%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:22:20 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:11:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.41 fof(f1,axiom,(
% 0.09/0.41 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) )) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f2,axiom,(
% 0.09/0.41 (! [A,B] :( ( top_str(A)& element(B,powerset(the_carrier(A))) )=> element(interior(A,B),powerset(the_carrier(A))) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f4,axiom,(
% 0.09/0.41 (! [A,B] :( element(B,powerset(A))=> element(subset_complement(A,B),powerset(A)) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f5,axiom,(
% 0.09/0.41 (! [A,B] :( ( top_str(A)& element(B,powerset(the_carrier(A))) )=> element(topstr_closure(A,B),powerset(the_carrier(A))) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f12,axiom,(
% 0.09/0.41 (! [A] :(? [B] : element(B,A) ))),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f13,axiom,(
% 0.09/0.41 (! [A,B] :( ( topological_space(A)& top_str(A)& element(B,powerset(the_carrier(A))) )=> closed_subset(topstr_closure(A,B),A) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f14,axiom,(
% 0.09/0.41 (! [A,B] :( ( topological_space(A)& top_str(A)& closed_subset(B,A)& element(B,powerset(the_carrier(A))) )=> open_subset(subset_complement(the_carrier(A),B),A) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f16,axiom,(
% 0.09/0.41 (! [A,B] :( ( topological_space(A)& top_str(A)& element(B,powerset(the_carrier(A))) )=> open_subset(interior(A,B),A) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f17,axiom,(
% 0.09/0.41 (! [A,B] :( element(B,powerset(A))=> subset_complement(A,subset_complement(A,B)) = B ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f18,axiom,(
% 0.09/0.41 (! [A] :( ( topological_space(A)& top_str(A) )=> (? [B] :( element(B,powerset(the_carrier(A)))& open_subset(B,A) ) )) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f19,axiom,(
% 0.09/0.41 (! [A] :( ( topological_space(A)& top_str(A) )=> (? [B] :( element(B,powerset(the_carrier(A)))& open_subset(B,A)& closed_subset(B,A) ) )) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f20,axiom,(
% 0.09/0.41 (! [A] :( ( topological_space(A)& top_str(A) )=> (? [B] :( element(B,powerset(the_carrier(A)))& closed_subset(B,A) ) )) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f22,axiom,(
% 0.09/0.41 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( open_subset(B,A)<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) )) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f24,axiom,(
% 0.09/0.41 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( ( closed_subset(B,A)=> topstr_closure(A,B) = B )& ( ( topological_space(A)& topstr_closure(A,B) = B )=> closed_subset(B,A) ) ) ) )) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f25,conjecture,(
% 0.09/0.41 (! [A] :( ( topological_space(A)& top_str(A) )=> (! [B] :( top_str(B)=> (! [C] :( element(C,powerset(the_carrier(A)))=> (! [D] :( element(D,powerset(the_carrier(B)))=> ( ( open_subset(D,B)=> interior(B,D) = D )& ( interior(A,C) = C=> open_subset(C,A) ) ) ) )) )) )) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f26,negated_conjecture,(
% 0.09/0.41 ~((! [A] :( ( topological_space(A)& top_str(A) )=> (! [B] :( top_str(B)=> (! [C] :( element(C,powerset(the_carrier(A)))=> (! [D] :( element(D,powerset(the_carrier(B)))=> ( ( open_subset(D,B)=> interior(B,D) = D )& ( interior(A,C) = C=> open_subset(C,A) ) ) ) )) )) )) ))),
% 0.09/0.41 inference(negated_conjecture,[status(cth)],[f25])).
% 0.09/0.41 fof(f27,plain,(
% 0.09/0.41 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|interior(A,B)=subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.09/0.41 fof(f28,plain,(
% 0.09/0.41 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|interior(X0,X1)=subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f27])).
% 0.09/0.41 fof(f29,plain,(
% 0.09/0.41 ![A,B]: ((~top_str(A)|~element(B,powerset(the_carrier(A))))|element(interior(A,B),powerset(the_carrier(A))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.09/0.41 fof(f30,plain,(
% 0.09/0.41 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|element(interior(X0,X1),powerset(the_carrier(X0))))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f29])).
% 0.09/0.41 fof(f31,plain,(
% 0.09/0.41 ![A,B]: (~element(B,powerset(A))|element(subset_complement(A,B),powerset(A)))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.09/0.41 fof(f32,plain,(
% 0.09/0.41 ![X0,X1]: (~element(X0,powerset(X1))|element(subset_complement(X1,X0),powerset(X1)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.41 fof(f33,plain,(
% 0.09/0.41 ![A,B]: ((~top_str(A)|~element(B,powerset(the_carrier(A))))|element(topstr_closure(A,B),powerset(the_carrier(A))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.09/0.41 fof(f34,plain,(
% 0.09/0.41 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|element(topstr_closure(X0,X1),powerset(the_carrier(X0))))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.41 fof(f41,plain,(
% 0.09/0.41 ![A]: element(sK2_skl(A),A)),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B,sK2_skl(A))],[f12])).
% 0.09/0.41 fof(f42,plain,(
% 0.09/0.41 ![X0]: (element(sK2_skl(X0),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f41])).
% 0.09/0.41 fof(f43,plain,(
% 0.09/0.41 ![A,B]: (((~topological_space(A)|~top_str(A))|~element(B,powerset(the_carrier(A))))|closed_subset(topstr_closure(A,B),A))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.09/0.41 fof(f44,plain,(
% 0.09/0.41 ![X0,X1]: (~topological_space(X0)|~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|closed_subset(topstr_closure(X0,X1),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f43])).
% 0.09/0.41 fof(f45,plain,(
% 0.09/0.41 ![A,B]: ((((~topological_space(A)|~top_str(A))|~closed_subset(B,A))|~element(B,powerset(the_carrier(A))))|open_subset(subset_complement(the_carrier(A),B),A))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.09/0.41 fof(f46,plain,(
% 0.09/0.41 ![X0,X1]: (~topological_space(X0)|~top_str(X0)|~closed_subset(X1,X0)|~element(X1,powerset(the_carrier(X0)))|open_subset(subset_complement(the_carrier(X0),X1),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f45])).
% 0.09/0.41 fof(f49,plain,(
% 0.09/0.41 ![A,B]: (((~topological_space(A)|~top_str(A))|~element(B,powerset(the_carrier(A))))|open_subset(interior(A,B),A))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.09/0.41 fof(f50,plain,(
% 0.09/0.41 ![X0,X1]: (~topological_space(X0)|~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|open_subset(interior(X0,X1),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f49])).
% 0.09/0.41 fof(f51,plain,(
% 0.09/0.41 ![A,B]: (~element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B)),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.09/0.41 fof(f52,plain,(
% 0.09/0.41 ![X0,X1]: (~element(X0,powerset(X1))|subset_complement(X1,subset_complement(X1,X0))=X0)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f51])).
% 0.09/0.41 fof(f53,plain,(
% 0.09/0.41 ![A]: ((~topological_space(A)|~top_str(A))|(?[B]: (element(B,powerset(the_carrier(A)))&open_subset(B,A))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.09/0.41 fof(f54,plain,(
% 0.09/0.41 ![A]: ((~topological_space(A)|~top_str(A))|(element(sK3_skl(A),powerset(the_carrier(A)))&open_subset(sK3_skl(A),A)))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl(A))],[f53])).
% 0.09/0.41 fof(f55,plain,(
% 0.09/0.41 ![X0]: (~topological_space(X0)|~top_str(X0)|element(sK3_skl(X0),powerset(the_carrier(X0))))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f54])).
% 0.09/0.41 fof(f56,plain,(
% 0.09/0.41 ![X0]: (~topological_space(X0)|~top_str(X0)|open_subset(sK3_skl(X0),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f54])).
% 0.09/0.41 fof(f57,plain,(
% 0.09/0.41 ![A]: ((~topological_space(A)|~top_str(A))|(?[B]: ((element(B,powerset(the_carrier(A)))&open_subset(B,A))&closed_subset(B,A))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.09/0.41 fof(f58,plain,(
% 0.09/0.41 ![A]: ((~topological_space(A)|~top_str(A))|((element(sK4_skl(A),powerset(the_carrier(A)))&open_subset(sK4_skl(A),A))&closed_subset(sK4_skl(A),A)))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(B,sK4_skl(A))],[f57])).
