%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET590+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:00:12 PM UTC 2025 % Result : Theorem 3.81s 3.98s % Output : Proof 3.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET590+3 : TPTP v9.2.0. Released v2.2.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n001.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 13:43:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.81/3.98 SZS status Theorem for theBenchmark.p % 3.81/3.98 SZS output start Proof for theBenchmark.p % 3.81/3.98 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (difference B C)) (And (member D B) (Not (member D C)))) True % 3.81/3.98 Clause #1 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 3.81/3.98 Clause #3 (by assumption #[]): Eq (Not (∀ (B C : Iota), subset (difference B C) B)) True % 3.81/3.98 Clause #5 (by clausification #[3]): Eq (∀ (B C : Iota), subset (difference B C) B) False % 3.81/3.98 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), subset (difference (skS.0 0 a) C) (skS.0 0 a))) True % 3.81/3.98 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (C : Iota), subset (difference (skS.0 0 a) C) (skS.0 0 a)) False % 3.81/3.98 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (Not (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a))) True % 3.81/3.98 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (subset (difference (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 0 a)) False % 3.81/3.98 Clause #10 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 3.81/3.98 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 3.81/3.98 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False) % 3.81/3.98 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 3.81/3.98 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 2 a a_1 a_2) a → member (skS.0 2 a a_1 a_2) a_1)) True) % 3.81/3.98 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 3.81/3.98 Or (Eq (subset a a_1) True) (Eq (member (skS.0 2 a a_1 a_2) a → member (skS.0 2 a a_1 a_2) a_1) False) % 3.81/3.98 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 2 a a_1 a_2) a) True) % 3.81/3.98 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 2 a a_1 a_2) a_1) False) % 3.81/3.98 Clause #22 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (difference a C)) (And (member D a) (Not (member D C)))) True % 3.81/3.98 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (difference a a_1)) (And (member D a) (Not (member D a_1)))) True % 3.81/3.98 Clause #24 (by clausification #[23]): ∀ (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 % 3.81/3.98 Clause #26 (by clausification #[24]): ∀ (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) % 3.81/3.98 Clause #31 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (member a a_1) True) % 3.81/3.98 Clause #34 (by superposition #[31, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 3.81/3.98 Or (Eq (member (skS.0 2 (difference a a_1) a_2 a_3) a) True) % 3.81/3.98 (Or (Eq (subset (difference a a_1) a_2) True) (Eq False True)) % 3.81/3.98 Clause #43 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), % 3.81/3.98 Or (Eq (member (skS.0 2 (difference a a_1) a_2 a_3) a) True) (Eq (subset (difference a a_1) a_2) True) % 3.81/3.98 Clause #46 (by superposition #[43, 17]): ∀ (a a_1 : Iota), % 3.81/3.98 Or (Eq (subset (difference a a_1) a) True) (Or (Eq (subset (difference a a_1) a) True) (Eq True False)) % 3.81/3.98 Clause #56 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (subset (difference a a_1) a) True) (Eq (subset (difference a a_1) a) True) % 3.81/3.98 Clause #57 (by eliminate duplicate literals #[56]): ∀ (a a_1 : Iota), Eq (subset (difference a a_1) a) True % 3.81/3.98 Clause #58 (by superposition #[57, 9]): Eq True False % 3.81/3.98 Clause #60 (by clausification #[58]): False % 3.81/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------