PREFIX log: <http://www.w3.org/2000/10/swap/log#>
PREFIX owl: <http://www.w3.org/2002/07/owl#>
PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#>
PREFIX : <http://www.agfa.com/w3c/euler/graph.axiom#>
PREFIX math: <http://www.w3.org/2000/10/swap/math#>
PREFIX list: <http://www.w3.org/2000/10/swap/list#>
PREFIX xsd: <http://www.w3.org/2001/XMLSchema#>
PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
PREFIX ns1: <http://eulersharp.sourceforge.net/2003/03swap/rpo-rules#>
PREFIX r: <http://www.w3.org/2000/10/swap/reason#>

[] a r:Proof, r:Conjunction;
  r:component <#lemma1>;
  r:gives {
    :paris :path :nantes.
  }.

<#lemma1> a r:Inference;
  r:gives {
    :paris :path :nantes.
  };
  r:evidence (
    <#lemma2>
  );
  r:rule <#lemma3>.

<#lemma2> a r:Inference;
  r:gives {
    :paris :path :nantes.
  };
  r:evidence (
    <#lemma4>
    <#lemma5>
    <#lemma6>
  );
  r:rule <#lemma7>.

<#lemma3> a r:Extraction;
  r:gives {
    {:paris :path :nantes} => {:paris :path :nantes}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/graph.filter.n3>].

<#lemma4> a r:Extraction;
  r:gives {
    :path a owl:TransitiveProperty.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/graph.axiom.n3>].

<#lemma5> a r:Inference;
  r:gives {
    :angers :path :nantes.
  };
  r:evidence (
    <#lemma8>
    <#lemma9>
  );
  r:rule <#lemma10>.

<#lemma6> a r:Inference;
  r:gives {
    :paris :path :angers.
  };
  r:evidence (
    <#lemma4>
    <#lemma11>
    <#lemma12>
  );
  r:rule <#lemma7>.

<#lemma7> a r:Extraction;
  r:gives {
    {?x_0_2 a owl:TransitiveProperty.
     ?x_1_2 ?x_0_2 ?x_2_2.
     ?x_3_2 ?x_0_2 ?x_1_2} => {?x_3_2 ?x_0_2 ?x_2_2}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/rpo-rules.n3>].

<#lemma8> a r:Extraction;
  r:gives {
    :oneway rdfs:subPropertyOf :path.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/graph.axiom.n3>].

<#lemma9> a r:Extraction;
  r:gives {
    :angers :oneway :nantes.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/graph.axiom.n3>].

<#lemma10> a r:Extraction;
  r:gives {
    {?x_0_3 rdfs:subPropertyOf ?x_1_3.
     ?x_2_3 ?x_0_3 ?x_3_3} => {?x_2_3 ?x_1_3 ?x_3_3}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/rpo-rules.n3>].

<#lemma11> a r:Inference;
  r:gives {
    :lemans :path :angers.
  };
  r:evidence (
    <#lemma8>
    <#lemma13>
  );
  r:rule <#lemma10>.

<#lemma12> a r:Inference;
  r:gives {
    :paris :path :lemans.
  };
  r:evidence (
    <#lemma4>
    <#lemma14>
    <#lemma15>
  );
  r:rule <#lemma7>.

<#lemma13> a r:Extraction;
  r:gives {
    :lemans :oneway :angers.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/graph.axiom.n3>].

<#lemma14> a r:Inference;
  r:gives {
    :chartres :path :lemans.
  };
  r:evidence (
    <#lemma8>
    <#lemma16>
  );
  r:rule <#lemma10>.

<#lemma15> a r:Inference;
  r:gives {
    :paris :path :chartres.
  };
  r:evidence (
    <#lemma8>
    <#lemma17>
  );
  r:rule <#lemma10>.

<#lemma16> a r:Extraction;
  r:gives {
    :chartres :oneway :lemans.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/graph.axiom.n3>].

<#lemma17> a r:Extraction;
  r:gives {
    :paris :oneway :chartres.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/eye/reasoning/graph/graph.axiom.n3>].

