%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU337+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 : n018.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 0.14s 0.83s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU337+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.75 % Computer : n018.cluster.edu
% 0.11/0.75 % Model : x86_64 x86_64
% 0.11/0.75 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.75 % Memory : 8046.5625MB
% 0.11/0.75 % OS : Linux 6.8.0-71-generic
% 0.11/0.75 % CPULimit : 300
% 0.11/0.75 % WCLimit : 300
% 0.11/0.75 % DateTime : Mon Sep 21 06:15:29 UTC 2026
% 0.11/0.75 % CPUTime :
% 0.11/0.78 % Drodi V4.1.1
% 0.14/0.83 % Refutation found
% 0.14/0.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.83 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.83 fof(f169,axiom,(
% 0.14/0.83 (! [A,B] :( element(B,powerset(powerset(A)))=> element(complements_of_subsets(A,B),powerset(powerset(A))) ) )),
% 0.14/0.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.83 fof(f260,axiom,(
% 0.14/0.83 (! [A,B] :( element(B,powerset(powerset(A)))=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ) )),
% 0.14/0.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.83 fof(f404,lemma,(
% 0.14/0.83 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(powerset(the_carrier(A))))=> ( closed_subsets(B,A)<=> open_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) )) )),
% 0.14/0.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.83 fof(f410,conjecture,(
% 0.14/0.83 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(powerset(the_carrier(A))))=> ( open_subsets(B,A)<=> closed_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) )) )),
% 0.14/0.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.83 fof(f411,negated_conjecture,(
% 0.14/0.83 ~((! [A] :( top_str(A)=> (! [B] :( element(B,powerset(powerset(the_carrier(A))))=> ( open_subsets(B,A)<=> closed_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) )) ))),
% 0.14/0.83 inference(negated_conjecture,[status(cth)],[f410])).
% 0.14/0.83 fof(f1305,plain,(
% 0.14/0.83 ![A,B]: (~element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))))),
% 0.14/0.83 inference(pre_NNF_transformation,[status(thm)],[f169])).
% 0.14/0.83 fof(f1306,plain,(
% 0.14/0.83 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|element(complements_of_subsets(X1,X0),powerset(powerset(X1))))),
% 0.14/0.83 inference(cnf_transformation,[status(thm)],[f1305])).
% 0.14/0.83 fof(f1573,plain,(
% 0.14/0.83 ![A,B]: (~element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B)),
% 0.14/0.83 inference(pre_NNF_transformation,[status(thm)],[f260])).
% 0.14/0.83 fof(f1574,plain,(
% 0.14/0.83 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|complements_of_subsets(X1,complements_of_subsets(X1,X0))=X0)),
% 0.14/0.83 inference(cnf_transformation,[status(thm)],[f1573])).
% 0.14/0.83 fof(f2411,plain,(
% 0.14/0.83 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|(closed_subsets(B,A)<=>open_subsets(complements_of_subsets(the_carrier(A),B),A)))))),
% 0.14/0.83 inference(pre_NNF_transformation,[status(thm)],[f404])).
% 0.14/0.83 fof(f2412,plain,(
% 0.14/0.83 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|((~closed_subsets(B,A)|open_subsets(complements_of_subsets(the_carrier(A),B),A))&(closed_subsets(B,A)|~open_subsets(complements_of_subsets(the_carrier(A),B),A))))))),
% 0.14/0.83 inference(NNF_transformation,[status(thm)],[f2411])).
% 0.14/0.83 fof(f2413,plain,(
% 0.14/0.83 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|~closed_subsets(X1,X0)|open_subsets(complements_of_subsets(the_carrier(X0),X1),X0))),
% 0.14/0.83 inference(cnf_transformation,[status(thm)],[f2412])).
% 0.14/0.83 fof(f2414,plain,(
% 0.14/0.83 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|closed_subsets(X1,X0)|~open_subsets(complements_of_subsets(the_carrier(X0),X1),X0))),
% 0.14/0.83 inference(cnf_transformation,[status(thm)],[f2412])).
% 0.14/0.83 fof(f2432,plain,(
% 0.14/0.83 (?[A]: (top_str(A)&(?[B]: (element(B,powerset(powerset(the_carrier(A))))&(open_subsets(B,A)<~>closed_subsets(complements_of_subsets(the_carrier(A),B),A))))))),
% 0.14/0.83 inference(pre_NNF_transformation,[status(thm)],[f411])).
% 0.14/0.83 fof(f2433,plain,(
% 0.14/0.83 ?[A]: (top_str(A)&(?[B]: (element(B,powerset(powerset(the_carrier(A))))&((open_subsets(B,A)|closed_subsets(complements_of_subsets(the_carrier(A),B),A))&(~open_subsets(B,A)|~closed_subsets(complements_of_subsets(the_carrier(A),B),A))))))),
% 0.14/0.83 inference(NNF_transformation,[status(thm)],[f2432])).
