%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU319+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 : 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 02:22:19 PM UTC 2026
% Result : Theorem 0.15s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34 % Computer : n005.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8046.5625MB
% 0.11/0.34 % OS : Linux 6.8.0-71-generic
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon Sep 21 06:11:18 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 % Drodi V4.1.1
% 0.15/0.37 % Refutation found
% 0.15/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.37 fof(f1,axiom,(
% 0.15/0.37 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( closed_subset(B,A)<=> open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) ) ) )) )),
% 0.15/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.37 fof(f3,axiom,(
% 0.15/0.37 (! [A] :( one_sorted_str(A)=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ) )),
% 0.15/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.37 fof(f4,axiom,(
% 0.15/0.37 (! [A,B] :( element(B,powerset(A))=> element(subset_complement(A,B),powerset(A)) ) )),
% 0.15/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.37 fof(f7,axiom,(
% 0.15/0.37 (! [A] :( top_str(A)=> one_sorted_str(A) ) )),
% 0.15/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.37 fof(f17,axiom,(
% 0.15/0.37 (! [A] :( one_sorted_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) )) )),
% 0.15/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.37 fof(f18,conjecture,(
% 0.15/0.37 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( closed_subset(B,A)<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) )) )),
% 0.15/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.37 fof(f19,negated_conjecture,(
% 0.15/0.37 ~((! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( closed_subset(B,A)<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) )) ))),
% 0.15/0.37 inference(negated_conjecture,[status(cth)],[f18])).
% 0.15/0.37 fof(f21,plain,(
% 0.15/0.37 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|(closed_subset(B,A)<=>open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A)))))),
% 0.15/0.37 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.15/0.37 fof(f22,plain,(
% 0.15/0.37 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|((~closed_subset(B,A)|open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A))&(closed_subset(B,A)|~open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A))))))),
% 0.15/0.37 inference(NNF_transformation,[status(thm)],[f21])).
% 0.15/0.37 fof(f23,plain,(
% 0.15/0.37 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~closed_subset(X1,X0)|open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0))),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f22])).
% 0.15/0.37 fof(f24,plain,(
% 0.15/0.37 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|closed_subset(X1,X0)|~open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0))),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f22])).
% 0.15/0.37 fof(f25,plain,(
% 0.15/0.37 ![A]: (~one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))))),
% 0.15/0.37 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.15/0.37 fof(f26,plain,(
% 0.15/0.37 ![X0]: (~one_sorted_str(X0)|element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))))),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f25])).
% 0.15/0.37 fof(f27,plain,(
% 0.15/0.37 ![A,B]: (~element(B,powerset(A))|element(subset_complement(A,B),powerset(A)))),
% 0.15/0.37 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.15/0.37 fof(f28,plain,(
% 0.15/0.37 ![X0,X1]: (~element(X0,powerset(X1))|element(subset_complement(X1,X0),powerset(X1)))),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.37 fof(f31,plain,(
% 0.15/0.37 ![A]: (~top_str(A)|one_sorted_str(A))),
% 0.15/0.37 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.15/0.37 fof(f32,plain,(
% 0.15/0.37 ![X0]: (~top_str(X0)|one_sorted_str(X0))),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f31])).
% 0.15/0.37 fof(f45,plain,(
% 0.15/0.37 ![A]: (~one_sorted_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|subset_complement(the_carrier(A),B)=subset_difference(the_carrier(A),cast_as_carrier_subset(A),B))))),
% 0.15/0.37 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.15/0.37 fof(f46,plain,(
% 0.15/0.37 ![X0,X1]: (~one_sorted_str(X0)|~element(X1,powerset(the_carrier(X0)))|subset_complement(the_carrier(X0),X1)=subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1))),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f45])).
% 0.15/0.37 fof(f47,plain,(
% 0.15/0.37 (?[A]: (top_str(A)&(?[B]: (element(B,powerset(the_carrier(A)))&(closed_subset(B,A)<~>open_subset(subset_complement(the_carrier(A),B),A))))))),
% 0.15/0.37 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.15/0.37 fof(f48,plain,(
% 0.15/0.37 ?[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))))))),
% 0.15/0.37 inference(NNF_transformation,[status(thm)],[f47])).
% 0.15/0.37 fof(f49,plain,(
% 0.15/0.37 (top_str(sK3_skl)&(element(sK4_skl,powerset(the_carrier(sK3_skl)))&((closed_subset(sK4_skl,sK3_skl)|open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl))&(~closed_subset(sK4_skl,sK3_skl)|~open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)))))),
% 0.15/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f48])).
