%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU186+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:01:04 PM UTC 2025 % Result : Theorem 62.86s 63.03s % Output : Proof 62.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU186+1 : TPTP v9.2.0. Released v3.3.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 : Fri Oct 3 06:01:08 EDT 2025 % 0.13/0.34 % CPUTime : % 62.86/63.03 SZS status Theorem for theBenchmark.p % 62.86/63.03 SZS output start Proof for theBenchmark.p % 62.86/63.03 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Iff (relation A) (∀ (B : Iota), Not (And (in B A) (∀ (C D : Iota), Ne B (ordered_pair C D))))) True % 62.86/63.03 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Exists fun B => element B A) True % 62.86/63.03 Clause #17 (by assumption #[]): Eq (∀ (A B : Iota), element A B → Or (empty B) (in A B)) True % 62.86/63.03 Clause #18 (by assumption #[]): Eq (Not (∀ (A : Iota), relation A → (∀ (B C : Iota), Not (in (ordered_pair B C) A)) → Eq A empty_set)) True % 62.86/63.03 Clause #19 (by assumption #[]): Eq (∀ (A : Iota), empty A → Eq A empty_set) True % 62.86/63.03 Clause #35 (by clausification #[19]): ∀ (a : Iota), Eq (empty a → Eq a empty_set) True % 62.86/63.03 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (Eq a empty_set) True) % 62.86/63.03 Clause #37 (by clausification #[36]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq a empty_set) % 62.86/63.03 Clause #52 (by clausification #[6]): ∀ (a : Iota), Eq (Exists fun B => element B a) True % 62.86/63.03 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (element (skS.0 2 a a_1) a) True % 62.86/63.03 Clause #60 (by clausification #[3]): ∀ (a : Iota), Eq (Iff (relation a) (∀ (B : Iota), Not (And (in B a) (∀ (C D : Iota), Ne B (ordered_pair C D))))) True % 62.86/63.03 Clause #62 (by clausification #[60]): ∀ (a : Iota), % 62.86/63.03 Or (Eq (relation a) False) (Eq (∀ (B : Iota), Not (And (in B a) (∀ (C D : Iota), Ne B (ordered_pair C D)))) True) % 62.86/63.03 Clause #73 (by clausification #[18]): Eq (∀ (A : Iota), relation A → (∀ (B C : Iota), Not (in (ordered_pair B C) A)) → Eq A empty_set) False % 62.86/63.03 Clause #74 (by clausification #[73]): ∀ (a : Iota), % 62.86/63.03 Eq (Not (relation (skS.0 5 a) → (∀ (B C : Iota), Not (in (ordered_pair B C) (skS.0 5 a))) → Eq (skS.0 5 a) empty_set)) % 62.86/63.03 True % 62.86/63.03 Clause #75 (by clausification #[74]): ∀ (a : Iota), % 62.86/63.03 Eq (relation (skS.0 5 a) → (∀ (B C : Iota), Not (in (ordered_pair B C) (skS.0 5 a))) → Eq (skS.0 5 a) empty_set) False % 62.86/63.03 Clause #76 (by clausification #[75]): ∀ (a : Iota), Eq (relation (skS.0 5 a)) True % 62.86/63.03 Clause #77 (by clausification #[75]): ∀ (a : Iota), Eq ((∀ (B C : Iota), Not (in (ordered_pair B C) (skS.0 5 a))) → Eq (skS.0 5 a) empty_set) False % 62.86/63.03 Clause #105 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (B : Iota), element a B → Or (empty B) (in a B)) True % 62.86/63.03 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (element a a_1 → Or (empty a_1) (in a a_1)) True % 62.86/63.03 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Eq (Or (empty a_1) (in a a_1)) True) % 62.86/63.03 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (empty a_1) True) (Eq (in a a_1) True)) % 62.86/63.03 Clause #109 (by superposition #[108, 53]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Or (Eq (in (skS.0 2 a a_1) a) True) (Eq False True)) % 62.86/63.03 Clause #110 (by clausification #[77]): ∀ (a : Iota), Eq (∀ (B C : Iota), Not (in (ordered_pair B C) (skS.0 5 a))) True % 62.86/63.03 Clause #111 (by clausification #[77]): ∀ (a : Iota), Eq (Eq (skS.0 5 a) empty_set) False % 62.86/63.03 Clause #112 (by clausification #[110]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Not (in (ordered_pair a C) (skS.0 5 a_1))) True % 62.86/63.03 Clause #113 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (ordered_pair a a_1) (skS.0 5 a_2))) True % 62.86/63.03 