TSTP Solution File: SET591+3 by Duper---1.0
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% File : Duper---1.0
% Problem : SET591+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n013.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 14:46:56 EDT 2023
% Result : Theorem 5.02s 5.30s
% Output : Proof 5.02s
% 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 : SET591+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:13:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.02/5.30 SZS status Theorem for theBenchmark.p
% 5.02/5.30 SZS output start Proof for theBenchmark.p
% 5.02/5.30 Clause #0 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True
% 5.02/5.30 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (difference B C)) (And (member D B) (Not (member D C)))) True
% 5.02/5.30 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True
% 5.02/5.30 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True
% 5.02/5.30 Clause #5 (by assumption #[]): Eq (∀ (B : Iota), Iff (empty B) (∀ (C : Iota), Not (member C B))) True
% 5.02/5.30 Clause #6 (by assumption #[]): Eq (Not (∀ (B C : Iota), subset B (difference C B) → Eq B empty_set)) True
% 5.02/5.30 Clause #8 (by clausification #[2]): ∀ (a : Iota), Eq (Not (member a empty_set)) True
% 5.02/5.30 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (member a empty_set) False
% 5.02/5.30 Clause #10 (by clausification #[6]): Eq (∀ (B C : Iota), subset B (difference C B) → Eq B empty_set) False
% 5.02/5.30 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Not (∀ (C : Iota), subset (skS.0 0 a) (difference C (skS.0 0 a)) → Eq (skS.0 0 a) empty_set)) True
% 5.02/5.30 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (C : Iota), subset (skS.0 0 a) (difference C (skS.0 0 a)) → Eq (skS.0 0 a) empty_set) False
% 5.02/5.30 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 0 a)) → Eq (skS.0 0 a) empty_set)) True
% 5.02/5.30 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 0 a)) → Eq (skS.0 0 a) empty_set) False
% 5.02/5.30 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (difference (skS.0 1 a a_1) (skS.0 0 a))) True
% 5.02/5.30 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Eq (skS.0 0 a) empty_set) False
% 5.02/5.30 Clause #17 (by clausification #[5]): ∀ (a : Iota), Eq (Iff (empty a) (∀ (C : Iota), Not (member C a))) True
% 5.02/5.30 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (∀ (C : Iota), Not (member C a)) False)
% 5.02/5.30 Clause #19 (by clausification #[17]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (∀ (C : Iota), Not (member C a)) True)
% 5.02/5.30 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (Not (member (skS.0 2 a a_1) a))) True)
% 5.02/5.30 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (member (skS.0 2 a a_1) a)) False)
% 5.02/5.30 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 2 a a_1) a) True)
% 5.02/5.30 Clause #25 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True
% 5.02/5.30 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True
% 5.02/5.30 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False)
% 5.02/5.30 Clause #28 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (∀ (D : Iota), member D a → member D a_1) True)
% 5.02/5.30 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.30 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 3 a a_1 a_2) a → member (skS.0 3 a a_1 a_2) a_1)) True)
% 5.02/5.30 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.30 Or (Eq (subset a a_1) True) (Eq (member (skS.0 3 a a_1 a_2) a → member (skS.0 3 a a_1 a_2) a_1) False)
% 5.02/5.30 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 3 a a_1 a_2) a) True)
% 5.02/5.30 Clause #33 (by superposition #[31, 9]): ∀ (a : Iota), Or (Eq (subset empty_set a) True) (Eq True False)
% 5.02/5.30 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (subset empty_set a) True
% 5.02/5.30 Clause #35 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (Not (member a_1 a)) True)
% 5.02/5.30 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (member a_1 a) False)
% 5.02/5.30 Clause #38 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (member a_2 a → member a_2 a_1) True)
