TSTP Solution File: SET593^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET593^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n026.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 14:46:57 EDT 2023
% Result : Theorem 5.46s 5.65s
% Output : Proof 5.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET593^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 12:03:03 EDT 2023
% 0.14/0.36 % CPUTime :
% 5.46/5.65 SZS status Theorem for theBenchmark.p
% 5.46/5.65 SZS output start Proof for theBenchmark.p
% 5.46/5.65 Clause #0 (by assumption #[]): Eq
% 5.46/5.65 (Not
% 5.46/5.65 (∀ (X Y Z : a → Prop),
% 5.46/5.65 (∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) →
% 5.46/5.65 And (∀ (Xx : a), And (X Xx) (Not (Y Xx)) → Z Xx) (∀ (Xx : a), And (X Xx) (Not (Z Xx)) → Y Xx)))
% 5.46/5.65 True
% 5.46/5.65 Clause #1 (by clausification #[0]): Eq
% 5.46/5.65 (∀ (X Y Z : a → Prop),
% 5.46/5.65 (∀ (Xx : a), X Xx → Or (Y Xx) (Z Xx)) →
% 5.46/5.65 And (∀ (Xx : a), And (X Xx) (Not (Y Xx)) → Z Xx) (∀ (Xx : a), And (X Xx) (Not (Z Xx)) → Y Xx))
% 5.46/5.65 False
% 5.46/5.65 Clause #2 (by clausification #[1]): ∀ (a_1 : a → Prop),
% 5.46/5.65 Eq
% 5.46/5.65 (Not
% 5.46/5.65 (∀ (Y Z : a → Prop),
% 5.46/5.65 (∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx)) →
% 5.46/5.65 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Y Xx)) → Z Xx)
% 5.46/5.65 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Z Xx)) → Y Xx)))
% 5.46/5.65 True
% 5.46/5.65 Clause #3 (by clausification #[2]): ∀ (a_1 : a → Prop),
% 5.46/5.65 Eq
% 5.46/5.65 (∀ (Y Z : a → Prop),
% 5.46/5.65 (∀ (Xx : a), skS.0 0 a_1 Xx → Or (Y Xx) (Z Xx)) →
% 5.46/5.65 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Y Xx)) → Z Xx)
% 5.46/5.65 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Z Xx)) → Y Xx))
% 5.46/5.65 False
% 5.46/5.65 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : a → Prop),
% 5.46/5.65 Eq
% 5.46/5.65 (Not
% 5.46/5.65 (∀ (Z : a → Prop),
% 5.46/5.65 (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx)) →
% 5.46/5.65 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → Z Xx)
% 5.46/5.65 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Z Xx)) → skS.0 1 a_1 a_2 Xx)))
% 5.46/5.65 True
% 5.46/5.65 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 : a → Prop),
% 5.46/5.65 Eq
% 5.46/5.65 (∀ (Z : a → Prop),
% 5.46/5.65 (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (Z Xx)) →
% 5.46/5.65 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → Z Xx)
% 5.46/5.65 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (Z Xx)) → skS.0 1 a_1 a_2 Xx))
% 5.46/5.65 False
% 5.46/5.65 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 a_3 : a → Prop),
% 5.46/5.65 Eq
% 5.46/5.65 (Not
% 5.46/5.65 ((∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) →
% 5.46/5.65 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx)
% 5.46/5.65 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx)))
% 5.46/5.65 True
% 5.46/5.65 Clause #7 (by clausification #[6]): ∀ (a_1 a_2 a_3 : a → Prop),
% 5.46/5.65 Eq
% 5.46/5.65 ((∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) →
% 5.46/5.65 And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx)
% 5.46/5.65 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx))
% 5.46/5.65 False
% 5.46/5.65 Clause #8 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop), Eq (∀ (Xx : a), skS.0 0 a_1 Xx → Or (skS.0 1 a_1 a_2 Xx) (skS.0 2 a_1 a_2 a_3 Xx)) True
% 5.46/5.65 Clause #9 (by clausification #[7]): ∀ (a_1 a_2 a_3 : a → Prop),
% 5.46/5.65 Eq
% 5.46/5.65 (And (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx)
% 5.46/5.65 (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx))
% 5.46/5.65 False
% 5.46/5.65 Clause #10 (by clausification #[8]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop),
% 5.46/5.65 Eq (skS.0 0 a_1 a_2 → Or (skS.0 1 a_1 a_3 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True
% 5.46/5.65 Clause #11 (by clausification #[10]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop),
% 5.46/5.65 Or (Eq (skS.0 0 a_1 a_2) False) (Eq (Or (skS.0 1 a_1 a_3 a_2) (skS.0 2 a_1 a_3 a_4 a_2)) True)
% 5.46/5.65 Clause #12 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : a) (a_3 a_4 : a → Prop),
% 5.46/5.65 Or (Eq (skS.0 0 a_1 a_2) False) (Or (Eq (skS.0 1 a_1 a_3 a_2) True) (Eq (skS.0 2 a_1 a_3 a_4 a_2) True))
% 5.46/5.65 Clause #13 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop),
% 5.46/5.65 Or (Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 1 a_1 a_2 Xx)) → skS.0 2 a_1 a_2 a_3 Xx) False)
% 5.46/5.65 (Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) False)
% 5.46/5.65 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 5.46/5.65 Or (Eq (∀ (Xx : a), And (skS.0 0 a_1 Xx) (Not (skS.0 2 a_1 a_2 a_3 Xx)) → skS.0 1 a_1 a_2 Xx) False)
% 5.46/5.67 (Eq
% 5.46/5.67 (Not
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) →
% 5.46/5.67 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)))
% 5.46/5.67 True)
% 5.46/5.67 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or
% 5.46/5.67 (Eq
% 5.46/5.67 (Not
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) →
% 5.46/5.67 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)))
% 5.46/5.67 True)
% 5.46/5.67 (Eq
% 5.46/5.67 (Not
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) →
