%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU008+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 : n009.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 02:21:34 PM UTC 2026
% Result : Theorem 1.16s 0.60s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU008+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:46:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 1.16/0.60 % Refutation found
% 1.16/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.16/0.60 % SZS output start CNFRefutation for theBenchmark
% 1.16/0.60 fof(f5,axiom,(
% 1.16/0.60 (! [A,B,C] :( C = set_intersection2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& in(D,B) ) ) )) )),
% 1.16/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.16/0.60 fof(f7,axiom,(
% 1.16/0.60 (! [A] : relation(identity_relation(A)) )),
% 1.16/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.16/0.60 fof(f15,axiom,(
% 1.16/0.60 (! [A] :( relation(identity_relation(A))& function(identity_relation(A)) ) )),
% 1.16/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.16/0.60 fof(f31,axiom,(
% 1.16/0.60 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(B))=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) )) )),
% 1.16/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.16/0.60 fof(f34,axiom,(
% 1.16/0.60 (! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) )),
% 1.16/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.16/0.60 fof(f35,conjecture,(
% 1.16/0.60 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,set_intersection2(relation_dom(C),A))=> apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ) )),
% 1.16/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.16/0.60 fof(f36,negated_conjecture,(
% 1.16/0.60 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,set_intersection2(relation_dom(C),A))=> apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ) ))),
% 1.16/0.60 inference(negated_conjecture,[status(cth)],[f35])).
% 1.16/0.60 fof(f50,plain,(
% 1.16/0.60 ![A,B,C]: ((~C=set_intersection2(A,B)|(![D]: ((~in(D,C)|(in(D,A)&in(D,B)))&(in(D,C)|(~in(D,A)|~in(D,B))))))&(C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 1.16/0.60 inference(NNF_transformation,[status(thm)],[f5])).
% 1.16/0.60 fof(f51,plain,(
% 1.16/0.60 (![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|~in(D,B)))&(in(D,C)|(in(D,A)&in(D,B)))))))),
% 1.16/0.60 inference(miniscoping,[status(thm)],[f50])).
% 1.16/0.60 fof(f52,plain,(
% 1.16/0.60 (![A,B,C]: (~C=set_intersection2(A,B)|((![D]: (~in(D,C)|(in(D,A)&in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|~in(D,B)))))))&(![A,B,C]: (C=set_intersection2(A,B)|((~in(sK0_skl(C,B,A),C)|(~in(sK0_skl(C,B,A),A)|~in(sK0_skl(C,B,A),B)))&(in(sK0_skl(C,B,A),C)|(in(sK0_skl(C,B,A),A)&in(sK0_skl(C,B,A),B))))))),
% 1.16/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f51])).
% 1.16/0.60 fof(f54,plain,(
% 1.16/0.60 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|~in(X3,X0)|in(X3,X2))),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f52])).
% 1.16/0.60 fof(f61,plain,(
% 1.16/0.60 ![X0]: (relation(identity_relation(X0)))),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f7])).
% 1.16/0.60 fof(f77,plain,(
% 1.16/0.60 (![A]: relation(identity_relation(A)))&(![A]: function(identity_relation(A)))),
% 1.16/0.60 inference(miniscoping,[status(thm)],[f15])).
% 1.16/0.60 fof(f79,plain,(
% 1.16/0.60 ![X0]: (function(identity_relation(X0)))),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f77])).
% 1.16/0.60 fof(f119,plain,(
% 1.16/0.60 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(~in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A))))))),
% 1.16/0.60 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 1.16/0.60 fof(f120,plain,(
% 1.16/0.60 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(![A]: (~in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A)))))))),
% 1.16/0.60 inference(miniscoping,[status(thm)],[f119])).
% 1.16/0.60 fof(f121,plain,(
% 1.16/0.60 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~in(X2,relation_dom(X0))|apply(relation_composition(X0,X1),X2)=apply(X1,apply(X0,X2)))),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f120])).
