TSTP Solution File: SEU027+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:35:43 EDT 2023
% Result : Theorem 1.68s 0.57s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 09:38:02 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 1.68/0.57 % Refutation found
% 1.68/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.68/0.57 % SZS output start CNFRefutation for theBenchmark
% 1.68/0.57 fof(f5,axiom,(
% 1.68/0.57 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(D,relation_dom(A))& C = apply(A,D) ) )) )) )) )),
% 1.68/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.68/0.57 fof(f6,axiom,(
% 1.68/0.57 (! [A] :( ( relation(A)& function(A) )=> ( relation(function_inverse(A))& function(function_inverse(A)) ) ) )),
% 1.68/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.68/0.57 fof(f31,axiom,(
% 1.68/0.57 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> (! [B] :( ( relation(B)& function(B) )=> ( B = function_inverse(A)<=> ( relation_dom(B) = relation_rng(A)& (! [C,D] :( ( ( in(C,relation_rng(A))& D = apply(B,C) )=> ( in(D,relation_dom(A))& C = apply(A,D) ) )& ( ( in(D,relation_dom(A))& C = apply(A,D) )=> ( in(C,relation_rng(A))& D = apply(B,C) ) ) ) )) ) ) )) ) )),
% 1.68/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.68/0.57 fof(f33,conjecture,(
% 1.68/0.57 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( ( relation(B)& function(B) )=> ( ( one_to_one(A)& relation_dom(A) = relation_rng(B)& relation_rng(A) = relation_dom(B)& (! [C,D] :( ( in(C,relation_dom(A))& in(D,relation_dom(B)) )=> ( apply(A,C) = D<=> apply(B,D) = C ) ) ))=> B = function_inverse(A) ) ) )) )),
% 1.68/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.68/0.57 fof(f34,negated_conjecture,(
% 1.68/0.57 ~((! [A] :( ( relation(A)& function(A) )=> (! [B] :( ( relation(B)& function(B) )=> ( ( one_to_one(A)& relation_dom(A) = relation_rng(B)& relation_rng(A) = relation_dom(B)& (! [C,D] :( ( in(C,relation_dom(A))& in(D,relation_dom(B)) )=> ( apply(A,C) = D<=> apply(B,D) = C ) ) ))=> B = function_inverse(A) ) ) )) ))),
% 1.68/0.57 inference(negated_conjecture,[status(cth)],[f33])).
% 1.68/0.57 fof(f38,axiom,(
% 1.68/0.57 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( ( relation(B)& function(B) )=> ( ( relation_dom(A) = relation_dom(B)& (! [C] :( in(C,relation_dom(A))=> apply(A,C) = apply(B,C) ) ))=> A = B ) ) )) )),
% 1.68/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.68/0.57 fof(f49,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))),
% 1.68/0.57 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 1.68/0.57 fof(f50,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))&(in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D)))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 1.68/0.57 inference(NNF_transformation,[status(esa)],[f49])).
% 1.68/0.57 fof(f51,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 1.68/0.57 inference(miniscoping,[status(esa)],[f50])).
% 1.68/0.57 fof(f52,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(in(sk0_0(C,B,A),relation_dom(A))&C=apply(A,sk0_0(C,B,A)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|((~in(sk0_1(B,A),B)|(![D]: (~in(D,relation_dom(A))|~sk0_1(B,A)=apply(A,D))))&(in(sk0_1(B,A),B)|(in(sk0_2(B,A),relation_dom(A))&sk0_1(B,A)=apply(A,sk0_2(B,A)))))))))),
% 1.68/0.57 inference(skolemization,[status(esa)],[f51])).
% 1.68/0.57 fof(f55,plain,(
% 1.68/0.57 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|in(X2,X1)|~in(X3,relation_dom(X0))|~X2=apply(X0,X3))),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f52])).
% 1.68/0.57 fof(f59,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(relation(function_inverse(A))&function(function_inverse(A))))),
% 1.68/0.57 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 1.68/0.57 fof(f60,plain,(
% 1.68/0.57 ![X0]: (~relation(X0)|~function(X0)|relation(function_inverse(X0)))),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f59])).
