TSTP Solution File: SEU324+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU324+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 : Wed May 31 12:36:42 EDT 2023
% Result : Theorem 0.16s 0.37s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU324+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n015.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 09:26:19 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Drodi V3.5.1
% 0.16/0.37 % Refutation found
% 0.16/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.37 fof(f1,axiom,(
% 0.16/0.37 (! [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))) ) )) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f2,axiom,(
% 0.16/0.37 (! [A,B] :( ( top_str(A)& element(B,powerset(the_carrier(A))) )=> element(interior(A,B),powerset(the_carrier(A))) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f4,axiom,(
% 0.16/0.37 (! [A,B] :( element(B,powerset(A))=> element(subset_complement(A,B),powerset(A)) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f5,axiom,(
% 0.16/0.37 (! [A,B] :( ( top_str(A)& element(B,powerset(the_carrier(A))) )=> element(topstr_closure(A,B),powerset(the_carrier(A))) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f10,axiom,(
% 0.16/0.37 (? [A] : top_str(A) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f12,axiom,(
% 0.16/0.37 (! [A] :(? [B] : element(B,A) ))),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f13,axiom,(
% 0.16/0.37 (! [A,B] :( ( topological_space(A)& top_str(A)& element(B,powerset(the_carrier(A))) )=> closed_subset(topstr_closure(A,B),A) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f14,axiom,(
% 0.16/0.37 (! [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) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f16,axiom,(
% 0.16/0.37 (! [A,B] :( ( topological_space(A)& top_str(A)& element(B,powerset(the_carrier(A))) )=> open_subset(interior(A,B),A) ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f17,axiom,(
% 0.16/0.37 (! [A,B] :( element(B,powerset(A))=> subset_complement(A,subset_complement(A,B)) = B ) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f18,axiom,(
% 0.16/0.37 (! [A] :( ( topological_space(A)& top_str(A) )=> (? [B] :( element(B,powerset(the_carrier(A)))& open_subset(B,A) ) )) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f22,axiom,(
% 0.16/0.37 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( open_subset(B,A)<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) )) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f24,axiom,(
% 0.16/0.37 (! [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) ) ) ) )) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f25,conjecture,(
% 0.16/0.37 (! [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) ) ) ) )) )) )) )),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.37 fof(f26,negated_conjecture,(
% 0.16/0.37 ~((! [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) ) ) ) )) )) )) ))),
% 0.16/0.37 inference(negated_conjecture,[status(cth)],[f25])).
% 0.16/0.37 fof(f27,plain,(
% 0.16/0.37 ![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))))))),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.16/0.37 fof(f28,plain,(
% 0.16/0.37 ![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))))),
% 0.16/0.37 inference(cnf_transformation,[status(esa)],[f27])).
% 0.16/0.37 fof(f29,plain,(
% 0.16/0.37 ![A,B]: ((~top_str(A)|~element(B,powerset(the_carrier(A))))|element(interior(A,B),powerset(the_carrier(A))))),
% 0.16/0.37 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.16/0.38 fof(f30,plain,(
% 0.16/0.38 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|element(interior(X0,X1),powerset(the_carrier(X0))))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f29])).
% 0.16/0.38 fof(f31,plain,(
% 0.16/0.38 ![A,B]: (~element(B,powerset(A))|element(subset_complement(A,B),powerset(A)))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.16/0.38 fof(f32,plain,(
% 0.16/0.38 ![X0,X1]: (~element(X0,powerset(X1))|element(subset_complement(X1,X0),powerset(X1)))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f31])).
% 0.16/0.38 fof(f33,plain,(
% 0.16/0.38 ![A,B]: ((~top_str(A)|~element(B,powerset(the_carrier(A))))|element(topstr_closure(A,B),powerset(the_carrier(A))))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.16/0.38 fof(f34,plain,(
% 0.16/0.38 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|element(topstr_closure(X0,X1),powerset(the_carrier(X0))))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f33])).
% 0.16/0.38 fof(f37,plain,(
% 0.16/0.38 top_str(sk0_0)),
% 0.16/0.38 inference(skolemization,[status(esa)],[f10])).
% 0.16/0.38 fof(f38,plain,(
% 0.16/0.38 top_str(sk0_0)),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f37])).
% 0.16/0.38 fof(f41,plain,(
% 0.16/0.38 ![A]: element(sk0_2(A),A)),
% 0.16/0.38 inference(skolemization,[status(esa)],[f12])).
% 0.16/0.38 fof(f42,plain,(
% 0.16/0.38 ![X0]: (element(sk0_2(X0),X0))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f41])).
% 0.16/0.38 fof(f43,plain,(
% 0.16/0.38 ![A,B]: (((~topological_space(A)|~top_str(A))|~element(B,powerset(the_carrier(A))))|closed_subset(topstr_closure(A,B),A))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.16/0.38 fof(f44,plain,(
% 0.16/0.38 ![X0,X1]: (~topological_space(X0)|~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|closed_subset(topstr_closure(X0,X1),X0))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f43])).