% 1.16/0.60 fof(f125,plain,(
% 1.16/0.60 ![A,B]: ((~relation(B)|~function(B))|(B=identity_relation(A)<=>(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))),
% 1.16/0.60 inference(pre_NNF_transformation,[status(thm)],[f34])).
% 1.16/0.60 fof(f126,plain,(
% 1.16/0.60 ![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))))))),
% 1.16/0.60 inference(NNF_transformation,[status(thm)],[f125])).
% 1.16/0.60 fof(f127,plain,(
% 1.16/0.60 ![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)))))))),
% 1.16/0.60 inference(miniscoping,[status(thm)],[f126])).
% 1.16/0.60 fof(f128,plain,(
% 1.16/0.60 ![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(sK10_skl(A,B),A)&~apply(B,sK10_skl(A,B))=sK10_skl(A,B)))))))),
% 1.16/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(A,B))],[f127])).
% 1.16/0.60 fof(f129,plain,(
% 1.16/0.60 ![X0,X1]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|relation_dom(X0)=X1)),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f128])).
% 1.16/0.60 fof(f130,plain,(
% 1.16/0.60 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|~in(X2,X1)|apply(X0,X2)=X2)),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f128])).
% 1.16/0.60 fof(f133,plain,(
% 1.16/0.60 (?[A,B,C]: ((relation(C)&function(C))&(in(B,set_intersection2(relation_dom(C),A))&~apply(C,B)=apply(relation_composition(identity_relation(A),C),B))))),
% 1.16/0.60 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 1.16/0.60 fof(f134,plain,(
% 1.16/0.60 ?[C]: ((relation(C)&function(C))&(?[A,B]: (in(B,set_intersection2(relation_dom(C),A))&~apply(C,B)=apply(relation_composition(identity_relation(A),C),B))))),
% 1.16/0.60 inference(miniscoping,[status(thm)],[f133])).
% 1.16/0.60 fof(f135,plain,(
% 1.16/0.60 ((relation(sK11_skl)&function(sK11_skl))&(in(sK13_skl,set_intersection2(relation_dom(sK11_skl),sK12_skl))&~apply(sK11_skl,sK13_skl)=apply(relation_composition(identity_relation(sK12_skl),sK11_skl),sK13_skl)))),
% 1.16/0.60 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)],[f134])).
% 1.16/0.60 fof(f136,plain,(
% 1.16/0.60 relation(sK11_skl)),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f135])).
% 1.16/0.60 fof(f137,plain,(
% 1.16/0.60 function(sK11_skl)),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f135])).
% 1.16/0.60 fof(f138,plain,(
% 1.16/0.60 in(sK13_skl,set_intersection2(relation_dom(sK11_skl),sK12_skl))),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f135])).
% 1.16/0.60 fof(f139,plain,(
% 1.16/0.60 ~apply(sK11_skl,sK13_skl)=apply(relation_composition(identity_relation(sK12_skl),sK11_skl),sK13_skl)),
% 1.16/0.60 inference(cnf_transformation,[status(thm)],[f135])).
% 1.16/0.60 fof(f159,plain,(
% 1.16/0.60 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|in(X0,X2))),
% 1.16/0.60 inference(destructive_equality_resolution,[status(thm)],[f54])).
% 1.16/0.60 fof(f161,plain,(
% 1.16/0.60 ![X0]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 1.16/0.60 inference(destructive_equality_resolution,[status(thm)],[f129])).
% 1.16/0.60 fof(f162,plain,(
% 1.16/0.60 ![X0,X1]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 1.16/0.60 inference(destructive_equality_resolution,[status(thm)],[f130])).
% 1.16/0.60 fof(f175,plain,(
% 1.16/0.60 in(sK13_skl,sK12_skl)),
% 1.16/0.60 inference(resolution,[status(thm)],[f159,f138])).
