%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU336+1 : 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 : n003.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 02:22:21 PM UTC 2026
% Result : Theorem 14.33s 2.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU336+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 06:13:46 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 14.33/2.44 % Refutation found
% 14.33/2.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.33/2.44 % SZS output start CNFRefutation for theBenchmark
% 14.33/2.44 fof(f17,axiom,(
% 14.33/2.44 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(powerset(the_carrier(A))))=> ( open_subsets(B,A)<=> (! [C] :( element(C,powerset(the_carrier(A)))=> ( in(C,B)=> open_subset(C,A) ) ) )) ) )) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f18,axiom,(
% 14.33/2.44 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(powerset(the_carrier(A))))=> ( closed_subsets(B,A)<=> (! [C] :( element(C,powerset(the_carrier(A)))=> ( in(C,B)=> closed_subset(C,A) ) ) )) ) )) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f19,axiom,(
% 14.33/2.44 (! [A,B] :( element(B,powerset(powerset(A)))=> (! [C] :( element(C,powerset(powerset(A)))=> ( C = complements_of_subsets(A,B)<=> (! [D] :( element(D,powerset(A))=> ( in(D,C)<=> in(subset_complement(A,D),B) ) ) )) ) )) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f23,axiom,(
% 14.33/2.44 (! [A,B] :( element(B,powerset(powerset(A)))=> element(complements_of_subsets(A,B),powerset(powerset(A))) ) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f34,axiom,(
% 14.33/2.44 (! [A,B] :( element(B,powerset(powerset(A)))=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f39,conjecture,(
% 14.33/2.44 (! [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) ) ) )) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f40,negated_conjecture,(
% 14.33/2.44 ~((! [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) ) ) )) ))),
% 14.33/2.44 inference(negated_conjecture,[status(cth)],[f39])).
% 14.33/2.44 fof(f42,axiom,(
% 14.33/2.44 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( closed_subset(B,A)<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) )) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f44,axiom,(
% 14.33/2.44 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( open_subset(B,A)<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) )) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f46,axiom,(
% 14.33/2.44 (! [A,B,C] :( ( in(A,B)& element(B,powerset(C)) )=> element(A,C) ) )),
% 14.33/2.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 14.33/2.44 fof(f107,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|(open_subsets(B,A)<=>(![C]: (~element(C,powerset(the_carrier(A)))|(~in(C,B)|open_subset(C,A))))))))),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 14.33/2.44 fof(f108,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|((~open_subsets(B,A)|(![C]: (~element(C,powerset(the_carrier(A)))|(~in(C,B)|open_subset(C,A)))))&(open_subsets(B,A)|(?[C]: (element(C,powerset(the_carrier(A)))&(in(C,B)&~open_subset(C,A)))))))))),
% 14.33/2.44 inference(NNF_transformation,[status(thm)],[f107])).
% 14.33/2.44 fof(f109,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|((~open_subsets(B,A)|(![C]: (~element(C,powerset(the_carrier(A)))|(~in(C,B)|open_subset(C,A)))))&(open_subsets(B,A)|(element(sK0_skl(B,A),powerset(the_carrier(A)))&(in(sK0_skl(B,A),B)&~open_subset(sK0_skl(B,A),A))))))))),
% 14.33/2.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f108])).
% 14.33/2.44 fof(f110,plain,(
% 14.33/2.44 ![X0,X1,X2]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|~open_subsets(X1,X0)|~element(X2,powerset(the_carrier(X0)))|~in(X2,X1)|open_subset(X2,X0))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f109])).
% 14.33/2.44 fof(f111,plain,(
% 14.33/2.44 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|open_subsets(X1,X0)|element(sK0_skl(X1,X0),powerset(the_carrier(X0))))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f109])).
% 14.33/2.44 fof(f112,plain,(
% 14.33/2.44 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|open_subsets(X1,X0)|in(sK0_skl(X1,X0),X1))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f109])).
% 14.33/2.44 fof(f113,plain,(
% 14.33/2.44 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|open_subsets(X1,X0)|~open_subset(sK0_skl(X1,X0),X0))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f109])).
% 14.33/2.44 fof(f114,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|(closed_subsets(B,A)<=>(![C]: (~element(C,powerset(the_carrier(A)))|(~in(C,B)|closed_subset(C,A))))))))),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 14.33/2.44 fof(f115,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|((~closed_subsets(B,A)|(![C]: (~element(C,powerset(the_carrier(A)))|(~in(C,B)|closed_subset(C,A)))))&(closed_subsets(B,A)|(?[C]: (element(C,powerset(the_carrier(A)))&(in(C,B)&~closed_subset(C,A)))))))))),
% 14.33/2.44 inference(NNF_transformation,[status(thm)],[f114])).