% 0.16/0.38 fof(f45,plain,(
% 0.16/0.38 ![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))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 0.16/0.38 fof(f46,plain,(
% 0.16/0.38 ![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))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f45])).
% 0.16/0.38 fof(f49,plain,(
% 0.16/0.38 ![A,B]: (((~topological_space(A)|~top_str(A))|~element(B,powerset(the_carrier(A))))|open_subset(interior(A,B),A))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.16/0.38 fof(f50,plain,(
% 0.16/0.38 ![X0,X1]: (~topological_space(X0)|~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|open_subset(interior(X0,X1),X0))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f49])).
% 0.16/0.38 fof(f51,plain,(
% 0.16/0.38 ![A,B]: (~element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B)),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 0.16/0.38 fof(f52,plain,(
% 0.16/0.38 ![X0,X1]: (~element(X0,powerset(X1))|subset_complement(X1,subset_complement(X1,X0))=X0)),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f51])).
% 0.16/0.38 fof(f53,plain,(
% 0.16/0.38 ![A]: ((~topological_space(A)|~top_str(A))|(?[B]: (element(B,powerset(the_carrier(A)))&open_subset(B,A))))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 0.16/0.38 fof(f54,plain,(
% 0.16/0.38 ![A]: ((~topological_space(A)|~top_str(A))|(element(sk0_3(A),powerset(the_carrier(A)))&open_subset(sk0_3(A),A)))),
% 0.16/0.38 inference(skolemization,[status(esa)],[f53])).
% 0.16/0.38 fof(f55,plain,(
% 0.16/0.38 ![X0]: (~topological_space(X0)|~top_str(X0)|element(sk0_3(X0),powerset(the_carrier(X0))))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f54])).
% 0.16/0.38 fof(f68,plain,(
% 0.16/0.38 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|(open_subset(B,A)<=>closed_subset(subset_complement(the_carrier(A),B),A)))))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f22])).
% 0.16/0.38 fof(f69,plain,(
% 0.16/0.38 ![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))))))),
% 0.16/0.38 inference(NNF_transformation,[status(esa)],[f68])).
% 0.16/0.38 fof(f70,plain,(
% 0.16/0.38 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~open_subset(X1,X0)|closed_subset(subset_complement(the_carrier(X0),X1),X0))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f69])).
% 0.16/0.38 fof(f71,plain,(
% 0.16/0.38 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|open_subset(X1,X0)|~closed_subset(subset_complement(the_carrier(X0),X1),X0))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f69])).
% 0.16/0.38 fof(f76,plain,(
% 0.16/0.38 ![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))))))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f24])).
% 0.16/0.38 fof(f77,plain,(
% 0.16/0.38 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~closed_subset(X1,X0)|topstr_closure(X0,X1)=X1)),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f76])).
% 0.16/0.38 fof(f78,plain,(
% 0.16/0.38 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~topological_space(X0)|~topstr_closure(X0,X1)=X1|closed_subset(X1,X0))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f76])).
% 0.16/0.38 fof(f79,plain,(
% 0.16/0.38 (?[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)))))))))))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f26])).
% 0.16/0.38 fof(f80,plain,(
% 0.16/0.38 ![B,D]: (pd0_0(D,B)=>(open_subset(D,B)&~interior(B,D)=D))),
% 0.16/0.38 introduced(predicate_definition,[f79])).
% 0.16/0.38 fof(f81,plain,(
% 0.16/0.38 ?[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)))&(pd0_0(D,B)|(interior(A,C)=C&~open_subset(C,A))))))))))),
% 0.16/0.38 inference(formula_renaming,[status(thm)],[f79,f80])).
% 0.16/0.38 fof(f82,plain,(
% 0.16/0.38 ((topological_space(sk0_6)&top_str(sk0_6))&(top_str(sk0_7)&(element(sk0_8,powerset(the_carrier(sk0_6)))&(element(sk0_9,powerset(the_carrier(sk0_7)))&(pd0_0(sk0_9,sk0_7)|(interior(sk0_6,sk0_8)=sk0_8&~open_subset(sk0_8,sk0_6)))))))),
% 0.16/0.38 inference(skolemization,[status(esa)],[f81])).
% 0.16/0.38 fof(f83,plain,(
% 0.16/0.38 topological_space(sk0_6)),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f82])).
% 0.16/0.38 fof(f84,plain,(
% 0.16/0.38 top_str(sk0_6)),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f82])).
% 0.16/0.38 fof(f85,plain,(
% 0.16/0.38 top_str(sk0_7)),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f82])).
% 0.16/0.38 fof(f86,plain,(
% 0.16/0.38 element(sk0_8,powerset(the_carrier(sk0_6)))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f82])).
% 0.16/0.38 fof(f87,plain,(
% 0.16/0.38 element(sk0_9,powerset(the_carrier(sk0_7)))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f82])).
% 0.16/0.38 fof(f88,plain,(
% 0.16/0.38 pd0_0(sk0_9,sk0_7)|interior(sk0_6,sk0_8)=sk0_8),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f82])).
