TSTP Solution File: SEU009+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 12:35:41 EDT 2023
% Result : Theorem 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:17:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.19/0.37 % Refutation found
% 0.19/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.37 fof(f4,axiom,(
% 0.19/0.37 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 0.19/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.37 fof(f5,axiom,(
% 0.19/0.37 (! [A] : relation(identity_relation(A)) )),
% 0.19/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.37 fof(f9,axiom,(
% 0.19/0.37 (! [A,B] :( ( relation(A)& function(A)& relation(B)& function(B) )=> ( relation(relation_composition(A,B))& function(relation_composition(A,B)) ) ) )),
% 0.19/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.37 fof(f12,axiom,(
% 0.19/0.37 (! [A] :( relation(identity_relation(A))& function(identity_relation(A)) ) )),
% 0.19/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.37 fof(f27,axiom,(
% 0.19/0.37 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(relation_composition(C,B)))<=> ( in(A,relation_dom(C))& in(apply(C,A),relation_dom(B)) ) ) ) )) )),
% 0.19/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.37 fof(f29,axiom,(
% 0.19/0.37 (! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) )),
% 0.19/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.37 fof(f31,conjecture,(
% 0.19/0.37 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_composition(C,identity_relation(A))))<=> ( in(B,relation_dom(C))& in(apply(C,B),A) ) ) ) )),
% 0.19/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.37 fof(f32,negated_conjecture,(
% 0.19/0.37 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_composition(C,identity_relation(A))))<=> ( in(B,relation_dom(C))& in(apply(C,B),A) ) ) ) ))),
% 0.19/0.37 inference(negated_conjecture,[status(cth)],[f31])).
% 0.19/0.37 fof(f44,plain,(
% 0.19/0.37 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 0.19/0.37 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.19/0.37 fof(f45,plain,(
% 0.19/0.37 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f44])).
% 0.19/0.37 fof(f46,plain,(
% 0.19/0.37 ![X0]: (relation(identity_relation(X0)))),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f5])).
% 0.19/0.37 fof(f55,plain,(
% 0.19/0.37 ![A,B]: ((((~relation(A)|~function(A))|~relation(B))|~function(B))|(relation(relation_composition(A,B))&function(relation_composition(A,B))))),
% 0.19/0.37 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 0.19/0.37 fof(f57,plain,(
% 0.19/0.37 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|function(relation_composition(X0,X1)))),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f55])).
% 0.19/0.37 fof(f60,plain,(
% 0.19/0.37 (![A]: relation(identity_relation(A)))&(![A]: function(identity_relation(A)))),
% 0.19/0.37 inference(miniscoping,[status(esa)],[f12])).
% 0.19/0.37 fof(f62,plain,(
% 0.19/0.37 ![X0]: (function(identity_relation(X0)))),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f60])).
% 0.19/0.37 fof(f100,plain,(
% 0.19/0.37 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(in(A,relation_dom(relation_composition(C,B)))<=>(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B)))))))),
% 0.19/0.37 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 0.19/0.37 fof(f101,plain,(
% 0.19/0.37 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~in(A,relation_dom(relation_composition(C,B)))|(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B))))&(in(A,relation_dom(relation_composition(C,B)))|(~in(A,relation_dom(C))|~in(apply(C,A),relation_dom(B))))))))),
% 0.19/0.37 inference(NNF_transformation,[status(esa)],[f100])).
% 0.19/0.37 fof(f102,plain,(
% 0.19/0.37 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~in(A,relation_dom(relation_composition(C,B)))|(in(A,relation_dom(C))&in(apply(C,A),relation_dom(B)))))&(![A]: (in(A,relation_dom(relation_composition(C,B)))|(~in(A,relation_dom(C))|~in(apply(C,A),relation_dom(B)))))))))),
% 0.19/0.37 inference(miniscoping,[status(esa)],[f101])).
% 0.19/0.37 fof(f103,plain,(
% 0.19/0.37 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~in(X2,relation_dom(relation_composition(X1,X0)))|in(X2,relation_dom(X1)))),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f102])).
% 0.19/0.37 fof(f104,plain,(
% 0.19/0.37 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~in(X2,relation_dom(relation_composition(X1,X0)))|in(apply(X1,X2),relation_dom(X0)))),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f102])).
% 0.19/0.37 fof(f105,plain,(
% 0.19/0.37 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|in(X2,relation_dom(relation_composition(X1,X0)))|~in(X2,relation_dom(X1))|~in(apply(X1,X2),relation_dom(X0)))),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f102])).
% 0.19/0.37 fof(f108,plain,(
% 0.19/0.37 ![A,B]: ((~relation(B)|~function(B))|(B=identity_relation(A)<=>(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))),
% 0.19/0.37 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 0.19/0.37 fof(f109,plain,(
% 0.19/0.37 ![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))))))),
% 0.19/0.37 inference(NNF_transformation,[status(esa)],[f108])).
% 0.19/0.37 fof(f110,plain,(
% 0.19/0.37 ![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)))))))),
% 0.19/0.37 inference(miniscoping,[status(esa)],[f109])).
% 0.19/0.37 fof(f111,plain,(
% 0.19/0.37 ![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(sk0_9(A,B),A)&~apply(B,sk0_9(A,B))=sk0_9(A,B)))))))),
% 0.19/0.37 inference(skolemization,[status(esa)],[f110])).
% 0.19/0.37 fof(f112,plain,(
% 0.19/0.37 ![X0,X1]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|relation_dom(X0)=X1)),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f111])).
% 0.19/0.37 fof(f113,plain,(
% 0.19/0.37 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|~in(X2,X1)|apply(X0,X2)=X2)),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f111])).
% 0.19/0.37 fof(f120,plain,(
% 0.19/0.37 (?[A,B,C]: ((relation(C)&function(C))&(in(B,relation_dom(relation_composition(C,identity_relation(A))))<~>(in(B,relation_dom(C))&in(apply(C,B),A)))))),
% 0.19/0.37 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 0.19/0.37 fof(f121,plain,(
% 0.19/0.37 ?[A,B,C]: ((relation(C)&function(C))&((in(B,relation_dom(relation_composition(C,identity_relation(A))))|(in(B,relation_dom(C))&in(apply(C,B),A)))&(~in(B,relation_dom(relation_composition(C,identity_relation(A))))|(~in(B,relation_dom(C))|~in(apply(C,B),A)))))),
% 0.19/0.37 inference(NNF_transformation,[status(esa)],[f120])).
