%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET630+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:00:18 PM UTC 2025 % Result : Theorem 5.85s 6.06s % Output : Proof 5.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET630+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n011.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 13:49:53 EDT 2025 % 0.12/0.34 % CPUTime : % 5.85/6.06 SZS status Theorem for theBenchmark.p % 5.85/6.06 SZS output start Proof for theBenchmark.p % 5.85/6.06 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Eq (symmetric_difference B C) (union (difference B C) (difference C B))) True % 5.85/6.06 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (intersect B (union C D)) (Or (intersect B C) (intersect B D))) True % 5.85/6.06 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), disjoint (intersection B C) (difference B C)) True % 5.85/6.06 Clause #5 (by assumption #[]): Eq (∀ (B C : Iota), Iff (disjoint B C) (Not (intersect B C))) True % 5.85/6.06 Clause #6 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True % 5.85/6.06 Clause #7 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True % 5.85/6.06 Clause #11 (by assumption #[]): Eq (Not (∀ (B C : Iota), disjoint (intersection B C) (symmetric_difference B C))) True % 5.85/6.06 Clause #15 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), disjoint (intersection a C) (difference a C)) True % 5.85/6.06 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (disjoint (intersection a a_1) (difference a a_1)) True % 5.85/6.06 Clause #20 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True % 5.85/6.06 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True % 5.85/6.06 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a) % 5.85/6.06 Clause #23 (by superposition #[22, 16]): ∀ (a a_1 : Iota), Eq (disjoint (intersection a a_1) (difference a_1 a)) True % 5.85/6.06 Clause #24 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (symmetric_difference a C) (union (difference a C) (difference C a))) True % 5.85/6.06 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a))) True % 5.85/6.06 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (union (difference a a_1) (difference a_1 a)) % 5.85/6.06 Clause #27 (by clausification #[11]): Eq (∀ (B C : Iota), disjoint (intersection B C) (symmetric_difference B C)) False % 5.85/6.06 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), disjoint (intersection (skS.0 0 a) C) (symmetric_difference (skS.0 0 a) C))) True % 5.85/6.06 Clause #29 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (C : Iota), disjoint (intersection (skS.0 0 a) C) (symmetric_difference (skS.0 0 a) C)) False % 5.85/6.06 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 5.85/6.06 Eq (Not (disjoint (intersection (skS.0 0 a) (skS.0 1 a a_1)) (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1)))) True % 5.85/6.06 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 5.85/6.06 Eq (disjoint (intersection (skS.0 0 a) (skS.0 1 a a_1)) (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1))) False % 5.85/6.06 Clause #32 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (disjoint a C) (Not (intersect a C))) True % 5.85/6.06 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Iff (disjoint a a_1) (Not (intersect a a_1))) True % 5.85/6.06 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (Not (intersect a a_1)) False) % 5.85/6.06 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (Not (intersect a a_1)) True) % 5.85/6.06 Clause #36 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) True) (Eq (intersect a a_1) True) % 5.85/6.06 Clause #37 (by superposition #[36, 31]): ∀ (a a_1 : Iota), % 5.85/6.06 Or (Eq (intersect (intersection (skS.0 0 a) (skS.0 1 a a_1)) (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1))) True) % 5.85/6.06 (Eq True False) % 5.85/6.06 Clause #38 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (disjoint a a_1) False) (Eq (intersect a a_1) False) % 5.85/6.06 Clause #40 (by superposition #[38, 23]): ∀ (a a_1 : Iota), Or (Eq (intersect (intersection a a_1) (difference a_1 a)) False) (Eq False True) % 5.85/6.06 Clause #43 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (intersect (intersection a a_1) (difference a_1 a)) False % 5.85/6.06 Clause #44 (by superposition #[43, 22]): ∀ (a a_1 : Iota), Eq (intersect (intersection a a_1) (difference a a_1)) False % 5.85/6.06 Clause #45 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (intersect a (union C D)) (Or (intersect a C) (intersect a D))) True % 5.90/6.08 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (intersect a (union a_1 D)) (Or (intersect a a_1) (intersect a D))) True % 5.90/6.08 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Eq (Iff (intersect a (union a_1 a_2)) (Or (intersect a a_1) (intersect a a_2))) True % 5.90/6.08 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (intersect a (union a_1 a_2)) False) (Eq (Or (intersect a a_1) (intersect a a_2)) True) % 5.90/6.08 Clause #52 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True % 5.90/6.08 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True % 5.90/6.08 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a) % 5.90/6.08 Clause #55 (by superposition #[54, 26]): ∀ (a a_1 : Iota), Eq (symmetric_difference a a_1) (union (difference a_1 a) (difference a a_1)) % 5.90/6.08 Clause #63 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 5.90/6.08 Or (Eq (intersect a (union a_1 a_2)) False) (Or (Eq (intersect a a_1) True) (Eq (intersect a a_2) True)) % 5.90/6.08 Clause #65 (by superposition #[63, 55]): ∀ (a a_1 a_2 : Iota), % 5.90/6.08 Or (Eq (intersect a (symmetric_difference a_1 a_2)) False) % 5.90/6.08 (Or (Eq (intersect a (difference a_2 a_1)) True) (Eq (intersect a (difference a_1 a_2)) True)) % 5.90/6.08 Clause #93 (by clausification #[37]): ∀ (a a_1 : Iota), % 5.90/6.08 Eq (intersect (intersection (skS.0 0 a) (skS.0 1 a a_1)) (symmetric_difference (skS.0 0 a) (skS.0 1 a a_1))) True % 5.90/6.08 Clause #99 (by superposition #[65, 93]): ∀ (a a_1 : Iota), % 5.90/6.08 Or (Eq True False) % 5.90/6.08 (Or (Eq (intersect (intersection (skS.0 0 a) (skS.0 1 a a_1)) (difference (skS.0 1 a a_1) (skS.0 0 a))) True) % 5.90/6.08 (Eq (intersect (intersection (skS.0 0 a) (skS.0 1 a a_1)) (difference (skS.0 0 a) (skS.0 1 a a_1))) True)) % 5.90/6.08 Clause #1139 (by clausification #[99]): ∀ (a a_1 : Iota), % 5.90/6.08 Or (Eq (intersect (intersection (skS.0 0 a) (skS.0 1 a a_1)) (difference (skS.0 1 a a_1) (skS.0 0 a))) True) % 5.90/6.08 (Eq (intersect (intersection (skS.0 0 a) (skS.0 1 a a_1)) (difference (skS.0 0 a) (skS.0 1 a a_1))) True) % 5.90/6.08 Clause #1140 (by forward demodulation #[1139, 44]): ∀ (a a_1 : Iota), % 5.90/6.08 Or (Eq (intersect (intersection (skS.0 0 a) (skS.0 1 a a_1)) (difference (skS.0 1 a a_1) (skS.0 0 a))) True) % 5.90/6.08 (Eq False True) % 5.90/6.08 Clause #1141 (by clausification #[1140]): ∀ (a a_1 : Iota), % 5.90/6.08 Eq (intersect (intersection (skS.0 0 a) (skS.0 1 a a_1)) (difference (skS.0 1 a a_1) (skS.0 0 a))) True % 5.90/6.08 Clause #1142 (by superposition #[1141, 43]): Eq True False % 5.90/6.08 Clause #1188 (by clausification #[1142]): False % 5.90/6.08 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------