TSTP Solution File: SEV061^5 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV061^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 19:24:10 EDT 2023
% Result : Theorem 4.18s 4.37s
% Output : Proof 4.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV061^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : duper %s
% 0.17/0.35 % Computer : n016.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 24 02:31:38 EDT 2023
% 0.17/0.36 % CPUTime :
% 4.18/4.37 SZS status Theorem for theBenchmark.p
% 4.18/4.37 SZS output start Proof for theBenchmark.p
% 4.18/4.37 Clause #0 (by assumption #[]): Eq
% 4.18/4.37 (Not
% 4.18/4.37 (∀ (Xx : b) (Xy : a) (Xs Xk : b → a → Prop),
% 4.18/4.37 (∀ (Xx_2 : b) (Xy_47 : a), Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 Xx) (Eq Xy_47 Xy))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a), And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 Xx) (Eq Xy_48 Xy))) → Xs Xx_3 Xy_48))
% 4.18/4.37 True
% 4.18/4.37 Clause #1 (by clausification #[0]): Eq
% 4.18/4.37 (∀ (Xx : b) (Xy : a) (Xs Xk : b → a → Prop),
% 4.18/4.37 (∀ (Xx_2 : b) (Xy_47 : a), Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 Xx) (Eq Xy_47 Xy))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a), And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 Xx) (Eq Xy_48 Xy))) → Xs Xx_3 Xy_48)
% 4.18/4.37 False
% 4.18/4.37 Clause #2 (by clausification #[1]): ∀ (a_1 : b),
% 4.18/4.37 Eq
% 4.18/4.37 (Not
% 4.18/4.37 (∀ (Xy : a) (Xs Xk : b → a → Prop),
% 4.18/4.37 (∀ (Xx_2 : b) (Xy_47 : a), Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 Xy))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a),
% 4.18/4.37 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 Xy))) → Xs Xx_3 Xy_48))
% 4.18/4.37 True
% 4.18/4.37 Clause #3 (by clausification #[2]): ∀ (a_1 : b),
% 4.18/4.37 Eq
% 4.18/4.37 (∀ (Xy : a) (Xs Xk : b → a → Prop),
% 4.18/4.37 (∀ (Xx_2 : b) (Xy_47 : a), Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 Xy))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a), And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 Xy))) → Xs Xx_3 Xy_48)
% 4.18/4.37 False
% 4.18/4.37 Clause #4 (by clausification #[3]): ∀ (a_1 : b) (a_2 : a),
% 4.18/4.37 Eq
% 4.18/4.37 (Not
% 4.18/4.37 (∀ (Xs Xk : b → a → Prop),
% 4.18/4.37 (∀ (Xx_2 : b) (Xy_47 : a),
% 4.18/4.37 Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a),
% 4.18/4.37 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → Xs Xx_3 Xy_48))
% 4.18/4.37 True
% 4.18/4.37 Clause #5 (by clausification #[4]): ∀ (a_1 : b) (a_2 : a),
% 4.18/4.37 Eq
% 4.18/4.37 (∀ (Xs Xk : b → a → Prop),
% 4.18/4.37 (∀ (Xx_2 : b) (Xy_47 : a),
% 4.18/4.37 Xk Xx_2 Xy_47 → Or (Xs Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a),
% 4.18/4.37 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) → Xs Xx_3 Xy_48)
% 4.18/4.37 False
% 4.18/4.37 Clause #6 (by clausification #[5]): ∀ (a_1 : b) (a_2 : a) (a_3 : b → a → Prop),
% 4.18/4.37 Eq
% 4.18/4.37 (Not
% 4.18/4.37 (∀ (Xk : b → a → Prop),
% 4.18/4.37 (∀ (Xx_2 : b) (Xy_47 : a),
% 4.18/4.37 Xk Xx_2 Xy_47 →
% 4.18/4.37 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a),
% 4.18/4.37 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) →
% 4.18/4.37 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48))
% 4.18/4.37 True
% 4.18/4.37 Clause #7 (by clausification #[6]): ∀ (a_1 : b) (a_2 : a) (a_3 : b → a → Prop),
% 4.18/4.37 Eq
% 4.18/4.37 (∀ (Xk : b → a → Prop),
% 4.18/4.37 (∀ (Xx_2 : b) (Xy_47 : a),
% 4.18/4.37 Xk Xx_2 Xy_47 →
% 4.18/4.37 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a),
% 4.18/4.37 And (Xk Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) →
% 4.18/4.37 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48)
% 4.18/4.37 False
% 4.18/4.37 Clause #8 (by clausification #[7]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop),
% 4.18/4.37 Eq
% 4.18/4.37 (Not
% 4.18/4.37 ((∀ (Xx_2 : b) (Xy_47 : a),
% 4.18/4.37 skS.0 3 a_1 a_2 a_3 a_4 Xx_2 Xy_47 →
% 4.18/4.37 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) →
% 4.18/4.37 ∀ (Xx_3 : b) (Xy_48 : a),
% 4.18/4.37 And (skS.0 3 a_1 a_2 a_3 a_4 Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) →
% 4.18/4.37 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48))
% 4.18/4.37 True
% 4.18/4.37 Clause #9 (by clausification #[8]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop),
% 4.18/4.37 Eq
% 4.18/4.37 ((∀ (Xx_2 : b) (Xy_47 : a),
% 4.18/4.37 skS.0 3 a_1 a_2 a_3 a_4 Xx_2 Xy_47 →
% 4.18/4.37 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2)))) →
% 4.18/4.39 ∀ (Xx_3 : b) (Xy_48 : a),
% 4.18/4.39 And (skS.0 3 a_1 a_2 a_3 a_4 Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) →
