%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU320+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 : n011.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 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+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
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 06:11:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f2,axiom,(
% 0.09/0.40 (! [A,B] :( element(B,powerset(A))=> element(subset_complement(A,B),powerset(A)) ) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f10,axiom,(
% 0.09/0.40 (! [A,B] :( element(B,powerset(A))=> subset_complement(A,subset_complement(A,B)) = B ) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f12,axiom,(
% 0.09/0.40 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( closed_subset(B,A)<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) )) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f13,conjecture,(
% 0.09/0.40 (! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( open_subset(B,A)<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) )) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f14,negated_conjecture,(
% 0.09/0.40 ~((! [A] :( top_str(A)=> (! [B] :( element(B,powerset(the_carrier(A)))=> ( open_subset(B,A)<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) )) ))),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f13])).
% 0.09/0.40 fof(f16,plain,(
% 0.09/0.40 ![A,B]: (~element(B,powerset(A))|element(subset_complement(A,B),powerset(A)))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.09/0.40 fof(f17,plain,(
% 0.09/0.40 ![X0,X1]: (~element(X0,powerset(X1))|element(subset_complement(X1,X0),powerset(X1)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f16])).
% 0.09/0.40 fof(f26,plain,(
% 0.09/0.40 ![A,B]: (~element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B)),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.09/0.40 fof(f27,plain,(
% 0.09/0.40 ![X0,X1]: (~element(X0,powerset(X1))|subset_complement(X1,subset_complement(X1,X0))=X0)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f26])).
% 0.09/0.40 fof(f30,plain,(
% 0.09/0.40 ![A]: (~top_str(A)|(![B]: (~element(B,powerset(the_carrier(A)))|(closed_subset(B,A)<=>open_subset(subset_complement(the_carrier(A),B),A)))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.09/0.40 fof(f31,plain,(
% 0.09/0.40 ![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))))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f30])).
% 0.09/0.40 fof(f32,plain,(
% 0.09/0.40 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|~closed_subset(X1,X0)|open_subset(subset_complement(the_carrier(X0),X1),X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.40 fof(f33,plain,(
% 0.09/0.40 ![X0,X1]: (~top_str(X0)|~element(X1,powerset(the_carrier(X0)))|closed_subset(X1,X0)|~open_subset(subset_complement(the_carrier(X0),X1),X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.40 fof(f34,plain,(
% 0.09/0.40 (?[A]: (top_str(A)&(?[B]: (element(B,powerset(the_carrier(A)))&(open_subset(B,A)<~>closed_subset(subset_complement(the_carrier(A),B),A))))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.09/0.40 fof(f35,plain,(
% 0.09/0.40 ?[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))))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f34])).
% 0.09/0.40 fof(f36,plain,(
% 0.09/0.40 (top_str(sK3_skl)&(element(sK4_skl,powerset(the_carrier(sK3_skl)))&((open_subset(sK4_skl,sK3_skl)|closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl))&(~open_subset(sK4_skl,sK3_skl)|~closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)))))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f35])).
% 0.09/0.40 fof(f37,plain,(
% 0.09/0.40 top_str(sK3_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f36])).
% 0.09/0.40 fof(f38,plain,(
% 0.09/0.40 element(sK4_skl,powerset(the_carrier(sK3_skl)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f36])).
% 0.09/0.40 fof(f39,plain,(
% 0.09/0.40 open_subset(sK4_skl,sK3_skl)|closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f36])).
% 0.09/0.40 fof(f40,plain,(
% 0.09/0.40 ~open_subset(sK4_skl,sK3_skl)|~closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f36])).
% 0.09/0.40 fof(f45,definition,(
% 0.09/0.40 sQ0_spl <=> (open_subset(sK4_skl,sK3_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f47,plain,(
% 0.09/0.40 ~open_subset(sK4_skl,sK3_skl)|sQ0_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f45])).
% 0.09/0.40 fof(f48,definition,(
% 0.09/0.40 sQ1_spl <=> (closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f51,plain,(
% 0.09/0.40 sQ0_spl|sQ1_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f39,f45,f48])).