% 1.68/0.57 fof(f61,plain,(
% 1.68/0.57 ![X0]: (~relation(X0)|~function(X0)|function(function_inverse(X0)))),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f59])).
% 1.68/0.57 fof(f125,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|(B=function_inverse(A)<=>(relation_dom(B)=relation_rng(A)&(![C,D]: (((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D)))&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))))))),
% 1.68/0.57 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 1.68/0.57 fof(f126,plain,(
% 1.68/0.57 ![A,B,C,D]: (pd0_0(D,C,B,A)<=>((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D))))),
% 1.68/0.57 introduced(predicate_definition,[f125])).
% 1.68/0.57 fof(f127,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|(B=function_inverse(A)<=>(relation_dom(B)=relation_rng(A)&(![C,D]: (pd0_0(D,C,B,A)&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))))))),
% 1.68/0.57 inference(formula_renaming,[status(thm)],[f125,f126])).
% 1.68/0.57 fof(f128,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&(![C,D]: (pd0_0(D,C,B,A)&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|(?[C,D]: (~pd0_0(D,C,B,A)|((in(D,relation_dom(A))&C=apply(A,D))&(~in(C,relation_rng(A))|~D=apply(B,C))))))))))))),
% 1.68/0.57 inference(NNF_transformation,[status(esa)],[f127])).
% 1.68/0.57 fof(f129,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&((![C,D]: pd0_0(D,C,B,A))&(![C,D]: ((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|((?[C,D]: ~pd0_0(D,C,B,A))|(?[C,D]: ((in(D,relation_dom(A))&C=apply(A,D))&(~in(C,relation_rng(A))|~D=apply(B,C))))))))))))),
% 1.68/0.57 inference(miniscoping,[status(esa)],[f128])).
% 1.68/0.57 fof(f130,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&((![C,D]: pd0_0(D,C,B,A))&(![C,D]: ((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|(~pd0_0(sk0_15(B,A),sk0_14(B,A),B,A)|((in(sk0_17(B,A),relation_dom(A))&sk0_16(B,A)=apply(A,sk0_17(B,A)))&(~in(sk0_16(B,A),relation_rng(A))|~sk0_17(B,A)=apply(B,sk0_16(B,A))))))))))))),
% 1.68/0.57 inference(skolemization,[status(esa)],[f129])).
% 1.68/0.57 fof(f131,plain,(
% 1.68/0.57 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~relation(X1)|~function(X1)|~X1=function_inverse(X0)|relation_dom(X1)=relation_rng(X0))),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f130])).
% 1.68/0.57 fof(f134,plain,(
% 1.68/0.57 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~relation(X1)|~function(X1)|~X1=function_inverse(X0)|~in(X2,relation_dom(X0))|~X3=apply(X0,X2)|X2=apply(X1,X3))),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f130])).
% 1.68/0.57 fof(f141,plain,(
% 1.68/0.57 (?[A]: ((relation(A)&function(A))&(?[B]: ((relation(B)&function(B))&((((one_to_one(A)&relation_dom(A)=relation_rng(B))&relation_rng(A)=relation_dom(B))&(![C,D]: ((~in(C,relation_dom(A))|~in(D,relation_dom(B)))|(apply(A,C)=D<=>apply(B,D)=C))))&~B=function_inverse(A))))))),
% 1.68/0.57 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 1.68/0.57 fof(f142,plain,(
% 1.68/0.57 ?[A]: ((relation(A)&function(A))&(?[B]: ((relation(B)&function(B))&((((one_to_one(A)&relation_dom(A)=relation_rng(B))&relation_rng(A)=relation_dom(B))&(![C,D]: ((~in(C,relation_dom(A))|~in(D,relation_dom(B)))|((~apply(A,C)=D|apply(B,D)=C)&(apply(A,C)=D|~apply(B,D)=C)))))&~B=function_inverse(A)))))),
% 1.68/0.57 inference(NNF_transformation,[status(esa)],[f141])).
