TSTP Solution File: ALG001^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : ALG001^5 : 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 : Wed Aug 30 16:11:05 EDT 2023
% Result : Theorem 3.76s 3.99s
% Output : Proof 3.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG001^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 05:09:49 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.76/3.99 SZS status Theorem for theBenchmark.p
% 3.76/3.99 SZS output start Proof for theBenchmark.p
% 3.76/3.99 Clause #0 (by assumption #[]): Eq
% 3.76/3.99 (Not
% 3.76/3.99 (∀ (Xh1 : g → b) (Xh2 : b → a) (Xf1 : g → g → g) (Xf2 : b → b → b) (Xf3 : a → a → a),
% 3.76/3.99 And (∀ (Xx Xy : g), Eq (Xh1 (Xf1 Xx Xy)) (Xf2 (Xh1 Xx) (Xh1 Xy)))
% 3.76/3.99 (∀ (Xx Xy : b), Eq (Xh2 (Xf2 Xx Xy)) (Xf3 (Xh2 Xx) (Xh2 Xy))) →
% 3.76/3.99 ∀ (Xx Xy : g), Eq (Xh2 (Xh1 (Xf1 Xx Xy))) (Xf3 (Xh2 (Xh1 Xx)) (Xh2 (Xh1 Xy)))))
% 3.76/3.99 True
% 3.76/3.99 Clause #1 (by clausification #[0]): Eq
% 3.76/3.99 (∀ (Xh1 : g → b) (Xh2 : b → a) (Xf1 : g → g → g) (Xf2 : b → b → b) (Xf3 : a → a → a),
% 3.76/3.99 And (∀ (Xx Xy : g), Eq (Xh1 (Xf1 Xx Xy)) (Xf2 (Xh1 Xx) (Xh1 Xy)))
% 3.76/3.99 (∀ (Xx Xy : b), Eq (Xh2 (Xf2 Xx Xy)) (Xf3 (Xh2 Xx) (Xh2 Xy))) →
% 3.76/3.99 ∀ (Xx Xy : g), Eq (Xh2 (Xh1 (Xf1 Xx Xy))) (Xf3 (Xh2 (Xh1 Xx)) (Xh2 (Xh1 Xy))))
% 3.76/3.99 False
% 3.76/3.99 Clause #2 (by clausification #[1]): ∀ (a_1 : g → b),
% 3.76/3.99 Eq
% 3.76/3.99 (Not
% 3.76/3.99 (∀ (Xh2 : b → a) (Xf1 : g → g → g) (Xf2 : b → b → b) (Xf3 : a → a → a),
% 3.76/3.99 And (∀ (Xx Xy : g), Eq (skS.0 0 a_1 (Xf1 Xx Xy)) (Xf2 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.76/3.99 (∀ (Xx Xy : b), Eq (Xh2 (Xf2 Xx Xy)) (Xf3 (Xh2 Xx) (Xh2 Xy))) →
% 3.76/3.99 ∀ (Xx Xy : g), Eq (Xh2 (skS.0 0 a_1 (Xf1 Xx Xy))) (Xf3 (Xh2 (skS.0 0 a_1 Xx)) (Xh2 (skS.0 0 a_1 Xy)))))
% 3.76/3.99 True
% 3.76/3.99 Clause #3 (by clausification #[2]): ∀ (a_1 : g → b),
% 3.76/3.99 Eq
% 3.76/3.99 (∀ (Xh2 : b → a) (Xf1 : g → g → g) (Xf2 : b → b → b) (Xf3 : a → a → a),
% 3.76/3.99 And (∀ (Xx Xy : g), Eq (skS.0 0 a_1 (Xf1 Xx Xy)) (Xf2 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.76/3.99 (∀ (Xx Xy : b), Eq (Xh2 (Xf2 Xx Xy)) (Xf3 (Xh2 Xx) (Xh2 Xy))) →
% 3.76/3.99 ∀ (Xx Xy : g), Eq (Xh2 (skS.0 0 a_1 (Xf1 Xx Xy))) (Xf3 (Xh2 (skS.0 0 a_1 Xx)) (Xh2 (skS.0 0 a_1 Xy))))
% 3.76/3.99 False
% 3.76/3.99 Clause #4 (by clausification #[3]): ∀ (a_1 : g → b) (a_2 : b → a),
% 3.76/3.99 Eq
% 3.76/3.99 (Not
% 3.76/3.99 (∀ (Xf1 : g → g → g) (Xf2 : b → b → b) (Xf3 : a → a → a),
% 3.76/3.99 And (∀ (Xx Xy : g), Eq (skS.0 0 a_1 (Xf1 Xx Xy)) (Xf2 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.76/3.99 (∀ (Xx Xy : b), Eq (skS.0 1 a_1 a_2 (Xf2 Xx Xy)) (Xf3 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 3.76/3.99 ∀ (Xx Xy : g),
% 3.76/3.99 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (Xf1 Xx Xy)))
% 3.76/3.99 (Xf3 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)))))
% 3.76/3.99 True
% 3.76/3.99 Clause #5 (by clausification #[4]): ∀ (a_1 : g → b) (a_2 : b → a),
% 3.76/3.99 Eq
% 3.76/3.99 (∀ (Xf1 : g → g → g) (Xf2 : b → b → b) (Xf3 : a → a → a),
% 3.76/3.99 And (∀ (Xx Xy : g), Eq (skS.0 0 a_1 (Xf1 Xx Xy)) (Xf2 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.76/3.99 (∀ (Xx Xy : b), Eq (skS.0 1 a_1 a_2 (Xf2 Xx Xy)) (Xf3 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 3.76/3.99 ∀ (Xx Xy : g),