% 14.33/2.44 fof(f116,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(powerset(the_carrier(A))))|((~closed_subsets(B,A)|(![C]: (~element(C,powerset(the_carrier(A)))|(~in(C,B)|closed_subset(C,A)))))&(closed_subsets(B,A)|(element(sK1_skl(B,A),powerset(the_carrier(A)))&(in(sK1_skl(B,A),B)&~closed_subset(sK1_skl(B,A),A))))))))),
% 14.33/2.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f115])).
% 14.33/2.44 fof(f117,plain,(
% 14.33/2.44 ![X0,X1,X2]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|~closed_subsets(X1,X0)|~element(X2,powerset(the_carrier(X0)))|~in(X2,X1)|closed_subset(X2,X0))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f116])).
% 14.33/2.44 fof(f118,plain,(
% 14.33/2.44 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|closed_subsets(X1,X0)|element(sK1_skl(X1,X0),powerset(the_carrier(X0))))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f116])).
% 14.33/2.44 fof(f119,plain,(
% 14.33/2.44 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|closed_subsets(X1,X0)|in(sK1_skl(X1,X0),X1))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f116])).
% 14.33/2.44 fof(f120,plain,(
% 14.33/2.44 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(powerset(the_carrier(X0))))|closed_subsets(X1,X0)|~closed_subset(sK1_skl(X1,X0),X0))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f116])).
% 14.33/2.44 fof(f121,plain,(
% 14.33/2.44 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|(C=complements_of_subsets(A,B)<=>(![D]: (~element(D,powerset(A))|(in(D,C)<=>in(subset_complement(A,D),B))))))))),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 14.33/2.44 fof(f122,plain,(
% 14.33/2.44 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|((~C=complements_of_subsets(A,B)|(![D]: (~element(D,powerset(A))|((~in(D,C)|in(subset_complement(A,D),B))&(in(D,C)|~in(subset_complement(A,D),B))))))&(C=complements_of_subsets(A,B)|(?[D]: (element(D,powerset(A))&((~in(D,C)|~in(subset_complement(A,D),B))&(in(D,C)|in(subset_complement(A,D),B))))))))))),
% 14.33/2.44 inference(NNF_transformation,[status(thm)],[f121])).
% 14.33/2.44 fof(f123,plain,(
% 14.33/2.44 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|((~C=complements_of_subsets(A,B)|(![D]: (~element(D,powerset(A))|((~in(D,C)|in(subset_complement(A,D),B))&(in(D,C)|~in(subset_complement(A,D),B))))))&(C=complements_of_subsets(A,B)|(element(sK2_skl(C,B,A),powerset(A))&((~in(sK2_skl(C,B,A),C)|~in(subset_complement(A,sK2_skl(C,B,A)),B))&(in(sK2_skl(C,B,A),C)|in(subset_complement(A,sK2_skl(C,B,A)),B)))))))))),
% 14.33/2.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f122])).
% 14.33/2.44 fof(f124,plain,(
% 14.33/2.44 ![X0,X1,X2,X3]: (~element(X0,powerset(powerset(X1)))|~element(X2,powerset(powerset(X1)))|~X2=complements_of_subsets(X1,X0)|~element(X3,powerset(X1))|~in(X3,X2)|in(subset_complement(X1,X3),X0))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f123])).
% 14.33/2.44 fof(f131,plain,(
% 14.33/2.44 ![A,B]: (~element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))))),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 14.33/2.44 fof(f132,plain,(
% 14.33/2.44 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|element(complements_of_subsets(X1,X0),powerset(powerset(X1))))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f131])).
% 14.33/2.44 fof(f150,plain,(
% 14.33/2.44 ![A,B]: (~element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B)),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f34])).
% 14.33/2.44 fof(f151,plain,(
% 14.33/2.44 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|complements_of_subsets(X1,complements_of_subsets(X1,X0))=X0)),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f150])).
% 14.33/2.44 fof(f168,plain,(
% 14.33/2.44 (?[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))))))),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 14.33/2.44 fof(f169,plain,(
% 14.33/2.44 ?[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))))))),
% 14.33/2.44 inference(NNF_transformation,[status(thm)],[f168])).