% 0.09/0.41 fof(f59,plain,(
% 0.09/0.41 ![X0]: (~topological_space(X0)|~top_str(X0)|element(sK4_skl(X0),powerset(the_carrier(X0))))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f58])).
% 0.09/0.41 fof(f60,plain,(
% 0.09/0.41 ![X0]: (~topological_space(X0)|~top_str(X0)|open_subset(sK4_skl(X0),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f58])).
% 0.09/0.41 fof(f61,plain,(
% 0.09/0.41 ![X0]: (~topological_space(X0)|~top_str(X0)|closed_subset(sK4_skl(X0),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f58])).
% 0.09/0.41 fof(f62,plain,(
% 0.09/0.41 ![A]: ((~topological_space(A)|~top_str(A))|(?[B]: (element(B,powerset(the_carrier(A)))&closed_subset(B,A))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.09/0.41 fof(f63,plain,(
% 0.09/0.41 ![A]: ((~topological_space(A)|~top_str(A))|(element(sK5_skl(A),powerset(the_carrier(A)))&closed_subset(sK5_skl(A),A)))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(B,sK5_skl(A))],[f62])).
% 0.09/0.41 fof(f64,plain,(
% 0.09/0.41 ![X0]: (~topological_space(X0)|~top_str(X0)|element(sK5_skl(X0),powerset(the_carrier(X0))))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f63])).
% 0.09/0.41 fof(f65,plain,(
% 0.09/0.41 ![X0]: (~topological_space(X0)|~top_str(X0)|closed_subset(sK5_skl(X0),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f63])).
% 0.09/0.41 fof(f68,plain,(
% 0.09/0.41 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|(open_subset(B,A)<=>closed_subset(subset_complement(the_carrier(A),B),A)))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.09/0.41 fof(f69,plain,(
% 0.09/0.41 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|((~open_subset(B,A)|closed_subset(subset_complement(the_carrier(A),B),A))&(open_subset(B,A)|~closed_subset(subset_complement(the_carrier(A),B),A))))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f68])).
% 0.09/0.41 fof(f70,plain,(
% 0.09/0.41 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~open_subset(X1,X0)|closed_subset(subset_complement(the_carrier(X0),X1),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f69])).
% 0.09/0.41 fof(f71,plain,(
% 0.09/0.41 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|open_subset(X1,X0)|~closed_subset(subset_complement(the_carrier(X0),X1),X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f69])).
% 0.09/0.41 fof(f76,plain,(
% 0.09/0.41 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|((~closed_subset(B,A)|topstr_closure(A,B)=B)&((~topological_space(A)|~topstr_closure(A,B)=B)|closed_subset(B,A))))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.09/0.41 fof(f77,plain,(
% 0.09/0.41 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~closed_subset(X1,X0)|topstr_closure(X0,X1)=X1)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f76])).
% 0.09/0.41 fof(f78,plain,(
% 0.09/0.41 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~topological_space(X0)|~topstr_closure(X0,X1)=X1|closed_subset(X1,X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f76])).
% 0.09/0.41 fof(f79,plain,(
% 0.09/0.41 (?[A]: ((topological_space(A)&top_str(A))&(?[B]: (top_str(B)&(?[C]: (element(C,powerset(the_carrier(A)))&(?[D]: (element(D,powerset(the_carrier(B)))&((open_subset(D,B)&~interior(B,D)=D)|(interior(A,C)=C&~open_subset(C,A)))))))))))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 0.09/0.41 fof(f80,definition,(
% 0.09/0.41 ![B,D]: (sP0_prd(D,B)<=>(open_subset(D,B)&~interior(B,D)=D))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.41 fof(f81,plain,(
% 0.09/0.41 ?[A]: ((topological_space(A)&top_str(A))&(?[B]: (top_str(B)&(?[C]: (element(C,powerset(the_carrier(A)))&(?[D]: (element(D,powerset(the_carrier(B)))&(sP0_prd(D,B)|(interior(A,C)=C&~open_subset(C,A))))))))))),
% 0.09/0.41 inference(formula_renaming,[status(thm)],[f79,f80])).
% 0.09/0.41 fof(f82,plain,(
% 0.09/0.41 ((topological_space(sK6_skl)&top_str(sK6_skl))&(top_str(sK7_skl)&(element(sK8_skl,powerset(the_carrier(sK6_skl)))&(element(sK9_skl,powerset(the_carrier(sK7_skl)))&(sP0_prd(sK9_skl,sK7_skl)|(interior(sK6_skl,sK8_skl)=sK8_skl&~open_subset(sK8_skl,sK6_skl)))))))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl),skolemize(C,sK8_skl),skolemize(D,sK9_skl)],[f81])).
% 0.09/0.41 fof(f83,plain,(
% 0.09/0.41 topological_space(sK6_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f82])).
% 0.09/0.41 fof(f84,plain,(
% 0.09/0.41 top_str(sK6_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f82])).
% 0.09/0.41 fof(f85,plain,(
% 0.09/0.41 top_str(sK7_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f82])).
% 0.09/0.41 fof(f86,plain,(
% 0.09/0.41 element(sK8_skl,powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f82])).
% 0.09/0.41 fof(f87,plain,(
% 0.09/0.41 element(sK9_skl,powerset(the_carrier(sK7_skl)))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f82])).
% 0.09/0.41 fof(f88,plain,(
% 0.09/0.41 sP0_prd(sK9_skl,sK7_skl)|interior(sK6_skl,sK8_skl)=sK8_skl),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f82])).
% 0.09/0.41 fof(f89,plain,(
% 0.09/0.41 sP0_prd(sK9_skl,sK7_skl)|~open_subset(sK8_skl,sK6_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f82])).
% 0.09/0.41 fof(f90,plain,(
% 0.09/0.41 ![B,D]: ((~sP0_prd(D,B)|(open_subset(D,B)&~interior(B,D)=D))&(sP0_prd(D,B)|(~open_subset(D,B)|interior(B,D)=D)))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f80])).
% 0.09/0.41 fof(f91,plain,(
% 0.09/0.41 (![B,D]: (~sP0_prd(D,B)|(open_subset(D,B)&~interior(B,D)=D)))&(![B,D]: (sP0_prd(D,B)|(~open_subset(D,B)|interior(B,D)=D)))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f90])).
% 0.09/0.41 fof(f92,plain,(
% 0.09/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|open_subset(X0,X1))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f91])).
% 0.09/0.41 fof(f93,plain,(
% 0.09/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|~interior(X1,X0)=X0)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f91])).
% 0.09/0.41 fof(f95,definition,(
% 0.09/0.41 sQ0_spl <=> (sP0_prd(sK9_skl,sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f96,plain,(
% 0.09/0.41 sP0_prd(sK9_skl,sK7_skl)|~sQ0_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f95])).
% 0.09/0.41 fof(f98,definition,(
% 0.09/0.41 sQ1_spl <=> (interior(sK6_skl,sK8_skl)=sK8_skl)),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f99,plain,(
% 0.09/0.41 interior(sK6_skl,sK8_skl)=sK8_skl|~sQ1_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f98])).
% 0.09/0.41 fof(f101,plain,(
% 0.09/0.41 sQ0_spl|sQ1_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f88,f95,f98])).
% 0.09/0.41 fof(f102,definition,(
% 0.09/0.41 sQ2_spl <=> (open_subset(sK8_skl,sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f104,plain,(
% 0.09/0.41 ~open_subset(sK8_skl,sK6_skl)|sQ2_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f102])).
% 0.09/0.41 fof(f105,plain,(
% 0.09/0.41 sQ0_spl|~sQ2_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f89,f95,f102])).
% 0.09/0.41 fof(f106,plain,(
% 0.09/0.41 open_subset(sK9_skl,sK7_skl)|~sQ0_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f92,f96])).
% 0.09/0.41 fof(f107,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|open_subset(interior(sK6_skl,sK8_skl),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f86,f50])).
% 0.09/0.41 fof(f108,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(interior(sK6_skl,sK8_skl),powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f86,f30])).
% 0.09/0.41 fof(f109,definition,(
% 0.09/0.41 sQ3_spl <=> (topological_space(sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f111,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|sQ3_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f109])).