% 1.16/0.60 fof(f251,plain,(
% 1.16/0.60 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(sK11_skl)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sK11_skl),X1)=apply(sK11_skl,apply(X0,X1)))),
% 1.16/0.60 inference(resolution,[status(thm)],[f121,f137])).
% 1.16/0.60 fof(f255,plain,(
% 1.16/0.60 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sK11_skl),X1)=apply(sK11_skl,apply(X0,X1)))),
% 1.16/0.60 inference(forward_subsumption_resolution,[status(thm)],[f251,f136])).
% 1.16/0.60 fof(f270,plain,(
% 1.16/0.60 ![X0,X1]: (~relation(identity_relation(X0))|~in(X1,relation_dom(identity_relation(X0)))|apply(relation_composition(identity_relation(X0),sK11_skl),X1)=apply(sK11_skl,apply(identity_relation(X0),X1)))),
% 1.16/0.60 inference(resolution,[status(thm)],[f255,f79])).
% 1.16/0.60 fof(f275,plain,(
% 1.16/0.60 ![X0,X1]: (~in(X0,relation_dom(identity_relation(X1)))|apply(relation_composition(identity_relation(X1),sK11_skl),X0)=apply(sK11_skl,apply(identity_relation(X1),X0)))),
% 1.16/0.60 inference(forward_subsumption_resolution,[status(thm)],[f270,f61])).
% 1.16/0.61 fof(f294,plain,(
% 1.16/0.61 ![X0]: (~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 1.16/0.61 inference(forward_subsumption_resolution,[status(thm)],[f161,f61])).
% 1.16/0.61 fof(f295,plain,(
% 1.16/0.61 ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 1.16/0.61 inference(resolution,[status(thm)],[f294,f79])).
% 1.16/0.61 fof(f297,plain,(
% 1.16/0.61 ![X0,X1]: (~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 1.16/0.61 inference(forward_subsumption_resolution,[status(thm)],[f162,f61])).
% 1.16/0.61 fof(f298,plain,(
% 1.16/0.61 ![X0,X1]: (~in(X0,X1)|apply(identity_relation(X1),X0)=X0)),
% 1.16/0.61 inference(resolution,[status(thm)],[f297,f79])).
% 1.16/0.61 fof(f1733,plain,(
% 1.16/0.61 apply(identity_relation(sK12_skl),sK13_skl)=sK13_skl),
% 1.16/0.61 inference(resolution,[status(thm)],[f298,f175])).
% 1.16/0.61 fof(f1755,plain,(
% 1.16/0.61 ![X0,X1]: (~in(X0,X1)|apply(relation_composition(identity_relation(X1),sK11_skl),X0)=apply(sK11_skl,apply(identity_relation(X1),X0)))),
% 1.16/0.61 inference(forward_demodulation,[status(thm)],[f295,f275])).
% 1.16/0.61 fof(f1807,plain,(
% 1.16/0.61 apply(relation_composition(identity_relation(sK12_skl),sK11_skl),sK13_skl)=apply(sK11_skl,apply(identity_relation(sK12_skl),sK13_skl))),
% 1.16/0.61 inference(resolution,[status(thm)],[f1755,f175])).
% 1.16/0.61 fof(f1815,plain,(
% 1.16/0.61 apply(relation_composition(identity_relation(sK12_skl),sK11_skl),sK13_skl)=apply(sK11_skl,sK13_skl)),
% 1.16/0.61 inference(forward_demodulation,[status(thm)],[f1733,f1807])).
% 1.16/0.61 fof(f1816,plain,(
% 1.16/0.61 $false),
% 1.16/0.61 inference(forward_subsumption_resolution,[status(thm)],[f1815,f139])).
% 1.16/0.61 % SZS output end CNFRefutation for theBenchmark.p
% 1.16/0.62 % Elapsed time: 0.261684 seconds
% 1.16/0.62 % CPU time: 1.828119 seconds
% 1.16/0.62 % Total memory used: 132.548 MB
% 1.16/0.62 % Net memory used: 130.208 MB
%------------------------------------------------------------------------------