% 3.76/3.99 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (Xf1 Xx Xy)))
% 3.76/3.99 (Xf3 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy))))
% 3.76/3.99 False
% 3.76/3.99 Clause #6 (by clausification #[5]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g),
% 3.76/3.99 Eq
% 3.76/3.99 (Not
% 3.76/3.99 (∀ (Xf2 : b → b → b) (Xf3 : a → a → a),
% 3.76/3.99 And (∀ (Xx Xy : g), Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)) (Xf2 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.76/3.99 (∀ (Xx Xy : b), Eq (skS.0 1 a_1 a_2 (Xf2 Xx Xy)) (Xf3 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 3.76/3.99 ∀ (Xx Xy : g),
% 3.76/3.99 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)))
% 3.76/3.99 (Xf3 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)))))
% 3.76/3.99 True
% 3.76/3.99 Clause #7 (by clausification #[6]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g),
% 3.76/3.99 Eq
% 3.76/3.99 (∀ (Xf2 : b → b → b) (Xf3 : a → a → a),
% 3.76/3.99 And (∀ (Xx Xy : g), Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)) (Xf2 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.76/3.99 (∀ (Xx Xy : b), Eq (skS.0 1 a_1 a_2 (Xf2 Xx Xy)) (Xf3 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 3.76/3.99 ∀ (Xx Xy : g),
% 3.76/3.99 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)))
% 3.76/3.99 (Xf3 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy))))
% 3.76/3.99 False
% 3.76/3.99 Clause #8 (by clausification #[7]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b),
% 3.85/4.01 Eq
% 3.85/4.01 (Not
% 3.85/4.01 (∀ (Xf3 : a → a → a),
% 3.85/4.01 And
% 3.85/4.01 (∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.85/4.01 (∀ (Xx Xy : b),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 Xx Xy)) (Xf3 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 3.85/4.01 ∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)))
% 3.85/4.01 (Xf3 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)))))
% 3.85/4.01 True
% 3.85/4.01 Clause #9 (by clausification #[8]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b),
% 3.85/4.01 Eq
% 3.85/4.01 (∀ (Xf3 : a → a → a),
% 3.85/4.01 And
% 3.85/4.01 (∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.85/4.01 (∀ (Xx Xy : b),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 Xx Xy)) (Xf3 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 3.85/4.01 ∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)))
% 3.85/4.01 (Xf3 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy))))
% 3.85/4.01 False
% 3.85/4.01 Clause #10 (by clausification #[9]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a),
% 3.85/4.01 Eq
% 3.85/4.01 (Not
% 3.85/4.01 (And
% 3.85/4.01 (∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.85/4.01 (∀ (Xx Xy : b),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 Xx Xy))
% 3.85/4.01 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 3.85/4.01 ∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)))
% 3.85/4.01 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)))))
% 3.85/4.01 True
% 3.85/4.01 Clause #11 (by clausification #[10]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a),
% 3.85/4.01 Eq
% 3.85/4.01 (And