% 0.09/0.41 fof(f112,definition,(
% 0.09/0.41 sQ4_spl <=> (top_str(sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f114,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|sQ4_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f112])).
% 0.09/0.41 fof(f115,definition,(
% 0.09/0.41 sQ5_spl <=> (open_subset(interior(sK6_skl,sK8_skl),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f116,plain,(
% 0.09/0.41 open_subset(interior(sK6_skl,sK8_skl),sK6_skl)|~sQ5_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f115])).
% 0.09/0.41 fof(f118,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ5_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f107,f109,f112,f115])).
% 0.09/0.41 fof(f119,definition,(
% 0.09/0.41 sQ6_spl <=> (element(interior(sK6_skl,sK8_skl),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f120,plain,(
% 0.09/0.41 element(interior(sK6_skl,sK8_skl),powerset(the_carrier(sK6_skl)))|~sQ6_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f119])).
% 0.09/0.41 fof(f122,plain,(
% 0.09/0.41 ~sQ4_spl|sQ6_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f108,f112,f119])).
% 0.09/0.41 fof(f123,plain,(
% 0.09/0.41 $false|sQ4_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f114,f84])).
% 0.09/0.41 fof(f124,plain,(
% 0.09/0.41 sQ4_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f123])).
% 0.09/0.41 fof(f125,plain,(
% 0.09/0.41 $false|sQ3_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f111,f83])).
% 0.09/0.41 fof(f126,plain,(
% 0.09/0.41 sQ3_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f125])).
% 0.09/0.41 fof(f127,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|open_subset(interior(sK7_skl,sK9_skl),sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f87,f50])).
% 0.09/0.41 fof(f128,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|element(interior(sK7_skl,sK9_skl),powerset(the_carrier(sK7_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f87,f30])).
% 0.09/0.41 fof(f129,definition,(
% 0.09/0.41 sQ7_spl <=> (topological_space(sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f132,definition,(
% 0.09/0.41 sQ8_spl <=> (top_str(sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f134,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|sQ8_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f132])).
% 0.09/0.41 fof(f135,definition,(
% 0.09/0.41 sQ9_spl <=> (open_subset(interior(sK7_skl,sK9_skl),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f138,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|sQ9_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f127,f129,f132,f135])).
% 0.09/0.41 fof(f139,definition,(
% 0.09/0.41 sQ10_spl <=> (element(interior(sK7_skl,sK9_skl),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f140,plain,(
% 0.09/0.41 element(interior(sK7_skl,sK9_skl),powerset(the_carrier(sK7_skl)))|~sQ10_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f139])).
% 0.09/0.41 fof(f142,plain,(
% 0.09/0.41 ~sQ8_spl|sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f128,f132,f139])).
% 0.09/0.41 fof(f143,plain,(
% 0.09/0.41 $false|sQ8_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f134,f85])).
% 0.09/0.41 fof(f144,plain,(
% 0.09/0.41 sQ8_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f143])).
% 0.09/0.41 fof(f145,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|interior(sK7_skl,sK9_skl)=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f28,f87])).
% 0.09/0.41 fof(f146,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|interior(sK6_skl,sK8_skl)=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f28,f86])).
% 0.09/0.41 fof(f147,definition,(
% 0.09/0.41 sQ11_spl <=> (interior(sK7_skl,sK9_skl)=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f148,plain,(
% 0.09/0.41 interior(sK7_skl,sK9_skl)=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)))|~sQ11_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f147])).
% 0.09/0.41 fof(f150,plain,(
% 0.09/0.41 ~sQ8_spl|sQ11_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f145,f132,f147])).
% 0.09/0.41 fof(f151,definition,(
% 0.09/0.41 sQ12_spl <=> (interior(sK6_skl,sK8_skl)=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f154,plain,(
% 0.09/0.41 ~sQ4_spl|sQ12_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f146,f112,f151])).
% 0.09/0.41 fof(f155,plain,(
% 0.09/0.41 element(subset_complement(the_carrier(sK7_skl),sK9_skl),powerset(the_carrier(sK7_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f32,f87])).
% 0.09/0.41 fof(f156,plain,(
% 0.09/0.41 element(subset_complement(the_carrier(sK6_skl),sK8_skl),powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f32,f86])).
% 0.09/0.41 fof(f157,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|element(topstr_closure(sK7_skl,sK9_skl),powerset(the_carrier(sK7_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f34,f87])).
% 0.09/0.41 fof(f158,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(topstr_closure(sK6_skl,sK8_skl),powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f34,f86])).
% 0.09/0.41 fof(f159,definition,(
% 0.09/0.41 sQ13_spl <=> (element(topstr_closure(sK7_skl,sK9_skl),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f160,plain,(
% 0.09/0.41 element(topstr_closure(sK7_skl,sK9_skl),powerset(the_carrier(sK7_skl)))|~sQ13_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f159])).
% 0.09/0.41 fof(f162,plain,(
% 0.09/0.41 ~sQ8_spl|sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f157,f132,f159])).
% 0.09/0.41 fof(f163,definition,(
% 0.09/0.41 sQ14_spl <=> (element(topstr_closure(sK6_skl,sK8_skl),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f164,plain,(
% 0.09/0.41 element(topstr_closure(sK6_skl,sK8_skl),powerset(the_carrier(sK6_skl)))|~sQ14_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f163])).
% 0.09/0.41 fof(f166,plain,(
% 0.09/0.41 ~sQ4_spl|sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f158,f112,f163])).
% 0.09/0.41 fof(f172,plain,(
% 0.09/0.41 ![X0]: (~topological_space(X0)|~top_str(X0)|open_subset(interior(X0,sK2_skl(powerset(the_carrier(X0)))),X0))),
% 0.09/0.41 inference(resolution,[status(thm)],[f42,f50])).
% 0.09/0.41 fof(f176,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|closed_subset(topstr_closure(sK7_skl,sK9_skl),sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f44,f87])).
% 0.09/0.41 fof(f177,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|closed_subset(topstr_closure(sK6_skl,sK8_skl),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f44,f86])).
% 0.09/0.41 fof(f178,definition,(
% 0.09/0.41 sQ15_spl <=> (closed_subset(topstr_closure(sK7_skl,sK9_skl),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f181,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|sQ15_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f176,f129,f132,f178])).
% 0.09/0.41 fof(f182,definition,(
% 0.09/0.41 sQ16_spl <=> (closed_subset(topstr_closure(sK6_skl,sK8_skl),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f185,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ16_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f177,f109,f112,f182])).
% 0.09/0.41 fof(f191,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|closed_subset(topstr_closure(sK6_skl,interior(sK6_skl,sK8_skl)),sK6_skl)|~sQ6_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f120,f44])).
% 0.09/0.41 fof(f192,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(topstr_closure(sK6_skl,interior(sK6_skl,sK8_skl)),powerset(the_carrier(sK6_skl)))|~sQ6_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f120,f34])).
% 0.09/0.41 fof(f193,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|interior(sK6_skl,interior(sK6_skl,sK8_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),interior(sK6_skl,sK8_skl))))|~sQ6_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f120,f28])).
% 0.09/0.41 fof(f194,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|open_subset(interior(sK6_skl,interior(sK6_skl,sK8_skl)),sK6_skl)|~sQ6_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f120,f50])).
% 0.09/0.41 fof(f195,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(interior(sK6_skl,interior(sK6_skl,sK8_skl)),powerset(the_carrier(sK6_skl)))|~sQ6_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f120,f30])).
% 0.09/0.41 fof(f197,definition,(
% 0.09/0.41 sQ18_spl <=> (closed_subset(topstr_closure(sK6_skl,interior(sK6_skl,sK8_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f200,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ18_spl|~sQ6_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f191,f109,f112,f197,f119])).
% 0.09/0.41 fof(f201,definition,(
% 0.09/0.41 sQ19_spl <=> (element(topstr_closure(sK6_skl,interior(sK6_skl,sK8_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f204,plain,(
% 0.09/0.41 ~sQ4_spl|sQ19_spl|~sQ6_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f192,f112,f201,f119])).
% 0.09/0.41 fof(f205,definition,(
% 0.09/0.41 sQ20_spl <=> (interior(sK6_skl,interior(sK6_skl,sK8_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),interior(sK6_skl,sK8_skl)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f208,plain,(
% 0.09/0.41 ~sQ4_spl|sQ20_spl|~sQ6_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f193,f112,f205,f119])).
