#Processed by EYE v20.0218.2044 josd
#eye --no-genid http://josd.github.io/brain/graph/graph.axiom.n3 http://josd.github.io/brain/graph/rpo-rules.n3 --query http://josd.github.io/brain/graph/graph.filter.n3

@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#>.
@prefix var: <http://josd.github.io/var#>.
@prefix n3: <http://www.w3.org/2004/06/rei#>.

[] 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:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#path"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#angers"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#nantes"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#paris"]];
  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/brain/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/brain/graph/graph.axiom.n3>].

<#lemma5> a r:Inference;
  r:gives {
    :angers :path :nantes.
  };
  r:evidence (
    <#lemma8>
    <#lemma9>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#oneway"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#path"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#angers"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#nantes"]];
  r:rule <#lemma10>.

<#lemma6> a r:Inference;
  r:gives {
    :paris :path :angers.
  };
  r:evidence (
    <#lemma4>
    <#lemma11>
    <#lemma12>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#path"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#lemans"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#angers"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#paris"]];
  r:rule <#lemma7>.

<#lemma7> a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1, var:x_2, var:x_3. {var:x_0 a owl:TransitiveProperty.
     var:x_1 var:x_0 var:x_2.
     var:x_3 var:x_0 var:x_1} => {var:x_3 var:x_0 var:x_2}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/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/brain/graph/graph.axiom.n3>].

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

<#lemma10> a r:Extraction;
  r:gives {
    @forAll var:x_0, var:x_1, var:x_2, var:x_3. {var:x_0 rdfs:subPropertyOf var:x_1.
     var:x_2 var:x_0 var:x_3} => {var:x_2 var:x_1 var:x_3}.
  };
  r:because [ a r:Parsing; r:source <http://josd.github.io/brain/graph/rpo-rules.n3>].

<#lemma11> a r:Inference;
  r:gives {
    :lemans :path :angers.
  };
  r:evidence (
    <#lemma8>
    <#lemma13>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#oneway"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#path"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#lemans"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#angers"]];
  r:rule <#lemma10>.

<#lemma12> a r:Inference;
  r:gives {
    :paris :path :lemans.
  };
  r:evidence (
    <#lemma4>
    <#lemma14>
    <#lemma15>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#path"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#chartres"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#lemans"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#paris"]];
  r:rule <#lemma7>.

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

<#lemma14> a r:Inference;
  r:gives {
    :chartres :path :lemans.
  };
  r:evidence (
    <#lemma8>
    <#lemma16>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#oneway"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#path"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#chartres"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#lemans"]];
  r:rule <#lemma10>.

<#lemma15> a r:Inference;
  r:gives {
    :paris :path :chartres.
  };
  r:evidence (
    <#lemma8>
    <#lemma17>
  );
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_0"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#oneway"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_1"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#path"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_2"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#paris"]];
  r:binding [ r:variable [ n3:uri "http://josd.github.io/var#x_3"]; r:boundTo [ n3:uri "http://www.agfa.com/w3c/euler/graph.axiom#chartres"]];
  r:rule <#lemma10>.

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

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

#2020-02-22T21:51:49.851Z in=89 out=1 ent=24 step=70 brake=2 inf=91092 sec=0.117 inf/sec=778564
#ENDS