% 14.33/2.44 fof(f170,plain,(
% 14.33/2.44 (top_str(sK9_skl)&(element(sK10_skl,powerset(powerset(the_carrier(sK9_skl))))&((closed_subsets(sK10_skl,sK9_skl)|open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl))&(~closed_subsets(sK10_skl,sK9_skl)|~open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)))))),
% 14.33/2.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(A,sK9_skl),skolemize(B,sK10_skl)],[f169])).
% 14.33/2.44 fof(f171,plain,(
% 14.33/2.44 top_str(sK9_skl)),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f170])).
% 14.33/2.44 fof(f172,plain,(
% 14.33/2.44 element(sK10_skl,powerset(powerset(the_carrier(sK9_skl))))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f170])).
% 14.33/2.44 fof(f173,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f170])).
% 14.33/2.44 fof(f174,plain,(
% 14.33/2.44 ~closed_subsets(sK10_skl,sK9_skl)|~open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f170])).
% 14.33/2.44 fof(f177,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|(closed_subset(B,A)<=>open_subset(subset_complement(the_carrier(A),B),A)))))),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 14.33/2.44 fof(f178,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|((~closed_subset(B,A)|open_subset(subset_complement(the_carrier(A),B),A))&(closed_subset(B,A)|~open_subset(subset_complement(the_carrier(A),B),A))))))),
% 14.33/2.44 inference(NNF_transformation,[status(thm)],[f177])).
% 14.33/2.44 fof(f180,plain,(
% 14.33/2.44 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|closed_subset(X1,X0)|~open_subset(subset_complement(the_carrier(X0),X1),X0))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f178])).
% 14.33/2.44 fof(f183,plain,(
% 14.33/2.44 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|(open_subset(B,A)<=>closed_subset(subset_complement(the_carrier(A),B),A)))))),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 14.33/2.44 fof(f184,plain,(
% 14.33/2.44 ![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))))))),
% 14.33/2.44 inference(NNF_transformation,[status(thm)],[f183])).
% 14.33/2.44 fof(f186,plain,(
% 14.33/2.44 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|open_subset(X1,X0)|~closed_subset(subset_complement(the_carrier(X0),X1),X0))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f184])).
% 14.33/2.44 fof(f191,plain,(
% 14.33/2.44 ![A,B,C]: ((~in(A,B)|~element(B,powerset(C)))|element(A,C))),
% 14.33/2.44 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 14.33/2.44 fof(f192,plain,(
% 14.33/2.44 ![A,C]: ((![B]: (~in(A,B)|~element(B,powerset(C))))|element(A,C))),
% 14.33/2.44 inference(miniscoping,[status(thm)],[f191])).
% 14.33/2.44 fof(f193,plain,(
% 14.33/2.44 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|element(X0,X2))),
% 14.33/2.44 inference(cnf_transformation,[status(thm)],[f192])).
% 14.33/2.44 fof(f205,plain,(
% 14.33/2.44 ![X0,X1,X2]: (~element(X0,powerset(powerset(X1)))|~element(complements_of_subsets(X1,X0),powerset(powerset(X1)))|~element(X2,powerset(X1))|~in(X2,complements_of_subsets(X1,X0))|in(subset_complement(X1,X2),X0))),
% 14.33/2.44 inference(destructive_equality_resolution,[status(thm)],[f124])).
% 14.33/2.44 fof(f208,plain,(
% 14.33/2.44 complements_of_subsets(the_carrier(sK9_skl),complements_of_subsets(the_carrier(sK9_skl),sK10_skl))=sK10_skl),
% 14.33/2.44 inference(resolution,[status(thm)],[f151,f172])).
% 14.33/2.44 fof(f209,plain,(
% 14.33/2.44 ![X0,X1]: (~element(X0,powerset(powerset(the_carrier(sK9_skl))))|~open_subsets(X0,sK9_skl)|~element(X1,powerset(the_carrier(sK9_skl)))|~in(X1,X0)|open_subset(X1,sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f110,f171])).
% 14.33/2.44 fof(f210,plain,(
% 14.33/2.44 element(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),powerset(powerset(the_carrier(sK9_skl))))),
% 14.33/2.44 inference(resolution,[status(thm)],[f132,f172])).
