%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU019+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:21:35 PM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU019+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n011.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 05:46:55 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.49 % Refutation found
% 0.19/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.49 fof(f4,axiom,(
% 0.19/0.49 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)<=> (! [B,C] :( ( in(B,relation_dom(A))& in(C,relation_dom(A))& apply(A,B) = apply(A,C) )=> B = C ) )) ) )),
% 0.19/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.49 fof(f5,axiom,(
% 0.19/0.49 (! [A] : relation(identity_relation(A)) )),
% 0.19/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.49 fof(f10,axiom,(
% 0.19/0.49 (! [A] :( relation(identity_relation(A))& function(identity_relation(A)) ) )),
% 0.19/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.49 fof(f25,axiom,(
% 0.19/0.49 (! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) )),
% 0.19/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.49 fof(f28,conjecture,(
% 0.19/0.49 (! [A] : one_to_one(identity_relation(A)) )),
% 0.19/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.49 fof(f29,negated_conjecture,(
% 0.19/0.49 ~((! [A] : one_to_one(identity_relation(A)) ))),
% 0.19/0.49 inference(negated_conjecture,[status(cth)],[f28])).
% 0.19/0.49 fof(f40,plain,(
% 0.19/0.49 ![A]: ((~relation(A)|~function(A))|(one_to_one(A)<=>(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C))))),
% 0.19/0.49 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.19/0.49 fof(f41,plain,(
% 0.19/0.49 ![A]: ((~relation(A)|~function(A))|((~one_to_one(A)|(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C)))&(one_to_one(A)|(?[B,C]: (((in(B,relation_dom(A))&in(C,relation_dom(A)))&apply(A,B)=apply(A,C))&~B=C)))))),
% 0.19/0.49 inference(NNF_transformation,[status(thm)],[f40])).
% 0.19/0.49 fof(f42,plain,(
% 0.19/0.49 ![A]: ((~relation(A)|~function(A))|((~one_to_one(A)|(![B,C]: (((~in(B,relation_dom(A))|~in(C,relation_dom(A)))|~apply(A,B)=apply(A,C))|B=C)))&(one_to_one(A)|(((in(sK0_skl(A),relation_dom(A))&in(sK1_skl(A),relation_dom(A)))&apply(A,sK0_skl(A))=apply(A,sK1_skl(A)))&~sK0_skl(A)=sK1_skl(A)))))),
% 0.19/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(B,sK0_skl(A)),skolemize(C,sK1_skl(A))],[f41])).
% 0.19/0.49 fof(f44,plain,(
% 0.19/0.49 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|in(sK0_skl(X0),relation_dom(X0)))),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f42])).
% 0.19/0.49 fof(f45,plain,(
% 0.19/0.49 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|in(sK1_skl(X0),relation_dom(X0)))),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f42])).
% 0.19/0.49 fof(f46,plain,(
% 0.19/0.49 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|apply(X0,sK0_skl(X0))=apply(X0,sK1_skl(X0)))),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f42])).
% 0.19/0.49 fof(f47,plain,(
% 0.19/0.49 ![X0]: (~relation(X0)|~function(X0)|one_to_one(X0)|~sK0_skl(X0)=sK1_skl(X0))),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f42])).
% 0.19/0.49 fof(f48,plain,(
% 0.19/0.49 ![X0]: (relation(identity_relation(X0)))),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f5])).
% 0.19/0.49 fof(f56,plain,(
% 0.19/0.49 (![A]: relation(identity_relation(A)))&(![A]: function(identity_relation(A)))),
% 0.19/0.49 inference(miniscoping,[status(thm)],[f10])).
% 0.19/0.49 fof(f58,plain,(
% 0.19/0.49 ![X0]: (function(identity_relation(X0)))),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f56])).
% 0.19/0.49 fof(f95,plain,(
% 0.19/0.49 ![A,B]: ((~relation(B)|~function(B))|(B=identity_relation(A)<=>(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))),
% 0.19/0.49 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.19/0.49 fof(f96,plain,(
% 0.19/0.49 ![A,B]: ((~relation(B)|~function(B))|((~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C))))&(B=identity_relation(A)|(~relation_dom(B)=A|(?[C]: (in(C,A)&~apply(B,C)=C))))))),
% 0.19/0.49 inference(NNF_transformation,[status(thm)],[f95])).
% 0.19/0.49 fof(f97,plain,(
% 0.19/0.49 ![B]: ((~relation(B)|~function(B))|((![A]: (~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))&(![A]: (B=identity_relation(A)|(~relation_dom(B)=A|(?[C]: (in(C,A)&~apply(B,C)=C)))))))),
% 0.19/0.49 inference(miniscoping,[status(thm)],[f96])).