% 1.68/0.57 fof(f143,plain,(
% 1.68/0.57 ((relation(sk0_18)&function(sk0_18))&((relation(sk0_19)&function(sk0_19))&((((one_to_one(sk0_18)&relation_dom(sk0_18)=relation_rng(sk0_19))&relation_rng(sk0_18)=relation_dom(sk0_19))&(![C,D]: ((~in(C,relation_dom(sk0_18))|~in(D,relation_dom(sk0_19)))|((~apply(sk0_18,C)=D|apply(sk0_19,D)=C)&(apply(sk0_18,C)=D|~apply(sk0_19,D)=C)))))&~sk0_19=function_inverse(sk0_18))))),
% 1.68/0.57 inference(skolemization,[status(esa)],[f142])).
% 1.68/0.57 fof(f144,plain,(
% 1.68/0.57 relation(sk0_18)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f145,plain,(
% 1.68/0.57 function(sk0_18)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f146,plain,(
% 1.68/0.57 relation(sk0_19)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f147,plain,(
% 1.68/0.57 function(sk0_19)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f148,plain,(
% 1.68/0.57 one_to_one(sk0_18)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f149,plain,(
% 1.68/0.57 relation_dom(sk0_18)=relation_rng(sk0_19)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f150,plain,(
% 1.68/0.57 relation_rng(sk0_18)=relation_dom(sk0_19)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f152,plain,(
% 1.68/0.57 ![X0,X1]: (~in(X0,relation_dom(sk0_18))|~in(X1,relation_dom(sk0_19))|apply(sk0_18,X0)=X1|~apply(sk0_19,X1)=X0)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f153,plain,(
% 1.68/0.57 ~sk0_19=function_inverse(sk0_18)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f143])).
% 1.68/0.57 fof(f162,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(![B]: ((~relation(B)|~function(B))|((~relation_dom(A)=relation_dom(B)|(?[C]: (in(C,relation_dom(A))&~apply(A,C)=apply(B,C))))|A=B))))),
% 1.68/0.57 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 1.68/0.57 fof(f163,plain,(
% 1.68/0.57 ![A]: ((~relation(A)|~function(A))|(![B]: ((~relation(B)|~function(B))|((~relation_dom(A)=relation_dom(B)|(in(sk0_20(B,A),relation_dom(A))&~apply(A,sk0_20(B,A))=apply(B,sk0_20(B,A))))|A=B))))),
% 1.68/0.57 inference(skolemization,[status(esa)],[f162])).
% 1.68/0.57 fof(f164,plain,(
% 1.68/0.57 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation_dom(X0)=relation_dom(X1)|in(sk0_20(X1,X0),relation_dom(X0))|X0=X1)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f163])).
% 1.68/0.57 fof(f165,plain,(
% 1.68/0.57 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation_dom(X0)=relation_dom(X1)|~apply(X0,sk0_20(X1,X0))=apply(X1,sk0_20(X1,X0))|X0=X1)),
% 1.68/0.57 inference(cnf_transformation,[status(esa)],[f163])).
% 1.68/0.57 fof(f176,plain,(
% 1.68/0.57 ![X0,X1]: (~relation(X0)|~function(X0)|in(apply(X0,X1),relation_rng(X0))|~in(X1,relation_dom(X0)))),
% 1.68/0.57 inference(destructive_equality_resolution,[status(esa)],[f55])).
% 1.68/0.57 fof(f177,plain,(
% 1.68/0.57 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~relation(function_inverse(X0))|~function(function_inverse(X0))|relation_dom(function_inverse(X0))=relation_rng(X0))),
% 1.68/0.57 inference(destructive_equality_resolution,[status(esa)],[f131])).
% 1.68/0.57 fof(f178,plain,(
% 1.68/0.57 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~function(function_inverse(X0))|relation_dom(function_inverse(X0))=relation_rng(X0))),
% 1.68/0.57 inference(forward_subsumption_resolution,[status(thm)],[f177,f60])).