% 0.09/0.41 fof(f209,definition,(
% 0.09/0.41 sQ21_spl <=> (open_subset(interior(sK6_skl,interior(sK6_skl,sK8_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f212,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ21_spl|~sQ6_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f194,f109,f112,f209,f119])).
% 0.09/0.41 fof(f213,definition,(
% 0.09/0.41 sQ22_spl <=> (element(interior(sK6_skl,interior(sK6_skl,sK8_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f216,plain,(
% 0.09/0.41 ~sQ4_spl|sQ22_spl|~sQ6_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f195,f112,f213,f119])).
% 0.09/0.41 fof(f225,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|closed_subset(topstr_closure(sK7_skl,interior(sK7_skl,sK9_skl)),sK7_skl)|~sQ10_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f140,f44])).
% 0.09/0.41 fof(f226,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|element(topstr_closure(sK7_skl,interior(sK7_skl,sK9_skl)),powerset(the_carrier(sK7_skl)))|~sQ10_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f140,f34])).
% 0.09/0.41 fof(f227,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|interior(sK7_skl,interior(sK7_skl,sK9_skl))=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),interior(sK7_skl,sK9_skl))))|~sQ10_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f140,f28])).
% 0.09/0.41 fof(f228,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|open_subset(interior(sK7_skl,interior(sK7_skl,sK9_skl)),sK7_skl)|~sQ10_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f140,f50])).
% 0.09/0.41 fof(f229,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|element(interior(sK7_skl,interior(sK7_skl,sK9_skl)),powerset(the_carrier(sK7_skl)))|~sQ10_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f140,f30])).
% 0.09/0.41 fof(f231,definition,(
% 0.09/0.41 sQ25_spl <=> (closed_subset(topstr_closure(sK7_skl,interior(sK7_skl,sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f234,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|sQ25_spl|~sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f225,f129,f132,f231,f139])).
% 0.09/0.41 fof(f235,definition,(
% 0.09/0.41 sQ26_spl <=> (element(topstr_closure(sK7_skl,interior(sK7_skl,sK9_skl)),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f238,plain,(
% 0.09/0.41 ~sQ8_spl|sQ26_spl|~sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f226,f132,f235,f139])).
% 0.09/0.41 fof(f239,definition,(
% 0.09/0.41 sQ27_spl <=> (interior(sK7_skl,interior(sK7_skl,sK9_skl))=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),interior(sK7_skl,sK9_skl)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f242,plain,(
% 0.09/0.41 ~sQ8_spl|sQ27_spl|~sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f227,f132,f239,f139])).
% 0.09/0.41 fof(f243,definition,(
% 0.09/0.41 sQ28_spl <=> (open_subset(interior(sK7_skl,interior(sK7_skl,sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f246,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|sQ28_spl|~sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f228,f129,f132,f243,f139])).
% 0.09/0.41 fof(f247,definition,(
% 0.09/0.41 sQ29_spl <=> (element(interior(sK7_skl,interior(sK7_skl,sK9_skl)),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f250,plain,(
% 0.09/0.41 ~sQ8_spl|sQ29_spl|~sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f229,f132,f247,f139])).
% 0.09/0.41 fof(f256,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|~closed_subset(interior(sK7_skl,sK9_skl),sK7_skl)|open_subset(subset_complement(the_carrier(sK7_skl),interior(sK7_skl,sK9_skl)),sK7_skl)|~sQ10_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f46,f140])).
% 0.09/0.41 fof(f259,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|~closed_subset(sK9_skl,sK7_skl)|open_subset(subset_complement(the_carrier(sK7_skl),sK9_skl),sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f46,f87])).
% 0.09/0.41 fof(f261,definition,(
% 0.09/0.41 sQ30_spl <=> (closed_subset(interior(sK7_skl,sK9_skl),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f264,definition,(
% 0.09/0.41 sQ31_spl <=> (open_subset(subset_complement(the_carrier(sK7_skl),interior(sK7_skl,sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f267,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|~sQ30_spl|sQ31_spl|~sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f256,f129,f132,f261,f264,f139])).
% 0.09/0.41 fof(f275,definition,(
% 0.09/0.41 sQ34_spl <=> (closed_subset(sK9_skl,sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f278,definition,(
% 0.09/0.41 sQ35_spl <=> (open_subset(subset_complement(the_carrier(sK7_skl),sK9_skl),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f281,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|~sQ34_spl|sQ35_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f259,f129,f132,f275,f278])).
% 0.09/0.41 fof(f292,plain,(
% 0.09/0.41 subset_complement(the_carrier(sK7_skl),subset_complement(the_carrier(sK7_skl),sK9_skl))=sK9_skl),
% 0.09/0.41 inference(resolution,[status(thm)],[f52,f87])).
% 0.09/0.41 fof(f294,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(sK3_skl(sK6_skl),powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f55,f83])).
% 0.09/0.41 fof(f295,definition,(
% 0.09/0.41 sQ38_spl <=> (element(sK3_skl(sK6_skl),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f296,plain,(
% 0.09/0.41 element(sK3_skl(sK6_skl),powerset(the_carrier(sK6_skl)))|~sQ38_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f295])).
% 0.09/0.41 fof(f298,plain,(
% 0.09/0.41 ~sQ4_spl|sQ38_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f294,f112,f295])).
% 0.09/0.41 fof(f299,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|open_subset(sK3_skl(sK6_skl),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f56,f83])).
% 0.09/0.41 fof(f300,definition,(
% 0.09/0.41 sQ39_spl <=> (open_subset(sK3_skl(sK6_skl),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f303,plain,(
% 0.09/0.41 ~sQ4_spl|sQ39_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f299,f112,f300])).
% 0.09/0.41 fof(f304,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(sK4_skl(sK6_skl),powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f59,f83])).
% 0.09/0.41 fof(f305,definition,(
% 0.09/0.41 sQ40_spl <=> (element(sK4_skl(sK6_skl),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f306,plain,(
% 0.09/0.41 element(sK4_skl(sK6_skl),powerset(the_carrier(sK6_skl)))|~sQ40_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f305])).
% 0.09/0.41 fof(f308,plain,(
% 0.09/0.41 ~sQ4_spl|sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f304,f112,f305])).
% 0.09/0.41 fof(f309,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|open_subset(sK4_skl(sK6_skl),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f60,f83])).
% 0.09/0.41 fof(f310,definition,(
% 0.09/0.41 sQ41_spl <=> (open_subset(sK4_skl(sK6_skl),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f313,plain,(
% 0.09/0.41 ~sQ4_spl|sQ41_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f309,f112,f310])).
% 0.09/0.41 fof(f314,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|~closed_subset(subset_complement(the_carrier(sK7_skl),sK9_skl),sK7_skl)|open_subset(subset_complement(the_carrier(sK7_skl),subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f155,f46])).
% 0.09/0.41 fof(f315,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|closed_subset(topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f155,f44])).
% 0.09/0.41 fof(f316,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|element(topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),powerset(the_carrier(sK7_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f155,f34])).
% 0.09/0.41 fof(f317,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|interior(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl))=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),subset_complement(the_carrier(sK7_skl),sK9_skl))))),
% 0.09/0.41 inference(resolution,[status(thm)],[f155,f28])).
% 0.09/0.41 fof(f318,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|open_subset(interior(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f155,f50])).
% 0.09/0.41 fof(f319,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|element(interior(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),powerset(the_carrier(sK7_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f155,f30])).
% 0.09/0.41 fof(f323,definition,(
% 0.09/0.41 sQ42_spl <=> (closed_subset(subset_complement(the_carrier(sK7_skl),sK9_skl),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f326,definition,(
% 0.09/0.41 sQ43_spl <=> (open_subset(subset_complement(the_carrier(sK7_skl),subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f329,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|~sQ42_spl|sQ43_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f314,f129,f132,f323,f326])).
% 0.09/0.41 fof(f330,definition,(
% 0.09/0.41 sQ44_spl <=> (closed_subset(topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f333,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|sQ44_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f315,f129,f132,f330])).
