TSTP Solution File: SEU323+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n012.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 16:41:26 EDT 2023
% Result : Timeout 292.45s 292.75s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU323+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.34 % Computer : n012.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 : Thu Aug 24 01:12:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 292.45/292.75 SZS status Theorem for theBenchmark.p
% 292.45/292.75 SZS output start Proof for theBenchmark.p
% 292.45/292.75 Clause #0 (by assumption #[]): Eq
% 292.45/292.75 (∀ (A B : Iota),
% 292.45/292.75 And (And (And (topological_space A) (top_str A)) (closed_subset B A)) (element B (powerset (the_carrier A))) →
% 292.45/292.75 open_subset (subset_complement (the_carrier A) B) A)
% 292.45/292.75 True
% 292.45/292.75 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), element B (powerset A) → element (subset_complement A B) (powerset A)) True
% 292.45/292.75 Clause #6 (by assumption #[]): Eq
% 292.45/292.75 (∀ (A B : Iota),
% 292.45/292.75 And (top_str A) (element B (powerset (the_carrier A))) → element (topstr_closure A B) (powerset (the_carrier A)))
% 292.45/292.75 True
% 292.45/292.75 Clause #8 (by assumption #[]): Eq
% 292.45/292.75 (∀ (A B : Iota),
% 292.45/292.75 And (And (topological_space A) (top_str A)) (element B (powerset (the_carrier A))) →
% 292.45/292.75 closed_subset (topstr_closure A B) A)
% 292.45/292.75 True
% 292.45/292.75 Clause #16 (by assumption #[]): Eq
% 292.45/292.75 (∀ (A : Iota),
% 292.45/292.75 top_str A →
% 292.45/292.75 ∀ (B : Iota),
% 292.45/292.75 element B (powerset (the_carrier A)) →
% 292.45/292.75 Eq (interior A B)
% 292.45/292.75 (subset_complement (the_carrier A) (topstr_closure A (subset_complement (the_carrier A) B))))
% 292.45/292.75 True
% 292.45/292.75 Clause #17 (by assumption #[]): Eq
% 292.45/292.75 (Not
% 292.45/292.75 (∀ (A : Iota),
% 292.45/292.75 And (topological_space A) (top_str A) →
% 292.45/292.75 ∀ (B : Iota), element B (powerset (the_carrier A)) → open_subset (interior A B) A))
% 292.45/292.75 True
% 292.45/292.75 Clause #27 (by clausification #[0]): ∀ (a : Iota),
% 292.45/292.75 Eq
% 292.45/292.75 (∀ (B : Iota),
% 292.45/292.75 And (And (And (topological_space a) (top_str a)) (closed_subset B a)) (element B (powerset (the_carrier a))) →
% 292.45/292.75 open_subset (subset_complement (the_carrier a) B) a)
% 292.45/292.75 True
% 292.45/292.75 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota),
% 292.45/292.75 Eq
% 292.45/292.75 (And (And (And (topological_space a) (top_str a)) (closed_subset a_1 a)) (element a_1 (powerset (the_carrier a))) →
% 292.45/292.75 open_subset (subset_complement (the_carrier a) a_1) a)
% 292.45/292.75 True
% 292.45/292.75 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota),
% 292.45/292.75 Or
% 292.45/292.75 (Eq
% 292.45/292.75 (And (And (And (topological_space a) (top_str a)) (closed_subset a_1 a)) (element a_1 (powerset (the_carrier a))))
% 292.45/292.75 False)
% 292.45/292.75 (Eq (open_subset (subset_complement (the_carrier a) a_1) a) True)
% 292.45/292.75 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota),
% 292.45/292.75 Or (Eq (open_subset (subset_complement (the_carrier a) a_1) a) True)
% 292.45/292.75 (Or (Eq (And (And (topological_space a) (top_str a)) (closed_subset a_1 a)) False)
% 292.45/292.75 (Eq (element a_1 (powerset (the_carrier a))) False))
% 292.45/292.75 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota),
% 292.45/292.75 Or (Eq (open_subset (subset_complement (the_carrier a) a_1) a) True)
% 292.45/292.75 (Or (Eq (element a_1 (powerset (the_carrier a))) False)