% 0.19/0.37 fof(f122,plain,(
% 0.19/0.37 ?[C]: ((relation(C)&function(C))&(?[A,B]: ((in(B,relation_dom(relation_composition(C,identity_relation(A))))|(in(B,relation_dom(C))&in(apply(C,B),A)))&(~in(B,relation_dom(relation_composition(C,identity_relation(A))))|(~in(B,relation_dom(C))|~in(apply(C,B),A))))))),
% 0.19/0.37 inference(miniscoping,[status(esa)],[f121])).
% 0.19/0.37 fof(f123,plain,(
% 0.19/0.37 ((relation(sk0_10)&function(sk0_10))&((in(sk0_12,relation_dom(relation_composition(sk0_10,identity_relation(sk0_11))))|(in(sk0_12,relation_dom(sk0_10))&in(apply(sk0_10,sk0_12),sk0_11)))&(~in(sk0_12,relation_dom(relation_composition(sk0_10,identity_relation(sk0_11))))|(~in(sk0_12,relation_dom(sk0_10))|~in(apply(sk0_10,sk0_12),sk0_11)))))),
% 0.19/0.37 inference(skolemization,[status(esa)],[f122])).
% 0.19/0.37 fof(f124,plain,(
% 0.19/0.37 relation(sk0_10)),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f123])).
% 0.19/0.37 fof(f125,plain,(
% 0.19/0.37 function(sk0_10)),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f123])).
% 0.19/0.37 fof(f126,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(relation_composition(sk0_10,identity_relation(sk0_11))))|in(sk0_12,relation_dom(sk0_10))),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f123])).
% 0.19/0.37 fof(f127,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(relation_composition(sk0_10,identity_relation(sk0_11))))|in(apply(sk0_10,sk0_12),sk0_11)),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f123])).
% 0.19/0.37 fof(f128,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(relation_composition(sk0_10,identity_relation(sk0_11))))|~in(sk0_12,relation_dom(sk0_10))|~in(apply(sk0_10,sk0_12),sk0_11)),
% 0.19/0.37 inference(cnf_transformation,[status(esa)],[f123])).
% 0.19/0.37 fof(f143,plain,(
% 0.19/0.37 spl0_0 <=> in(sk0_12,relation_dom(relation_composition(sk0_10,identity_relation(sk0_11))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f144,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(relation_composition(sk0_10,identity_relation(sk0_11))))|~spl0_0),
% 0.19/0.37 inference(component_clause,[status(thm)],[f143])).
% 0.19/0.37 fof(f146,plain,(
% 0.19/0.37 spl0_1 <=> in(sk0_12,relation_dom(sk0_10))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f147,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(sk0_10))|~spl0_1),
% 0.19/0.37 inference(component_clause,[status(thm)],[f146])).
% 0.19/0.37 fof(f149,plain,(
% 0.19/0.37 spl0_0|spl0_1),
% 0.19/0.37 inference(split_clause,[status(thm)],[f126,f143,f146])).
% 0.19/0.37 fof(f150,plain,(
% 0.19/0.37 spl0_2 <=> in(apply(sk0_10,sk0_12),sk0_11)),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f151,plain,(
% 0.19/0.37 in(apply(sk0_10,sk0_12),sk0_11)|~spl0_2),
% 0.19/0.37 inference(component_clause,[status(thm)],[f150])).
% 0.19/0.37 fof(f153,plain,(
% 0.19/0.37 spl0_0|spl0_2),
% 0.19/0.37 inference(split_clause,[status(thm)],[f127,f143,f150])).
% 0.19/0.37 fof(f154,plain,(
% 0.19/0.37 ~spl0_0|~spl0_1|~spl0_2),
% 0.19/0.37 inference(split_clause,[status(thm)],[f128,f143,f146,f150])).
% 0.19/0.37 fof(f155,plain,(
% 0.19/0.37 ![X0]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 0.19/0.37 inference(destructive_equality_resolution,[status(esa)],[f112])).
% 0.19/0.37 fof(f156,plain,(
% 0.19/0.37 ![X0,X1]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 0.19/0.37 inference(destructive_equality_resolution,[status(esa)],[f113])).
% 0.19/0.37 fof(f160,plain,(
% 0.19/0.37 ![X0]: (~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f155,f46])).
% 0.19/0.37 fof(f161,plain,(
% 0.19/0.37 ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 0.19/0.37 inference(resolution,[status(thm)],[f160,f62])).
% 0.19/0.37 fof(f165,plain,(
% 0.19/0.37 spl0_3 <=> relation(identity_relation(sk0_11))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f167,plain,(
% 0.19/0.37 ~relation(identity_relation(sk0_11))|spl0_3),
% 0.19/0.37 inference(component_clause,[status(thm)],[f165])).
% 0.19/0.37 fof(f168,plain,(
% 0.19/0.37 spl0_4 <=> function(identity_relation(sk0_11))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f170,plain,(
% 0.19/0.37 ~function(identity_relation(sk0_11))|spl0_4),
% 0.19/0.37 inference(component_clause,[status(thm)],[f168])).
% 0.19/0.37 fof(f171,plain,(
% 0.19/0.37 spl0_5 <=> relation(sk0_10)),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f173,plain,(
% 0.19/0.37 ~relation(sk0_10)|spl0_5),
% 0.19/0.37 inference(component_clause,[status(thm)],[f171])).
% 0.19/0.37 fof(f174,plain,(
% 0.19/0.37 spl0_6 <=> function(sk0_10)),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f176,plain,(
% 0.19/0.37 ~function(sk0_10)|spl0_6),
% 0.19/0.37 inference(component_clause,[status(thm)],[f174])).
% 0.19/0.37 fof(f177,plain,(
% 0.19/0.37 ~relation(identity_relation(sk0_11))|~function(identity_relation(sk0_11))|~relation(sk0_10)|~function(sk0_10)|in(sk0_12,relation_dom(sk0_10))|~spl0_0),
% 0.19/0.37 inference(resolution,[status(thm)],[f103,f144])).
% 0.19/0.37 fof(f178,plain,(
% 0.19/0.37 ~spl0_3|~spl0_4|~spl0_5|~spl0_6|spl0_1|~spl0_0),
% 0.19/0.37 inference(split_clause,[status(thm)],[f177,f165,f168,f171,f174,f146,f143])).
