%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET589+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:00:11 PM UTC 2025 % Result : Theorem 16.19s 16.35s % Output : Proof 16.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET589+3 : TPTP v9.2.0. Released v2.2.0. % 0.03/0.14 % Command : duper %s % 0.13/0.35 % Computer : n014.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 : Thu Oct 2 13:55:08 EDT 2025 % 0.13/0.35 % CPUTime : % 16.19/16.35 SZS status Theorem for theBenchmark.p % 16.19/16.35 SZS output start Proof for theBenchmark.p % 16.19/16.35 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), And (subset B C) (subset C D) → subset B D) True % 16.19/16.35 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), subset B C → subset (difference B D) (difference C D)) True % 16.19/16.35 Clause #2 (by assumption #[]): Eq (∀ (B C D : Iota), subset B C → subset (difference D C) (difference D B)) True % 16.19/16.35 Clause #6 (by assumption #[]): Eq (Not (∀ (B C D E : Iota), And (subset B C) (subset D E) → subset (difference B E) (difference C D))) True % 16.19/16.35 Clause #8 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), And (subset a C) (subset C D) → subset a D) True % 16.19/16.35 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), And (subset a a_1) (subset a_1 D) → subset a D) True % 16.19/16.35 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True % 16.19/16.35 Clause #11 (by clausification #[10]): ∀ (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) % 16.19/16.35 Clause #12 (by clausification #[11]): ∀ (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)) % 16.19/16.35 Clause #15 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), subset a C → subset (difference a D) (difference C D)) True % 16.19/16.35 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), subset a a_1 → subset (difference a D) (difference a_1 D)) True % 16.19/16.35 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → subset (difference a a_2) (difference a_1 a_2)) True % 16.19/16.35 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (subset (difference a a_2) (difference a_1 a_2)) True) % 16.19/16.35 Clause #21 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C D : Iota), subset a C → subset (difference D C) (difference D a)) True % 16.19/16.35 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), subset a a_1 → subset (difference D a_1) (difference D a)) True % 16.19/16.35 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → subset (difference a_2 a_1) (difference a_2 a)) True % 16.19/16.35 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (subset (difference a_2 a_1) (difference a_2 a)) True) % 16.19/16.35 Clause #37 (by clausification #[6]): Eq (∀ (B C D E : Iota), And (subset B C) (subset D E) → subset (difference B E) (difference C D)) False % 16.19/16.35 Clause #38 (by clausification #[37]): ∀ (a : Iota), % 16.19/16.35 Eq % 16.19/16.35 (Not % 16.19/16.35 (∀ (C D E : Iota), And (subset (skS.0 1 a) C) (subset D E) → subset (difference (skS.0 1 a) E) (difference C D))) % 16.19/16.35 True % 16.19/16.35 Clause #39 (by clausification #[38]): ∀ (a : Iota), % 16.19/16.35 Eq (∀ (C D E : Iota), And (subset (skS.0 1 a) C) (subset D E) → subset (difference (skS.0 1 a) E) (difference C D)) % 16.19/16.35 False % 16.19/16.35 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 16.19/16.35 Eq % 16.19/16.35 (Not % 16.19/16.35 (∀ (D E : Iota), % 16.19/16.35 And (subset (skS.0 1 a) (skS.0 2 a a_1)) (subset D E) → % 16.19/16.35 subset (difference (skS.0 1 a) E) (difference (skS.0 2 a a_1) D))) % 16.19/16.35 True % 16.19/16.35 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 16.19/16.35 Eq % 16.19/16.35 (∀ (D E : Iota), % 16.19/16.35 And (subset (skS.0 1 a) (skS.0 2 a a_1)) (subset D E) → % 16.19/16.35 subset (difference (skS.0 1 a) E) (difference (skS.0 2 a a_1) D)) % 16.19/16.35 False % 16.19/16.35 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 16.19/16.35 