TSTP Solution File: SEU664^2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU664^2 : TPTP v8.1.2. Released v3.7.0.
% 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 16:43:17 EDT 2023
% Result : Theorem 8.93s 9.29s
% Output : Proof 9.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU664^2 : TPTP v8.1.2. Released v3.7.0.
% 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 14:35:39 EDT 2023
% 0.13/0.36 % CPUTime :
% 8.93/9.29 SZS status Theorem for theBenchmark.p
% 8.93/9.29 SZS output start Proof for theBenchmark.p
% 8.93/9.29 Clause #0 (by assumption #[]): Eq
% 8.93/9.29 (Eq cartprodmempair1
% 8.93/9.29 (∀ (A B Xu : Iota),
% 8.93/9.29 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))))
% 8.93/9.29 True
% 8.93/9.29 Clause #1 (by assumption #[]): Eq (Eq cartprodfstpairEq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (kfst (kpair Xx Xy)) Xx)) True
% 8.93/9.29 Clause #2 (by assumption #[]): Eq (Eq cartprodsndpairEq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy)) True
% 8.93/9.29 Clause #3 (by assumption #[]): Eq
% 8.93/9.29 (Not
% 8.93/9.29 (cartprodmempair1 →
% 8.93/9.29 cartprodfstpairEq →
% 8.93/9.29 cartprodsndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu))
% 8.93/9.29 True
% 8.93/9.29 Clause #4 (by clausification #[3]): Eq
% 8.93/9.29 (cartprodmempair1 →
% 8.93/9.29 cartprodfstpairEq → cartprodsndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu)
% 8.93/9.29 False
% 8.93/9.29 Clause #5 (by clausification #[4]): Eq cartprodmempair1 True
% 8.93/9.29 Clause #6 (by clausification #[4]): Eq (cartprodfstpairEq → cartprodsndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu)
% 8.93/9.29 False
% 8.93/9.29 Clause #7 (by clausification #[6]): Eq cartprodfstpairEq True
% 8.93/9.29 Clause #8 (by clausification #[6]): Eq (cartprodsndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) False
% 8.93/9.29 Clause #9 (by clausification #[8]): Eq cartprodsndpairEq True
% 8.93/9.29 Clause #10 (by clausification #[8]): Eq (∀ (A B Xu : Iota), in Xu (cartprod A B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) False
% 8.93/9.29 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Not (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu)) True
% 8.93/9.29 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) False
% 8.93/9.29 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota),
% 8.93/9.29 Eq (Not (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu)) True
% 8.93/9.29 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 8.93/9.29 Eq (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → Eq (kpair (kfst Xu) (ksnd Xu)) Xu) False
% 8.93/9.29 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 8.93/9.29 Eq
% 8.93/9.29 (Not
% 8.93/9.29 (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) →
% 8.93/9.29 Eq (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) (skS.0 2 a a_1 a_2)))
% 8.93/9.29 True
% 8.93/9.29 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota),
% 8.93/9.29 Eq
% 8.93/9.29 (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) →
% 8.93/9.29 Eq (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) (skS.0 2 a a_1 a_2))
% 8.93/9.29 False
% 8.93/9.29 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1))) True
% 8.93/9.29 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (Eq (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) (skS.0 2 a a_1 a_2)) False
% 8.93/9.29 Clause #19 (by clausification #[1]): Eq cartprodfstpairEq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (kfst (kpair Xx Xy)) Xx)
% 8.93/9.29 Clause #20 (by forward demodulation #[19, 7]): Eq True (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (kfst (kpair Xx Xy)) Xx)
% 8.93/9.29 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy B → Eq (kfst (kpair Xx Xy)) Xx) True
% 8.93/9.29 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a_1 → Eq (kfst (kpair Xx Xy)) Xx) True
% 8.93/9.29 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → ∀ (Xy : Iota), in Xy a_2 → Eq (kfst (kpair a Xy)) a) True
% 8.93/9.29 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (∀ (Xy : Iota), in Xy a_2 → Eq (kfst (kpair a Xy)) a) True)
% 8.93/9.29 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Eq (in a_2 a_3 → Eq (kfst (kpair a a_2)) a) True)
% 9.14/9.32 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 a_3) False) (Eq (Eq (kfst (kpair a a_2)) a) True))