% 0.19/0.37 fof(f181,plain,(
% 0.19/0.37 ![X0,X1,X2]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|~relation(X1)|~function(X1)|in(X2,relation_dom(relation_composition(X1,identity_relation(X0))))|~in(X2,relation_dom(X1))|~in(apply(X1,X2),X0))),
% 0.19/0.37 inference(paramodulation,[status(thm)],[f161,f105])).
% 0.19/0.37 fof(f182,plain,(
% 0.19/0.37 ![X0,X1,X2]: (~function(identity_relation(X0))|~relation(X1)|~function(X1)|in(X2,relation_dom(relation_composition(X1,identity_relation(X0))))|~in(X2,relation_dom(X1))|~in(apply(X1,X2),X0))),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f181,f46])).
% 0.19/0.37 fof(f183,plain,(
% 0.19/0.37 ![X0,X1]: (~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f156,f46])).
% 0.19/0.37 fof(f184,plain,(
% 0.19/0.37 ![X0,X1]: (~in(X0,X1)|apply(identity_relation(X1),X0)=X0)),
% 0.19/0.37 inference(resolution,[status(thm)],[f183,f62])).
% 0.19/0.37 fof(f187,plain,(
% 0.19/0.37 apply(identity_relation(relation_dom(sk0_10)),sk0_12)=sk0_12|~spl0_1),
% 0.19/0.37 inference(resolution,[status(thm)],[f184,f147])).
% 0.19/0.37 fof(f191,plain,(
% 0.19/0.37 spl0_8 <=> in(apply(sk0_10,sk0_12),relation_dom(identity_relation(sk0_11)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f192,plain,(
% 0.19/0.37 in(apply(sk0_10,sk0_12),relation_dom(identity_relation(sk0_11)))|~spl0_8),
% 0.19/0.37 inference(component_clause,[status(thm)],[f191])).
% 0.19/0.37 fof(f196,plain,(
% 0.19/0.37 spl0_9 <=> ~relation(X0)|~function(X0)|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),X0)))|~in(sk0_12,relation_dom(X0))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f197,plain,(
% 0.19/0.37 ![X0]: (~relation(X0)|~function(X0)|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),X0)))|~in(sk0_12,relation_dom(X0))|~spl0_9)),
% 0.19/0.37 inference(component_clause,[status(thm)],[f196])).
% 0.19/0.37 fof(f199,plain,(
% 0.19/0.37 spl0_10 <=> relation(identity_relation(relation_dom(sk0_10)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f201,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|spl0_10),
% 0.19/0.37 inference(component_clause,[status(thm)],[f199])).
% 0.19/0.37 fof(f202,plain,(
% 0.19/0.37 spl0_11 <=> function(identity_relation(relation_dom(sk0_10)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f204,plain,(
% 0.19/0.37 ~function(identity_relation(relation_dom(sk0_10)))|spl0_11),
% 0.19/0.37 inference(component_clause,[status(thm)],[f202])).
% 0.19/0.37 fof(f205,plain,(
% 0.19/0.37 spl0_12 <=> in(sk0_12,relation_dom(identity_relation(relation_dom(sk0_10))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f207,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(identity_relation(relation_dom(sk0_10))))|spl0_12),
% 0.19/0.37 inference(component_clause,[status(thm)],[f205])).
% 0.19/0.37 fof(f208,plain,(
% 0.19/0.37 ![X0]: (~relation(X0)|~function(X0)|~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),X0)))|~in(sk0_12,relation_dom(identity_relation(relation_dom(sk0_10))))|~in(sk0_12,relation_dom(X0))|~spl0_1)),
% 0.19/0.37 inference(paramodulation,[status(thm)],[f187,f105])).
% 0.19/0.37 fof(f209,plain,(
% 0.19/0.37 spl0_9|~spl0_10|~spl0_11|~spl0_12|~spl0_1),
% 0.19/0.37 inference(split_clause,[status(thm)],[f208,f196,f199,f202,f205,f146])).
% 0.19/0.37 fof(f210,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(sk0_10))|spl0_12),
% 0.19/0.37 inference(forward_demodulation,[status(thm)],[f161,f207])).
% 0.19/0.37 fof(f211,plain,(
% 0.19/0.37 $false|spl0_11),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f204,f62])).
% 0.19/0.37 fof(f212,plain,(
% 0.19/0.37 spl0_11),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f211])).
% 0.19/0.37 fof(f213,plain,(
% 0.19/0.37 $false|spl0_10),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f201,f46])).
% 0.19/0.37 fof(f214,plain,(
% 0.19/0.37 spl0_10),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f213])).
% 0.19/0.37 fof(f216,plain,(
% 0.19/0.37 $false|spl0_6),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f176,f125])).
% 0.19/0.37 fof(f217,plain,(
% 0.19/0.37 spl0_6),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f216])).
% 0.19/0.37 fof(f218,plain,(
% 0.19/0.37 $false|spl0_5),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f173,f124])).
% 0.19/0.37 fof(f219,plain,(
% 0.19/0.37 spl0_5),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f218])).
% 0.19/0.37 fof(f220,plain,(
% 0.19/0.37 $false|spl0_4),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f170,f62])).
% 0.19/0.37 fof(f221,plain,(
% 0.19/0.37 spl0_4),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f220])).
% 0.19/0.37 fof(f222,plain,(
% 0.19/0.37 $false|spl0_3),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f167,f46])).
% 0.19/0.37 fof(f223,plain,(
% 0.19/0.37 spl0_3),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f222])).
% 0.19/0.37 fof(f226,plain,(
% 0.19/0.37 $false|spl0_12|~spl0_1),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f147,f210])).
% 0.19/0.37 fof(f227,plain,(
% 0.19/0.37 spl0_12|~spl0_1),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f226])).
% 0.19/0.37 fof(f231,plain,(
% 0.19/0.37 ~relation(identity_relation(sk0_11))|~function(identity_relation(sk0_11))|~relation(sk0_10)|~function(sk0_10)|in(apply(sk0_10,sk0_12),relation_dom(identity_relation(sk0_11)))|~spl0_0),
% 0.19/0.37 inference(resolution,[status(thm)],[f144,f104])).
% 0.19/0.37 fof(f232,plain,(
% 0.19/0.37 ~spl0_3|~spl0_4|~spl0_5|~spl0_6|spl0_8|~spl0_0),
% 0.19/0.37 inference(split_clause,[status(thm)],[f231,f165,f168,f171,f174,f191,f143])).