% 0.09/0.41 fof(f334,definition,(
% 0.09/0.41 sQ45_spl <=> (element(topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f337,plain,(
% 0.09/0.41 ~sQ8_spl|sQ45_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f316,f132,f334])).
% 0.09/0.41 fof(f338,definition,(
% 0.09/0.41 sQ46_spl <=> (interior(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl))=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),subset_complement(the_carrier(sK7_skl),sK9_skl)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f341,plain,(
% 0.09/0.41 ~sQ8_spl|sQ46_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f317,f132,f338])).
% 0.09/0.41 fof(f342,definition,(
% 0.09/0.41 sQ47_spl <=> (open_subset(interior(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f345,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|sQ47_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f318,f129,f132,f342])).
% 0.09/0.41 fof(f346,definition,(
% 0.09/0.41 sQ48_spl <=> (element(interior(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f349,plain,(
% 0.09/0.41 ~sQ8_spl|sQ48_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f319,f132,f346])).
% 0.09/0.41 fof(f353,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|closed_subset(topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f156,f44])).
% 0.09/0.41 fof(f354,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)),powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f156,f34])).
% 0.09/0.41 fof(f355,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|interior(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),subset_complement(the_carrier(sK6_skl),sK8_skl))))),
% 0.09/0.41 inference(resolution,[status(thm)],[f156,f28])).
% 0.09/0.41 fof(f356,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|open_subset(interior(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f156,f50])).
% 0.09/0.41 fof(f357,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(interior(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)),powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f156,f30])).
% 0.09/0.41 fof(f368,definition,(
% 0.09/0.41 sQ51_spl <=> (closed_subset(topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f371,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ51_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f353,f109,f112,f368])).
% 0.09/0.41 fof(f372,definition,(
% 0.09/0.41 sQ52_spl <=> (element(topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f375,plain,(
% 0.09/0.41 ~sQ4_spl|sQ52_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f354,f112,f372])).
% 0.09/0.41 fof(f376,definition,(
% 0.09/0.41 sQ53_spl <=> (interior(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),subset_complement(the_carrier(sK6_skl),sK8_skl)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f379,plain,(
% 0.09/0.41 ~sQ4_spl|sQ53_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f355,f112,f376])).
% 0.09/0.41 fof(f380,definition,(
% 0.09/0.41 sQ54_spl <=> (open_subset(interior(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f383,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ54_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f356,f109,f112,f380])).
% 0.09/0.41 fof(f384,definition,(
% 0.09/0.41 sQ55_spl <=> (element(interior(sK6_skl,subset_complement(the_carrier(sK6_skl),sK8_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f387,plain,(
% 0.09/0.41 ~sQ4_spl|sQ55_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f357,f112,f384])).
% 0.09/0.41 fof(f390,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|~closed_subset(topstr_closure(sK6_skl,sK8_skl),sK6_skl)|open_subset(subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,sK8_skl)),sK6_skl)|~sQ14_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f164,f46])).
% 0.09/0.41 fof(f391,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|closed_subset(topstr_closure(sK6_skl,topstr_closure(sK6_skl,sK8_skl)),sK6_skl)|~sQ14_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f164,f44])).
% 0.09/0.41 fof(f392,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(topstr_closure(sK6_skl,topstr_closure(sK6_skl,sK8_skl)),powerset(the_carrier(sK6_skl)))|~sQ14_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f164,f34])).
% 0.09/0.41 fof(f393,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|interior(sK6_skl,topstr_closure(sK6_skl,sK8_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,sK8_skl))))|~sQ14_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f164,f28])).
% 0.09/0.41 fof(f394,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|open_subset(interior(sK6_skl,topstr_closure(sK6_skl,sK8_skl)),sK6_skl)|~sQ14_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f164,f50])).
% 0.09/0.41 fof(f395,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(interior(sK6_skl,topstr_closure(sK6_skl,sK8_skl)),powerset(the_carrier(sK6_skl)))|~sQ14_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f164,f30])).
% 0.09/0.41 fof(f399,definition,(
% 0.09/0.41 sQ56_spl <=> (open_subset(subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,sK8_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f402,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|~sQ16_spl|sQ56_spl|~sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f390,f109,f112,f182,f399,f163])).
% 0.09/0.41 fof(f403,definition,(
% 0.09/0.41 sQ57_spl <=> (closed_subset(topstr_closure(sK6_skl,topstr_closure(sK6_skl,sK8_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f406,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ57_spl|~sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f391,f109,f112,f403,f163])).
% 0.09/0.41 fof(f407,definition,(
% 0.09/0.41 sQ58_spl <=> (element(topstr_closure(sK6_skl,topstr_closure(sK6_skl,sK8_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f410,plain,(
% 0.09/0.41 ~sQ4_spl|sQ58_spl|~sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f392,f112,f407,f163])).
% 0.09/0.41 fof(f411,definition,(
% 0.09/0.41 sQ59_spl <=> (interior(sK6_skl,topstr_closure(sK6_skl,sK8_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,sK8_skl)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f414,plain,(
% 0.09/0.41 ~sQ4_spl|sQ59_spl|~sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f393,f112,f411,f163])).
% 0.09/0.41 fof(f415,definition,(
% 0.09/0.41 sQ60_spl <=> (open_subset(interior(sK6_skl,topstr_closure(sK6_skl,sK8_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f418,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ60_spl|~sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f394,f109,f112,f415,f163])).
% 0.09/0.41 fof(f419,definition,(
% 0.09/0.41 sQ61_spl <=> (element(interior(sK6_skl,topstr_closure(sK6_skl,sK8_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f422,plain,(
% 0.09/0.41 ~sQ4_spl|sQ61_spl|~sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f395,f112,f419,f163])).
% 0.09/0.41 fof(f427,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|~closed_subset(topstr_closure(sK7_skl,sK9_skl),sK7_skl)|open_subset(subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,sK9_skl)),sK7_skl)|~sQ13_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f160,f46])).
% 0.09/0.41 fof(f428,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|closed_subset(topstr_closure(sK7_skl,topstr_closure(sK7_skl,sK9_skl)),sK7_skl)|~sQ13_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f160,f44])).
% 0.09/0.41 fof(f429,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|element(topstr_closure(sK7_skl,topstr_closure(sK7_skl,sK9_skl)),powerset(the_carrier(sK7_skl)))|~sQ13_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f160,f34])).
% 0.09/0.41 fof(f430,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|interior(sK7_skl,topstr_closure(sK7_skl,sK9_skl))=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,sK9_skl))))|~sQ13_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f160,f28])).
% 0.09/0.41 fof(f431,plain,(
% 0.09/0.41 ~topological_space(sK7_skl)|~top_str(sK7_skl)|open_subset(interior(sK7_skl,topstr_closure(sK7_skl,sK9_skl)),sK7_skl)|~sQ13_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f160,f50])).
% 0.09/0.41 fof(f432,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|element(interior(sK7_skl,topstr_closure(sK7_skl,sK9_skl)),powerset(the_carrier(sK7_skl)))|~sQ13_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f160,f30])).
% 0.09/0.41 fof(f436,definition,(
% 0.09/0.41 sQ62_spl <=> (open_subset(subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f439,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|~sQ15_spl|sQ62_spl|~sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f427,f129,f132,f178,f436,f159])).
% 0.09/0.41 fof(f440,definition,(
% 0.09/0.41 sQ63_spl <=> (closed_subset(topstr_closure(sK7_skl,topstr_closure(sK7_skl,sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f443,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|sQ63_spl|~sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f428,f129,f132,f440,f159])).
% 0.09/0.41 fof(f444,definition,(
% 0.09/0.41 sQ64_spl <=> (element(topstr_closure(sK7_skl,topstr_closure(sK7_skl,sK9_skl)),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f447,plain,(
% 0.09/0.41 ~sQ8_spl|sQ64_spl|~sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f429,f132,f444,f159])).
% 0.09/0.41 fof(f448,definition,(
% 0.09/0.41 sQ65_spl <=> (interior(sK7_skl,topstr_closure(sK7_skl,sK9_skl))=subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,sK9_skl)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f451,plain,(
% 0.09/0.41 ~sQ8_spl|sQ65_spl|~sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f430,f132,f448,f159])).