% 292.45/292.75 (Or (Eq (And (topological_space a) (top_str a)) False) (Eq (closed_subset a_1 a) False)))
% 292.45/292.75 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota),
% 292.45/292.75 Or (Eq (open_subset (subset_complement (the_carrier a) a_1) a) True)
% 292.45/292.75 (Or (Eq (element a_1 (powerset (the_carrier a))) False)
% 292.45/292.75 (Or (Eq (closed_subset a_1 a) False) (Or (Eq (topological_space a) False) (Eq (top_str a) False))))
% 292.45/292.75 Clause #36 (by clausification #[8]): ∀ (a : Iota),
% 292.45/292.75 Eq
% 292.45/292.75 (∀ (B : Iota),
% 292.45/292.75 And (And (topological_space a) (top_str a)) (element B (powerset (the_carrier a))) →
% 292.45/292.75 closed_subset (topstr_closure a B) a)
% 292.45/292.75 True
% 292.45/292.75 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 292.45/292.75 Eq
% 292.45/292.75 (And (And (topological_space a) (top_str a)) (element a_1 (powerset (the_carrier a))) →
% 292.45/292.75 closed_subset (topstr_closure a a_1) a)
% 292.45/292.75 True
% 292.45/292.75 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota),
% 292.45/292.75 Or (Eq (And (And (topological_space a) (top_str a)) (element a_1 (powerset (the_carrier a)))) False)
% 292.45/292.75 (Eq (closed_subset (topstr_closure a a_1) a) True)
% 292.45/292.75 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota),
% 292.45/292.75 Or (Eq (closed_subset (topstr_closure a a_1) a) True)
% 292.45/292.75 (Or (Eq (And (topological_space a) (top_str a)) False) (Eq (element a_1 (powerset (the_carrier a))) False))
% 292.45/292.75 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 292.45/292.75 Or (Eq (closed_subset (topstr_closure a a_1) a) True)
% 292.45/292.75 (Or (Eq (element a_1 (powerset (the_carrier a))) False)
% 292.45/292.75 (Or (Eq (topological_space a) False) (Eq (top_str a) False)))
% 292.51/292.78 Clause #49 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), element B (powerset a) → element (subset_complement a B) (powerset a)) True
% 292.51/292.78 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Eq (element a (powerset a_1) → element (subset_complement a_1 a) (powerset a_1)) True
% 292.51/292.78 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (element a (powerset a_1)) False) (Eq (element (subset_complement a_1 a) (powerset a_1)) True)
% 292.51/292.78 Clause #60 (by clausification #[17]): Eq
% 292.51/292.78 (∀ (A : Iota),
% 292.51/292.78 And (topological_space A) (top_str A) →
% 292.51/292.78 ∀ (B : Iota), element B (powerset (the_carrier A)) → open_subset (interior A B) A)
% 292.51/292.78 False
% 292.51/292.78 Clause #61 (by clausification #[60]): ∀ (a : Iota),
% 292.51/292.78 Eq
% 292.51/292.78 (Not
% 292.51/292.78 (And (topological_space (skS.0 4 a)) (top_str (skS.0 4 a)) →
% 292.51/292.78 ∀ (B : Iota),
% 292.51/292.78 element B (powerset (the_carrier (skS.0 4 a))) → open_subset (interior (skS.0 4 a) B) (skS.0 4 a)))
% 292.51/292.78 True
% 292.51/292.78 Clause #62 (by clausification #[61]): ∀ (a : Iota),
% 292.51/292.78 Eq
% 292.51/292.78 (And (topological_space (skS.0 4 a)) (top_str (skS.0 4 a)) →
% 292.51/292.78 ∀ (B : Iota), element B (powerset (the_carrier (skS.0 4 a))) → open_subset (interior (skS.0 4 a) B) (skS.0 4 a))
% 292.51/292.78 False
% 292.51/292.78 Clause #63 (by clausification #[62]): ∀ (a : Iota), Eq (And (topological_space (skS.0 4 a)) (top_str (skS.0 4 a))) True
% 292.51/292.78 Clause #64 (by clausification #[62]): ∀ (a : Iota),
% 292.51/292.78 Eq (∀ (B : Iota), element B (powerset (the_carrier (skS.0 4 a))) → open_subset (interior (skS.0 4 a) B) (skS.0 4 a))
% 292.51/292.78 False
% 292.51/292.78 Clause #65 (by clausification #[63]): ∀ (a : Iota), Eq (top_str (skS.0 4 a)) True
% 292.51/292.78 Clause #66 (by clausification #[63]): ∀ (a : Iota), Eq (topological_space (skS.0 4 a)) True
