%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU341+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:22:22 PM UTC 2026
% Result : Theorem 9.94s 1.84s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU341+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % Computer : n005.cluster.edu
% 0.17/0.47 % Model : x86_64 x86_64
% 0.17/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.47 % Memory : 8046.5625MB
% 0.17/0.47 % OS : Linux 6.8.0-71-generic
% 0.17/0.47 % CPULimit : 300
% 0.17/0.47 % WCLimit : 300
% 0.17/0.47 % DateTime : Mon Sep 21 06:13:47 UTC 2026
% 0.17/0.47 % CPUTime :
% 0.21/0.54 % Drodi V4.1.1
% 9.94/1.84 % Refutation found
% 9.94/1.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.94/1.84 % SZS output start CNFRefutation for theBenchmark
% 9.94/1.84 fof(f51,axiom,(
% 9.94/1.84 (! [A] :( ( ~ empty_carrier(A)& topological_space(A)& top_str(A) )=> (! [B] :( element(B,the_carrier(A))=> (! [C] :( element(C,powerset(the_carrier(A)))=> ( point_neighbourhood(C,A,B)<=> in(B,interior(A,C)) ) ) )) )) )),
% 9.94/1.84 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.94/1.84 fof(f528,lemma,(
% 9.94/1.84 (! [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) ) ) ) )) )) )) )),
% 9.94/1.84 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.94/1.84 fof(f531,conjecture,(
% 9.94/1.84 (! [A] :( ( ~ empty_carrier(A)& topological_space(A)& top_str(A) )=> (! [B] :( element(B,powerset(the_carrier(A)))=> (! [C] :( element(C,the_carrier(A))=> ( ( open_subset(B,A)& in(C,B) )=> point_neighbourhood(B,A,C) ) ) )) )) )),
% 9.94/1.84 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.94/1.84 fof(f532,negated_conjecture,(
% 9.94/1.84 ~((! [A] :( ( ~ empty_carrier(A)& topological_space(A)& top_str(A) )=> (! [B] :( element(B,powerset(the_carrier(A)))=> (! [C] :( element(C,the_carrier(A))=> ( ( open_subset(B,A)& in(C,B) )=> point_neighbourhood(B,A,C) ) ) )) )) ))),
% 9.94/1.84 inference(negated_conjecture,[status(cth)],[f531])).
% 9.94/1.84 fof(f786,plain,(
% 9.94/1.84 ![A]: (((empty_carrier(A)|~topological_space(A))|~top_str(A))|(![B]: (~element(B,the_carrier(A))|(![C]: (~element(C,powerset(the_carrier(A)))|(point_neighbourhood(C,A,B)<=>in(B,interior(A,C))))))))),
% 9.94/1.84 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 9.94/1.84 fof(f787,plain,(
% 9.94/1.84 ![A]: (((empty_carrier(A)|~topological_space(A))|~top_str(A))|(![B]: (~element(B,the_carrier(A))|(![C]: (~element(C,powerset(the_carrier(A)))|((~point_neighbourhood(C,A,B)|in(B,interior(A,C)))&(point_neighbourhood(C,A,B)|~in(B,interior(A,C)))))))))),
% 9.94/1.84 inference(NNF_transformation,[status(thm)],[f786])).
% 9.94/1.84 fof(f789,plain,(
% 9.94/1.84 ![X0,X1,X2]: (empty_carrier(X0)|~topological_space(X0)|~top_str(X0)|~element(X1,the_carrier(X0))|~element(X2,powerset(the_carrier(X0)))|point_neighbourhood(X2,X0,X1)|~in(X1,interior(X0,X2)))),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f787])).
% 9.94/1.84 fof(f2852,plain,(
% 9.94/1.84 ![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))))))))))),
% 9.94/1.84 inference(pre_NNF_transformation,[status(thm)],[f528])).
% 9.94/1.84 fof(f2853,plain,(
% 9.94/1.84 ![X0,X1,X2,X3]: (~topological_space(X0)|~top_str(X0)|~top_str(X1)|~element(X2,powerset(the_carrier(X0)))|~element(X3,powerset(the_carrier(X1)))|~open_subset(X3,X1)|interior(X1,X3)=X3)),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2852])).
% 9.94/1.84 fof(f2862,plain,(
% 9.94/1.84 (?[A]: (((~empty_carrier(A)&topological_space(A))&top_str(A))&(?[B]: (element(B,powerset(the_carrier(A)))&(?[C]: (element(C,the_carrier(A))&((open_subset(B,A)&in(C,B))&~point_neighbourhood(B,A,C))))))))),
% 9.94/1.84 inference(pre_NNF_transformation,[status(thm)],[f532])).