% 0.09/0.41 fof(f452,definition,(
% 0.09/0.41 sQ66_spl <=> (open_subset(interior(sK7_skl,topstr_closure(sK7_skl,sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f455,plain,(
% 0.09/0.41 ~sQ7_spl|~sQ8_spl|sQ66_spl|~sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f431,f129,f132,f452,f159])).
% 0.09/0.41 fof(f456,definition,(
% 0.09/0.41 sQ67_spl <=> (element(interior(sK7_skl,topstr_closure(sK7_skl,sK9_skl)),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f459,plain,(
% 0.09/0.41 ~sQ8_spl|sQ67_spl|~sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f432,f132,f456,f159])).
% 0.09/0.41 fof(f480,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|closed_subset(sK4_skl(sK6_skl),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f61,f83])).
% 0.09/0.41 fof(f481,definition,(
% 0.09/0.41 sQ72_spl <=> (closed_subset(sK4_skl(sK6_skl),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f484,plain,(
% 0.09/0.41 ~sQ4_spl|sQ72_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f480,f112,f481])).
% 0.09/0.41 fof(f485,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(sK5_skl(sK6_skl),powerset(the_carrier(sK6_skl)))),
% 0.09/0.41 inference(resolution,[status(thm)],[f64,f83])).
% 0.09/0.41 fof(f486,definition,(
% 0.09/0.41 sQ73_spl <=> (element(sK5_skl(sK6_skl),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f487,plain,(
% 0.09/0.41 element(sK5_skl(sK6_skl),powerset(the_carrier(sK6_skl)))|~sQ73_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f486])).
% 0.09/0.41 fof(f489,plain,(
% 0.09/0.41 ~sQ4_spl|sQ73_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f485,f112,f486])).
% 0.09/0.41 fof(f490,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|closed_subset(sK5_skl(sK6_skl),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f65,f83])).
% 0.09/0.41 fof(f491,definition,(
% 0.09/0.41 sQ74_spl <=> (closed_subset(sK5_skl(sK6_skl),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f494,plain,(
% 0.09/0.41 ~sQ4_spl|sQ74_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f490,f112,f491])).
% 0.09/0.41 fof(f495,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~open_subset(topstr_closure(sK7_skl,sK9_skl),sK7_skl)|closed_subset(subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,sK9_skl)),sK7_skl)|~sQ13_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f70,f160])).
% 0.09/0.41 fof(f498,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~open_subset(subset_complement(the_carrier(sK7_skl),sK9_skl),sK7_skl)|closed_subset(subset_complement(the_carrier(sK7_skl),subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f70,f155])).
% 0.09/0.41 fof(f499,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~open_subset(interior(sK7_skl,sK9_skl),sK7_skl)|closed_subset(subset_complement(the_carrier(sK7_skl),interior(sK7_skl,sK9_skl)),sK7_skl)|~sQ10_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f70,f140])).
% 0.09/0.41 fof(f500,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|~open_subset(interior(sK6_skl,sK8_skl),sK6_skl)|closed_subset(subset_complement(the_carrier(sK6_skl),interior(sK6_skl,sK8_skl)),sK6_skl)|~sQ6_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f70,f120])).
% 0.09/0.41 fof(f502,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~open_subset(sK9_skl,sK7_skl)|closed_subset(subset_complement(the_carrier(sK7_skl),sK9_skl),sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f70,f87])).
% 0.09/0.41 fof(f504,definition,(
% 0.09/0.41 sQ75_spl <=> (open_subset(topstr_closure(sK7_skl,sK9_skl),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f507,definition,(
% 0.09/0.41 sQ76_spl <=> (closed_subset(subset_complement(the_carrier(sK7_skl),topstr_closure(sK7_skl,sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f510,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ75_spl|sQ76_spl|~sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f495,f132,f504,f507,f159])).
% 0.09/0.41 fof(f522,definition,(
% 0.09/0.41 sQ80_spl <=> (closed_subset(subset_complement(the_carrier(sK7_skl),subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f525,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ35_spl|sQ80_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f498,f132,f278,f522])).
% 0.09/0.41 fof(f526,definition,(
% 0.09/0.41 sQ81_spl <=> (closed_subset(subset_complement(the_carrier(sK7_skl),interior(sK7_skl,sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f529,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ9_spl|sQ81_spl|~sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f499,f132,f135,f526,f139])).
% 0.09/0.41 fof(f530,definition,(
% 0.09/0.41 sQ82_spl <=> (closed_subset(subset_complement(the_carrier(sK6_skl),interior(sK6_skl,sK8_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f533,plain,(
% 0.09/0.41 ~sQ4_spl|~sQ5_spl|sQ82_spl|~sQ6_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f500,f112,f115,f530,f119])).
% 0.09/0.41 fof(f534,definition,(
% 0.09/0.41 sQ83_spl <=> (open_subset(sK9_skl,sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f536,plain,(
% 0.09/0.41 ~open_subset(sK9_skl,sK7_skl)|sQ83_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f534])).
% 0.09/0.41 fof(f537,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ83_spl|sQ42_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f502,f132,f534,f323])).
% 0.09/0.41 fof(f546,plain,(
% 0.09/0.41 $false|~sQ0_spl|sQ83_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f536,f106])).
% 0.09/0.41 fof(f547,plain,(
% 0.09/0.41 ~sQ0_spl|sQ83_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f546])).
% 0.09/0.41 fof(f551,plain,(
% 0.09/0.41 open_subset(sK8_skl,sK6_skl)|~sQ1_spl|~sQ5_spl),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f99,f116])).
% 0.09/0.41 fof(f564,plain,(
% 0.09/0.41 $false|sQ2_spl|~sQ1_spl|~sQ5_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f551,f104])).
% 0.09/0.41 fof(f565,plain,(
% 0.09/0.41 sQ2_spl|~sQ1_spl|~sQ5_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f564])).
% 0.09/0.41 fof(f566,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~element(topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),powerset(the_carrier(sK7_skl)))|open_subset(topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl)|~closed_subset(interior(sK7_skl,sK9_skl),sK7_skl)|~sQ11_spl),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f148,f71])).
% 0.09/0.41 fof(f567,definition,(
% 0.09/0.41 sQ84_spl <=> (open_subset(topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl)),sK7_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f570,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ45_spl|sQ84_spl|~sQ30_spl|~sQ11_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f566,f132,f334,f567,f261,f147])).
% 0.09/0.41 fof(f583,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|open_subset(interior(sK6_skl,sK2_skl(powerset(the_carrier(sK6_skl)))),sK6_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f172,f83])).
% 0.09/0.41 fof(f584,definition,(
% 0.09/0.41 sQ86_spl <=> (open_subset(interior(sK6_skl,sK2_skl(powerset(the_carrier(sK6_skl)))),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f587,plain,(
% 0.09/0.41 ~sQ4_spl|sQ86_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f583,f112,f584])).
% 0.09/0.41 fof(f591,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~element(subset_complement(the_carrier(sK7_skl),sK9_skl),powerset(the_carrier(sK7_skl)))|open_subset(subset_complement(the_carrier(sK7_skl),sK9_skl),sK7_skl)|~closed_subset(sK9_skl,sK7_skl)),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f292,f71])).
% 0.09/0.41 fof(f592,definition,(
% 0.09/0.41 sQ87_spl <=> (element(subset_complement(the_carrier(sK7_skl),sK9_skl),powerset(the_carrier(sK7_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f595,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ87_spl|sQ35_spl|~sQ34_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f591,f132,f592,f278,f275])).
% 0.09/0.41 fof(f607,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~closed_subset(topstr_closure(sK7_skl,sK9_skl),sK7_skl)|topstr_closure(sK7_skl,topstr_closure(sK7_skl,sK9_skl))=topstr_closure(sK7_skl,sK9_skl)|~sQ13_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f77,f160])).
% 0.09/0.41 fof(f608,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|~closed_subset(topstr_closure(sK6_skl,sK8_skl),sK6_skl)|topstr_closure(sK6_skl,topstr_closure(sK6_skl,sK8_skl))=topstr_closure(sK6_skl,sK8_skl)|~sQ14_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f77,f164])).
% 0.09/0.41 fof(f610,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~closed_subset(subset_complement(the_carrier(sK7_skl),sK9_skl),sK7_skl)|topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl))=subset_complement(the_carrier(sK7_skl),sK9_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f77,f155])).
