%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU216+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 : n002.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 02:22:01 PM UTC 2026
% Result : Theorem 164.76s 21.28s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n002.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 06:01:16 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 % Drodi V4.1.1
% 164.76/21.28 % Refutation found
% 164.76/21.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 164.76/21.28 % SZS output start CNFRefutation for theBenchmark
% 164.76/21.28 fof(f5,axiom,(
% 164.76/21.28 (! [A,B] :( relation(B)=> ( B = identity_relation(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> ( in(C,A)& C = D ) ) )) ) )),
% 164.76/21.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 164.76/21.28 fof(f6,axiom,(
% 164.76/21.28 (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( ( in(B,relation_dom(A))=> ( C = apply(A,B)<=> in(ordered_pair(B,C),A) ) )& ( ~ in(B,relation_dom(A))=> ( C = apply(A,B)<=> C = empty_set ) ) ) )) )),
% 164.76/21.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 164.76/21.28 fof(f37,conjecture,(
% 164.76/21.28 (! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) )),
% 164.76/21.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 164.76/21.28 fof(f38,negated_conjecture,(
% 164.76/21.28 ~((! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) ))),
% 164.76/21.28 inference(negated_conjecture,[status(cth)],[f37])).
% 164.76/21.28 fof(f40,axiom,(
% 164.76/21.28 (! [A] :( relation_dom(identity_relation(A)) = A& relation_rng(identity_relation(A)) = A ) )),
% 164.76/21.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 164.76/21.28 fof(f43,axiom,(
% 164.76/21.28 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(ordered_pair(A,B),C)<=> ( in(A,relation_dom(C))& B = apply(C,A) ) ) ) )),
% 164.76/21.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 164.76/21.28 fof(f51,plain,(
% 164.76/21.28 ![A,B]: (~relation(B)|(B=identity_relation(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>(in(C,A)&C=D)))))),
% 164.76/21.28 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 164.76/21.28 fof(f52,plain,(
% 164.76/21.28 ![A,B]: (~relation(B)|((~B=identity_relation(A)|(![C,D]: ((~in(ordered_pair(C,D),B)|(in(C,A)&C=D))&(in(ordered_pair(C,D),B)|(~in(C,A)|~C=D)))))&(B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D)))))))),
% 164.76/21.28 inference(NNF_transformation,[status(thm)],[f51])).
% 164.76/21.28 fof(f53,plain,(
% 164.76/21.28 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D))))))))),
% 164.76/21.28 inference(miniscoping,[status(thm)],[f52])).
% 164.76/21.28 fof(f54,plain,(
% 164.76/21.28 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|((~in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(~in(sK0_skl(A,B),A)|~sK0_skl(A,B)=sK1_skl(A,B)))&(in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(in(sK0_skl(A,B),A)&sK0_skl(A,B)=sK1_skl(A,B))))))))),
% 164.76/21.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f53])).
% 164.76/21.28 fof(f57,plain,(
% 164.76/21.28 ![X0,X1,X2,X3]: (~relation(X0)|~X0=identity_relation(X1)|in(ordered_pair(X2,X3),X0)|~in(X2,X1)|~X2=X3)),
% 164.76/21.28 inference(cnf_transformation,[status(thm)],[f54])).
% 164.76/21.28 fof(f58,plain,(
% 164.76/21.28 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|~in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|~in(sK0_skl(X1,X0),X1)|~sK0_skl(X1,X0)=sK1_skl(X1,X0))),
% 164.76/21.28 inference(cnf_transformation,[status(thm)],[f54])).
% 164.76/21.28 fof(f59,plain,(
% 164.76/21.28 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|in(sK0_skl(X1,X0),X1))),
% 164.76/21.28 inference(cnf_transformation,[status(thm)],[f54])).
% 164.76/21.28 fof(f60,plain,(
% 164.76/21.28 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|sK0_skl(X1,X0)=sK1_skl(X1,X0))),
% 164.76/21.28 inference(cnf_transformation,[status(thm)],[f54])).