% 14.33/2.44 fof(f214,plain,(
% 14.33/2.44 ![X0,X1]: (~element(X0,powerset(powerset(the_carrier(sK9_skl))))|~closed_subsets(X0,sK9_skl)|~element(X1,powerset(the_carrier(sK9_skl)))|~in(X1,X0)|closed_subset(X1,sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f117,f171])).
% 14.33/2.44 fof(f215,plain,(
% 14.33/2.44 ![X0]: (~open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)|~element(X0,powerset(the_carrier(sK9_skl)))|~in(X0,complements_of_subsets(the_carrier(sK9_skl),sK10_skl))|open_subset(X0,sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f209,f210])).
% 14.33/2.44 fof(f218,plain,(
% 14.33/2.44 ![X0]: (~closed_subsets(sK10_skl,sK9_skl)|~element(X0,powerset(the_carrier(sK9_skl)))|~in(X0,sK10_skl)|closed_subset(X0,sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f214,f172])).
% 14.33/2.44 fof(f219,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(the_carrier(sK9_skl)))|~in(X0,complements_of_subsets(the_carrier(sK9_skl),sK10_skl))|open_subset(X0,sK9_skl)|closed_subsets(sK10_skl,sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f215,f173])).
% 14.33/2.44 fof(f220,plain,(
% 14.33/2.44 ![X0,X1,X2]: (~element(X0,powerset(powerset(X1)))|~element(X2,powerset(X1))|~in(X2,complements_of_subsets(X1,X0))|in(subset_complement(X1,X2),X0))),
% 14.33/2.44 inference(forward_subsumption_resolution,[status(thm)],[f205,f132])).
% 14.33/2.44 fof(f221,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(the_carrier(sK9_skl)))|~in(X0,complements_of_subsets(the_carrier(sK9_skl),complements_of_subsets(the_carrier(sK9_skl),sK10_skl)))|in(subset_complement(the_carrier(sK9_skl),X0),complements_of_subsets(the_carrier(sK9_skl),sK10_skl)))),
% 14.33/2.44 inference(resolution,[status(thm)],[f220,f210])).
% 14.33/2.44 fof(f222,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(the_carrier(sK9_skl)))|~in(X0,complements_of_subsets(the_carrier(sK9_skl),sK10_skl))|in(subset_complement(the_carrier(sK9_skl),X0),sK10_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f220,f172])).
% 14.33/2.44 fof(f223,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(the_carrier(sK9_skl)))|~in(X0,sK10_skl)|in(subset_complement(the_carrier(sK9_skl),X0),complements_of_subsets(the_carrier(sK9_skl),sK10_skl)))),
% 14.33/2.44 inference(forward_demodulation,[status(thm)],[f208,f221])).
% 14.33/2.44 fof(f789,plain,(
% 14.33/2.44 ~top_str(sK9_skl)|open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)|element(sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl),powerset(the_carrier(sK9_skl)))),
% 14.33/2.44 inference(resolution,[status(thm)],[f111,f210])).
% 14.33/2.44 fof(f797,plain,(
% 14.33/2.44 open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)|element(sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl),powerset(the_carrier(sK9_skl)))),
% 14.33/2.44 inference(forward_subsumption_resolution,[status(thm)],[f789,f171])).
% 14.33/2.44 fof(f800,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(powerset(the_carrier(sK9_skl))))|open_subsets(X0,sK9_skl)|in(sK0_skl(X0,sK9_skl),X0))),
% 14.33/2.44 inference(resolution,[status(thm)],[f112,f171])).
% 14.33/2.44 fof(f802,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(powerset(the_carrier(sK9_skl))))|open_subsets(X0,sK9_skl)|~open_subset(sK0_skl(X0,sK9_skl),sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f113,f171])).
% 14.33/2.44 fof(f816,plain,(
% 14.33/2.44 open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)|in(sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl),complements_of_subsets(the_carrier(sK9_skl),sK10_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f800,f210])).
% 14.33/2.44 fof(f880,plain,(
% 14.33/2.44 ~top_str(sK9_skl)|closed_subsets(sK10_skl,sK9_skl)|element(sK1_skl(sK10_skl,sK9_skl),powerset(the_carrier(sK9_skl)))),
% 14.33/2.44 inference(resolution,[status(thm)],[f118,f172])).
% 14.33/2.44 fof(f884,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|element(sK1_skl(sK10_skl,sK9_skl),powerset(the_carrier(sK9_skl)))),
% 14.33/2.44 inference(forward_subsumption_resolution,[status(thm)],[f880,f171])).
