%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET008+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 07:59:20 PM UTC 2025 % Result : Theorem 4.78s 4.94s % Output : Proof 4.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET008+3 : TPTP v9.2.0. Released v2.2.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n019.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 13:44:38 EDT 2025 % 0.12/0.34 % CPUTime : % 4.78/4.94 SZS status Theorem for theBenchmark.p % 4.78/4.94 SZS output start Proof for theBenchmark.p % 4.78/4.94 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (intersection B C)) (And (member D B) (member D C))) True % 4.78/4.94 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (difference B C)) (And (member D B) (Not (member D C)))) True % 4.78/4.94 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True % 4.78/4.94 Clause #4 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True % 4.78/4.94 Clause #7 (by assumption #[]): Eq (∀ (B : Iota), Iff (empty B) (∀ (C : Iota), Not (member C B))) True % 4.78/4.94 Clause #8 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (∀ (D : Iota), Iff (member D B) (member D C))) True % 4.78/4.94 Clause #9 (by assumption #[]): Eq (Not (∀ (B C : Iota), Eq (intersection (difference B C) C) empty_set)) True % 4.78/4.94 Clause #11 (by clausification #[2]): ∀ (a : Iota), Eq (Not (member a empty_set)) True % 4.78/4.94 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (member a empty_set) False % 4.78/4.94 Clause #13 (by clausification #[7]): ∀ (a : Iota), Eq (Iff (empty a) (∀ (C : Iota), Not (member C a))) True % 4.78/4.94 Clause #14 (by clausification #[13]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (∀ (C : Iota), Not (member C a)) False) % 4.78/4.94 Clause #15 (by clausification #[13]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (∀ (C : Iota), Not (member C a)) True) % 4.78/4.94 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (Not (member (skS.0 0 a a_1) a))) True) % 4.78/4.94 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (member (skS.0 0 a a_1) a)) False) % 4.78/4.94 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 0 a a_1) a) True) % 4.78/4.94 Clause #21 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (Not (member a_1 a)) True) % 4.78/4.94 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (member a_1 a) False) % 4.78/4.94 Clause #24 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (intersection a C)) (And (member D a) (member D C))) True % 4.78/4.94 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (intersection a a_1)) (And (member D a) (member D a_1))) True % 4.78/4.94 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (intersection a_1 a_2)) (And (member a a_1) (member a a_2))) True % 4.78/4.94 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) False) (Eq (And (member a a_1) (member a a_2)) True) % 4.78/4.94 Clause #31 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True % 4.78/4.94 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True % 4.78/4.94 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a) % 4.78/4.94 Clause #34 (by clausification #[9]): Eq (∀ (B C : Iota), Eq (intersection (difference B C) C) empty_set) False % 4.78/4.94 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), Eq (intersection (difference (skS.0 1 a) C) C) empty_set)) True % 4.78/4.94 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection (difference (skS.0 1 a) C) C) empty_set) False % 4.78/4.94 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Not (Eq (intersection (difference (skS.0 1 a) (skS.0 2 a a_1)) (skS.0 2 a a_1)) empty_set)) True % 4.78/4.94 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Eq (intersection (difference (skS.0 1 a) (skS.0 2 a a_1)) (skS.0 2 a a_1)) empty_set) False % 4.78/4.94 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Ne (intersection (difference (skS.0 1 a) (skS.0 2 a a_1)) (skS.0 2 a a_1)) empty_set % 4.78/4.94 Clause #40 (by forward demodulation #[39, 33]): ∀ (a a_1 : Iota), Ne (intersection (skS.0 2 a a_1) (difference (skS.0 1 a) (skS.0 2 a a_1))) empty_set % 4.78/4.94 Clause #52 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (difference a C)) (And (member D a) (Not (member D C)))) True % 4.78/4.94 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (difference a a_1)) (And (member D a) (Not (member D a_1)))) True % 4.78/4.96 