% 292.51/292.78 Clause #99 (by clausification #[6]): ∀ (a : Iota),
% 292.51/292.78 Eq
% 292.51/292.78 (∀ (B : Iota),
% 292.51/292.78 And (top_str a) (element B (powerset (the_carrier a))) → element (topstr_closure a B) (powerset (the_carrier a)))
% 292.51/292.78 True
% 292.51/292.78 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota),
% 292.51/292.78 Eq
% 292.51/292.78 (And (top_str a) (element a_1 (powerset (the_carrier a))) →
% 292.51/292.78 element (topstr_closure a a_1) (powerset (the_carrier a)))
% 292.51/292.78 True
% 292.51/292.78 Clause #101 (by clausification #[100]): ∀ (a a_1 : Iota),
% 292.51/292.78 Or (Eq (And (top_str a) (element a_1 (powerset (the_carrier a)))) False)
% 292.51/292.78 (Eq (element (topstr_closure a a_1) (powerset (the_carrier a))) True)
% 292.51/292.78 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota),
% 292.51/292.78 Or (Eq (element (topstr_closure a a_1) (powerset (the_carrier a))) True)
% 292.51/292.78 (Or (Eq (top_str a) False) (Eq (element a_1 (powerset (the_carrier a))) False))
% 292.51/292.78 Clause #104 (by superposition #[102, 65]): ∀ (a a_1 : Iota),
% 292.51/292.78 Or (Eq (element (topstr_closure (skS.0 4 a) a_1) (powerset (the_carrier (skS.0 4 a)))) True)
% 292.51/292.78 (Or (Eq (element a_1 (powerset (the_carrier (skS.0 4 a)))) False) (Eq False True))
% 292.51/292.78 Clause #135 (by clausification #[16]): ∀ (a : Iota),
% 292.51/292.78 Eq
% 292.51/292.78 (top_str a →
% 292.51/292.78 ∀ (B : Iota),
% 292.51/292.78 element B (powerset (the_carrier a)) →
% 292.51/292.78 Eq (interior a B)
% 292.51/292.78 (subset_complement (the_carrier a) (topstr_closure a (subset_complement (the_carrier a) B))))
% 292.51/292.78 True
% 292.51/292.78 Clause #136 (by clausification #[135]): ∀ (a : Iota),
% 292.51/292.78 Or (Eq (top_str a) False)
% 292.51/292.78 (Eq
% 292.51/292.78 (∀ (B : Iota),
% 292.51/292.78 element B (powerset (the_carrier a)) →
% 292.51/292.78 Eq (interior a B)
% 292.51/292.78 (subset_complement (the_carrier a) (topstr_closure a (subset_complement (the_carrier a) B))))
% 292.51/292.78 True)
% 292.51/292.78 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota),
% 292.51/292.78 Or (Eq (top_str a) False)
% 292.51/292.78 (Eq
% 292.51/292.78 (element a_1 (powerset (the_carrier a)) →
% 292.51/292.78 Eq (interior a a_1)
% 292.51/292.78 (subset_complement (the_carrier a) (topstr_closure a (subset_complement (the_carrier a) a_1))))
% 292.51/292.78 True)
% 292.51/292.78 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota),
% 292.51/292.78 Or (Eq (top_str a) False)
% 292.51/292.78 (Or (Eq (element a_1 (powerset (the_carrier a))) False)
% 292.51/292.78 (Eq
% 292.51/292.78 (Eq (interior a a_1)
% 292.51/292.78 (subset_complement (the_carrier a) (topstr_closure a (subset_complement (the_carrier a) a_1))))
% 292.51/292.78 True))
% 292.51/292.78 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota),
% 292.51/292.78 Or (Eq (top_str a) False)
% 292.51/292.78 (Or (Eq (element a_1 (powerset (the_carrier a))) False)
% 292.51/292.80 (Eq (interior a a_1)
% 292.51/292.80 (subset_complement (the_carrier a) (topstr_closure a (subset_complement (the_carrier a) a_1)))))
% 292.51/292.80 Clause #141 (by superposition #[139, 65]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or (Eq (element a (powerset (the_carrier (skS.0 4 a_1)))) False)
% 292.51/292.80 (Or
% 292.51/292.80 (Eq (interior (skS.0 4 a_1) a)
% 292.51/292.80 (subset_complement (the_carrier (skS.0 4 a_1))
% 292.51/292.80 (topstr_closure (skS.0 4 a_1) (subset_complement (the_carrier (skS.0 4 a_1)) a))))
% 292.51/292.80 (Eq False True))
% 292.51/292.80 Clause #142 (by clausification #[64]): ∀ (a a_1 : Iota),
% 292.51/292.80 Eq
% 292.51/292.80 (Not