% 14.33/2.44 fof(f886,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(powerset(the_carrier(sK9_skl))))|closed_subsets(X0,sK9_skl)|in(sK1_skl(X0,sK9_skl),X0))),
% 14.33/2.44 inference(resolution,[status(thm)],[f119,f171])).
% 14.33/2.44 fof(f888,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(powerset(the_carrier(sK9_skl))))|closed_subsets(X0,sK9_skl)|~closed_subset(sK1_skl(X0,sK9_skl),sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f120,f171])).
% 14.33/2.44 fof(f910,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|in(sK1_skl(sK10_skl,sK9_skl),sK10_skl)),
% 14.33/2.44 inference(resolution,[status(thm)],[f886,f172])).
% 14.33/2.44 fof(f1332,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(the_carrier(sK9_skl)))|closed_subset(X0,sK9_skl)|~open_subset(subset_complement(the_carrier(sK9_skl),X0),sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f180,f171])).
% 14.33/2.44 fof(f1336,plain,(
% 14.33/2.44 ![X0]: (~element(X0,powerset(the_carrier(sK9_skl)))|open_subset(X0,sK9_skl)|~closed_subset(subset_complement(the_carrier(sK9_skl),X0),sK9_skl))),
% 14.33/2.44 inference(resolution,[status(thm)],[f186,f171])).
% 14.33/2.44 fof(f1539,plain,(
% 14.33/2.44 ![X0]: (~in(X0,complements_of_subsets(the_carrier(sK9_skl),sK10_skl))|element(X0,powerset(the_carrier(sK9_skl))))),
% 14.33/2.44 inference(resolution,[status(thm)],[f193,f210])).
% 14.33/2.44 fof(f1544,plain,(
% 14.33/2.44 ![X0]: (~in(X0,sK10_skl)|element(X0,powerset(the_carrier(sK9_skl))))),
% 14.33/2.44 inference(resolution,[status(thm)],[f193,f172])).
% 14.33/2.44 fof(f1550,plain,(
% 14.33/2.44 ![X0]: (~closed_subsets(sK10_skl,sK9_skl)|~in(X0,sK10_skl)|closed_subset(X0,sK9_skl))),
% 14.33/2.44 inference(backward_subsumption_resolution,[status(thm)],[f218,f1544])).
% 14.33/2.44 fof(f1552,plain,(
% 14.33/2.44 ![X0]: (~in(X0,sK10_skl)|in(subset_complement(the_carrier(sK9_skl),X0),complements_of_subsets(the_carrier(sK9_skl),sK10_skl)))),
% 14.33/2.44 inference(backward_subsumption_resolution,[status(thm)],[f223,f1544])).
% 14.33/2.44 fof(f2157,plain,(
% 14.33/2.44 ![X0]: (~in(X0,complements_of_subsets(the_carrier(sK9_skl),sK10_skl))|in(subset_complement(the_carrier(sK9_skl),X0),sK10_skl))),
% 14.33/2.44 inference(backward_subsumption_resolution,[status(thm)],[f222,f1539])).
% 14.33/2.44 fof(f2159,plain,(
% 14.33/2.44 ![X0]: (~in(X0,complements_of_subsets(the_carrier(sK9_skl),sK10_skl))|open_subset(X0,sK9_skl)|closed_subsets(sK10_skl,sK9_skl))),
% 14.33/2.44 inference(backward_subsumption_resolution,[status(thm)],[f219,f1539])).
% 14.33/2.44 fof(f2402,plain,(
% 14.33/2.44 in(subset_complement(the_carrier(sK9_skl),sK1_skl(sK10_skl,sK9_skl)),complements_of_subsets(the_carrier(sK9_skl),sK10_skl))|closed_subsets(sK10_skl,sK9_skl)),
% 14.33/2.44 inference(resolution,[status(thm)],[f1552,f910])).
% 14.33/2.44 fof(f10671,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|open_subset(subset_complement(the_carrier(sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)|closed_subsets(sK10_skl,sK9_skl)),
% 14.33/2.44 inference(resolution,[status(thm)],[f2402,f2159])).
% 14.33/2.44 fof(f10676,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|open_subset(subset_complement(the_carrier(sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)),
% 14.33/2.44 inference(duplicate_literals_removal,[status(thm)],[f10671])).
