TSTP Solution File: SEU341+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 16:41:31 EDT 2023
% Result : Theorem 72.05s 72.24s
% Output : Proof 72.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 16:05:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 72.05/72.24 SZS status Theorem for theBenchmark.p
% 72.05/72.24 SZS output start Proof for theBenchmark.p
% 72.05/72.24 Clause #16 (by assumption #[]): Eq
% 72.05/72.24 (∀ (A : Iota),
% 72.05/72.24 And (And (Not (empty_carrier A)) (topological_space A)) (top_str A) →
% 72.05/72.24 ∀ (B : Iota),
% 72.05/72.24 element B (the_carrier A) →
% 72.05/72.24 ∀ (C : Iota), element C (powerset (the_carrier A)) → Iff (point_neighbourhood C A B) (in B (interior A C)))
% 72.05/72.24 True
% 72.05/72.24 Clause #29 (by assumption #[]): Eq (∀ (A : Iota), Exists fun B => And (element B (powerset A)) (empty B)) True
% 72.05/72.24 Clause #35 (by assumption #[]): Eq
% 72.05/72.24 (∀ (A : Iota),
% 72.05/72.24 And (topological_space A) (top_str A) →
% 72.05/72.24 ∀ (B : Iota),
% 72.05/72.24 top_str B →
% 72.05/72.24 ∀ (C : Iota),
% 72.05/72.24 element C (powerset (the_carrier A)) →
% 72.05/72.24 ∀ (D : Iota),
% 72.05/72.24 element D (powerset (the_carrier B)) →
% 72.05/72.24 And (open_subset D B → Eq (interior B D) D) (Eq (interior A C) C → open_subset C A))
% 72.05/72.24 True
% 72.05/72.24 Clause #36 (by assumption #[]): Eq
% 72.05/72.24 (Not
% 72.05/72.24 (∀ (A : Iota),
% 72.05/72.24 And (And (Not (empty_carrier A)) (topological_space A)) (top_str A) →
% 72.05/72.25 ∀ (B : Iota),
% 72.05/72.25 element B (powerset (the_carrier A)) →
% 72.05/72.25 ∀ (C : Iota), element C (the_carrier A) → And (open_subset B A) (in C B) → point_neighbourhood B A C))
% 72.05/72.25 True
% 72.05/72.25 Clause #38 (by assumption #[]): Eq (∀ (A : Iota), empty A → Eq A empty_set) True
% 72.05/72.25 Clause #68 (by clausification #[38]): ∀ (a : Iota), Eq (empty a → Eq a empty_set) True
% 72.05/72.25 Clause #69 (by clausification #[68]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (Eq a empty_set) True)
% 72.05/72.25 Clause #70 (by clausification #[69]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq a empty_set)
% 72.05/72.25 Clause #167 (by clausification #[29]): ∀ (a : Iota), Eq (Exists fun B => And (element B (powerset a)) (empty B)) True
% 72.05/72.25 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (And (element (skS.0 4 a a_1) (powerset a)) (empty (skS.0 4 a a_1))) True
% 72.05/72.25 Clause #169 (by clausification #[168]): ∀ (a a_1 : Iota), Eq (empty (skS.0 4 a a_1)) True
% 72.05/72.25 Clause #170 (by clausification #[168]): ∀ (a a_1 : Iota), Eq (element (skS.0 4 a a_1) (powerset a)) True
% 72.05/72.25 Clause #171 (by superposition #[169, 70]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 4 a a_1) empty_set)
% 72.05/72.25 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), Eq (skS.0 4 a a_1) empty_set
% 72.05/72.25 Clause #235 (by forward demodulation #[170, 172]): ∀ (a : Iota), Eq (element empty_set (powerset a)) True
% 72.05/72.25 Clause #239 (by clausification #[16]): ∀ (a : Iota),
% 72.05/72.25 Eq
% 72.05/72.25 (And (And (Not (empty_carrier a)) (topological_space a)) (top_str a) →
% 72.05/72.25 ∀ (B : Iota),
% 72.05/72.25 element B (the_carrier a) →
% 72.05/72.25 ∀ (C : Iota), element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a B) (in B (interior a C)))