% 0.19/0.37 fof(f241,plain,(
% 0.19/0.37 spl0_13 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f242,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))|~spl0_13),
% 0.19/0.37 inference(component_clause,[status(thm)],[f241])).
% 0.19/0.37 fof(f244,plain,(
% 0.19/0.37 ~relation(sk0_10)|~function(sk0_10)|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))|~spl0_9|~spl0_1),
% 0.19/0.37 inference(resolution,[status(thm)],[f197,f147])).
% 0.19/0.37 fof(f245,plain,(
% 0.19/0.37 ~spl0_5|~spl0_6|spl0_13|~spl0_9|~spl0_1),
% 0.19/0.37 inference(split_clause,[status(thm)],[f244,f171,f174,f241,f196,f146])).
% 0.19/0.37 fof(f246,plain,(
% 0.19/0.37 ![X0]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(X0))))|~in(sk0_12,X0)|~spl0_9)),
% 0.19/0.37 inference(paramodulation,[status(thm)],[f161,f197])).
% 0.19/0.37 fof(f247,plain,(
% 0.19/0.37 ![X0]: (~function(identity_relation(X0))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(X0))))|~in(sk0_12,X0)|~spl0_9)),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f246,f46])).
% 0.19/0.37 fof(f248,plain,(
% 0.19/0.37 spl0_14 <=> relation(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f250,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|spl0_14),
% 0.19/0.37 inference(component_clause,[status(thm)],[f248])).
% 0.19/0.37 fof(f251,plain,(
% 0.19/0.37 spl0_15 <=> function(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f253,plain,(
% 0.19/0.37 ~function(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|spl0_15),
% 0.19/0.37 inference(component_clause,[status(thm)],[f251])).
% 0.19/0.37 fof(f254,plain,(
% 0.19/0.37 spl0_16 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f255,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|~spl0_16),
% 0.19/0.37 inference(component_clause,[status(thm)],[f254])).
% 0.19/0.37 fof(f257,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|~spl0_13|~spl0_9),
% 0.19/0.37 inference(resolution,[status(thm)],[f242,f197])).
% 0.19/0.37 fof(f258,plain,(
% 0.19/0.37 ~spl0_14|~spl0_15|spl0_16|~spl0_13|~spl0_9),
% 0.19/0.37 inference(split_clause,[status(thm)],[f257,f248,f251,f254,f241,f196])).
% 0.19/0.37 fof(f259,plain,(
% 0.19/0.37 spl0_17 <=> in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(sk0_10))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f262,plain,(
% 0.19/0.37 ~relation(sk0_10)|~function(sk0_10)|~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(sk0_10))|~spl0_13),
% 0.19/0.37 inference(resolution,[status(thm)],[f242,f104])).
% 0.19/0.37 fof(f263,plain,(
% 0.19/0.37 ~spl0_5|~spl0_6|~spl0_10|~spl0_11|spl0_17|~spl0_13),
% 0.19/0.37 inference(split_clause,[status(thm)],[f262,f171,f174,f199,f202,f259,f241])).
% 0.19/0.37 fof(f266,plain,(
% 0.19/0.37 apply(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))),sk0_12)=sk0_12|~spl0_13),
% 0.19/0.37 inference(resolution,[status(thm)],[f242,f184])).
% 0.19/0.37 fof(f269,plain,(
% 0.19/0.37 in(apply(sk0_10,sk0_12),sk0_11)|~spl0_8),
% 0.19/0.37 inference(forward_demodulation,[status(thm)],[f161,f192])).
% 0.19/0.37 fof(f270,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|~relation(sk0_10)|~function(sk0_10)|spl0_15),
% 0.19/0.37 inference(resolution,[status(thm)],[f253,f57])).
% 0.19/0.37 fof(f271,plain,(
% 0.19/0.37 ~spl0_10|~spl0_11|~spl0_5|~spl0_6|spl0_15),
% 0.19/0.37 inference(split_clause,[status(thm)],[f270,f199,f202,f171,f174,f251])).
% 0.19/0.37 fof(f283,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~relation(sk0_10)|spl0_14),
% 0.19/0.37 inference(resolution,[status(thm)],[f250,f45])).
% 0.19/0.37 fof(f284,plain,(
% 0.19/0.37 ~spl0_10|~spl0_5|spl0_14),
% 0.19/0.37 inference(split_clause,[status(thm)],[f283,f199,f171,f248])).
% 0.19/0.37 fof(f285,plain,(
% 0.19/0.37 spl0_20 <=> relation(relation_composition(sk0_10,identity_relation(sk0_11)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f287,plain,(
% 0.19/0.37 ~relation(relation_composition(sk0_10,identity_relation(sk0_11)))|spl0_20),
% 0.19/0.37 inference(component_clause,[status(thm)],[f285])).
% 0.19/0.37 fof(f288,plain,(
% 0.19/0.37 spl0_21 <=> function(relation_composition(sk0_10,identity_relation(sk0_11)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f290,plain,(
% 0.19/0.37 ~function(relation_composition(sk0_10,identity_relation(sk0_11)))|spl0_21),
% 0.19/0.37 inference(component_clause,[status(thm)],[f288])).
% 0.19/0.37 fof(f305,plain,(
% 0.19/0.37 spl0_24 <=> relation(identity_relation(relation_dom(relation_composition(sk0_10,identity_relation(sk0_11)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f307,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(relation_composition(sk0_10,identity_relation(sk0_11)))))|spl0_24),
% 0.19/0.37 inference(component_clause,[status(thm)],[f305])).
% 0.19/0.37 fof(f308,plain,(
% 0.19/0.37 spl0_25 <=> function(identity_relation(relation_dom(relation_composition(sk0_10,identity_relation(sk0_11)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f310,plain,(
% 0.19/0.37 ~function(identity_relation(relation_dom(relation_composition(sk0_10,identity_relation(sk0_11)))))|spl0_25),
% 0.19/0.37 inference(component_clause,[status(thm)],[f308])).
% 0.19/0.37 fof(f319,plain,(
% 0.19/0.37 $false|spl0_25),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f310,f62])).
% 0.19/0.37 fof(f320,plain,(
% 0.19/0.37 spl0_25),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f319])).