% 0.19/0.49 fof(f98,plain,(
% 0.19/0.49 ![B]: ((~relation(B)|~function(B))|((![A]: (~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))&(![A]: (B=identity_relation(A)|(~relation_dom(B)=A|(in(sK11_skl(A,B),A)&~apply(B,sK11_skl(A,B))=sK11_skl(A,B)))))))),
% 0.19/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(C,sK11_skl(A,B))],[f97])).
% 0.19/0.49 fof(f99,plain,(
% 0.19/0.49 ![X0,X1]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|relation_dom(X0)=X1)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f98])).
% 0.19/0.49 fof(f100,plain,(
% 0.19/0.49 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|~in(X2,X1)|apply(X0,X2)=X2)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f98])).
% 0.19/0.49 fof(f110,plain,(
% 0.19/0.49 (?[A]: ~one_to_one(identity_relation(A)))),
% 0.19/0.49 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.19/0.49 fof(f111,plain,(
% 0.19/0.49 ~one_to_one(identity_relation(sK12_skl))),
% 0.19/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f110])).
% 0.19/0.49 fof(f112,plain,(
% 0.19/0.49 ~one_to_one(identity_relation(sK12_skl))),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f111])).
% 0.19/0.49 fof(f124,plain,(
% 0.19/0.49 ![X1]: (~relation(identity_relation(X1))|~function(identity_relation(X1))|relation_dom(identity_relation(X1))=X1)),
% 0.19/0.49 inference(destructive_equality_resolution,[status(thm)],[f99])).
% 0.19/0.49 fof(f125,plain,(
% 0.19/0.49 ![X0]: (~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f124,f48])).
% 0.19/0.49 fof(f126,plain,(
% 0.19/0.49 ![X1,X2]: (~relation(identity_relation(X1))|~function(identity_relation(X1))|~in(X2,X1)|apply(identity_relation(X1),X2)=X2)),
% 0.19/0.49 inference(destructive_equality_resolution,[status(thm)],[f100])).
% 0.19/0.49 fof(f127,plain,(
% 0.19/0.49 ![X0,X1]: (~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f126,f48])).
% 0.19/0.49 fof(f131,plain,(
% 0.19/0.49 ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 0.19/0.49 inference(resolution,[status(thm)],[f125,f58])).
% 0.19/0.49 fof(f133,plain,(
% 0.19/0.49 ![X0,X1]: (~in(X0,X1)|apply(identity_relation(X1),X0)=X0)),
% 0.19/0.49 inference(resolution,[status(thm)],[f127,f58])).
% 0.19/0.49 fof(f137,plain,(
% 0.19/0.49 ![X0]: (~function(identity_relation(X0))|one_to_one(identity_relation(X0))|in(sK0_skl(identity_relation(X0)),relation_dom(identity_relation(X0))))),
% 0.19/0.49 inference(resolution,[status(thm)],[f44,f48])).
% 0.19/0.49 fof(f148,plain,(
% 0.19/0.49 ![X0]: (~function(identity_relation(X0))|one_to_one(identity_relation(X0))|in(sK0_skl(identity_relation(X0)),X0))),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f131,f137])).
% 0.19/0.49 fof(f149,plain,(
% 0.19/0.49 ![X0]: (one_to_one(identity_relation(X0))|in(sK0_skl(identity_relation(X0)),X0))),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f148,f58])).
% 0.19/0.49 fof(f151,plain,(
% 0.19/0.49 ![X0]: (~function(identity_relation(X0))|one_to_one(identity_relation(X0))|in(sK1_skl(identity_relation(X0)),relation_dom(identity_relation(X0))))),
% 0.19/0.49 inference(resolution,[status(thm)],[f45,f48])).
% 0.19/0.49 fof(f156,plain,(
% 0.19/0.49 ![X0]: (~function(identity_relation(X0))|one_to_one(identity_relation(X0))|in(sK1_skl(identity_relation(X0)),X0))),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f131,f151])).
% 0.19/0.49 fof(f157,plain,(
% 0.19/0.49 ![X0]: (one_to_one(identity_relation(X0))|in(sK1_skl(identity_relation(X0)),X0))),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f156,f58])).
% 0.19/0.49 fof(f159,plain,(
% 0.19/0.49 ![X0]: (~function(identity_relation(X0))|one_to_one(identity_relation(X0))|apply(identity_relation(X0),sK0_skl(identity_relation(X0)))=apply(identity_relation(X0),sK1_skl(identity_relation(X0))))),
% 0.19/0.49 inference(resolution,[status(thm)],[f46,f48])).
% 0.19/0.49 fof(f164,plain,(
% 0.19/0.49 ![X0]: (one_to_one(identity_relation(X0))|apply(identity_relation(X0),sK0_skl(identity_relation(X0)))=apply(identity_relation(X0),sK1_skl(identity_relation(X0))))),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f159,f58])).
% 0.19/0.49 fof(f166,plain,(
% 0.19/0.49 ![X0]: (one_to_one(identity_relation(X0))|apply(identity_relation(X0),sK0_skl(identity_relation(X0)))=sK0_skl(identity_relation(X0)))),
% 0.19/0.49 inference(resolution,[status(thm)],[f149,f133])).