% 72.05/72.25 True
% 72.05/72.25 Clause #240 (by clausification #[239]): ∀ (a : Iota),
% 72.05/72.25 Or (Eq (And (And (Not (empty_carrier a)) (topological_space a)) (top_str a)) False)
% 72.05/72.25 (Eq
% 72.05/72.25 (∀ (B : Iota),
% 72.05/72.25 element B (the_carrier a) →
% 72.05/72.25 ∀ (C : Iota), element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a B) (in B (interior a C)))
% 72.05/72.25 True)
% 72.05/72.25 Clause #241 (by clausification #[240]): ∀ (a : Iota),
% 72.05/72.25 Or
% 72.05/72.25 (Eq
% 72.05/72.25 (∀ (B : Iota),
% 72.05/72.25 element B (the_carrier a) →
% 72.05/72.25 ∀ (C : Iota), element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a B) (in B (interior a C)))
% 72.05/72.25 True)
% 72.05/72.25 (Or (Eq (And (Not (empty_carrier a)) (topological_space a)) False) (Eq (top_str a) False))
% 72.05/72.25 Clause #242 (by clausification #[241]): ∀ (a a_1 : Iota),
% 72.05/72.25 Or (Eq (And (Not (empty_carrier a)) (topological_space a)) False)
% 72.05/72.25 (Or (Eq (top_str a) False)
% 72.05/72.25 (Eq
% 72.05/72.25 (element a_1 (the_carrier a) →
% 72.05/72.25 ∀ (C : Iota),
% 72.05/72.25 element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a a_1) (in a_1 (interior a C)))
% 72.05/72.25 True))
% 72.05/72.25 Clause #243 (by clausification #[242]): ∀ (a a_1 : Iota),
% 72.05/72.25 Or (Eq (top_str a) False)
% 72.05/72.25 (Or
% 72.05/72.25 (Eq
% 72.05/72.25 (element a_1 (the_carrier a) →
% 72.05/72.25 ∀ (C : Iota),
% 72.05/72.25 element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a a_1) (in a_1 (interior a C)))
% 72.05/72.27 True)
% 72.05/72.27 (Or (Eq (Not (empty_carrier a)) False) (Eq (topological_space a) False)))
% 72.05/72.27 Clause #244 (by clausification #[243]): ∀ (a a_1 : Iota),
% 72.05/72.27 Or (Eq (top_str a) False)
% 72.05/72.27 (Or (Eq (Not (empty_carrier a)) False)
% 72.05/72.27 (Or (Eq (topological_space a) False)
% 72.05/72.27 (Or (Eq (element a_1 (the_carrier a)) False)
% 72.05/72.27 (Eq
% 72.05/72.27 (∀ (C : Iota),
% 72.05/72.27 element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a a_1) (in a_1 (interior a C)))
% 72.05/72.27 True))))
% 72.05/72.27 Clause #245 (by clausification #[244]): ∀ (a a_1 : Iota),
% 72.05/72.27 Or (Eq (top_str a) False)
% 72.05/72.27 (Or (Eq (topological_space a) False)
% 72.05/72.27 (Or (Eq (element a_1 (the_carrier a)) False)
% 72.05/72.27 (Or
% 72.05/72.27 (Eq
% 72.05/72.27 (∀ (C : Iota),
% 72.05/72.27 element C (powerset (the_carrier a)) → Iff (point_neighbourhood C a a_1) (in a_1 (interior a C)))
% 72.05/72.27 True)
% 72.05/72.27 (Eq (empty_carrier a) True))))
% 72.05/72.27 Clause #246 (by clausification #[245]): ∀ (a a_1 a_2 : Iota),
% 72.05/72.27 Or (Eq (top_str a) False)
% 72.05/72.27 (Or (Eq (topological_space a) False)
% 72.05/72.27 (Or (Eq (element a_1 (the_carrier a)) False)
% 72.05/72.27 (Or (Eq (empty_carrier a) True)
% 72.05/72.27 (Eq (element a_2 (powerset (the_carrier a)) → Iff (point_neighbourhood a_2 a a_1) (in a_1 (interior a a_2)))
% 72.05/72.27 True))))
% 72.05/72.27 Clause #247 (by clausification #[246]): ∀ (a a_1 a_2 : Iota),
% 72.05/72.27 Or (Eq (top_str a) False)
% 72.05/72.27 (Or (Eq (topological_space a) False)
% 72.05/72.27 (Or (Eq (element a_1 (the_carrier a)) False)
% 72.05/72.27 (Or (Eq (empty_carrier a) True)
% 72.05/72.27 (Or (Eq (element a_2 (powerset (the_carrier a))) False)
