%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU223+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:22:03 PM UTC 2026
% Result : Theorem 0.18s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n019.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 21 05:59:50 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.18/0.42 % Drodi V4.1.1
% 0.18/0.44 % Refutation found
% 0.18/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.44 fof(f30,axiom,(
% 0.18/0.44 (! [A,B] :( relation(A)=> relation(relation_dom_restriction(A,B)) ) )),
% 0.18/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.44 fof(f32,axiom,(
% 0.18/0.44 (! [A,B] :( ( relation(A)& function(A) )=> ( relation(relation_dom_restriction(A,B))& function(relation_dom_restriction(A,B)) ) ) )),
% 0.18/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.44 fof(f36,conjecture,(
% 0.18/0.44 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_dom_restriction(C,A)))=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ) )),
% 0.18/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.44 fof(f37,negated_conjecture,(
% 0.18/0.44 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_dom_restriction(C,A)))=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ) ))),
% 0.18/0.44 inference(negated_conjecture,[status(cth)],[f36])).
% 0.18/0.44 fof(f38,axiom,(
% 0.18/0.44 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( B = relation_dom_restriction(C,A)<=> ( relation_dom(B) = set_intersection2(relation_dom(C),A)& (! [D] :( in(D,relation_dom(B))=> apply(B,D) = apply(C,D) ) )) ) ) )) )),
% 0.18/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.44 fof(f98,plain,(
% 0.18/0.44 ![A,B]: (~relation(A)|relation(relation_dom_restriction(A,B)))),
% 0.18/0.44 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.18/0.44 fof(f99,plain,(
% 0.18/0.44 ![A]: (~relation(A)|(![B]: relation(relation_dom_restriction(A,B))))),
% 0.18/0.44 inference(miniscoping,[status(thm)],[f98])).
% 0.18/0.44 fof(f100,plain,(
% 0.18/0.44 ![X0,X1]: (~relation(X0)|relation(relation_dom_restriction(X0,X1)))),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f99])).
% 0.18/0.44 fof(f104,plain,(
% 0.18/0.44 ![A,B]: ((~relation(A)|~function(A))|(relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))))),
% 0.18/0.44 inference(pre_NNF_transformation,[status(thm)],[f32])).
% 0.18/0.44 fof(f105,plain,(
% 0.18/0.44 ![A]: ((~relation(A)|~function(A))|((![B]: relation(relation_dom_restriction(A,B)))&(![B]: function(relation_dom_restriction(A,B)))))),
% 0.18/0.44 inference(miniscoping,[status(thm)],[f104])).
% 0.18/0.44 fof(f107,plain,(
% 0.18/0.44 ![X0,X1]: (~relation(X0)|~function(X0)|function(relation_dom_restriction(X0,X1)))),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f105])).
% 0.18/0.44 fof(f115,plain,(
% 0.18/0.44 (?[A,B,C]: ((relation(C)&function(C))&(in(B,relation_dom(relation_dom_restriction(C,A)))&~apply(relation_dom_restriction(C,A),B)=apply(C,B))))),
% 0.18/0.44 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.18/0.44 fof(f116,plain,(
% 0.18/0.44 ?[C]: ((relation(C)&function(C))&(?[A,B]: (in(B,relation_dom(relation_dom_restriction(C,A)))&~apply(relation_dom_restriction(C,A),B)=apply(C,B))))),
% 0.18/0.44 inference(miniscoping,[status(thm)],[f115])).
% 0.18/0.44 fof(f117,plain,(
% 0.18/0.44 ((relation(sK9_skl)&function(sK9_skl))&(in(sK11_skl,relation_dom(relation_dom_restriction(sK9_skl,sK10_skl)))&~apply(relation_dom_restriction(sK9_skl,sK10_skl),sK11_skl)=apply(sK9_skl,sK11_skl)))),
% 0.18/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(C,sK9_skl),skolemize(A,sK10_skl),skolemize(B,sK11_skl)],[f116])).
% 0.18/0.44 fof(f118,plain,(
% 0.18/0.44 relation(sK9_skl)),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f117])).