% 0.16/0.38 fof(f89,plain,(
% 0.16/0.38 pd0_0(sk0_9,sk0_7)|~open_subset(sk0_8,sk0_6)),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f82])).
% 0.16/0.38 fof(f90,plain,(
% 0.16/0.38 ![B,D]: (~pd0_0(D,B)|(open_subset(D,B)&~interior(B,D)=D))),
% 0.16/0.38 inference(pre_NNF_transformation,[status(esa)],[f80])).
% 0.16/0.38 fof(f91,plain,(
% 0.16/0.38 ![X0,X1]: (~pd0_0(X0,X1)|open_subset(X0,X1))),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f90])).
% 0.16/0.38 fof(f92,plain,(
% 0.16/0.38 ![X0,X1]: (~pd0_0(X0,X1)|~interior(X1,X0)=X0)),
% 0.16/0.38 inference(cnf_transformation,[status(esa)],[f90])).
% 0.16/0.38 fof(f93,plain,(
% 0.16/0.38 spl0_0 <=> pd0_0(sk0_9,sk0_7)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f94,plain,(
% 0.16/0.38 pd0_0(sk0_9,sk0_7)|~spl0_0),
% 0.16/0.38 inference(component_clause,[status(thm)],[f93])).
% 0.16/0.38 fof(f96,plain,(
% 0.16/0.38 spl0_1 <=> interior(sk0_6,sk0_8)=sk0_8),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f97,plain,(
% 0.16/0.38 interior(sk0_6,sk0_8)=sk0_8|~spl0_1),
% 0.16/0.38 inference(component_clause,[status(thm)],[f96])).
% 0.16/0.38 fof(f99,plain,(
% 0.16/0.38 spl0_0|spl0_1),
% 0.16/0.38 inference(split_clause,[status(thm)],[f88,f93,f96])).
% 0.16/0.38 fof(f100,plain,(
% 0.16/0.38 spl0_2 <=> open_subset(sk0_8,sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f103,plain,(
% 0.16/0.38 spl0_0|~spl0_2),
% 0.16/0.38 inference(split_clause,[status(thm)],[f89,f93,f100])).
% 0.16/0.38 fof(f104,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_7)))|interior(sk0_7,X0)=subset_complement(the_carrier(sk0_7),topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),X0))))),
% 0.16/0.38 inference(resolution,[status(thm)],[f28,f85])).
% 0.16/0.38 fof(f105,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_6)))|interior(sk0_6,X0)=subset_complement(the_carrier(sk0_6),topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),X0))))),
% 0.16/0.38 inference(resolution,[status(thm)],[f28,f84])).
% 0.16/0.38 fof(f106,plain,(
% 0.16/0.38 spl0_3 <=> interior(sk0_7,interior(sk0_7,X0))=subset_complement(the_carrier(sk0_7),topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),interior(sk0_7,X0))))|~element(X0,powerset(the_carrier(sk0_7)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f109,plain,(
% 0.16/0.38 spl0_4 <=> top_str(sk0_7)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f111,plain,(
% 0.16/0.38 ~top_str(sk0_7)|spl0_4),
% 0.16/0.38 inference(component_clause,[status(thm)],[f109])).
% 0.16/0.38 fof(f112,plain,(
% 0.16/0.38 ![X0]: (interior(sk0_7,interior(sk0_7,X0))=subset_complement(the_carrier(sk0_7),topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),interior(sk0_7,X0))))|~top_str(sk0_7)|~element(X0,powerset(the_carrier(sk0_7))))),
% 0.16/0.38 inference(resolution,[status(thm)],[f104,f30])).
% 0.16/0.38 fof(f113,plain,(
% 0.16/0.38 spl0_3|~spl0_4),
% 0.16/0.38 inference(split_clause,[status(thm)],[f112,f106,f109])).
% 0.16/0.38 fof(f114,plain,(
% 0.16/0.38 interior(sk0_7,sk0_9)=subset_complement(the_carrier(sk0_7),topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),sk0_9)))),
% 0.16/0.38 inference(resolution,[status(thm)],[f104,f87])).
% 0.16/0.38 fof(f115,plain,(
% 0.16/0.38 $false|spl0_4),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f111,f85])).
% 0.16/0.38 fof(f116,plain,(
% 0.16/0.38 spl0_4),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f115])).
% 0.16/0.38 fof(f139,plain,(
% 0.16/0.38 spl0_11 <=> interior(sk0_6,interior(sk0_6,X0))=subset_complement(the_carrier(sk0_6),topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),interior(sk0_6,X0))))|~element(X0,powerset(the_carrier(sk0_6)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f142,plain,(
% 0.16/0.38 spl0_12 <=> top_str(sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f144,plain,(
% 0.16/0.38 ~top_str(sk0_6)|spl0_12),
% 0.16/0.38 inference(component_clause,[status(thm)],[f142])).
% 0.16/0.38 fof(f145,plain,(
% 0.16/0.38 ![X0]: (interior(sk0_6,interior(sk0_6,X0))=subset_complement(the_carrier(sk0_6),topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),interior(sk0_6,X0))))|~top_str(sk0_6)|~element(X0,powerset(the_carrier(sk0_6))))),
% 0.16/0.38 inference(resolution,[status(thm)],[f105,f30])).