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (difference a_1 a_2)) (And (member a a_1) (Not (member a a_2)))) True % 4.78/4.96 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (And (member a a_1) (Not (member a a_2))) True) % 4.78/4.96 Clause #68 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) False) (Eq (member a a_1) True) % 4.78/4.96 Clause #71 (by superposition #[68, 18]): ∀ (a a_1 a_2 : Iota), % 4.78/4.96 Or (Eq (member (skS.0 0 (intersection a a_1) a_2) a) True) (Or (Eq (empty (intersection a a_1)) True) (Eq False True)) % 4.78/4.96 Clause #88 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (∀ (D : Iota), Iff (member D a) (member D C))) True % 4.78/4.96 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (∀ (D : Iota), Iff (member D a) (member D a_1))) True % 4.78/4.96 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (∀ (D : Iota), Iff (member D a) (member D a_1)) False) % 4.78/4.96 Clause #92 (by clausification #[90]): ∀ (a a_1 : Iota), Or (Eq (∀ (D : Iota), Iff (member D a) (member D a_1)) False) (Eq a a_1) % 4.78/4.96 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), % 4.78/4.96 Or (Eq a a_1) (Eq (Not (Iff (member (skS.0 4 a a_1 a_2) a) (member (skS.0 4 a a_1 a_2) a_1))) True) % 4.78/4.96 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 : Iota), Or (Eq a a_1) (Eq (Iff (member (skS.0 4 a a_1 a_2) a) (member (skS.0 4 a a_1 a_2) a_1)) False) % 4.78/4.96 Clause #96 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), % 4.78/4.96 Or (Eq a a_1) (Or (Eq (member (skS.0 4 a a_1 a_2) a) True) (Eq (member (skS.0 4 a a_1 a_2) a_1) True)) % 4.78/4.96 Clause #102 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (Not (member a a_2)) True) % 4.78/4.96 Clause #104 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (member a a_2) False) % 4.78/4.96 Clause #113 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Or (Eq (member (skS.0 0 (intersection a a_1) a_2) a) True) (Eq (empty (intersection a a_1)) True) % 4.78/4.96 Clause #117 (by superposition #[113, 104]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (empty (intersection (difference a a_1) a_2)) True) % 4.78/4.96 (Or (Eq True False) (Eq (member (skS.0 0 (intersection (difference a a_1) a_2) a_3) a_1) False)) % 4.78/4.96 Clause #122 (by superposition #[113, 33]): ∀ (a a_1 a_2 : Iota), % 4.78/4.96 Or (Eq (member (skS.0 0 (intersection a a_1) a_2) a_1) True) (Eq (empty (intersection a a_1)) True) % 4.78/4.96 Clause #299 (by superposition #[96, 12]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Or (Eq (member (skS.0 4 a empty_set a_1) a) True) (Eq True False)) % 4.78/4.96 Clause #319 (by clausification #[299]): ∀ (a a_1 : Iota), Or (Eq a empty_set) (Eq (member (skS.0 4 a empty_set a_1) a) True) % 4.78/4.96 Clause #552 (by clausification #[117]): ∀ (a a_1 a_2 a_3 : Iota), % 4.78/4.96 Or (Eq (empty (intersection (difference a a_1) a_2)) True) % 4.78/4.96 (Eq (member (skS.0 0 (intersection (difference a a_1) a_2) a_3) a_1) False) % 4.78/4.96 Clause #553 (by superposition #[552, 122]): ∀ (a a_1 : Iota), % 4.78/4.96 Or (Eq (empty (intersection (difference a a_1) a_1)) True) % 4.78/4.96 (Or (Eq False True) (Eq (empty (intersection (difference a a_1) a_1)) True)) % 4.78/4.96 Clause #623 (by clausification #[553]): ∀ (a a_1 : Iota), % 4.78/4.96 Or (Eq (empty (intersection (difference a a_1) a_1)) True) (Eq (empty (intersection (difference a a_1) a_1)) True) % 4.78/4.96 Clause #624 (by eliminate duplicate literals #[623]): ∀ (a a_1 : Iota), Eq (empty (intersection (difference a a_1) a_1)) True % 4.78/4.96 Clause #625 (by forward demodulation #[624, 33]): ∀ (a a_1 : Iota), Eq (empty (intersection a (difference a_1 a))) True % 4.78/4.96 Clause #626 (by superposition #[625, 22]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (member a (intersection a_1 (difference a_2 a_1))) False) % 4.78/4.96 Clause #649 (by clausification #[626]): ∀ (a a_1 a_2 : Iota), Eq (member a (intersection a_1 (difference a_2 a_1))) False % 4.78/4.96 Clause #658 (by superposition #[649, 319]): ∀ (a a_1 : Iota), Or (Eq (intersection a (difference a_1 a)) empty_set) (Eq False True) % 4.78/4.96 Clause #670 (by clausification #[658]): ∀ (a a_1 : Iota), Eq (intersection a (difference a_1 a)) empty_set % 4.78/4.96 Clause #672 (by backward contextual literal cutting #[670, 40]): False % 4.78/4.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------