% 72.05/72.27 (Eq (Iff (point_neighbourhood a_2 a a_1) (in a_1 (interior a a_2))) True)))))
% 72.05/72.27 Clause #248 (by clausification #[247]): ∀ (a a_1 a_2 : Iota),
% 72.05/72.27 Or (Eq (top_str a) False)
% 72.05/72.27 (Or (Eq (topological_space a) False)
% 72.05/72.27 (Or (Eq (element a_1 (the_carrier a)) False)
% 72.05/72.27 (Or (Eq (empty_carrier a) True)
% 72.05/72.27 (Or (Eq (element a_2 (powerset (the_carrier a))) False)
% 72.05/72.27 (Or (Eq (point_neighbourhood a_2 a a_1) True) (Eq (in a_1 (interior a a_2)) False))))))
% 72.05/72.27 Clause #303 (by clausification #[36]): Eq
% 72.05/72.27 (∀ (A : Iota),
% 72.05/72.27 And (And (Not (empty_carrier A)) (topological_space A)) (top_str A) →
% 72.05/72.27 ∀ (B : Iota),
% 72.05/72.27 element B (powerset (the_carrier A)) →
% 72.05/72.27 ∀ (C : Iota), element C (the_carrier A) → And (open_subset B A) (in C B) → point_neighbourhood B A C)
% 72.05/72.27 False
% 72.05/72.27 Clause #304 (by clausification #[303]): ∀ (a : Iota),
% 72.05/72.27 Eq
% 72.05/72.27 (Not
% 72.05/72.27 (And (And (Not (empty_carrier (skS.0 7 a))) (topological_space (skS.0 7 a))) (top_str (skS.0 7 a)) →
% 72.05/72.27 ∀ (B : Iota),
% 72.05/72.27 element B (powerset (the_carrier (skS.0 7 a))) →
% 72.05/72.27 ∀ (C : Iota),
% 72.05/72.27 element C (the_carrier (skS.0 7 a)) →
% 72.05/72.27 And (open_subset B (skS.0 7 a)) (in C B) → point_neighbourhood B (skS.0 7 a) C))
% 72.05/72.27 True
% 72.05/72.27 Clause #305 (by clausification #[304]): ∀ (a : Iota),
% 72.05/72.27 Eq
% 72.05/72.27 (And (And (Not (empty_carrier (skS.0 7 a))) (topological_space (skS.0 7 a))) (top_str (skS.0 7 a)) →
% 72.05/72.27 ∀ (B : Iota),
% 72.05/72.27 element B (powerset (the_carrier (skS.0 7 a))) →
% 72.05/72.27 ∀ (C : Iota),
% 72.05/72.27 element C (the_carrier (skS.0 7 a)) →
% 72.05/72.27 And (open_subset B (skS.0 7 a)) (in C B) → point_neighbourhood B (skS.0 7 a) C)
% 72.05/72.27 False
% 72.05/72.27 Clause #306 (by clausification #[305]): ∀ (a : Iota),
% 72.05/72.27 Eq (And (And (Not (empty_carrier (skS.0 7 a))) (topological_space (skS.0 7 a))) (top_str (skS.0 7 a))) True
% 72.05/72.27 Clause #307 (by clausification #[305]): ∀ (a : Iota),
% 72.05/72.27 Eq
% 72.05/72.27 (∀ (B : Iota),
% 72.05/72.27 element B (powerset (the_carrier (skS.0 7 a))) →
% 72.05/72.27 ∀ (C : Iota),
% 72.05/72.27 element C (the_carrier (skS.0 7 a)) →
% 72.05/72.27 And (open_subset B (skS.0 7 a)) (in C B) → point_neighbourhood B (skS.0 7 a) C)
% 72.05/72.27 False
% 72.05/72.27 Clause #308 (by clausification #[306]): ∀ (a : Iota), Eq (top_str (skS.0 7 a)) True
% 72.05/72.27 Clause #309 (by clausification #[306]): ∀ (a : Iota), Eq (And (Not (empty_carrier (skS.0 7 a))) (topological_space (skS.0 7 a))) True
% 72.05/72.27 Clause #312 (by superposition #[308, 248]): ∀ (a a_1 a_2 : Iota),
% 72.05/72.27 Or (Eq True False)
% 72.05/72.27 (Or (Eq (topological_space (skS.0 7 a)) False)
% 72.05/72.29 (Or (Eq (element a_1 (the_carrier (skS.0 7 a))) False)
% 72.05/72.29 (Or (Eq (empty_carrier (skS.0 7 a)) True)
% 72.05/72.29 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a)))) False)
% 72.05/72.29 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a) a_1) True) (Eq (in a_1 (interior (skS.0 7 a) a_2)) False))))))
% 72.05/72.29 Clause #313 (by clausification #[35]): ∀ (a : Iota),
% 72.05/72.29 Eq
% 72.05/72.29 (And (topological_space a) (top_str a) →