% 4.18/4.39 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48)
% 4.18/4.39 False
% 4.18/4.39 Clause #10 (by clausification #[9]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop),
% 4.18/4.39 Eq
% 4.18/4.39 (∀ (Xx_2 : b) (Xy_47 : a),
% 4.18/4.39 skS.0 3 a_1 a_2 a_3 a_4 Xx_2 Xy_47 →
% 4.18/4.39 Or (skS.0 2 a_1 a_2 a_3 Xx_2 Xy_47) (And (Eq Xx_2 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2))))
% 4.18/4.39 True
% 4.18/4.39 Clause #11 (by clausification #[9]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop),
% 4.18/4.39 Eq
% 4.18/4.39 (∀ (Xx_3 : b) (Xy_48 : a),
% 4.18/4.39 And (skS.0 3 a_1 a_2 a_3 a_4 Xx_3 Xy_48) (Not (And (Eq Xx_3 (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) →
% 4.18/4.39 skS.0 2 a_1 a_2 a_3 Xx_3 Xy_48)
% 4.18/4.39 False
% 4.18/4.39 Clause #12 (by clausification #[10]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b),
% 4.18/4.39 Eq
% 4.18/4.39 (∀ (Xy_47 : a),
% 4.18/4.39 skS.0 3 a_1 a_2 a_3 a_4 a_5 Xy_47 →
% 4.18/4.39 Or (skS.0 2 a_1 a_2 a_3 a_5 Xy_47) (And (Eq a_5 (skS.0 0 a_1)) (Eq Xy_47 (skS.0 1 a_1 a_2))))
% 4.18/4.39 True
% 4.18/4.39 Clause #13 (by clausification #[12]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.39 Eq
% 4.18/4.39 (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6 →
% 4.18/4.39 Or (skS.0 2 a_1 a_2 a_3 a_5 a_6) (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2))))
% 4.18/4.39 True
% 4.18/4.39 Clause #14 (by clausification #[13]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.39 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False)
% 4.18/4.39 (Eq (Or (skS.0 2 a_1 a_2 a_3 a_5 a_6) (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2)))) True)
% 4.18/4.39 Clause #15 (by clausification #[14]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.39 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False)
% 4.18/4.39 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (And (Eq a_5 (skS.0 0 a_1)) (Eq a_6 (skS.0 1 a_1 a_2))) True))
% 4.18/4.39 Clause #16 (by clausification #[15]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.39 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False)
% 4.18/4.39 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (Eq a_6 (skS.0 1 a_1 a_2)) True))
% 4.18/4.39 Clause #17 (by clausification #[15]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.39 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False)
% 4.18/4.39 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq (Eq a_5 (skS.0 0 a_1)) True))
% 4.18/4.39 Clause #18 (by clausification #[16]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.39 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False)
% 4.18/4.39 (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq a_6 (skS.0 1 a_1 a_2)))
% 4.18/4.39 Clause #19 (by clausification #[11]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b),
% 4.18/4.39 Eq
% 4.18/4.39 (Not
% 4.18/4.39 (∀ (Xy_48 : a),
% 4.18/4.39 And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy_48)
% 4.18/4.39 (Not (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) →
% 4.18/4.39 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy_48))
% 4.18/4.39 True
% 4.18/4.39 Clause #20 (by clausification #[19]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b),
% 4.18/4.39 Eq
% 4.18/4.39 (∀ (Xy_48 : a),
% 4.18/4.39 And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy_48)
% 4.18/4.39 (Not (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq Xy_48 (skS.0 1 a_1 a_2)))) →
% 4.18/4.39 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) Xy_48)
% 4.18/4.39 False
% 4.18/4.39 Clause #21 (by clausification #[20]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.39 Eq
% 4.18/4.39 (Not
% 4.18/4.39 (And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))
% 4.18/4.39 (Not
% 4.18/4.39 (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1))
% 4.18/4.39 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)))) →
% 4.18/4.39 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)))
% 4.18/4.39 True
% 4.18/4.39 Clause #22 (by clausification #[21]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.39 Eq
% 4.18/4.39 (And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))
% 4.18/4.42 (Not
% 4.18/4.42 (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1))
% 4.18/4.42 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)))) →
% 4.18/4.42 skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))
% 4.18/4.42 False
% 4.18/4.42 Clause #23 (by clausification #[22]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Eq
% 4.18/4.42 (And (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6))
% 4.18/4.42 (Not