% 164.76/21.28 fof(f61,plain,(
% 164.76/21.28 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|(C=apply(A,B)<=>in(ordered_pair(B,C),A)))&(in(B,relation_dom(A))|(C=apply(A,B)<=>C=empty_set)))))),
% 164.76/21.28 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 164.76/21.28 fof(f62,plain,(
% 164.76/21.28 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|((~C=apply(A,B)|in(ordered_pair(B,C),A))&(C=apply(A,B)|~in(ordered_pair(B,C),A))))&(in(B,relation_dom(A))|((~C=apply(A,B)|C=empty_set)&(C=apply(A,B)|~C=empty_set))))))),
% 164.76/21.28 inference(NNF_transformation,[status(thm)],[f61])).
% 164.76/21.28 fof(f63,plain,(
% 164.76/21.28 ![A]: ((~relation(A)|~function(A))|((![B]: (~in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|in(ordered_pair(B,C),A)))&(![C]: (C=apply(A,B)|~in(ordered_pair(B,C),A))))))&(![B]: (in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|C=empty_set))&(![C]: (C=apply(A,B)|~C=empty_set)))))))),
% 164.76/21.28 inference(miniscoping,[status(thm)],[f62])).
% 164.76/21.28 fof(f64,plain,(
% 164.76/21.28 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|~X2=apply(X0,X1)|in(ordered_pair(X1,X2),X0))),
% 164.76/21.28 inference(cnf_transformation,[status(thm)],[f63])).
% 164.76/21.28 fof(f65,plain,(
% 164.76/21.28 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X2=apply(X0,X1)|~in(ordered_pair(X1,X2),X0))),
% 164.76/21.28 inference(cnf_transformation,[status(thm)],[f63])).
% 164.76/21.28 fof(f114,plain,(
% 164.76/21.28 (?[A,B]: ((relation(B)&function(B))&(B=identity_relation(A)<~>(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C))))))),
% 164.76/21.28 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 164.76/21.29 fof(f115,plain,(
% 164.76/21.29 ?[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))))))),
% 164.76/21.29 inference(NNF_transformation,[status(thm)],[f114])).
% 164.76/21.29 fof(f116,plain,(
% 164.76/21.29 ?[B]: ((relation(B)&function(B))&(?[A]: ((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)))))))),
% 164.76/21.29 inference(miniscoping,[status(thm)],[f115])).
% 164.76/21.29 fof(f117,plain,(
% 164.76/21.29 ((relation(sK9_skl)&function(sK9_skl))&((sK9_skl=identity_relation(sK10_skl)|(relation_dom(sK9_skl)=sK10_skl&(![C]: (~in(C,sK10_skl)|apply(sK9_skl,C)=C))))&(~sK9_skl=identity_relation(sK10_skl)|(~relation_dom(sK9_skl)=sK10_skl|(in(sK11_skl,sK10_skl)&~apply(sK9_skl,sK11_skl)=sK11_skl)))))),
% 164.76/21.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(B,sK9_skl),skolemize(A,sK10_skl),skolemize(C,sK11_skl)],[f116])).
% 164.76/21.29 fof(f118,plain,(
% 164.76/21.29 relation(sK9_skl)),
% 164.76/21.29 inference(cnf_transformation,[status(thm)],[f117])).
% 164.76/21.29 fof(f119,plain,(
% 164.76/21.29 function(sK9_skl)),
% 164.76/21.29 inference(cnf_transformation,[status(thm)],[f117])).
% 164.76/21.29 fof(f120,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|relation_dom(sK9_skl)=sK10_skl),
% 164.76/21.29 inference(cnf_transformation,[status(thm)],[f117])).
% 164.76/21.29 fof(f121,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(sK10_skl)|~in(X0,sK10_skl)|apply(sK9_skl,X0)=X0)),
% 164.76/21.29 inference(cnf_transformation,[status(thm)],[f117])).
% 164.76/21.29 fof(f122,plain,(
% 164.76/21.29 ~sK9_skl=identity_relation(sK10_skl)|~relation_dom(sK9_skl)=sK10_skl|in(sK11_skl,sK10_skl)),
% 164.76/21.29 inference(cnf_transformation,[status(thm)],[f117])).
% 164.76/21.29 fof(f123,plain,(
% 164.76/21.29 ~sK9_skl=identity_relation(sK10_skl)|~relation_dom(sK9_skl)=sK10_skl|~apply(sK9_skl,sK11_skl)=sK11_skl),
% 164.76/21.29 inference(cnf_transformation,[status(thm)],[f117])).