% 0.15/0.37 fof(f50,plain,(
% 0.15/0.37 top_str(sK3_skl)),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f49])).
% 0.15/0.37 fof(f51,plain,(
% 0.15/0.37 element(sK4_skl,powerset(the_carrier(sK3_skl)))),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f49])).
% 0.15/0.37 fof(f52,plain,(
% 0.15/0.37 closed_subset(sK4_skl,sK3_skl)|open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f49])).
% 0.15/0.37 fof(f53,plain,(
% 0.15/0.37 ~closed_subset(sK4_skl,sK3_skl)|~open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)),
% 0.15/0.37 inference(cnf_transformation,[status(thm)],[f49])).
% 0.15/0.37 fof(f58,definition,(
% 0.15/0.37 sQ0_spl <=> (closed_subset(sK4_skl,sK3_skl))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f61,definition,(
% 0.15/0.37 sQ1_spl <=> (open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f64,plain,(
% 0.15/0.37 sQ0_spl|sQ1_spl),
% 0.15/0.37 inference(split_clause,[status(thm)],[f52,f58,f61])).
% 0.15/0.37 fof(f65,plain,(
% 0.15/0.37 ~sQ0_spl|~sQ1_spl),
% 0.15/0.37 inference(split_clause,[status(thm)],[f53,f58,f61])).
% 0.15/0.37 fof(f67,plain,(
% 0.15/0.37 ~top_str(sK3_skl)|~closed_subset(sK4_skl,sK3_skl)|open_subset(subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl),sK3_skl)),
% 0.15/0.37 inference(resolution,[status(thm)],[f23,f51])).
% 0.15/0.37 fof(f68,definition,(
% 0.15/0.37 sQ2_spl <=> (top_str(sK3_skl))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f70,plain,(
% 0.15/0.37 ~top_str(sK3_skl)|sQ2_spl),
% 0.15/0.37 inference(component_clause,[status(thm)],[f68])).
% 0.15/0.37 fof(f71,definition,(
% 0.15/0.37 sQ3_spl <=> (open_subset(subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl),sK3_skl))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f72,plain,(
% 0.15/0.37 open_subset(subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl),sK3_skl)|~sQ3_spl),
% 0.15/0.37 inference(component_clause,[status(thm)],[f71])).
% 0.15/0.37 fof(f74,plain,(
% 0.15/0.37 ~sQ2_spl|~sQ0_spl|sQ3_spl),
% 0.15/0.37 inference(split_clause,[status(thm)],[f67,f68,f58,f71])).
% 0.15/0.37 fof(f75,plain,(
% 0.15/0.37 $false|sQ2_spl),
% 0.15/0.37 inference(forward_subsumption_resolution,[status(thm)],[f70,f50])).
% 0.15/0.37 fof(f76,plain,(
% 0.15/0.37 sQ2_spl),
% 0.15/0.37 inference(contradiction_clause,[status(thm)],[f75])).
% 0.15/0.37 fof(f77,plain,(
% 0.15/0.37 element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl)))),
% 0.15/0.37 inference(resolution,[status(thm)],[f28,f51])).
% 0.15/0.37 fof(f81,plain,(
% 0.15/0.37 one_sorted_str(sK3_skl)),
% 0.15/0.37 inference(resolution,[status(thm)],[f32,f50])).
% 0.15/0.37 fof(f89,plain,(
% 0.15/0.37 ~one_sorted_str(sK3_skl)|subset_complement(the_carrier(sK3_skl),sK4_skl)=subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl)),
% 0.15/0.37 inference(resolution,[status(thm)],[f46,f51])).
% 0.15/0.37 fof(f90,definition,(
% 0.15/0.37 sQ4_spl <=> (one_sorted_str(sK3_skl))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f92,plain,(
% 0.15/0.37 ~one_sorted_str(sK3_skl)|sQ4_spl),
% 0.15/0.37 inference(component_clause,[status(thm)],[f90])).
% 0.15/0.37 fof(f93,definition,(
% 0.15/0.37 sQ5_spl <=> (subset_complement(the_carrier(sK3_skl),sK4_skl)=subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f94,plain,(
% 0.15/0.37 subset_complement(the_carrier(sK3_skl),sK4_skl)=subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),sK4_skl)|~sQ5_spl),
% 0.15/0.37 inference(component_clause,[status(thm)],[f93])).
% 0.15/0.37 fof(f96,plain,(
% 0.15/0.37 ~sQ4_spl|sQ5_spl),
% 0.15/0.37 inference(split_clause,[status(thm)],[f89,f90,f93])).