% 0.18/0.44 fof(f119,plain,(
% 0.18/0.44 function(sK9_skl)),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f117])).
% 0.18/0.44 fof(f120,plain,(
% 0.18/0.44 in(sK11_skl,relation_dom(relation_dom_restriction(sK9_skl,sK10_skl)))),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f117])).
% 0.18/0.44 fof(f121,plain,(
% 0.18/0.44 ~apply(relation_dom_restriction(sK9_skl,sK10_skl),sK11_skl)=apply(sK9_skl,sK11_skl)),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f117])).
% 0.18/0.44 fof(f122,plain,(
% 0.18/0.44 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(B=relation_dom_restriction(C,A)<=>(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))))),
% 0.18/0.44 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.18/0.44 fof(f123,plain,(
% 0.18/0.44 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D)))))&(B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D)))))))))),
% 0.18/0.44 inference(NNF_transformation,[status(thm)],[f122])).
% 0.18/0.44 fof(f124,plain,(
% 0.18/0.44 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D))))))))))),
% 0.18/0.44 inference(miniscoping,[status(thm)],[f123])).
% 0.18/0.44 fof(f125,plain,(
% 0.18/0.44 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(in(sK12_skl(A,C,B),relation_dom(B))&~apply(B,sK12_skl(A,C,B))=apply(C,sK12_skl(A,C,B))))))))))),
% 0.18/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(D,sK12_skl(A,C,B))],[f124])).
% 0.18/0.44 fof(f127,plain,(
% 0.18/0.44 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~X0=relation_dom_restriction(X1,X2)|~in(X3,relation_dom(X0))|apply(X0,X3)=apply(X1,X3))),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f125])).
% 0.18/0.44 fof(f131,plain,(
% 0.18/0.44 ![X0,X1,X2]: (~relation(relation_dom_restriction(X0,X1))|~function(relation_dom_restriction(X0,X1))|~relation(X0)|~function(X0)|~in(X2,relation_dom(relation_dom_restriction(X0,X1)))|apply(relation_dom_restriction(X0,X1),X2)=apply(X0,X2))),
% 0.18/0.44 inference(destructive_equality_resolution,[status(thm)],[f127])).
% 0.18/0.44 fof(f139,plain,(
% 0.18/0.44 ![X0]: (~function(sK9_skl)|function(relation_dom_restriction(sK9_skl,X0)))),
% 0.18/0.44 inference(resolution,[status(thm)],[f107,f118])).
% 0.18/0.44 fof(f140,definition,(
% 0.18/0.44 sQ0_spl <=> (function(sK9_skl))),
% 0.18/0.44 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.18/0.44 fof(f142,plain,(
% 0.18/0.44 ~function(sK9_skl)|sQ0_spl),
% 0.18/0.44 inference(component_clause,[status(thm)],[f140])).
% 0.18/0.44 fof(f143,definition,(
% 0.18/0.44 ![X0]: (sQ1_spl <=> (function(relation_dom_restriction(sK9_skl,X0))))),
% 0.18/0.44 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.18/0.44 fof(f144,plain,(
% 0.18/0.44 ![X0]: (function(relation_dom_restriction(sK9_skl,X0))|~sQ1_spl)),
% 0.18/0.44 inference(component_clause,[status(thm)],[f143])).
% 0.18/0.44 fof(f146,plain,(
% 0.18/0.44 ~sQ0_spl|sQ1_spl),
% 0.18/0.44 inference(split_clause,[status(thm)],[f139,f140,f143])).
% 0.18/0.44 fof(f147,plain,(
% 0.18/0.44 $false|sQ0_spl),
% 0.18/0.44 inference(forward_subsumption_resolution,[status(thm)],[f142,f119])).
% 0.18/0.44 fof(f148,plain,(
% 0.18/0.44 sQ0_spl),
% 0.18/0.44 inference(contradiction_clause,[status(thm)],[f147])).
% 0.18/0.44 fof(f149,plain,(
% 0.18/0.44 ![X0,X1,X2]: (~function(relation_dom_restriction(X0,X1))|~relation(X0)|~function(X0)|~in(X2,relation_dom(relation_dom_restriction(X0,X1)))|apply(relation_dom_restriction(X0,X1),X2)=apply(X0,X2))),
% 0.18/0.44 inference(forward_subsumption_resolution,[status(thm)],[f131,f100])).
