TSTP Solution File: SEU852^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU852^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 9.39s 9.57s
% Output : Proof 9.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU852^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 18:30:21 EDT 2023
% 0.14/0.35 % CPUTime :
% 9.39/9.57 SZS status Theorem for theBenchmark.p
% 9.39/9.57 SZS output start Proof for theBenchmark.p
% 9.39/9.57 Clause #0 (by assumption #[]): Eq
% 9.39/9.57 (Not
% 9.39/9.57 (∀ (S T U : a → Prop),
% 9.39/9.57 And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) →
% 9.39/9.57 Iff (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), And (And (S Xx) (U Xx)) (Not (T Xx)) → T Xx)))
% 9.39/9.57 True
% 9.39/9.57 Clause #1 (by clausification #[0]): Eq
% 9.39/9.57 (∀ (S T U : a → Prop),
% 9.39/9.57 And (∀ (Xx : a), S Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) →
% 9.39/9.57 Iff (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), And (And (S Xx) (U Xx)) (Not (T Xx)) → T Xx))
% 9.39/9.57 False
% 9.39/9.57 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop),
% 9.39/9.57 Eq
% 9.39/9.57 (Not
% 9.39/9.57 (∀ (T U : a → Prop),
% 9.39/9.57 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) →
% 9.39/9.57 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (T Xx)) → T Xx)))
% 9.39/9.57 True
% 9.39/9.57 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop),
% 9.39/9.57 Eq
% 9.39/9.57 (∀ (T U : a → Prop),
% 9.39/9.57 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), T Xx → U Xx) →
% 9.39/9.57 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (T Xx)) → T Xx))
% 9.39/9.57 False
% 9.39/9.57 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop),
% 9.39/9.57 Eq
% 9.39/9.57 (Not
% 9.39/9.57 (∀ (U : a → Prop),
% 9.39/9.57 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx) →
% 9.39/9.57 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 9.39/9.57 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx)))
% 9.39/9.57 True
% 9.39/9.57 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop),
% 9.39/9.57 Eq
% 9.39/9.57 (∀ (U : a → Prop),
% 9.39/9.57 And (∀ (Xx : a), skS.0 0 a_1 Xx → U Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx) →
% 9.39/9.57 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 9.39/9.57 (∀ (Xx : a), And (And (skS.0 0 a_1 Xx) (U Xx)) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 1 a_1 a_2 Xx))
% 9.39/9.57 False
% 9.39/9.57 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop),
% 9.39/9.57 Eq
% 9.39/9.57 (Not
% 9.39/9.57 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 9.39/9.57 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) →
% 9.39/9.57 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 9.39/9.57 (∀ (Xx : a),
% 9.39/9.57 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)) → skS.0 1 a_1 a_2 Xx)))
% 9.39/9.57 True
% 9.39/9.57 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop),
% 9.39/9.57 Eq
% 9.39/9.57 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 9.39/9.57 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) →
% 9.39/9.57 Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 9.39/9.57 (∀ (Xx : a),
% 9.39/9.57 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)) → skS.0 1 a_1 a_2 Xx))
% 9.39/9.57 False
% 9.39/9.57 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 9.39/9.57 Eq
% 9.39/9.57 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 2 a_1 a_2 a_3 Xx)
% 9.39/9.57 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx))
% 9.39/9.57 True
% 9.39/9.57 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 9.39/9.57 Eq
% 9.39/9.57 (Iff (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 9.39/9.57 (∀ (Xx : a), 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)) → skS.0 1 a_1 a_2 Xx))
% 9.39/9.57 False
% 9.39/9.57 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
% 9.39/9.57 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
% 9.39/9.57 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)
% 9.39/9.57 Clause #16 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop),
% 9.39/9.57 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False)
% 9.39/9.57 (Eq
% 9.39/9.57 (∀ (Xx : a), 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)) → skS.0 1 a_1 a_2 Xx)
% 9.39/9.57 False)
% 9.43/9.59 Clause #17 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop),
% 9.43/9.59 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) True)
% 9.43/9.59 (Eq
% 9.43/9.59 (∀ (Xx : a), 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)) → skS.0 1 a_1 a_2 Xx)
% 9.43/9.59 True)
% 9.43/9.59 Clause #18 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 9.43/9.59 Or
% 9.43/9.59 (Eq
% 9.43/9.59 (∀ (Xx : a), 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)) → skS.0 1 a_1 a_2 Xx)
% 9.43/9.59 False)
% 9.43/9.59 (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)
% 9.43/9.59 Clause #19 (by clausification #[18]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.59 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)
% 9.43/9.59 (Eq
% 9.43/9.59 (Not
% 9.43/9.59 (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)))
% 9.43/9.59 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) →
% 9.43/9.59 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5)))
% 9.43/9.59 True)
