TSTP Solution File: SET603+3 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SET603+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n009.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 14:47:01 EDT 2023
% Result : Theorem 30.28s 30.49s
% Output : Proof 30.38s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET603+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n009.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 12:36:05 EDT 2023
% 0.15/0.35 % CPUTime :
% 30.28/30.49 SZS status Theorem for theBenchmark.p
% 30.28/30.49 SZS output start Proof for theBenchmark.p
% 30.28/30.49 Clause #1 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (difference B C)) (And (member D B) (Not (member D C)))) True
% 30.28/30.49 Clause #2 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True
% 30.28/30.49 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True
% 30.28/30.49 Clause #5 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True
% 30.28/30.49 Clause #8 (by assumption #[]): Eq (Not (∀ (B : Iota), Eq (difference B empty_set) B)) True
% 30.28/30.49 Clause #10 (by clausification #[2]): ∀ (a : Iota), Eq (Not (member a empty_set)) True
% 30.28/30.49 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (member a empty_set) False
% 30.28/30.49 Clause #20 (by clausification #[8]): Eq (∀ (B : Iota), Eq (difference B empty_set) B) False
% 30.28/30.49 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (Not (Eq (difference (skS.0 1 a) empty_set) (skS.0 1 a))) True
% 30.28/30.49 Clause #22 (by clausification #[21]): ∀ (a : Iota), Eq (Eq (difference (skS.0 1 a) empty_set) (skS.0 1 a)) False
% 30.28/30.49 Clause #23 (by clausification #[22]): ∀ (a : Iota), Ne (difference (skS.0 1 a) empty_set) (skS.0 1 a)
% 30.28/30.49 Clause #31 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (difference a C)) (And (member D a) (Not (member D C)))) True
% 30.28/30.49 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (difference a a_1)) (And (member D a) (Not (member D a_1)))) True
% 30.28/30.49 Clause #33 (by clausification #[32]): ∀ (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
% 30.28/30.49 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) True) (Eq (And (member a a_1) (Not (member a a_2))) False)
% 30.28/30.49 Clause #35 (by clausification #[33]): ∀ (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)
% 30.28/30.49 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota),
% 30.28/30.49 Or (Eq (member a (difference a_1 a_2)) True) (Or (Eq (member a a_1) False) (Eq (Not (member a a_2)) False))
% 30.28/30.49 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 30.28/30.49 Or (Eq (member a (difference a_1 a_2)) True) (Or (Eq (member a a_1) False) (Eq (member a a_2) True))
% 30.28/30.49 Clause #43 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True
% 30.28/30.49 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True
% 30.28/30.49 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False)
% 30.28/30.49 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota),
% 30.28/30.49 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)
% 30.28/30.49 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota),
% 30.28/30.49 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)
% 30.28/30.49 Clause #49 (by clausification #[48]): ∀ (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)
% 30.28/30.49 Clause #50 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 3 a a_1 a_2) a_1) False)
% 30.28/30.49 Clause #52 (by superposition #[49, 37]): ∀ (a a_1 a_2 a_3 : Iota),
% 30.28/30.49 Or (Eq (subset a a_1) True)
% 30.28/30.49 (Or (Eq (member (skS.0 3 a a_1 a_2) (difference a a_3)) True)
% 30.28/30.49 (Or (Eq True False) (Eq (member (skS.0 3 a a_1 a_2) a_3) True)))
% 30.28/30.49 Clause #54 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True
% 30.28/30.49 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True
% 30.28/30.49 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False)
% 30.28/30.49 Clause #58 (by clausification #[56]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1)
% 30.28/30.49 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False))
% 30.38/30.60 Clause #120 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (difference a_1 a_2)) False) (Eq (member a a_1) True)
% 30.38/30.60 Clause #129 (by superposition #[120, 49]): ∀ (a a_1 a_2 a_3 : Iota),
% 30.38/30.60 Or (Eq (member (skS.0 3 (difference a a_1) a_2 a_3) a) True)
% 30.38/30.60 (Or (Eq (subset (difference a a_1) a_2) True) (Eq False True))
% 30.38/30.60 Clause #191 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota),
% 30.38/30.60 Or (Eq (subset a a_1) True)
% 30.38/30.60 (Or (Eq (member (skS.0 3 a a_1 a_2) (difference a a_3)) True) (Eq (member (skS.0 3 a a_1 a_2) a_3) True))
% 30.38/30.60 Clause #194 (by superposition #[191, 50]): ∀ (a a_1 a_2 : Iota),
% 30.38/30.60 Or (Eq (subset a (difference a a_1)) True)
% 30.38/30.60 (Or (Eq (member (skS.0 3 a (difference a a_1) a_2) a_1) True)
% 30.38/30.60 (Or (Eq (subset a (difference a a_1)) True) (Eq True False)))
% 30.38/30.60 Clause #3315 (by clausification #[129]): ∀ (a a_1 a_2 a_3 : Iota),
% 30.38/30.60 Or (Eq (member (skS.0 3 (difference a a_1) a_2 a_3) a) True) (Eq (subset (difference a a_1) a_2) True)
% 30.38/30.60 Clause #3318 (by superposition #[3315, 50]): ∀ (a a_1 : Iota),
% 30.38/30.60 Or (Eq (subset (difference a a_1) a) True) (Or (Eq (subset (difference a a_1) a) True) (Eq True False))
% 30.38/30.60 Clause #3364 (by clausification #[3318]): ∀ (a a_1 : Iota), Or (Eq (subset (difference a a_1) a) True) (Eq (subset (difference a a_1) a) True)
% 30.38/30.60 Clause #3365 (by eliminate duplicate literals #[3364]): ∀ (a a_1 : Iota), Eq (subset (difference a a_1) a) True
% 30.38/30.60 Clause #3366 (by superposition #[3365, 59]): ∀ (a a_1 : Iota), Or (Eq (difference a a_1) a) (Or (Eq True False) (Eq (subset a (difference a a_1)) False))
% 30.38/30.60 Clause #3395 (by clausification #[3366]): ∀ (a a_1 : Iota), Or (Eq (difference a a_1) a) (Eq (subset a (difference a a_1)) False)
% 30.38/30.60 Clause #11625 (by clausification #[194]): ∀ (a a_1 a_2 : Iota),
% 30.38/30.60 Or (Eq (subset a (difference a a_1)) True)
% 30.38/30.60 (Or (Eq (member (skS.0 3 a (difference a a_1) a_2) a_1) True) (Eq (subset a (difference a a_1)) True))
% 30.38/30.60 Clause #11626 (by eliminate duplicate literals #[11625]): ∀ (a a_1 a_2 : Iota),
% 30.38/30.60 Or (Eq (subset a (difference a a_1)) True) (Eq (member (skS.0 3 a (difference a a_1) a_2) a_1) True)
% 30.38/30.60 Clause #11627 (by superposition #[11626, 11]): ∀ (a : Iota), Or (Eq (subset a (difference a empty_set)) True) (Eq True False)
% 30.38/30.60 Clause #11708 (by clausification #[11627]): ∀ (a : Iota), Eq (subset a (difference a empty_set)) True
% 30.38/30.60 Clause #11709 (by superposition #[11708, 3395]): ∀ (a : Iota), Or (Eq (difference a empty_set) a) (Eq True False)
% 30.38/30.60 Clause #11768 (by clausification #[11709]): ∀ (a : Iota), Eq (difference a empty_set) a
% 30.38/30.60 Clause #11774 (by backward contextual literal cutting #[11768, 23]): False
% 30.38/30.60 SZS output end Proof for theBenchmark.p
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