% 0.19/0.49 fof(f168,plain,(
% 0.19/0.49 ![X0]: (one_to_one(identity_relation(X0))|apply(identity_relation(X0),sK1_skl(identity_relation(X0)))=sK1_skl(identity_relation(X0)))),
% 0.19/0.49 inference(resolution,[status(thm)],[f157,f133])).
% 0.19/0.49 fof(f169,plain,(
% 0.19/0.49 apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl)))=apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl)))),
% 0.19/0.50 inference(resolution,[status(thm)],[f164,f112])).
% 0.19/0.50 fof(f170,plain,(
% 0.19/0.50 apply(identity_relation(sK12_skl),sK0_skl(identity_relation(sK12_skl)))=sK0_skl(identity_relation(sK12_skl))),
% 0.19/0.50 inference(resolution,[status(thm)],[f166,f112])).
% 0.19/0.50 fof(f171,plain,(
% 0.19/0.50 sK0_skl(identity_relation(sK12_skl))=apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl)))),
% 0.19/0.50 inference(backward_demodulation,[status(thm)],[f170,f169])).
% 0.19/0.50 fof(f172,plain,(
% 0.19/0.50 apply(identity_relation(sK12_skl),sK1_skl(identity_relation(sK12_skl)))=sK1_skl(identity_relation(sK12_skl))),
% 0.19/0.50 inference(resolution,[status(thm)],[f168,f112])).
% 0.19/0.50 fof(f174,plain,(
% 0.19/0.50 sK0_skl(identity_relation(sK12_skl))=sK1_skl(identity_relation(sK12_skl))),
% 0.19/0.50 inference(forward_demodulation,[status(thm)],[f171,f172])).
% 0.19/0.50 fof(f177,definition,(
% 0.19/0.50 sQ5_spl <=> (relation(identity_relation(sK12_skl)))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f179,plain,(
% 0.19/0.50 ~relation(identity_relation(sK12_skl))|sQ5_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f177])).
% 0.19/0.50 fof(f180,definition,(
% 0.19/0.50 sQ6_spl <=> (function(identity_relation(sK12_skl)))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f182,plain,(
% 0.19/0.50 ~function(identity_relation(sK12_skl))|sQ6_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f180])).
% 0.19/0.50 fof(f183,definition,(
% 0.19/0.50 sQ7_spl <=> (one_to_one(identity_relation(sK12_skl)))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f184,plain,(
% 0.19/0.50 one_to_one(identity_relation(sK12_skl))|~sQ7_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f183])).
% 0.19/0.50 fof(f197,plain,(
% 0.19/0.50 ~relation(identity_relation(sK12_skl))|~function(identity_relation(sK12_skl))|one_to_one(identity_relation(sK12_skl))),
% 0.19/0.50 inference(resolution,[status(thm)],[f174,f47])).
% 0.19/0.50 fof(f201,plain,(
% 0.19/0.50 ~sQ5_spl|~sQ6_spl|sQ7_spl),
% 0.19/0.50 inference(split_clause,[status(thm)],[f197,f177,f180,f183])).
% 0.19/0.50 fof(f214,plain,(
% 0.19/0.50 $false|sQ6_spl),
% 0.19/0.50 inference(forward_subsumption_resolution,[status(thm)],[f182,f58])).
% 0.19/0.50 fof(f215,plain,(
% 0.19/0.50 sQ6_spl),
% 0.19/0.50 inference(contradiction_clause,[status(thm)],[f214])).
% 0.19/0.50 fof(f216,plain,(
% 0.19/0.50 $false|~sQ7_spl),
% 0.19/0.50 inference(forward_subsumption_resolution,[status(thm)],[f184,f112])).
% 0.19/0.50 fof(f217,plain,(
% 0.19/0.50 ~sQ7_spl),
% 0.19/0.50 inference(contradiction_clause,[status(thm)],[f216])).
% 0.19/0.50 fof(f218,plain,(
% 0.19/0.50 $false|sQ5_spl),
% 0.19/0.50 inference(forward_subsumption_resolution,[status(thm)],[f179,f48])).
% 0.19/0.50 fof(f219,plain,(
% 0.19/0.50 sQ5_spl),
% 0.19/0.50 inference(contradiction_clause,[status(thm)],[f218])).
% 0.19/0.50 fof(f220,plain,(
% 0.19/0.50 $false),
% 0.19/0.50 inference(sat_refutation,[status(thm)],[f201,f215,f217,f219])).
% 0.19/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.25/0.55 % Elapsed time: 0.092897 seconds
% 0.25/0.55 % CPU time: 0.129614 seconds
% 0.25/0.55 % Total memory used: 13.117 MB
% 0.25/0.55 % Net memory used: 13.105 MB
%------------------------------------------------------------------------------