%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU155+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:00:59 PM UTC 2025 % Result : Theorem 4.33s 4.52s % Output : Proof 4.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU155+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n023.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 04:58:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.33/4.52 SZS status Theorem for theBenchmark.p % 4.33/4.52 SZS output start Proof for theBenchmark.p % 4.33/4.52 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 4.33/4.52 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (union A)) (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in C D) (in D A)))) True % 4.33/4.52 Clause #4 (by assumption #[]): Eq (Not (∀ (A B : Iota), in A B → subset A (union B))) True % 4.33/4.52 Clause #12 (by clausification #[4]): Eq (∀ (A B : Iota), in A B → subset A (union B)) False % 4.33/4.52 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), in (skS.0 0 a) B → subset (skS.0 0 a) (union B))) True % 4.33/4.52 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (B : Iota), in (skS.0 0 a) B → subset (skS.0 0 a) (union B)) False % 4.33/4.52 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 0 a) (skS.0 1 a a_1) → subset (skS.0 0 a) (union (skS.0 1 a a_1)))) True % 4.33/4.52 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1) → subset (skS.0 0 a) (union (skS.0 1 a a_1))) False % 4.33/4.52 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True % 4.33/4.52 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) False % 4.33/4.52 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 4.33/4.52 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 4.33/4.52 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 4.33/4.52 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 4.33/4.52 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1)) True) % 4.33/4.52 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False) % 4.33/4.52 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a) True) % 4.33/4.52 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a_1) False) % 4.33/4.52 Clause #29 (by clausification #[2]): ∀ (a : Iota), % 4.33/4.52 Eq (∀ (B : Iota), Iff (Eq B (union a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in C D) (in D a)))) True % 4.33/4.52 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 4.33/4.52 Eq (Iff (Eq a (union a_1)) (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1)))) True % 4.33/4.52 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota), % 4.33/4.52 Or (Eq (Eq a (union a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1))) True) % 4.33/4.52 Clause #49 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Exists fun D => And (in C D) (in D a_1))) True) (Ne a (union a_1)) % 4.33/4.52 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Or (Ne a (union a_1)) (Eq (Iff (in a_2 a) (Exists fun D => And (in a_2 D) (in D a_1))) True) % 4.33/4.52 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 4.33/4.52 Or (Ne a (union a_1)) (Or (Eq (in a_2 a) True) (Eq (Exists fun D => And (in a_2 D) (in D a_1)) False)) % 4.33/4.52 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (union a_1)) (Or (Eq (in a_2 a) True) (Eq (And (in a_2 a_3) (in a_3 a_1)) False)) % 4.33/4.52 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.52 Or (Ne a (union a_1)) (Or (Eq (in a_2 a) True) (Or (Eq (in a_2 a_3) False) (Eq (in a_3 a_1) False))) % 4.33/4.52 Clause #55 (by destructive equality resolution #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (union a_1)) True) (Or (Eq (in a a_2) False) (Eq (in a_2 a_1) False)) % 4.33/4.52 Clause #57 (by superposition #[55, 26]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.52 Or (Eq (in (skS.0 2 a a_1 a_2) (union a_3)) True) % 4.33/4.52 (Or (Eq (in a a_3) False) (Or (Eq (subset a a_1) True) (Eq False True))) % 4.33/4.52 Clause #82 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.52 Or (Eq (in (skS.0 2 a a_1 a_2) (union a_3)) True) (Or (Eq (in a a_3) False) (Eq (subset a a_1) True)) % 4.33/4.53 Clause #83 (by superposition #[82, 17]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.53 Or (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (union (skS.0 1 a a_3))) True) % 4.33/4.53 (Or (Eq (subset (skS.0 0 a) a_1) True) (Eq False True)) % 4.33/4.53 Clause #110 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), % 4.33/4.53 Or (Eq (in (skS.0 2 (skS.0 0 a) a_1 a_2) (union (skS.0 1 a a_3))) True) (Eq (subset (skS.0 0 a) a_1) True) % 4.33/4.53 Clause #113 (by superposition #[110, 27]): ∀ (a a_1 : Iota), % 4.33/4.53 Or (Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True) % 4.33/4.53 (Or (Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True) (Eq True False)) % 4.33/4.53 Clause #119 (by clausification #[113]): ∀ (a a_1 : Iota), % 4.33/4.53 Or (Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True) (Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True) % 4.33/4.53 Clause #120 (by eliminate duplicate literals #[119]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (union (skS.0 1 a a_1))) True % 4.33/4.53 Clause #121 (by superposition #[120, 18]): Eq True False % 4.33/4.53 Clause #124 (by clausification #[121]): False % 4.33/4.53 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------