% 1.68/0.57 fof(f182,plain,(
% 1.68/0.57 ![X0,X2]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~relation(function_inverse(X0))|~function(function_inverse(X0))|~in(X2,relation_dom(X0))|X2=apply(function_inverse(X0),apply(X0,X2)))),
% 1.68/0.57 inference(destructive_equality_resolution,[status(esa)],[f134])).
% 1.68/0.57 fof(f183,plain,(
% 1.68/0.57 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~function(function_inverse(X0))|~in(X1,relation_dom(X0))|X1=apply(function_inverse(X0),apply(X0,X1)))),
% 1.68/0.57 inference(forward_subsumption_resolution,[status(thm)],[f182,f60])).
% 1.68/0.57 fof(f187,plain,(
% 1.68/0.57 ![X0,X1]: (~in(X0,relation_rng(sk0_19))|~in(X1,relation_dom(sk0_19))|apply(sk0_18,X0)=X1|~apply(sk0_19,X1)=X0)),
% 1.68/0.57 inference(forward_demodulation,[status(thm)],[f149,f152])).
% 1.68/0.57 fof(f188,plain,(
% 1.68/0.57 ![X0,X1]: (~in(X0,relation_rng(sk0_19))|~in(X1,relation_rng(sk0_18))|apply(sk0_18,X0)=X1|~apply(sk0_19,X1)=X0)),
% 1.68/0.57 inference(forward_demodulation,[status(thm)],[f150,f187])).
% 1.68/0.57 fof(f189,plain,(
% 1.68/0.57 ![X0]: (~in(apply(sk0_19,X0),relation_rng(sk0_19))|~in(X0,relation_rng(sk0_18))|apply(sk0_18,apply(sk0_19,X0))=X0)),
% 1.68/0.57 inference(destructive_equality_resolution,[status(esa)],[f188])).
% 1.68/0.57 fof(f193,plain,(
% 1.68/0.57 spl0_0 <=> relation(sk0_19)),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f195,plain,(
% 1.68/0.57 ~relation(sk0_19)|spl0_0),
% 1.68/0.57 inference(component_clause,[status(thm)],[f193])).
% 1.68/0.57 fof(f196,plain,(
% 1.68/0.57 spl0_1 <=> in(apply(sk0_19,X0),relation_rng(sk0_19))|~in(X0,relation_dom(sk0_19))),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f197,plain,(
% 1.68/0.57 ![X0]: (in(apply(sk0_19,X0),relation_rng(sk0_19))|~in(X0,relation_dom(sk0_19))|~spl0_1)),
% 1.68/0.57 inference(component_clause,[status(thm)],[f196])).
% 1.68/0.57 fof(f199,plain,(
% 1.68/0.57 ![X0]: (~relation(sk0_19)|in(apply(sk0_19,X0),relation_rng(sk0_19))|~in(X0,relation_dom(sk0_19)))),
% 1.68/0.57 inference(resolution,[status(thm)],[f176,f147])).
% 1.68/0.57 fof(f200,plain,(
% 1.68/0.57 ~spl0_0|spl0_1),
% 1.68/0.57 inference(split_clause,[status(thm)],[f199,f193,f196])).
% 1.68/0.57 fof(f201,plain,(
% 1.68/0.57 spl0_2 <=> relation(sk0_18)),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f203,plain,(
% 1.68/0.57 ~relation(sk0_18)|spl0_2),
% 1.68/0.57 inference(component_clause,[status(thm)],[f201])).
% 1.68/0.57 fof(f209,plain,(
% 1.68/0.57 $false|spl0_2),
% 1.68/0.57 inference(forward_subsumption_resolution,[status(thm)],[f203,f144])).
% 1.68/0.57 fof(f210,plain,(
% 1.68/0.57 spl0_2),
% 1.68/0.57 inference(contradiction_clause,[status(thm)],[f209])).