% 292.51/292.80 (element (skS.0 6 a a_1) (powerset (the_carrier (skS.0 4 a))) →
% 292.51/292.80 open_subset (interior (skS.0 4 a) (skS.0 6 a a_1)) (skS.0 4 a)))
% 292.51/292.80 True
% 292.51/292.80 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota),
% 292.51/292.80 Eq
% 292.51/292.80 (element (skS.0 6 a a_1) (powerset (the_carrier (skS.0 4 a))) →
% 292.51/292.80 open_subset (interior (skS.0 4 a) (skS.0 6 a a_1)) (skS.0 4 a))
% 292.51/292.80 False
% 292.51/292.80 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota), Eq (element (skS.0 6 a a_1) (powerset (the_carrier (skS.0 4 a)))) True
% 292.51/292.80 Clause #145 (by clausification #[143]): ∀ (a a_1 : Iota), Eq (open_subset (interior (skS.0 4 a) (skS.0 6 a a_1)) (skS.0 4 a)) False
% 292.51/292.80 Clause #149 (by superposition #[144, 51]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or (Eq True False)
% 292.51/292.80 (Eq (element (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)) (powerset (the_carrier (skS.0 4 a))))
% 292.51/292.80 True)
% 292.51/292.80 Clause #202 (by clausification #[149]): ∀ (a a_1 : Iota),
% 292.51/292.80 Eq (element (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)) (powerset (the_carrier (skS.0 4 a)))) True
% 292.51/292.80 Clause #204 (by superposition #[202, 40]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or
% 292.51/292.80 (Eq
% 292.51/292.80 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.80 (skS.0 4 a))
% 292.51/292.80 True)
% 292.51/292.80 (Or (Eq True False) (Or (Eq (topological_space (skS.0 4 a)) False) (Eq (top_str (skS.0 4 a)) False)))
% 292.51/292.80 Clause #228 (by clausification #[104]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or (Eq (element (topstr_closure (skS.0 4 a) a_1) (powerset (the_carrier (skS.0 4 a)))) True)
% 292.51/292.80 (Eq (element a_1 (powerset (the_carrier (skS.0 4 a)))) False)
% 292.51/292.80 Clause #232 (by superposition #[228, 202]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or
% 292.51/292.80 (Eq
% 292.51/292.80 (element (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.80 (powerset (the_carrier (skS.0 4 a))))
% 292.51/292.80 True)
% 292.51/292.80 (Eq False True)
% 292.51/292.80 Clause #400 (by clausification #[141]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or (Eq (element a (powerset (the_carrier (skS.0 4 a_1)))) False)
% 292.51/292.80 (Eq (interior (skS.0 4 a_1) a)
% 292.51/292.80 (subset_complement (the_carrier (skS.0 4 a_1))
% 292.51/292.80 (topstr_closure (skS.0 4 a_1) (subset_complement (the_carrier (skS.0 4 a_1)) a))))
% 292.51/292.80 Clause #403 (by superposition #[400, 144]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or
% 292.51/292.80 (Eq (interior (skS.0 4 a) (skS.0 6 a a_1))
% 292.51/292.80 (subset_complement (the_carrier (skS.0 4 a))
% 292.51/292.80 (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))))
% 292.51/292.80 (Eq False True)
% 292.51/292.80 Clause #789 (by clausification #[232]): ∀ (a a_1 : Iota),
% 292.51/292.80 Eq
% 292.51/292.80 (element (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.80 (powerset (the_carrier (skS.0 4 a))))
% 292.51/292.80 True
% 292.51/292.80 Clause #790 (by superposition #[789, 32]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or
% 292.51/292.80 (Eq
% 292.51/292.80 (open_subset
% 292.51/292.80 (subset_complement (the_carrier (skS.0 4 a))
% 292.51/292.80 (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1))))
% 292.51/292.80 (skS.0 4 a))
% 292.51/292.80 True)
% 292.51/292.80 (Or (Eq True False)
% 292.51/292.80 (Or
% 292.51/292.80 (Eq
% 292.51/292.80 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.80 (skS.0 4 a))
% 292.51/292.80 False)
% 292.51/292.80 (Or (Eq (topological_space (skS.0 4 a)) False) (Eq (top_str (skS.0 4 a)) False))))
