TSTP Solution File: SEU850^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU850^5 : 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 19.74s 19.97s
% Output : Proof 19.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU850^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:10:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 19.74/19.97 SZS status Theorem for theBenchmark.p
% 19.74/19.97 SZS output start Proof for theBenchmark.p
% 19.74/19.97 Clause #0 (by assumption #[]): Eq
% 19.74/19.97 (Not
% 19.74/19.97 (∀ (S T U : a → Prop),
% 19.74/19.97 And (Eq S T) (Eq T U) → And (And (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), T Xx → U Xx)) (∀ (Xx : a), U Xx → S Xx)))
% 19.74/19.97 True
% 19.74/19.97 Clause #1 (by clausification #[0]): Eq
% 19.74/19.97 (∀ (S T U : a → Prop),
% 19.74/19.97 And (Eq S T) (Eq T U) → And (And (∀ (Xx : a), S Xx → T Xx) (∀ (Xx : a), T Xx → U Xx)) (∀ (Xx : a), U Xx → S Xx))
% 19.74/19.97 False
% 19.74/19.97 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop),
% 19.74/19.97 Eq
% 19.74/19.97 (Not
% 19.74/19.97 (∀ (T U : a → Prop),
% 19.74/19.97 And (Eq (skS.0 0 a_1) T) (Eq T U) →
% 19.74/19.97 And (And (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) (∀ (Xx : a), T Xx → U Xx)) (∀ (Xx : a), U Xx → skS.0 0 a_1 Xx)))
% 19.74/19.97 True
% 19.74/19.97 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop),
% 19.74/19.97 Eq
% 19.74/19.97 (∀ (T U : a → Prop),
% 19.74/19.97 And (Eq (skS.0 0 a_1) T) (Eq T U) →
% 19.74/19.97 And (And (∀ (Xx : a), skS.0 0 a_1 Xx → T Xx) (∀ (Xx : a), T Xx → U Xx)) (∀ (Xx : a), U Xx → skS.0 0 a_1 Xx))
% 19.74/19.97 False
% 19.74/19.97 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop),
% 19.74/19.97 Eq
% 19.74/19.97 (Not
% 19.74/19.97 (∀ (U : a → Prop),
% 19.74/19.97 And (Eq (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (Eq (skS.0 1 a_1 a_2) U) →
% 19.74/19.97 And (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx))
% 19.74/19.97 (∀ (Xx : a), U Xx → skS.0 0 a_1 Xx)))
% 19.74/19.97 True
% 19.74/19.97 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop),
% 19.74/19.97 Eq
% 19.74/19.97 (∀ (U : a → Prop),
% 19.74/19.97 And (Eq (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (Eq (skS.0 1 a_1 a_2) U) →
% 19.74/19.97 And (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → U Xx))
% 19.74/19.97 (∀ (Xx : a), U Xx → skS.0 0 a_1 Xx))
% 19.74/19.97 False
% 19.74/19.97 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.74/19.97 Eq
% 19.74/19.97 (Not
% 19.74/19.97 (And (Eq (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (Eq (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) →
% 19.74/19.97 And
% 19.74/19.97 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 19.74/19.97 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx))
% 19.74/19.97 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 0 a_1 Xx)))
% 19.74/19.97 True
% 19.74/19.97 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.74/19.97 Eq
% 19.74/19.97 (And (Eq (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (Eq (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) →
% 19.74/19.97 And
% 19.74/19.97 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx)
% 19.74/19.97 (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx))
% 19.74/19.97 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 0 a_1 Xx))
% 19.74/19.97 False
% 19.74/19.97 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.74/19.97 Eq (And (Eq (skS.0 0 a_1) (skS.0 1 a_1 a_2)) (Eq (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3))) True
% 19.74/19.97 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.74/19.97 Eq
% 19.74/19.97 (And
% 19.74/19.97 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx))
% 19.74/19.97 (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 0 a_1 Xx))
% 19.74/19.97 False
% 19.74/19.97 Clause #10 (by clausification #[8]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (Eq (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)) True
% 19.74/19.97 Clause #11 (by clausification #[8]): ∀ (a_1 a_2 : a → Prop), Eq (Eq (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True
% 19.74/19.97 Clause #12 (by clausification #[10]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (skS.0 1 a_1 a_2) (skS.0 2 a_1 a_2 a_3)
% 19.74/19.97 Clause #14 (by clausification #[11]): ∀ (a_1 a_2 : a → Prop), Eq (skS.0 0 a_1) (skS.0 1 a_1 a_2)
% 19.74/19.97 Clause #15 (by backward demodulation #[14, 12]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (skS.0 0 a_1) (skS.0 2 a_1 a_2 a_3)
% 19.74/19.97 Clause #16 (by argument congruence #[14]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Eq (skS.0 0 a_1 a_2) (skS.0 1 a_1 a_3 a_2)
% 19.74/19.97 Clause #18 (by clausify Prop equality #[16]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 : a → Prop), Or (Eq (skS.0 0 a_1 a_2) False) (Eq (skS.0 1 a_1 a_3 a_2) True)
% 19.74/19.97 Clause #19 (by argument congruence #[15]): ∀ (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)