% 0.09/0.40 fof(f52,plain,(
% 0.09/0.40 ~sQ0_spl|~sQ1_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f40,f45,f48])).
% 0.09/0.40 fof(f53,plain,(
% 0.09/0.40 subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl))=sK4_skl),
% 0.09/0.40 inference(resolution,[status(thm)],[f27,f38])).
% 0.09/0.40 fof(f54,plain,(
% 0.09/0.40 element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl)))),
% 0.09/0.40 inference(resolution,[status(thm)],[f17,f38])).
% 0.09/0.40 fof(f55,plain,(
% 0.09/0.40 ~top_str(sK3_skl)|~closed_subset(sK4_skl,sK3_skl)|open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)),
% 0.09/0.40 inference(resolution,[status(thm)],[f32,f38])).
% 0.09/0.40 fof(f56,definition,(
% 0.09/0.40 sQ2_spl <=> (top_str(sK3_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f58,plain,(
% 0.09/0.40 ~top_str(sK3_skl)|sQ2_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f56])).
% 0.09/0.40 fof(f59,definition,(
% 0.09/0.40 sQ3_spl <=> (closed_subset(sK4_skl,sK3_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f62,definition,(
% 0.09/0.40 sQ4_spl <=> (open_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f65,plain,(
% 0.09/0.40 ~sQ2_spl|~sQ3_spl|sQ4_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f55,f56,f59,f62])).
% 0.09/0.40 fof(f74,plain,(
% 0.09/0.40 ~top_str(sK3_skl)|~element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl)))|closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)|~open_subset(sK4_skl,sK3_skl)),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f53,f33])).
% 0.09/0.40 fof(f75,definition,(
% 0.09/0.40 sQ5_spl <=> (element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl))))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f77,plain,(
% 0.09/0.40 ~element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl)))|sQ5_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f75])).
% 0.09/0.40 fof(f78,plain,(
% 0.09/0.40 ~sQ2_spl|~sQ5_spl|sQ1_spl|~sQ0_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f74,f56,f75,f48,f45])).
% 0.09/0.40 fof(f79,plain,(
% 0.09/0.40 $false|sQ2_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f58,f37])).
% 0.09/0.40 fof(f80,plain,(
% 0.09/0.40 sQ2_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f79])).
% 0.09/0.40 fof(f81,plain,(
% 0.09/0.40 $false|sQ5_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f77,f54])).
% 0.09/0.40 fof(f82,plain,(
% 0.09/0.40 sQ5_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f81])).
% 0.09/0.40 fof(f84,plain,(
% 0.09/0.40 ~top_str(sK3_skl)|~closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)|open_subset(subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)),sK3_skl)),
% 0.09/0.40 inference(resolution,[status(thm)],[f54,f32])).
% 0.09/0.40 fof(f88,definition,(
% 0.09/0.40 sQ6_spl <=> (open_subset(subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)),sK3_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f89,plain,(
% 0.09/0.40 open_subset(subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)),sK3_skl)|~sQ6_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f88])).
% 0.09/0.40 fof(f91,plain,(
% 0.09/0.40 ~sQ2_spl|~sQ1_spl|sQ6_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f84,f56,f48,f88])).
% 0.09/0.40 fof(f93,plain,(
% 0.09/0.40 open_subset(sK4_skl,sK3_skl)|~sQ6_spl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f53,f89])).
% 0.09/0.40 fof(f94,plain,(
% 0.09/0.40 $false|sQ0_spl|~sQ6_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f93,f47])).
% 0.09/0.40 fof(f95,plain,(
% 0.09/0.40 sQ0_spl|~sQ6_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f94])).
% 0.09/0.40 fof(f96,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(sat_refutation,[status(thm)],[f51,f52,f65,f78,f80,f82,f91,f95])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.42 % Elapsed time: 0.045254 seconds
% 0.09/0.42 % CPU time: 0.133431 seconds
% 0.09/0.42 % Total memory used: 65.257 MB
% 0.09/0.42 % Net memory used: 64.898 MB
%------------------------------------------------------------------------------