% 5.02/5.33 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (member a_2 a) False) (Eq (member a_2 a_1) True))
% 5.02/5.33 Clause #40 (by superposition #[39, 15]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.33 Or (Eq (member a (skS.0 0 a_1)) False)
% 5.02/5.33 (Or (Eq (member a (difference (skS.0 1 a_1 a_2) (skS.0 0 a_1))) True) (Eq False True))
% 5.02/5.33 Clause #44 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (difference a C)) (And (member D a) (Not (member D C)))) True
% 5.02/5.33 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (difference a a_1)) (And (member D a) (Not (member D a_1)))) True
% 5.02/5.33 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (difference a_1 a_2)) (And (member a a_1) (Not (member a a_2)))) True
% 5.02/5.33 Clause #48 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (And (member a a_1) (Not (member a a_2))) True)
% 5.02/5.33 Clause #54 (by clausification #[16]): ∀ (a : Iota), Ne (skS.0 0 a) empty_set
% 5.02/5.33 Clause #55 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (Not (member a a_2)) True)
% 5.02/5.33 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (member a a_2) False)
% 5.02/5.33 Clause #62 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True
% 5.02/5.33 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True
% 5.02/5.33 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False)
% 5.02/5.33 Clause #66 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1)
% 5.02/5.33 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False))
% 5.02/5.33 Clause #69 (by superposition #[67, 34]): ∀ (a : Iota), Or (Eq empty_set a) (Or (Eq (subset a empty_set) False) (Eq False True))
% 5.02/5.33 Clause #73 (by clausification #[69]): ∀ (a : Iota), Or (Eq empty_set a) (Eq (subset a empty_set) False)
% 5.02/5.33 Clause #80 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.33 Or (Eq (member a (skS.0 0 a_1)) False) (Eq (member a (difference (skS.0 1 a_1 a_2) (skS.0 0 a_1))) True)
% 5.02/5.33 Clause #81 (by superposition #[80, 22]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.33 Or (Eq (member (skS.0 2 (skS.0 0 a) a_1) (difference (skS.0 1 a a_2) (skS.0 0 a))) True)
% 5.02/5.33 (Or (Eq (empty (skS.0 0 a)) True) (Eq False True))
% 5.02/5.33 Clause #168 (by clausification #[81]): ∀ (a a_1 a_2 : Iota),
% 5.02/5.33 Or (Eq (member (skS.0 2 (skS.0 0 a) a_1) (difference (skS.0 1 a a_2) (skS.0 0 a))) True) (Eq (empty (skS.0 0 a)) True)
% 5.02/5.33 Clause #169 (by superposition #[168, 57]): ∀ (a a_1 : Iota),
% 5.02/5.33 Or (Eq (empty (skS.0 0 a)) True) (Or (Eq True False) (Eq (member (skS.0 2 (skS.0 0 a) a_1) (skS.0 0 a)) False))
% 5.02/5.33 Clause #443 (by clausification #[169]): ∀ (a a_1 : Iota), Or (Eq (empty (skS.0 0 a)) True) (Eq (member (skS.0 2 (skS.0 0 a) a_1) (skS.0 0 a)) False)
% 5.02/5.33 Clause #444 (by superposition #[443, 22]): ∀ (a : Iota), Or (Eq (empty (skS.0 0 a)) True) (Or (Eq (empty (skS.0 0 a)) True) (Eq False True))
% 5.02/5.33 Clause #446 (by clausification #[444]): ∀ (a : Iota), Or (Eq (empty (skS.0 0 a)) True) (Eq (empty (skS.0 0 a)) True)
% 5.02/5.33 Clause #447 (by eliminate duplicate literals #[446]): ∀ (a : Iota), Eq (empty (skS.0 0 a)) True
% 5.02/5.33 Clause #450 (by superposition #[447, 36]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (member a (skS.0 0 a_1)) False)
% 5.02/5.33 Clause #451 (by clausification #[450]): ∀ (a a_1 : Iota), Eq (member a (skS.0 0 a_1)) False
% 5.02/5.33 Clause #454 (by superposition #[451, 31]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 0 a) a_1) True) (Eq False True)
% 5.02/5.33 Clause #462 (by clausification #[454]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) a_1) True
% 5.02/5.33 Clause #464 (by superposition #[462, 73]): ∀ (a : Iota), Or (Eq empty_set (skS.0 0 a)) (Eq True False)
% 5.02/5.33 Clause #469 (by clausification #[464]): ∀ (a : Iota), Eq empty_set (skS.0 0 a)
% 5.02/5.33 Clause #470 (by forward contextual literal cutting #[469, 54]): False
% 5.02/5.33 SZS output end Proof for theBenchmark.p
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