x) a_5 (skS.0 3 (fun x => a_1 x) a_2 a_6)) True)
% 19.35/19.59 (Or (Eq (skS.0 2 (fun x => a_1 x) a_5 a_7 (skS.0 3 a_1 a_8 a_9)) False)
% 19.35/19.59 (Or (Eq (skS.0 1 (fun x => a_1 x) a_5 (skS.0 3 a_1 a_8 a_9)) True)
% 19.35/19.59 (Or (Eq False True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_8 a_10 a_11)) True)))))
% 19.35/19.59 Clause #105 (by betaEtaReduce #[89]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 a_8 : a → Prop) (a_9 : a) (a_10 : a → Prop)
% 19.35/19.59 (a_11 : a),
% 19.35/19.59 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.59 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.59 (Or (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 3 a_1 a_8 a_9)) False)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_8 a_9)) True)
% 19.35/19.62 (Or (Eq False True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_8 a_10 a_11)) True)))))
% 19.35/19.62 Clause #106 (by clausification #[105]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 a_8 : a → Prop) (a_9 : a) (a_10 : a → Prop)
% 19.35/19.62 (a_11 : a),
% 19.35/19.62 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.62 (Or (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 3 a_1 a_8 a_9)) False)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_8 a_9)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_8 a_10 a_11)) True))))
% 19.35/19.62 Clause #107 (by superposition #[106, 58]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a)
% 19.35/19.62 (a_11 : a → Prop) (a_12 : a),
% 19.35/19.62 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3 a_4)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_5 x) (skS.0 3 (fun x => a_1 x) a_2 a_6)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_5 x) (skS.0 3 (fun x => a_1 x) (fun x => a_7 x) a_8)) True)
% 19.35/19.62 (Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_7 x) a_9 a_10)) True)
% 19.35/19.62 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True) (Eq False True)))))
% 19.35/19.62 Clause #267 (by betaEtaReduce #[107]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a)
% 19.35/19.62 (a_11 : a → Prop) (a_12 : a),
% 19.35/19.62 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 19.35/19.62 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True)
% 19.35/19.62 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True) (Eq False True)))))
% 19.35/19.62 Clause #268 (by clausification #[267]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a)
% 19.35/19.62 (a_11 : a → Prop) (a_12 : a),
% 19.35/19.62 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 19.35/19.62 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True))))
% 19.35/19.62 Clause #293 (by equality factoring #[268]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a),
% 19.35/19.62 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 19.35/19.62 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 (fun x => a_9 x) a_10)) True))))
% 19.35/19.62 Clause #481 (by betaEtaReduce #[293]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a),
% 19.35/19.62 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 19.35/19.62 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True))))
% 19.35/19.62 Clause #482 (by clausification #[481]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a),
% 19.35/19.62 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 19.35/19.62 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) (Or (Eq True False) (Eq True False)))))
% 19.35/19.62 Clause #484 (by clausification #[482]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a),
% 19.35/19.62 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 19.35/19.62 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) (Eq True False))))
% 19.35/19.66 Clause #485 (by clausification #[484]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop) (a_10 : a),
% 19.35/19.66 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.66 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 19.35/19.66 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True)))
% 19.35/19.66 Clause #509 (by equality factoring #[485]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a),
% 19.35/19.66 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 (fun x => a_2 x) a_3 a_4)) True)
% 19.35/19.66 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 19.35/19.66 (Or (Ne True True) (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 (fun x => a_2 x) a_8)) True)))
% 19.35/19.66 Clause #510 (by betaEtaReduce #[509]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a),
% 19.35/19.66 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.66 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 19.35/19.66 (Or (Ne True True) (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True)))
% 19.35/19.66 Clause #511 (by clausification #[510]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a),
% 19.35/19.66 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.66 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 19.35/19.66 (Or (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True) (Or (Eq True False) (Eq True False))))
% 19.35/19.66 Clause #513 (by clausification #[511]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a),
% 19.35/19.66 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.66 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 19.35/19.66 (Or (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True) (Eq True False)))