% 0.19/0.37 fof(f321,plain,(
% 0.19/0.37 $false|spl0_24),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f307,f46])).
% 0.19/0.37 fof(f322,plain,(
% 0.19/0.37 spl0_24),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f321])).
% 0.19/0.37 fof(f323,plain,(
% 0.19/0.37 ~relation(sk0_10)|~function(sk0_10)|~relation(identity_relation(sk0_11))|~function(identity_relation(sk0_11))|spl0_21),
% 0.19/0.37 inference(resolution,[status(thm)],[f290,f57])).
% 0.19/0.37 fof(f324,plain,(
% 0.19/0.37 ~spl0_5|~spl0_6|~spl0_3|~spl0_4|spl0_21),
% 0.19/0.37 inference(split_clause,[status(thm)],[f323,f171,f174,f165,f168,f288])).
% 0.19/0.37 fof(f333,plain,(
% 0.19/0.37 ~relation(sk0_10)|~relation(identity_relation(sk0_11))|spl0_20),
% 0.19/0.37 inference(resolution,[status(thm)],[f287,f45])).
% 0.19/0.37 fof(f334,plain,(
% 0.19/0.37 ~spl0_5|~spl0_3|spl0_20),
% 0.19/0.37 inference(split_clause,[status(thm)],[f333,f171,f165,f285])).
% 0.19/0.37 fof(f339,plain,(
% 0.19/0.37 spl0_28 <=> ~relation(X0)|~function(X0)|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))),X0)))|~in(sk0_12,relation_dom(X0))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f342,plain,(
% 0.19/0.37 spl0_29 <=> relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f344,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|spl0_29),
% 0.19/0.37 inference(component_clause,[status(thm)],[f342])).
% 0.19/0.37 fof(f345,plain,(
% 0.19/0.37 spl0_30 <=> function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f347,plain,(
% 0.19/0.37 ~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|spl0_30),
% 0.19/0.37 inference(component_clause,[status(thm)],[f345])).
% 0.19/0.37 fof(f348,plain,(
% 0.19/0.37 spl0_31 <=> in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f350,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|spl0_31),
% 0.19/0.37 inference(component_clause,[status(thm)],[f348])).
% 0.19/0.37 fof(f351,plain,(
% 0.19/0.37 ![X0]: (~relation(X0)|~function(X0)|~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))),X0)))|~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|~in(sk0_12,relation_dom(X0))|~spl0_13)),
% 0.19/0.37 inference(paramodulation,[status(thm)],[f266,f105])).
% 0.19/0.37 fof(f352,plain,(
% 0.19/0.37 spl0_28|~spl0_29|~spl0_30|~spl0_31|~spl0_13),
% 0.19/0.37 inference(split_clause,[status(thm)],[f351,f339,f342,f345,f348,f241])).
% 0.19/0.37 fof(f353,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))|spl0_31),
% 0.19/0.37 inference(forward_demodulation,[status(thm)],[f161,f350])).
% 0.19/0.37 fof(f354,plain,(
% 0.19/0.37 $false|~spl0_13|spl0_31),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f353,f242])).
% 0.19/0.37 fof(f355,plain,(
% 0.19/0.37 ~spl0_13|spl0_31),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f354])).
% 0.19/0.37 fof(f356,plain,(
% 0.19/0.37 $false|spl0_30),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f347,f62])).
% 0.19/0.37 fof(f357,plain,(
% 0.19/0.37 spl0_30),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f356])).
% 0.19/0.37 fof(f358,plain,(
% 0.19/0.37 $false|spl0_29),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f344,f46])).
% 0.19/0.37 fof(f359,plain,(
% 0.19/0.37 spl0_29),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f358])).
% 0.19/0.37 fof(f360,plain,(
% 0.19/0.37 spl0_32 <=> relation(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f362,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))|spl0_32),
% 0.19/0.37 inference(component_clause,[status(thm)],[f360])).
% 0.19/0.37 fof(f363,plain,(
% 0.19/0.37 spl0_33 <=> function(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f365,plain,(
% 0.19/0.37 ~function(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))|spl0_33),
% 0.19/0.37 inference(component_clause,[status(thm)],[f363])).
% 0.19/0.37 fof(f366,plain,(
% 0.19/0.37 spl0_34 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f369,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|~spl0_16|~spl0_9),
% 0.19/0.37 inference(resolution,[status(thm)],[f255,f197])).
% 0.19/0.37 fof(f370,plain,(
% 0.19/0.37 ~spl0_32|~spl0_33|spl0_34|~spl0_16|~spl0_9),
% 0.19/0.37 inference(split_clause,[status(thm)],[f369,f360,f363,f366,f254,f196])).
% 0.19/0.37 fof(f371,plain,(
% 0.19/0.37 spl0_35 <=> in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f374,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))|~spl0_16),
% 0.19/0.37 inference(resolution,[status(thm)],[f255,f104])).
% 0.19/0.37 fof(f375,plain,(
% 0.19/0.37 ~spl0_14|~spl0_15|~spl0_10|~spl0_11|spl0_35|~spl0_16),
% 0.19/0.37 inference(split_clause,[status(thm)],[f374,f248,f251,f199,f202,f371,f254])).
% 0.19/0.37 fof(f378,plain,(
% 0.19/0.37 apply(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),sk0_12)=sk0_12|~spl0_16),
% 0.19/0.37 inference(resolution,[status(thm)],[f255,f184])).
% 0.19/0.37 fof(f380,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|~relation(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|spl0_33),
% 0.19/0.37 inference(resolution,[status(thm)],[f365,f57])).
% 0.19/0.37 fof(f381,plain,(
% 0.19/0.37 ~spl0_10|~spl0_11|~spl0_14|~spl0_15|spl0_33),
% 0.19/0.37 inference(split_clause,[status(thm)],[f380,f199,f202,f248,f251,f363])).
% 0.19/0.37 fof(f390,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~relation(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))|spl0_32),
% 0.19/0.37 inference(resolution,[status(thm)],[f362,f45])).
% 0.19/0.37 fof(f391,plain,(
% 0.19/0.37 ~spl0_10|~spl0_14|spl0_32),
% 0.19/0.37 inference(split_clause,[status(thm)],[f390,f199,f248,f360])).
% 0.19/0.37 fof(f392,plain,(
% 0.19/0.37 ![X0]: (in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(X0))))|~in(sk0_12,X0)|~spl0_9)),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f247,f62])).