% 9.14/9.32 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 a_3) False) (Eq (kfst (kpair a a_2)) a))
% 9.14/9.32 Clause #29 (by clausification #[0]): Eq cartprodmempair1
% 9.14/9.32 (∀ (A B Xu : Iota),
% 9.14/9.32 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 9.14/9.32 Clause #30 (by forward demodulation #[29, 5]): Eq True
% 9.14/9.32 (∀ (A B Xu : Iota),
% 9.14/9.32 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 9.14/9.32 Clause #31 (by clausification #[30]): ∀ (a : Iota),
% 9.14/9.32 Eq
% 9.14/9.32 (∀ (B Xu : Iota),
% 9.14/9.32 in Xu (cartprod a B) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 9.14/9.32 True
% 9.14/9.32 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota),
% 9.14/9.32 Eq
% 9.14/9.32 (∀ (Xu : Iota),
% 9.14/9.32 in Xu (cartprod a a_1) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy a_1) (Eq Xu (kpair Xx Xy))))
% 9.14/9.32 True
% 9.14/9.32 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota),
% 9.14/9.32 Eq
% 9.14/9.32 (in a (cartprod a_1 a_2) → Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy))))
% 9.14/9.32 True
% 9.14/9.32 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota),
% 9.14/9.32 Or (Eq (in a (cartprod a_1 a_2)) False)
% 9.14/9.32 (Eq (Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) True)
% 9.14/9.32 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota),
% 9.14/9.32 Or (Eq (in a (cartprod a_1 a_2)) False)
% 9.14/9.32 (Eq
% 9.14/9.32 (And (in (skS.0 3 a_1 a_2 a a_3) a_1)
% 9.14/9.32 (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy))))
% 9.14/9.32 True)
% 9.14/9.32 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota),
% 9.14/9.32 Or (Eq (in a (cartprod a_1 a_2)) False)
% 9.14/9.32 (Eq (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy))) True)
% 9.14/9.32 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (in (skS.0 3 a_1 a_2 a a_3) a_1) True)
% 9.14/9.32 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.14/9.32 Or (Eq (in a (cartprod a_1 a_2)) False)
% 9.14/9.32 (Eq (And (in (skS.0 4 a_2 a a_1 a_3 a_4) a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) (skS.0 4 a_2 a a_1 a_3 a_4))))
% 9.14/9.32 True)
% 9.14/9.32 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.14/9.32 Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) (skS.0 4 a_2 a a_1 a_3 a_4))) True)
% 9.14/9.32 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (in (skS.0 4 a_2 a a_1 a_3 a_4) a_2) True)
% 9.14/9.32 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.14/9.32 Or (Eq (in a (cartprod a_1 a_2)) False) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) (skS.0 4 a_2 a a_1 a_3 a_4)))
% 9.14/9.32 Clause #42 (by superposition #[41, 17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.14/9.32 Or
% 9.14/9.32 (Eq (skS.0 2 a a_1 a_2)
% 9.14/9.32 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 9.14/9.32 (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4)))
% 9.14/9.32 (Eq False True)
% 9.14/9.32 Clause #43 (by clausification #[2]): Eq cartprodsndpairEq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy)
% 9.14/9.32 Clause #44 (by forward demodulation #[43, 9]): Eq True (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy)
% 9.14/9.32 Clause #45 (by clausification #[44]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy) True
% 9.14/9.32 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a_1 → Eq (ksnd (kpair Xx Xy)) Xy) True
% 9.14/9.32 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → ∀ (Xy : Iota), in Xy a_2 → Eq (ksnd (kpair a Xy)) Xy) True
% 9.14/9.32 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (∀ (Xy : Iota), in Xy a_2 → Eq (ksnd (kpair a Xy)) Xy) True)
% 9.17/9.35 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Eq (in a_2 a_3 → Eq (ksnd (kpair a a_2)) a_2) True)
% 9.17/9.35 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 a_3) False) (Eq (Eq (ksnd (kpair a a_2)) a_2) True))
% 9.17/9.35 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 a_3) False) (Eq (ksnd (kpair a a_2)) a_2))
% 9.17/9.35 Clause #55 (by superposition #[37, 17]): ∀ (a a_1 a_2 a_3 : Iota),
% 9.17/9.35 Or (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) (skS.0 0 a)) True) (Eq False True)
% 9.17/9.35 Clause #56 (by superposition #[40, 17]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.17/9.35 Or (Eq (in (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4) (skS.0 1 a a_1)) True) (Eq False True)
