%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU658^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:02:09 PM UTC 2025 % Result : Theorem 4.07s 4.26s % Output : Proof 4.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU658^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n019.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 : Fri Oct 3 04:09:08 EDT 2025 % 0.13/0.35 % CPUTime : % 4.07/4.26 SZS status Theorem for theBenchmark.p % 4.07/4.26 SZS output start Proof for theBenchmark.p % 4.07/4.26 Clause #0 (by assumption #[]): Eq % 4.07/4.26 (Eq cartprodmempair1 % 4.07/4.26 (∀ (A B Xu : Iota), % 4.07/4.26 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))) % 4.07/4.26 True % 4.07/4.26 Clause #1 (by assumption #[]): Eq (Eq ksndpairEq (∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy)) True % 4.07/4.26 Clause #2 (by assumption #[]): Eq (Not (cartprodmempair1 → ksndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (ksnd Xu) B)) True % 4.07/4.26 Clause #3 (by clausification #[2]): Eq (cartprodmempair1 → ksndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (ksnd Xu) B) False % 4.07/4.26 Clause #4 (by clausification #[3]): Eq cartprodmempair1 True % 4.07/4.26 Clause #5 (by clausification #[3]): Eq (ksndpairEq → ∀ (A B Xu : Iota), in Xu (cartprod A B) → in (ksnd Xu) B) False % 4.07/4.26 Clause #6 (by clausification #[5]): Eq ksndpairEq True % 4.07/4.26 Clause #7 (by clausification #[5]): Eq (∀ (A B Xu : Iota), in Xu (cartprod A B) → in (ksnd Xu) B) False % 4.07/4.26 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → in (ksnd Xu) B)) True % 4.07/4.26 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → in (ksnd Xu) B) False % 4.07/4.26 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 4.07/4.26 Eq (Not (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in (ksnd Xu) (skS.0 1 a a_1))) True % 4.07/4.26 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in (ksnd Xu) (skS.0 1 a a_1)) False % 4.07/4.26 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.07/4.26 Eq % 4.07/4.26 (Not % 4.07/4.26 (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in (ksnd (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1))) % 4.07/4.26 True % 4.07/4.26 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 4.07/4.26 Eq (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → in (ksnd (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1)) % 4.07/4.26 False % 4.07/4.26 Clause #14 (by clausification #[13]): ∀ (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 % 4.07/4.26 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Eq (in (ksnd (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1)) False % 4.07/4.26 Clause #16 (by clausification #[1]): Eq ksndpairEq (∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) % 4.07/4.26 Clause #17 (by forward demodulation #[16, 6]): Eq True (∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) % 4.07/4.26 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Eq (ksnd (kpair a Xy)) Xy) True % 4.07/4.26 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Eq (ksnd (kpair a a_1)) a_1) True % 4.07/4.26 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (ksnd (kpair a a_1)) a_1 % 4.07/4.26 Clause #21 (by clausification #[0]): Eq cartprodmempair1 % 4.07/4.26 (∀ (A B Xu : Iota), % 4.07/4.26 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.07/4.26 Clause #22 (by forward demodulation #[21, 4]): Eq True % 4.07/4.26 (∀ (A B Xu : Iota), % 4.07/4.26 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.07/4.26 Clause #23 (by clausification #[22]): ∀ (a : Iota), % 4.07/4.26 Eq % 4.07/4.26 (∀ (B Xu : Iota), % 4.07/4.26 in Xu (cartprod a B) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.07/4.26 True % 4.07/4.26 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), % 4.07/4.26 Eq % 4.07/4.26 (∀ (Xu : Iota), % 4.07/4.26 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)))) % 4.07/4.26 True % 4.07/4.26 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 4.07/4.26 Eq % 4.07/4.26 (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)))) % 4.07/4.26 True % 4.07/4.26 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 4.07/4.26 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.07/4.26 (Eq (Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) True) % 4.07/4.26 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), % 4.07/4.26 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.07/4.28 (Eq % 4.07/4.28 (And (in (skS.0 3 a_1 a_2 a a_3) a_1) % 4.07/4.28 (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy)))) % 4.07/4.28 True) % 4.07/4.28 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota), % 4.07/4.28 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.07/4.28 (Eq (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy))) True) % 4.07/4.28 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.07/4.28 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.07/4.28 (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)))) % 4.07/4.28 True) % 4.07/4.28 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.07/4.28 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) % 4.07/4.28 Clause #32 (by clausification #[30]): ∀ (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) % 4.07/4.28 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.07/4.28 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))) % 4.07/4.28 Clause #34 (by superposition #[33, 14]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.07/4.28 Or % 4.07/4.28 (Eq (skS.0 2 a a_1 a_2) % 4.07/4.28 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 4.07/4.28 (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))) % 4.07/4.28 (Eq False True) % 4.07/4.28 Clause #36 (by superposition #[32, 14]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.07/4.28 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) % 4.07/4.28 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.07/4.28 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 % 4.07/4.28 Clause #39 (by clausification #[34]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.07/4.28 Eq (skS.0 2 a a_1 a_2) % 4.07/4.28 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 4.07/4.28 (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)) % 4.07/4.28 Clause #40 (by superposition #[39, 20]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.07/4.28 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) % 4.07/4.28 Clause #41 (by backward demodulation #[40, 38]): ∀ (a a_1 a_2 : Iota), Eq (in (ksnd (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1)) True % 4.07/4.28 Clause #43 (by superposition #[41, 15]): Eq True False % 4.07/4.28 Clause #44 (by clausification #[43]): False % 4.07/4.28 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------