% 72.05/72.29 ∀ (B : Iota),
% 72.05/72.29 top_str B →
% 72.05/72.29 ∀ (C : Iota),
% 72.05/72.29 element C (powerset (the_carrier a)) →
% 72.05/72.29 ∀ (D : Iota),
% 72.05/72.29 element D (powerset (the_carrier B)) →
% 72.05/72.29 And (open_subset D B → Eq (interior B D) D) (Eq (interior a C) C → open_subset C a))
% 72.05/72.29 True
% 72.05/72.29 Clause #314 (by clausification #[313]): ∀ (a : Iota),
% 72.05/72.29 Or (Eq (And (topological_space a) (top_str a)) False)
% 72.05/72.29 (Eq
% 72.05/72.29 (∀ (B : Iota),
% 72.05/72.29 top_str B →
% 72.05/72.29 ∀ (C : Iota),
% 72.05/72.29 element C (powerset (the_carrier a)) →
% 72.05/72.29 ∀ (D : Iota),
% 72.05/72.29 element D (powerset (the_carrier B)) →
% 72.05/72.29 And (open_subset D B → Eq (interior B D) D) (Eq (interior a C) C → open_subset C a))
% 72.05/72.29 True)
% 72.05/72.29 Clause #315 (by clausification #[314]): ∀ (a : Iota),
% 72.05/72.29 Or
% 72.05/72.29 (Eq
% 72.05/72.29 (∀ (B : Iota),
% 72.05/72.29 top_str B →
% 72.05/72.29 ∀ (C : Iota),
% 72.05/72.29 element C (powerset (the_carrier a)) →
% 72.05/72.29 ∀ (D : Iota),
% 72.05/72.29 element D (powerset (the_carrier B)) →
% 72.05/72.29 And (open_subset D B → Eq (interior B D) D) (Eq (interior a C) C → open_subset C a))
% 72.05/72.29 True)
% 72.05/72.29 (Or (Eq (topological_space a) False) (Eq (top_str a) False))
% 72.05/72.29 Clause #316 (by clausification #[315]): ∀ (a a_1 : Iota),
% 72.05/72.29 Or (Eq (topological_space a) False)
% 72.05/72.29 (Or (Eq (top_str a) False)
% 72.05/72.29 (Eq
% 72.05/72.29 (top_str a_1 →
% 72.05/72.29 ∀ (C : Iota),
% 72.05/72.29 element C (powerset (the_carrier a)) →
% 72.05/72.29 ∀ (D : Iota),
% 72.05/72.29 element D (powerset (the_carrier a_1)) →
% 72.05/72.29 And (open_subset D a_1 → Eq (interior a_1 D) D) (Eq (interior a C) C → open_subset C a))
% 72.05/72.29 True))
% 72.05/72.29 Clause #317 (by clausification #[316]): ∀ (a a_1 : Iota),
% 72.05/72.29 Or (Eq (topological_space a) False)
% 72.05/72.29 (Or (Eq (top_str a) False)
% 72.05/72.29 (Or (Eq (top_str a_1) False)
% 72.05/72.29 (Eq
% 72.05/72.29 (∀ (C : Iota),
% 72.05/72.29 element C (powerset (the_carrier a)) →
% 72.05/72.29 ∀ (D : Iota),
% 72.05/72.29 element D (powerset (the_carrier a_1)) →
% 72.05/72.29 And (open_subset D a_1 → Eq (interior a_1 D) D) (Eq (interior a C) C → open_subset C a))
% 72.05/72.29 True)))
% 72.05/72.29 Clause #318 (by clausification #[317]): ∀ (a a_1 a_2 : Iota),
% 72.05/72.29 Or (Eq (topological_space a) False)
% 72.05/72.29 (Or (Eq (top_str a) False)
% 72.05/72.29 (Or (Eq (top_str a_1) False)
% 72.05/72.29 (Eq
% 72.05/72.29 (element a_2 (powerset (the_carrier a)) →
% 72.05/72.29 ∀ (D : Iota),
% 72.05/72.29 element D (powerset (the_carrier a_1)) →
% 72.05/72.29 And (open_subset D a_1 → Eq (interior a_1 D) D) (Eq (interior a a_2) a_2 → open_subset a_2 a))
% 72.05/72.29 True)))
% 72.05/72.29 Clause #319 (by clausification #[318]): ∀ (a a_1 a_2 : Iota),
% 72.05/72.29 Or (Eq (topological_space a) False)
% 72.05/72.29 (Or (Eq (top_str a) False)
% 72.05/72.29 (Or (Eq (top_str a_1) False)
% 72.05/72.29 (Or (Eq (element a_2 (powerset (the_carrier a))) False)
% 72.05/72.29 (Eq
% 72.05/72.29 (∀ (D : Iota),
% 72.05/72.29 element D (powerset (the_carrier a_1)) →
% 72.05/72.29 And (open_subset D a_1 → Eq (interior a_1 D) D) (Eq (interior a a_2) a_2 → open_subset a_2 a))