Eq % 16.19/16.35 (Not % 16.19/16.35 (∀ (E : Iota), % 16.19/16.35 And (subset (skS.0 1 a) (skS.0 2 a a_1)) (subset (skS.0 3 a a_1 a_2) E) → % 16.19/16.35 subset (difference (skS.0 1 a) E) (difference (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)))) % 16.19/16.35 True % 16.19/16.35 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 16.19/16.35 Eq % 16.19/16.35 (∀ (E : Iota), % 16.19/16.35 And (subset (skS.0 1 a) (skS.0 2 a a_1)) (subset (skS.0 3 a a_1 a_2) E) → % 16.19/16.35 subset (difference (skS.0 1 a) E) (difference (skS.0 2 a a_1) (skS.0 3 a a_1 a_2))) % 16.19/16.35 False % 16.19/16.35 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 16.19/16.35 Eq % 16.19/16.35 (Not % 16.19/16.35 (And (subset (skS.0 1 a) (skS.0 2 a a_1)) (subset (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)) → % 16.19/16.38 subset (difference (skS.0 1 a) (skS.0 4 a a_1 a_2 a_3)) (difference (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)))) % 16.19/16.38 True % 16.19/16.38 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 16.19/16.38 Eq % 16.19/16.38 (And (subset (skS.0 1 a) (skS.0 2 a a_1)) (subset (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)) → % 16.19/16.38 subset (difference (skS.0 1 a) (skS.0 4 a a_1 a_2 a_3)) (difference (skS.0 2 a a_1) (skS.0 3 a a_1 a_2))) % 16.19/16.38 False % 16.19/16.38 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 16.19/16.38 Eq (And (subset (skS.0 1 a) (skS.0 2 a a_1)) (subset (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3))) True % 16.19/16.38 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 16.19/16.38 Eq (subset (difference (skS.0 1 a) (skS.0 4 a a_1 a_2 a_3)) (difference (skS.0 2 a a_1) (skS.0 3 a a_1 a_2))) False % 16.19/16.38 Clause #48 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 3 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3)) True % 16.19/16.38 Clause #49 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (subset (skS.0 1 a) (skS.0 2 a a_1)) True % 16.19/16.38 Clause #52 (by superposition #[48, 24]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 16.19/16.38 Or (Eq True False) (Eq (subset (difference a (skS.0 4 a_1 a_2 a_3 a_4)) (difference a (skS.0 3 a_1 a_2 a_3))) True) % 16.19/16.38 Clause #55 (by superposition #[49, 18]): ∀ (a a_1 a_2 : Iota), % 16.19/16.38 Or (Eq True False) (Eq (subset (difference (skS.0 1 a) a_1) (difference (skS.0 2 a a_2) a_1)) True) % 16.19/16.38 Clause #75 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Eq (subset (difference (skS.0 1 a) a_1) (difference (skS.0 2 a a_2) a_1)) True % 16.19/16.38 Clause #76 (by superposition #[75, 12]): ∀ (a a_1 a_2 a_3 : Iota), % 16.19/16.38 Or (Eq (subset (difference (skS.0 1 a) a_1) a_2) True) % 16.19/16.38 (Or (Eq True False) (Eq (subset (difference (skS.0 2 a a_3) a_1) a_2) False)) % 16.19/16.38 Clause #138 (by clausification #[52]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 16.19/16.38 Eq (subset (difference a (skS.0 4 a_1 a_2 a_3 a_4)) (difference a (skS.0 3 a_1 a_2 a_3))) True % 16.19/16.38 Clause #254 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 16.19/16.38 Or (Eq (subset (difference (skS.0 1 a) a_1) a_2) True) (Eq (subset (difference (skS.0 2 a a_3) a_1) a_2) False) % 16.19/16.38 Clause #258 (by superposition #[254, 138]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 16.19/16.38 Or % 16.19/16.38 (Eq (subset (difference (skS.0 1 a) (skS.0 4 a_1 a_2 a_3 a_4)) (difference (skS.0 2 a a_5) (skS.0 3 a_1 a_2 a_3))) % 16.19/16.38 True) % 16.19/16.38 (Eq False True) % 16.19/16.38 Clause #2713 (by clausification #[258]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 16.19/16.38 Eq (subset (difference (skS.0 1 a) (skS.0 4 a_1 a_2 a_3 a_4)) (difference (skS.0 2 a a_5) (skS.0 3 a_1 a_2 a_3))) True % 16.19/16.38 Clause #2714 (by superposition #[2713, 47]): Eq True False % 16.19/16.38 Clause #2726 (by clausification #[2714]): False % 16.19/16.38 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------