%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET591+3 : TPTP v9.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 5.57s 5.77s % Output : Proof 5.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET591+3 : TPTP v9.2.0. Released v2.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 14:04:08 EDT 2025 % 0.13/0.34 % CPUTime : % 5.57/5.77 SZS status Theorem for theBenchmark.p % 5.57/5.77 SZS output start Proof for theBenchmark.p % 5.57/5.77 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True % 5.57/5.77 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (difference B C)) (And (member D B) (Not (member D C)))) True % 5.57/5.77 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True % 5.57/5.77 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True % 5.57/5.77 Clause #5 (by assumption #[]): Eq (∀ (B : Iota), Iff (empty B) (∀ (C : Iota), Not (member C B))) True % 5.57/5.77 Clause #6 (by assumption #[]): Eq (Not (∀ (B C : Iota), subset B (difference C B) → Eq B empty_set)) True % 5.57/5.77 Clause #8 (by clausification #[2]): ∀ (a : Iota), Eq (Not (member a empty_set)) True % 5.57/5.77 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (member a empty_set) False % 5.57/5.77 Clause #10 (by clausification #[6]): Eq (∀ (B C : Iota), subset B (difference C B) → Eq B empty_set) False % 5.57/5.77 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), subset (skS.0 0 a) (difference C (skS.0 0 a)) → Eq (skS.0 0 a) empty_set)) True % 5.57/5.77 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (C : Iota), subset (skS.0 0 a) (difference C (skS.0 0 a)) → Eq (skS.0 0 a) empty_set) False % 5.57/5.77 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 0 a)) → Eq (skS.0 0 a) empty_set)) True % 5.57/5.77 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 0 a)) → Eq (skS.0 0 a) empty_set) False % 5.57/5.77 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 0 a))) True % 5.57/5.77 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Eq (skS.0 0 a) empty_set) False % 5.57/5.77 Clause #17 (by clausification #[5]): ∀ (a : Iota), Eq (Iff (empty a) (∀ (C : Iota), Not (member C a))) True % 5.57/5.77 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (∀ (C : Iota), Not (member C a)) False) % 5.57/5.77 Clause #19 (by clausification #[17]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (∀ (C : Iota), Not (member C a)) True) % 5.57/5.77 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (Not (member (skS.0 2 a a_1) a))) True) % 5.57/5.77 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (member (skS.0 2 a a_1) a)) False) % 5.57/5.77 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 2 a a_1) a) True) % 5.57/5.77 Clause #25 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True % 5.57/5.77 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True % 5.57/5.77 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False) % 5.57/5.77 Clause #28 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (D : Iota), member D a → member D a_1) True) % 5.57/5.77 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 5.57/5.77 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 3 a a_1 a_2) a → member (skS.0 3 a a_1 a_2) a_1)) True) % 5.57/5.77 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 5.57/5.77 Or (Eq (subset a a_1) True) (Eq (member (skS.0 3 a a_1 a_2) a → member (skS.0 3 a a_1 a_2) a_1) False) % 5.57/5.77 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 3 a a_1 a_2) a) True) % 5.57/5.77 Clause #33 (by superposition #[31, 9]): ∀ (a : Iota), Or (Eq (subset empty_set a) True) (Eq True False) % 5.57/5.77 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (subset empty_set a) True % 5.57/5.77 Clause #35 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (Not (member a_1 a)) True) % 5.57/5.77 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (member a_1 a) False) % 5.57/5.77 Clause #38 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (member a_2 a → member a_2 a_1) True) % 5.57/5.80 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) True)) % 5.57/5.80 Clause #40 (by superposition #[39, 15]): ∀ (a a_1 a_2 : Iota), % 5.57/5.80 Or (Eq (member a (skS.0 0 a_1)) False) % 5.57/5.80 (Or (Eq (member a (difference (skS.0 1 a_1 a_2) (skS.0 0 a_1))) True) (Eq False True)) % 5.57/5.80 Clause #44 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (difference a C)) (And (member D a) (Not (member D C)))) True % 5.57/5.80 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (difference a a_1)) (And (member D a) (Not (member D a_1)))) True % 5.57/5.80 Clause #46 (by clausification #[45]): ∀ (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 % 5.57/5.80 Clause #48 (by clausification #[46]): ∀ (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) % 5.57/5.80 Clause #54 (by clausification #[16]): ∀ (a : Iota), Ne (skS.0 0 a) empty_set % 5.57/5.80 Clause #55 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (Not (member a a_2)) True) % 5.57/5.80 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (member a a_2) False) % 5.57/5.80 Clause #62 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True % 5.57/5.80 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 5.57/5.80 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 5.57/5.80 Clause #66 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 5.57/5.80 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 5.57/5.80 Clause #69 (by superposition #[67, 34]): ∀ (a : Iota), Or (Eq empty_set a) (Or (Eq (subset a empty_set) False) (Eq False True)) % 5.57/5.80 Clause #73 (by clausification #[69]): ∀ (a : Iota), Or (Eq empty_set a) (Eq (subset a empty_set) False) % 5.57/5.80 Clause #80 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 5.57/5.80 Or (Eq (member a (skS.0 0 a_1)) False) (Eq (member a (difference (skS.0 1 a_1 a_2) (skS.0 0 a_1))) True) % 5.57/5.80 Clause #81 (by superposition #[80, 22]): ∀ (a a_1 a_2 : Iota), % 5.57/5.80 Or (Eq (member (skS.0 2 (skS.0 0 a) a_1) (difference (skS.0 1 a a_2) (skS.0 0 a))) True) % 5.57/5.80 (Or (Eq (empty (skS.0 0 a)) True) (Eq False True)) % 5.57/5.80 Clause #168 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), % 5.57/5.80 Or (Eq (member (skS.0 2 (skS.0 0 a) a_1) (difference (skS.0 1 a a_2) (skS.0 0 a))) True) (Eq (empty (skS.0 0 a)) True) % 5.57/5.80 Clause #169 (by superposition #[168, 57]): ∀ (a a_1 : Iota), % 5.57/5.80 Or (Eq (empty (skS.0 0 a)) True) (Or (Eq True False) (Eq (member (skS.0 2 (skS.0 0 a) a_1) (skS.0 0 a)) False)) % 5.57/5.80 Clause #443 (by clausification #[169]): ∀ (a a_1 : Iota), Or (Eq (empty (skS.0 0 a)) True) (Eq (member (skS.0 2 (skS.0 0 a) a_1) (skS.0 0 a)) False) % 5.57/5.80 Clause #444 (by superposition #[443, 22]): ∀ (a : Iota), Or (Eq (empty (skS.0 0 a)) True) (Or (Eq (empty (skS.0 0 a)) True) (Eq False True)) % 5.57/5.80 Clause #446 (by clausification #[444]): ∀ (a : Iota), Or (Eq (empty (skS.0 0 a)) True) (Eq (empty (skS.0 0 a)) True) % 5.57/5.80 Clause #447 (by eliminate duplicate literals #[446]): ∀ (a : Iota), Eq (empty (skS.0 0 a)) True % 5.57/5.80 Clause #450 (by superposition #[447, 36]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (member a (skS.0 0 a_1)) False) % 5.57/5.80 Clause #451 (by clausification #[450]): ∀ (a a_1 : Iota), Eq (member a (skS.0 0 a_1)) False % 5.57/5.80 Clause #454 (by superposition #[451, 31]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 0 a) a_1) True) (Eq False True) % 5.57/5.80 Clause #462 (by clausification #[454]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) a_1) True % 5.57/5.80 Clause #464 (by superposition #[462, 73]): ∀ (a : Iota), Or (Eq empty_set (skS.0 0 a)) (Eq True False) % 5.57/5.80 Clause #469 (by clausification #[464]): ∀ (a : Iota), Eq empty_set (skS.0 0 a) % 5.57/5.80 Clause #470 (by forward contextual literal cutting #[469, 54]): False % 5.57/5.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------