% 0.19/0.37 fof(f394,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))))|~spl0_9|~spl0_13),
% 0.19/0.37 inference(resolution,[status(thm)],[f392,f242])).
% 0.19/0.37 fof(f395,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))|~spl0_9|~spl0_1),
% 0.19/0.37 inference(resolution,[status(thm)],[f392,f147])).
% 0.19/0.37 fof(f396,plain,(
% 0.19/0.37 spl0_37 <=> relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f398,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|spl0_37),
% 0.19/0.37 inference(component_clause,[status(thm)],[f396])).
% 0.19/0.37 fof(f399,plain,(
% 0.19/0.37 spl0_38 <=> function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f401,plain,(
% 0.19/0.37 ~function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|spl0_38),
% 0.19/0.37 inference(component_clause,[status(thm)],[f399])).
% 0.19/0.37 fof(f402,plain,(
% 0.19/0.37 spl0_39 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f403,plain,(
% 0.19/0.37 in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))|~spl0_39),
% 0.19/0.37 inference(component_clause,[status(thm)],[f402])).
% 0.19/0.37 fof(f405,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))|~spl0_1|~spl0_9),
% 0.19/0.37 inference(resolution,[status(thm)],[f395,f197])).
% 0.19/0.37 fof(f406,plain,(
% 0.19/0.37 ~spl0_37|~spl0_38|spl0_39|~spl0_1|~spl0_9),
% 0.19/0.37 inference(split_clause,[status(thm)],[f405,f396,f399,f402,f146,f196])).
% 0.19/0.37 fof(f408,plain,(
% 0.19/0.37 spl0_40 <=> in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(identity_relation(relation_dom(sk0_10))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f411,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(identity_relation(relation_dom(sk0_10))))|~spl0_9|~spl0_1),
% 0.19/0.37 inference(resolution,[status(thm)],[f395,f104])).
% 0.19/0.37 fof(f412,plain,(
% 0.19/0.37 ~spl0_10|~spl0_11|spl0_40|~spl0_9|~spl0_1),
% 0.19/0.37 inference(split_clause,[status(thm)],[f411,f199,f202,f408,f196,f146])).
% 0.19/0.37 fof(f415,plain,(
% 0.19/0.37 apply(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))),sk0_12)=sk0_12|~spl0_9|~spl0_1),
% 0.19/0.37 inference(resolution,[status(thm)],[f395,f184])).
% 0.19/0.37 fof(f419,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|spl0_38),
% 0.19/0.37 inference(resolution,[status(thm)],[f401,f57])).
% 0.19/0.37 fof(f420,plain,(
% 0.19/0.37 ~spl0_10|~spl0_11|spl0_38),
% 0.19/0.37 inference(split_clause,[status(thm)],[f419,f199,f202,f399])).
% 0.19/0.37 fof(f426,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~relation(identity_relation(relation_dom(sk0_10)))|spl0_37),
% 0.19/0.37 inference(resolution,[status(thm)],[f398,f45])).
% 0.19/0.37 fof(f427,plain,(
% 0.19/0.37 ~spl0_10|spl0_37),
% 0.19/0.37 inference(split_clause,[status(thm)],[f426,f199,f396])).
% 0.19/0.37 fof(f428,plain,(
% 0.19/0.37 spl0_41 <=> ~relation(X0)|~function(X0)|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))),X0)))|~in(sk0_12,relation_dom(X0))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f431,plain,(
% 0.19/0.37 spl0_42 <=> relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f433,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))|spl0_42),
% 0.19/0.37 inference(component_clause,[status(thm)],[f431])).
% 0.19/0.37 fof(f434,plain,(
% 0.19/0.37 spl0_43 <=> function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f436,plain,(
% 0.19/0.37 ~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))|spl0_43),
% 0.19/0.37 inference(component_clause,[status(thm)],[f434])).
% 0.19/0.37 fof(f437,plain,(
% 0.19/0.37 spl0_44 <=> in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f439,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))))|spl0_44),
% 0.19/0.37 inference(component_clause,[status(thm)],[f437])).
% 0.19/0.37 fof(f440,plain,(
% 0.19/0.37 ![X0]: (~relation(X0)|~function(X0)|~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))|~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))),X0)))|~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))))|~in(sk0_12,relation_dom(X0))|~spl0_9|~spl0_1)),
% 0.19/0.37 inference(paramodulation,[status(thm)],[f415,f105])).
% 0.19/0.37 fof(f441,plain,(
% 0.19/0.37 spl0_41|~spl0_42|~spl0_43|~spl0_44|~spl0_9|~spl0_1),
% 0.19/0.37 inference(split_clause,[status(thm)],[f440,f428,f431,f434,f437,f196,f146])).
% 0.19/0.37 fof(f442,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))|spl0_44),
% 0.19/0.37 inference(forward_demodulation,[status(thm)],[f161,f439])).
% 0.19/0.37 fof(f443,plain,(
% 0.19/0.37 $false|~spl0_9|~spl0_1|spl0_44),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f442,f395])).
% 0.19/0.37 fof(f444,plain,(
% 0.19/0.37 ~spl0_9|~spl0_1|spl0_44),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f443])).
% 0.19/0.37 fof(f445,plain,(
% 0.19/0.37 $false|spl0_43),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f436,f62])).
% 0.19/0.37 fof(f446,plain,(
% 0.19/0.37 spl0_43),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f445])).
% 0.19/0.37 fof(f447,plain,(
% 0.19/0.37 $false|spl0_42),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f433,f46])).
% 0.19/0.37 fof(f448,plain,(
% 0.19/0.37 spl0_42),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f447])).
% 0.19/0.37 fof(f449,plain,(
% 0.19/0.37 spl0_45 <=> ~relation(X0)|~function(X0)|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),X0)))|~in(sk0_12,relation_dom(X0))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f452,plain,(
% 0.19/0.37 spl0_46 <=> relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f454,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|spl0_46),
% 0.19/0.37 inference(component_clause,[status(thm)],[f452])).
% 0.19/0.37 fof(f455,plain,(
% 0.19/0.37 spl0_47 <=> function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f457,plain,(
% 0.19/0.37 ~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|spl0_47),
% 0.19/0.37 inference(component_clause,[status(thm)],[f455])).