% 19.35/19.66 Clause #514 (by clausification #[513]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop) (a_8 : a),
% 19.35/19.66 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.66 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True) (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True))
% 19.35/19.66 Clause #525 (by equality factoring #[514]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.66 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.66 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 (fun x => a_5 x) a_6)) True))
% 19.35/19.66 Clause #526 (by betaEtaReduce #[525]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.66 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.66 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True))
% 19.35/19.66 Clause #527 (by clausification #[526]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.66 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.66 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True) (Or (Eq True False) (Eq True False)))
% 19.35/19.66 Clause #529 (by clausification #[527]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.66 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.66 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True) (Eq True False))
% 19.35/19.66 Clause #530 (by clausification #[529]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.66 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True)
% 19.35/19.66 Clause #533 (by superposition #[530, 70]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.66 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) a_3 a_4)) True)
% 19.35/19.66 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True))
% 19.35/19.66 Clause #541 (by betaEtaReduce #[533]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.66 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.66 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True))
% 19.35/19.66 Clause #542 (by clausification #[541]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.66 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 19.35/19.66 Clause #548 (by equality factoring #[542]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 (fun x => a_3 x) a_4)) True)
% 19.35/19.69 Clause #549 (by betaEtaReduce #[548]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 19.35/19.69 Clause #550 (by clausification #[549]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 19.35/19.69 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Or (Eq True False) (Eq True False))
% 19.35/19.69 Clause #552 (by clausification #[550]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq True False)
% 19.35/19.69 Clause #553 (by clausification #[552]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True
% 19.35/19.69 Clause #554 (by superposition #[553, 15]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a),
% 19.35/19.69 Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_4 a_5 a_6)) True)
% 19.35/19.69 Clause #555 (by superposition #[553, 39]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 a_6 : a) (a_7 : a → Prop),
% 19.35/19.69 Or (Eq True False)
% 19.35/19.69 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 19.35/19.69 (Or (Eq (skS.0 0 a_1 a_6) False) (Or (Eq (skS.0 2 a_1 a_2 a_7 a_6) False) (Eq (skS.0 1 a_1 a_2 a_6) True))))
% 19.35/19.69 Clause #559 (by clausification #[554]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_4 a_5 a_6)) True
% 19.35/19.69 Clause #574 (by clausification #[555]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 a_6 : a) (a_7 : a → Prop),
% 19.35/19.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 19.35/19.69 (Or (Eq (skS.0 0 a_1 a_6) False) (Or (Eq (skS.0 2 a_1 a_2 a_7 a_6) False) (Eq (skS.0 1 a_1 a_2 a_6) True)))
% 19.35/19.69 Clause #575 (by superposition #[574, 553]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 a_8 : a → Prop) (a_9 : a),
% 19.35/19.69 Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 4 (fun x => a_1 x) a_3 a_4 a_5)) True)
% 19.35/19.69 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_6 (skS.0 4 a_1 a_7 a_8 a_9)) False)
% 19.35/19.69 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 4 a_1 a_7 a_8 a_9)) True) (Eq False True)))
% 19.35/19.69 Clause #624 (by betaEtaReduce #[575]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 a_8 : a → Prop) (a_9 : a),
% 19.35/19.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 19.35/19.69 (Or (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 4 a_1 a_7 a_8 a_9)) False)
% 19.35/19.69 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_7 a_8 a_9)) True) (Eq False True)))
% 19.35/19.69 Clause #625 (by clausification #[624]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 a_8 : a → Prop) (a_9 : a),
% 19.35/19.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 19.35/19.69 (Or (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 4 a_1 a_7 a_8 a_9)) False)
% 19.35/19.69 (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_7 a_8 a_9)) True))
% 19.35/19.69 Clause #626 (by superposition #[625, 559]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a),
% 19.35/19.69 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 4 (fun x => a_1 x) a_3 a_4 a_5)) True)
% 19.35/19.69 (Or