% 1.68/0.57 fof(f211,plain,(
% 1.68/0.57 $false|spl0_0),
% 1.68/0.57 inference(forward_subsumption_resolution,[status(thm)],[f195,f146])).
% 1.68/0.57 fof(f212,plain,(
% 1.68/0.57 spl0_0),
% 1.68/0.57 inference(contradiction_clause,[status(thm)],[f211])).
% 1.68/0.57 fof(f214,plain,(
% 1.68/0.57 ![X0]: (in(apply(sk0_19,X0),relation_rng(sk0_19))|~in(X0,relation_rng(sk0_18))|~spl0_1)),
% 1.68/0.57 inference(forward_demodulation,[status(thm)],[f150,f197])).
% 1.68/0.57 fof(f216,plain,(
% 1.68/0.57 ![X0]: (~in(X0,relation_rng(sk0_18))|apply(sk0_18,apply(sk0_19,X0))=X0|~spl0_1)),
% 1.68/0.57 inference(backward_subsumption_resolution,[status(thm)],[f189,f214])).
% 1.68/0.57 fof(f219,plain,(
% 1.68/0.57 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_dom(function_inverse(X0))=relation_rng(X0)|~relation(X0)|~function(X0))),
% 1.68/0.57 inference(resolution,[status(thm)],[f178,f61])).
% 1.68/0.57 fof(f220,plain,(
% 1.68/0.57 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_dom(function_inverse(X0))=relation_rng(X0))),
% 1.68/0.57 inference(duplicate_literals_removal,[status(esa)],[f219])).
% 1.68/0.57 fof(f221,plain,(
% 1.68/0.57 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_dom(X0))|X1=apply(function_inverse(X0),apply(X0,X1))|~relation(X0)|~function(X0))),
% 1.68/0.57 inference(resolution,[status(thm)],[f183,f61])).
% 1.68/0.57 fof(f222,plain,(
% 1.68/0.57 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_dom(X0))|X1=apply(function_inverse(X0),apply(X0,X1)))),
% 1.68/0.57 inference(duplicate_literals_removal,[status(esa)],[f221])).
% 1.68/0.57 fof(f223,plain,(
% 1.68/0.57 spl0_4 <=> function(sk0_18)),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f225,plain,(
% 1.68/0.57 ~function(sk0_18)|spl0_4),
% 1.68/0.57 inference(component_clause,[status(thm)],[f223])).
% 1.68/0.57 fof(f226,plain,(
% 1.68/0.57 spl0_5 <=> ~in(X0,relation_dom(sk0_18))|X0=apply(function_inverse(sk0_18),apply(sk0_18,X0))),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f227,plain,(
% 1.68/0.57 ![X0]: (~in(X0,relation_dom(sk0_18))|X0=apply(function_inverse(sk0_18),apply(sk0_18,X0))|~spl0_5)),
% 1.68/0.57 inference(component_clause,[status(thm)],[f226])).
% 1.68/0.57 fof(f229,plain,(
% 1.68/0.57 ![X0]: (~relation(sk0_18)|~function(sk0_18)|~in(X0,relation_dom(sk0_18))|X0=apply(function_inverse(sk0_18),apply(sk0_18,X0)))),
% 1.68/0.57 inference(resolution,[status(thm)],[f222,f148])).
% 1.68/0.57 fof(f230,plain,(
% 1.68/0.57 ~spl0_2|~spl0_4|spl0_5),
% 1.68/0.57 inference(split_clause,[status(thm)],[f229,f201,f223,f226])).
% 1.68/0.57 fof(f234,plain,(
% 1.68/0.57 $false|spl0_4),
% 1.68/0.57 inference(forward_subsumption_resolution,[status(thm)],[f225,f145])).
% 1.68/0.57 fof(f235,plain,(
% 1.68/0.57 spl0_4),
% 1.68/0.57 inference(contradiction_clause,[status(thm)],[f234])).