% 19.74/19.97 Clause #21 (by clausify Prop equality #[19]): ∀ (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)
% 19.74/20.00 Clause #22 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.74/20.00 Or
% 19.74/20.00 (Eq
% 19.74/20.00 (And (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx))
% 19.74/20.00 False)
% 19.74/20.00 (Eq (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 0 a_1 Xx) False)
% 19.74/20.00 Clause #23 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a → Prop),
% 19.74/20.00 Or (Eq (∀ (Xx : a), skS.0 2 a_1 a_2 a_3 Xx → skS.0 0 a_1 Xx) False)
% 19.74/20.00 (Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False)
% 19.74/20.00 (Eq (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) False))
% 19.74/20.00 Clause #24 (by clausification #[23]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 19.74/20.00 Or (Eq (∀ (Xx : a), skS.0 0 a_1 Xx → skS.0 1 a_1 a_2 Xx) False)
% 19.74/20.00 (Or (Eq (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) False)
% 19.74/20.00 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4) → skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) True))
% 19.74/20.00 Clause #25 (by clausification #[24]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.74/20.00 Or (Eq (∀ (Xx : a), skS.0 1 a_1 a_2 Xx → skS.0 2 a_1 a_2 a_3 Xx) False)
% 19.74/20.00 (Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4) → skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) True)
% 19.74/20.00 (Eq (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_5))) True))
% 19.74/20.00 Clause #26 (by clausification #[25]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.74/20.00 Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4) → skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4))) True)
% 19.74/20.00 (Or (Eq (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_5))) True)
% 19.74/20.00 (Eq (Not (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_6) → skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_6))) True))
% 19.74/20.00 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 19.74/20.00 Or (Eq (Not (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3))) True)
% 19.74/20.00 (Or (Eq (Not (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_5) → skS.0 2 a_1 a_2 a_4 (skS.0 5 a_1 a_2 a_4 a_5))) True)
% 19.74/20.00 (Eq (skS.0 2 a_1 a_2 a_4 (skS.0 3 a_1 a_2 a_4 a_6) → skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_6)) False))
% 19.74/20.00 Clause #28 (by clausification #[27]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.74/20.00 Or (Eq (Not (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4) → skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4))) True)
% 19.74/20.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5) → skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) False)
% 19.74/20.00 (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_6)) False))
% 19.74/20.00 Clause #29 (by clausification #[28]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.74/20.00 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4) → skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 19.74/20.00 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_5)) False)
% 19.74/20.00 (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_6) → skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_6)) False))
% 19.74/20.00 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 19.74/20.00 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3)) False)
% 19.74/20.00 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_5) → skS.0 2 a_1 a_2 a_4 (skS.0 5 a_1 a_2 a_4 a_5)) False)
% 19.74/20.00 (Eq (skS.0 2 a_1 a_2 a_4 (skS.0 3 a_1 a_2 a_4 a_6)) True))
% 19.74/20.00 Clause #31 (by clausification #[29]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 19.74/20.00 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3) → skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3)) False)
% 19.74/20.00 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_5) → skS.0 2 a_1 a_2 a_4 (skS.0 5 a_1 a_2 a_4 a_5)) False)
% 19.74/20.00 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_6)) False))
% 19.74/20.00 Clause #32 (by clausification #[30]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.74/20.00 Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4) → skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4)) False)
% 19.74/20.00 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6)) True))
% 19.84/20.02 Clause #33 (by clausification #[30]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4) → skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4)) False)
% 19.84/20.02 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_6)) False))
% 19.84/20.02 Clause #34 (by clausification #[32]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.84/20.02 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_6)) True))
% 19.84/20.02 Clause #35 (by clausification #[32]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.84/20.02 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_6)) False))