% 164.76/21.29 fof(f126,plain,(
% 164.76/21.29 (![A]: relation_dom(identity_relation(A))=A)&(![A]: relation_rng(identity_relation(A))=A)),
% 164.76/21.29 inference(miniscoping,[status(thm)],[f40])).
% 164.76/21.29 fof(f127,plain,(
% 164.76/21.29 ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 164.76/21.29 inference(cnf_transformation,[status(thm)],[f126])).
% 164.76/21.29 fof(f135,plain,(
% 164.76/21.29 ![A,B,C]: ((~relation(C)|~function(C))|(in(ordered_pair(A,B),C)<=>(in(A,relation_dom(C))&B=apply(C,A))))),
% 164.76/21.29 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 164.76/21.29 fof(f136,plain,(
% 164.76/21.29 ![A,B,C]: ((~relation(C)|~function(C))|((~in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A)))&(in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A)))))),
% 164.76/21.29 inference(NNF_transformation,[status(thm)],[f135])).
% 164.76/21.29 fof(f137,plain,(
% 164.76/21.29 ![C]: ((~relation(C)|~function(C))|((![A,B]: (~in(ordered_pair(A,B),C)|(in(A,relation_dom(C))&B=apply(C,A))))&(![A,B]: (in(ordered_pair(A,B),C)|(~in(A,relation_dom(C))|~B=apply(C,A))))))),
% 164.76/21.29 inference(miniscoping,[status(thm)],[f136])).
% 164.76/21.29 fof(f138,plain,(
% 164.76/21.29 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(ordered_pair(X1,X2),X0)|in(X1,relation_dom(X0)))),
% 164.76/21.29 inference(cnf_transformation,[status(thm)],[f137])).
% 164.76/21.29 fof(f141,plain,(
% 164.76/21.29 ![X0,X1,X2]: (~relation(X0)|~X0=identity_relation(X1)|in(ordered_pair(X2,X2),X0)|~in(X2,X1))),
% 164.76/21.29 inference(destructive_equality_resolution,[status(thm)],[f57])).
% 164.76/21.29 fof(f143,plain,(
% 164.76/21.29 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=apply(X0,X2)|~in(ordered_pair(X2,X1),X0))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f65,f138])).
% 164.76/21.29 fof(f665,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)|in(sK0_skl(X0,sK9_skl),X0))),
% 164.76/21.29 inference(resolution,[status(thm)],[f59,f118])).
% 164.76/21.29 fof(f1144,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)|sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl))),
% 164.76/21.29 inference(resolution,[status(thm)],[f60,f118])).
% 164.76/21.29 fof(f1166,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),X0)|~relation(sK9_skl)|~function(sK9_skl)|sK1_skl(X0,sK9_skl)=apply(sK9_skl,sK0_skl(X0,sK9_skl)))),
% 164.76/21.29 inference(resolution,[status(thm)],[f665,f143])).
% 164.76/21.29 fof(f1167,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),X0)|~relation(sK9_skl)|~function(sK9_skl)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl)))),
% 164.76/21.29 inference(resolution,[status(thm)],[f665,f138])).
% 164.76/21.29 fof(f1171,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),X0)|~function(sK9_skl)|sK1_skl(X0,sK9_skl)=apply(sK9_skl,sK0_skl(X0,sK9_skl)))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1166,f118])).
% 164.76/21.29 fof(f1172,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),X0)|~function(sK9_skl)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl)))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1167,f118])).
% 164.76/21.29 fof(f1196,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl)|~relation(sK9_skl)|~function(sK9_skl)|sK1_skl(X0,sK9_skl)=apply(sK9_skl,sK0_skl(X0,sK9_skl)))),
% 164.76/21.29 inference(resolution,[status(thm)],[f1144,f143])).
% 164.76/21.29 fof(f1197,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl)|~relation(sK9_skl)|~function(sK9_skl)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl)))),
% 164.76/21.29 inference(resolution,[status(thm)],[f1144,f138])).
% 164.76/21.29 fof(f1202,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl)|~function(sK9_skl)|sK1_skl(X0,sK9_skl)=apply(sK9_skl,sK0_skl(X0,sK9_skl)))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1196,f118])).
