%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET585+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 5.82s 6.06s % Output : Proof 5.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET585+3 : TPTP v9.2.0. Released v2.2.0. % 0.10/0.11 % Command : duper %s % 0.10/0.31 % Computer : n028.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Thu Oct 2 14:07:38 EDT 2025 % 0.10/0.31 % CPUTime : % 5.82/6.06 SZS status Theorem for theBenchmark.p % 5.82/6.06 SZS output start Proof for theBenchmark.p % 5.82/6.06 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), And (subset B C) (subset C D) → subset B D) True % 5.82/6.06 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), subset B (union B C)) True % 5.82/6.06 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), subset (intersection B C) B) True % 5.82/6.06 Clause #7 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True % 5.82/6.06 Clause #10 (by assumption #[]): Eq (Not (∀ (B C D : Iota), subset (intersection B C) (union B D))) True % 5.82/6.06 Clause #12 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), subset (intersection a C) a) True % 5.82/6.06 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (subset (intersection a a_1) a) True % 5.82/6.06 Clause #14 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), subset a (union a C)) True % 5.82/6.06 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (subset a (union a a_1)) True % 5.82/6.06 Clause #16 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), And (subset a C) (subset C D) → subset a D) True % 5.82/6.06 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), And (subset a a_1) (subset a_1 D) → subset a D) True % 5.82/6.06 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True % 5.82/6.06 Clause #19 (by clausification #[18]): ∀ (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) % 5.82/6.06 Clause #20 (by clausification #[19]): ∀ (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)) % 5.82/6.06 Clause #32 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True % 5.82/6.06 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True % 5.82/6.06 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a) % 5.82/6.06 Clause #35 (by superposition #[34, 13]): ∀ (a a_1 : Iota), Eq (subset (intersection a a_1) a_1) True % 5.82/6.06 Clause #36 (by superposition #[35, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (intersection a a_1) a_2) True) (Or (Eq True False) (Eq (subset a_1 a_2) False)) % 5.82/6.06 Clause #48 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (intersection a a_1) a_2) True) (Eq (subset a_1 a_2) False) % 5.82/6.06 Clause #49 (by superposition #[48, 15]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (intersection a a_1) (union a_1 a_2)) True) (Eq False True) % 5.82/6.06 Clause #89 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Eq (subset (intersection a a_1) (union a_1 a_2)) True % 5.82/6.06 Clause #94 (by superposition #[89, 34]): ∀ (a a_1 a_2 : Iota), Eq (subset (intersection a a_1) (union a a_2)) True % 5.82/6.06 Clause #119 (by clausification #[10]): Eq (∀ (B C D : Iota), subset (intersection B C) (union B D)) False % 5.82/6.06 Clause #120 (by clausification #[119]): ∀ (a : Iota), Eq (Not (∀ (C D : Iota), subset (intersection (skS.0 2 a) C) (union (skS.0 2 a) D))) True % 5.82/6.06 Clause #121 (by clausification #[120]): ∀ (a : Iota), Eq (∀ (C D : Iota), subset (intersection (skS.0 2 a) C) (union (skS.0 2 a) D)) False % 5.82/6.06 Clause #122 (by clausification #[121]): ∀ (a a_1 : Iota), Eq (Not (∀ (D : Iota), subset (intersection (skS.0 2 a) (skS.0 3 a a_1)) (union (skS.0 2 a) D))) True % 5.82/6.06 Clause #123 (by clausification #[122]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), subset (intersection (skS.0 2 a) (skS.0 3 a a_1)) (union (skS.0 2 a) D)) False % 5.82/6.06 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), % 5.82/6.06 Eq (Not (subset (intersection (skS.0 2 a) (skS.0 3 a a_1)) (union (skS.0 2 a) (skS.0 4 a a_1 a_2)))) True % 5.82/6.06 Clause #125 (by clausification #[124]): ∀ (a a_1 a_2 : Iota), % 5.82/6.06 Eq (subset (intersection (skS.0 2 a) (skS.0 3 a a_1)) (union (skS.0 2 a) (skS.0 4 a a_1 a_2))) False % 5.82/6.06 Clause #126 (by superposition #[125, 94]): Eq False True % 5.82/6.06 Clause #127 (by clausification #[126]): False % 5.82/6.06 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------