% 19.35/19.69 (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 4 (fun x => a_1 x) (fun x => a_6 x) (fun x => a_7 x) a_8))
% 19.35/19.69 True)
% 19.35/19.69 (Eq False True))
% 19.35/19.69 Clause #629 (by betaEtaReduce #[626]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a),
% 19.35/19.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 19.35/19.69 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True) (Eq False True))
% 19.35/19.69 Clause #630 (by clausification #[629]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a),
% 19.35/19.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True)
% 19.35/19.69 Clause #633 (by equality factoring #[630]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 19.35/19.69 Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 (fun x => a_3 x) (fun x => a_4 x) a_5)) True)
% 19.35/19.69 Clause #634 (by betaEtaReduce #[633]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 19.35/19.69 Clause #635 (by clausification #[634]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 19.35/19.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Or (Eq True False) (Eq True False))
% 19.35/19.69 Clause #637 (by clausification #[635]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Eq True False)
% 19.35/19.73 Clause #638 (by clausification #[637]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True
% 19.35/19.73 Clause #639 (by superposition #[638, 28]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True) (Eq True False)
% 19.35/19.73 Clause #640 (by clausification #[639]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True
% 19.35/19.73 Clause #641 (by superposition #[640, 15]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5)) True)
% 19.35/19.73 Clause #642 (by superposition #[640, 39]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a) (a_6 : a → Prop),
% 19.35/19.73 Or (Eq True False)
% 19.35/19.73 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.73 (Or (Eq (skS.0 0 a_1 a_5) False) (Or (Eq (skS.0 2 a_1 a_2 a_6 a_5) False) (Eq (skS.0 1 a_1 a_2 a_5) True))))
% 19.35/19.73 Clause #643 (by clausification #[641]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_4 a_5)) True
% 19.35/19.73 Clause #650 (by clausification #[642]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a) (a_6 : a → Prop),
% 19.35/19.73 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.73 (Or (Eq (skS.0 0 a_1 a_5) False) (Or (Eq (skS.0 2 a_1 a_2 a_6 a_5) False) (Eq (skS.0 1 a_1 a_2 a_5) True)))
% 19.35/19.73 Clause #652 (by superposition #[650, 640]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.35/19.73 Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 (fun x => a_1 x) a_3 a_4)) True)
% 19.35/19.73 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_5 (skS.0 3 a_1 a_6 a_7)) False)
% 19.35/19.73 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_6 a_7)) True) (Eq False True)))
% 19.35/19.73 Clause #653 (by betaEtaReduce #[652]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.35/19.73 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.73 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_6 a_7)) False)
% 19.35/19.73 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_6 a_7)) True) (Eq False True)))
% 19.35/19.73 Clause #654 (by clausification #[653]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.35/19.73 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.73 (Or (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 3 a_1 a_6 a_7)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_6 a_7)) True))
% 19.35/19.73 Clause #655 (by superposition #[654, 643]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.73 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) a_3 a_4)) True)
% 19.35/19.73 (Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 3 (fun x => a_1 x) (fun x => a_5 x) a_6)) True)
% 19.35/19.73 (Eq False True))
% 19.35/19.73 Clause #656 (by betaEtaReduce #[655]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.73 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.73 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True) (Eq False True))
% 19.35/19.73 Clause #657 (by clausification #[656]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.35/19.73 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True)
% 19.35/19.73 Clause #660 (by equality factoring #[657]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 (fun x => a_3 x) a_4)) True)
% 19.35/19.73 Clause #663 (by betaEtaReduce #[660]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 19.35/19.73 Clause #664 (by clausification #[663]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 19.35/19.73 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Or (Eq True False) (Eq True False))
% 19.35/19.73 Clause #666 (by clausification #[664]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True) (Eq True False)
% 19.35/19.73 Clause #667 (by clausification #[666]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True
% 19.35/19.73 Clause #668 (by superposition #[667, 48]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False)
% 19.35/19.73 Clause #669 (by clausification #[668]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False
% 19.35/19.74 Clause #670 (by superposition #[669, 638]): Eq False True
% 19.35/19.74 Clause #671 (by clausification #[670]): False
% 19.35/19.74 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------