% 164.76/21.29 fof(f1203,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl)|~function(sK9_skl)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl)))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1197,f118])).
% 164.76/21.29 fof(f1248,plain,(
% 164.76/21.29 ![X0,X1]: (~sK9_skl=identity_relation(X0)|in(ordered_pair(X1,X1),sK9_skl)|~in(X1,X0))),
% 164.76/21.29 inference(resolution,[status(thm)],[f141,f118])).
% 164.76/21.29 fof(f1259,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),X0)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl)))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1172,f119])).
% 164.76/21.29 fof(f1260,plain,(
% 164.76/21.29 sK9_skl=identity_relation(relation_dom(sK9_skl))|~relation(sK9_skl)|sK9_skl=identity_relation(relation_dom(sK9_skl))|~in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),sK1_skl(relation_dom(sK9_skl),sK9_skl)),sK9_skl)|~sK0_skl(relation_dom(sK9_skl),sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(resolution,[status(thm)],[f1259,f58])).
% 164.76/21.29 fof(f1261,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl))|~relation(sK9_skl)|sK9_skl=identity_relation(X0)|~in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)|~sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl))),
% 164.76/21.29 inference(resolution,[status(thm)],[f1259,f58])).
% 164.76/21.29 fof(f1262,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|in(sK0_skl(sK10_skl,sK9_skl),relation_dom(sK9_skl))|sK9_skl=identity_relation(sK10_skl)|apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))=sK0_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(resolution,[status(thm)],[f1259,f121])).
% 164.76/21.29 fof(f1263,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(relation_dom(sK9_skl))|~relation(sK9_skl)|~function(sK9_skl)|~X0=apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),sK9_skl))|in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),X0),sK9_skl))),
% 164.76/21.29 inference(resolution,[status(thm)],[f1259,f64])).
% 164.76/21.29 fof(f1270,plain,(
% 164.76/21.29 sK9_skl=identity_relation(relation_dom(sK9_skl))|~relation(sK9_skl)|~in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),sK1_skl(relation_dom(sK9_skl),sK9_skl)),sK9_skl)|~sK0_skl(relation_dom(sK9_skl),sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(duplicate_literals_removal,[status(thm)],[f1260])).
% 164.76/21.29 fof(f1271,plain,(
% 164.76/21.29 sK9_skl=identity_relation(relation_dom(sK9_skl))|~in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),sK1_skl(relation_dom(sK9_skl),sK9_skl)),sK9_skl)|~sK0_skl(relation_dom(sK9_skl),sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1270,f118])).
% 164.76/21.29 fof(f1272,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl))|~relation(sK9_skl)|~in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)|~sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl))),
% 164.76/21.29 inference(duplicate_literals_removal,[status(thm)],[f1261])).
% 164.76/21.29 fof(f1273,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl))|~in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)|~sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1272,f118])).
% 164.76/21.29 fof(f1274,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|in(sK0_skl(sK10_skl,sK9_skl),relation_dom(sK9_skl))|apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))=sK0_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(duplicate_literals_removal,[status(thm)],[f1262])).
% 164.76/21.29 fof(f1275,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(relation_dom(sK9_skl))|~function(sK9_skl)|~X0=apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),sK9_skl))|in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),X0),sK9_skl))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1263,f118])).
% 164.76/21.29 fof(f1281,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl)|in(sK0_skl(X0,sK9_skl),relation_dom(sK9_skl)))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1203,f119])).
% 164.76/21.29 fof(f1756,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),X0)|sK1_skl(X0,sK9_skl)=apply(sK9_skl,sK0_skl(X0,sK9_skl)))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1171,f119])).
% 164.76/21.29 fof(f4201,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl)|sK1_skl(X0,sK9_skl)=apply(sK9_skl,sK0_skl(X0,sK9_skl)))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f1202,f119])).
% 164.76/21.29 fof(f4304,plain,(
% 164.76/21.29 relation_dom(sK9_skl)=sK10_skl|relation_dom(sK9_skl)=sK10_skl),
% 164.76/21.29 inference(paramodulation,[status(thm)],[f120,f127])).