% 1.68/0.57 fof(f236,plain,(
% 1.68/0.57 ![X0]: (~in(X0,relation_rng(sk0_19))|X0=apply(function_inverse(sk0_18),apply(sk0_18,X0))|~spl0_5)),
% 1.68/0.57 inference(forward_demodulation,[status(thm)],[f149,f227])).
% 1.68/0.57 fof(f253,plain,(
% 1.68/0.57 spl0_10 <=> relation_dom(function_inverse(sk0_18))=relation_rng(sk0_18)),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f254,plain,(
% 1.68/0.57 relation_dom(function_inverse(sk0_18))=relation_rng(sk0_18)|~spl0_10),
% 1.68/0.57 inference(component_clause,[status(thm)],[f253])).
% 1.68/0.57 fof(f256,plain,(
% 1.68/0.57 ~relation(sk0_18)|~function(sk0_18)|relation_dom(function_inverse(sk0_18))=relation_rng(sk0_18)),
% 1.68/0.57 inference(resolution,[status(thm)],[f220,f148])).
% 1.68/0.57 fof(f257,plain,(
% 1.68/0.57 ~spl0_2|~spl0_4|spl0_10),
% 1.68/0.57 inference(split_clause,[status(thm)],[f256,f201,f223,f253])).
% 1.68/0.57 fof(f269,plain,(
% 1.68/0.57 spl0_13 <=> relation(function_inverse(sk0_18))),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f271,plain,(
% 1.68/0.57 ~relation(function_inverse(sk0_18))|spl0_13),
% 1.68/0.57 inference(component_clause,[status(thm)],[f269])).
% 1.68/0.57 fof(f375,plain,(
% 1.68/0.57 spl0_33 <=> function(sk0_19)),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f377,plain,(
% 1.68/0.57 ~function(sk0_19)|spl0_33),
% 1.68/0.57 inference(component_clause,[status(thm)],[f375])).
% 1.68/0.57 fof(f386,plain,(
% 1.68/0.57 $false|spl0_33),
% 1.68/0.57 inference(forward_subsumption_resolution,[status(thm)],[f377,f147])).
% 1.68/0.57 fof(f387,plain,(
% 1.68/0.57 spl0_33),
% 1.68/0.57 inference(contradiction_clause,[status(thm)],[f386])).
% 1.68/0.57 fof(f452,plain,(
% 1.68/0.57 spl0_44 <=> function(function_inverse(sk0_18))),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f453,plain,(
% 1.68/0.57 function(function_inverse(sk0_18))|~spl0_44),
% 1.68/0.57 inference(component_clause,[status(thm)],[f452])).
% 1.68/0.57 fof(f454,plain,(
% 1.68/0.57 ~function(function_inverse(sk0_18))|spl0_44),
% 1.68/0.57 inference(component_clause,[status(thm)],[f452])).
% 1.68/0.57 fof(f466,plain,(
% 1.68/0.57 ~relation(sk0_18)|~function(sk0_18)|spl0_44),
% 1.68/0.57 inference(resolution,[status(thm)],[f454,f61])).
% 1.68/0.57 fof(f467,plain,(
% 1.68/0.57 ~spl0_2|~spl0_4|spl0_44),
% 1.68/0.57 inference(split_clause,[status(thm)],[f466,f201,f223,f452])).
% 1.68/0.57 fof(f468,plain,(
% 1.68/0.57 ~relation(sk0_18)|~function(sk0_18)|spl0_13),
% 1.68/0.57 inference(resolution,[status(thm)],[f271,f60])).
% 1.68/0.57 fof(f469,plain,(
% 1.68/0.57 ~spl0_2|~spl0_4|spl0_13),
% 1.68/0.57 inference(split_clause,[status(thm)],[f468,f201,f223,f269])).
% 1.68/0.57 fof(f1811,plain,(
% 1.68/0.57 spl0_153 <=> ~relation(X0)|~function(X0)|~relation_dom(sk0_19)=relation_dom(X0)|in(sk0_20(X0,sk0_19),relation_rng(sk0_18))|sk0_19=X0),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f1812,plain,(
% 1.68/0.57 ![X0]: (~relation(X0)|~function(X0)|~relation_dom(sk0_19)=relation_dom(X0)|in(sk0_20(X0,sk0_19),relation_rng(sk0_18))|sk0_19=X0|~spl0_153)),
% 1.68/0.57 inference(component_clause,[status(thm)],[f1811])).