% 0.14/0.83 fof(f2434,plain,(
% 0.14/0.83 (top_str(sK329_skl)&(element(sK330_skl,powerset(powerset(the_carrier(sK329_skl))))&((open_subsets(sK330_skl,sK329_skl)|closed_subsets(complements_of_subsets(the_carrier(sK329_skl),sK330_skl),sK329_skl))&(~open_subsets(sK330_skl,sK329_skl)|~closed_subsets(complements_of_subsets(the_carrier(sK329_skl),sK330_skl),sK329_skl)))))),
% 0.14/0.83 inference(skolemize,[status(esa),new_symbols(skolem,[sK329_skl,sK330_skl]),skolemize(A,sK329_skl),skolemize(B,sK330_skl)],[f2433])).
% 0.14/0.83 fof(f2435,plain,(
% 0.14/0.83 top_str(sK329_skl)),
% 0.14/0.83 inference(cnf_transformation,[status(thm)],[f2434])).
% 0.14/0.83 fof(f2436,plain,(
% 0.14/0.83 element(sK330_skl,powerset(powerset(the_carrier(sK329_skl))))),
% 0.14/0.83 inference(cnf_transformation,[status(thm)],[f2434])).
% 0.14/0.83 fof(f2437,plain,(
% 0.14/0.83 open_subsets(sK330_skl,sK329_skl)|closed_subsets(complements_of_subsets(the_carrier(sK329_skl),sK330_skl),sK329_skl)),
% 0.14/0.83 inference(cnf_transformation,[status(thm)],[f2434])).
% 0.14/0.83 fof(f2438,plain,(
% 0.14/0.83 ~open_subsets(sK330_skl,sK329_skl)|~closed_subsets(complements_of_subsets(the_carrier(sK329_skl),sK330_skl),sK329_skl)),
% 0.14/0.83 inference(cnf_transformation,[status(thm)],[f2434])).
% 0.14/0.83 fof(f3576,definition,(
% 0.14/0.83 sQ31_spl <=> (open_subsets(sK330_skl,sK329_skl))),
% 0.14/0.83 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.14/0.83 fof(f3577,plain,(
% 0.14/0.83 open_subsets(sK330_skl,sK329_skl)|~sQ31_spl),
% 0.14/0.83 inference(component_clause,[status(thm)],[f3576])).
% 0.14/0.83 fof(f3578,plain,(
% 0.14/0.83 ~open_subsets(sK330_skl,sK329_skl)|sQ31_spl),
% 0.14/0.83 inference(component_clause,[status(thm)],[f3576])).
% 0.14/0.83 fof(f3579,definition,(
% 0.14/0.83 sQ32_spl <=> (closed_subsets(complements_of_subsets(the_carrier(sK329_skl),sK330_skl),sK329_skl))),
% 0.14/0.83 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.14/0.83 fof(f3582,plain,(
% 0.14/0.83 sQ31_spl|sQ32_spl),
% 0.14/0.83 inference(split_clause,[status(thm)],[f2437,f3576,f3579])).
% 0.14/0.83 fof(f3583,plain,(
% 0.14/0.83 ~sQ31_spl|~sQ32_spl),
% 0.14/0.83 inference(split_clause,[status(thm)],[f2438,f3576,f3579])).
% 0.14/0.83 fof(f4025,definition,(
% 0.14/0.83 sQ63_spl <=> (top_str(sK329_skl))),
% 0.14/0.83 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 0.14/0.83 fof(f4027,plain,(
% 0.14/0.83 ~top_str(sK329_skl)|sQ63_spl),
% 0.14/0.83 inference(component_clause,[status(thm)],[f4025])).
% 0.14/0.83 fof(f4032,plain,(
% 0.14/0.83 $false|sQ63_spl),
% 0.14/0.83 inference(forward_subsumption_resolution,[status(thm)],[f4027,f2435])).
% 0.14/0.83 fof(f4033,plain,(
% 0.14/0.83 sQ63_spl),
% 0.14/0.83 inference(contradiction_clause,[status(thm)],[f4032])).
% 0.14/0.83 fof(f4037,plain,(
% 0.14/0.83 complements_of_subsets(the_carrier(sK329_skl),complements_of_subsets(the_carrier(sK329_skl),sK330_skl))=sK330_skl),
% 0.14/0.83 inference(resolution,[status(thm)],[f1574,f2436])).