% 0.18/0.44 fof(f150,plain,(
% 0.18/0.44 ~function(relation_dom_restriction(sK9_skl,sK10_skl))|~relation(sK9_skl)|~function(sK9_skl)|apply(relation_dom_restriction(sK9_skl,sK10_skl),sK11_skl)=apply(sK9_skl,sK11_skl)),
% 0.18/0.44 inference(resolution,[status(thm)],[f149,f120])).
% 0.18/0.44 fof(f151,definition,(
% 0.18/0.44 sQ2_spl <=> (function(relation_dom_restriction(sK9_skl,sK10_skl)))),
% 0.18/0.44 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.18/0.44 fof(f153,plain,(
% 0.18/0.44 ~function(relation_dom_restriction(sK9_skl,sK10_skl))|sQ2_spl),
% 0.18/0.44 inference(component_clause,[status(thm)],[f151])).
% 0.18/0.44 fof(f154,definition,(
% 0.18/0.44 sQ3_spl <=> (relation(sK9_skl))),
% 0.18/0.44 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.18/0.44 fof(f156,plain,(
% 0.18/0.44 ~relation(sK9_skl)|sQ3_spl),
% 0.18/0.44 inference(component_clause,[status(thm)],[f154])).
% 0.18/0.44 fof(f157,definition,(
% 0.18/0.44 sQ4_spl <=> (apply(relation_dom_restriction(sK9_skl,sK10_skl),sK11_skl)=apply(sK9_skl,sK11_skl))),
% 0.18/0.44 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.18/0.44 fof(f158,plain,(
% 0.18/0.44 apply(relation_dom_restriction(sK9_skl,sK10_skl),sK11_skl)=apply(sK9_skl,sK11_skl)|~sQ4_spl),
% 0.18/0.44 inference(component_clause,[status(thm)],[f157])).
% 0.18/0.44 fof(f160,plain,(
% 0.18/0.44 ~sQ2_spl|~sQ3_spl|~sQ0_spl|sQ4_spl),
% 0.18/0.44 inference(split_clause,[status(thm)],[f150,f151,f154,f140,f157])).
% 0.18/0.44 fof(f161,plain,(
% 0.18/0.44 $false|~sQ4_spl),
% 0.18/0.44 inference(forward_subsumption_resolution,[status(thm)],[f158,f121])).
% 0.18/0.44 fof(f162,plain,(
% 0.18/0.44 ~sQ4_spl),
% 0.18/0.44 inference(contradiction_clause,[status(thm)],[f161])).
% 0.18/0.44 fof(f254,plain,(
% 0.18/0.44 $false|~sQ1_spl|sQ2_spl),
% 0.18/0.44 inference(forward_subsumption_resolution,[status(thm)],[f153,f144])).
% 0.18/0.44 fof(f255,plain,(
% 0.18/0.44 ~sQ1_spl|sQ2_spl),
% 0.18/0.44 inference(contradiction_clause,[status(thm)],[f254])).
% 0.18/0.44 fof(f256,plain,(
% 0.18/0.44 $false|sQ3_spl),
% 0.18/0.44 inference(forward_subsumption_resolution,[status(thm)],[f156,f118])).
% 0.18/0.44 fof(f257,plain,(
% 0.18/0.44 sQ3_spl),
% 0.18/0.44 inference(contradiction_clause,[status(thm)],[f256])).
% 0.18/0.44 fof(f258,plain,(
% 0.18/0.44 $false),
% 0.18/0.44 inference(sat_refutation,[status(thm)],[f146,f148,f160,f162,f255,f257])).
% 0.18/0.44 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.53 % Elapsed time: 0.115526 seconds
% 0.18/0.53 % CPU time: 0.109036 seconds
% 0.18/0.53 % Total memory used: 3.277 MB
% 0.18/0.53 % Net memory used: 3.276 MB
%------------------------------------------------------------------------------