% 14.33/2.44 fof(f10677,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|~element(sK1_skl(sK10_skl,sK9_skl),powerset(the_carrier(sK9_skl)))|closed_subset(sK1_skl(sK10_skl,sK9_skl),sK9_skl)),
% 14.33/2.44 inference(resolution,[status(thm)],[f10676,f1332])).
% 14.33/2.44 fof(f10678,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|closed_subset(sK1_skl(sK10_skl,sK9_skl),sK9_skl)),
% 14.33/2.44 inference(forward_subsumption_resolution,[status(thm)],[f10677,f884])).
% 14.33/2.44 fof(f10679,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|~element(sK10_skl,powerset(powerset(the_carrier(sK9_skl))))|closed_subsets(sK10_skl,sK9_skl)),
% 14.33/2.44 inference(resolution,[status(thm)],[f10678,f888])).
% 14.33/2.44 fof(f10680,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)|~element(sK10_skl,powerset(powerset(the_carrier(sK9_skl))))),
% 14.33/2.44 inference(duplicate_literals_removal,[status(thm)],[f10679])).
% 14.33/2.44 fof(f10681,plain,(
% 14.33/2.44 closed_subsets(sK10_skl,sK9_skl)),
% 14.33/2.44 inference(forward_subsumption_resolution,[status(thm)],[f10680,f172])).
% 14.33/2.44 fof(f10682,plain,(
% 14.33/2.44 ~open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)),
% 14.33/2.46 inference(backward_subsumption_resolution,[status(thm)],[f174,f10681])).
% 14.33/2.46 fof(f10683,plain,(
% 14.33/2.46 ![X0]: (~in(X0,sK10_skl)|closed_subset(X0,sK9_skl))),
% 14.33/2.46 inference(backward_subsumption_resolution,[status(thm)],[f1550,f10681])).
% 14.33/2.46 fof(f10684,plain,(
% 14.33/2.46 in(sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl),complements_of_subsets(the_carrier(sK9_skl),sK10_skl))),
% 14.33/2.46 inference(backward_subsumption_resolution,[status(thm)],[f816,f10682])).
% 14.33/2.46 fof(f10685,plain,(
% 14.33/2.46 element(sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl),powerset(the_carrier(sK9_skl)))),
% 14.33/2.46 inference(backward_subsumption_resolution,[status(thm)],[f797,f10682])).
% 14.33/2.46 fof(f12112,plain,(
% 14.33/2.46 in(subset_complement(the_carrier(sK9_skl),sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)),sK10_skl)),
% 14.33/2.46 inference(resolution,[status(thm)],[f10684,f2157])).
% 14.33/2.46 fof(f12122,plain,(
% 14.33/2.46 closed_subset(subset_complement(the_carrier(sK9_skl),sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)),sK9_skl)),
% 14.33/2.47 inference(resolution,[status(thm)],[f12112,f10683])).
% 14.33/2.47 fof(f12810,plain,(
% 14.33/2.47 ~element(sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl),powerset(the_carrier(sK9_skl)))|open_subset(sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl),sK9_skl)),
% 14.33/2.47 inference(resolution,[status(thm)],[f12122,f1336])).
% 14.33/2.47 fof(f12811,plain,(
% 14.33/2.47 open_subset(sK0_skl(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl),sK9_skl)),
% 14.33/2.47 inference(forward_subsumption_resolution,[status(thm)],[f12810,f10685])).
% 14.33/2.47 fof(f12812,plain,(
% 14.33/2.47 ~element(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),powerset(powerset(the_carrier(sK9_skl))))|open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)),
% 14.33/2.47 inference(resolution,[status(thm)],[f12811,f802])).
% 14.33/2.47 fof(f12813,plain,(
% 14.33/2.47 open_subsets(complements_of_subsets(the_carrier(sK9_skl),sK10_skl),sK9_skl)),
% 14.33/2.47 inference(forward_subsumption_resolution,[status(thm)],[f12812,f210])).
% 14.33/2.47 fof(f12814,plain,(
% 14.33/2.47 $false),
% 14.33/2.47 inference(forward_subsumption_resolution,[status(thm)],[f12813,f10682])).
% 14.33/2.47 % SZS output end CNFRefutation for theBenchmark.p
% 14.33/2.48 % Elapsed time: 2.116731 seconds
% 14.33/2.48 % CPU time: 16.372149 seconds
% 14.33/2.48 % Total memory used: 252.045 MB
% 14.33/2.48 % Net memory used: 240.934 MB
%------------------------------------------------------------------------------