%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET942+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:00:44 PM UTC 2025 % Result : Theorem 12.22s 12.41s % Output : Proof 12.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.16 % Problem : SET942+1 : TPTP v9.2.0. Released v3.2.0. % 0.15/0.18 % Command : duper %s % 0.17/0.40 % Computer : n005.cluster.edu % 0.17/0.40 % Model : x86_64 x86_64 % 0.17/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.40 % Memory : 8042.1875MB % 0.17/0.40 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.40 % CPULimit : 300 % 0.17/0.40 % WCLimit : 300 % 0.17/0.40 % DateTime : Thu Oct 2 14:45:53 EDT 2025 % 0.17/0.40 % CPUTime : % 12.22/12.41 SZS status Theorem for theBenchmark.p % 12.22/12.41 SZS output start Proof for theBenchmark.p % 12.22/12.41 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 12.22/12.41 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 % 12.22/12.41 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset A B → subset (union A) (union B))) True % 12.22/12.41 Clause #17 (by clausification #[6]): Eq (∀ (A B : Iota), subset A B → subset (union A) (union B)) False % 12.22/12.41 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (skS.0 2 a) B → subset (union (skS.0 2 a)) (union B))) True % 12.22/12.41 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (skS.0 2 a) B → subset (union (skS.0 2 a)) (union B)) False % 12.22/12.41 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 12.22/12.41 Eq (Not (subset (skS.0 2 a) (skS.0 3 a a_1) → subset (union (skS.0 2 a)) (union (skS.0 3 a a_1)))) True % 12.22/12.41 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1) → subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) False % 12.22/12.41 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True % 12.22/12.41 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) False % 12.22/12.41 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 12.22/12.41 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 12.22/12.41 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 12.22/12.41 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (C : Iota), in C a → in C a_1) True) % 12.22/12.41 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 12.22/12.41 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1)) True) % 12.22/12.41 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1) False) % 12.22/12.41 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a) True) % 12.22/12.41 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a_1) False) % 12.22/12.41 Clause #33 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 12.22/12.41 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 12.22/12.41 Clause #35 (by superposition #[34, 22]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Or (Eq (in a (skS.0 3 a_1 a_2)) True) (Eq False True)) % 12.22/12.41 Clause #41 (by clausification #[2]): ∀ (a : Iota), % 12.22/12.41 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 % 12.22/12.41 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 12.22/12.41 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 % 12.22/12.41 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota), % 12.22/12.41 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) % 12.22/12.41 Clause #53 (by clausification #[44]): ∀ (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)) % 12.22/12.41 Clause #54 (by clausification #[53]): ∀ (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) % 12.22/12.41 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 12.22/12.41 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)) % 12.22/12.41 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 12.22/12.41 Or (Ne a (union a_1)) (Or (Eq (in a_2 a) False) (Eq (Exists fun D => And (in a_2 D) (in D a_1)) True)) % 12.24/12.44 Clause #57 (by clausification #[55]): ∀ (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)) % 12.24/12.44 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 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))) % 12.24/12.44 Clause #59 (by destructive equality resolution #[58]): ∀ (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)) % 12.24/12.44 Clause #61 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 Or (Ne a (union a_1)) % 12.24/12.44 (Or (Eq (in a_2 a) False) (Eq (And (in a_2 (skS.0 6 a_2 a_1 a_3)) (in (skS.0 6 a_2 a_1 a_3) a_1)) True)) % 12.24/12.44 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (union a_1)) (Or (Eq (in a_2 a) False) (Eq (in (skS.0 6 a_2 a_1 a_3) a_1) True)) % 12.24/12.44 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (union a_1)) (Or (Eq (in a_2 a) False) (Eq (in a_2 (skS.0 6 a_2 a_1 a_3)) True)) % 12.24/12.44 Clause #64 (by destructive equality resolution #[62]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (union a_1)) False) (Eq (in (skS.0 6 a a_1 a_2) a_1) True) % 12.24/12.44 Clause #65 (by superposition #[64, 30]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 Or (Eq (in (skS.0 6 (skS.0 4 (union a) a_1 a_2) a a_3) a) True) (Or (Eq (subset (union a) a_1) True) (Eq False True)) % 12.24/12.44 Clause #66 (by destructive equality resolution #[63]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (union a_1)) False) (Eq (in a (skS.0 6 a a_1 a_2)) True) % 12.24/12.44 Clause #67 (by superposition #[66, 30]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 Or (Eq (in (skS.0 4 (union a) a_1 a_2) (skS.0 6 (skS.0 4 (union a) a_1 a_2) a a_3)) True) % 12.24/12.44 (Or (Eq (subset (union a) a_1) True) (Eq False True)) % 12.24/12.44 Clause #68 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Eq (in a (skS.0 3 a_1 a_2)) True) % 12.24/12.44 Clause #93 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 Or (Eq (in (skS.0 6 (skS.0 4 (union a) a_1 a_2) a a_3) a) True) (Eq (subset (union a) a_1) True) % 12.24/12.44 Clause #96 (by superposition #[93, 68]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 12.24/12.44 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 12.24/12.44 (Or (Eq True False) (Eq (in (skS.0 6 (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (skS.0 2 a) a_3) (skS.0 3 a a_4)) True)) % 12.24/12.44 Clause #105 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 Or (Eq (in (skS.0 4 (union a) a_1 a_2) (skS.0 6 (skS.0 4 (union a) a_1 a_2) a a_3)) True) % 12.24/12.44 (Eq (subset (union a) a_1) True) % 12.24/12.44 Clause #107 (by superposition #[105, 59]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 12.24/12.44 Or (Eq (subset (union a) a_1) True) % 12.24/12.44 (Or (Eq (in (skS.0 4 (union a) a_1 a_2) (union a_3)) True) % 12.24/12.44 (Or (Eq True False) (Eq (in (skS.0 6 (skS.0 4 (union a) a_1 a_2) a a_4) a_3) False))) % 12.24/12.44 Clause #616 (by clausification #[107]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 12.24/12.44 Or (Eq (subset (union a) a_1) True) % 12.24/12.44 (Or (Eq (in (skS.0 4 (union a) a_1 a_2) (union a_3)) True) % 12.24/12.44 (Eq (in (skS.0 6 (skS.0 4 (union a) a_1 a_2) a a_4) a_3) False)) % 12.24/12.44 Clause #1720 (by clausification #[96]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 12.24/12.44 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 12.24/12.44 (Eq (in (skS.0 6 (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (skS.0 2 a) a_3) (skS.0 3 a a_4)) True) % 12.24/12.44 Clause #1721 (by superposition #[1720, 616]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 12.24/12.44 (Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 12.24/12.44 (Or (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (union (skS.0 3 a a_3))) True) (Eq True False))) % 12.24/12.44 Clause #2401 (by clausification #[1721]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 12.24/12.44 (Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 12.24/12.44 (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (union (skS.0 3 a a_3))) True)) % 12.24/12.44 Clause #2402 (by eliminate duplicate literals #[2401]): ∀ (a a_1 a_2 a_3 : Iota), % 12.24/12.44 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 12.24/12.44 (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (union (skS.0 3 a a_3))) True) % 12.24/12.44 Clause #2405 (by superposition #[2402, 31]): ∀ (a a_1 : Iota), % 12.24/12.44 Or (Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True) % 12.24/12.44 (Or (Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True) (Eq True False)) % 12.24/12.47 Clause #2453 (by clausification #[2405]): ∀ (a a_1 : Iota), % 12.24/12.47 Or (Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True) % 12.24/12.47 (Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True) % 12.24/12.47 Clause #2454 (by eliminate duplicate literals #[2453]): ∀ (a a_1 : Iota), Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True % 12.24/12.47 Clause #2455 (by superposition #[2454, 23]): Eq True False % 12.24/12.47 Clause #2484 (by clausification #[2455]): False % 12.24/12.47 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------