%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU167+3 : TPTP v9.2.0. Released v3.2.0. % 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 08:01:02 PM UTC 2025 % Result : Theorem 5.40s 5.55s % Output : Proof 5.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SEU167+3 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.14 % Command : duper %s % 0.15/0.35 % Computer : n001.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 : Fri Oct 3 05:46:53 EDT 2025 % 0.15/0.35 % CPUTime : % 5.40/5.55 SZS status Theorem for theBenchmark.p % 5.40/5.55 SZS output start Proof for theBenchmark.p % 5.40/5.55 Clause #3 (by assumption #[]): Eq % 5.40/5.55 (∀ (A B C : Iota), % 5.40/5.55 subset A B → % 5.40/5.55 And (subset (cartesian_product2 A C) (cartesian_product2 B C)) % 5.40/5.55 (subset (cartesian_product2 C A) (cartesian_product2 C B))) % 5.40/5.55 True % 5.40/5.55 Clause #4 (by assumption #[]): Eq (Not (∀ (A B C D : Iota), And (subset A B) (subset C D) → subset (cartesian_product2 A C) (cartesian_product2 B D))) % 5.40/5.55 True % 5.40/5.55 Clause #5 (by assumption #[]): Eq (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C) True % 5.40/5.55 Clause #12 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset a B) (subset B C) → subset a C) True % 5.40/5.55 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (subset a a_1) (subset a_1 C) → subset a C) True % 5.40/5.55 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True % 5.40/5.55 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a_2)) False) (Eq (subset a a_2) True) % 5.40/5.55 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Or (Eq (subset a a_2) False) (Eq (subset a_2 a_1) False)) % 5.40/5.55 Clause #19 (by clausification #[3]): ∀ (a : Iota), % 5.40/5.55 Eq % 5.40/5.55 (∀ (B C : Iota), % 5.40/5.55 subset a B → % 5.40/5.55 And (subset (cartesian_product2 a C) (cartesian_product2 B C)) % 5.40/5.55 (subset (cartesian_product2 C a) (cartesian_product2 C B))) % 5.40/5.55 True % 5.40/5.55 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 5.40/5.55 Eq % 5.40/5.55 (∀ (C : Iota), % 5.40/5.55 subset a a_1 → % 5.40/5.55 And (subset (cartesian_product2 a C) (cartesian_product2 a_1 C)) % 5.40/5.55 (subset (cartesian_product2 C a) (cartesian_product2 C a_1))) % 5.40/5.55 True % 5.40/5.55 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 5.40/5.55 Eq % 5.40/5.55 (subset a a_1 → % 5.40/5.55 And (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)) % 5.40/5.55 (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1))) % 5.40/5.55 True % 5.40/5.55 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 5.40/5.55 Or (Eq (subset a a_1) False) % 5.40/5.55 (Eq % 5.40/5.55 (And (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)) % 5.40/5.55 (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1))) % 5.40/5.55 True) % 5.40/5.55 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 5.40/5.55 Or (Eq (subset a a_1) False) (Eq (subset (cartesian_product2 a_2 a) (cartesian_product2 a_2 a_1)) True) % 5.40/5.55 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 5.40/5.55 Or (Eq (subset a a_1) False) (Eq (subset (cartesian_product2 a a_2) (cartesian_product2 a_1 a_2)) True) % 5.40/5.55 Clause #27 (by clausification #[4]): Eq (∀ (A B C D : Iota), And (subset A B) (subset C D) → subset (cartesian_product2 A C) (cartesian_product2 B D)) False % 5.40/5.55 Clause #28 (by clausification #[27]): ∀ (a : Iota), % 5.40/5.55 Eq % 5.40/5.55 (Not % 5.40/5.55 (∀ (B C D : Iota), % 5.40/5.55 And (subset (skS.0 2 a) B) (subset C D) → subset (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 B D))) % 5.40/5.55 True % 5.40/5.55 Clause #29 (by clausification #[28]): ∀ (a : Iota), % 5.40/5.55 Eq % 5.40/5.55 (∀ (B C D : Iota), % 5.40/5.55 And (subset (skS.0 2 a) B) (subset C D) → subset (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 B D)) % 5.40/5.55 False % 5.40/5.55 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 5.40/5.55 Eq % 5.40/5.55 (Not % 5.40/5.55 (∀ (C D : Iota), % 5.40/5.55 And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset C D) → % 5.40/5.55 subset (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 3 a a_1) D))) % 5.40/5.55 True % 5.40/5.55 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 