% 9.94/1.84 fof(f2863,plain,(
% 9.94/1.84 (((~empty_carrier(sK362_skl)&topological_space(sK362_skl))&top_str(sK362_skl))&(element(sK363_skl,powerset(the_carrier(sK362_skl)))&(element(sK364_skl,the_carrier(sK362_skl))&((open_subset(sK363_skl,sK362_skl)&in(sK364_skl,sK363_skl))&~point_neighbourhood(sK363_skl,sK362_skl,sK364_skl)))))),
% 9.94/1.84 inference(skolemize,[status(esa),new_symbols(skolem,[sK362_skl,sK363_skl,sK364_skl]),skolemize(A,sK362_skl),skolemize(B,sK363_skl),skolemize(C,sK364_skl)],[f2862])).
% 9.94/1.84 fof(f2864,plain,(
% 9.94/1.84 ~empty_carrier(sK362_skl)),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2863])).
% 9.94/1.84 fof(f2865,plain,(
% 9.94/1.84 topological_space(sK362_skl)),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2863])).
% 9.94/1.84 fof(f2866,plain,(
% 9.94/1.84 top_str(sK362_skl)),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2863])).
% 9.94/1.84 fof(f2867,plain,(
% 9.94/1.84 element(sK363_skl,powerset(the_carrier(sK362_skl)))),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2863])).
% 9.94/1.84 fof(f2868,plain,(
% 9.94/1.84 element(sK364_skl,the_carrier(sK362_skl))),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2863])).
% 9.94/1.84 fof(f2869,plain,(
% 9.94/1.84 open_subset(sK363_skl,sK362_skl)),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2863])).
% 9.94/1.84 fof(f2870,plain,(
% 9.94/1.84 in(sK364_skl,sK363_skl)),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2863])).
% 9.94/1.84 fof(f2871,plain,(
% 9.94/1.84 ~point_neighbourhood(sK363_skl,sK362_skl,sK364_skl)),
% 9.94/1.84 inference(cnf_transformation,[status(thm)],[f2863])).
% 9.94/1.84 fof(f3670,definition,(
% 9.94/1.84 ![X0,X2]: (sQ31_spl <=> (~topological_space(X0)|~top_str(X0)|~element(X2,powerset(the_carrier(X0)))))),
% 9.94/1.84 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 9.94/1.84 fof(f3671,plain,(
% 9.94/1.84 ![X0,X1]: (~topological_space(X0)|~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~sQ31_spl)),
% 9.94/1.84 inference(component_clause,[status(thm)],[f3670])).
% 9.94/1.84 fof(f3673,definition,(
% 9.94/1.84 ![X1,X3]: (sQ32_spl <=> (~top_str(X1)|~element(X3,powerset(the_carrier(X1)))|~open_subset(X3,X1)|interior(X1,X3)=X3))),
% 9.94/1.84 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 9.94/1.84 fof(f3674,plain,(
% 9.94/1.84 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~open_subset(X1,X0)|interior(X0,X1)=X1|~sQ32_spl)),
% 9.94/1.84 inference(component_clause,[status(thm)],[f3673])).
% 9.94/1.84 fof(f3676,plain,(
% 9.94/1.84 sQ31_spl|sQ32_spl),
% 9.94/1.84 inference(split_clause,[status(thm)],[f2853,f3670,f3673])).
% 9.94/1.84 fof(f4112,plain,(
% 9.94/1.84 ![X0]: (empty_carrier(sK362_skl)|~topological_space(sK362_skl)|~top_str(sK362_skl)|~element(X0,powerset(the_carrier(sK362_skl)))|point_neighbourhood(X0,sK362_skl,sK364_skl)|~in(sK364_skl,interior(sK362_skl,X0)))),
% 9.94/1.84 inference(resolution,[status(thm)],[f2868,f789])).
% 9.94/1.84 fof(f4114,definition,(
% 9.94/1.84 sQ61_spl <=> (empty_carrier(sK362_skl))),
% 9.94/1.84 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 9.94/1.84 fof(f4115,plain,(
% 9.94/1.84 empty_carrier(sK362_skl)|~sQ61_spl),
% 9.94/1.84 inference(component_clause,[status(thm)],[f4114])).
% 9.94/1.84 fof(f4117,definition,(
% 9.94/1.84 sQ62_spl <=> (topological_space(sK362_skl))),
% 9.94/1.84 introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition])).
% 9.94/1.84 fof(f4119,plain,(
% 9.94/1.84 ~topological_space(sK362_skl)|sQ62_spl),
% 9.94/1.84 inference(component_clause,[status(thm)],[f4117])).