% 19.84/20.02 Clause #36 (by superposition #[34, 19]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 19.84/20.02 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)) True)
% 19.84/20.02 (Or
% 19.84/20.02 (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 5 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_4 x) a_5))
% 19.84/20.02 True)
% 19.84/20.02 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_6)) True))
% 19.84/20.02 Clause #44 (by superposition #[35, 19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or
% 19.84/20.02 (Eq
% 19.84/20.02 (skS.0 2 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x)
% 19.84/20.02 (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4))
% 19.84/20.02 True)
% 19.84/20.02 (Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) a_5)) True)
% 19.84/20.02 (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_6)) False))
% 19.84/20.02 Clause #45 (by clausification #[31]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4) → skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4)) False)
% 19.84/20.02 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6)) True))
% 19.84/20.02 Clause #46 (by clausification #[31]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4) → skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4)) False)
% 19.84/20.02 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_6)) False))
% 19.84/20.02 Clause #47 (by clausification #[45]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 19.84/20.02 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_6)) True))
% 19.84/20.02 Clause #48 (by clausification #[45]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 19.84/20.02 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_6)) False))
% 19.84/20.02 Clause #49 (by clausification #[46]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 19.84/20.02 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_5)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_6)) True))
% 19.84/20.02 Clause #50 (by clausification #[46]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 19.84/20.02 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_5)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_6)) False))
% 19.84/20.02 Clause #51 (by clausification #[33]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.84/20.02 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_5)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_6)) True))
% 19.84/20.02 Clause #52 (by clausification #[33]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.84/20.02 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_5)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_6)) False))
% 19.84/20.02 Clause #74 (by betaEtaReduce #[36]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 19.84/20.02 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.02 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_5)) True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_6)) True))
% 19.84/20.05 Clause #79 (by superposition #[74, 47]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 a_7 : a),
% 19.84/20.05 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)) True)
% 19.84/20.05 (Or
% 19.84/20.05 (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 5 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_4 x) a_5))
% 19.84/20.05 True)
% 19.84/20.05 (Or (Eq True False)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_7)) True))))
% 19.84/20.05 Clause #176 (by betaEtaReduce #[44]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 19.84/20.05 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_6)) False))
% 19.84/20.05 Clause #431 (by betaEtaReduce #[79]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 a_7 : a),
% 19.84/20.05 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.05 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_5)) True)
% 19.84/20.05 (Or (Eq True False)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_7)) True))))
% 19.84/20.05 Clause #432 (by clausification #[431]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 a_7 : a),
% 19.84/20.05 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.05 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_5)) True)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_7)) True)))
% 19.84/20.05 Clause #444 (by equality factoring #[432]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.84/20.05 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True)
% 19.84/20.05 (Or (Ne True True) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_5 a_6)) True)))
% 19.84/20.05 Clause #445 (by clausification #[444]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.84/20.05 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True)
% 19.84/20.05 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_5 a_6)) True) (Or (Eq True False) (Eq True False))))
% 19.84/20.05 Clause #447 (by clausification #[445]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.84/20.05 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True)