5.40/5.55 Eq % 5.40/5.55 (∀ (C D : Iota), % 5.40/5.55 And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset C D) → % 5.40/5.55 subset (cartesian_product2 (skS.0 2 a) C) (cartesian_product2 (skS.0 3 a a_1) D)) % 5.40/5.55 False % 5.40/5.55 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 5.40/5.55 Eq % 5.40/5.55 (Not % 5.40/5.55 (∀ (D : Iota), % 5.40/5.55 And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) D) → % 5.40/5.55 subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 3 a a_1) D))) % 5.40/5.55 True % 5.40/5.55 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 5.40/5.55 Eq % 5.40/5.55 (∀ (D : Iota), % 5.40/5.57 And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) D) → % 5.40/5.57 subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) (cartesian_product2 (skS.0 3 a a_1) D)) % 5.40/5.57 False % 5.40/5.57 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 5.40/5.57 Eq % 5.40/5.57 (Not % 5.40/5.57 (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) → % 5.40/5.57 subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 5.40/5.57 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3)))) % 5.40/5.57 True % 5.40/5.57 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), % 5.40/5.57 Eq % 5.40/5.57 (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) → % 5.40/5.57 subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 5.40/5.57 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))) % 5.40/5.57 False % 5.40/5.57 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 5.40/5.57 Eq (And (subset (skS.0 2 a) (skS.0 3 a a_1)) (subset (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3))) True % 5.40/5.57 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 5.40/5.57 Eq % 5.40/5.57 (subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a a_1 a_2)) % 5.40/5.57 (cartesian_product2 (skS.0 3 a a_1) (skS.0 5 a a_1 a_2 a_3))) % 5.40/5.57 False % 5.40/5.57 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 4 a a_1 a_2) (skS.0 5 a a_1 a_2 a_3)) True % 5.40/5.57 Clause #39 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True % 5.40/5.57 Clause #41 (by superposition #[38, 23]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.40/5.57 Or (Eq True False) % 5.40/5.57 (Eq (subset (cartesian_product2 a (skS.0 4 a_1 a_2 a_3)) (cartesian_product2 a (skS.0 5 a_1 a_2 a_3 a_4))) True) % 5.40/5.57 Clause #45 (by superposition #[39, 24]): ∀ (a a_1 a_2 : Iota), % 5.40/5.57 Or (Eq True False) (Eq (subset (cartesian_product2 (skS.0 2 a) a_1) (cartesian_product2 (skS.0 3 a a_2) a_1)) True) % 5.40/5.57 Clause #52 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Eq (subset (cartesian_product2 (skS.0 2 a) a_1) (cartesian_product2 (skS.0 3 a a_2) a_1)) True % 5.40/5.57 Clause #53 (by superposition #[52, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 5.40/5.57 Or (Eq (subset (cartesian_product2 (skS.0 2 a) a_1) a_2) True) % 5.40/5.57 (Or (Eq True False) (Eq (subset (cartesian_product2 (skS.0 3 a a_3) a_1) a_2) False)) % 5.40/5.57 Clause #75 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 5.40/5.57 Or (Eq (subset (cartesian_product2 (skS.0 2 a) a_1) a_2) True) % 5.40/5.57 (Eq (subset (cartesian_product2 (skS.0 3 a a_3) a_1) a_2) False) % 5.40/5.57 Clause #78 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.40/5.57 Eq (subset (cartesian_product2 a (skS.0 4 a_1 a_2 a_3)) (cartesian_product2 a (skS.0 5 a_1 a_2 a_3 a_4))) True % 5.40/5.57 Clause #79 (by superposition #[78, 75]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.40/5.57 Or % 5.40/5.57 (Eq % 5.40/5.57 (subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a_1 a_2 a_3)) % 5.40/5.57 (cartesian_product2 (skS.0 3 a a_4) (skS.0 5 a_1 a_2 a_3 a_5))) % 5.40/5.57 True) % 5.40/5.57 (Eq True False) % 5.40/5.57 Clause #339 (by clausification #[79]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.40/5.57 Eq % 5.40/5.57 (subset (cartesian_product2 (skS.0 2 a) (skS.0 4 a_1 a_2 a_3)) % 5.40/5.57 (cartesian_product2 (skS.0 3 a a_4) (skS.0 5 a_1 a_2 a_3 a_5))) % 5.40/5.57 True % 5.40/5.57 Clause #340 (by superposition #[339, 37]): Eq True False % 5.40/5.57 Clause #344 (by clausification #[340]): False % 5.40/5.57 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------