% 0.09/0.41 fof(f611,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~closed_subset(interior(sK7_skl,sK9_skl),sK7_skl)|topstr_closure(sK7_skl,interior(sK7_skl,sK9_skl))=interior(sK7_skl,sK9_skl)|~sQ10_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f77,f140])).
% 0.09/0.41 fof(f613,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~closed_subset(sK9_skl,sK7_skl)|topstr_closure(sK7_skl,sK9_skl)=sK9_skl),
% 0.09/0.41 inference(resolution,[status(thm)],[f77,f87])).
% 0.09/0.41 fof(f616,definition,(
% 0.09/0.41 sQ88_spl <=> (topstr_closure(sK7_skl,topstr_closure(sK7_skl,sK9_skl))=topstr_closure(sK7_skl,sK9_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f619,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ15_spl|sQ88_spl|~sQ13_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f607,f132,f178,f616,f159])).
% 0.09/0.41 fof(f620,definition,(
% 0.09/0.41 sQ89_spl <=> (topstr_closure(sK6_skl,topstr_closure(sK6_skl,sK8_skl))=topstr_closure(sK6_skl,sK8_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f623,plain,(
% 0.09/0.41 ~sQ4_spl|~sQ16_spl|sQ89_spl|~sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f608,f112,f182,f620,f163])).
% 0.09/0.41 fof(f628,definition,(
% 0.09/0.41 sQ91_spl <=> (topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl))=subset_complement(the_carrier(sK7_skl),sK9_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f629,plain,(
% 0.09/0.41 topstr_closure(sK7_skl,subset_complement(the_carrier(sK7_skl),sK9_skl))=subset_complement(the_carrier(sK7_skl),sK9_skl)|~sQ91_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f628])).
% 0.09/0.41 fof(f631,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ42_spl|sQ91_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f610,f132,f323,f628])).
% 0.09/0.41 fof(f632,definition,(
% 0.09/0.41 sQ92_spl <=> (topstr_closure(sK7_skl,interior(sK7_skl,sK9_skl))=interior(sK7_skl,sK9_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f635,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ30_spl|sQ92_spl|~sQ10_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f611,f132,f261,f632,f139])).
% 0.09/0.41 fof(f636,definition,(
% 0.09/0.41 sQ93_spl <=> (topstr_closure(sK7_skl,sK9_skl)=sK9_skl)),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f639,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ34_spl|sQ93_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f613,f132,f275,f636])).
% 0.09/0.41 fof(f646,plain,(
% 0.09/0.41 interior(sK7_skl,sK9_skl)=subset_complement(the_carrier(sK7_skl),subset_complement(the_carrier(sK7_skl),sK9_skl))|~sQ91_spl|~sQ11_spl),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f629,f148])).
% 0.09/0.41 fof(f658,plain,(
% 0.09/0.41 interior(sK7_skl,sK9_skl)=sK9_skl|~sQ91_spl|~sQ11_spl),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f292,f646])).
% 0.09/0.41 fof(f696,plain,(
% 0.09/0.41 ~top_str(sK7_skl)|~topological_space(sK7_skl)|~topstr_closure(sK7_skl,sK9_skl)=sK9_skl|closed_subset(sK9_skl,sK7_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f78,f87])).
% 0.09/0.41 fof(f703,plain,(
% 0.09/0.41 ~sQ8_spl|~sQ7_spl|~sQ93_spl|sQ34_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f696,f132,f129,f636,f275])).
% 0.09/0.41 fof(f760,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|~open_subset(sK3_skl(sK6_skl),sK6_skl)|closed_subset(subset_complement(the_carrier(sK6_skl),sK3_skl(sK6_skl)),sK6_skl)|~sQ38_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f296,f70])).
% 0.09/0.41 fof(f762,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|closed_subset(topstr_closure(sK6_skl,sK3_skl(sK6_skl)),sK6_skl)|~sQ38_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f296,f44])).
% 0.09/0.41 fof(f763,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(topstr_closure(sK6_skl,sK3_skl(sK6_skl)),powerset(the_carrier(sK6_skl)))|~sQ38_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f296,f34])).
% 0.09/0.41 fof(f764,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|interior(sK6_skl,sK3_skl(sK6_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK3_skl(sK6_skl))))|~sQ38_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f296,f28])).
% 0.09/0.41 fof(f765,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|open_subset(interior(sK6_skl,sK3_skl(sK6_skl)),sK6_skl)|~sQ38_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f296,f50])).
% 0.09/0.41 fof(f766,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(interior(sK6_skl,sK3_skl(sK6_skl)),powerset(the_carrier(sK6_skl)))|~sQ38_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f296,f30])).
% 0.09/0.41 fof(f778,definition,(
% 0.09/0.41 sQ98_spl <=> (closed_subset(subset_complement(the_carrier(sK6_skl),sK3_skl(sK6_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f781,plain,(
% 0.09/0.41 ~sQ4_spl|~sQ39_spl|sQ98_spl|~sQ38_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f760,f112,f300,f778,f295])).
% 0.09/0.41 fof(f786,definition,(
% 0.09/0.41 sQ100_spl <=> (closed_subset(topstr_closure(sK6_skl,sK3_skl(sK6_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f789,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ100_spl|~sQ38_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f762,f109,f112,f786,f295])).
% 0.09/0.41 fof(f790,definition,(
% 0.09/0.41 sQ101_spl <=> (element(topstr_closure(sK6_skl,sK3_skl(sK6_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f793,plain,(
% 0.09/0.41 ~sQ4_spl|sQ101_spl|~sQ38_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f763,f112,f790,f295])).
% 0.09/0.41 fof(f794,definition,(
% 0.09/0.41 sQ102_spl <=> (interior(sK6_skl,sK3_skl(sK6_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK3_skl(sK6_skl)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f797,plain,(
% 0.09/0.41 ~sQ4_spl|sQ102_spl|~sQ38_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f764,f112,f794,f295])).
% 0.09/0.41 fof(f798,definition,(
% 0.09/0.41 sQ103_spl <=> (open_subset(interior(sK6_skl,sK3_skl(sK6_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f801,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ103_spl|~sQ38_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f765,f109,f112,f798,f295])).
% 0.09/0.41 fof(f802,definition,(
% 0.09/0.41 sQ104_spl <=> (element(interior(sK6_skl,sK3_skl(sK6_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f805,plain,(
% 0.09/0.41 ~sQ4_spl|sQ104_spl|~sQ38_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f766,f112,f802,f295])).
% 0.09/0.41 fof(f810,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|~closed_subset(sK4_skl(sK6_skl),sK6_skl)|topstr_closure(sK6_skl,sK4_skl(sK6_skl))=sK4_skl(sK6_skl)|~sQ40_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f306,f77])).
% 0.09/0.41 fof(f811,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|~open_subset(sK4_skl(sK6_skl),sK6_skl)|closed_subset(subset_complement(the_carrier(sK6_skl),sK4_skl(sK6_skl)),sK6_skl)|~sQ40_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f306,f70])).
% 0.09/0.41 fof(f812,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|~closed_subset(sK4_skl(sK6_skl),sK6_skl)|open_subset(subset_complement(the_carrier(sK6_skl),sK4_skl(sK6_skl)),sK6_skl)|~sQ40_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f306,f46])).
% 0.09/0.41 fof(f813,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|closed_subset(topstr_closure(sK6_skl,sK4_skl(sK6_skl)),sK6_skl)|~sQ40_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f306,f44])).
% 0.09/0.41 fof(f814,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(topstr_closure(sK6_skl,sK4_skl(sK6_skl)),powerset(the_carrier(sK6_skl)))|~sQ40_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f306,f34])).
% 0.09/0.41 fof(f815,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|interior(sK6_skl,sK4_skl(sK6_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK4_skl(sK6_skl))))|~sQ40_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f306,f28])).
% 0.09/0.41 fof(f816,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|open_subset(interior(sK6_skl,sK4_skl(sK6_skl)),sK6_skl)|~sQ40_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f306,f50])).
% 0.09/0.41 fof(f817,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(interior(sK6_skl,sK4_skl(sK6_skl)),powerset(the_carrier(sK6_skl)))|~sQ40_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f306,f30])).
