TSTP Solution File: SET942+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET942+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 12.01s 12.22s
% Output : Proof 12.01s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET942+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n004.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 : Sat Aug 26 13:40:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 12.01/12.22 SZS status Theorem for theBenchmark.p
% 12.01/12.22 SZS output start Proof for theBenchmark.p
% 12.01/12.22 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True
% 12.01/12.22 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
% 12.01/12.22 Clause #6 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset A B → subset (union A) (union B))) True
% 12.01/12.22 Clause #17 (by clausification #[6]): Eq (∀ (A B : Iota), subset A B → subset (union A) (union B)) False
% 12.01/12.22 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
% 12.01/12.22 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
% 12.01/12.22 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 12.01/12.22 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
% 12.01/12.22 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
% 12.01/12.22 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True
% 12.01/12.22 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) False
% 12.01/12.22 Clause #24 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True
% 12.01/12.22 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
% 12.01/12.22 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)
% 12.01/12.22 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)
% 12.01/12.22 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 12.01/12.22 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)
% 12.01/12.22 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)
% 12.01/12.22 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)
% 12.01/12.22 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)
% 12.01/12.22 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)
% 12.01/12.22 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))
% 12.01/12.22 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))
% 12.01/12.22 Clause #41 (by clausification #[2]): ∀ (a : Iota),
% 12.01/12.22 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
% 12.01/12.22 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 12.01/12.22 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
% 12.01/12.22 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota),
% 12.01/12.22 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)
% 12.01/12.22 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))
% 12.01/12.22 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)
% 12.01/12.22 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota),
% 12.01/12.22 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))
% 12.01/12.22 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota),
% 12.01/12.22 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))
% 12.01/12.24 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))
% 12.01/12.24 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 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)))
% 12.01/12.24 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))
% 12.01/12.24 Clause #61 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 Or (Ne a (union a_1))
% 12.01/12.24 (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))
% 12.01/12.24 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))
% 12.01/12.24 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))
% 12.01/12.24 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)
% 12.01/12.24 Clause #65 (by superposition #[64, 30]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 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))
% 12.01/12.24 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)
% 12.01/12.24 Clause #67 (by superposition #[66, 30]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 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)
% 12.01/12.24 (Or (Eq (subset (union a) a_1) True) (Eq False True))
% 12.01/12.24 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)
% 12.01/12.24 Clause #93 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 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)
% 12.01/12.24 Clause #96 (by superposition #[93, 68]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.01/12.24 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 12.01/12.24 (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))
% 12.01/12.24 Clause #105 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 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)
% 12.01/12.24 (Eq (subset (union a) a_1) True)
% 12.01/12.24 Clause #107 (by superposition #[105, 59]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.01/12.24 Or (Eq (subset (union a) a_1) True)
% 12.01/12.24 (Or (Eq (in (skS.0 4 (union a) a_1 a_2) (union a_3)) True)
% 12.01/12.24 (Or (Eq True False) (Eq (in (skS.0 6 (skS.0 4 (union a) a_1 a_2) a a_4) a_3) False)))
% 12.01/12.24 Clause #616 (by clausification #[107]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.01/12.24 Or (Eq (subset (union a) a_1) True)
% 12.01/12.24 (Or (Eq (in (skS.0 4 (union a) a_1 a_2) (union a_3)) True)
% 12.01/12.24 (Eq (in (skS.0 6 (skS.0 4 (union a) a_1 a_2) a a_4) a_3) False))
% 12.01/12.24 Clause #1720 (by clausification #[96]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.01/12.24 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 12.01/12.24 (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)
% 12.01/12.24 Clause #1721 (by superposition #[1720, 616]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 12.01/12.24 (Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 12.01/12.24 (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)))
% 12.01/12.24 Clause #2401 (by clausification #[1721]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 12.01/12.24 (Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 12.01/12.24 (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (union (skS.0 3 a a_3))) True))
% 12.01/12.24 Clause #2402 (by eliminate duplicate literals #[2401]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.01/12.24 Or (Eq (subset (union (skS.0 2 a)) a_1) True)
% 12.01/12.24 (Eq (in (skS.0 4 (union (skS.0 2 a)) a_1 a_2) (union (skS.0 3 a a_3))) True)
% 12.01/12.24 Clause #2405 (by superposition #[2402, 31]): ∀ (a a_1 : Iota),
% 12.01/12.24 Or (Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True)
% 12.01/12.24 (Or (Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True) (Eq True False))
% 12.01/12.27 Clause #2453 (by clausification #[2405]): ∀ (a a_1 : Iota),
% 12.01/12.27 Or (Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True)
% 12.01/12.27 (Eq (subset (union (skS.0 2 a)) (union (skS.0 3 a a_1))) True)
% 12.01/12.27 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
% 12.01/12.27 Clause #2455 (by superposition #[2454, 23]): Eq True False
% 12.01/12.27 Clause #2484 (by clausification #[2455]): False
% 12.01/12.27 SZS output end Proof for theBenchmark.p
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