% 9.17/9.35 Clause #59 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Ne (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2))) (skS.0 2 a a_1 a_2)
% 9.17/9.35 Clause #62 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) (skS.0 0 a)) True
% 9.17/9.35 Clause #63 (by superposition #[62, 27]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 9.17/9.35 Or (Eq True False)
% 9.17/9.35 (Or (Eq (in a a_1) False)
% 9.17/9.35 (Eq (kfst (kpair (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) a))
% 9.17/9.35 (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5)))
% 9.17/9.35 Clause #64 (by superposition #[62, 51]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 9.17/9.35 Or (Eq True False)
% 9.17/9.35 (Or (Eq (in a a_1) False)
% 9.17/9.35 (Eq (ksnd (kpair (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) a)) a))
% 9.17/9.35 Clause #67 (by clausification #[64]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 9.17/9.35 Or (Eq (in a a_1) False) (Eq (ksnd (kpair (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) a)) a)
% 9.17/9.35 Clause #70 (by clausification #[56]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.17/9.35 Eq (in (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4) (skS.0 1 a a_1)) True
% 9.17/9.35 Clause #75 (by superposition #[70, 67]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 9.17/9.35 Or (Eq True False)
% 9.17/9.35 (Eq
% 9.17/9.35 (ksnd
% 9.17/9.35 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 9.17/9.35 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8)))
% 9.17/9.35 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8))
% 9.17/9.35 Clause #76 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.17/9.35 Eq (skS.0 2 a a_1 a_2)
% 9.17/9.35 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 9.17/9.35 (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4))
% 9.17/9.35 Clause #85 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 9.17/9.35 Or (Eq (in a a_1) False)
% 9.17/9.35 (Eq (kfst (kpair (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) a))
% 9.17/9.35 (skS.0 3 (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5))
% 9.17/9.35 Clause #88 (by superposition #[85, 70]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 9.17/9.35 Or
% 9.17/9.35 (Eq
% 9.17/9.35 (kfst
% 9.17/9.35 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 9.17/9.35 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8)))
% 9.17/9.35 (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3))
% 9.17/9.35 (Eq False True)
% 9.17/9.35 Clause #100 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 9.17/9.35 Eq
% 9.17/9.35 (kfst
% 9.17/9.35 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 9.17/9.35 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8)))
% 9.17/9.35 (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 9.17/9.35 Clause #101 (by superposition #[100, 76]): ∀ (a a_1 a_2 a_3 : Iota), Eq (kfst (skS.0 2 a a_1 a_2)) (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 9.17/9.35 Clause #104 (by backward demodulation #[101, 76]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.17/9.35 Eq (skS.0 2 a a_1 a_2)
% 9.17/9.35 (kpair (kfst (skS.0 2 a a_1 a_2)) (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4))
% 9.17/9.35 Clause #116 (by clausification #[75]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 9.17/9.35 Eq
% 9.17/9.35 (ksnd
% 9.17/9.35 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 9.17/9.35 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8)))
% 9.17/9.35 (skS.0 4 (skS.0 1 a_4 a_5) (skS.0 2 a_4 a_5 a_6) (skS.0 0 a_4) a_7 a_8)
% 9.17/9.35 Clause #117 (by forward demodulation #[116, 101]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 9.17/9.35 Eq (ksnd (kpair (kfst (skS.0 2 a a_1 a_2)) (skS.0 4 (skS.0 1 a_3 a_4) (skS.0 2 a_3 a_4 a_5) (skS.0 0 a_3) a_6 a_7)))
% 9.17/9.35 (skS.0 4 (skS.0 1 a_3 a_4) (skS.0 2 a_3 a_4 a_5) (skS.0 0 a_3) a_6 a_7)
% 9.17/9.35 Clause #136 (by superposition #[104, 117]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 9.17/9.35 Eq (ksnd (skS.0 2 a a_1 a_2)) (skS.0 4 (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) a_3 a_4)
% 9.17/9.35 Clause #148 (by backward demodulation #[136, 104]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 2 a a_1 a_2) (kpair (kfst (skS.0 2 a a_1 a_2)) (ksnd (skS.0 2 a a_1 a_2)))
% 9.17/9.35 Clause #164 (by forward contextual literal cutting #[148, 59]): False
% 9.17/9.35 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------