% 9.43/9.59 Clause #20 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 9.43/9.59 Or
% 9.43/9.59 (Eq
% 9.43/9.59 (Not
% 9.43/9.59 (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)))
% 9.43/9.59 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 9.43/9.59 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)))
% 9.43/9.59 True)
% 9.43/9.59 (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)
% 9.43/9.59 Clause #21 (by clausification #[20]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.59 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)
% 9.43/9.59 (Eq
% 9.43/9.59 (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)))
% 9.43/9.59 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))) →
% 9.43/9.59 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))
% 9.43/9.59 False)
% 9.43/9.59 Clause #22 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 9.43/9.59 Or
% 9.43/9.59 (Eq
% 9.43/9.59 (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)))
% 9.43/9.59 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 9.43/9.59 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))
% 9.43/9.59 False)
% 9.43/9.59 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_5)) True)
% 9.43/9.59 Clause #23 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 9.43/9.59 Or
% 9.43/9.59 (Eq
% 9.43/9.59 (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)))
% 9.43/9.59 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 9.43/9.59 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))
% 9.43/9.59 False)
% 9.43/9.59 (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_5)) False)
% 9.43/9.59 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.59 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True)
% 9.43/9.59 (Eq
% 9.43/9.59 (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)))
% 9.43/9.59 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))))
% 9.43/9.59 True)
% 9.43/9.59 Clause #25 (by clausification #[22]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.59 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)
% 9.43/9.59 Clause #27 (by clausification #[24]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.59 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3)) True)
% 9.43/9.59 (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)
% 9.43/9.59 Clause #28 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 9.43/9.59 Or
% 9.43/9.59 (Eq
% 9.43/9.59 (∀ (Xx : a), 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)) → skS.0 1 a_1 a_2 Xx)
% 9.43/9.59 True)
% 9.43/9.59 (Eq (skS.0 0 a_1 a_4 → skS.0 1 a_1 a_2 a_4) True)
% 9.43/9.59 Clause #29 (by clausification #[28]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 9.43/9.59 Or (Eq (skS.0 0 a_1 a_2 → skS.0 1 a_1 a_3 a_2) True)
% 9.43/9.59 (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)) → skS.0 1 a_1 a_3 a_4) True)
% 9.43/9.62 Clause #30 (by clausification #[29]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop) (a_5 : a),
% 9.43/9.62 Or (Eq (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)) → skS.0 1 a_1 a_3 a_2) True)
% 9.43/9.62 (Or (Eq (skS.0 0 a_1 a_5) False) (Eq (skS.0 1 a_1 a_3 a_5) True))
% 9.43/9.62 Clause #31 (by clausification #[30]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 9.43/9.62 Or (Eq (skS.0 0 a_1 a_2) False)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 9.43/9.62 (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)
% 9.43/9.62 (Eq (skS.0 1 a_1 a_3 a_4) True)))
% 9.43/9.62 Clause #32 (by clausification #[31]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 9.43/9.62 Or (Eq (skS.0 0 a_1 a_2) False)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 a_4) True)
% 9.43/9.62 (Or (Eq (And (skS.0 0 a_1 a_4) (skS.0 2 a_1 a_3 a_5 a_4)) False) (Eq (Not (skS.0 1 a_1 a_3 a_4)) False))))
% 9.43/9.62 Clause #33 (by clausification #[32]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 9.43/9.62 Or (Eq (skS.0 0 a_1 a_2) False)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 a_4) True)
% 9.43/9.62 (Or (Eq (Not (skS.0 1 a_1 a_3 a_4)) False)
% 9.43/9.62 (Or (Eq (skS.0 0 a_1 a_4) False) (Eq (skS.0 2 a_1 a_3 a_5 a_4) False)))))
% 9.43/9.62 Clause #34 (by clausification #[33]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 9.43/9.62 Or (Eq (skS.0 0 a_1 a_2) False)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 a_4) True)
% 9.43/9.62 (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)))))
% 9.43/9.62 Clause #35 (by eliminate duplicate literals #[34]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop),
% 9.43/9.62 Or (Eq (skS.0 0 a_1 a_2) False)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 a_2) True)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_3 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))))
% 9.43/9.62 Clause #36 (by clausification #[23]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.62 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False)
% 9.43/9.62 (Eq
% 9.43/9.62 (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)))
% 9.43/9.62 (Not (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_4 a_5))))
% 9.43/9.62 True)
% 9.43/9.62 Clause #37 (by clausification #[23]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.62 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)
