%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET941+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:00:43 PM UTC 2025 % Result : Theorem 118.44s 118.60s % Output : Proof 118.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET941+1 : TPTP v9.2.0. Released v3.2.0. % 0.10/0.13 % Command : duper %s % 0.14/0.34 % Computer : n003.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 : Thu Oct 2 14:57:23 EDT 2025 % 0.14/0.34 % CPUTime : % 118.44/118.60 SZS status Theorem for theBenchmark.p % 118.44/118.60 SZS output start Proof for theBenchmark.p % 118.44/118.60 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 118.44/118.60 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 % 118.44/118.60 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), (∀ (C : Iota), in C A → subset C B) → subset (union A) B)) True % 118.44/118.60 Clause #17 (by clausification #[6]): Eq (∀ (A B : Iota), (∀ (C : Iota), in C A → subset C B) → subset (union A) B) False % 118.44/118.60 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), (∀ (C : Iota), in C (skS.0 2 a) → subset C B) → subset (union (skS.0 2 a)) B)) True % 118.44/118.60 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (C : Iota), in C (skS.0 2 a) → subset C B) → subset (union (skS.0 2 a)) B) False % 118.44/118.60 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 118.44/118.60 Eq (Not ((∀ (C : Iota), in C (skS.0 2 a) → subset C (skS.0 3 a a_1)) → subset (union (skS.0 2 a)) (skS.0 3 a a_1))) % 118.44/118.60 True % 118.44/118.60 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 118.44/118.60 Eq ((∀ (C : Iota), in C (skS.0 2 a) → subset C (skS.0 3 a a_1)) → subset (union (skS.0 2 a)) (skS.0 3 a a_1)) False % 118.44/118.60 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), in C (skS.0 2 a) → subset C (skS.0 3 a a_1)) True % 118.44/118.60 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) False % 118.44/118.60 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (in a (skS.0 2 a_1) → subset a (skS.0 3 a_1 a_2)) True % 118.44/118.60 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Eq (subset a (skS.0 3 a_1 a_2)) True) % 118.44/118.60 Clause #26 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 118.44/118.60 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 118.44/118.60 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 118.44/118.60 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (C : Iota), in C a → in C a_1) True) % 118.44/118.60 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 118.44/118.60 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) % 118.44/118.60 Clause #31 (by clausification #[30]): ∀ (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) % 118.44/118.60 Clause #32 (by clausification #[31]): ∀ (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) % 118.44/118.60 Clause #33 (by clausification #[31]): ∀ (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) % 118.44/118.60 Clause #36 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 118.44/118.60 Clause #37 (by clausification #[36]): ∀ (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)) % 118.44/118.60 Clause #43 (by clausification #[2]): ∀ (a : Iota), % 118.44/118.60 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 % 118.44/118.60 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), % 118.44/118.60 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 % 118.44/118.60 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), % 118.44/118.60 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) % 118.44/118.60 Clause #55 (by clausification #[46]): ∀ (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)) % 118.44/118.60 Clause #56 (by clausification #[55]): ∀ (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) % 118.44/118.60 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 118.44/118.60 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)) % 118.78/118.93 Clause #63 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 118.78/118.93 Or (Ne a (union a_1)) % 118.78/118.93 (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)) % 118.78/118.93 Clause #64 (by clausification #[63]): ∀ (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)) % 118.78/118.93 Clause #65 (by clausification #[63]): ∀ (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)) % 118.78/118.93 Clause #66 (by destructive equality resolution #[64]): ∀ (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) % 118.78/118.93 Clause #67 (by superposition #[66, 32]): ∀ (a a_1 a_2 a_3 : Iota), % 118.78/118.93 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)) % 118.78/118.93 Clause #68 (by destructive equality resolution #[65]): ∀ (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) % 118.78/118.93 Clause #69 (by superposition #[68, 32]): ∀ (a a_1 a_2 a_3 : Iota), % 118.78/118.93 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) % 118.78/118.93 (Or (Eq (subset (union a) a_1) True) (Eq False True)) % 118.78/118.93 Clause #74 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 118.78/118.93 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) % 118.78/118.93 Clause #75 (by superposition #[74, 25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 118.78/118.93 (Or (Eq True False) % 118.78/118.93 (Eq (subset (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)) % 118.78/118.93 Clause #110 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), % 118.78/118.93 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) % 118.78/118.93 (Eq (subset (union a) a_1) True) % 118.78/118.93 Clause #186 (by clausification #[75]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 118.78/118.93 (Eq (subset (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) % 118.78/118.93 Clause #187 (by superposition #[186, 37]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 118.78/118.93 (Or (Eq True False) % 118.78/118.93 (Or (Eq (in a_2 (skS.0 6 (skS.0 4 (union (skS.0 2 a)) a_1 a_3) (skS.0 2 a) a_4)) False) % 118.78/118.93 (Eq (in a_2 (skS.0 3 a a_5)) True))) % 118.78/118.93 Clause #24452 (by clausification #[187]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 118.78/118.93 (Or (Eq (in a_2 (skS.0 6 (skS.0 4 (union (skS.0 2 a)) a_1 a_3) (skS.0 2 a) a_4)) False) % 118.78/118.93 (Eq (in a_2 (skS.0 3 a a_5)) True)) % 118.78/118.93 Clause #24453 (by superposition #[24452, 110]): ∀ (a a_1 a_2 a_3 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 118.78/118.93 (Or (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (skS.0 3 a a_3)) True) % 118.78/118.93 (Or (Eq False True) (Eq (subset (union (skS.0 2 a)) a_1) True))) % 118.78/118.93 Clause #24610 (by clausification #[24453]): ∀ (a a_1 a_2 a_3 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) a_1) True) % 118.78/118.93 (Or (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (skS.0 3 a a_3)) True) (Eq (subset (union (skS.0 2 a)) a_1) True)) % 118.78/118.93 Clause #24611 (by eliminate duplicate literals #[24610]): ∀ (a a_1 a_2 a_3 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) a_1) True) (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (skS.0 3 a a_3)) True) % 118.78/118.93 Clause #24612 (by superposition #[24611, 33]): ∀ (a a_1 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) True) % 118.78/118.93 (Or (Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) True) (Eq True False)) % 118.78/118.93 Clause #24724 (by clausification #[24612]): ∀ (a a_1 : Iota), % 118.78/118.93 Or (Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) True) (Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) True) % 118.78/118.93 Clause #24725 (by eliminate duplicate literals #[24724]): ∀ (a a_1 : Iota), Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) True % 118.78/118.93 Clause #24726 (by superposition #[24725, 23]): Eq True False % 118.78/118.93 Clause #24784 (by clausification #[24726]): False % 118.78/118.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------