% 72.05/72.29 True))))
% 72.05/72.29 Clause #320 (by clausification #[319]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.05/72.29 Or (Eq (topological_space a) False)
% 72.05/72.29 (Or (Eq (top_str a) False)
% 72.05/72.29 (Or (Eq (top_str a_1) False)
% 72.05/72.29 (Or (Eq (element a_2 (powerset (the_carrier a))) False)
% 72.05/72.29 (Eq
% 72.05/72.29 (element a_3 (powerset (the_carrier a_1)) →
% 72.05/72.29 And (open_subset a_3 a_1 → Eq (interior a_1 a_3) a_3) (Eq (interior a a_2) a_2 → open_subset a_2 a))
% 72.05/72.29 True))))
% 72.05/72.29 Clause #321 (by clausification #[320]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.05/72.29 Or (Eq (topological_space a) False)
% 72.05/72.29 (Or (Eq (top_str a) False)
% 72.15/72.31 (Or (Eq (top_str a_1) False)
% 72.15/72.31 (Or (Eq (element a_2 (powerset (the_carrier a))) False)
% 72.15/72.31 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False)
% 72.15/72.31 (Eq (And (open_subset a_3 a_1 → Eq (interior a_1 a_3) a_3) (Eq (interior a a_2) a_2 → open_subset a_2 a))
% 72.15/72.31 True)))))
% 72.15/72.31 Clause #323 (by clausification #[321]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.31 Or (Eq (topological_space a) False)
% 72.15/72.31 (Or (Eq (top_str a) False)
% 72.15/72.31 (Or (Eq (top_str a_1) False)
% 72.15/72.31 (Or (Eq (element a_2 (powerset (the_carrier a))) False)
% 72.15/72.31 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False)
% 72.15/72.31 (Eq (open_subset a_3 a_1 → Eq (interior a_1 a_3) a_3) True)))))
% 72.15/72.31 Clause #425 (by clausification #[307]): ∀ (a a_1 : Iota),
% 72.15/72.31 Eq
% 72.15/72.31 (Not
% 72.15/72.31 (element (skS.0 8 a a_1) (powerset (the_carrier (skS.0 7 a))) →
% 72.15/72.31 ∀ (C : Iota),
% 72.15/72.31 element C (the_carrier (skS.0 7 a)) →
% 72.15/72.31 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in C (skS.0 8 a a_1)) →
% 72.15/72.31 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) C))
% 72.15/72.31 True
% 72.15/72.31 Clause #426 (by clausification #[425]): ∀ (a a_1 : Iota),
% 72.15/72.31 Eq
% 72.15/72.31 (element (skS.0 8 a a_1) (powerset (the_carrier (skS.0 7 a))) →
% 72.15/72.31 ∀ (C : Iota),
% 72.15/72.31 element C (the_carrier (skS.0 7 a)) →
% 72.15/72.31 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in C (skS.0 8 a a_1)) →
% 72.15/72.31 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) C)
% 72.15/72.31 False
% 72.15/72.31 Clause #427 (by clausification #[426]): ∀ (a a_1 : Iota), Eq (element (skS.0 8 a a_1) (powerset (the_carrier (skS.0 7 a)))) True
% 72.15/72.31 Clause #428 (by clausification #[426]): ∀ (a a_1 : Iota),
% 72.15/72.31 Eq
% 72.15/72.31 (∀ (C : Iota),
% 72.15/72.31 element C (the_carrier (skS.0 7 a)) →
% 72.15/72.31 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in C (skS.0 8 a a_1)) →
% 72.15/72.31 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) C)
% 72.15/72.31 False
% 72.15/72.31 Clause #515 (by clausification #[309]): ∀ (a : Iota), Eq (topological_space (skS.0 7 a)) True
% 72.15/72.31 Clause #516 (by clausification #[309]): ∀ (a : Iota), Eq (Not (empty_carrier (skS.0 7 a))) True
% 72.15/72.31 Clause #518 (by clausification #[516]): ∀ (a : Iota), Eq (empty_carrier (skS.0 7 a)) False
% 72.15/72.31 Clause #545 (by clausification #[312]): ∀ (a a_1 a_2 : Iota),
% 72.15/72.31 Or (Eq (topological_space (skS.0 7 a)) False)
