%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU160+3 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:01:00 PM UTC 2025 % Result : Theorem 4.05s 4.24s % Output : Proof 4.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU160+3 : TPTP v9.2.0. Released v3.2.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n016.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 05:22:53 EDT 2025 % 0.12/0.34 % CPUTime : % 4.05/4.24 SZS status Theorem for theBenchmark.p % 4.05/4.24 SZS output start Proof for theBenchmark.p % 4.05/4.24 Clause #0 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 4.05/4.24 Clause #4 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B))))) True % 4.05/4.24 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) True % 4.05/4.24 Clause #6 (by clausification #[0]): ∀ (a : Iota), Eq (Iota → subset a a) True % 4.05/4.24 Clause #7 (by clausification #[6]): ∀ (a : Iota), Iota → Eq (subset a a) True % 4.05/4.24 Clause #12 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a (singleton B)) (Or (Eq a empty_set) (Eq a (singleton B)))) True % 4.05/4.24 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Iff (subset a (singleton a_1)) (Or (Eq a empty_set) (Eq a (singleton a_1)))) True % 4.05/4.24 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) False) % 4.05/4.24 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) True) % 4.05/4.24 Clause #17 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Eq (Eq a empty_set) False) % 4.05/4.24 Clause #20 (by clausification #[4]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) False % 4.05/4.24 Clause #21 (by clausification #[20]): ∀ (a : Iota), % 4.05/4.24 Eq % 4.05/4.24 (Not % 4.05/4.24 (∀ (B : Iota), % 4.05/4.24 Iff (subset (skS.0 2 a) (singleton B)) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton B))))) % 4.05/4.24 True % 4.05/4.24 Clause #22 (by clausification #[21]): ∀ (a : Iota), % 4.05/4.24 Eq % 4.05/4.24 (∀ (B : Iota), % 4.05/4.24 Iff (subset (skS.0 2 a) (singleton B)) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton B)))) % 4.05/4.24 False % 4.05/4.24 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 4.05/4.24 Eq % 4.05/4.24 (Not % 4.05/4.24 (Iff (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 4.05/4.24 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))))) % 4.05/4.24 True % 4.05/4.24 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), % 4.05/4.24 Eq % 4.05/4.24 (Iff (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 4.05/4.24 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))) % 4.05/4.24 False % 4.05/4.24 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), % 4.05/4.24 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) % 4.05/4.24 (Eq (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) False) % 4.05/4.24 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), % 4.05/4.24 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 4.05/4.24 (Eq (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) True) % 4.05/4.24 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), % 4.05/4.24 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) % 4.05/4.24 Clause #28 (by clausification #[25]): ∀ (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) % 4.05/4.24 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), % 4.05/4.24 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))) % 4.05/4.24 Clause #30 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Ne a empty_set) % 4.05/4.24 Clause #31 (by destructive equality resolution #[30]): ∀ (a : Iota), Eq (subset empty_set (singleton a)) True % 4.05/4.24 Clause #32 (by clausification #[15]): ∀ (a a_1 : Iota), % 4.05/4.24 Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq a (singleton a_1)) True)) % 4.05/4.24 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a (singleton a_1)) True) (Eq a empty_set)) % 4.05/4.24 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq a empty_set) (Eq a (singleton a_1))) % 4.05/4.24 Clause #39 (by clausification #[28]): ∀ (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) % 4.05/4.24 Clause #40 (by clausification #[26]): ∀ (a a_1 : Iota), % 4.05/4.25 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 4.05/4.25 (Or (Eq (Eq (skS.0 2 a) empty_set) True) (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) True)) % 4.05/4.25 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 4.05/4.25 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 4.05/4.25 (Or (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Eq (skS.0 2 a) empty_set)) % 4.05/4.25 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 4.05/4.25 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 4.05/4.25 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) % 4.05/4.25 Clause #45 (by superposition #[42, 34]): ∀ (a a_1 : Iota), % 4.05/4.25 Or (Eq (skS.0 2 a) empty_set) % 4.05/4.25 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 4.05/4.25 (Or (Eq True False) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))))) % 4.05/4.25 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), % 4.05/4.25 Or (Eq (skS.0 2 a) empty_set) % 4.05/4.25 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 4.05/4.25 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))) % 4.05/4.25 Clause #49 (by eliminate duplicate literals #[48]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 4.05/4.25 Clause #50 (by superposition #[49, 29]): ∀ (a : Iota), % 4.05/4.25 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))) % 4.05/4.25 Clause #56 (by eliminate resolved literals #[50]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (subset (skS.0 2 a) (skS.0 2 a)) False) % 4.05/4.25 Clause #57 (by superposition #[56, 7]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq False True) % 4.05/4.25 Clause #58 (by clausification #[57]): ∀ (a : Iota), Eq (skS.0 2 a) empty_set % 4.05/4.25 Clause #65 (by backward contextual literal cutting #[58, 39]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False % 4.05/4.25 Clause #66 (by forward demodulation #[65, 58]): ∀ (a a_1 : Iota), Eq (subset empty_set (singleton (skS.0 3 a a_1))) False % 4.05/4.25 Clause #67 (by superposition #[66, 31]): Eq False True % 4.05/4.25 Clause #68 (by clausification #[67]): False % 4.05/4.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------