% 4.18/4.42 (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1))
% 4.18/4.42 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)))))
% 4.18/4.42 True
% 4.18/4.42 Clause #24 (by clausification #[22]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) False
% 4.18/4.42 Clause #25 (by clausification #[23]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Eq
% 4.18/4.42 (Not
% 4.18/4.42 (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2))))
% 4.18/4.42 True
% 4.18/4.42 Clause #26 (by clausification #[23]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Eq (skS.0 3 a_1 a_2 a_3 a_4 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True
% 4.18/4.42 Clause #27 (by clausification #[25]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Eq (And (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)))
% 4.18/4.42 False
% 4.18/4.42 Clause #28 (by clausification #[27]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or (Eq (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) False)
% 4.18/4.42 (Eq (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) False)
% 4.18/4.42 Clause #29 (by clausification #[28]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or (Eq (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) False)
% 4.18/4.42 (Ne (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1))
% 4.18/4.42 Clause #30 (by clausification #[29]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or (Ne (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Ne (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2))
% 4.18/4.42 Clause #31 (by clausification #[17]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or (Eq (skS.0 3 a_1 a_2 a_3 a_4 a_5 a_6) False) (Or (Eq (skS.0 2 a_1 a_2 a_3 a_5 a_6) True) (Eq a_5 (skS.0 0 a_1)))
% 4.18/4.42 Clause #32 (by superposition #[26, 18]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or (Eq True False)
% 4.18/4.42 (Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True)
% 4.18/4.42 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)))
% 4.18/4.42 Clause #33 (by superposition #[26, 31]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or
% 4.18/4.42 (Eq (skS.0 2 a_1 a_2 (fun x x_1 => a_3 x x_1) (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True)
% 4.18/4.42 (Or (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq False True))
% 4.18/4.42 Clause #34 (by clausification #[32]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True)
% 4.18/4.42 (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2))
% 4.18/4.42 Clause #35 (by superposition #[34, 24]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or (Eq (skS.0 5 a_1 a_2 (fun x x_1 => a_3 x x_1) (fun x x_1 => a_4 x x_1) a_5 a_6) (skS.0 1 a_1 a_2)) (Eq True False)
% 4.18/4.42 Clause #36 (by betaEtaReduce #[35]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Or (Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)) (Eq True False)
% 4.18/4.42 Clause #37 (by clausification #[36]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.42 Eq (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 1 a_1 a_2)
% 4.18/4.42 Clause #39 (by backward demodulation #[37, 24]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b),
% 4.18/4.42 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) False
% 4.18/4.43 Clause #42 (by backward contextual literal cutting #[37, 30]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b), Ne (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)
% 4.18/4.43 Clause #44 (by betaEtaReduce #[33]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.43 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True)
% 4.18/4.43 (Or (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1)) (Eq False True))
% 4.18/4.43 Clause #45 (by clausification #[44]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b) (a_6 : a),
% 4.18/4.43 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 5 a_1 a_2 a_3 a_4 a_5 a_6)) True)
% 4.18/4.43 (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1))
% 4.18/4.43 Clause #46 (by forward demodulation #[45, 37]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b),
% 4.18/4.43 Or (Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) True)
% 4.18/4.43 (Eq (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 0 a_1))
% 4.18/4.43 Clause #47 (by forward contextual literal cutting #[46, 42]): ∀ (a_1 : b) (a_2 : a) (a_3 a_4 : b → a → Prop) (a_5 : b),
% 4.18/4.43 Eq (skS.0 2 a_1 a_2 a_3 (skS.0 4 a_1 a_2 a_3 a_4 a_5) (skS.0 1 a_1 a_2)) True
% 4.18/4.43 Clause #48 (by superposition #[47, 39]): Eq True False
% 4.18/4.43 Clause #49 (by clausification #[48]): False
% 4.18/4.43 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------