% 0.16/0.38 fof(f146,plain,(
% 0.16/0.38 spl0_11|~spl0_12),
% 0.16/0.38 inference(split_clause,[status(thm)],[f145,f139,f142])).
% 0.16/0.38 fof(f147,plain,(
% 0.16/0.38 interior(sk0_6,sk0_8)=subset_complement(the_carrier(sk0_6),topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)))),
% 0.16/0.38 inference(resolution,[status(thm)],[f105,f86])).
% 0.16/0.38 fof(f148,plain,(
% 0.16/0.38 $false|spl0_12),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f144,f84])).
% 0.16/0.38 fof(f149,plain,(
% 0.16/0.38 spl0_12),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f148])).
% 0.16/0.38 fof(f150,plain,(
% 0.16/0.38 spl0_13 <=> topological_space(sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f152,plain,(
% 0.16/0.38 ~topological_space(sk0_6)|spl0_13),
% 0.16/0.38 inference(component_clause,[status(thm)],[f150])).
% 0.16/0.38 fof(f153,plain,(
% 0.16/0.38 spl0_14 <=> closed_subset(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f155,plain,(
% 0.16/0.38 ~closed_subset(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),sk0_6)|spl0_14),
% 0.16/0.38 inference(component_clause,[status(thm)],[f153])).
% 0.16/0.38 fof(f156,plain,(
% 0.16/0.38 spl0_15 <=> element(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),powerset(the_carrier(sk0_6)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f159,plain,(
% 0.16/0.38 spl0_16 <=> open_subset(interior(sk0_6,sk0_8),sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f162,plain,(
% 0.16/0.38 ~topological_space(sk0_6)|~top_str(sk0_6)|~closed_subset(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),sk0_6)|~element(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),powerset(the_carrier(sk0_6)))|open_subset(interior(sk0_6,sk0_8),sk0_6)),
% 0.16/0.38 inference(paramodulation,[status(thm)],[f147,f46])).
% 0.16/0.38 fof(f163,plain,(
% 0.16/0.38 ~spl0_13|~spl0_12|~spl0_14|~spl0_15|spl0_16),
% 0.16/0.38 inference(split_clause,[status(thm)],[f162,f150,f142,f153,f156,f159])).
% 0.16/0.38 fof(f164,plain,(
% 0.16/0.38 spl0_17 <=> open_subset(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f166,plain,(
% 0.16/0.38 ~open_subset(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),sk0_6)|spl0_17),
% 0.16/0.38 inference(component_clause,[status(thm)],[f164])).
% 0.16/0.38 fof(f167,plain,(
% 0.16/0.38 spl0_18 <=> closed_subset(interior(sk0_6,sk0_8),sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f170,plain,(
% 0.16/0.38 ~top_str(sk0_6)|~element(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),powerset(the_carrier(sk0_6)))|~open_subset(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),sk0_6)|closed_subset(interior(sk0_6,sk0_8),sk0_6)),
% 0.16/0.38 inference(paramodulation,[status(thm)],[f147,f70])).
% 0.16/0.38 fof(f171,plain,(
% 0.16/0.38 ~spl0_12|~spl0_15|~spl0_17|spl0_18),
% 0.16/0.38 inference(split_clause,[status(thm)],[f170,f142,f156,f164,f167])).
% 0.16/0.38 fof(f172,plain,(
% 0.16/0.38 $false|spl0_13),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f152,f83])).
% 0.16/0.38 fof(f173,plain,(
% 0.16/0.38 spl0_13),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f172])).
% 0.16/0.38 fof(f176,plain,(
% 0.16/0.38 element(subset_complement(the_carrier(sk0_6),sk0_8),powerset(the_carrier(sk0_6)))),
% 0.16/0.38 inference(resolution,[status(thm)],[f32,f86])).
% 0.16/0.38 fof(f181,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_0)))|~closed_subset(X0,sk0_0)|topstr_closure(sk0_0,X0)=X0)),
% 0.16/0.38 inference(resolution,[status(thm)],[f77,f38])).
% 0.16/0.38 fof(f182,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_7)))|~closed_subset(X0,sk0_7)|topstr_closure(sk0_7,X0)=X0)),
% 0.16/0.38 inference(resolution,[status(thm)],[f77,f85])).
% 0.16/0.38 fof(f183,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_6)))|~closed_subset(X0,sk0_6)|topstr_closure(sk0_6,X0)=X0)),
% 0.16/0.38 inference(resolution,[status(thm)],[f77,f84])).
% 0.16/0.38 fof(f192,plain,(
% 0.16/0.38 spl0_21 <=> ~closed_subset(interior(sk0_0,X0),sk0_0)|topstr_closure(sk0_0,interior(sk0_0,X0))=interior(sk0_0,X0)|~element(X0,powerset(the_carrier(sk0_0)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f195,plain,(
% 0.16/0.38 spl0_22 <=> top_str(sk0_0)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f197,plain,(
% 0.16/0.38 ~top_str(sk0_0)|spl0_22),
% 0.16/0.38 inference(component_clause,[status(thm)],[f195])).