% 9.94/1.84 fof(f4120,definition,(
% 9.94/1.84 sQ63_spl <=> (top_str(sK362_skl))),
% 9.94/1.84 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 9.94/1.84 fof(f4122,plain,(
% 9.94/1.84 ~top_str(sK362_skl)|sQ63_spl),
% 9.94/1.84 inference(component_clause,[status(thm)],[f4120])).
% 9.94/1.84 fof(f4123,definition,(
% 9.94/1.84 ![X0]: (sQ64_spl <=> (~element(X0,powerset(the_carrier(sK362_skl)))|point_neighbourhood(X0,sK362_skl,sK364_skl)|~in(sK364_skl,interior(sK362_skl,X0))))),
% 9.94/1.84 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 9.94/1.84 fof(f4124,plain,(
% 9.94/1.84 ![X0]: (~element(X0,powerset(the_carrier(sK362_skl)))|point_neighbourhood(X0,sK362_skl,sK364_skl)|~in(sK364_skl,interior(sK362_skl,X0))|~sQ64_spl)),
% 9.94/1.84 inference(component_clause,[status(thm)],[f4123])).
% 9.94/1.84 fof(f4126,plain,(
% 9.94/1.84 sQ61_spl|~sQ62_spl|~sQ63_spl|sQ64_spl),
% 9.94/1.84 inference(split_clause,[status(thm)],[f4112,f4114,f4117,f4120,f4123])).
% 9.94/1.84 fof(f4131,plain,(
% 9.94/1.84 $false|sQ63_spl),
% 9.94/1.84 inference(forward_subsumption_resolution,[status(thm)],[f4122,f2866])).
% 9.94/1.84 fof(f4132,plain,(
% 9.94/1.84 sQ63_spl),
% 9.94/1.84 inference(contradiction_clause,[status(thm)],[f4131])).
% 9.94/1.84 fof(f4133,plain,(
% 9.94/1.84 $false|sQ62_spl),
% 9.94/1.84 inference(forward_subsumption_resolution,[status(thm)],[f4119,f2865])).
% 9.94/1.84 fof(f4134,plain,(
% 9.94/1.84 sQ62_spl),
% 9.94/1.84 inference(contradiction_clause,[status(thm)],[f4133])).
% 9.94/1.84 fof(f4135,plain,(
% 9.94/1.84 $false|~sQ61_spl),
% 9.94/1.84 inference(forward_subsumption_resolution,[status(thm)],[f4115,f2864])).
% 9.94/1.84 fof(f4136,plain,(
% 9.94/1.84 ~sQ61_spl),
% 9.94/1.84 inference(contradiction_clause,[status(thm)],[f4135])).
% 9.94/1.84 fof(f4166,definition,(
% 9.94/1.84 sQ70_spl <=> (element(sK363_skl,powerset(the_carrier(sK362_skl))))),
% 9.94/1.84 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 9.94/1.84 fof(f4168,plain,(
% 9.94/1.84 ~element(sK363_skl,powerset(the_carrier(sK362_skl)))|sQ70_spl),
% 9.94/1.84 inference(component_clause,[status(thm)],[f4166])).
% 9.94/1.84 fof(f4242,definition,(
% 9.94/1.84 sQ78_spl <=> (in(sK364_skl,sK363_skl))),
% 9.94/1.84 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 9.94/1.86 fof(f4244,plain,(
% 9.94/1.86 ~in(sK364_skl,sK363_skl)|sQ78_spl),
% 9.94/1.86 inference(component_clause,[status(thm)],[f4242])).
% 9.94/1.86 fof(f4252,plain,(
% 9.94/1.86 $false|sQ70_spl),
% 9.94/1.86 inference(forward_subsumption_resolution,[status(thm)],[f4168,f2867])).
% 9.94/1.86 fof(f4253,plain,(
% 9.94/1.86 sQ70_spl),
% 9.94/1.86 inference(contradiction_clause,[status(thm)],[f4252])).
% 9.94/1.86 fof(f4254,plain,(
% 9.94/1.86 $false|sQ78_spl),
% 9.94/1.86 inference(forward_subsumption_resolution,[status(thm)],[f4244,f2870])).
% 9.94/1.86 fof(f4255,plain,(
% 9.94/1.86 sQ78_spl),
% 9.94/1.86 inference(contradiction_clause,[status(thm)],[f4254])).
% 9.94/1.86 fof(f4556,plain,(
% 9.94/1.86 ![X0]: (~top_str(sK362_skl)|~element(X0,powerset(the_carrier(sK362_skl)))|~sQ31_spl)),
% 9.94/1.86 inference(resolution,[status(thm)],[f3671,f2865])).
% 9.94/1.86 fof(f4557,definition,(
% 9.94/1.86 ![X0]: (sQ107_spl <=> (~element(X0,powerset(the_carrier(sK362_skl)))))),
% 9.94/1.86 introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition])).