% 164.76/21.29 fof(f4326,plain,(
% 164.76/21.29 relation_dom(sK9_skl)=sK10_skl),
% 164.76/21.29 inference(duplicate_literals_removal,[status(thm)],[f4304])).
% 164.76/21.29 fof(f4944,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl)|in(sK0_skl(X0,sK9_skl),sK10_skl))),
% 164.76/21.29 inference(backward_demodulation,[status(thm)],[f4326,f1281])).
% 164.76/21.29 fof(f4947,plain,(
% 164.76/21.29 ~sK9_skl=identity_relation(sK10_skl)|~sK10_skl=sK10_skl|~apply(sK9_skl,sK11_skl)=sK11_skl),
% 164.76/21.29 inference(backward_demodulation,[status(thm)],[f4326,f123])).
% 164.76/21.29 fof(f4985,plain,(
% 164.76/21.29 ~sK9_skl=identity_relation(sK10_skl)|~sK10_skl=sK10_skl|in(sK11_skl,sK10_skl)),
% 164.76/21.29 inference(backward_demodulation,[status(thm)],[f4326,f122])).
% 164.76/21.29 fof(f4987,plain,(
% 164.76/21.29 ![X0,X1]: (~relation(sK9_skl)|~function(sK9_skl)|~in(X0,sK10_skl)|~X1=apply(sK9_skl,X0)|in(ordered_pair(X0,X1),sK9_skl))),
% 164.76/21.29 inference(paramodulation,[status(thm)],[f4326,f64])).
% 164.76/21.29 fof(f4999,plain,(
% 164.76/21.29 ~sK9_skl=identity_relation(sK10_skl)|~apply(sK9_skl,sK11_skl)=sK11_skl),
% 164.76/21.29 inference(trivial_equality_resolution,[status(thm)],[f4947])).
% 164.76/21.29 fof(f5016,plain,(
% 164.76/21.29 ~sK9_skl=identity_relation(sK10_skl)|in(sK11_skl,sK10_skl)),
% 164.76/21.29 inference(trivial_equality_resolution,[status(thm)],[f4985])).
% 164.76/21.29 fof(f5018,plain,(
% 164.76/21.29 ![X0,X1]: (~function(sK9_skl)|~in(X0,sK10_skl)|~X1=apply(sK9_skl,X0)|in(ordered_pair(X0,X1),sK9_skl))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f4987,f118])).
% 164.76/21.29 fof(f5567,plain,(
% 164.76/21.29 ![X0,X1]: (~sK9_skl=identity_relation(X0)|~in(X1,X0)|~relation(sK9_skl)|~function(sK9_skl)|X1=apply(sK9_skl,X1))),
% 164.76/21.29 inference(resolution,[status(thm)],[f1248,f143])).
% 164.76/21.29 fof(f5572,plain,(
% 164.76/21.29 ![X0,X1]: (~sK9_skl=identity_relation(X0)|~in(X1,X0)|~function(sK9_skl)|X1=apply(sK9_skl,X1))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f5567,f118])).
% 164.76/21.29 fof(f9898,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),sK10_skl)|~in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl)|~sK0_skl(X0,sK9_skl)=sK1_skl(X0,sK9_skl))),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f1273])).
% 164.76/21.29 fof(f9899,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(X0)|in(sK0_skl(X0,sK9_skl),sK10_skl)|~in(ordered_pair(sK0_skl(X0,sK9_skl),sK1_skl(X0,sK9_skl)),sK9_skl))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f9898,f4944])).
% 164.76/21.29 fof(f9910,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|in(sK0_skl(sK10_skl,sK9_skl),sK10_skl)|apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))=sK0_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f1274])).
% 164.76/21.29 fof(f9911,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))=sK0_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f9910,f121])).
% 164.76/21.29 fof(f9919,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|sK1_skl(sK10_skl,sK9_skl)=sK0_skl(sK10_skl,sK9_skl)|sK9_skl=identity_relation(sK10_skl)|sK0_skl(sK10_skl,sK9_skl)=sK1_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(paramodulation,[status(thm)],[f4201,f9911])).
% 164.76/21.29 fof(f9938,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|sK1_skl(sK10_skl,sK9_skl)=sK0_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(duplicate_literals_removal,[status(thm)],[f9919])).