% 72.15/72.31 (Or (Eq (element a_1 (the_carrier (skS.0 7 a))) False)
% 72.15/72.31 (Or (Eq (empty_carrier (skS.0 7 a)) True)
% 72.15/72.31 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a)))) False)
% 72.15/72.31 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a) a_1) True) (Eq (in a_1 (interior (skS.0 7 a) a_2)) False)))))
% 72.15/72.31 Clause #546 (by forward demodulation #[545, 515]): ∀ (a a_1 a_2 : Iota),
% 72.15/72.31 Or (Eq True False)
% 72.15/72.31 (Or (Eq (element a (the_carrier (skS.0 7 a_1))) False)
% 72.15/72.31 (Or (Eq (empty_carrier (skS.0 7 a_1)) True)
% 72.15/72.31 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.31 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a_1) a) True) (Eq (in a (interior (skS.0 7 a_1) a_2)) False)))))
% 72.15/72.31 Clause #547 (by clausification #[546]): ∀ (a a_1 a_2 : Iota),
% 72.15/72.31 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False)
% 72.15/72.31 (Or (Eq (empty_carrier (skS.0 7 a_1)) True)
% 72.15/72.31 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.31 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a_1) a) True) (Eq (in a (interior (skS.0 7 a_1) a_2)) False))))
% 72.15/72.31 Clause #548 (by forward demodulation #[547, 518]): ∀ (a a_1 a_2 : Iota),
% 72.15/72.31 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False)
% 72.15/72.31 (Or (Eq False True)
% 72.15/72.31 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.31 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a_1) a) True) (Eq (in a (interior (skS.0 7 a_1) a_2)) False))))
% 72.15/72.31 Clause #549 (by clausification #[548]): ∀ (a a_1 a_2 : Iota),
% 72.15/72.31 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False)
% 72.15/72.31 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.31 (Or (Eq (point_neighbourhood a_2 (skS.0 7 a_1) a) True) (Eq (in a (interior (skS.0 7 a_1) a_2)) False)))
% 72.15/72.31 Clause #556 (by clausification #[323]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.31 Or (Eq (topological_space a) False)
% 72.15/72.31 (Or (Eq (top_str a) False)
% 72.15/72.34 (Or (Eq (top_str a_1) False)
% 72.15/72.34 (Or (Eq (element a_2 (powerset (the_carrier a))) False)
% 72.15/72.34 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False)
% 72.15/72.34 (Or (Eq (open_subset a_3 a_1) False) (Eq (Eq (interior a_1 a_3) a_3) True))))))
% 72.15/72.34 Clause #557 (by clausification #[556]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.34 Or (Eq (topological_space a) False)
% 72.15/72.34 (Or (Eq (top_str a) False)
% 72.15/72.34 (Or (Eq (top_str a_1) False)
% 72.15/72.34 (Or (Eq (element a_2 (powerset (the_carrier a))) False)
% 72.15/72.34 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False)
% 72.15/72.34 (Or (Eq (open_subset a_3 a_1) False) (Eq (interior a_1 a_3) a_3))))))
% 72.15/72.34 Clause #558 (by superposition #[557, 515]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.34 Or (Eq (top_str (skS.0 7 a)) False)
% 72.15/72.34 (Or (Eq (top_str a_1) False)
% 72.15/72.34 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a)))) False)
% 72.15/72.34 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False)
% 72.15/72.34 (Or (Eq (open_subset a_3 a_1) False) (Or (Eq (interior a_1 a_3) a_3) (Eq False True))))))
% 72.15/72.34 Clause #562 (by clausification #[428]): ∀ (a a_1 a_2 : Iota),
% 72.15/72.34 Eq
% 72.15/72.34 (Not
