TSTP Solution File: SEU646^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU646^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 16:43:11 EDT 2023
% Result : Theorem 17.59s 17.79s
% Output : Proof 17.70s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU646^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n004.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 18:32:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 17.59/17.79 SZS status Theorem for theBenchmark.p
% 17.59/17.79 SZS output start Proof for theBenchmark.p
% 17.59/17.79 Clause #1 (by assumption #[]): Eq
% 17.59/17.79 (Eq cartprodmempair1
% 17.59/17.79 (∀ (A B Xu : Iota),
% 17.59/17.79 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))))
% 17.59/17.79 True
% 17.59/17.79 Clause #2 (by assumption #[]): Eq (Eq kfstpairEq (∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx)) True
% 17.59/17.79 Clause #3 (by assumption #[]): Eq (Not (cartprodmempair1 → kfstpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (kfst Xu) A)) True
% 17.59/17.79 Clause #4 (by clausification #[3]): Eq (cartprodmempair1 → kfstpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (kfst Xu) A) False
% 17.59/17.79 Clause #5 (by clausification #[4]): Eq cartprodmempair1 True
% 17.59/17.79 Clause #6 (by clausification #[4]): Eq (kfstpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (kfst Xu) A) False
% 17.59/17.79 Clause #7 (by clausification #[6]): Eq kfstpairEq True
% 17.59/17.79 Clause #8 (by clausification #[6]): Eq (∀ (A B Xu : Iota), in Xu (cartprod A B) → in (kfst Xu) A) False
% 17.59/17.79 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (Not (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → in (kfst Xu) (skS.0 0 a))) True
% 17.59/17.79 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → in (kfst Xu) (skS.0 0 a)) False
% 17.59/17.79 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Not (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in (kfst Xu) (skS.0 0 a))) True
% 17.59/17.79 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in (kfst Xu) (skS.0 0 a)) False
% 17.59/17.79 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota),
% 17.59/17.79 Eq (Not (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in (kfst (skS.0 2 a a_1 a_2)) (skS.0 0 a)))
% 17.59/17.79 True
% 17.59/17.79 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota),
% 17.59/17.79 Eq (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in (kfst (skS.0 2 a a_1 a_2)) (skS.0 0 a)) False
% 17.59/17.79 Clause #15 (by clausification #[14]): ∀ (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
% 17.59/17.79 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Eq (in (kfst (skS.0 2 a a_1 a_2)) (skS.0 0 a)) False
% 17.59/17.79 Clause #17 (by clausification #[2]): Eq kfstpairEq (∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx)
% 17.59/17.79 Clause #18 (by forward demodulation #[17, 7]): Eq True (∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx)
% 17.59/17.79 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Eq (kfst (kpair a Xy)) a) True
% 17.59/17.79 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Eq (kfst (kpair a a_1)) a) True
% 17.59/17.79 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (kfst (kpair a a_1)) a
% 17.59/17.79 Clause #33 (by clausification #[1]): Eq cartprodmempair1
% 17.59/17.79 (∀ (A B Xu : Iota),
% 17.59/17.79 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 17.59/17.79 Clause #34 (by forward demodulation #[33, 5]): Eq True
% 17.59/17.79 (∀ (A B Xu : Iota),
% 17.59/17.79 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 17.59/17.79 Clause #35 (by clausification #[34]): ∀ (a : Iota),
% 17.59/17.79 Eq
% 17.59/17.79 (∀ (B Xu : Iota),
% 17.59/17.79 in Xu (cartprod a B) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))
% 17.59/17.79 True
% 17.59/17.79 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 17.59/17.79 Eq
% 17.59/17.79 (∀ (Xu : Iota),
% 17.59/17.79 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))))
% 17.59/17.79 True
% 17.59/17.79 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 17.59/17.79 Eq
% 17.59/17.79 (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))))
% 17.59/17.79 True
% 17.59/17.79 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 17.59/17.79 Or (Eq (in a (cartprod a_1 a_2)) False)
% 17.59/17.79 (Eq (Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) True)
% 17.59/17.79 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota),
% 17.59/17.79 Or (Eq (in a (cartprod a_1 a_2)) False)
% 17.59/17.79 (Eq
% 17.70/17.92 (And (in (skS.0 3 a_1 a_2 a a_3) a_1)
% 17.70/17.92 (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy))))
% 17.70/17.92 True)
% 17.70/17.92 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota),
% 17.70/17.92 Or (Eq (in a (cartprod a_1 a_2)) False)
% 17.70/17.92 (Eq (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy))) True)
% 17.70/17.92 Clause #41 (by clausification #[39]): ∀ (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)
% 17.70/17.92 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 17.70/17.92 Or (Eq (in a (cartprod a_1 a_2)) False)
% 17.70/17.92 (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))))
% 17.70/17.92 True)
% 17.70/17.92 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 17.70/17.92 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)
% 17.70/17.92 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 17.70/17.92 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)))
% 17.70/17.92 Clause #46 (by superposition #[45, 15]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 17.70/17.92 Or
% 17.70/17.92 (Eq (skS.0 2 a a_1 a_2)
% 17.70/17.92 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 17.70/17.92 (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)))
% 17.70/17.92 (Eq False True)
% 17.70/17.92 Clause #107 (by superposition #[41, 15]): ∀ (a a_1 a_2 a_3 : Iota),
% 17.70/17.92 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)
% 17.70/17.92 Clause #131 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 17.70/17.92 Eq (skS.0 2 a a_1 a_2)
% 17.70/17.92 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3)
% 17.70/17.92 (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))
% 17.70/17.92 Clause #132 (by superposition #[131, 21]): ∀ (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)
% 17.70/17.92 Clause #1542 (by clausification #[107]): ∀ (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
% 17.70/17.92 Clause #3738 (by backward demodulation #[132, 1542]): ∀ (a a_1 a_2 : Iota), Eq (in (kfst (skS.0 2 a a_1 a_2)) (skS.0 0 a)) True
% 17.70/17.92 Clause #3817 (by superposition #[3738, 16]): Eq True False
% 17.70/17.92 Clause #3840 (by clausification #[3817]): False
% 17.70/17.92 SZS output end Proof for theBenchmark.p
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