% 164.76/21.29 fof(f9943,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(sK10_skl)|~function(sK9_skl)|~X0=apply(sK9_skl,sK0_skl(relation_dom(sK9_skl),sK9_skl))|in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),X0),sK9_skl))),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f1275])).
% 164.76/21.29 fof(f9944,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(sK10_skl)|~function(sK9_skl)|~X0=apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))|in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),X0),sK9_skl))),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f9943])).
% 164.76/21.29 fof(f9945,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(sK10_skl)|~function(sK9_skl)|~X0=apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))|in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),X0),sK9_skl))),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f9944])).
% 164.76/21.29 fof(f9946,plain,(
% 164.76/21.29 ![X0]: (sK9_skl=identity_relation(sK10_skl)|~X0=apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))|in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),X0),sK9_skl))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f9945,f119])).
% 164.76/21.29 fof(f9947,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~sK1_skl(sK10_skl,sK9_skl)=apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))|sK9_skl=identity_relation(sK10_skl)|in(sK0_skl(sK10_skl,sK9_skl),sK10_skl)),
% 164.76/21.29 inference(resolution,[status(thm)],[f9946,f9899])).
% 164.76/21.29 fof(f9957,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~sK1_skl(sK10_skl,sK9_skl)=apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))|in(sK0_skl(sK10_skl,sK9_skl),sK10_skl)),
% 164.76/21.29 inference(duplicate_literals_removal,[status(thm)],[f9947])).
% 164.76/21.29 fof(f9958,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|in(sK0_skl(sK10_skl,sK9_skl),sK10_skl)),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f9957,f1756])).
% 164.76/21.29 fof(f9973,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|in(sK1_skl(sK10_skl,sK9_skl),sK10_skl)|sK9_skl=identity_relation(sK10_skl)),
% 164.76/21.29 inference(paramodulation,[status(thm)],[f9938,f9958])).
% 164.76/21.29 fof(f10002,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|in(sK1_skl(sK10_skl,sK9_skl),sK10_skl)),
% 164.76/21.29 inference(duplicate_literals_removal,[status(thm)],[f9973])).
% 164.76/21.29 fof(f10968,plain,(
% 164.76/21.29 ![X0,X1]: (~in(X0,sK10_skl)|~X1=apply(sK9_skl,X0)|in(ordered_pair(X0,X1),sK9_skl))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f5018,f119])).
% 164.76/21.29 fof(f12692,plain,(
% 164.76/21.29 ![X0]: (~in(X0,sK10_skl)|apply(sK9_skl,X0)=X0)),
% 164.76/21.29 inference(backward_subsumption_resolution,[status(thm)],[f121,f12693])).
% 164.76/21.29 fof(f12693,plain,(
% 164.76/21.29 ![X0,X1]: (~sK9_skl=identity_relation(X0)|~in(X1,X0)|X1=apply(sK9_skl,X1))),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f5572,f119])).
% 164.76/21.29 fof(f14915,plain,(
% 164.76/21.29 apply(sK9_skl,sK11_skl)=sK11_skl|~sK9_skl=identity_relation(sK10_skl)),
% 164.76/21.29 inference(resolution,[status(thm)],[f12692,f5016])).
% 164.76/21.29 fof(f14957,plain,(
% 164.76/21.29 ~sK9_skl=identity_relation(sK10_skl)),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f14915,f4999])).
% 164.76/21.29 fof(f14966,plain,(
% 164.76/21.29 in(sK1_skl(sK10_skl,sK9_skl),sK10_skl)),
% 164.76/21.29 inference(backward_subsumption_resolution,[status(thm)],[f10002,f14957])).
% 164.76/21.29 fof(f14967,plain,(
% 164.76/21.29 sK1_skl(sK10_skl,sK9_skl)=sK0_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(backward_subsumption_resolution,[status(thm)],[f9938,f14957])).
% 164.76/21.29 fof(f14970,plain,(
% 164.76/21.29 apply(sK9_skl,sK0_skl(sK10_skl,sK9_skl))=sK0_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(backward_subsumption_resolution,[status(thm)],[f9911,f14957])).
