TSTP Solution File: SEU660^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU660^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n003.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 16:43:16 EDT 2023
% Result : Theorem 3.99s 4.27s
% Output : Proof 3.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU660^2 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n003.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 : Wed Aug 23 15:05:22 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.99/4.27 SZS status Theorem for theBenchmark.p
% 3.99/4.27 SZS output start Proof for theBenchmark.p
% 3.99/4.27 Clause #0 (by assumption #[]): Eq
% 3.99/4.27 (Eq cartprodmempair1
% 3.99/4.27 (∀ (A B Xu : Iota),
% 3.99/4.27 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))))
% 3.99/4.27 True
% 3.99/4.27 Clause #1 (by assumption #[]): Eq (Eq setukpairinjR (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu)) True
% 3.99/4.27 Clause #2 (by assumption #[]): Eq (Not (cartprodmempair1 → setukpairinjR → ∀ (A B Xx Xy : Iota), in (kpair Xx Xy) (cartprod A B) → in Xy B)) True
% 3.99/4.27 Clause #3 (by clausification #[2]): Eq (cartprodmempair1 → setukpairinjR → ∀ (A B Xx Xy : Iota), in (kpair Xx Xy) (cartprod A B) → in Xy B) False
% 3.99/4.27 Clause #4 (by clausification #[3]): Eq cartprodmempair1 True
% 3.99/4.27 Clause #5 (by clausification #[3]): Eq (setukpairinjR → ∀ (A B Xx Xy : Iota), in (kpair Xx Xy) (cartprod A B) → in Xy B) False
% 3.99/4.27 Clause #6 (by clausification #[5]): Eq setukpairinjR True
% 3.99/4.27 Clause #7 (by clausification #[5]): Eq (∀ (A B Xx Xy : Iota), in (kpair Xx Xy) (cartprod A B) → in Xy B) False
% 3.99/4.27 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (B Xx Xy : Iota), in (kpair Xx Xy) (cartprod (skS.0 0 a) B) → in Xy B)) True
% 3.99/4.27 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B Xx Xy : Iota), in (kpair Xx Xy) (cartprod (skS.0 0 a) B) → in Xy B) False
% 3.99/4.27 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota),
% 3.99/4.27 Eq (Not (∀ (Xx Xy : Iota), in (kpair Xx Xy) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in Xy (skS.0 1 a a_1))) True
% 3.99/4.27 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota),
% 3.99/4.27 Eq (∀ (Xx Xy : Iota), in (kpair Xx Xy) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in Xy (skS.0 1 a a_1)) False
% 3.99/4.27 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.27 Eq
% 3.99/4.27 (Not
% 3.99/4.27 (∀ (Xy : Iota), in (kpair (skS.0 2 a a_1 a_2) Xy) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in Xy (skS.0 1 a a_1)))
% 3.99/4.27 True
% 3.99/4.27 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.27 Eq (∀ (Xy : Iota), in (kpair (skS.0 2 a a_1 a_2) Xy) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in Xy (skS.0 1 a a_1))
% 3.99/4.27 False
% 3.99/4.27 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.27 Eq
% 3.99/4.27 (Not
% 3.99/4.27 (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.99/4.27 in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)))
% 3.99/4.27 True
% 3.99/4.27 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.27 Eq
% 3.99/4.27 (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) →
% 3.99/4.27 in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1))
% 3.99/4.27 False
% 3.99/4.27 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.27 Eq (in (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (cartprod (skS.0 0 a) (skS.0 1 a a_1))) True
% 3.99/4.27 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)) False
% 3.99/4.27 Clause #18 (by clausification #[1]): Eq setukpairinjR (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu)
% 3.99/4.27 Clause #19 (by forward demodulation #[18, 6]): Eq True (∀ (Xx Xy Xz Xu : Iota), Eq (kpair Xx Xy) (kpair Xz Xu) → Eq Xy Xu)
% 3.99/4.27 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (Xy Xz Xu : Iota), Eq (kpair a Xy) (kpair Xz Xu) → Eq Xy Xu) True
% 3.99/4.27 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (∀ (Xz Xu : Iota), Eq (kpair a a_1) (kpair Xz Xu) → Eq a_1 Xu) True
% 3.99/4.27 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xu : Iota), Eq (kpair a a_1) (kpair a_2 Xu) → Eq a_1 Xu) True
% 3.99/4.27 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (kpair a a_1) (kpair a_2 a_3) → Eq a_1 a_3) True
% 3.99/4.27 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Eq (kpair a a_1) (kpair a_2 a_3)) False) (Eq (Eq a_1 a_3) True)
% 3.99/4.27 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (Eq a a_1) True) (Ne (kpair a_2 a) (kpair a_3 a_1))