% 72.15/72.34 (element (skS.0 9 a a_1 a_2) (the_carrier (skS.0 7 a)) →
% 72.15/72.34 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1)) →
% 72.15/72.34 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)))
% 72.15/72.34 True
% 72.15/72.34 Clause #563 (by clausification #[562]): ∀ (a a_1 a_2 : Iota),
% 72.15/72.34 Eq
% 72.15/72.34 (element (skS.0 9 a a_1 a_2) (the_carrier (skS.0 7 a)) →
% 72.15/72.34 And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1)) →
% 72.15/72.34 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2))
% 72.15/72.34 False
% 72.15/72.34 Clause #564 (by clausification #[563]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 9 a a_1 a_2) (the_carrier (skS.0 7 a))) True
% 72.15/72.34 Clause #565 (by clausification #[563]): ∀ (a a_1 a_2 : Iota),
% 72.15/72.34 Eq
% 72.15/72.34 (And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1)) →
% 72.15/72.34 point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2))
% 72.15/72.34 False
% 72.15/72.34 Clause #568 (by superposition #[564, 549]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.34 Or (Eq True False)
% 72.15/72.34 (Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.34 (Or (Eq (point_neighbourhood a (skS.0 7 a_1) (skS.0 9 a_1 a_2 a_3)) True)
% 72.15/72.34 (Eq (in (skS.0 9 a_1 a_2 a_3) (interior (skS.0 7 a_1) a)) False)))
% 72.15/72.34 Clause #825 (by clausification #[558]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.34 Or (Eq (top_str (skS.0 7 a)) False)
% 72.15/72.34 (Or (Eq (top_str a_1) False)
% 72.15/72.34 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a)))) False)
% 72.15/72.34 (Or (Eq (element a_3 (powerset (the_carrier a_1))) False)
% 72.15/72.34 (Or (Eq (open_subset a_3 a_1) False) (Eq (interior a_1 a_3) a_3)))))
% 72.15/72.34 Clause #826 (by forward demodulation #[825, 308]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.34 Or (Eq True False)
% 72.15/72.34 (Or (Eq (top_str a) False)
% 72.15/72.34 (Or (Eq (element a_1 (powerset (the_carrier (skS.0 7 a_2)))) False)
% 72.15/72.34 (Or (Eq (element a_3 (powerset (the_carrier a))) False)
% 72.15/72.34 (Or (Eq (open_subset a_3 a) False) (Eq (interior a a_3) a_3)))))
% 72.15/72.34 Clause #827 (by clausification #[826]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.34 Or (Eq (top_str a) False)
% 72.15/72.34 (Or (Eq (element a_1 (powerset (the_carrier (skS.0 7 a_2)))) False)
% 72.15/72.34 (Or (Eq (element a_3 (powerset (the_carrier a))) False)
% 72.15/72.34 (Or (Eq (open_subset a_3 a) False) (Eq (interior a a_3) a_3))))
% 72.15/72.34 Clause #829 (by superposition #[827, 308]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.34 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.34 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_3)))) False)
% 72.15/72.34 (Or (Eq (open_subset a_2 (skS.0 7 a_3)) False) (Or (Eq (interior (skS.0 7 a_3) a_2) a_2) (Eq False True))))
% 72.15/72.34 Clause #834 (by clausification #[565]): ∀ (a a_1 a_2 : Iota), Eq (And (open_subset (skS.0 8 a a_1) (skS.0 7 a)) (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1))) True
% 72.15/72.34 Clause #835 (by clausification #[565]): ∀ (a a_1 a_2 : Iota), Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)) False
% 72.15/72.34 Clause #836 (by clausification #[834]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 9 a a_1 a_2) (skS.0 8 a a_1)) True
