%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU044+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 : n016.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 02:21:37 PM UTC 2026
% Result : Theorem 0.21s 15.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU044+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
% 0.17/15.45 % Computer : n016.cluster.edu
% 0.17/15.45 % Model : x86_64 x86_64
% 0.17/15.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/15.45 % Memory : 8046.5625MB
% 0.17/15.45 % OS : Linux 6.8.0-71-generic
% 0.17/15.45 % CPULimit : 300
% 0.17/15.45 % WCLimit : 300
% 0.17/15.45 % DateTime : Mon Sep 21 05:52:54 UTC 2026
% 0.17/15.46 % CPUTime :
% 0.17/15.47 % Drodi V4.1.1
% 0.21/15.52 % Refutation found
% 0.21/15.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/15.52 % SZS output start CNFRefutation for theBenchmark
% 0.21/15.52 fof(f19,axiom,(
% 0.21/15.52 (! [A,B] :( relation(B)=> relation(relation_rng_restriction(A,B)) ) )),
% 0.21/15.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/15.52 fof(f20,axiom,(
% 0.21/15.52 (! [A,B] :( ( relation(B)& function(B) )=> ( relation(relation_rng_restriction(A,B))& function(relation_rng_restriction(A,B)) ) ) )),
% 0.21/15.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/15.52 fof(f33,conjecture,(
% 0.21/15.52 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_rng_restriction(A,C)))<=> ( in(B,relation_dom(C))& in(apply(C,B),A) ) ) ) )),
% 0.21/15.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/15.52 fof(f34,negated_conjecture,(
% 0.21/15.52 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_rng_restriction(A,C)))<=> ( in(B,relation_dom(C))& in(apply(C,B),A) ) ) ) ))),
% 0.21/15.52 inference(negated_conjecture,[status(cth)],[f33])).
% 0.21/15.52 fof(f35,axiom,(
% 0.21/15.52 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( B = relation_rng_restriction(A,C)<=> ( (! [D] :( in(D,relation_dom(B))<=> ( in(D,relation_dom(C))& in(apply(C,D),A) ) ))& (! [D] :( in(D,relation_dom(B))=> apply(B,D) = apply(C,D) ) )) ) ) )) )),
% 0.21/15.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/15.52 fof(f79,plain,(
% 0.21/15.52 ![A,B]: (~relation(B)|relation(relation_rng_restriction(A,B)))),
% 0.21/15.52 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.21/15.52 fof(f80,plain,(
% 0.21/15.52 ![B]: (~relation(B)|(![A]: relation(relation_rng_restriction(A,B))))),
% 0.21/15.52 inference(miniscoping,[status(thm)],[f79])).
% 0.21/15.52 fof(f81,plain,(
% 0.21/15.52 ![X0,X1]: (~relation(X0)|relation(relation_rng_restriction(X1,X0)))),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f80])).
% 0.21/15.52 fof(f82,plain,(
% 0.21/15.52 ![A,B]: ((~relation(B)|~function(B))|(relation(relation_rng_restriction(A,B))&function(relation_rng_restriction(A,B))))),
% 0.21/15.52 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.21/15.52 fof(f83,plain,(
% 0.21/15.52 ![B]: ((~relation(B)|~function(B))|((![A]: relation(relation_rng_restriction(A,B)))&(![A]: function(relation_rng_restriction(A,B)))))),
% 0.21/15.52 inference(miniscoping,[status(thm)],[f82])).
% 0.21/15.52 fof(f85,plain,(
% 0.21/15.52 ![X0,X1]: (~relation(X0)|~function(X0)|function(relation_rng_restriction(X1,X0)))),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f83])).
% 0.21/15.52 fof(f122,plain,(
% 0.21/15.52 (?[A,B,C]: ((relation(C)&function(C))&(in(B,relation_dom(relation_rng_restriction(A,C)))<~>(in(B,relation_dom(C))&in(apply(C,B),A)))))),
% 0.21/15.52 inference(pre_NNF_transformation,[status(thm)],[f34])).
% 0.21/15.52 fof(f123,plain,(
% 0.21/15.52 ?[A,B,C]: ((relation(C)&function(C))&((in(B,relation_dom(relation_rng_restriction(A,C)))|(in(B,relation_dom(C))&in(apply(C,B),A)))&(~in(B,relation_dom(relation_rng_restriction(A,C)))|(~in(B,relation_dom(C))|~in(apply(C,B),A)))))),
% 0.21/15.52 inference(NNF_transformation,[status(thm)],[f122])).
