%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU146+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:00:57 PM UTC 2025 % Result : Theorem 8.15s 8.36s % Output : Proof 8.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU146+1 : TPTP v9.2.0. Released v3.3.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 04:59:23 EDT 2025 % 0.14/0.34 % CPUTime : % 8.15/8.36 SZS status Theorem for theBenchmark.p % 8.15/8.36 SZS output start Proof for theBenchmark.p % 8.15/8.36 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq A B) (And (subset A B) (subset B A))) True % 8.15/8.36 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B)) True % 8.15/8.36 Clause #5 (by assumption #[]): Eq (∀ (A B C : Iota), subset A B → Or (in C A) (subset A (set_difference B (singleton C)))) True % 8.15/8.36 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B))))) True % 8.15/8.36 Clause #9 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 8.15/8.36 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), subset empty_set A) True % 8.15/8.36 Clause #11 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A B) empty_set) (subset A B)) True % 8.15/8.36 Clause #13 (by clausification #[10]): ∀ (a : Iota), Eq (subset empty_set a) True % 8.15/8.36 Clause #16 (by clausification #[9]): ∀ (a : Iota), Eq (Iota → subset a a) True % 8.15/8.36 Clause #17 (by clausification #[16]): ∀ (a : Iota), Iota → Eq (subset a a) True % 8.15/8.36 Clause #29 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset (singleton a) B) (in a B)) True % 8.15/8.36 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (Iff (subset (singleton a) a_1) (in a a_1)) True % 8.15/8.36 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False) % 8.15/8.36 Clause #34 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq a B) (And (subset a B) (subset B a))) True % 8.15/8.36 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True % 8.15/8.36 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False) % 8.15/8.36 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1) % 8.15/8.36 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False)) % 8.15/8.36 Clause #49 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset a B → Or (in C a) (subset a (set_difference B (singleton C)))) True % 8.15/8.36 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), subset a a_1 → Or (in C a) (subset a (set_difference a_1 (singleton C)))) True % 8.15/8.36 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → Or (in a_2 a) (subset a (set_difference a_1 (singleton a_2)))) True % 8.15/8.36 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 8.15/8.36 Or (Eq (subset a a_1) False) (Eq (Or (in a_2 a) (subset a (set_difference a_1 (singleton a_2)))) True) % 8.15/8.36 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 8.15/8.36 Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) True) (Eq (subset a (set_difference a_1 (singleton a_2))) True)) % 8.15/8.36 Clause #55 (by superposition #[53, 17]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Or (Eq (subset a_1 (set_difference a_1 (singleton a))) True) (Eq False True)) % 8.15/8.36 Clause #56 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a B) empty_set) (subset a B)) True % 8.15/8.36 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a a_1) empty_set) (subset a a_1)) True % 8.15/8.36 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) True) (Eq (subset a a_1) False) % 8.15/8.36 Clause #60 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_difference a a_1) empty_set) % 8.15/8.36 Clause #69 (by clausification #[6]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) False % 8.15/8.36 Clause #70 (by clausification #[69]): ∀ (a : Iota), % 8.15/8.36 Eq % 8.15/8.36 (Not % 8.15/8.36 (∀ (B : Iota), % 8.15/8.36 Iff (subset (skS.0 2 a) (singleton B)) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton B))))) % 8.15/8.36 True % 8.15/8.36 Clause #71 (by clausification #[70]): ∀ (a : Iota), % 8.15/8.36 Eq % 8.15/8.36 (∀ (B : Iota), % 8.15/8.36 Iff (subset (skS.0 2 a) (singleton B)) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton B)))) % 8.15/8.36 False % 8.15/8.36 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), % 8.22/8.39 Eq % 8.22/8.39 (Not % 8.22/8.39 (Iff (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.39 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))))) % 8.22/8.39 True % 8.22/8.39 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), % 8.22/8.39 Eq % 8.22/8.39 (Iff (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.39 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))) % 8.22/8.39 False % 8.22/8.39 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) % 8.22/8.39 (Eq (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) False) % 8.22/8.39 Clause #75 (by clausification #[73]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 8.22/8.39 (Eq (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) True) % 8.22/8.39 Clause #76 (by clausification #[74]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) % 8.22/8.39 Clause #77 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) (Eq (Eq (skS.0 2 a) empty_set) False) % 8.22/8.39 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) (Ne (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.39 Clause #79 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Eq (subset a_1 (set_difference a_1 (singleton a))) True) % 8.22/8.39 Clause #81 (by superposition #[79, 39]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (in a a_1) True) % 8.22/8.39 (Or (Eq a_1 (set_difference a_1 (singleton a))) % 8.22/8.39 (Or (Eq