TSTP Solution File: SEU320+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n029.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 16:41:25 EDT 2023
% Result : Theorem 4.51s 4.70s
% Output : Proof 4.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : duper %s
% 0.18/0.35 % Computer : n029.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 24 01:00:38 EDT 2023
% 0.18/0.35 % CPUTime :
% 4.51/4.70 SZS status Theorem for theBenchmark.p
% 4.51/4.70 SZS output start Proof for theBenchmark.p
% 4.51/4.70 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), element B (powerset A) → element (subset_complement A B) (powerset A)) True
% 4.51/4.70 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), element B (powerset A) → Eq (subset_complement A (subset_complement A B)) B) True
% 4.51/4.70 Clause #8 (by assumption #[]): Eq
% 4.51/4.70 (∀ (A : Iota),
% 4.51/4.70 top_str A →
% 4.51/4.70 ∀ (B : Iota),
% 4.51/4.70 element B (powerset (the_carrier A)) →
% 4.51/4.70 Iff (closed_subset B A) (open_subset (subset_complement (the_carrier A) B) A))
% 4.51/4.70 True
% 4.51/4.70 Clause #9 (by assumption #[]): Eq
% 4.51/4.70 (Not
% 4.51/4.70 (∀ (A : Iota),
% 4.51/4.70 top_str A →
% 4.51/4.70 ∀ (B : Iota),
% 4.51/4.70 element B (powerset (the_carrier A)) →
% 4.51/4.70 Iff (open_subset B A) (closed_subset (subset_complement (the_carrier A) B) A)))
% 4.51/4.70 True
% 4.51/4.70 Clause #20 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), element B (powerset a) → element (subset_complement a B) (powerset a)) True
% 4.51/4.70 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (element a (powerset a_1) → element (subset_complement a_1 a) (powerset a_1)) True
% 4.51/4.70 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) False) (Eq (element (subset_complement a_1 a) (powerset a_1)) True)
% 4.51/4.70 Clause #36 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), element B (powerset a) → Eq (subset_complement a (subset_complement a B)) B) True
% 4.51/4.70 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (element a (powerset a_1) → Eq (subset_complement a_1 (subset_complement a_1 a)) a) True
% 4.51/4.70 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 4.51/4.70 Or (Eq (element a (powerset a_1)) False) (Eq (Eq (subset_complement a_1 (subset_complement a_1 a)) a) True)
% 4.51/4.70 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) False) (Eq (subset_complement a_1 (subset_complement a_1 a)) a)
% 4.51/4.70 Clause #50 (by clausification #[8]): ∀ (a : Iota),
% 4.51/4.70 Eq
% 4.51/4.70 (top_str a →
% 4.51/4.70 ∀ (B : Iota),
% 4.51/4.70 element B (powerset (the_carrier a)) →
% 4.51/4.70 Iff (closed_subset B a) (open_subset (subset_complement (the_carrier a) B) a))
% 4.51/4.70 True
% 4.51/4.70 Clause #51 (by clausification #[50]): ∀ (a : Iota),
% 4.51/4.70 Or (Eq (top_str a) False)
% 4.51/4.70 (Eq
% 4.51/4.70 (∀ (B : Iota),
% 4.51/4.70 element B (powerset (the_carrier a)) →
% 4.51/4.70 Iff (closed_subset B a) (open_subset (subset_complement (the_carrier a) B) a))
% 4.51/4.70 True)
% 4.51/4.70 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota),
% 4.51/4.70 Or (Eq (top_str a) False)
% 4.51/4.70 (Eq
% 4.51/4.70 (element a_1 (powerset (the_carrier a)) →
% 4.51/4.70 Iff (closed_subset a_1 a) (open_subset (subset_complement (the_carrier a) a_1) a))
% 4.51/4.70 True)
% 4.51/4.70 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota),
% 4.51/4.70 Or (Eq (top_str a) False)
% 4.51/4.70 (Or (Eq (element a_1 (powerset (the_carrier a))) False)
% 4.51/4.70 (Eq (Iff (closed_subset a_1 a) (open_subset (subset_complement (the_carrier a) a_1) a)) True))
% 4.51/4.70 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota),
% 4.51/4.70 Or (Eq (top_str a) False)
% 4.51/4.70 (Or (Eq (element a_1 (powerset (the_carrier a))) False)
% 4.51/4.70 (Or (Eq (closed_subset a_1 a) True) (Eq (open_subset (subset_complement (the_carrier a) a_1) a) False)))
% 4.51/4.70 Clause #55 (by clausification #[53]): ∀ (a a_1 : Iota),
% 4.51/4.70 Or (Eq (top_str a) False)
% 4.51/4.70 (Or (Eq (element a_1 (powerset (the_carrier a))) False)
