%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU160+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 3.80s 3.98s % Output : Proof 3.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU160+1 : TPTP v9.2.0. Released v3.3.0. % 0.11/0.14 % Command : duper %s % 0.13/0.35 % Computer : n015.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 04:10:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.80/3.98 SZS status Theorem for theBenchmark.p % 3.80/3.98 SZS output start Proof for theBenchmark.p % 3.80/3.98 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 3.80/3.98 Clause #5 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B))))) True % 3.80/3.98 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) True % 3.80/3.98 Clause #9 (by clausification #[2]): ∀ (a : Iota), Eq (Iota → subset a a) True % 3.80/3.98 Clause #10 (by clausification #[9]): ∀ (a : Iota), Iota → Eq (subset a a) True % 3.80/3.98 Clause #13 (by clausification #[5]): Eq (∀ (A B : Iota), Iff (subset A (singleton B)) (Or (Eq A empty_set) (Eq A (singleton B)))) False % 3.80/3.98 Clause #14 (by clausification #[13]): ∀ (a : Iota), % 3.80/3.98 Eq % 3.80/3.98 (Not % 3.80/3.98 (∀ (B : Iota), % 3.80/3.98 Iff (subset (skS.0 2 a) (singleton B)) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton B))))) % 3.80/3.98 True % 3.80/3.98 Clause #15 (by clausification #[14]): ∀ (a : Iota), % 3.80/3.98 Eq % 3.80/3.98 (∀ (B : Iota), % 3.80/3.98 Iff (subset (skS.0 2 a) (singleton B)) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton B)))) % 3.80/3.98 False % 3.80/3.98 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 3.80/3.98 Eq % 3.80/3.98 (Not % 3.80/3.98 (Iff (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 3.80/3.98 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))))) % 3.80/3.98 True % 3.80/3.98 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 3.80/3.98 Eq % 3.80/3.98 (Iff (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 3.80/3.98 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))) % 3.80/3.98 False % 3.80/3.98 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 3.80/3.98 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False) % 3.80/3.98 (Eq (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) False) % 3.80/3.98 Clause #19 (by clausification #[17]): ∀ (a a_1 : Iota), % 3.80/3.98 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 3.80/3.98 (Eq (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) True) % 3.80/3.98 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), % 3.80/3.98 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) % 3.80/3.98 Clause #21 (by clausification #[18]): ∀ (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) % 3.80/3.98 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), % 3.80/3.98 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))) % 3.80/3.98 Clause #23 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a (singleton B)) (Or (Eq a empty_set) (Eq a (singleton B)))) True % 3.80/3.98 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Iff (subset a (singleton a_1)) (Or (Eq a empty_set) (Eq a (singleton a_1)))) True % 3.80/3.98 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) False) % 3.80/3.98 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Eq (Or (Eq a empty_set) (Eq a (singleton a_1))) True) % 3.80/3.98 Clause #28 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Eq (Eq a empty_set) False) % 3.80/3.98 Clause #31 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) True) (Ne a empty_set) % 3.80/3.98 Clause #32 (by destructive equality resolution #[31]): ∀ (a : Iota), Eq (subset empty_set (singleton a)) True % 3.80/3.98 Clause #33 (by clausification #[26]): ∀ (a a_1 : Iota), % 3.80/3.98 Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq a (singleton a_1)) True)) % 3.80/3.98 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq (Eq a (singleton a_1)) True) (Eq a empty_set)) % 3.80/3.98 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq (subset a (singleton a_1)) False) (Or (Eq a empty_set) (Eq a (singleton a_1))) % 3.80/3.98 Clause #40 (by clausification #[19]): ∀ (a a_1 : Iota), % 3.80/3.98 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 3.80/3.98 (Or (Eq (Eq (skS.0 2 a) empty_set) True) (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) True)) % 3.83/3.99 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 3.83/3.99 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 3.83/3.99 (Or (Eq (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) (Eq (skS.0 2 a) empty_set)) % 3.83/3.99 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 3.83/3.99 Or (Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) True) % 3.83/3.99 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))) % 3.83/3.99 Clause #44 (by superposition #[42, 35]): ∀ (a a_1 : Iota), % 3.83/3.99 Or (Eq (skS.0 2 a) empty_set) % 3.83/3.99 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 3.83/3.99 (Or (Eq True False) (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1)))))) % 3.83/3.99 Clause #45 (by clausification #[21]): ∀ (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) % 3.83/3.99 Clause #49 (by clausification #[44]): ∀ (a a_1 : Iota), % 3.83/3.99 Or (Eq (skS.0 2 a) empty_set) % 3.83/3.99 (Or (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 3.83/3.99 (Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))))) % 3.83/3.99 Clause #50 (by eliminate duplicate literals #[49]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (skS.0 2 a) (singleton (skS.0 3 a a_1))) % 3.83/3.99 Clause #51 (by superposition #[50, 22]): ∀ (a : Iota), % 3.83/3.99 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))) % 3.83/3.99 Clause #55 (by eliminate resolved literals #[51]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq (subset (skS.0 2 a) (skS.0 2 a)) False) % 3.83/3.99 Clause #56 (by superposition #[55, 10]): ∀ (a : Iota), Or (Eq (skS.0 2 a) empty_set) (Eq False True) % 3.83/3.99 Clause #57 (by clausification #[56]): ∀ (a : Iota), Eq (skS.0 2 a) empty_set % 3.83/3.99 Clause #63 (by backward contextual literal cutting #[57, 45]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (singleton (skS.0 3 a a_1))) False % 3.83/3.99 Clause #64 (by forward demodulation #[63, 57]): ∀ (a a_1 : Iota), Eq (subset empty_set (singleton (skS.0 3 a a_1))) False % 3.83/3.99 Clause #65 (by superposition #[64, 32]): Eq False True % 3.83/3.99 Clause #66 (by clausification #[65]): False % 3.83/3.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------