% 72.15/72.38 Clause #837 (by clausification #[834]): ∀ (a a_1 : Iota), Eq (open_subset (skS.0 8 a a_1) (skS.0 7 a)) True
% 72.15/72.38 Clause #883 (by clausification #[568]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.38 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.38 (Or (Eq (point_neighbourhood a (skS.0 7 a_1) (skS.0 9 a_1 a_2 a_3)) True)
% 72.15/72.38 (Eq (in (skS.0 9 a_1 a_2 a_3) (interior (skS.0 7 a_1) a)) False))
% 72.15/72.38 Clause #885 (by superposition #[883, 427]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.38 Or (Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_2 a_3)) True)
% 72.15/72.38 (Or (Eq (in (skS.0 9 a a_2 a_3) (interior (skS.0 7 a) (skS.0 8 a a_1))) False) (Eq False True))
% 72.15/72.38 Clause #2004 (by clausification #[829]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.38 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.38 (Or (Eq (element a_2 (powerset (the_carrier (skS.0 7 a_3)))) False)
% 72.15/72.38 (Or (Eq (open_subset a_2 (skS.0 7 a_3)) False) (Eq (interior (skS.0 7 a_3) a_2) a_2)))
% 72.15/72.38 Clause #2005 (by superposition #[2004, 235]): ∀ (a a_1 : Iota),
% 72.15/72.38 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.38 (Or (Eq (open_subset a (skS.0 7 a_1)) False) (Or (Eq (interior (skS.0 7 a_1) a) a) (Eq False True)))
% 72.15/72.38 Clause #2011 (by clausification #[2005]): ∀ (a a_1 : Iota),
% 72.15/72.38 Or (Eq (element a (powerset (the_carrier (skS.0 7 a_1)))) False)
% 72.15/72.38 (Or (Eq (open_subset a (skS.0 7 a_1)) False) (Eq (interior (skS.0 7 a_1) a) a))
% 72.15/72.38 Clause #2013 (by superposition #[2011, 427]): ∀ (a a_1 : Iota),
% 72.15/72.38 Or (Eq (open_subset (skS.0 8 a a_1) (skS.0 7 a)) False)
% 72.15/72.38 (Or (Eq (interior (skS.0 7 a) (skS.0 8 a a_1)) (skS.0 8 a a_1)) (Eq False True))
% 72.15/72.38 Clause #2055 (by clausification #[885]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.38 Or (Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_2 a_3)) True)
% 72.15/72.38 (Eq (in (skS.0 9 a a_2 a_3) (interior (skS.0 7 a) (skS.0 8 a a_1))) False)
% 72.15/72.38 Clause #2850 (by clausification #[2013]): ∀ (a a_1 : Iota),
% 72.15/72.38 Or (Eq (open_subset (skS.0 8 a a_1) (skS.0 7 a)) False) (Eq (interior (skS.0 7 a) (skS.0 8 a a_1)) (skS.0 8 a a_1))
% 72.15/72.38 Clause #2851 (by superposition #[2850, 837]): ∀ (a a_1 : Iota), Or (Eq (interior (skS.0 7 a) (skS.0 8 a a_1)) (skS.0 8 a a_1)) (Eq False True)
% 72.15/72.38 Clause #2852 (by clausification #[2851]): ∀ (a a_1 : Iota), Eq (interior (skS.0 7 a) (skS.0 8 a a_1)) (skS.0 8 a a_1)
% 72.15/72.38 Clause #2856 (by backward demodulation #[2852, 2055]): ∀ (a a_1 a_2 a_3 : Iota),
% 72.15/72.38 Or (Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_2 a_3)) True)
% 72.15/72.38 (Eq (in (skS.0 9 a a_2 a_3) (skS.0 8 a a_1)) False)
% 72.15/72.38 Clause #3592 (by superposition #[2856, 836]): ∀ (a a_1 a_2 : Iota), Or (Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)) True) (Eq False True)
% 72.15/72.38 Clause #3593 (by clausification #[3592]): ∀ (a a_1 a_2 : Iota), Eq (point_neighbourhood (skS.0 8 a a_1) (skS.0 7 a) (skS.0 9 a a_1 a_2)) True
% 72.15/72.38 Clause #3594 (by superposition #[3593, 835]): Eq True False
% 72.15/72.38 Clause #3603 (by clausification #[3594]): False
% 72.15/72.38 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------