%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET146+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 07:59:43 PM UTC 2025 % Result : Theorem 3.51s 3.71s % Output : Proof 3.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.07 % Problem : SET146+3 : TPTP v9.2.0. Released v2.2.0. % 0.06/0.08 % Command : duper %s % 0.07/0.26 % Computer : n014.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Thu Oct 2 14:37:08 EDT 2025 % 0.07/0.27 % CPUTime : % 3.51/3.71 SZS status Theorem for theBenchmark.p % 3.51/3.71 SZS output start Proof for theBenchmark.p % 3.51/3.71 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (intersection B C)) (And (member D B) (member D C))) True % 3.51/3.71 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True % 3.51/3.71 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True % 3.51/3.71 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Eq (intersection B C) (intersection C B)) True % 3.51/3.71 Clause #4 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 3.51/3.71 Clause #6 (by assumption #[]): Eq (∀ (B : Iota), Iff (empty B) (∀ (C : Iota), Not (member C B))) True % 3.51/3.71 Clause #8 (by assumption #[]): Eq (Not (∀ (B : Iota), Eq (intersection B empty_set) empty_set)) True % 3.51/3.71 Clause #10 (by clausification #[1]): ∀ (a : Iota), Eq (Not (member a empty_set)) True % 3.51/3.71 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (member a empty_set) False % 3.51/3.71 Clause #12 (by clausification #[8]): Eq (∀ (B : Iota), Eq (intersection B empty_set) empty_set) False % 3.51/3.71 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (Not (Eq (intersection (skS.0 0 a) empty_set) empty_set)) True % 3.51/3.71 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (Eq (intersection (skS.0 0 a) empty_set) empty_set) False % 3.51/3.71 Clause #15 (by clausification #[14]): ∀ (a : Iota), Ne (intersection (skS.0 0 a) empty_set) empty_set % 3.51/3.71 Clause #16 (by clausification #[6]): ∀ (a : Iota), Eq (Iff (empty a) (∀ (C : Iota), Not (member C a))) True % 3.51/3.71 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (∀ (C : Iota), Not (member C a)) False) % 3.51/3.71 Clause #18 (by clausification #[16]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (∀ (C : Iota), Not (member C a)) True) % 3.51/3.71 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (Not (member (skS.0 1 a a_1) a))) True) % 3.51/3.71 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (member (skS.0 1 a a_1) a)) False) % 3.51/3.71 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 1 a a_1) a) True) % 3.51/3.71 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 % 3.51/3.71 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 % 3.51/3.71 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 % 3.51/3.71 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) % 3.51/3.71 Clause #31 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (Not (member a_1 a)) True) % 3.51/3.71 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (member a_1 a) False) % 3.51/3.71 Clause #34 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (intersection a C) (intersection C a)) True % 3.51/3.71 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Eq (intersection a a_1) (intersection a_1 a)) True % 3.51/3.71 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (intersection a a_1) (intersection a_1 a) % 3.51/3.71 Clause #37 (by superposition #[36, 15]): ∀ (a : Iota), Ne (intersection empty_set (skS.0 0 a)) empty_set % 3.51/3.71 Clause #38 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 3.51/3.71 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 3.51/3.71 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False) % 3.51/3.71 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.51/3.71 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) % 3.51/3.71 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 3.51/3.71 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) % 3.51/3.73 Clause #44 (by clausification #[43]): ∀ (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) % 3.51/3.73 Clause #46 (by superposition #[44, 11]): ∀ (a : Iota), Or (Eq (subset empty_set a) True) (Eq True False) % 3.51/3.73 Clause #48 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True % 3.51/3.73 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 3.51/3.73 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 3.51/3.73 Clause #52 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 3.51/3.73 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 3.51/3.73 Clause #55 (by clausification #[46]): ∀ (a : Iota), Eq (subset empty_set a) True % 3.51/3.73 Clause #56 (by superposition #[55, 53]): ∀ (a : Iota), Or (Eq empty_set a) (Or (Eq True False) (Eq (subset a empty_set) False)) % 3.51/3.73 Clause #58 (by clausification #[56]): ∀ (a : Iota), Or (Eq empty_set a) (Eq (subset a empty_set) False) % 3.51/3.73 Clause #79 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (intersection a_1 a_2)) False) (Eq (member a a_2) True) % 3.51/3.73 Clause #81 (by superposition #[79, 21]): ∀ (a a_1 a_2 : Iota), % 3.51/3.73 Or (Eq (member (skS.0 1 (intersection a a_1) a_2) a_1) True) % 3.51/3.73 (Or (Eq (empty (intersection a a_1)) True) (Eq False True)) % 3.51/3.73 Clause #96 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), % 3.51/3.73 Or (Eq (member (skS.0 1 (intersection a a_1) a_2) a_1) True) (Eq (empty (intersection a a_1)) True) % 3.51/3.73 Clause #97 (by superposition #[96, 11]): ∀ (a : Iota), Or (Eq (empty (intersection a empty_set)) True) (Eq True False) % 3.51/3.73 Clause #103 (by clausification #[97]): ∀ (a : Iota), Eq (empty (intersection a empty_set)) True % 3.51/3.73 Clause #104 (by superposition #[103, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (member a (intersection a_1 empty_set)) False) % 3.51/3.73 Clause #107 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (member a (intersection a_1 empty_set)) False % 3.51/3.73 Clause #109 (by superposition #[107, 44]): ∀ (a a_1 : Iota), Or (Eq (subset (intersection a empty_set) a_1) True) (Eq False True) % 3.51/3.73 Clause #191 (by clausification #[109]): ∀ (a a_1 : Iota), Eq (subset (intersection a empty_set) a_1) True % 3.51/3.73 Clause #195 (by superposition #[191, 36]): ∀ (a a_1 : Iota), Eq (subset (intersection empty_set a) a_1) True % 3.51/3.73 Clause #200 (by superposition #[195, 58]): ∀ (a : Iota), Or (Eq empty_set (intersection empty_set a)) (Eq True False) % 3.51/3.73 Clause #221 (by clausification #[200]): ∀ (a : Iota), Eq empty_set (intersection empty_set a) % 3.51/3.73 Clause #223 (by backward contextual literal cutting #[221, 37]): False % 3.51/3.73 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------