% 292.51/292.80 Clause #866 (by clausification #[204]): ∀ (a a_1 : Iota),
% 292.51/292.80 Or
% 292.51/292.80 (Eq
% 292.51/292.80 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.80 (skS.0 4 a))
% 292.51/292.80 True)
% 292.51/292.80 (Or (Eq (topological_space (skS.0 4 a)) False) (Eq (top_str (skS.0 4 a)) False))
% 292.51/292.87 Clause #867 (by forward demodulation #[866, 66]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 True)
% 292.51/292.87 (Or (Eq True False) (Eq (top_str (skS.0 4 a)) False))
% 292.51/292.87 Clause #868 (by clausification #[867]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 True)
% 292.51/292.87 (Eq (top_str (skS.0 4 a)) False)
% 292.51/292.87 Clause #869 (by forward demodulation #[868, 65]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 True)
% 292.51/292.87 (Eq True False)
% 292.51/292.87 Clause #870 (by clausification #[869]): ∀ (a a_1 : Iota),
% 292.51/292.87 Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 True
% 292.51/292.87 Clause #2772 (by clausification #[403]): ∀ (a a_1 : Iota),
% 292.51/292.87 Eq (interior (skS.0 4 a) (skS.0 6 a a_1))
% 292.51/292.87 (subset_complement (the_carrier (skS.0 4 a))
% 292.51/292.87 (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1))))
% 292.51/292.87 Clause #6670 (by clausification #[790]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or
% 292.51/292.87 (Eq
% 292.51/292.87 (open_subset
% 292.51/292.87 (subset_complement (the_carrier (skS.0 4 a))
% 292.51/292.87 (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1))))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 True)
% 292.51/292.87 (Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 False)
% 292.51/292.87 (Or (Eq (topological_space (skS.0 4 a)) False) (Eq (top_str (skS.0 4 a)) False)))
% 292.51/292.87 Clause #6671 (by forward demodulation #[6670, 2772]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or (Eq (open_subset (interior (skS.0 4 a) (skS.0 6 a a_1)) (skS.0 4 a)) True)
% 292.51/292.87 (Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 False)
% 292.51/292.87 (Or (Eq (topological_space (skS.0 4 a)) False) (Eq (top_str (skS.0 4 a)) False)))
% 292.51/292.87 Clause #6672 (by forward demodulation #[6671, 145]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or (Eq False True)
% 292.51/292.87 (Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 False)
% 292.51/292.87 (Or (Eq (topological_space (skS.0 4 a)) False) (Eq (top_str (skS.0 4 a)) False)))
% 292.51/292.87 Clause #6673 (by clausification #[6672]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 False)
% 292.51/292.87 (Or (Eq (topological_space (skS.0 4 a)) False) (Eq (top_str (skS.0 4 a)) False))
% 292.51/292.87 Clause #6674 (by forward demodulation #[6673, 66]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 False)
% 292.51/292.87 (Or (Eq True False) (Eq (top_str (skS.0 4 a)) False))
% 292.51/292.87 Clause #6675 (by clausification #[6674]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 False)
% 292.51/292.87 (Eq (top_str (skS.0 4 a)) False)
% 292.51/292.87 Clause #6676 (by forward demodulation #[6675, 65]): ∀ (a a_1 : Iota),
% 292.51/292.87 Or
% 292.51/292.87 (Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 False)
% 292.51/292.87 (Eq True False)
% 292.51/292.87 Clause #6677 (by clausification #[6676]): ∀ (a a_1 : Iota),
% 292.51/292.87 Eq
% 292.51/292.87 (closed_subset (topstr_closure (skS.0 4 a) (subset_complement (the_carrier (skS.0 4 a)) (skS.0 6 a a_1)))
% 292.51/292.87 (skS.0 4 a))
% 292.51/292.87 False
% 292.51/292.87 Clause #6678 (by superposition #[6677, 870]): Eq False True
% 292.51/292.87 Clause #6679 (by clausification #[6678]): False
% 292.51/292.87 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------