%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET635+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:00:19 PM UTC 2025 % Result : Theorem 3.81s 3.99s % Output : Proof 3.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET635+3 : TPTP v9.2.0. Released v2.2.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 14:45:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.81/3.99 SZS status Theorem for theBenchmark.p % 3.81/3.99 SZS output start Proof for theBenchmark.p % 3.81/3.99 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), subset (intersection B C) B) True % 3.81/3.99 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq (difference B C) empty_set) (subset B C)) True % 3.81/3.99 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Eq (union B empty_set) B) True % 3.81/3.99 Clause #3 (by assumption #[]): Eq (∀ (B C D : Iota), Eq (difference B (intersection C D)) (union (difference B C) (difference B D))) True % 3.81/3.99 Clause #4 (by assumption #[]): Eq (∀ (B C D : Iota), Eq (intersection B (difference C D)) (difference (intersection B C) D)) True % 3.81/3.99 Clause #10 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True % 3.81/3.99 Clause #15 (by assumption #[]): Eq (Not (∀ (B C D : Iota), Eq (intersection B (difference C D)) (difference (intersection B C) (intersection B D)))) % 3.81/3.99 True % 3.81/3.99 Clause #19 (by clausification #[2]): ∀ (a : Iota), Eq (Eq (union a empty_set) a) True % 3.81/3.99 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (union a empty_set) a % 3.81/3.99 Clause #21 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), subset (intersection a C) a) True % 3.81/3.99 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (intersection a a_1) a) True % 3.81/3.99 Clause #30 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq (difference a C) empty_set) (subset a C)) True % 3.81/3.99 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Iff (Eq (difference a a_1) empty_set) (subset a a_1)) True % 3.81/3.99 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (Eq (difference a a_1) empty_set) True) (Eq (subset a a_1) False) % 3.81/3.99 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (difference a a_1) empty_set) % 3.81/3.99 Clause #35 (by superposition #[34, 22]): ∀ (a a_1 : Iota), Or (Eq (difference (intersection a a_1) a) empty_set) (Eq False True) % 3.81/3.99 Clause #39 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (difference (intersection a a_1) a) empty_set % 3.81/3.99 Clause #43 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C D : Iota), Eq (difference a (intersection C D)) (union (difference a C) (difference a D))) True % 3.81/3.99 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), % 3.81/3.99 Eq (∀ (D : Iota), Eq (difference a (intersection a_1 D)) (union (difference a a_1) (difference a D))) True % 3.81/3.99 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (Eq (difference a (intersection a_1 a_2)) (union (difference a a_1) (difference a a_2))) True % 3.81/3.99 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Eq (difference a (intersection a_1 a_2)) (union (difference a a_1) (difference a a_2)) % 3.81/3.99 Clause #47 (by superposition #[46, 39]): ∀ (a a_1 a_2 : Iota), % 3.81/3.99 Eq (difference (intersection a a_1) (intersection a_2 a)) (union (difference (intersection a a_1) a_2) empty_set) % 3.81/3.99 Clause #67 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (C D : Iota), Eq (intersection a (difference C D)) (difference (intersection a C) D)) True % 3.81/3.99 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Eq (intersection a (difference a_1 D)) (difference (intersection a a_1) D)) True % 3.81/3.99 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Eq (Eq (intersection a (difference a_1 a_2)) (difference (intersection a a_1) a_2)) True % 3.81/3.99 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Eq (intersection