%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU646^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 : Fri Oct 3 08:02:07 PM UTC 2025 % Result : Theorem 18.00s 18.17s % Output : Proof 18.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU646^2 : TPTP v9.2.0. Released v3.7.0. % 0.13/0.14 % Command : duper %s % 0.14/0.35 % Computer : n024.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 06:11:38 EDT 2025 % 0.14/0.35 % CPUTime : % 18.00/18.17 SZS status Theorem for theBenchmark.p % 18.00/18.17 SZS output start Proof for theBenchmark.p % 18.00/18.17 Clause #1 (by assumption #[]): Eq % 18.00/18.17 (Eq cartprodmempair1 % 18.00/18.17 (∀ (A B Xu : Iota), % 18.00/18.17 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))) % 18.00/18.17 True % 18.00/18.17 Clause #2 (by assumption #[]): Eq (Eq kfstpairEq (∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx)) True % 18.00/18.17 Clause #3 (by assumption #[]): Eq (Not (cartprodmempair1 → kfstpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (kfst Xu) A)) True % 18.00/18.17 Clause #4 (by clausification #[3]): Eq (cartprodmempair1 → kfstpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (kfst Xu) A) False % 18.00/18.17 Clause #5 (by clausification #[4]): Eq cartprodmempair1 True % 18.00/18.17 Clause #6 (by clausification #[4]): Eq (kfstpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (kfst Xu) A) False % 18.00/18.17 Clause #7 (by clausification #[6]): Eq kfstpairEq True % 18.00/18.17 Clause #8 (by clausification #[6]): Eq (∀ (A B Xu : Iota), in Xu (cartprod A B) → in (kfst Xu) A) False % 18.00/18.17 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 % 18.00/18.17 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 % 18.00/18.17 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 % 18.00/18.17 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 % 18.00/18.17 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 18.00/18.17 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))) % 18.00/18.17 True % 18.00/18.17 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 18.00/18.17 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 % 18.00/18.17 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 % 18.00/18.17 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 % 18.00/18.17 Clause #17 (by clausification #[2]): Eq kfstpairEq (∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx) % 18.00/18.17 Clause #18 (by forward demodulation #[17, 7]): Eq True (∀ (Xx Xy : Iota), Eq (kfst (kpair Xx Xy)) Xx) % 18.00/18.17 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Eq (kfst (kpair a Xy)) a) True % 18.00/18.17 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Eq (kfst (kpair a a_1)) a) True % 18.00/18.17 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (kfst (kpair a a_1)) a % 18.00/18.17 Clause #33 (by clausification #[1]): Eq cartprodmempair1 % 18.00/18.17 (∀ (A B Xu : Iota), % 18.00/18.17 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 18.00/18.17 Clause #34 (by forward demodulation #[33, 5]): Eq True % 18.00/18.17 (∀ (A B Xu : Iota), % 18.00/18.17 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 18.00/18.17 Clause #35 (by clausification #[34]): ∀ (a : Iota), % 18.00/18.17 Eq % 18.00/18.17 (∀ (B Xu : Iota), % 18.00/18.17 in Xu (cartprod a B) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 18.00/18.17 True % 18.00/18.17 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 18.00/18.17 Eq % 18.00/18.17 (∀ (Xu : Iota), % 18.00/18.17 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)))) % 18.00/18.17 True % 18.00/18.17 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 18.00/18.17 Eq % 18.00/18.17 (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)))) % 18.00/18.17 True % 18.00/18.17 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 18.00/18.17 Or (Eq (in a (cartprod a_1 a_2)) False) % 18.00/18.17 (Eq (Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) True) % 18.00/18.17 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 18.00/18.17 Or (Eq (in a (cartprod a_1 a_2)) False) % 18.00/18.17 (Eq % 18.08/18.32 (And (in (skS.0 3 a_1 a_2 a a_3) a_1) % 18.08/18.32 (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy)))) % 18.08/18.32 True) % 18.08/18.32 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 18.08/18.32 Or (Eq (in a (cartprod a_1 a_2)) False) % 18.08/18.32 (Eq (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy))) True) % 18.08/18.32 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) % 18.08/18.32 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.08/18.32 Or (Eq (in a (cartprod a_1 a_2)) False) % 18.08/18.32 (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)))) % 18.08/18.32 True) % 18.08/18.32 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.08/18.32 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) % 18.08/18.32 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.08/18.32 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))) % 18.08/18.32 Clause #46 (by superposition #[45, 15]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.08/18.32 Or % 18.08/18.32 (Eq (skS.0 2 a a_1 a_2) % 18.08/18.32 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 18.08/18.32 (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))) % 18.08/18.32 (Eq False True) % 18.08/18.32 Clause #107 (by superposition #[41, 15]): ∀ (a a_1 a_2 a_3 : Iota), % 18.08/18.32 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) % 18.08/18.32 Clause #131 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.08/18.32 Eq (skS.0 2 a a_1 a_2) % 18.08/18.32 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 18.08/18.32 (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)) % 18.08/18.32 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) % 18.08/18.32 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 % 18.16/18.32 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 % 18.16/18.32 Clause #3817 (by superposition #[3738, 16]): Eq True False % 18.16/18.32 Clause #3840 (by clausification #[3817]): False % 18.16/18.32 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------