% 0.16/0.38 fof(f198,plain,(
% 0.16/0.38 ![X0]: (~closed_subset(interior(sk0_0,X0),sk0_0)|topstr_closure(sk0_0,interior(sk0_0,X0))=interior(sk0_0,X0)|~top_str(sk0_0)|~element(X0,powerset(the_carrier(sk0_0))))),
% 0.16/0.38 inference(resolution,[status(thm)],[f181,f30])).
% 0.16/0.38 fof(f199,plain,(
% 0.16/0.38 spl0_21|~spl0_22),
% 0.16/0.38 inference(split_clause,[status(thm)],[f198,f192,f195])).
% 0.16/0.38 fof(f200,plain,(
% 0.16/0.38 $false|spl0_22),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f197,f38])).
% 0.16/0.38 fof(f201,plain,(
% 0.16/0.38 spl0_22),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f200])).
% 0.16/0.38 fof(f218,plain,(
% 0.16/0.38 spl0_27 <=> ~element(subset_complement(the_carrier(sk0_7),X0),powerset(the_carrier(sk0_7)))|topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),X0))=subset_complement(the_carrier(sk0_7),X0)|~element(X0,powerset(the_carrier(sk0_7)))|~open_subset(X0,sk0_7)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f219,plain,(
% 0.16/0.38 ![X0]: (~element(subset_complement(the_carrier(sk0_7),X0),powerset(the_carrier(sk0_7)))|topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),X0))=subset_complement(the_carrier(sk0_7),X0)|~element(X0,powerset(the_carrier(sk0_7)))|~open_subset(X0,sk0_7)|~spl0_27)),
% 0.16/0.38 inference(component_clause,[status(thm)],[f218])).
% 0.16/0.38 fof(f221,plain,(
% 0.16/0.38 ![X0]: (~element(subset_complement(the_carrier(sk0_7),X0),powerset(the_carrier(sk0_7)))|topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),X0))=subset_complement(the_carrier(sk0_7),X0)|~top_str(sk0_7)|~element(X0,powerset(the_carrier(sk0_7)))|~open_subset(X0,sk0_7))),
% 0.16/0.38 inference(resolution,[status(thm)],[f182,f70])).
% 0.16/0.38 fof(f222,plain,(
% 0.16/0.38 spl0_27|~spl0_4),
% 0.16/0.38 inference(split_clause,[status(thm)],[f221,f218,f109])).
% 0.16/0.38 fof(f223,plain,(
% 0.16/0.38 ![X0]: (topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),X0))=subset_complement(the_carrier(sk0_7),X0)|~element(X0,powerset(the_carrier(sk0_7)))|~open_subset(X0,sk0_7)|~spl0_27)),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f219,f32])).
% 0.16/0.38 fof(f240,plain,(
% 0.16/0.38 spl0_32 <=> ~element(subset_complement(the_carrier(sk0_6),X0),powerset(the_carrier(sk0_6)))|topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),X0))=subset_complement(the_carrier(sk0_6),X0)|~element(X0,powerset(the_carrier(sk0_6)))|~open_subset(X0,sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f243,plain,(
% 0.16/0.38 ![X0]: (~element(subset_complement(the_carrier(sk0_6),X0),powerset(the_carrier(sk0_6)))|topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),X0))=subset_complement(the_carrier(sk0_6),X0)|~top_str(sk0_6)|~element(X0,powerset(the_carrier(sk0_6)))|~open_subset(X0,sk0_6))),
% 0.16/0.38 inference(resolution,[status(thm)],[f183,f70])).
% 0.16/0.38 fof(f244,plain,(
% 0.16/0.38 spl0_32|~spl0_12),
% 0.16/0.38 inference(split_clause,[status(thm)],[f243,f240,f142])).
% 0.16/0.38 fof(f246,plain,(
% 0.16/0.38 spl0_33 <=> ~element(X0,powerset(the_carrier(sk0_6)))|closed_subset(topstr_closure(sk0_6,X0),sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f247,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_6)))|closed_subset(topstr_closure(sk0_6,X0),sk0_6)|~spl0_33)),
% 0.16/0.38 inference(component_clause,[status(thm)],[f246])).
% 0.16/0.38 fof(f249,plain,(
% 0.16/0.38 ![X0]: (~top_str(sk0_6)|~element(X0,powerset(the_carrier(sk0_6)))|closed_subset(topstr_closure(sk0_6,X0),sk0_6))),
% 0.16/0.38 inference(resolution,[status(thm)],[f44,f83])).
% 0.16/0.38 fof(f250,plain,(
% 0.16/0.38 ~spl0_12|spl0_33),
% 0.16/0.38 inference(split_clause,[status(thm)],[f249,f142,f246])).
