TSTP Solution File: SET941+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 : Thu Aug 31 14:48:08 EDT 2023
% Result : Theorem 110.94s 111.13s
% Output : Proof 111.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 08:47:17 EDT 2023
% 0.15/0.36 % CPUTime :
% 110.94/111.13 SZS status Theorem for theBenchmark.p
% 110.94/111.13 SZS output start Proof for theBenchmark.p
% 110.94/111.13 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True
% 110.94/111.13 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
% 110.94/111.13 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), (∀ (C : Iota), in C A → subset C B) → subset (union A) B)) True
% 110.94/111.13 Clause #17 (by clausification #[6]): Eq (∀ (A B : Iota), (∀ (C : Iota), in C A → subset C B) → subset (union A) B) False
% 110.94/111.13 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
% 110.94/111.13 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
% 110.94/111.13 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 110.94/111.13 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)))
% 110.94/111.13 True
% 110.94/111.13 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota),
% 110.94/111.13 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
% 110.94/111.13 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
% 110.94/111.13 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) False
% 110.94/111.13 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
% 110.94/111.13 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)
% 110.94/111.13 Clause #26 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True
% 110.94/111.13 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
% 110.94/111.13 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)
% 110.94/111.13 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)
% 110.94/111.13 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota),
% 110.94/111.13 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)
% 110.94/111.13 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)
% 110.94/111.13 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)
% 110.94/111.13 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)
% 110.94/111.13 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)
% 110.94/111.13 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))
% 110.94/111.13 Clause #43 (by clausification #[2]): ∀ (a : Iota),
% 110.94/111.13 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
% 110.94/111.13 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota),
% 110.94/111.13 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
% 110.94/111.13 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota),
% 110.94/111.13 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)
% 110.94/111.13 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))
% 110.94/111.13 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)
% 110.94/111.13 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 110.94/111.13 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))
% 111.17/111.47 Clause #63 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.17/111.47 Or (Ne a (union a_1))
% 111.17/111.47 (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))
% 111.17/111.47 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))
% 111.17/111.47 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))
% 111.17/111.47 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)
% 111.17/111.47 Clause #67 (by superposition #[66, 32]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.17/111.47 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))
% 111.17/111.47 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)
% 111.17/111.47 Clause #69 (by superposition #[68, 32]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.17/111.47 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)
% 111.17/111.47 (Or (Eq (subset (union a) a_1) True) (Eq False True))
% 111.17/111.47 Clause #74 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.17/111.47 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)
% 111.17/111.47 Clause #75 (by superposition #[74, 25]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 111.17/111.47 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 111.17/111.47 (Or (Eq True False)
% 111.17/111.47 (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))
% 111.17/111.47 Clause #110 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.17/111.47 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)
% 111.17/111.47 (Eq (subset (union a) a_1) True)
% 111.17/111.47 Clause #186 (by clausification #[75]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 111.17/111.47 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 111.17/111.47 (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)
% 111.17/111.47 Clause #187 (by superposition #[186, 37]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 111.17/111.47 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 111.17/111.47 (Or (Eq True False)
% 111.17/111.47 (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)
% 111.17/111.47 (Eq (in a_2 (skS.0 3 a a_5)) True)))
% 111.17/111.47 Clause #24452 (by clausification #[187]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 111.17/111.47 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 111.17/111.47 (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)
% 111.17/111.47 (Eq (in a_2 (skS.0 3 a a_5)) True))
% 111.17/111.47 Clause #24453 (by superposition #[24452, 110]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.17/111.47 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 111.17/111.47 (Or (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (skS.0 3 a a_3)) True)
% 111.17/111.47 (Or (Eq False True) (Eq (subset (union (skS.0 2 a)) a_1) True)))
% 111.17/111.47 Clause #24610 (by clausification #[24453]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.17/111.47 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 111.17/111.47 (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))
% 111.17/111.47 Clause #24611 (by eliminate duplicate literals #[24610]): ∀ (a a_1 a_2 a_3 : Iota),
% 111.17/111.47 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)
% 111.17/111.47 Clause #24612 (by superposition #[24611, 33]): ∀ (a a_1 : Iota),
% 111.17/111.47 Or (Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) True)
% 111.17/111.47 (Or (Eq (subset (union (skS.0 2 a)) (skS.0 3 a a_1)) True) (Eq True False))
% 111.17/111.47 Clause #24724 (by clausification #[24612]): ∀ (a a_1 : Iota),
% 111.17/111.47 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)
% 111.17/111.47 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
% 111.17/111.47 Clause #24726 (by superposition #[24725, 23]): Eq True False
% 111.17/111.47 Clause #24784 (by clausification #[24726]): False
% 111.17/111.47 SZS output end Proof for theBenchmark.p
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