% 19.84/20.05 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_5 a_6)) True) (Eq True False)))
% 19.84/20.05 Clause #448 (by clausification #[447]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.84/20.05 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_5 a_6)) True))
% 19.84/20.05 Clause #454 (by equality factoring #[448]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.84/20.05 Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4)) True)
% 19.84/20.05 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True))
% 19.84/20.05 Clause #455 (by clausification #[454]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.84/20.05 Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4)) True)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Or (Eq True False) (Eq True False)))
% 19.84/20.05 Clause #457 (by clausification #[455]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.84/20.05 Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4)) True)
% 19.84/20.05 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq True False))
% 19.84/20.05 Clause #458 (by clausification #[457]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.84/20.05 Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True)
% 19.84/20.05 Clause #459 (by superposition #[458, 16]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.84/20.05 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)) True)
% 19.84/20.05 (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_4 a_5)) True)
% 19.84/20.05 Clause #464 (by betaEtaReduce #[459]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.84/20.05 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True) (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_4 a_5)) True)
% 19.84/20.05 Clause #468 (by superposition #[464, 176]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 19.84/20.07 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)) True)
% 19.84/20.07 (Or (Eq (skS.0 2 a_1 a_2 a_4 (skS.0 3 a_1 a_2 a_4 a_5)) True)
% 19.84/20.07 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6)) True) (Eq True False)))
% 19.84/20.07 Clause #470 (by superposition #[464, 21]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 a_5 a_6 : a → Prop) (a_7 : a),
% 19.84/20.07 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) a_2 a_3)) True)
% 19.84/20.07 (Or (Eq True False) (Eq (skS.0 2 a_1 a_4 a_5 (skS.0 5 a_1 a_2 a_6 a_7)) True))
% 19.84/20.07 Clause #525 (by betaEtaReduce #[470]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 a_5 a_6 : a → Prop) (a_7 : a),
% 19.84/20.07 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.07 (Or (Eq True False) (Eq (skS.0 2 a_1 a_4 a_5 (skS.0 5 a_1 a_2 a_6 a_7)) True))
% 19.84/20.07 Clause #526 (by clausification #[525]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 a_5 a_6 : a → Prop) (a_7 : a),
% 19.84/20.07 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True) (Eq (skS.0 2 a_1 a_4 a_5 (skS.0 5 a_1 a_2 a_6 a_7)) True)
% 19.84/20.07 Clause #575 (by betaEtaReduce #[468]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 19.84/20.07 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.07 (Or (Eq (skS.0 2 a_1 a_2 a_4 (skS.0 3 a_1 a_2 a_4 a_5)) True)
% 19.84/20.07 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6)) True) (Eq True False)))
% 19.84/20.07 Clause #576 (by clausification #[575]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 a_6 : a),
% 19.84/20.07 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.07 (Or (Eq (skS.0 2 a_1 a_2 a_4 (skS.0 3 a_1 a_2 a_4 a_5)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_6)) True))
% 19.84/20.07 Clause #587 (by equality factoring #[576]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.84/20.07 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.84/20.07 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True))
% 19.84/20.07 Clause #590 (by clausification #[587]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.84/20.07 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.84/20.07 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Or (Eq True False) (Eq True False)))
% 19.84/20.07 Clause #592 (by clausification #[590]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.84/20.07 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.84/20.07 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq True False))
% 19.84/20.07 Clause #593 (by clausification #[592]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.84/20.07 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True)
% 19.84/20.07 Clause #594 (by superposition #[593, 19]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.84/20.07 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)) True)
% 19.84/20.07 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5)) True)
% 19.84/20.07 Clause #599 (by betaEtaReduce #[594]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.84/20.07 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_4 a_5)) True)