% 0.16/0.38 fof(f251,plain,(
% 0.16/0.38 spl0_34 <=> ~element(X0,powerset(the_carrier(sk0_6)))|~topstr_closure(sk0_6,X0)=X0|closed_subset(X0,sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f252,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_6)))|~topstr_closure(sk0_6,X0)=X0|closed_subset(X0,sk0_6)|~spl0_34)),
% 0.16/0.38 inference(component_clause,[status(thm)],[f251])).
% 0.16/0.38 fof(f254,plain,(
% 0.16/0.38 ![X0]: (~top_str(sk0_6)|~element(X0,powerset(the_carrier(sk0_6)))|~topstr_closure(sk0_6,X0)=X0|closed_subset(X0,sk0_6))),
% 0.16/0.38 inference(resolution,[status(thm)],[f78,f83])).
% 0.16/0.38 fof(f255,plain,(
% 0.16/0.38 ~spl0_12|spl0_34),
% 0.16/0.38 inference(split_clause,[status(thm)],[f254,f142,f251])).
% 0.16/0.38 fof(f258,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_6)))|element(topstr_closure(sk0_6,X0),powerset(the_carrier(sk0_6))))),
% 0.16/0.38 inference(resolution,[status(thm)],[f34,f84])).
% 0.16/0.38 fof(f261,plain,(
% 0.16/0.38 subset_complement(the_carrier(sk0_7),subset_complement(the_carrier(sk0_7),sk0_9))=sk0_9),
% 0.16/0.38 inference(resolution,[status(thm)],[f52,f87])).
% 0.16/0.38 fof(f263,plain,(
% 0.16/0.38 spl0_35 <=> element(sk0_3(sk0_6),powerset(the_carrier(sk0_6)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f266,plain,(
% 0.16/0.38 ~top_str(sk0_6)|element(sk0_3(sk0_6),powerset(the_carrier(sk0_6)))),
% 0.16/0.38 inference(resolution,[status(thm)],[f55,f83])).
% 0.16/0.38 fof(f267,plain,(
% 0.16/0.38 ~spl0_12|spl0_35),
% 0.16/0.38 inference(split_clause,[status(thm)],[f266,f142,f263])).
% 0.16/0.38 fof(f268,plain,(
% 0.16/0.38 spl0_36 <=> element(sk0_8,powerset(the_carrier(sk0_6)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f270,plain,(
% 0.16/0.38 ~element(sk0_8,powerset(the_carrier(sk0_6)))|spl0_36),
% 0.16/0.38 inference(component_clause,[status(thm)],[f268])).
% 0.16/0.38 fof(f276,plain,(
% 0.16/0.38 $false|spl0_36),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f270,f86])).
% 0.16/0.38 fof(f277,plain,(
% 0.16/0.38 spl0_36),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f276])).
% 0.16/0.38 fof(f278,plain,(
% 0.16/0.38 ~interior(sk0_7,sk0_9)=sk0_9|~spl0_0),
% 0.16/0.38 inference(resolution,[status(thm)],[f94,f92])).
% 0.16/0.38 fof(f279,plain,(
% 0.16/0.38 open_subset(sk0_9,sk0_7)|~spl0_0),
% 0.16/0.38 inference(resolution,[status(thm)],[f94,f91])).
% 0.16/0.38 fof(f282,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_6)))|~element(topstr_closure(sk0_6,X0),powerset(the_carrier(sk0_6)))|topstr_closure(sk0_6,topstr_closure(sk0_6,X0))=topstr_closure(sk0_6,X0)|~spl0_33)),
% 0.16/0.38 inference(resolution,[status(thm)],[f247,f183])).
% 0.16/0.38 fof(f283,plain,(
% 0.16/0.38 ![X0]: (~element(X0,powerset(the_carrier(sk0_6)))|topstr_closure(sk0_6,topstr_closure(sk0_6,X0))=topstr_closure(sk0_6,X0)|~spl0_33)),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f282,f258])).
% 0.16/0.38 fof(f290,plain,(
% 0.16/0.38 spl0_39 <=> closed_subset(subset_complement(the_carrier(sk0_6),topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8))),sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f292,plain,(
% 0.16/0.38 ~closed_subset(subset_complement(the_carrier(sk0_6),topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8))),sk0_6)|spl0_39),
% 0.16/0.38 inference(component_clause,[status(thm)],[f290])).
% 0.16/0.38 fof(f293,plain,(
% 0.16/0.38 ~top_str(sk0_6)|~element(topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8)),powerset(the_carrier(sk0_6)))|~closed_subset(subset_complement(the_carrier(sk0_6),topstr_closure(sk0_6,subset_complement(the_carrier(sk0_6),sk0_8))),sk0_6)|spl0_17),
% 0.16/0.38 inference(resolution,[status(thm)],[f166,f71])).
% 0.16/0.38 fof(f294,plain,(
% 0.16/0.38 ~spl0_12|~spl0_15|~spl0_39|spl0_17),
% 0.16/0.38 inference(split_clause,[status(thm)],[f293,f142,f156,f290,f164])).