% 0.21/15.52 fof(f124,plain,(
% 0.21/15.52 ?[C]: ((relation(C)&function(C))&(?[A,B]: ((in(B,relation_dom(relation_rng_restriction(A,C)))|(in(B,relation_dom(C))&in(apply(C,B),A)))&(~in(B,relation_dom(relation_rng_restriction(A,C)))|(~in(B,relation_dom(C))|~in(apply(C,B),A))))))),
% 0.21/15.52 inference(miniscoping,[status(thm)],[f123])).
% 0.21/15.52 fof(f125,plain,(
% 0.21/15.52 ((relation(sK11_skl)&function(sK11_skl))&((in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))|(in(sK13_skl,relation_dom(sK11_skl))&in(apply(sK11_skl,sK13_skl),sK12_skl)))&(~in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))|(~in(sK13_skl,relation_dom(sK11_skl))|~in(apply(sK11_skl,sK13_skl),sK12_skl)))))),
% 0.21/15.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(C,sK11_skl),skolemize(A,sK12_skl),skolemize(B,sK13_skl)],[f124])).
% 0.21/15.52 fof(f126,plain,(
% 0.21/15.52 relation(sK11_skl)),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f125])).
% 0.21/15.52 fof(f127,plain,(
% 0.21/15.52 function(sK11_skl)),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f125])).
% 0.21/15.52 fof(f128,plain,(
% 0.21/15.52 in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))|in(sK13_skl,relation_dom(sK11_skl))),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f125])).
% 0.21/15.52 fof(f129,plain,(
% 0.21/15.52 in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))|in(apply(sK11_skl,sK13_skl),sK12_skl)),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f125])).
% 0.21/15.52 fof(f130,plain,(
% 0.21/15.52 ~in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))|~in(sK13_skl,relation_dom(sK11_skl))|~in(apply(sK11_skl,sK13_skl),sK12_skl)),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f125])).
% 0.21/15.52 fof(f131,plain,(
% 0.21/15.52 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(B=relation_rng_restriction(A,C)<=>((![D]: (in(D,relation_dom(B))<=>(in(D,relation_dom(C))&in(apply(C,D),A))))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))))),
% 0.21/15.52 inference(pre_NNF_transformation,[status(thm)],[f35])).
% 0.21/15.52 fof(f132,definition,(
% 0.21/15.52 ![A,C,D]: (sP0_prd(D,C,A)<=>(in(D,relation_dom(C))&in(apply(C,D),A)))),
% 0.21/15.52 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.21/15.52 fof(f133,plain,(
% 0.21/15.52 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(B=relation_rng_restriction(A,C)<=>((![D]: (in(D,relation_dom(B))<=>sP0_prd(D,C,A)))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))))),
% 0.21/15.52 inference(formula_renaming,[status(thm)],[f131,f132])).
% 0.21/15.52 fof(f134,plain,(
% 0.21/15.52 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~B=relation_rng_restriction(A,C)|((![D]: ((~in(D,relation_dom(B))|sP0_prd(D,C,A))&(in(D,relation_dom(B))|~sP0_prd(D,C,A))))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D)))))&(B=relation_rng_restriction(A,C)|((?[D]: ((~in(D,relation_dom(B))|~sP0_prd(D,C,A))&(in(D,relation_dom(B))|sP0_prd(D,C,A))))|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D)))))))))),
% 0.21/15.52 inference(NNF_transformation,[status(thm)],[f133])).
% 0.21/15.52 fof(f135,plain,(
% 0.21/15.52 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_rng_restriction(A,C)|(((![D]: (~in(D,relation_dom(B))|sP0_prd(D,C,A)))&(![D]: (in(D,relation_dom(B))|~sP0_prd(D,C,A))))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_rng_restriction(A,C)|((?[D]: ((~in(D,relation_dom(B))|~sP0_prd(D,C,A))&(in(D,relation_dom(B))|sP0_prd(D,C,A))))|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D))))))))))),
% 0.21/15.52 inference(miniscoping,[status(thm)],[f134])).
% 0.21/15.52 fof(f136,plain,(
% 0.21/15.52 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_rng_restriction(A,C)|(((![D]: (~in(D,relation_dom(B))|sP0_prd(D,C,A)))&(![D]: (in(D,relation_dom(B))|~sP0_prd(D,C,A))))&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_rng_restriction(A,C)|(((~in(sK14_skl(A,C,B),relation_dom(B))|~sP0_prd(sK14_skl(A,C,B),C,A))&(in(sK14_skl(A,C,B),relation_dom(B))|sP0_prd(sK14_skl(A,C,B),C,A)))|(in(sK15_skl(A,C,B),relation_dom(B))&~apply(B,sK15_skl(A,C,B))=apply(C,sK15_skl(A,C,B))))))))))),
% 0.21/15.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(D,sK14_skl(A,C,B)),skolemize(D,sK15_skl(A,C,B))],[f135])).