% 0.19/0.37 fof(f458,plain,(
% 0.19/0.37 spl0_48 <=> in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f460,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))))|spl0_48),
% 0.19/0.37 inference(component_clause,[status(thm)],[f458])).
% 0.19/0.37 fof(f461,plain,(
% 0.19/0.37 ![X0]: (~relation(X0)|~function(X0)|~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),X0)))|~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))))|~in(sk0_12,relation_dom(X0))|~spl0_16)),
% 0.19/0.37 inference(paramodulation,[status(thm)],[f378,f105])).
% 0.19/0.37 fof(f462,plain,(
% 0.19/0.37 spl0_45|~spl0_46|~spl0_47|~spl0_48|~spl0_16),
% 0.19/0.37 inference(split_clause,[status(thm)],[f461,f449,f452,f455,f458,f254])).
% 0.19/0.37 fof(f463,plain,(
% 0.19/0.37 ~in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|spl0_48),
% 0.19/0.37 inference(forward_demodulation,[status(thm)],[f161,f460])).
% 0.19/0.37 fof(f464,plain,(
% 0.19/0.37 $false|~spl0_16|spl0_48),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f463,f255])).
% 0.19/0.37 fof(f465,plain,(
% 0.19/0.37 ~spl0_16|spl0_48),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f464])).
% 0.19/0.37 fof(f466,plain,(
% 0.19/0.37 $false|spl0_47),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f457,f62])).
% 0.19/0.37 fof(f467,plain,(
% 0.19/0.37 spl0_47),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f466])).
% 0.19/0.37 fof(f468,plain,(
% 0.19/0.37 $false|spl0_46),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f454,f46])).
% 0.19/0.37 fof(f469,plain,(
% 0.19/0.37 spl0_46),
% 0.19/0.37 inference(contradiction_clause,[status(thm)],[f468])).
% 0.19/0.37 fof(f470,plain,(
% 0.19/0.37 spl0_49 <=> relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f472,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|spl0_49),
% 0.19/0.37 inference(component_clause,[status(thm)],[f470])).
% 0.19/0.37 fof(f473,plain,(
% 0.19/0.37 spl0_50 <=> function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f475,plain,(
% 0.19/0.37 ~function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|spl0_50),
% 0.19/0.37 inference(component_clause,[status(thm)],[f473])).
% 0.19/0.37 fof(f476,plain,(
% 0.19/0.37 spl0_51 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f479,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))))|~spl0_13|~spl0_9),
% 0.19/0.37 inference(resolution,[status(thm)],[f394,f197])).
% 0.19/0.37 fof(f480,plain,(
% 0.19/0.37 ~spl0_49|~spl0_50|spl0_51|~spl0_13|~spl0_9),
% 0.19/0.37 inference(split_clause,[status(thm)],[f479,f470,f473,f476,f241,f196])).
% 0.19/0.37 fof(f482,plain,(
% 0.19/0.37 spl0_52 <=> in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f485,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|~spl0_9|~spl0_13),
% 0.19/0.37 inference(resolution,[status(thm)],[f394,f104])).
% 0.19/0.37 fof(f486,plain,(
% 0.19/0.37 ~spl0_29|~spl0_30|~spl0_10|~spl0_11|spl0_52|~spl0_9|~spl0_13),
% 0.19/0.37 inference(split_clause,[status(thm)],[f485,f342,f345,f199,f202,f482,f196,f241])).
% 0.19/0.37 fof(f492,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|spl0_50),
% 0.19/0.37 inference(resolution,[status(thm)],[f475,f57])).
% 0.19/0.37 fof(f493,plain,(
% 0.19/0.37 ~spl0_10|~spl0_11|~spl0_29|~spl0_30|spl0_50),
% 0.19/0.37 inference(split_clause,[status(thm)],[f492,f199,f202,f342,f345,f473])).
% 0.19/0.37 fof(f502,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|spl0_49),
% 0.19/0.37 inference(resolution,[status(thm)],[f472,f45])).
% 0.19/0.37 fof(f503,plain,(
% 0.19/0.37 ~spl0_10|~spl0_29|spl0_49),
% 0.19/0.37 inference(split_clause,[status(thm)],[f502,f199,f342,f470])).
% 0.19/0.37 fof(f504,plain,(
% 0.19/0.37 spl0_54 <=> relation(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f506,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))|spl0_54),
% 0.19/0.37 inference(component_clause,[status(thm)],[f504])).
% 0.19/0.37 fof(f507,plain,(
% 0.19/0.37 spl0_55 <=> function(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f509,plain,(
% 0.19/0.37 ~function(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))|spl0_55),
% 0.19/0.37 inference(component_clause,[status(thm)],[f507])).
% 0.19/0.37 fof(f510,plain,(
% 0.19/0.37 spl0_56 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f513,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))))|~spl0_39|~spl0_9),
% 0.19/0.37 inference(resolution,[status(thm)],[f403,f197])).
% 0.19/0.37 fof(f514,plain,(
% 0.19/0.37 ~spl0_54|~spl0_55|spl0_56|~spl0_39|~spl0_9),
% 0.19/0.37 inference(split_clause,[status(thm)],[f513,f504,f507,f510,f402,f196])).
% 0.19/0.37 fof(f516,plain,(
% 0.19/0.37 spl0_57 <=> in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f519,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|in(apply(identity_relation(relation_dom(sk0_10)),sk0_12),relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))|~spl0_39),
% 0.19/0.37 inference(resolution,[status(thm)],[f403,f104])).
% 0.19/0.37 fof(f520,plain,(
% 0.19/0.37 ~spl0_37|~spl0_38|~spl0_10|~spl0_11|spl0_57|~spl0_39),
% 0.19/0.37 inference(split_clause,[status(thm)],[f519,f396,f399,f199,f202,f516,f402])).
% 0.19/0.37 fof(f521,plain,(
% 0.19/0.37 ~relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|in(sk0_12,relation_dom(identity_relation(relation_dom(sk0_10))))|~spl0_39),
% 0.19/0.37 inference(resolution,[status(thm)],[f403,f103])).
% 0.19/0.37 fof(f522,plain,(
% 0.19/0.37 ~spl0_37|~spl0_38|~spl0_10|~spl0_11|spl0_12|~spl0_39),
% 0.19/0.37 inference(split_clause,[status(thm)],[f521,f396,f399,f199,f202,f205,f402])).