% 0.16/0.38 fof(f295,plain,(
% 0.16/0.38 ~closed_subset(interior(sk0_6,sk0_8),sk0_6)|spl0_39),
% 0.16/0.38 inference(forward_demodulation,[status(thm)],[f147,f292])).
% 0.16/0.38 fof(f296,plain,(
% 0.16/0.38 ~element(subset_complement(the_carrier(sk0_6),sk0_8),powerset(the_carrier(sk0_6)))|spl0_14|~spl0_33),
% 0.16/0.38 inference(resolution,[status(thm)],[f155,f247])).
% 0.16/0.38 fof(f297,plain,(
% 0.16/0.38 $false|spl0_14|~spl0_33),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f296,f176])).
% 0.16/0.38 fof(f298,plain,(
% 0.16/0.38 spl0_14|~spl0_33),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f297])).
% 0.16/0.38 fof(f300,plain,(
% 0.16/0.38 spl0_40 <=> topstr_closure(sk0_6,topstr_closure(sk0_6,interior(sk0_6,X0)))=topstr_closure(sk0_6,interior(sk0_6,X0))|~element(X0,powerset(the_carrier(sk0_6)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f303,plain,(
% 0.16/0.38 ![X0]: (topstr_closure(sk0_6,topstr_closure(sk0_6,interior(sk0_6,X0)))=topstr_closure(sk0_6,interior(sk0_6,X0))|~top_str(sk0_6)|~element(X0,powerset(the_carrier(sk0_6)))|~spl0_33)),
% 0.16/0.38 inference(resolution,[status(thm)],[f283,f30])).
% 0.16/0.38 fof(f304,plain,(
% 0.16/0.38 spl0_40|~spl0_12|~spl0_33),
% 0.16/0.38 inference(split_clause,[status(thm)],[f303,f300,f142,f246])).
% 0.16/0.38 fof(f305,plain,(
% 0.16/0.38 topstr_closure(sk0_6,topstr_closure(sk0_6,sk0_8))=topstr_closure(sk0_6,sk0_8)|~spl0_33),
% 0.16/0.38 inference(resolution,[status(thm)],[f283,f86])).
% 0.16/0.38 fof(f306,plain,(
% 0.16/0.38 spl0_41 <=> element(topstr_closure(sk0_6,sk0_8),powerset(the_carrier(sk0_6)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f309,plain,(
% 0.16/0.38 spl0_42 <=> closed_subset(topstr_closure(sk0_6,sk0_8),sk0_6)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f312,plain,(
% 0.16/0.38 ~element(topstr_closure(sk0_6,sk0_8),powerset(the_carrier(sk0_6)))|closed_subset(topstr_closure(sk0_6,sk0_8),sk0_6)|~spl0_33),
% 0.16/0.38 inference(paramodulation,[status(thm)],[f305,f247])).
% 0.16/0.38 fof(f313,plain,(
% 0.16/0.38 ~spl0_41|spl0_42|~spl0_33),
% 0.16/0.38 inference(split_clause,[status(thm)],[f312,f306,f309,f246])).
% 0.16/0.38 fof(f318,plain,(
% 0.16/0.38 spl0_43 <=> topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),sk0_2(powerset(the_carrier(sk0_7)))))=subset_complement(the_carrier(sk0_7),sk0_2(powerset(the_carrier(sk0_7))))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f321,plain,(
% 0.16/0.38 spl0_44 <=> open_subset(sk0_2(powerset(the_carrier(sk0_7))),sk0_7)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f324,plain,(
% 0.16/0.38 topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),sk0_2(powerset(the_carrier(sk0_7)))))=subset_complement(the_carrier(sk0_7),sk0_2(powerset(the_carrier(sk0_7))))|~open_subset(sk0_2(powerset(the_carrier(sk0_7))),sk0_7)|~spl0_27),
% 0.16/0.38 inference(resolution,[status(thm)],[f223,f42])).
% 0.16/0.38 fof(f325,plain,(
% 0.16/0.38 spl0_43|~spl0_44|~spl0_27),
% 0.16/0.38 inference(split_clause,[status(thm)],[f324,f318,f321,f218])).
% 0.16/0.38 fof(f326,plain,(
% 0.16/0.38 spl0_45 <=> topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),interior(sk0_7,X0)))=subset_complement(the_carrier(sk0_7),interior(sk0_7,X0))|~open_subset(interior(sk0_7,X0),sk0_7)|~element(X0,powerset(the_carrier(sk0_7)))),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f329,plain,(
% 0.16/0.38 ![X0]: (topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),interior(sk0_7,X0)))=subset_complement(the_carrier(sk0_7),interior(sk0_7,X0))|~open_subset(interior(sk0_7,X0),sk0_7)|~top_str(sk0_7)|~element(X0,powerset(the_carrier(sk0_7)))|~spl0_27)),
% 0.16/0.38 inference(resolution,[status(thm)],[f223,f30])).
% 0.16/0.38 fof(f330,plain,(
% 0.16/0.38 spl0_45|~spl0_4|~spl0_27),
% 0.16/0.38 inference(split_clause,[status(thm)],[f329,f326,f109,f218])).