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), Eq (in (ordered_pair a a_1) (skS.0 5 a_2)) False % 62.86/63.03 Clause #122 (by clausification #[111]): ∀ (a : Iota), Ne (skS.0 5 a) empty_set % 62.86/63.03 Clause #131 (by clausification #[62]): ∀ (a a_1 : Iota), % 62.86/63.03 Or (Eq (relation a) False) (Eq (Not (And (in a_1 a) (∀ (C D : Iota), Ne a_1 (ordered_pair C D)))) True) % 62.86/63.03 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota), Or (Eq (relation a) False) (Eq (And (in a_1 a) (∀ (C D : Iota), Ne a_1 (ordered_pair C D))) False) % 62.86/63.03 Clause #133 (by clausification #[132]): ∀ (a a_1 : Iota), % 62.86/63.03 Or (Eq (relation a) False) (Or (Eq (in a_1 a) False) (Eq (∀ (C D : Iota), Ne a_1 (ordered_pair C D)) False)) % 62.86/63.03 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 : Iota), % 62.86/63.03 Or (Eq (relation a) False) % 62.93/63.13 (Or (Eq (in a_1 a) False) (Eq (Not (∀ (D : Iota), Ne a_1 (ordered_pair (skS.0 7 a_1 a_2) D))) True)) % 62.93/63.13 Clause #135 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), % 62.93/63.13 Or (Eq (relation a) False) % 62.93/63.13 (Or (Eq (in a_1 a) False) (Eq (∀ (D : Iota), Ne a_1 (ordered_pair (skS.0 7 a_1 a_2) D)) False)) % 62.93/63.13 Clause #136 (by clausification #[135]): ∀ (a a_1 a_2 a_3 : Iota), % 62.93/63.13 Or (Eq (relation a) False) % 62.93/63.13 (Or (Eq (in a_1 a) False) (Eq (Not (Ne a_1 (ordered_pair (skS.0 7 a_1 a_2) (skS.0 8 a_1 a_2 a_3)))) True)) % 62.93/63.13 Clause #137 (by clausification #[136]): ∀ (a a_1 a_2 a_3 : Iota), % 62.93/63.13 Or (Eq (relation a) False) % 62.93/63.13 (Or (Eq (in a_1 a) False) (Eq (Ne a_1 (ordered_pair (skS.0 7 a_1 a_2) (skS.0 8 a_1 a_2 a_3))) False)) % 62.93/63.13 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 a_3 : Iota), % 62.93/63.13 Or (Eq (relation a) False) (Or (Eq (in a_1 a) False) (Eq a_1 (ordered_pair (skS.0 7 a_1 a_2) (skS.0 8 a_1 a_2 a_3)))) % 62.93/63.13 Clause #140 (by superposition #[138, 76]): ∀ (a a_1 a_2 a_3 : Iota), % 62.93/63.13 Or (Eq (in a (skS.0 5 a_1)) False) (Or (Eq a (ordered_pair (skS.0 7 a a_2) (skS.0 8 a a_2 a_3))) (Eq False True)) % 62.93/63.13 Clause #183 (by clausification #[109]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (in (skS.0 2 a a_1) a) True) % 62.93/63.13 Clause #313 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 5 a_1)) False) (Eq a (ordered_pair (skS.0 7 a a_2) (skS.0 8 a a_2 a_3))) % 62.93/63.13 Clause #315 (by superposition #[313, 183]): ∀ (a a_1 a_2 a_3 : Iota), % 62.93/63.13 Or % 62.93/63.13 (Eq (skS.0 2 (skS.0 5 a) a_1) % 62.93/63.13 (ordered_pair (skS.0 7 (skS.0 2 (skS.0 5 a) a_1) a_2) (skS.0 8 (skS.0 2 (skS.0 5 a) a_1) a_2 a_3))) % 62.93/63.13 (Or (Eq (empty (skS.0 5 a)) True) (Eq False True)) % 62.93/63.13 Clause #6408 (by clausification #[315]): ∀ (a a_1 a_2 a_3 : Iota), % 62.93/63.13 Or % 62.93/63.13 (Eq (skS.0 2 (skS.0 5 a) a_1) % 62.93/63.13 (ordered_pair (skS.0 7 (skS.0 2 (skS.0 5 a) a_1) a_2) (skS.0 8 (skS.0 2 (skS.0 5 a) a_1) a_2 a_3))) % 62.93/63.13 (Eq (empty (skS.0 5 a)) True) % 62.93/63.13 Clause #6411 (by superposition #[6408, 114]): ∀ (a a_1 a_2 : Iota), Or (Eq (empty (skS.0 5 a)) True) (Eq (in (skS.0 2 (skS.0 5 a) a_1) (skS.0 5 a_2)) False) % 62.93/63.13 Clause #6513 (by superposition #[6411, 183]): ∀ (a : Iota), Or (Eq (empty (skS.0 5 a)) True) (Or (Eq (empty (skS.0 5 a)) True) (Eq False True)) % 62.93/63.13 Clause #6514 (by clausification #[6513]): ∀ (a : Iota), Or (Eq (empty (skS.0 5 a)) True) (Eq (empty (skS.0 5 a)) True) % 62.93/63.13 Clause #6515 (by eliminate duplicate literals #[6514]): ∀ (a : Iota), Eq (empty (skS.0 5 a)) True % 62.93/63.13 Clause #6520 (by superposition #[6515, 37]): ∀ (a : Iota), Or (Eq True False) (Eq (skS.0 5 a) empty_set) % 62.93/63.13 Clause #6522 (by clausification #[6520]): ∀ (a : Iota), Eq (skS.0 5 a) empty_set % 62.93/63.13 Clause #6523 (by forward contextual literal cutting #[6522, 122]): False % 62.93/63.13 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------