% 4.51/4.70 (Or (Eq (closed_subset a_1 a) False) (Eq (open_subset (subset_complement (the_carrier a) a_1) a) True)))
% 4.51/4.70 Clause #63 (by clausification #[9]): Eq
% 4.51/4.70 (∀ (A : Iota),
% 4.51/4.70 top_str A →
% 4.51/4.70 ∀ (B : Iota),
% 4.51/4.70 element B (powerset (the_carrier A)) →
% 4.51/4.70 Iff (open_subset B A) (closed_subset (subset_complement (the_carrier A) B) A))
% 4.51/4.70 False
% 4.51/4.70 Clause #64 (by clausification #[63]): ∀ (a : Iota),
% 4.51/4.70 Eq
% 4.51/4.70 (Not
% 4.51/4.70 (top_str (skS.0 3 a) →
% 4.51/4.70 ∀ (B : Iota),
% 4.51/4.70 element B (powerset (the_carrier (skS.0 3 a))) →
% 4.51/4.70 Iff (open_subset B (skS.0 3 a))
% 4.51/4.70 (closed_subset (subset_complement (the_carrier (skS.0 3 a)) B) (skS.0 3 a))))
% 4.51/4.70 True
% 4.51/4.70 Clause #65 (by clausification #[64]): ∀ (a : Iota),
% 4.51/4.70 Eq
% 4.51/4.70 (top_str (skS.0 3 a) →
% 4.57/4.72 ∀ (B : Iota),
% 4.57/4.72 element B (powerset (the_carrier (skS.0 3 a))) →
% 4.57/4.72 Iff (open_subset B (skS.0 3 a)) (closed_subset (subset_complement (the_carrier (skS.0 3 a)) B) (skS.0 3 a)))
% 4.57/4.72 False
% 4.57/4.72 Clause #66 (by clausification #[65]): ∀ (a : Iota), Eq (top_str (skS.0 3 a)) True
% 4.57/4.72 Clause #67 (by clausification #[65]): ∀ (a : Iota),
% 4.57/4.72 Eq
% 4.57/4.72 (∀ (B : Iota),
% 4.57/4.72 element B (powerset (the_carrier (skS.0 3 a))) →
% 4.57/4.72 Iff (open_subset B (skS.0 3 a)) (closed_subset (subset_complement (the_carrier (skS.0 3 a)) B) (skS.0 3 a)))
% 4.57/4.72 False
% 4.57/4.72 Clause #69 (by superposition #[66, 54]): ∀ (a a_1 : Iota),
% 4.57/4.72 Or (Eq True False)
% 4.57/4.72 (Or (Eq (element a (powerset (the_carrier (skS.0 3 a_1)))) False)
% 4.57/4.72 (Or (Eq (closed_subset a (skS.0 3 a_1)) True)
% 4.57/4.72 (Eq (open_subset (subset_complement (the_carrier (skS.0 3 a_1)) a) (skS.0 3 a_1)) False)))
% 4.57/4.72 Clause #85 (by superposition #[55, 66]): ∀ (a a_1 : Iota),
% 4.57/4.72 Or (Eq True False)
% 4.57/4.72 (Or (Eq (element a (powerset (the_carrier (skS.0 3 a_1)))) False)
% 4.57/4.72 (Or (Eq (closed_subset a (skS.0 3 a_1)) False)
% 4.57/4.72 (Eq (open_subset (subset_complement (the_carrier (skS.0 3 a_1)) a) (skS.0 3 a_1)) True)))
% 4.57/4.72 Clause #87 (by clausification #[67]): ∀ (a a_1 : Iota),
% 4.57/4.72 Eq
% 4.57/4.72 (Not
% 4.57/4.72 (element (skS.0 4 a a_1) (powerset (the_carrier (skS.0 3 a))) →
% 4.57/4.72 Iff (open_subset (skS.0 4 a a_1) (skS.0 3 a))
% 4.57/4.72 (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a))))
% 4.57/4.72 True
% 4.57/4.72 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota),
% 4.57/4.72 Eq
% 4.57/4.72 (element (skS.0 4 a a_1) (powerset (the_carrier (skS.0 3 a))) →
% 4.57/4.72 Iff (open_subset (skS.0 4 a a_1) (skS.0 3 a))
% 4.57/4.72 (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)))
% 4.57/4.72 False
% 4.57/4.72 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (element (skS.0 4 a a_1) (powerset (the_carrier (skS.0 3 a)))) True
% 4.57/4.72 Clause #90 (by clausification #[88]): ∀ (a a_1 : Iota),
% 4.57/4.72 Eq
% 4.57/4.72 (Iff (open_subset (skS.0 4 a a_1) (skS.0 3 a))
% 4.57/4.72 (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)))
% 4.57/4.72 False
% 4.57/4.72 Clause #91 (by superposition #[89, 22]): ∀ (a a_1 : Iota),
% 4.57/4.72 Or (Eq True False)
% 4.57/4.72 (Eq (element (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (powerset (the_carrier (skS.0 3 a))))
% 4.57/4.72 True)
% 4.57/4.72 Clause #92 (by superposition #[89, 39]): ∀ (a a_1 : Iota),
% 4.57/4.72 Or (Eq True False)
% 4.57/4.72 (Eq (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)))
% 4.57/4.72 (skS.0 4 a a_1))
% 4.57/4.72 Clause #101 (by clausification #[91]): ∀ (a a_1 : Iota),
% 4.57/4.72 Eq (element (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (powerset (the_carrier (skS.0 3 a)))) True
% 4.57/4.72 Clause #109 (by clausification #[69]): ∀ (a a_1 : Iota),
% 4.57/4.72 Or (Eq (element a (powerset (the_carrier (skS.0 3 a_1)))) False)
% 4.57/4.72 (Or (Eq (closed_subset a (skS.0 3 a_1)) True)
% 4.57/4.72 (Eq (open_subset (subset_complement (the_carrier (skS.0 3 a_1)) a) (skS.0 3 a_1)) False))