% 0.16/0.38 fof(f331,plain,(
% 0.16/0.38 spl0_46 <=> topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),sk0_9))=subset_complement(the_carrier(sk0_7),sk0_9)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f332,plain,(
% 0.16/0.38 topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),sk0_9))=subset_complement(the_carrier(sk0_7),sk0_9)|~spl0_46),
% 0.16/0.38 inference(component_clause,[status(thm)],[f331])).
% 0.16/0.38 fof(f334,plain,(
% 0.16/0.38 spl0_47 <=> open_subset(sk0_9,sk0_7)),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f336,plain,(
% 0.16/0.38 ~open_subset(sk0_9,sk0_7)|spl0_47),
% 0.16/0.38 inference(component_clause,[status(thm)],[f334])).
% 0.16/0.38 fof(f337,plain,(
% 0.16/0.38 topstr_closure(sk0_7,subset_complement(the_carrier(sk0_7),sk0_9))=subset_complement(the_carrier(sk0_7),sk0_9)|~open_subset(sk0_9,sk0_7)|~spl0_27),
% 0.16/0.38 inference(resolution,[status(thm)],[f223,f87])).
% 0.16/0.38 fof(f338,plain,(
% 0.16/0.38 spl0_46|~spl0_47|~spl0_27),
% 0.16/0.38 inference(split_clause,[status(thm)],[f337,f331,f334,f218])).
% 0.16/0.38 fof(f339,plain,(
% 0.16/0.38 $false|~spl0_0|spl0_47),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f336,f279])).
% 0.16/0.38 fof(f340,plain,(
% 0.16/0.38 ~spl0_0|spl0_47),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f339])).
% 0.16/0.38 fof(f345,plain,(
% 0.16/0.38 interior(sk0_7,sk0_9)=subset_complement(the_carrier(sk0_7),subset_complement(the_carrier(sk0_7),sk0_9))|~spl0_46),
% 0.16/0.38 inference(backward_demodulation,[status(thm)],[f332,f114])).
% 0.16/0.38 fof(f346,plain,(
% 0.16/0.38 interior(sk0_7,sk0_9)=sk0_9|~spl0_46),
% 0.16/0.38 inference(forward_demodulation,[status(thm)],[f261,f345])).
% 0.16/0.38 fof(f347,plain,(
% 0.16/0.38 $false|~spl0_0|~spl0_46),
% 0.16/0.38 inference(forward_subsumption_resolution,[status(thm)],[f346,f278])).
% 0.16/0.38 fof(f348,plain,(
% 0.16/0.38 ~spl0_0|~spl0_46),
% 0.16/0.38 inference(contradiction_clause,[status(thm)],[f347])).
% 0.16/0.38 fof(f356,plain,(
% 0.16/0.38 ~closed_subset(sk0_8,sk0_6)|~spl0_1|spl0_39),
% 0.16/0.38 inference(backward_demodulation,[status(thm)],[f97,f295])).
% 0.16/0.38 fof(f359,plain,(
% 0.16/0.38 spl0_48 <=> topstr_closure(sk0_6,sk0_8)=sk0_8),
% 0.16/0.38 introduced(split_symbol_definition)).
% 0.16/0.38 fof(f362,plain,(
% 0.16/0.38 ~element(sk0_8,powerset(the_carrier(sk0_6)))|~topstr_closure(sk0_6,sk0_8)=sk0_8|~spl0_1|spl0_39|~spl0_34),
% 0.16/0.38 inference(resolution,[status(thm)],[f356,f252])).
% 0.16/0.38 fof(f363,plain,(
% 0.16/0.38 ~spl0_36|~spl0_48|~spl0_1|spl0_39|~spl0_34),
% 0.16/0.38 inference(split_clause,[status(thm)],[f362,f268,f359,f96,f290,f251])).
% 0.16/0.38 fof(f366,plain,(
% 0.16/0.38 ~topological_space(sk0_6)|~top_str(sk0_6)|~element(sk0_8,powerset(the_carrier(sk0_6)))|open_subset(sk0_8,sk0_6)|~spl0_1),
% 0.16/0.38 inference(paramodulation,[status(thm)],[f97,f50])).
% 0.16/0.38 fof(f367,plain,(
% 0.16/0.38 ~spl0_13|~spl0_12|~spl0_36|spl0_2|~spl0_1),
% 0.16/0.38 inference(split_clause,[status(thm)],[f366,f150,f142,f268,f100,f96])).
% 0.16/0.38 fof(f368,plain,(
% 0.16/0.38 $false),
% 0.16/0.38 inference(sat_refutation,[status(thm)],[f99,f103,f113,f116,f146,f149,f163,f171,f173,f199,f201,f222,f244,f250,f255,f267,f277,f294,f298,f304,f313,f325,f330,f338,f340,f348,f363,f367])).
% 0.16/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.39 % Elapsed time: 0.069779 seconds
% 0.16/0.39 % CPU time: 0.169654 seconds
% 0.16/0.39 % Memory used: 23.423 MB
%------------------------------------------------------------------------------