% 0.14/0.83 fof(f4055,plain,(
% 0.14/0.83 element(complements_of_subsets(the_carrier(sK329_skl),sK330_skl),powerset(powerset(the_carrier(sK329_skl))))),
% 0.14/0.83 inference(resolution,[status(thm)],[f1306,f2436])).
% 0.14/0.83 fof(f4105,plain,(
% 0.14/0.83 ~top_str(sK329_skl)|~closed_subsets(complements_of_subsets(the_carrier(sK329_skl),sK330_skl),sK329_skl)|open_subsets(complements_of_subsets(the_carrier(sK329_skl),complements_of_subsets(the_carrier(sK329_skl),sK330_skl)),sK329_skl)),
% 0.14/0.83 inference(resolution,[status(thm)],[f2413,f4055])).
% 0.14/0.83 fof(f4107,definition,(
% 0.14/0.83 sQ76_spl <=> (open_subsets(complements_of_subsets(the_carrier(sK329_skl),complements_of_subsets(the_carrier(sK329_skl),sK330_skl)),sK329_skl))),
% 0.14/0.83 introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition])).
% 0.14/0.83 fof(f4108,plain,(
% 0.14/0.83 open_subsets(complements_of_subsets(the_carrier(sK329_skl),complements_of_subsets(the_carrier(sK329_skl),sK330_skl)),sK329_skl)|~sQ76_spl),
% 0.14/0.83 inference(component_clause,[status(thm)],[f4107])).
% 0.14/0.83 fof(f4109,plain,(
% 0.14/0.83 ~open_subsets(complements_of_subsets(the_carrier(sK329_skl),complements_of_subsets(the_carrier(sK329_skl),sK330_skl)),sK329_skl)|sQ76_spl),
% 0.14/0.83 inference(component_clause,[status(thm)],[f4107])).
% 0.14/0.83 fof(f4110,plain,(
% 0.14/0.83 ~sQ63_spl|~sQ32_spl|sQ76_spl),
% 0.14/0.83 inference(split_clause,[status(thm)],[f4105,f4025,f3579,f4107])).
% 0.14/0.83 fof(f4115,plain,(
% 0.14/0.83 open_subsets(sK330_skl,sK329_skl)|~sQ76_spl),
% 0.14/0.83 inference(forward_demodulation,[status(thm)],[f4037,f4108])).
% 0.14/0.83 fof(f4116,plain,(
% 0.14/0.83 $false|sQ31_spl|~sQ76_spl),
% 0.14/0.83 inference(forward_subsumption_resolution,[status(thm)],[f4115,f3578])).
% 0.14/0.83 fof(f4117,plain,(
% 0.14/0.83 sQ31_spl|~sQ76_spl),
% 0.14/0.83 inference(contradiction_clause,[status(thm)],[f4116])).
% 0.14/0.83 fof(f4120,plain,(
% 0.14/0.83 ~top_str(sK329_skl)|closed_subsets(complements_of_subsets(the_carrier(sK329_skl),sK330_skl),sK329_skl)|~open_subsets(complements_of_subsets(the_carrier(sK329_skl),complements_of_subsets(the_carrier(sK329_skl),sK330_skl)),sK329_skl)),
% 0.14/0.83 inference(resolution,[status(thm)],[f2414,f4055])).
% 0.14/0.83 fof(f4122,plain,(
% 0.14/0.83 ~sQ63_spl|sQ32_spl|~sQ76_spl),
% 0.14/0.86 inference(split_clause,[status(thm)],[f4120,f4025,f3579,f4107])).
% 0.14/0.86 fof(f4124,plain,(
% 0.14/0.86 ~open_subsets(sK330_skl,sK329_skl)|sQ76_spl),
% 0.14/0.86 inference(forward_demodulation,[status(thm)],[f4037,f4109])).
% 0.14/0.86 fof(f4163,plain,(
% 0.14/0.86 $false|~sQ31_spl|sQ76_spl),
% 0.14/0.86 inference(forward_subsumption_resolution,[status(thm)],[f4124,f3577])).
% 0.14/0.86 fof(f4164,plain,(
% 0.14/0.86 ~sQ31_spl|sQ76_spl),
% 0.14/0.86 inference(contradiction_clause,[status(thm)],[f4163])).
% 0.14/0.86 fof(f4165,plain,(
% 0.14/0.86 $false),
% 0.14/0.86 inference(sat_refutation,[status(thm)],[f3582,f3583,f4033,f4110,f4117,f4122,f4164])).
% 0.14/0.86 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.88 % Elapsed time: 0.121564 seconds
% 0.14/0.88 % CPU time: 0.479642 seconds
% 0.14/0.88 % Total memory used: 189.134 MB
% 0.14/0.88 % Net memory used: 188.121 MB
%------------------------------------------------------------------------------