%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET622+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:00:16 PM UTC 2025 % Result : Theorem 4.53s 4.68s % Output : Proof 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET622+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n022.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 : Thu Oct 2 14:17:23 EDT 2025 % 0.14/0.35 % CPUTime : % 4.53/4.68 SZS status Theorem for theBenchmark.p % 4.53/4.68 SZS output start Proof for theBenchmark.p % 4.53/4.68 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Eq (intersection (intersection B C) D) (intersection B (intersection C D))) True % 4.53/4.68 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Eq (difference B (difference C D)) (union (difference B C) (intersection B D))) True % 4.53/4.68 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (difference (union B C) (intersection B C))) True % 4.53/4.68 Clause #8 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True % 4.53/4.68 Clause #14 (by assumption #[]): Eq % 4.53/4.68 (Not % 4.53/4.68 (∀ (B C D : Iota), % 4.53/4.68 Eq (difference B (symmetric_difference C D)) % 4.53/4.68 (union (difference B (union C D)) (intersection (intersection B C) D)))) % 4.53/4.68 True % 4.53/4.68 Clause #22 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True % 4.53/4.68 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True % 4.53/4.68 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a) % 4.53/4.68 Clause #33 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Eq (intersection (intersection a C) D) (intersection a (intersection C D))) True % 4.53/4.68 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Eq (intersection (intersection a a_1) D) (intersection a (intersection a_1 D))) True % 4.53/4.68 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (Eq (intersection (intersection a a_1) a_2) (intersection a (intersection a_1 a_2))) True % 4.53/4.68 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Eq (intersection (intersection a a_1) a_2) (intersection a (intersection a_1 a_2)) % 4.53/4.68 Clause #84 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Eq (difference a (difference C D)) (union (difference a C) (intersection a D))) True % 4.53/4.68 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), % 4.53/4.68 Eq (∀ (D : Iota), Eq (difference a (difference a_1 D)) (union (difference a a_1) (intersection a D))) True % 4.53/4.68 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), Eq (Eq (difference a (difference a_1 a_2)) (union (difference a a_1) (intersection a a_2))) True % 4.53/4.68 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), Eq (difference a (difference a_1 a_2)) (union (difference a a_1) (intersection a a_2)) % 4.53/4.68 Clause #89 (by superposition #[87, 24]): ∀ (a a_1 a_2 : Iota), Eq (union (intersection a a_1) (difference a a_2)) (difference a (difference a_2 a_1)) % 4.53/4.68 Clause #125 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (difference (union a C) (intersection a C))) True % 4.53/4.68 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (difference (union a a_1) (intersection a a_1))) True % 4.53/4.68 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (difference (union a a_1) (intersection a a_1)) % 4.53/4.68 Clause #718 (by clausification #[14]): Eq % 4.53/4.68 (∀ (B C D : Iota), % 4.53/4.68 Eq (difference B (symmetric_difference C D)) (union (difference B (union C D)) (intersection (intersection B C) D))) % 4.53/4.68 False % 4.53/4.68 Clause #719 (by clausification #[718]): ∀ (a : Iota), % 4.53/4.68 Eq % 4.53/4.68 (Not % 4.53/4.68 (∀ (C D : Iota), % 4.53/4.68 Eq (difference (skS.0 2 a) (symmetric_difference C D)) % 4.53/4.68 (union (difference (skS.0 2 a) (union C D)) (intersection (intersection (skS.0 2 a) C) D)))) % 4.53/4.68 True % 4.53/4.68 Clause #720 (by clausification #[719]): ∀ (a : Iota), % 4.53/4.68 Eq % 4.53/4.68 (∀ (C D : Iota), % 4.53/4.68 Eq (difference (skS.0 2 a) (symmetric_difference C D)) % 4.53/4.68 (union (difference (skS.0 2 a) (union C D)) (intersection (intersection (skS.0 2 a) C) D))) % 4.53/4.68 False % 4.53/4.68 Clause #721 (by clausification #[720]): ∀ (a a_1 : Iota), % 4.53/4.68 Eq % 4.53/4.68 (Not % 4.53/4.68 (∀ (D : Iota), % 4.53/4.68 Eq (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) D)) % 4.53/4.68 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) D)) % 4.53/4.68 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) D)))) % 4.53/4.68 True % 4.53/4.68 Clause #722 (by clausification #[721]): ∀ (a a_1 : Iota), % 4.53/4.68 Eq % 4.53/4.68 (∀ (D : Iota), % 4.53/4.68 Eq (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) D)) % 4.54/4.70 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) D)) % 4.54/4.70 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) D))) % 4.54/4.70 False % 4.54/4.70 Clause #723 (by clausification #[722]): ∀ (a a_1 a_2 : Iota), % 4.54/4.70 Eq % 4.54/4.70 (Not % 4.54/4.70 (Eq (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))))) % 4.54/4.70 True % 4.54/4.70 Clause #724 (by clausification #[723]): ∀ (a a_1 a_2 : Iota), % 4.54/4.70 Eq % 4.54/4.70 (Eq (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)))) % 4.54/4.70 False % 4.54/4.70 Clause #725 (by clausification #[724]): ∀ (a a_1 a_2 : Iota), % 4.54/4.70 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (union (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2))) % 4.54/4.70 Clause #726 (by forward demodulation #[725, 24]): ∀ (a a_1 a_2 : Iota), % 4.54/4.70 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (union (intersection (intersection (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) % 4.54/4.70 (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))) % 4.54/4.70 Clause #727 (by forward demodulation #[726, 36]): ∀ (a a_1 a_2 : Iota), % 4.54/4.70 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (union (intersection (skS.0 2 a) (intersection (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (difference (skS.0 2 a) (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))) % 4.54/4.70 Clause #728 (by forward demodulation #[727, 89]): ∀ (a a_1 a_2 : Iota), % 4.54/4.70 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (difference (skS.0 2 a) % 4.54/4.70 (difference (union (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (intersection (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))) % 4.54/4.70 Clause #729 (by forward demodulation #[728, 127]): ∀ (a a_1 a_2 : Iota), % 4.54/4.70 Ne (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 (difference (skS.0 2 a) (symmetric_difference (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 4.54/4.70 Clause #730 (by eliminate resolved literals #[729]): False % 4.54/4.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------