% 1.68/0.57 fof(f1814,plain,(
% 1.68/0.57 ![X0]: (~relation(sk0_19)|~function(sk0_19)|~relation(X0)|~function(X0)|~relation_dom(sk0_19)=relation_dom(X0)|in(sk0_20(X0,sk0_19),relation_rng(sk0_18))|sk0_19=X0)),
% 1.68/0.57 inference(paramodulation,[status(thm)],[f150,f164])).
% 1.68/0.57 fof(f1815,plain,(
% 1.68/0.57 ~spl0_0|~spl0_33|spl0_153),
% 1.68/0.57 inference(split_clause,[status(thm)],[f1814,f193,f375,f1811])).
% 1.68/0.57 fof(f1818,plain,(
% 1.68/0.57 ![X0]: (~relation(X0)|~function(X0)|~relation_rng(sk0_18)=relation_dom(X0)|in(sk0_20(X0,sk0_19),relation_rng(sk0_18))|sk0_19=X0|~spl0_153)),
% 1.68/0.57 inference(forward_demodulation,[status(thm)],[f150,f1812])).
% 1.68/0.57 fof(f1971,plain,(
% 1.68/0.57 spl0_175 <=> in(sk0_20(function_inverse(sk0_18),sk0_19),relation_rng(sk0_18))),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f1972,plain,(
% 1.68/0.57 in(sk0_20(function_inverse(sk0_18),sk0_19),relation_rng(sk0_18))|~spl0_175),
% 1.68/0.57 inference(component_clause,[status(thm)],[f1971])).
% 1.68/0.57 fof(f1974,plain,(
% 1.68/0.57 spl0_176 <=> sk0_19=function_inverse(sk0_18)),
% 1.68/0.57 introduced(split_symbol_definition)).
% 1.68/0.57 fof(f1975,plain,(
% 1.68/0.57 sk0_19=function_inverse(sk0_18)|~spl0_176),
% 1.68/0.57 inference(component_clause,[status(thm)],[f1974])).
% 1.68/0.57 fof(f1977,plain,(
% 1.68/0.57 ~relation(function_inverse(sk0_18))|~relation_rng(sk0_18)=relation_dom(function_inverse(sk0_18))|in(sk0_20(function_inverse(sk0_18),sk0_19),relation_rng(sk0_18))|sk0_19=function_inverse(sk0_18)|~spl0_153|~spl0_44),
% 1.68/0.57 inference(resolution,[status(thm)],[f1818,f453])).
% 1.68/0.57 fof(f1978,plain,(
% 1.68/0.57 ~spl0_13|~spl0_10|spl0_175|spl0_176|~spl0_153|~spl0_44),
% 1.68/0.57 inference(split_clause,[status(thm)],[f1977,f269,f253,f1971,f1974,f1811,f452])).
% 1.68/0.57 fof(f2015,plain,(
% 1.68/0.57 in(apply(sk0_19,sk0_20(function_inverse(sk0_18),sk0_19)),relation_rng(sk0_19))|~spl0_175|~spl0_1),
% 1.68/0.57 inference(resolution,[status(thm)],[f1972,f214])).
% 1.68/0.57 fof(f2016,plain,(
% 1.68/0.57 apply(sk0_18,apply(sk0_19,sk0_20(function_inverse(sk0_18),sk0_19)))=sk0_20(function_inverse(sk0_18),sk0_19)|~spl0_175|~spl0_1),
% 1.68/0.57 inference(resolution,[status(thm)],[f1972,f216])).
% 1.68/0.57 fof(f2110,plain,(
% 1.68/0.57 $false|~spl0_176),
% 1.68/0.57 inference(forward_subsumption_resolution,[status(thm)],[f1975,f153])).