% 19.84/20.07 Clause #603 (by superposition #[599, 48]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.84/20.07 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)) True)
% 19.84/20.07 (Or (Eq True False)
% 19.84/20.07 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 5 a_1 a_2 a_5 a_6)) False)))
% 19.84/20.07 Clause #702 (by betaEtaReduce #[603]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.84/20.07 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.07 (Or (Eq True False)
% 19.84/20.07 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 5 a_1 a_2 a_5 a_6)) False)))
% 19.84/20.07 Clause #703 (by clausification #[702]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a) (a_5 : a → Prop) (a_6 : a),
% 19.84/20.07 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.84/20.07 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_5 (skS.0 5 a_1 a_2 a_5 a_6)) False))
% 19.84/20.07 Clause #704 (by superposition #[703, 526]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 a_5 : a),
% 19.84/20.07 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)) True)
% 19.84/20.07 (Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) a_4)) True)
% 19.93/20.10 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq False True)))
% 19.93/20.10 Clause #710 (by betaEtaReduce #[704]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.93/20.10 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True)
% 19.93/20.10 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True) (Eq False True)))
% 19.93/20.10 Clause #711 (by clausification #[710]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.93/20.10 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_5)) True))
% 19.93/20.10 Clause #715 (by equality factoring #[711]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a),
% 19.93/20.10 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True) (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True))
% 19.93/20.10 Clause #716 (by clausification #[715]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a),
% 19.93/20.10 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.93/20.10 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True) (Or (Eq True False) (Eq True False)))
% 19.93/20.10 Clause #718 (by clausification #[716]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a),
% 19.93/20.10 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True) (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True) (Eq True False))
% 19.93/20.10 Clause #719 (by clausification #[718]): ∀ (a_1 a_2 : a → Prop) (a_3 a_4 : a),
% 19.93/20.10 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_4)) True)
% 19.93/20.10 Clause #723 (by equality factoring #[719]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True)
% 19.93/20.10 Clause #737 (by clausification #[723]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True) (Or (Eq True False) (Eq True False))
% 19.93/20.10 Clause #739 (by clausification #[737]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True) (Eq True False)
% 19.93/20.10 Clause #740 (by clausification #[739]): ∀ (a_1 a_2 : a → Prop) (a_3 : a), Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3)) True
% 19.93/20.10 Clause #742 (by superposition #[740, 18]): ∀ (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_3 a_4)) True)
% 19.93/20.10 Clause #744 (by clausification #[742]): ∀ (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_3 a_4)) True
% 19.93/20.10 Clause #745 (by superposition #[744, 51]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.93/20.10 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_5)) True))
% 19.93/20.10 Clause #746 (by superposition #[744, 52]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.93/20.10 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_5)) False))
% 19.93/20.10 Clause #755 (by clausification #[745]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_5)) True)
% 19.93/20.10 Clause #758 (by superposition #[755, 16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 2 (fun x => a_1 x) (fun x => a_2 x) a_3 (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) a_3 a_4)) True)
% 19.93/20.10 (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_5)) True)
% 19.93/20.10 Clause #760 (by clausification #[746]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.93/20.10 (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_5)) False)
% 19.93/20.10 Clause #763 (by betaEtaReduce #[758]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_5)) True)
% 19.93/20.10 Clause #764 (by superposition #[763, 19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 5 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True)
% 19.93/20.10 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)
% 19.93/20.10 Clause #768 (by betaEtaReduce #[764]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.10 Or (Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)