% 9.43/9.62 Clause #39 (by clausification #[36]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.62 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3)) False)
% 9.43/9.62 (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)
% 9.43/9.62 Clause #41 (by clausification #[27]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.62 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)
% 9.43/9.62 Clause #44 (by superposition #[41, 15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 9.43/9.62 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)
% 9.43/9.62 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True))
% 9.43/9.62 Clause #45 (by superposition #[41, 35]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop),
% 9.43/9.62 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)
% 9.43/9.62 (Or (Eq True False)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.43/9.62 (Or (Eq (skS.0 1 a_1 a_5 a_7) True) (Or (Eq (skS.0 0 a_1 a_7) False) (Eq (skS.0 2 a_1 a_5 a_8 a_7) False)))))
% 9.43/9.62 Clause #52 (by betaEtaReduce #[44]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 9.43/9.62 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.43/9.62 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 3 a_1 a_2 a_7)) True))
% 9.43/9.62 Clause #53 (by clausification #[52]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 9.43/9.64 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)
% 9.43/9.64 Clause #57 (by clausification #[39]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 9.43/9.64 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)
% 9.43/9.64 Clause #64 (by betaEtaReduce #[45]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop),
% 9.43/9.64 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.43/9.64 (Or (Eq True False)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 a_7) True) (Or (Eq (skS.0 0 a_1 a_7) False) (Eq (skS.0 2 a_1 a_5 a_8 a_7) False)))))
% 9.43/9.64 Clause #65 (by clausification #[64]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 a_7 : a) (a_8 : a → Prop),
% 9.43/9.64 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 a_7) True) (Or (Eq (skS.0 0 a_1 a_7) False) (Eq (skS.0 2 a_1 a_5 a_8 a_7) False))))
% 9.43/9.64 Clause #66 (by superposition #[65, 41]): ∀ (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_10 : a → Prop)
% 9.43/9.64 (a_11 : a),
% 9.43/9.64 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)
% 9.43/9.64 (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)
% 9.43/9.64 (Or (Eq (skS.0 1 (fun x => a_1 x) a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.43/9.64 (Or (Eq (skS.0 2 (fun x => a_1 x) a_5 a_9 (skS.0 3 a_1 a_7 a_8)) False)
% 9.43/9.64 (Or (Eq False True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_10 a_11)) True)))))
% 9.43/9.64 Clause #98 (by betaEtaReduce #[66]): ∀ (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_10 : a → Prop)
% 9.43/9.64 (a_11 : a),
% 9.43/9.64 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.43/9.64 (Or (Eq (skS.0 2 a_1 a_5 a_9 (skS.0 3 a_1 a_7 a_8)) False)
% 9.43/9.64 (Or (Eq False True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_10 a_11)) True)))))
% 9.43/9.64 Clause #99 (by clausification #[98]): ∀ (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_10 : a → Prop)
% 9.43/9.64 (a_11 : a),
% 9.43/9.64 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.43/9.64 (Or (Eq (skS.0 2 a_1 a_5 a_9 (skS.0 3 a_1 a_7 a_8)) False)
% 9.43/9.64 (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_10 a_11)) True))))
% 9.43/9.64 Clause #100 (by superposition #[99, 53]): ∀ (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)
% 9.43/9.64 (a_11 : a → Prop) (a_12 : a),
% 9.43/9.64 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)
% 9.43/9.64 (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)
% 9.43/9.64 (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)
% 9.43/9.64 (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)
% 9.43/9.64 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True) (Eq False True)))))
% 9.43/9.64 Clause #342 (by betaEtaReduce #[100]): ∀ (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)
% 9.43/9.64 (a_11 : a → Prop) (a_12 : a),
% 9.43/9.64 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.43/9.64 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.43/9.64 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True)
% 9.43/9.64 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_11 a_12)) True) (Eq False True)))))
% 9.43/9.64 Clause #343 (by clausification #[342]): ∀ (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)
% 9.43/9.64 (a_11 : a → Prop) (a_12 : a),
% 9.43/9.64 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.51/9.67 (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))))
% 9.51/9.67 Clause #368 (by equality factoring #[343]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.51/9.67 (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))))
% 9.51/9.67 Clause #377 (by betaEtaReduce #[368]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.51/9.67 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True))))
% 9.51/9.67 Clause #378 (by clausification #[377]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.51/9.67 (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)))))
% 9.51/9.67 Clause #380 (by clausification #[378]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_7 a_8)) True)