% 0.19/0.37 fof(f525,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|~relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|~function(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|spl0_55),
% 0.19/0.37 inference(resolution,[status(thm)],[f509,f57])).
% 0.19/0.37 fof(f526,plain,(
% 0.19/0.37 ~spl0_10|~spl0_11|~spl0_37|~spl0_38|spl0_55),
% 0.19/0.37 inference(split_clause,[status(thm)],[f525,f199,f202,f396,f399,f507])).
% 0.19/0.37 fof(f535,plain,(
% 0.19/0.37 ~relation(identity_relation(relation_dom(sk0_10)))|~relation(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))|spl0_54),
% 0.19/0.37 inference(resolution,[status(thm)],[f506,f45])).
% 0.19/0.37 fof(f536,plain,(
% 0.19/0.37 ~spl0_10|~spl0_37|spl0_54),
% 0.19/0.37 inference(split_clause,[status(thm)],[f535,f199,f396,f504])).
% 0.19/0.37 fof(f537,plain,(
% 0.19/0.37 ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_dom(relation_composition(X0,identity_relation(X2))))|~in(X1,relation_dom(X0))|~in(apply(X0,X1),X2))),
% 0.19/0.37 inference(forward_subsumption_resolution,[status(thm)],[f182,f62])).
% 0.19/0.37 fof(f538,plain,(
% 0.19/0.37 ~relation(sk0_10)|~function(sk0_10)|in(sk0_12,relation_dom(relation_composition(sk0_10,identity_relation(sk0_11))))|~in(sk0_12,relation_dom(sk0_10))|~spl0_2),
% 0.19/0.37 inference(resolution,[status(thm)],[f537,f151])).
% 0.19/0.37 fof(f539,plain,(
% 0.19/0.37 ~spl0_5|~spl0_6|spl0_0|~spl0_1|~spl0_2),
% 0.19/0.37 inference(split_clause,[status(thm)],[f538,f171,f174,f143,f146,f150])).
% 0.19/0.37 fof(f545,plain,(
% 0.19/0.37 spl0_60 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),identity_relation(X0))))|~in(sk0_12,X0)),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f548,plain,(
% 0.19/0.37 ![X0]: (~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))),identity_relation(X0))))|~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))))|~in(sk0_12,X0)|~spl0_16)),
% 0.19/0.37 inference(paramodulation,[status(thm)],[f378,f537])).
% 0.19/0.37 fof(f549,plain,(
% 0.19/0.37 ~spl0_46|~spl0_47|spl0_60|~spl0_48|~spl0_16),
% 0.19/0.37 inference(split_clause,[status(thm)],[f548,f452,f455,f545,f458,f254])).
% 0.19/0.37 fof(f550,plain,(
% 0.19/0.37 spl0_61 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))),identity_relation(X0))))|~in(sk0_12,X0)),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.37 fof(f553,plain,(
% 0.19/0.37 ![X0]: (~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))|~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10))))),identity_relation(X0))))|~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(relation_dom(sk0_10)))))))|~in(sk0_12,X0)|~spl0_9|~spl0_1)),
% 0.19/0.37 inference(paramodulation,[status(thm)],[f415,f537])).
% 0.19/0.37 fof(f554,plain,(
% 0.19/0.37 ~spl0_42|~spl0_43|spl0_61|~spl0_44|~spl0_9|~spl0_1),
% 0.19/0.37 inference(split_clause,[status(thm)],[f553,f431,f434,f550,f437,f196,f146])).
% 0.19/0.37 fof(f555,plain,(
% 0.19/0.37 spl0_62 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))),identity_relation(X0))))|~in(sk0_12,X0)),
% 0.19/0.37 introduced(split_symbol_definition)).
% 0.19/0.38 fof(f558,plain,(
% 0.19/0.38 ![X0]: (~relation(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|~function(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10))),identity_relation(X0))))|~in(sk0_12,relation_dom(identity_relation(relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),sk0_10)))))|~in(sk0_12,X0)|~spl0_13)),
% 0.19/0.38 inference(paramodulation,[status(thm)],[f266,f537])).
% 0.19/0.38 fof(f559,plain,(
% 0.19/0.38 ~spl0_29|~spl0_30|spl0_62|~spl0_31|~spl0_13),
% 0.19/0.38 inference(split_clause,[status(thm)],[f558,f342,f345,f555,f348,f241])).
% 0.19/0.38 fof(f560,plain,(
% 0.19/0.38 spl0_63 <=> in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(X0))))|~in(sk0_12,X0)),
% 0.19/0.38 introduced(split_symbol_definition)).
% 0.19/0.38 fof(f563,plain,(
% 0.19/0.38 ![X0]: (~relation(identity_relation(relation_dom(sk0_10)))|~function(identity_relation(relation_dom(sk0_10)))|in(sk0_12,relation_dom(relation_composition(identity_relation(relation_dom(sk0_10)),identity_relation(X0))))|~in(sk0_12,relation_dom(identity_relation(relation_dom(sk0_10))))|~in(sk0_12,X0)|~spl0_1)),
% 0.19/0.38 inference(paramodulation,[status(thm)],[f187,f537])).
% 0.19/0.38 fof(f564,plain,(
% 0.19/0.38 ~spl0_10|~spl0_11|spl0_63|~spl0_12|~spl0_1),
% 0.19/0.38 inference(split_clause,[status(thm)],[f563,f199,f202,f560,f205,f146])).
% 0.19/0.38 fof(f565,plain,(
% 0.19/0.38 spl0_2|~spl0_8),
% 0.19/0.38 inference(split_clause,[status(thm)],[f269,f150,f191])).
% 0.19/0.38 fof(f567,plain,(
% 0.19/0.38 $false),
% 0.19/0.38 inference(sat_refutation,[status(thm)],[f149,f153,f154,f178,f209,f212,f214,f217,f219,f221,f223,f227,f232,f245,f258,f263,f271,f284,f320,f322,f324,f334,f352,f355,f357,f359,f370,f375,f381,f391,f406,f412,f420,f427,f441,f444,f446,f448,f462,f465,f467,f469,f480,f486,f493,f503,f514,f520,f522,f526,f536,f539,f549,f554,f559,f564,f565])).
% 0.19/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.37/0.59 % Elapsed time: 0.033430 seconds
% 0.37/0.59 % CPU time: 0.138886 seconds
% 0.37/0.59 % Memory used: 16.185 MB
%------------------------------------------------------------------------------