% 5.46/5.67 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)))
% 5.46/5.67 True)
% 5.46/5.67 Clause #16 (by clausification #[15]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or
% 5.46/5.67 (Eq
% 5.46/5.67 (Not
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 5.46/5.67 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)))
% 5.46/5.67 True)
% 5.46/5.67 (Eq
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5))) →
% 5.46/5.67 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5))
% 5.46/5.67 False)
% 5.46/5.67 Clause #17 (by clausification #[16]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or
% 5.46/5.67 (Eq
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) →
% 5.46/5.67 skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4))
% 5.46/5.67 False)
% 5.46/5.67 (Eq
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) →
% 5.46/5.67 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5))
% 5.46/5.67 False)
% 5.46/5.67 Clause #18 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or
% 5.46/5.67 (Eq
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 5.46/5.67 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))
% 5.46/5.67 False)
% 5.46/5.67 (Eq (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)))) True)
% 5.46/5.67 Clause #19 (by clausification #[17]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or
% 5.46/5.67 (Eq
% 5.46/5.67 (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) →
% 5.46/5.67 skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4))
% 5.46/5.67 False)
% 5.46/5.67 (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_5)) False)
% 5.46/5.67 Clause #20 (by clausification #[18]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or (Eq (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)))) True)
% 5.46/5.67 (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)))) True)
% 5.46/5.67 Clause #21 (by clausification #[18]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or (Eq (And (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)))) True)
% 5.46/5.67 (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False)
% 5.46/5.67 Clause #22 (by clausification #[20]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)))) True)
% 5.46/5.67 (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5))) True)
% 5.46/5.67 Clause #23 (by clausification #[20]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)))) True)
% 5.46/5.67 (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)
% 5.46/5.67 Clause #24 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4))) True)
% 5.46/5.67 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) True)
% 5.46/5.67 Clause #25 (by clausification #[22]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or (Eq (Not (skS.0 1 a_1 a_2 (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_3 a_5)) True)
% 5.46/5.67 Clause #26 (by clausification #[24]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.46/5.67 Or (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4))) True)
% 5.46/5.67 (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) False)
% 5.46/5.67 Clause #27 (by clausification #[26]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False)
% 5.54/5.70 Clause #28 (by clausification #[25]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) False)
% 5.54/5.70 Clause #29 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 5.54/5.70 (Eq (And (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)))) True)
% 5.54/5.70 Clause #30 (by clausification #[19]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False)
% 5.54/5.70 Clause #31 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 5.54/5.70 (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) True)
% 5.54/5.70 Clause #32 (by clausification #[29]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True)
% 5.54/5.70 Clause #33 (by clausification #[31]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 3 a_1 a_2 a_3 a_4)) False)
% 5.54/5.70 (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False)
% 5.54/5.70 Clause #34 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False) (Eq (Not (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5))) True)
% 5.54/5.70 Clause #35 (by clausification #[21]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True)
% 5.54/5.70 Clause #36 (by clausification #[34]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) False) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) False)
% 5.54/5.70 Clause #37 (by clausification #[23]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (Not (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5))) True)
% 5.54/5.70 Clause #38 (by clausification #[23]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 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 4 a_1 a_2 a_3 a_5)) True)
% 5.54/5.70 Clause #39 (by clausification #[37]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.70 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 4 a_1 a_2 a_3 a_5)) False)
% 5.54/5.70 Clause #41 (by superposition #[38, 12]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop),
% 5.54/5.70 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)
% 5.54/5.70 (Or (Eq True False)