% 0.21/15.52 fof(f137,plain,(
% 0.21/15.52 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~X0=relation_rng_restriction(X2,X1)|~in(X3,relation_dom(X0))|sP0_prd(X3,X1,X2))),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f136])).
% 0.21/15.52 fof(f138,plain,(
% 0.21/15.52 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~X0=relation_rng_restriction(X2,X1)|in(X3,relation_dom(X0))|~sP0_prd(X3,X1,X2))),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f136])).
% 0.21/15.52 fof(f144,plain,(
% 0.21/15.52 ![A,C,D]: ((~sP0_prd(D,C,A)|(in(D,relation_dom(C))&in(apply(C,D),A)))&(sP0_prd(D,C,A)|(~in(D,relation_dom(C))|~in(apply(C,D),A))))),
% 0.21/15.52 inference(NNF_transformation,[status(thm)],[f132])).
% 0.21/15.52 fof(f145,plain,(
% 0.21/15.52 (![A,C,D]: (~sP0_prd(D,C,A)|(in(D,relation_dom(C))&in(apply(C,D),A))))&(![A,C,D]: (sP0_prd(D,C,A)|(~in(D,relation_dom(C))|~in(apply(C,D),A))))),
% 0.21/15.52 inference(miniscoping,[status(thm)],[f144])).
% 0.21/15.52 fof(f146,plain,(
% 0.21/15.52 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|in(X0,relation_dom(X1)))),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f145])).
% 0.21/15.52 fof(f147,plain,(
% 0.21/15.52 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|in(apply(X1,X0),X2))),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f145])).
% 0.21/15.52 fof(f148,plain,(
% 0.21/15.52 ![X0,X1,X2]: (sP0_prd(X0,X1,X2)|~in(X0,relation_dom(X1))|~in(apply(X1,X0),X2))),
% 0.21/15.52 inference(cnf_transformation,[status(thm)],[f145])).
% 0.21/15.52 fof(f149,plain,(
% 0.21/15.52 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|~in(X2,relation_dom(relation_rng_restriction(X0,X1)))|sP0_prd(X2,X1,X0))),
% 0.21/15.52 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.21/15.52 fof(f150,plain,(
% 0.21/15.52 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|in(X2,relation_dom(relation_rng_restriction(X0,X1)))|~sP0_prd(X2,X1,X0))),
% 0.21/15.52 inference(destructive_equality_resolution,[status(thm)],[f138])).
% 0.21/15.52 fof(f168,plain,(
% 0.21/15.52 ![X0]: (~relation(sK11_skl)|function(relation_rng_restriction(X0,sK11_skl)))),
% 0.21/15.52 inference(resolution,[status(thm)],[f85,f127])).
% 0.21/15.52 fof(f170,plain,(
% 0.21/15.52 ![X0]: (function(relation_rng_restriction(X0,sK11_skl)))),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f168,f126])).
% 0.21/15.52 fof(f289,plain,(
% 0.21/15.52 ![X0,X1,X2]: (~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|~in(X2,relation_dom(relation_rng_restriction(X0,X1)))|sP0_prd(X2,X1,X0))),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f149,f81])).
% 0.21/15.52 fof(f290,plain,(
% 0.21/15.52 ~function(relation_rng_restriction(sK12_skl,sK11_skl))|~relation(sK11_skl)|~function(sK11_skl)|sP0_prd(sK13_skl,sK11_skl,sK12_skl)|in(apply(sK11_skl,sK13_skl),sK12_skl)),
% 0.21/15.52 inference(resolution,[status(thm)],[f289,f129])).
% 0.21/15.52 fof(f291,plain,(
% 0.21/15.52 ~function(relation_rng_restriction(sK12_skl,sK11_skl))|~relation(sK11_skl)|~function(sK11_skl)|sP0_prd(sK13_skl,sK11_skl,sK12_skl)|in(sK13_skl,relation_dom(sK11_skl))),
% 0.21/15.52 inference(resolution,[status(thm)],[f289,f128])).
% 0.21/15.52 fof(f292,plain,(
% 0.21/15.52 ~relation(sK11_skl)|~function(sK11_skl)|sP0_prd(sK13_skl,sK11_skl,sK12_skl)|in(apply(sK11_skl,sK13_skl),sK12_skl)),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f290,f85])).