% 1.68/0.57 fof(f2111,plain,(
% 1.68/0.57 ~spl0_176),
% 1.68/0.57 inference(contradiction_clause,[status(thm)],[f2110])).
% 1.68/0.57 fof(f2189,plain,(
% 1.68/0.57 apply(sk0_19,sk0_20(function_inverse(sk0_18),sk0_19))=apply(function_inverse(sk0_18),apply(sk0_18,apply(sk0_19,sk0_20(function_inverse(sk0_18),sk0_19))))|~spl0_5|~spl0_175|~spl0_1),
% 1.68/0.58 inference(resolution,[status(thm)],[f236,f2015])).
% 1.68/0.58 fof(f2190,plain,(
% 1.68/0.58 apply(sk0_19,sk0_20(function_inverse(sk0_18),sk0_19))=apply(function_inverse(sk0_18),sk0_20(function_inverse(sk0_18),sk0_19))|~spl0_5|~spl0_175|~spl0_1),
% 1.68/0.58 inference(forward_demodulation,[status(thm)],[f2016,f2189])).
% 1.68/0.58 fof(f2196,plain,(
% 1.68/0.58 spl0_201 <=> relation_dom(sk0_19)=relation_dom(function_inverse(sk0_18))),
% 1.68/0.58 introduced(split_symbol_definition)).
% 1.68/0.58 fof(f2198,plain,(
% 1.68/0.58 ~relation_dom(sk0_19)=relation_dom(function_inverse(sk0_18))|spl0_201),
% 1.68/0.58 inference(component_clause,[status(thm)],[f2196])).
% 1.68/0.58 fof(f2199,plain,(
% 1.68/0.58 ~relation(sk0_19)|~function(sk0_19)|~relation(function_inverse(sk0_18))|~function(function_inverse(sk0_18))|~relation_dom(sk0_19)=relation_dom(function_inverse(sk0_18))|sk0_19=function_inverse(sk0_18)|~spl0_5|~spl0_175|~spl0_1),
% 1.68/0.58 inference(resolution,[status(thm)],[f2190,f165])).
% 1.68/0.58 fof(f2200,plain,(
% 1.68/0.58 ~spl0_0|~spl0_33|~spl0_13|~spl0_44|~spl0_201|spl0_176|~spl0_5|~spl0_175|~spl0_1),
% 1.68/0.58 inference(split_clause,[status(thm)],[f2199,f193,f375,f269,f452,f2196,f1974,f226,f1971,f196])).
% 1.68/0.58 fof(f2206,plain,(
% 1.68/0.58 ~relation_rng(sk0_18)=relation_dom(function_inverse(sk0_18))|spl0_201),
% 1.68/0.58 inference(forward_demodulation,[status(thm)],[f150,f2198])).
% 1.68/0.58 fof(f2207,plain,(
% 1.68/0.58 ~relation_rng(sk0_18)=relation_rng(sk0_18)|~spl0_10|spl0_201),
% 1.68/0.58 inference(forward_demodulation,[status(thm)],[f254,f2206])).
% 1.68/0.58 fof(f2208,plain,(
% 1.68/0.58 $false|~spl0_10|spl0_201),
% 1.68/0.58 inference(trivial_equality_resolution,[status(esa)],[f2207])).
% 1.68/0.58 fof(f2209,plain,(
% 1.68/0.58 ~spl0_10|spl0_201),
% 1.68/0.58 inference(contradiction_clause,[status(thm)],[f2208])).
% 1.68/0.58 fof(f2210,plain,(
% 1.68/0.58 $false),
% 1.68/0.58 inference(sat_refutation,[status(thm)],[f200,f210,f212,f230,f235,f257,f387,f467,f469,f1815,f1978,f2111,f2200,f2209])).
% 1.68/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 1.68/0.58 % Elapsed time: 0.242248 seconds
% 1.68/0.58 % CPU time: 1.788812 seconds
% 1.68/0.58 % Memory used: 83.830 MB
%------------------------------------------------------------------------------