% 3.85/4.01 (∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.85/4.01 (∀ (Xx Xy : b),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 Xx Xy))
% 3.85/4.01 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))) →
% 3.85/4.01 ∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)))
% 3.85/4.01 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy))))
% 3.85/4.01 False
% 3.85/4.01 Clause #12 (by clausification #[11]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a),
% 3.85/4.01 Eq
% 3.85/4.01 (And
% 3.85/4.01 (∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.85/4.01 (∀ (Xx Xy : b),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 Xx Xy))
% 3.85/4.01 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy))))
% 3.85/4.01 True
% 3.85/4.01 Clause #13 (by clausification #[11]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a),
% 3.85/4.01 Eq
% 3.85/4.01 (∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)))
% 3.85/4.01 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xx)) (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy))))
% 3.85/4.01 False
% 3.85/4.01 Clause #14 (by clausification #[12]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a),
% 3.85/4.01 Eq
% 3.85/4.01 (∀ (Xx Xy : b),
% 3.85/4.01 Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 Xx Xy))
% 3.85/4.01 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 Xx) (skS.0 1 a_1 a_2 Xy)))
% 3.85/4.01 True
% 3.85/4.01 Clause #15 (by clausification #[12]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b),
% 3.85/4.01 Eq
% 3.85/4.01 (∀ (Xx Xy : g),
% 3.85/4.01 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 Xx Xy)) (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1 Xx) (skS.0 0 a_1 Xy)))
% 3.85/4.03 True
% 3.85/4.03 Clause #16 (by clausification #[14]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : b) (a_6 : a → a → a),
% 3.85/4.03 Eq
% 3.85/4.03 (∀ (Xy : b),
% 3.85/4.03 Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 a_5 Xy))
% 3.85/4.03 (skS.0 4 a_1 a_2 a_3 a_4 a_6 (skS.0 1 a_1 a_2 a_5) (skS.0 1 a_1 a_2 Xy)))
% 3.85/4.03 True
% 3.85/4.03 Clause #17 (by clausification #[16]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 a_6 : b) (a_7 : a → a → a),
% 3.85/4.03 Eq
% 3.85/4.03 (Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6))
% 3.85/4.03 (skS.0 4 a_1 a_2 a_3 a_4 a_7 (skS.0 1 a_1 a_2 a_5) (skS.0 1 a_1 a_2 a_6)))
% 3.85/4.03 True
% 3.85/4.03 Clause #18 (by clausification #[17]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 a_6 : b) (a_7 : a → a → a),
% 3.85/4.03 Eq (skS.0 1 a_1 a_2 (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6))
% 3.85/4.03 (skS.0 4 a_1 a_2 a_3 a_4 a_7 (skS.0 1 a_1 a_2 a_5) (skS.0 1 a_1 a_2 a_6))
% 3.85/4.03 Clause #19 (by clausification #[15]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : g) (a_5 : b → b → b),
% 3.85/4.03 Eq
% 3.85/4.03 (∀ (Xy : g),
% 3.85/4.03 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 a_4 Xy)) (skS.0 3 a_1 a_2 a_3 a_5 (skS.0 0 a_1 a_4) (skS.0 0 a_1 Xy)))
% 3.85/4.03 True
% 3.85/4.03 Clause #20 (by clausification #[19]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 a_5 : g) (a_6 : b → b → b),
% 3.85/4.03 Eq (Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 a_4 a_5)) (skS.0 3 a_1 a_2 a_3 a_6 (skS.0 0 a_1 a_4) (skS.0 0 a_1 a_5))) True