% 0.09/0.41 fof(f821,definition,(
% 0.09/0.41 sQ105_spl <=> (topstr_closure(sK6_skl,sK4_skl(sK6_skl))=sK4_skl(sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f825,plain,(
% 0.09/0.41 ~sQ4_spl|~sQ72_spl|sQ105_spl|~sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f810,f112,f481,f821,f305])).
% 0.09/0.41 fof(f826,definition,(
% 0.09/0.41 sQ106_spl <=> (closed_subset(subset_complement(the_carrier(sK6_skl),sK4_skl(sK6_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f829,plain,(
% 0.09/0.41 ~sQ4_spl|~sQ41_spl|sQ106_spl|~sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f811,f112,f310,f826,f305])).
% 0.09/0.41 fof(f830,definition,(
% 0.09/0.41 sQ107_spl <=> (open_subset(subset_complement(the_carrier(sK6_skl),sK4_skl(sK6_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f833,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|~sQ72_spl|sQ107_spl|~sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f812,f109,f112,f481,f830,f305])).
% 0.09/0.41 fof(f834,definition,(
% 0.09/0.41 sQ108_spl <=> (closed_subset(topstr_closure(sK6_skl,sK4_skl(sK6_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f837,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ108_spl|~sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f813,f109,f112,f834,f305])).
% 0.09/0.41 fof(f838,definition,(
% 0.09/0.41 sQ109_spl <=> (element(topstr_closure(sK6_skl,sK4_skl(sK6_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f841,plain,(
% 0.09/0.41 ~sQ4_spl|sQ109_spl|~sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f814,f112,f838,f305])).
% 0.09/0.41 fof(f842,definition,(
% 0.09/0.41 sQ110_spl <=> (interior(sK6_skl,sK4_skl(sK6_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK4_skl(sK6_skl)))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f845,plain,(
% 0.09/0.41 ~sQ4_spl|sQ110_spl|~sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f815,f112,f842,f305])).
% 0.09/0.41 fof(f846,definition,(
% 0.09/0.41 sQ111_spl <=> (open_subset(interior(sK6_skl,sK4_skl(sK6_skl)),sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f849,plain,(
% 0.09/0.41 ~sQ3_spl|~sQ4_spl|sQ111_spl|~sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f816,f109,f112,f846,f305])).
% 0.09/0.41 fof(f850,definition,(
% 0.09/0.41 sQ112_spl <=> (element(interior(sK6_skl,sK4_skl(sK6_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f853,plain,(
% 0.09/0.41 ~sQ4_spl|sQ112_spl|~sQ40_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f817,f112,f850,f305])).
% 0.09/0.41 fof(f857,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|~closed_subset(sK5_skl(sK6_skl),sK6_skl)|topstr_closure(sK6_skl,sK5_skl(sK6_skl))=sK5_skl(sK6_skl)|~sQ73_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f487,f77])).
% 0.09/0.41 fof(f859,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|~closed_subset(sK5_skl(sK6_skl),sK6_skl)|open_subset(subset_complement(the_carrier(sK6_skl),sK5_skl(sK6_skl)),sK6_skl)|~sQ73_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f487,f46])).
% 0.09/0.41 fof(f860,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|closed_subset(topstr_closure(sK6_skl,sK5_skl(sK6_skl)),sK6_skl)|~sQ73_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f487,f44])).
% 0.09/0.41 fof(f861,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(topstr_closure(sK6_skl,sK5_skl(sK6_skl)),powerset(the_carrier(sK6_skl)))|~sQ73_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f487,f34])).
% 0.09/0.41 fof(f862,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|interior(sK6_skl,sK5_skl(sK6_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK5_skl(sK6_skl))))|~sQ73_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f487,f28])).
% 0.09/0.41 fof(f863,plain,(
% 0.09/0.41 ~topological_space(sK6_skl)|~top_str(sK6_skl)|open_subset(interior(sK6_skl,sK5_skl(sK6_skl)),sK6_skl)|~sQ73_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f487,f50])).
% 0.09/0.41 fof(f864,plain,(
% 0.09/0.41 ~top_str(sK6_skl)|element(interior(sK6_skl,sK5_skl(sK6_skl)),powerset(the_carrier(sK6_skl)))|~sQ73_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f487,f30])).
% 0.09/0.41 fof(f868,definition,(
% 0.09/0.41 sQ113_spl <=> (topstr_closure(sK6_skl,sK5_skl(sK6_skl))=sK5_skl(sK6_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f872,plain,(
% 0.09/0.41 ~sQ4_spl|~sQ74_spl|sQ113_spl|~sQ73_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f857,f112,f491,f868,f486])).
% 0.09/0.42 fof(f880,definition,(
% 0.09/0.42 sQ116_spl <=> (open_subset(subset_complement(the_carrier(sK6_skl),sK5_skl(sK6_skl)),sK6_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f883,plain,(
% 0.09/0.42 ~sQ3_spl|~sQ4_spl|~sQ74_spl|sQ116_spl|~sQ73_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f859,f109,f112,f491,f880,f486])).
% 0.09/0.42 fof(f884,definition,(
% 0.09/0.42 sQ117_spl <=> (closed_subset(topstr_closure(sK6_skl,sK5_skl(sK6_skl)),sK6_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f887,plain,(
% 0.09/0.42 ~sQ3_spl|~sQ4_spl|sQ117_spl|~sQ73_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f860,f109,f112,f884,f486])).
% 0.09/0.42 fof(f888,definition,(
% 0.09/0.42 sQ118_spl <=> (element(topstr_closure(sK6_skl,sK5_skl(sK6_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f891,plain,(
% 0.09/0.42 ~sQ4_spl|sQ118_spl|~sQ73_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f861,f112,f888,f486])).
% 0.09/0.42 fof(f892,definition,(
% 0.09/0.42 sQ119_spl <=> (interior(sK6_skl,sK5_skl(sK6_skl))=subset_complement(the_carrier(sK6_skl),topstr_closure(sK6_skl,subset_complement(the_carrier(sK6_skl),sK5_skl(sK6_skl)))))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f895,plain,(
% 0.09/0.42 ~sQ4_spl|sQ119_spl|~sQ73_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f862,f112,f892,f486])).
% 0.09/0.42 fof(f896,definition,(
% 0.09/0.42 sQ120_spl <=> (open_subset(interior(sK6_skl,sK5_skl(sK6_skl)),sK6_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f899,plain,(
% 0.09/0.42 ~sQ3_spl|~sQ4_spl|sQ120_spl|~sQ73_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f863,f109,f112,f896,f486])).
% 0.09/0.42 fof(f900,definition,(
% 0.09/0.42 sQ121_spl <=> (element(interior(sK6_skl,sK5_skl(sK6_skl)),powerset(the_carrier(sK6_skl))))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f903,plain,(
% 0.09/0.42 ~sQ4_spl|sQ121_spl|~sQ73_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f864,f112,f900,f486])).
% 0.09/0.42 fof(f908,plain,(
% 0.09/0.42 ~sP0_prd(sK9_skl,sK7_skl)|~sQ91_spl|~sQ11_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f658,f93])).
% 0.09/0.42 fof(f910,plain,(
% 0.09/0.42 ~sQ0_spl|~sQ91_spl|~sQ11_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f908,f95,f628,f147])).
% 0.09/0.42 fof(f915,plain,(
% 0.09/0.42 $false),
% 0.09/0.42 inference(sat_refutation,[status(thm)],[f101,f105,f118,f122,f124,f126,f138,f142,f144,f150,f154,f162,f166,f181,f185,f200,f204,f208,f212,f216,f234,f238,f242,f246,f250,f267,f281,f298,f303,f308,f313,f329,f333,f337,f341,f345,f349,f371,f375,f379,f383,f387,f402,f406,f410,f414,f418,f422,f439,f443,f447,f451,f455,f459,f484,f489,f494,f510,f525,f529,f533,f537,f547,f565,f570,f587,f595,f619,f623,f631,f635,f639,f703,f781,f789,f793,f797,f801,f805,f825,f829,f833,f837,f841,f845,f849,f853,f872,f883,f887,f891,f895,f899,f903,f910])).
% 0.09/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.43 % Elapsed time: 0.059847 seconds
% 0.09/0.43 % CPU time: 0.227013 seconds
% 0.09/0.43 % Total memory used: 84.936 MB
% 0.09/0.43 % Net memory used: 84.645 MB
%------------------------------------------------------------------------------