% 9.94/1.86 fof(f4558,plain,(
% 9.94/1.86 ![X0]: (~element(X0,powerset(the_carrier(sK362_skl)))|~sQ107_spl)),
% 9.94/1.86 inference(component_clause,[status(thm)],[f4557])).
% 9.94/1.86 fof(f4560,plain,(
% 9.94/1.86 ~sQ63_spl|sQ107_spl|~sQ31_spl),
% 9.94/1.86 inference(split_clause,[status(thm)],[f4556,f4120,f4557,f3670])).
% 9.94/1.86 fof(f4577,plain,(
% 9.94/1.86 $false|~sQ107_spl),
% 9.94/1.86 inference(backward_subsumption_resolution,[status(thm)],[f2867,f4558])).
% 9.94/1.86 fof(f4587,plain,(
% 9.94/1.86 ~sQ107_spl),
% 9.94/1.86 inference(contradiction_clause,[status(thm)],[f4577])).
% 9.94/1.86 fof(f5902,plain,(
% 9.94/1.86 ![X0]: (~element(X0,powerset(the_carrier(sK362_skl)))|~open_subset(X0,sK362_skl)|interior(sK362_skl,X0)=X0|~sQ32_spl)),
% 9.94/1.86 inference(resolution,[status(thm)],[f3674,f2866])).
% 9.94/1.86 fof(f5995,plain,(
% 9.94/1.86 ~element(sK363_skl,powerset(the_carrier(sK362_skl)))|interior(sK362_skl,sK363_skl)=sK363_skl|~sQ32_spl),
% 9.94/1.86 inference(resolution,[status(thm)],[f5902,f2869])).
% 9.94/1.86 fof(f6004,definition,(
% 9.94/1.86 sQ195_spl <=> (interior(sK362_skl,sK363_skl)=sK363_skl)),
% 9.94/1.86 introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition])).
% 9.94/1.86 fof(f6005,plain,(
% 9.94/1.86 interior(sK362_skl,sK363_skl)=sK363_skl|~sQ195_spl),
% 9.94/1.86 inference(component_clause,[status(thm)],[f6004])).
% 9.94/1.86 fof(f6007,plain,(
% 9.94/1.86 ~sQ70_spl|sQ195_spl|~sQ32_spl),
% 9.94/1.86 inference(split_clause,[status(thm)],[f5995,f4166,f6004,f3673])).
% 9.94/1.86 fof(f6009,plain,(
% 9.94/1.86 ~element(sK363_skl,powerset(the_carrier(sK362_skl)))|point_neighbourhood(sK363_skl,sK362_skl,sK364_skl)|~in(sK364_skl,sK363_skl)|~sQ64_spl|~sQ195_spl),
% 9.94/1.86 inference(paramodulation,[status(thm)],[f6005,f4124])).
% 9.94/1.86 fof(f6013,definition,(
% 9.94/1.86 sQ196_spl <=> (point_neighbourhood(sK363_skl,sK362_skl,sK364_skl))),
% 9.94/1.86 introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition])).
% 9.94/1.86 fof(f6014,plain,(
% 9.94/1.86 point_neighbourhood(sK363_skl,sK362_skl,sK364_skl)|~sQ196_spl),
% 9.94/1.86 inference(component_clause,[status(thm)],[f6013])).
% 9.94/1.86 fof(f6016,plain,(
% 9.94/1.86 ~sQ70_spl|sQ196_spl|~sQ78_spl|~sQ64_spl|~sQ195_spl),
% 9.94/1.86 inference(split_clause,[status(thm)],[f6009,f4166,f6013,f4242,f4123,f6004])).
% 9.94/1.86 fof(f6029,plain,(
% 9.94/1.86 $false|~sQ196_spl),
% 9.94/1.86 inference(forward_subsumption_resolution,[status(thm)],[f6014,f2871])).
% 9.94/1.86 fof(f6030,plain,(
% 9.94/1.86 ~sQ196_spl),
% 9.94/1.86 inference(contradiction_clause,[status(thm)],[f6029])).
% 9.94/1.86 fof(f6031,plain,(
% 9.94/1.86 $false),
% 9.94/1.86 inference(sat_refutation,[status(thm)],[f3676,f4126,f4132,f4134,f4136,f4253,f4255,f4560,f4587,f6007,f6016,f6030])).
% 9.94/1.86 % SZS output end CNFRefutation for theBenchmark.p
% 9.94/1.89 % Elapsed time: 1.400310 seconds
% 9.94/1.89 % CPU time: 10.336592 seconds
% 9.94/1.89 % Total memory used: 259.452 MB
% 9.94/1.89 % Net memory used: 251.116 MB
%------------------------------------------------------------------------------