% 5.54/5.70 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 4 a_1 a_2 a_3 a_6)) True)
% 5.54/5.70 (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 4 a_1 a_2 a_3 a_6)) True)))
% 5.54/5.70 Clause #48 (by betaEtaReduce #[41]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop),
% 5.54/5.70 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.70 (Or (Eq True False)
% 5.54/5.70 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 4 a_1 a_2 a_3 a_6)) True)
% 5.54/5.70 (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 4 a_1 a_2 a_3 a_6)) True)))
% 5.54/5.70 Clause #49 (by clausification #[48]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a) (a_5 : a → Prop) (a_6 : a) (a_7 : a → Prop),
% 5.54/5.70 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.70 (Or (Eq (skS.0 1 a_1 a_5 (skS.0 4 a_1 a_2 a_3 a_6)) True) (Eq (skS.0 2 a_1 a_5 a_7 (skS.0 4 a_1 a_2 a_3 a_6)) True))
% 5.54/5.70 Clause #51 (by superposition #[49, 39]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 5.54/5.70 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)
% 5.54/5.70 (Or
% 5.54/5.70 (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_2 x) (fun x => a_3 x) a_5))
% 5.54/5.70 True)
% 5.54/5.70 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_6)) True) (Eq True False)))
% 5.54/5.70 Clause #52 (by betaEtaReduce #[51]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 5.54/5.72 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.72 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True)
% 5.54/5.72 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_6)) True) (Eq True False)))
% 5.54/5.72 Clause #53 (by clausification #[52]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 a_6 : a),
% 5.54/5.72 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.72 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_6)) True))
% 5.54/5.72 Clause #58 (by equality factoring #[53]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 5.54/5.72 (Or (Ne True True) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True))
% 5.54/5.72 Clause #59 (by clausification #[58]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 5.54/5.72 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Or (Eq True False) (Eq True False)))
% 5.54/5.72 Clause #61 (by clausification #[59]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 5.54/5.72 (Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq True False))
% 5.54/5.72 Clause #62 (by clausification #[61]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 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)
% 5.54/5.72 Clause #64 (by superposition #[62, 35]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 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)
% 5.54/5.72 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True))
% 5.54/5.72 Clause #66 (by betaEtaReduce #[64]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 Or (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.72 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 3 a_1 a_2 a_3 a_5)) True))
% 5.54/5.72 Clause #67 (by clausification #[66]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 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)
% 5.54/5.72 Clause #69 (by equality factoring #[67]): ∀ (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)
% 5.54/5.72 Clause #70 (by clausification #[69]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 5.54/5.72 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))
% 5.54/5.72 Clause #72 (by clausification #[70]): ∀ (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)
% 5.54/5.72 Clause #73 (by clausification #[72]): ∀ (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
% 5.54/5.72 Clause #74 (by superposition #[73, 12]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop),
% 5.54/5.72 Or (Eq True False)
% 5.54/5.72 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 3 a_1 a_3 a_4 a_5)) True))
% 5.54/5.72 Clause #80 (by clausification #[74]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop),
% 5.54/5.72 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 3 a_1 a_3 a_4 a_5)) True)
% 5.54/5.72 Clause #81 (by superposition #[80, 33]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 Or
% 5.54/5.72 (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_2 x) (fun x => a_3 x) a_4))
% 5.54/5.72 True)
% 5.54/5.72 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False))
% 5.54/5.72 Clause #82 (by superposition #[80, 32]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 Or
% 5.54/5.72 (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_2 x) (fun x => a_3 x) a_4))
% 5.54/5.72 True)
% 5.54/5.72 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True))
% 5.54/5.72 Clause #83 (by superposition #[80, 30]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.72 Or
% 5.54/5.72 (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_2 x) (fun x => a_3 x) a_4))
% 5.54/5.72 True)
% 5.54/5.72 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False))
% 5.54/5.72 Clause #86 (by betaEtaReduce #[82]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.75 (Or (Eq True False) (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True))
% 5.54/5.75 Clause #87 (by clausification #[86]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (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_3 a_5)) True)