% 9.51/9.67 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_7 a_9 a_10)) True) (Eq True False))))
% 9.51/9.67 Clause #381 (by clausification #[380]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 3 a_1 a_2 a_6)) True)
% 9.51/9.67 (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)))
% 9.51/9.67 Clause #405 (by equality factoring #[381]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 (fun x => a_2 x) a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 9.51/9.67 (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)))
% 9.51/9.67 Clause #408 (by betaEtaReduce #[405]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 9.51/9.67 (Or (Ne True True) (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True)))
% 9.51/9.67 Clause #409 (by clausification #[408]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 9.51/9.67 (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))))
% 9.51/9.67 Clause #411 (by clausification #[409]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True)
% 9.51/9.67 (Or (Eq (skS.0 1 a_1 a_7 (skS.0 3 a_1 a_2 a_8)) True) (Eq True False)))
% 9.51/9.67 Clause #412 (by clausification #[411]): ∀ (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),
% 9.51/9.67 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.67 (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))
% 9.51/9.69 Clause #423 (by equality factoring #[412]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.51/9.69 (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))
% 9.51/9.69 Clause #424 (by betaEtaReduce #[423]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.51/9.69 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True))
% 9.51/9.69 Clause #425 (by clausification #[424]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.51/9.69 (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)))
% 9.51/9.69 Clause #427 (by clausification #[425]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.51/9.69 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_3 a_5 a_6)) True) (Eq True False))
% 9.51/9.69 Clause #428 (by clausification #[427]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 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)
% 9.51/9.69 Clause #431 (by superposition #[428, 57]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 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)
% 9.51/9.69 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True))
% 9.51/9.69 Clause #437 (by betaEtaReduce #[431]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 9.51/9.69 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5 a_6)) True))
% 9.51/9.69 Clause #438 (by clausification #[437]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 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)
% 9.51/9.69 Clause #444 (by equality factoring #[438]): ∀ (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)
% 9.51/9.69 Clause #445 (by betaEtaReduce #[444]): ∀ (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)
% 9.51/9.69 Clause #446 (by clausification #[445]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 9.51/9.69 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))
% 9.51/9.69 Clause #448 (by clausification #[446]): ∀ (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)
% 9.51/9.69 Clause #449 (by clausification #[448]): ∀ (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
% 9.51/9.69 Clause #450 (by superposition #[449, 15]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a),
% 9.51/9.69 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)
% 9.51/9.69 Clause #451 (by superposition #[449, 35]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 a_6 : a) (a_7 : a → Prop),
% 9.51/9.69 Or (Eq True False)
% 9.51/9.69 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 9.51/9.69 (Or (Eq (skS.0 1 a_1 a_2 a_6) True) (Or (Eq (skS.0 0 a_1 a_6) False) (Eq (skS.0 2 a_1 a_2 a_7 a_6) False))))
% 9.51/9.69 Clause #457 (by clausification #[450]): ∀ (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
% 9.51/9.69 Clause #489 (by clausification #[451]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 a_6 : a) (a_7 : a → Prop),
% 9.51/9.69 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 9.51/9.69 (Or (Eq (skS.0 1 a_1 a_2 a_6) True) (Or (Eq (skS.0 0 a_1 a_6) False) (Eq (skS.0 2 a_1 a_2 a_7 a_6) False)))
% 9.51/9.69 Clause #490 (by superposition #[489, 449]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop),
% 9.51/9.69 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)
% 9.51/9.69 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True)
% 9.51/9.69 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_9 (skS.0 4 a_1 a_6 a_7 a_8)) False) (Eq False True)))
% 9.51/9.69 Clause #527 (by betaEtaReduce #[490]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop),
% 9.56/9.71 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 9.56/9.71 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True)
% 9.56/9.71 (Or (Eq (skS.0 2 a_1 a_2 a_9 (skS.0 4 a_1 a_6 a_7 a_8)) False) (Eq False True)))
% 9.56/9.71 Clause #528 (by clausification #[527]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a) (a_9 : a → Prop),
% 9.56/9.71 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 9.56/9.71 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True)