% 3.99/4.27 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (kpair a a_1) (kpair a_2 a_3)) (Eq a_1 a_3)
% 3.99/4.27 Clause #28 (by clausification #[0]): Eq cartprodmempair1
% 3.99/4.30 (∀ (A B Xu : Iota),
% 3.99/4.30 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 3.99/4.30 Clause #29 (by forward demodulation #[28, 4]): Eq True
% 3.99/4.30 (∀ (A B Xu : Iota),
% 3.99/4.30 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 3.99/4.30 Clause #30 (by clausification #[29]): ∀ (a : Iota),
% 3.99/4.30 Eq
% 3.99/4.30 (∀ (B Xu : Iota),
% 3.99/4.30 in Xu (cartprod a B) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 3.99/4.30 True
% 3.99/4.30 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 3.99/4.30 Eq
% 3.99/4.30 (∀ (Xu : Iota),
% 3.99/4.30 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))))
% 3.99/4.30 True
% 3.99/4.30 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.30 Eq
% 3.99/4.30 (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))))
% 3.99/4.30 True
% 3.99/4.30 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota),
% 3.99/4.30 Or (Eq (in a (cartprod a_1 a_2)) False)
% 3.99/4.30 (Eq (Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) True)
% 3.99/4.30 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.30 Or (Eq (in a (cartprod a_1 a_2)) False)
% 3.99/4.30 (Eq
% 3.99/4.30 (And (in (skS.0 4 a_1 a_2 a a_3) a_1)
% 3.99/4.30 (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) Xy))))
% 3.99/4.30 True)
% 3.99/4.30 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.99/4.30 Or (Eq (in a (cartprod a_1 a_2)) False)
% 3.99/4.30 (Eq (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) Xy))) True)
% 3.99/4.30 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.30 Or (Eq (in a (cartprod a_1 a_2)) False)
% 3.99/4.30 (Eq (And (in (skS.0 5 a_2 a a_1 a_3 a_4) a_2) (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) (skS.0 5 a_2 a a_1 a_3 a_4))))
% 3.99/4.30 True)
% 3.99/4.30 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.30 Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) (skS.0 5 a_2 a a_1 a_3 a_4))) True)
% 3.99/4.30 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (in a (cartprod a_1 a_2)) False) (Eq (in (skS.0 5 a_2 a a_1 a_3 a_4) a_2) True)
% 3.99/4.30 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.99/4.30 Or (Eq (in a (cartprod a_1 a_2)) False) (Eq a (kpair (skS.0 4 a_1 a_2 a a_3) (skS.0 5 a_2 a a_1 a_3 a_4)))
% 3.99/4.30 Clause #41 (by superposition #[40, 16]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.99/4.30 Or
% 3.99/4.30 (Eq (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))
% 3.99/4.30 (kpair (skS.0 4 (skS.0 0 a) (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4)
% 3.99/4.30 (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5)))
% 3.99/4.30 (Eq False True)
% 3.99/4.30 Clause #43 (by superposition #[39, 16]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.99/4.30 Or
% 3.99/4.30 (Eq
% 3.99/4.30 (in (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5)
% 3.99/4.30 (skS.0 1 a a_1))
% 3.99/4.30 True)
% 3.99/4.30 (Eq False True)
% 3.99/4.30 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.99/4.30 Eq
% 3.99/4.30 (in (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5)
% 3.99/4.30 (skS.0 1 a a_1))
% 3.99/4.30 True
% 3.99/4.30 Clause #46 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.99/4.30 Eq (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3))
% 3.99/4.30 (kpair (skS.0 4 (skS.0 0 a) (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) a_4)
% 3.99/4.30 (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5))
% 3.99/4.30 Clause #48 (by superposition #[46, 26]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 3.99/4.30 Or (Ne (kpair a a_1) (kpair (skS.0 2 a_2 a_3 a_4) (skS.0 3 a_2 a_3 a_4 a_5)))
% 3.99/4.30 (Eq a_1 (skS.0 5 (skS.0 1 a_2 a_3) (kpair (skS.0 2 a_2 a_3 a_4) (skS.0 3 a_2 a_3 a_4 a_5)) (skS.0 0 a_2) a_6 a_7))
% 3.99/4.30 Clause #49 (by equality resolution #[48]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.99/4.30 Eq (skS.0 3 a a_1 a_2 a_3)
% 3.99/4.30 (skS.0 5 (skS.0 1 a a_1) (kpair (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) (skS.0 0 a) a_4 a_5)
% 3.99/4.30 Clause #51 (by backward demodulation #[49, 45]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 a a_1 a_2 a_3) (skS.0 1 a a_1)) True
% 3.99/4.30 Clause #54 (by superposition #[51, 17]): Eq True False
% 3.99/4.30 Clause #55 (by clausification #[54]): False
% 3.99/4.30 SZS output end Proof for theBenchmark.p
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