% 0.15/0.37 fof(f97,plain,(
% 0.15/0.37 $false|sQ4_spl),
% 0.15/0.37 inference(forward_subsumption_resolution,[status(thm)],[f92,f81])).
% 0.15/0.37 fof(f98,plain,(
% 0.15/0.37 sQ4_spl),
% 0.15/0.37 inference(contradiction_clause,[status(thm)],[f97])).
% 0.15/0.37 fof(f99,plain,(
% 0.15/0.37 element(cast_as_carrier_subset(sK3_skl),powerset(the_carrier(sK3_skl)))),
% 0.15/0.37 inference(resolution,[status(thm)],[f81,f26])).
% 0.15/0.37 fof(f100,plain,(
% 0.15/0.37 ~one_sorted_str(sK3_skl)|subset_complement(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl))=subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),cast_as_carrier_subset(sK3_skl))),
% 0.15/0.37 inference(resolution,[status(thm)],[f99,f46])).
% 0.15/0.37 fof(f106,definition,(
% 0.15/0.37 sQ6_spl <=> (subset_complement(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl))=subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),cast_as_carrier_subset(sK3_skl)))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f109,plain,(
% 0.15/0.37 ~sQ4_spl|sQ6_spl),
% 0.15/0.37 inference(split_clause,[status(thm)],[f100,f90,f106])).
% 0.15/0.37 fof(f117,plain,(
% 0.15/0.37 ~one_sorted_str(sK3_skl)|subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))=subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))),
% 0.15/0.37 inference(resolution,[status(thm)],[f77,f46])).
% 0.15/0.37 fof(f123,definition,(
% 0.15/0.37 sQ9_spl <=> (subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))=subset_difference(the_carrier(sK3_skl),cast_as_carrier_subset(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f126,plain,(
% 0.15/0.37 ~sQ4_spl|sQ9_spl),
% 0.15/0.37 inference(split_clause,[status(thm)],[f117,f90,f123])).
% 0.15/0.37 fof(f148,plain,(
% 0.15/0.37 ~top_str(sK3_skl)|~element(sK4_skl,powerset(the_carrier(sK3_skl)))|closed_subset(sK4_skl,sK3_skl)|~open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)|~sQ5_spl),
% 0.15/0.37 inference(paramodulation,[status(thm)],[f94,f24])).
% 0.15/0.37 fof(f149,definition,(
% 0.15/0.37 sQ12_spl <=> (element(sK4_skl,powerset(the_carrier(sK3_skl))))),
% 0.15/0.37 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.15/0.37 fof(f151,plain,(
% 0.15/0.37 ~element(sK4_skl,powerset(the_carrier(sK3_skl)))|sQ12_spl),
% 0.15/0.37 inference(component_clause,[status(thm)],[f149])).
% 0.15/0.37 fof(f152,plain,(
% 0.15/0.37 ~sQ2_spl|~sQ12_spl|sQ0_spl|~sQ1_spl|~sQ5_spl),
% 0.15/0.37 inference(split_clause,[status(thm)],[f148,f68,f149,f58,f61,f93])).
% 0.15/0.37 fof(f153,plain,(
% 0.15/0.37 open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)|~sQ5_spl|~sQ3_spl),
% 0.15/0.37 inference(forward_demodulation,[status(thm)],[f94,f72])).
% 0.15/0.37 fof(f154,plain,(
% 0.15/0.37 $false|sQ12_spl),
% 0.15/0.37 inference(forward_subsumption_resolution,[status(thm)],[f151,f51])).
% 0.15/0.37 fof(f155,plain,(
% 0.15/0.37 sQ12_spl),
% 0.15/0.37 inference(contradiction_clause,[status(thm)],[f154])).
% 0.15/0.37 fof(f156,plain,(
% 0.15/0.37 sQ1_spl|~sQ5_spl|~sQ3_spl),
% 0.15/0.37 inference(split_clause,[status(thm)],[f153,f61,f93,f71])).
% 0.15/0.37 fof(f157,plain,(
% 0.15/0.37 $false),
% 0.15/0.37 inference(sat_refutation,[status(thm)],[f64,f65,f74,f76,f96,f98,f109,f126,f152,f155,f156])).
% 0.15/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.39 % Elapsed time: 0.041058 seconds
% 0.15/0.39 % CPU time: 0.143492 seconds
% 0.15/0.39 % Total memory used: 81.127 MB
% 0.15/0.39 % Net memory used: 80.745 MB
%------------------------------------------------------------------------------