% 4.57/4.72 Clause #113 (by superposition #[109, 101]): ∀ (a a_1 : Iota),
% 4.57/4.72 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) True)
% 4.57/4.72 (Or
% 4.57/4.72 (Eq
% 4.57/4.72 (open_subset
% 4.57/4.72 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)))
% 4.57/4.72 (skS.0 3 a))
% 4.57/4.72 False)
% 4.57/4.72 (Eq False True))
% 4.57/4.72 Clause #118 (by clausification #[92]): ∀ (a a_1 : Iota),
% 4.57/4.72 Eq (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)))
% 4.57/4.72 (skS.0 4 a a_1)
% 4.57/4.72 Clause #120 (by clausification #[85]): ∀ (a a_1 : Iota),
% 4.57/4.72 Or (Eq (element a (powerset (the_carrier (skS.0 3 a_1)))) False)
% 4.57/4.72 (Or (Eq (closed_subset a (skS.0 3 a_1)) False)
% 4.57/4.72 (Eq (open_subset (subset_complement (the_carrier (skS.0 3 a_1)) a) (skS.0 3 a_1)) True))
% 4.57/4.72 Clause #124 (by superposition #[120, 101]): ∀ (a a_1 : Iota),
% 4.57/4.72 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False)
% 4.57/4.72 (Or
% 4.57/4.72 (Eq
% 4.57/4.72 (open_subset
% 4.57/4.72 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)))
% 4.57/4.74 (skS.0 3 a))
% 4.57/4.74 True)
% 4.57/4.74 (Eq False True))
% 4.57/4.74 Clause #132 (by clausification #[90]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) False)
% 4.57/4.74 (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False)
% 4.57/4.74 Clause #133 (by clausification #[90]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True)
% 4.57/4.74 (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) True)
% 4.57/4.74 Clause #158 (by clausification #[124]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False)
% 4.57/4.74 (Eq
% 4.57/4.74 (open_subset
% 4.57/4.74 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)))
% 4.57/4.74 (skS.0 3 a))
% 4.57/4.74 True)
% 4.57/4.74 Clause #159 (by forward demodulation #[158, 118]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False)
% 4.57/4.74 (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True)
% 4.57/4.74 Clause #160 (by superposition #[159, 133]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True)
% 4.57/4.74 (Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True) (Eq False True))
% 4.57/4.74 Clause #161 (by clausification #[160]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True) (Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True)
% 4.57/4.74 Clause #162 (by eliminate duplicate literals #[161]): ∀ (a a_1 : Iota), Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) True
% 4.57/4.74 Clause #163 (by backward demodulation #[162, 132]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq True False)
% 4.57/4.74 (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False)
% 4.57/4.74 Clause #166 (by clausification #[163]): ∀ (a a_1 : Iota), Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) False
% 4.57/4.74 Clause #167 (by clausification #[113]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq (closed_subset (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)) (skS.0 3 a)) True)
% 4.57/4.74 (Eq
% 4.57/4.74 (open_subset
% 4.57/4.74 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)))
% 4.57/4.74 (skS.0 3 a))
% 4.57/4.74 False)
% 4.57/4.74 Clause #168 (by forward demodulation #[167, 166]): ∀ (a a_1 : Iota),
% 4.57/4.74 Or (Eq False True)
% 4.57/4.74 (Eq
% 4.57/4.74 (open_subset
% 4.57/4.74 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)))
% 4.57/4.74 (skS.0 3 a))
% 4.57/4.74 False)
% 4.57/4.74 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota),
% 4.57/4.74 Eq
% 4.57/4.74 (open_subset
% 4.57/4.74 (subset_complement (the_carrier (skS.0 3 a)) (subset_complement (the_carrier (skS.0 3 a)) (skS.0 4 a a_1)))
% 4.57/4.74 (skS.0 3 a))
% 4.57/4.74 False
% 4.57/4.74 Clause #170 (by forward demodulation #[169, 118]): ∀ (a a_1 : Iota), Eq (open_subset (skS.0 4 a a_1) (skS.0 3 a)) False
% 4.57/4.74 Clause #171 (by superposition #[170, 162]): Eq False True
% 4.57/4.74 Clause #172 (by clausification #[171]): False
% 4.57/4.74 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------