% 19.93/20.10 Clause #770 (by superposition #[768, 21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.93/20.12 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) a_2 a_3 a_4)) True)
% 19.93/20.12 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 5 a_1 a_2 a_3 a_7)) True))
% 19.93/20.12 Clause #793 (by betaEtaReduce #[770]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.93/20.12 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.93/20.12 (Or (Eq True False) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 5 a_1 a_2 a_3 a_7)) True))
% 19.93/20.12 Clause #794 (by clausification #[793]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 a_6 : a → Prop) (a_7 : a),
% 19.93/20.12 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_5 a_6 (skS.0 5 a_1 a_2 a_3 a_7)) True)
% 19.93/20.12 Clause #799 (by superposition #[794, 760]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.12 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True)
% 19.93/20.12 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq True False))
% 19.93/20.12 Clause #842 (by betaEtaReduce #[799]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.12 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.93/20.12 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq True False))
% 19.93/20.12 Clause #843 (by clausification #[842]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.12 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5)) True)
% 19.93/20.12 Clause #848 (by superposition #[843, 19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.12 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 3 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True)
% 19.93/20.12 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)
% 19.93/20.12 Clause #850 (by betaEtaReduce #[848]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 19.93/20.12 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)
% 19.93/20.12 Clause #855 (by equality factoring #[850]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 19.93/20.12 Clause #856 (by clausification #[855]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 19.93/20.12 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Or (Eq True False) (Eq True False))
% 19.93/20.12 Clause #858 (by clausification #[856]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq True False)
% 19.93/20.12 Clause #859 (by clausification #[858]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True
% 19.93/20.12 Clause #860 (by superposition #[859, 49]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.93/20.12 Or (Eq True False)
% 19.93/20.12 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_5)) True))
% 19.93/20.12 Clause #861 (by superposition #[859, 50]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.93/20.12 Or (Eq True False)
% 19.93/20.12 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3)) False) (Eq (skS.0 2 a_1 a_2 a_4 (skS.0 5 a_1 a_2 a_4 a_5)) False))
% 19.93/20.12 Clause #868 (by clausification #[860]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.93/20.12 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_4 a_5)) True)
% 19.93/20.12 Clause #869 (by superposition #[868, 744]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 19.93/20.12 Or (Eq (skS.0 1 (fun x => a_1 x) (fun x => a_2 x) (skS.0 5 (fun x => a_1 x) (fun x => a_2 x) a_3 a_4)) True)
% 19.93/20.12 (Eq False True)
% 19.93/20.12 Clause #871 (by betaEtaReduce #[869]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4)) True) (Eq False True)
% 19.93/20.12 Clause #872 (by clausification #[871]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 1 a_1 a_2 (skS.0 5 a_1 a_2 a_3 a_4)) True
% 19.93/20.12 Clause #873 (by superposition #[872, 16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4)) True
% 19.93/20.12 Clause #878 (by superposition #[873, 21]): ∀ (a_1 a_2 a_3 a_4 a_5 : a → Prop) (a_6 : a),
% 19.93/20.12 Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_4 a_5 a_6)) True)
% 19.93/20.12 Clause #880 (by clausification #[878]): ∀ (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 5 a_1 a_4 a_5 a_6)) True
% 19.93/20.13 Clause #881 (by clausification #[861]): ∀ (a_1 a_2 : a → Prop) (a_3 : a) (a_4 : a → Prop) (a_5 : a),
% 19.93/20.13 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3)) False) (Eq (skS.0 2 a_1 a_2 a_4 (skS.0 5 a_1 a_2 a_4 a_5)) False)
% 19.93/20.13 Clause #882 (by superposition #[881, 744]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 19.93/20.13 Or (Eq (skS.0 2 (fun x => a_1 x) (fun x => a_2 x) a_3 (skS.0 5 (fun x => a_1 x) (fun x => a_2 x) a_3 a_4)) False)
% 19.93/20.13 (Eq False True)
% 19.93/20.13 Clause #886 (by betaEtaReduce #[882]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4)) False) (Eq False True)
% 19.93/20.13 Clause #887 (by clausification #[886]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4)) False
% 19.93/20.13 Clause #888 (by superposition #[887, 880]): Eq False True
% 19.93/20.13 Clause #890 (by clausification #[888]): False
% 19.93/20.13 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------