%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU632^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:02:05 PM UTC 2025 % Result : Theorem 4.51s 4.71s % Output : Proof 4.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU632^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n001.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 06:35:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.51/4.71 SZS status Theorem for theBenchmark.p % 4.51/4.71 SZS output start Proof for theBenchmark.p % 4.51/4.71 Clause #2 (by assumption #[]): Eq (Eq kpairp (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy))) True % 4.51/4.71 Clause #3 (by assumption #[]): Eq % 4.51/4.71 (Eq cartprodmempair1 % 4.51/4.71 (∀ (A B Xu : Iota), % 4.51/4.71 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy))))) % 4.51/4.71 True % 4.51/4.71 Clause #4 (by assumption #[]): Eq (Not (kpairp → cartprodmempair1 → ∀ (A B Xu : Iota), in Xu (cartprod A B) → iskpair Xu)) True % 4.51/4.71 Clause #5 (by clausification #[4]): Eq (kpairp → cartprodmempair1 → ∀ (A B Xu : Iota), in Xu (cartprod A B) → iskpair Xu) False % 4.51/4.71 Clause #6 (by clausification #[5]): Eq kpairp True % 4.51/4.71 Clause #7 (by clausification #[5]): Eq (cartprodmempair1 → ∀ (A B Xu : Iota), in Xu (cartprod A B) → iskpair Xu) False % 4.51/4.71 Clause #8 (by clausification #[7]): Eq cartprodmempair1 True % 4.51/4.71 Clause #9 (by clausification #[7]): Eq (∀ (A B Xu : Iota), in Xu (cartprod A B) → iskpair Xu) False % 4.51/4.71 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (Not (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → iskpair Xu)) True % 4.51/4.71 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (B Xu : Iota), in Xu (cartprod (skS.0 0 a) B) → iskpair Xu) False % 4.51/4.71 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (Not (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → iskpair Xu)) True % 4.51/4.71 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (∀ (Xu : Iota), in Xu (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → iskpair Xu) False % 4.51/4.71 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 4.51/4.71 Eq (Not (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → iskpair (skS.0 2 a a_1 a_2))) True % 4.51/4.71 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 4.51/4.71 Eq (in (skS.0 2 a a_1 a_2) (cartprod (skS.0 0 a) (skS.0 1 a a_1)) → iskpair (skS.0 2 a a_1 a_2)) False % 4.51/4.71 Clause #16 (by clausification #[15]): ∀ (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 % 4.51/4.71 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Eq (iskpair (skS.0 2 a a_1 a_2)) False % 4.51/4.71 Clause #18 (by clausification #[2]): Eq kpairp (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) % 4.51/4.71 Clause #19 (by forward demodulation #[18, 6]): Eq True (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) % 4.51/4.71 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (Xy : Iota), iskpair (kpair a Xy)) True % 4.51/4.71 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (iskpair (kpair a a_1)) True % 4.51/4.71 Clause #33 (by clausification #[3]): Eq cartprodmempair1 % 4.51/4.71 (∀ (A B Xu : Iota), % 4.51/4.71 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.51/4.71 Clause #34 (by forward demodulation #[33, 8]): Eq True % 4.51/4.71 (∀ (A B Xu : Iota), % 4.51/4.71 in Xu (cartprod A B) → Exists fun Xx => And (in Xx A) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.51/4.71 Clause #35 (by clausification #[34]): ∀ (a : Iota), % 4.51/4.71 Eq % 4.51/4.71 (∀ (B Xu : Iota), % 4.51/4.71 in Xu (cartprod a B) → Exists fun Xx => And (in Xx a) (Exists fun Xy => And (in Xy B) (Eq Xu (kpair Xx Xy)))) % 4.51/4.71 True % 4.51/4.71 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 4.51/4.71 Eq % 4.51/4.71 (∀ (Xu : Iota), % 4.51/4.71 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)))) % 4.51/4.71 True % 4.51/4.71 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 4.51/4.71 Eq % 4.51/4.71 (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)))) % 4.51/4.71 True % 4.51/4.71 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 4.51/4.71 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.51/4.71 (Eq (Exists fun Xx => And (in Xx a_1) (Exists fun Xy => And (in Xy a_2) (Eq a (kpair Xx Xy)))) True) % 4.51/4.71 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 4.51/4.71 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.51/4.71 (Eq % 4.51/4.71 (And (in (skS.0 3 a_1 a_2 a a_3) a_1) % 4.51/4.71 (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy)))) % 4.51/4.71 True) % 4.51/4.71 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 4.51/4.71 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.57/4.73 (Eq (Exists fun Xy => And (in Xy a_2) (Eq a (kpair (skS.0 3 a_1 a_2 a a_3) Xy))) True) % 4.57/4.73 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.57/4.73 Or (Eq (in a (cartprod a_1 a_2)) False) % 4.57/4.73 (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)))) % 4.57/4.73 True) % 4.57/4.73 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.57/4.73 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) % 4.57/4.73 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.57/4.73 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))) % 4.57/4.73 Clause #46 (by superposition #[45, 16]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.57/4.73 Or % 4.57/4.73 (Eq (skS.0 2 a a_1 a_2) % 4.57/4.73 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 4.57/4.73 (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))) % 4.57/4.73 (Eq False True) % 4.57/4.73 Clause #175 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.57/4.73 Eq (skS.0 2 a a_1 a_2) % 4.57/4.73 (kpair (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) a_3) % 4.57/4.73 (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)) % 4.57/4.73 Clause #176 (by superposition #[175, 21]): ∀ (a a_1 a_2 : Iota), Eq (iskpair (skS.0 2 a a_1 a_2)) True % 4.57/4.73 Clause #188 (by superposition #[176, 17]): Eq True False % 4.57/4.73 Clause #195 (by clausification #[188]): False % 4.57/4.73 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------