% 9.56/9.71 (Eq (skS.0 2 a_1 a_2 a_9 (skS.0 4 a_1 a_6 a_7 a_8)) False))
% 9.56/9.71 Clause #529 (by superposition #[528, 457]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a),
% 9.56/9.71 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)
% 9.56/9.71 (Or
% 9.56/9.71 (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))
% 9.56/9.71 True)
% 9.56/9.71 (Eq False True))
% 9.56/9.71 Clause #530 (by betaEtaReduce #[529]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a),
% 9.56/9.71 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 9.56/9.71 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_6 a_7 a_8)) True) (Eq False True))
% 9.56/9.71 Clause #531 (by clausification #[530]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 a_7 : a → Prop) (a_8 : a),
% 9.56/9.71 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)
% 9.56/9.71 Clause #534 (by equality factoring #[531]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 9.56/9.71 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)
% 9.56/9.71 Clause #535 (by betaEtaReduce #[534]): ∀ (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)
% 9.56/9.71 Clause #536 (by clausification #[535]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a),
% 9.56/9.71 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))
% 9.56/9.71 Clause #538 (by clausification #[536]): ∀ (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)
% 9.56/9.71 Clause #539 (by clausification #[538]): ∀ (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
% 9.56/9.71 Clause #540 (by superposition #[539, 25]): ∀ (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)
% 9.56/9.71 Clause #543 (by clausification #[540]): ∀ (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
% 9.56/9.71 Clause #544 (by superposition #[543, 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)
% 9.56/9.71 Clause #545 (by superposition #[543, 35]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a) (a_6 : a → Prop),
% 9.56/9.71 Or (Eq True False)
% 9.56/9.71 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.56/9.71 (Or (Eq (skS.0 1 a_1 a_2 a_5) True) (Or (Eq (skS.0 0 a_1 a_5) False) (Eq (skS.0 2 a_1 a_2 a_6 a_5) False))))
% 9.56/9.71 Clause #546 (by clausification #[544]): ∀ (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
% 9.56/9.71 Clause #553 (by clausification #[545]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a) (a_6 : a → Prop),
% 9.56/9.71 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.56/9.71 (Or (Eq (skS.0 1 a_1 a_2 a_5) True) (Or (Eq (skS.0 0 a_1 a_5) False) (Eq (skS.0 2 a_1 a_2 a_6 a_5) False)))
% 9.56/9.71 Clause #555 (by superposition #[553, 543]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop),
% 9.56/9.71 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)
% 9.56/9.71 (Or (Eq (skS.0 1 (fun x => a_1 x) a_2 (skS.0 3 a_1 a_5 a_6)) True)
% 9.56/9.71 (Or (Eq (skS.0 2 (fun x => a_1 x) a_2 a_7 (skS.0 3 a_1 a_5 a_6)) False) (Eq False True)))
% 9.56/9.71 Clause #556 (by betaEtaReduce #[555]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop),
% 9.56/9.71 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.56/9.71 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True)
% 9.56/9.71 (Or (Eq (skS.0 2 a_1 a_2 a_7 (skS.0 3 a_1 a_5 a_6)) False) (Eq False True)))
% 9.56/9.73 Clause #557 (by clausification #[556]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop),
% 9.56/9.73 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.56/9.73 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True) (Eq (skS.0 2 a_1 a_2 a_7 (skS.0 3 a_1 a_5 a_6)) False))
% 9.56/9.73 Clause #558 (by superposition #[557, 546]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.56/9.73 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)
% 9.56/9.73 (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)
% 9.56/9.73 (Eq False True))
% 9.56/9.73 Clause #559 (by betaEtaReduce #[558]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.56/9.73 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4)) True)
% 9.56/9.73 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_5 a_6)) True) (Eq False True))
% 9.56/9.73 Clause #560 (by clausification #[559]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 9.56/9.73 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)
% 9.56/9.73 Clause #563 (by equality factoring #[560]): ∀ (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)
% 9.56/9.73 Clause #564 (by betaEtaReduce #[563]): ∀ (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)
% 9.56/9.73 Clause #565 (by clausification #[564]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 9.56/9.73 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))
% 9.56/9.73 Clause #567 (by clausification #[565]): ∀ (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)
% 9.56/9.73 Clause #568 (by clausification #[567]): ∀ (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
% 9.56/9.73 Clause #569 (by superposition #[568, 37]): ∀ (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)
% 9.56/9.73 Clause #570 (by clausification #[569]): ∀ (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
% 9.56/9.73 Clause #571 (by superposition #[570, 539]): Eq False True
% 9.56/9.73 Clause #574 (by clausification #[571]): False
% 9.56/9.73 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------