% 164.76/21.29 fof(f27233,plain,(
% 164.76/21.29 apply(sK9_skl,sK1_skl(sK10_skl,sK9_skl))=sK0_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f14967,f14970])).
% 164.76/21.29 fof(f27234,plain,(
% 164.76/21.29 apply(sK9_skl,sK1_skl(sK10_skl,sK9_skl))=sK1_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f14967,f27233])).
% 164.76/21.29 fof(f31646,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~in(ordered_pair(sK0_skl(relation_dom(sK9_skl),sK9_skl),sK1_skl(relation_dom(sK9_skl),sK9_skl)),sK9_skl)|~sK0_skl(relation_dom(sK9_skl),sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f1271])).
% 164.76/21.29 fof(f31647,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~in(ordered_pair(sK0_skl(sK10_skl,sK9_skl),sK1_skl(relation_dom(sK9_skl),sK9_skl)),sK9_skl)|~sK0_skl(relation_dom(sK9_skl),sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f31646])).
% 164.76/21.29 fof(f31648,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~in(ordered_pair(sK1_skl(sK10_skl,sK9_skl),sK1_skl(relation_dom(sK9_skl),sK9_skl)),sK9_skl)|~sK0_skl(relation_dom(sK9_skl),sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f14967,f31647])).
% 164.76/21.29 fof(f31649,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~in(ordered_pair(sK1_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)|~sK0_skl(relation_dom(sK9_skl),sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f31648])).
% 164.76/21.29 fof(f31650,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~in(ordered_pair(sK1_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)|~sK0_skl(sK10_skl,sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f31649])).
% 164.76/21.29 fof(f31651,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~in(ordered_pair(sK1_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)|~sK1_skl(sK10_skl,sK9_skl)=sK1_skl(relation_dom(sK9_skl),sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f14967,f31650])).
% 164.76/21.29 fof(f31652,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~in(ordered_pair(sK1_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)|~sK1_skl(sK10_skl,sK9_skl)=sK1_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f4326,f31651])).
% 164.76/21.29 fof(f31653,plain,(
% 164.76/21.29 sK9_skl=identity_relation(sK10_skl)|~in(ordered_pair(sK1_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)),
% 164.76/21.29 inference(trivial_equality_resolution,[status(thm)],[f31652])).
% 164.76/21.29 fof(f31654,plain,(
% 164.76/21.29 ~in(ordered_pair(sK1_skl(sK10_skl,sK9_skl),sK1_skl(sK10_skl,sK9_skl)),sK9_skl)),
% 164.76/21.29 inference(forward_subsumption_resolution,[status(thm)],[f31653,f14957])).
% 164.76/21.29 fof(f31655,plain,(
% 164.76/21.29 ~in(sK1_skl(sK10_skl,sK9_skl),sK10_skl)|~sK1_skl(sK10_skl,sK9_skl)=apply(sK9_skl,sK1_skl(sK10_skl,sK9_skl))),
% 164.76/21.29 inference(resolution,[status(thm)],[f31654,f10968])).
% 164.76/21.29 fof(f31670,plain,(
% 164.76/21.29 ~in(sK1_skl(sK10_skl,sK9_skl),sK10_skl)|~sK1_skl(sK10_skl,sK9_skl)=sK1_skl(sK10_skl,sK9_skl)),
% 164.76/21.29 inference(forward_demodulation,[status(thm)],[f27234,f31655])).
% 164.76/21.29 fof(f31671,plain,(
% 164.76/21.29 ~in(sK1_skl(sK10_skl,sK9_skl),sK10_skl)),
% 164.76/21.29 inference(trivial_equality_resolution,[status(thm)],[f31670])).
% 164.76/21.29 fof(f31672,plain,(
% 164.76/21.29 $false),
% 164.76/21.33 inference(forward_subsumption_resolution,[status(thm)],[f31671,f14966])).
% 164.76/21.33 % SZS output end CNFRefutation for theBenchmark.p
% 20.90/21.48 % Elapsed time: 21.039372 seconds
% 20.90/21.48 % CPU time: 166.260853 seconds
% 20.90/21.48 % Total memory used: 1.340 GB
% 20.90/21.48 % Net memory used: 1.277 GB
%------------------------------------------------------------------------------