True False) (Eq (subset (set_difference a_1 (singleton a)) a_1) False))) % 8.22/8.39 Clause #95 (by clausification #[75]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 8.22/8.39 (Or (Eq (Eq (skS.0 2 a) empty_set) True) (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) True)) % 8.22/8.39 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 8.22/8.39 (Or (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Eq (skS.0 2 a) empty_set)) % 8.22/8.39 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 8.22/8.39 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) % 8.22/8.39 Clause #99 (by superposition #[97, 39]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.39 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.39 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.39 (Or (Eq True False) (Eq (subset (singleton (skS.0 3 a a_1)) (skS.0 2 a)) False)))) % 8.22/8.39 Clause #101 (by superposition #[97, 60]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.39 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.39 (Or (Eq True False) (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set))) % 8.22/8.39 Clause #109 (by clausification #[77]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) (Ne (skS.0 2 a) empty_set) % 8.22/8.39 Clause #111 (by clausification #[81]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (in a a_1) True) % 8.22/8.39 (Or (Eq a_1 (set_difference a_1 (singleton a))) (Eq (subset (set_difference a_1 (singleton a)) a_1) False)) % 8.22/8.39 Clause #136 (by clausification #[99]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.39 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.39 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) (Eq (subset (singleton (skS.0 3 a a_1)) (skS.0 2 a)) False))) % 8.22/8.39 Clause #137 (by eliminate duplicate literals #[136]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.39 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) (Eq (subset (singleton (skS.0 3 a a_1)) (skS.0 2 a)) False)) % 8.22/8.39 Clause #168 (by clausification #[101]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.39 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.39 (Eq (set_difference (skS.0 2 a) (singleton (skS.0 3 a a_1))) empty_set)) % 8.22/8.39 Clause #170 (by superposition #[168, 111]): ∀ (a a_1 : Iota), % 8.22/8.39 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.39 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.41 (Or (Eq (in (skS.0 3 a a_1) (skS.0 2 a)) True) % 8.22/8.41 (Or (Eq (skS.0 2 a) empty_set) (Eq (subset empty_set (skS.0 2 a)) False)))) % 8.22/8.41 Clause #300 (by eliminate duplicate literals #[170]): ∀ (a a_1 : Iota), % 8.22/8.41 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.41 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.41 (Or (Eq (in (skS.0 3 a a_1) (skS.0 2 a)) True) (Eq (subset empty_set (skS.0 2 a)) False))) % 8.22/8.41 Clause #301 (by forward demodulation #[300, 13]): ∀ (a a_1 : Iota), % 8.22/8.41 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.41 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) (Or (Eq (in (skS.0 3 a a_1) (skS.0 2 a)) True) (Eq True False))) % 8.22/8.41 Clause #302 (by clausification #[301]): ∀ (a a_1 : Iota), % 8.22/8.41 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.41 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) (Eq (in (skS.0 3 a a_1) (skS.0 2 a)) True)) % 8.22/8.41 Clause #304 (by superposition #[302, 31]): ∀ (a a_1 : Iota), % 8.22/8.41 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.41 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.41 (Or (Eq (subset (singleton (skS.0 3 a a_1)) (skS.0 2 a)) True) (Eq True False))) % 8.22/8.41 Clause #310 (by clausification #[304]): ∀ (a a_1 : Iota), % 8.22/8.41 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.41 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) (Eq (subset (singleton (skS.0 3 a a_1)) (skS.0 2 a)) True)) % 8.22/8.41 Clause #311 (by superposition #[310, 137]): ∀ (a a_1 : Iota), % 8.22/8.41 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.41 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.41 (Or (Eq (skS.0 2 a) empty_set) (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) (Eq True False)))) % 8.22/8.41 Clause #319 (by clausification #[311]): ∀ (a a_1 : Iota), % 8.22/8.41 Or (Eq (skS.0 2 a) empty_set) % 8.22/8.41 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.41 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))) % 8.22/8.41 Clause #320 (by eliminate duplicate literals #[319]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 8.22/8.41 Clause #321 (by superposition #[320, 78]): ∀ (a : Iota), % 8.22/8.41 Or (Eq (skS.0 2 a) empty_set) (Or (Eq (subset (skS.0 2 a) (skS.0 2 a)) False) (Ne (skS.0 2 a) (skS.0 2 a))) % 8.22/8.41 Clause #590 (by eliminate resolved literals #[321]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (subset (skS.0 2 a) (skS.0 2 a)) False) % 8.22/8.41 Clause #591 (by superposition #[590, 17]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq False True) % 8.22/8.41 Clause #595 (by clausification #[591]): ∀ (a : Iota), Eq (skS.0 2 a) empty_set % 8.22/8.41 Clause #615 (by backward contextual literal cutting #[595, 109]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False % 8.22/8.41 Clause #616 (by forward demodulation #[615, 595]): ∀ (a a_1 : Iota), Eq (subset empty_set (singleton (skS.0 3 a a_1))) False % 8.22/8.41 Clause #617 (by superposition #[616, 13]): Eq False True % 8.22/8.41 Clause #618 (by clausification #[617]): False % 8.22/8.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------