% 3.85/4.03 Clause #21 (by clausification #[20]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 a_5 : g) (a_6 : b → b → b),
% 3.85/4.03 Eq (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 a_4 a_5)) (skS.0 3 a_1 a_2 a_3 a_6 (skS.0 0 a_1 a_4) (skS.0 0 a_1 a_5))
% 3.85/4.03 Clause #22 (by clausification #[13]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a) (a_6 : g),
% 3.85/4.03 Eq
% 3.85/4.03 (Not
% 3.85/4.03 (∀ (Xy : g),
% 3.85/4.03 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) Xy)))
% 3.85/4.03 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)))
% 3.85/4.03 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy)))))
% 3.85/4.03 True
% 3.85/4.03 Clause #23 (by clausification #[22]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a) (a_6 : g),
% 3.85/4.03 Eq
% 3.85/4.03 (∀ (Xy : g),
% 3.85/4.03 Eq (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) Xy)))
% 3.85/4.03 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)))
% 3.85/4.03 (skS.0 1 a_1 a_2 (skS.0 0 a_1 Xy))))
% 3.85/4.03 False
% 3.85/4.03 Clause #24 (by clausification #[23]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a) (a_6 a_7 : g),
% 3.85/4.03 Eq
% 3.85/4.03 (Not
% 3.85/4.03 (Eq
% 3.85/4.03 (skS.0 1 a_1 a_2
% 3.85/4.03 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 3.85/4.03 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)))
% 3.85/4.03 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))))
% 3.85/4.03 True
% 3.85/4.03 Clause #25 (by clausification #[24]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a) (a_6 a_7 : g),
% 3.85/4.03 Eq
% 3.85/4.03 (Eq
% 3.85/4.03 (skS.0 1 a_1 a_2
% 3.85/4.03 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 3.85/4.03 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)))
% 3.85/4.03 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7)))))
% 3.85/4.03 False
% 3.85/4.03 Clause #26 (by clausification #[25]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a) (a_6 a_7 : g),
% 3.85/4.03 Ne
% 3.85/4.03 (skS.0 1 a_1 a_2
% 3.85/4.03 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 3.85/4.03 (skS.0 4 a_1 a_2 a_3 a_4 a_5 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)))
% 3.85/4.03 (skS.0 1 a_1 a_2 (skS.0 0 a_1 (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 3.85/4.04 Clause #27 (by forward demodulation #[26, 18]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a) (a_6 a_7 : g),
% 3.85/4.04 Ne
% 3.85/4.04 (skS.0 1 a_1 a_2
% 3.85/4.04 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 3.85/4.04 (skS.0 1 a_1 a_2
% 3.85/4.04 (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 0 a_1 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))
% 3.85/4.04 (skS.0 0 a_1 (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 3.85/4.04 Clause #28 (by forward demodulation #[27, 21]): ∀ (a_1 : g → b) (a_2 : b → a) (a_3 : g → g → g) (a_4 : b → b → b) (a_5 : a → a → a) (a_6 a_7 : g),
% 3.85/4.04 Ne
% 3.85/4.04 (skS.0 1 a_1 a_2
% 3.85/4.04 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 3.85/4.04 (skS.0 1 a_1 a_2
% 3.85/4.04 (skS.0 0 a_1 (skS.0 2 a_1 a_2 a_3 (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 6 a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 3.85/4.04 Clause #29 (by eliminate resolved literals #[28]): False
% 3.85/4.04 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------