% 0.21/15.52 fof(f293,plain,(
% 0.21/15.52 ~relation(sK11_skl)|~function(sK11_skl)|sP0_prd(sK13_skl,sK11_skl,sK12_skl)|in(sK13_skl,relation_dom(sK11_skl))),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f291,f85])).
% 0.21/15.52 fof(f294,plain,(
% 0.21/15.52 ![X0,X1,X2]: (~function(relation_rng_restriction(X0,X1))|~relation(X1)|~function(X1)|in(X2,relation_dom(relation_rng_restriction(X0,X1)))|~sP0_prd(X2,X1,X0))),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f150,f81])).
% 0.21/15.52 fof(f298,plain,(
% 0.21/15.52 ![X0,X1]: (~relation(sK11_skl)|~function(sK11_skl)|in(X0,relation_dom(relation_rng_restriction(X1,sK11_skl)))|~sP0_prd(X0,sK11_skl,X1))),
% 0.21/15.52 inference(resolution,[status(thm)],[f294,f170])).
% 0.21/15.52 fof(f302,plain,(
% 0.21/15.52 ![X0,X1]: (~function(sK11_skl)|in(X0,relation_dom(relation_rng_restriction(X1,sK11_skl)))|~sP0_prd(X0,sK11_skl,X1))),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f298,f126])).
% 0.21/15.52 fof(f367,plain,(
% 0.21/15.52 ~function(sK11_skl)|sP0_prd(sK13_skl,sK11_skl,sK12_skl)|in(apply(sK11_skl,sK13_skl),sK12_skl)),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f292,f126])).
% 0.21/15.52 fof(f368,plain,(
% 0.21/15.52 sP0_prd(sK13_skl,sK11_skl,sK12_skl)|in(apply(sK11_skl,sK13_skl),sK12_skl)),
% 0.21/15.52 inference(resolution,[status(thm)],[f367,f127])).
% 0.21/15.52 fof(f369,plain,(
% 0.21/15.52 in(apply(sK11_skl,sK13_skl),sK12_skl)),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f368,f147])).
% 0.21/15.52 fof(f370,plain,(
% 0.21/15.52 ~function(sK11_skl)|sP0_prd(sK13_skl,sK11_skl,sK12_skl)|in(sK13_skl,relation_dom(sK11_skl))),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f293,f126])).
% 0.21/15.52 fof(f371,plain,(
% 0.21/15.52 sP0_prd(sK13_skl,sK11_skl,sK12_skl)|in(sK13_skl,relation_dom(sK11_skl))),
% 0.21/15.52 inference(resolution,[status(thm)],[f370,f127])).
% 0.21/15.52 fof(f372,plain,(
% 0.21/15.52 in(sK13_skl,relation_dom(sK11_skl))),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f371,f146])).
% 0.21/15.52 fof(f415,plain,(
% 0.21/15.52 ~in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))|~in(apply(sK11_skl,sK13_skl),sK12_skl)),
% 0.21/15.52 inference(backward_subsumption_resolution,[status(thm)],[f130,f372])).
% 0.21/15.52 fof(f472,plain,(
% 0.21/15.52 ![X0,X1]: (in(X0,relation_dom(relation_rng_restriction(X1,sK11_skl)))|~sP0_prd(X0,sK11_skl,X1))),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f302,f127])).
% 0.21/15.52 fof(f559,plain,(
% 0.21/15.52 ~in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))),
% 0.21/15.52 inference(backward_subsumption_resolution,[status(thm)],[f415,f369])).
% 0.21/15.52 fof(f560,plain,(
% 0.21/15.52 sP0_prd(sK13_skl,sK11_skl,sK12_skl)|~in(sK13_skl,relation_dom(sK11_skl))),
% 0.21/15.52 inference(resolution,[status(thm)],[f369,f148])).
% 0.21/15.52 fof(f564,plain,(
% 0.21/15.52 sP0_prd(sK13_skl,sK11_skl,sK12_skl)),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f560,f372])).
% 0.21/15.52 fof(f728,plain,(
% 0.21/15.52 in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl)))),
% 0.21/15.52 inference(resolution,[status(thm)],[f564,f472])).
% 0.21/15.52 fof(f731,plain,(
% 0.21/15.52 $false),
% 0.21/15.52 inference(forward_subsumption_resolution,[status(thm)],[f728,f559])).
% 0.21/15.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/15.58 % Elapsed time: 0.113395 seconds
% 0.21/15.58 % CPU time: 0.281397 seconds
% 0.21/15.58 % Total memory used: 39.064 MB
% 0.21/15.58 % Net memory used: 38.852 MB
%------------------------------------------------------------------------------