% 5.54/5.75 Clause #89 (by superposition #[87, 28]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 0 (fun x => a_1 x) (skS.0 4 (fun x => a_1 x) (fun x => a_2 x) (fun x => a_3 x) a_4)) True)
% 5.54/5.75 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq True False))
% 5.54/5.75 Clause #91 (by betaEtaReduce #[89]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_4)) True)
% 5.54/5.75 (Or (Eq (skS.0 0 a_1 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq True False))
% 5.54/5.75 Clause #92 (by clausification #[91]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 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_3 a_5)) True)
% 5.54/5.75 Clause #94 (by equality factoring #[92]): ∀ (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)
% 5.54/5.75 Clause #97 (by clausification #[94]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 5.54/5.75 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))
% 5.54/5.75 Clause #99 (by clausification #[97]): ∀ (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)
% 5.54/5.75 Clause #100 (by clausification #[99]): ∀ (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
% 5.54/5.75 Clause #101 (by superposition #[100, 12]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop),
% 5.54/5.75 Or (Eq True False)
% 5.54/5.75 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 4 a_1 a_3 a_4 a_5)) True))
% 5.54/5.75 Clause #102 (by clausification #[101]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : a) (a_6 : a → Prop),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_3 a_4 a_5)) True) (Eq (skS.0 2 a_1 a_2 a_6 (skS.0 4 a_1 a_3 a_4 a_5)) True)
% 5.54/5.75 Clause #105 (by betaEtaReduce #[83]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.75 (Or (Eq True False) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False))
% 5.54/5.75 Clause #106 (by clausification #[105]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) False)
% 5.54/5.75 Clause #109 (by betaEtaReduce #[81]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.75 (Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False))
% 5.54/5.75 Clause #110 (by clausification #[109]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_5)) False)
% 5.54/5.75 Clause #111 (by superposition #[110, 102]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or
% 5.54/5.75 (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_2 x) (fun x => a_3 x) a_4))
% 5.54/5.75 True)
% 5.54/5.75 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq False True))
% 5.54/5.75 Clause #112 (by betaEtaReduce #[111]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.75 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True) (Eq False True))
% 5.54/5.75 Clause #113 (by clausification #[112]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_5)) True)
% 5.54/5.75 Clause #116 (by superposition #[113, 106]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or
% 5.54/5.75 (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_2 x) (fun x => a_3 x) a_4))
% 5.54/5.75 True)
% 5.54/5.75 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq True False))
% 5.54/5.75 Clause #117 (by betaEtaReduce #[116]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.75 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True)
% 5.54/5.76 (Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) True) (Eq True False))
% 5.54/5.76 Clause #118 (by clausification #[117]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 a_5 : a),
% 5.54/5.76 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_5)) True)
% 5.54/5.76 Clause #119 (by equality factoring #[118]): ∀ (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_2 a_3 a_4)) True)
% 5.54/5.76 Clause #120 (by clausification #[119]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a),
% 5.54/5.76 Or (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4)) True) (Or (Eq True False) (Eq True False))
% 5.54/5.76 Clause #122 (by clausification #[120]): ∀ (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_2 a_3 a_4)) True) (Eq True False)
% 5.54/5.76 Clause #123 (by clausification #[122]): ∀ (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_2 a_3 a_4)) True
% 5.54/5.76 Clause #124 (by superposition #[123, 27]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq True False) (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) False)
% 5.54/5.76 Clause #127 (by clausification #[124]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4)) False
% 5.54/5.76 Clause #128 (by superposition #[127, 102]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : a), Or (Eq (skS.0 1 a_1 a_2 (skS.0 4 a_1 a_2 a_3 a_4)) True) (Eq False True)
% 5.54/5.76 Clause #129 (by clausification #[128]): ∀ (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)) True
% 5.54/5.76 Clause #130 (by superposition #[129, 36]): ∀ (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 3 a_1 a_2 a_3 a_4)) False)
% 5.54/5.76 Clause #131 (by clausification #[130]): ∀ (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_2 a_3 a_4)) False
% 5.54/5.76 Clause #132 (by superposition #[131, 123]): Eq False True
% 5.54/5.76 Clause #133 (by clausification #[132]): False
% 5.54/5.76 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------