a (difference a_1 a_2)) (difference (intersection a a_1) a_2) % 3.81/3.99 Clause #172 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True % 3.81/3.99 Clause #173 (by clausification #[172]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True % 3.81/3.99 Clause #174 (by clausification #[173]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a) % 3.81/3.99 Clause #226 (by clausification #[15]): Eq (∀ (B C D : Iota), Eq (intersection B (difference C D)) (difference (intersection B C) (intersection B D))) False % 3.81/3.99 Clause #227 (by clausification #[226]): ∀ (a : Iota), % 3.81/3.99 Eq % 3.81/3.99 (Not % 3.81/3.99 (∀ (C D : Iota), % 3.81/3.99 Eq (intersection (skS.0 3 a) (difference C D)) % 3.81/3.99 (difference (intersection (skS.0 3 a) C) (intersection (skS.0 3 a) D)))) % 3.84/4.00 True % 3.84/4.00 Clause #228 (by clausification #[227]): ∀ (a : Iota), % 3.84/4.00 Eq % 3.84/4.00 (∀ (C D : Iota), % 3.84/4.00 Eq (intersection (skS.0 3 a) (difference C D)) % 3.84/4.00 (difference (intersection (skS.0 3 a) C) (intersection (skS.0 3 a) D))) % 3.84/4.00 False % 3.84/4.00 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), % 3.84/4.00 Eq % 3.84/4.00 (Not % 3.84/4.00 (∀ (D : Iota), % 3.84/4.00 Eq (intersection (skS.0 3 a) (difference (skS.0 4 a a_1) D)) % 3.84/4.00 (difference (intersection (skS.0 3 a) (skS.0 4 a a_1)) (intersection (skS.0 3 a) D)))) % 3.84/4.00 True % 3.84/4.00 Clause #230 (by clausification #[229]): ∀ (a a_1 : Iota), % 3.84/4.00 Eq % 3.84/4.00 (∀ (D : Iota), % 3.84/4.00 Eq (intersection (skS.0 3 a) (difference (skS.0 4 a a_1) D)) % 3.84/4.00 (difference (intersection (skS.0 3 a) (skS.0 4 a a_1)) (intersection (skS.0 3 a) D))) % 3.84/4.00 False % 3.84/4.00 Clause #231 (by clausification #[230]): ∀ (a a_1 a_2 : Iota), % 3.84/4.00 Eq % 3.84/4.00 (Not % 3.84/4.00 (Eq (intersection (skS.0 3 a) (difference (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 3.84/4.00 (difference (intersection (skS.0 3 a) (skS.0 4 a a_1)) (intersection (skS.0 3 a) (skS.0 5 a a_1 a_2))))) % 3.84/4.00 True % 3.84/4.00 Clause #232 (by clausification #[231]): ∀ (a a_1 a_2 : Iota), % 3.84/4.00 Eq % 3.84/4.00 (Eq (intersection (skS.0 3 a) (difference (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 3.84/4.00 (difference (intersection (skS.0 3 a) (skS.0 4 a a_1)) (intersection (skS.0 3 a) (skS.0 5 a a_1 a_2)))) % 3.84/4.00 False % 3.84/4.00 Clause #233 (by clausification #[232]): ∀ (a a_1 a_2 : Iota), % 3.84/4.00 Ne (intersection (skS.0 3 a) (difference (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 3.84/4.00 (difference (intersection (skS.0 3 a) (skS.0 4 a a_1)) (intersection (skS.0 3 a) (skS.0 5 a a_1 a_2))) % 3.84/4.00 Clause #234 (by forward demodulation #[233, 70]): ∀ (a a_1 a_2 : Iota), % 3.84/4.00 Ne (intersection (skS.0 3 a) (difference (skS.0 4 a a_1) (skS.0 5 a a_1 a_2))) % 3.84/4.00 (intersection (skS.0 3 a) (difference (skS.0 4 a a_1) (intersection (skS.0 3 a) (skS.0 5 a a_1 a_2)))) % 3.84/4.00 Clause #263 (by forward demodulation #[47, 70]): ∀ (a a_1 a_2 : Iota), % 3.84/4.00 Eq (intersection a (difference a_1 (intersection a_2 a))) (union (difference (intersection a a_1) a_2) empty_set) % 3.84/4.00 Clause #264 (by forward demodulation #[263, 20]): ∀ (a a_1 a_2 : Iota), Eq (intersection a (difference a_1 (intersection a_2 a))) (difference (intersection a a_1) a_2) % 3.84/4.00 Clause #265 (by forward demodulation #[264, 70]): ∀ (a a_1 a_2 : Iota), Eq (intersection a (difference a_1 (intersection a_2 a))) (intersection a (difference a_1 a_2)) % 3.84/4.00 Clause #288 (by superposition #[265, 174]): ∀ (a a_1 a_2 : Iota), Eq (intersection a (difference a_1 (intersection a a_2))) (intersection a (difference a_1 a_2)) % 3.84/4.00 Clause #292 (by backward contextual literal cutting #[288, 234]): False % 3.84/4.00 SZS output end Proof for theBenchmark.p 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