{
 (
 <http://www.agfa.com/w3c/euler/rdfs-rules.n3>.<http://www.w3.org/2000/10/swap/log#semantics>
 <http://www.agfa.com/w3c/euler/graph.axiom.n3>.<http://www.w3.org/2000/10/swap/log#semantics>
 <http://www.agfa.com/w3c/euler/owl-rules.n3>.<http://www.w3.org/2000/10/swap/log#semantics>
 ).<http://www.w3.org/2000/10/swap/log#conjunction> =>
 <http://www.agfa.com/w3c/euler/graph.proof.n3>.<http://www.w3.org/2000/10/swap/log#semantics>
}
<http://www.w3.org/2000/10/swap/reason#because>
{
# Generated with http://www.agfa.com/w3c/euler/#R3425 on 26 Apr 2003 13:45:01 GMT
@prefix str: <http://www.w3.org/2000/10/swap/string#>.
@prefix ns: <http://www.agfa.com/w3c/euler/owl-rules#>.
@prefix xsd: <http://www.w3.org/2001/XMLSchema#>.
@prefix : <http://www.agfa.com/w3c/euler/graph#>.
@prefix log: <http://www.w3.org/2000/10/swap/log#>.
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#>.
@prefix math: <http://www.w3.org/2000/10/swap/math#>.
@prefix nsns: <http://www.agfa.com/w3c/euler/rdfs-rules#>.
@prefix owl: <http://www.w3.org/2002/07/owl#>.
@prefix neg: <http://www.agfa.com/w3c/euler/negation#>.
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>.

{<http://www.agfa.com/w3c/euler/owl-rules#rule2t1>  . :path a
      owl:TransitiveProperty. {<http://www.agfa.com/w3c/euler/rdfs-rules#rdfs6>  . :twoway <http://www.w3.org/2000/01/rdf-schema#subPropertyOf>
          :path. {<http://www.agfa.com/w3c/euler/rdfs-rules#rdfs6>  . :oneway <http://www.w3.org/2000/01/rdf-schema#subPropertyOf>
              :twoway. {?S = :angers. ?O =
                  :nantes. ?S :oneway ?O}  => {:angers :oneway
                      :nantes} . ?S =
                  :angers. ?O = :nantes. ?S :twoway
                      ?O}  =>
                      {:angers :twoway
                          :nantes} . ?X =
              :angers. ?O = :nantes. ?X :path
                  ?O}  =>
                  {:angers :path
                      :nantes} . {<http://www.agfa.com/w3c/euler/owl-rules#rule2t1> 
          . :path a owl:TransitiveProperty. {<http://www.agfa.com/w3c/euler/rdfs-rules#rdfs6> 
              . :twoway <http://www.w3.org/2000/01/rdf-schema#subPropertyOf> :path. {<http://www.agfa.com/w3c/euler/rdfs-rules#rdfs6> 
                  . :oneway <http://www.w3.org/2000/01/rdf-schema#subPropertyOf> :twoway. {?S =
                      :lemans. ?O = :angers. ?S :oneway
                          ?O}  =>
                          {:lemans :oneway
                              :angers} . ?S = :lemans. ?O =
                          :angers. ?S :twoway ?O}  => {:lemans :twoway
                              :angers} . ?X = :lemans. ?O =
                      :angers. ?X :path ?O}  => {:lemans :path
                          :angers} . {<http://www.agfa.com/w3c/euler/owl-rules#rule2t1>  . :path a
                  owl:TransitiveProperty. {<http://www.agfa.com/w3c/euler/rdfs-rules#rdfs6>  . :twoway <http://www.w3.org/2000/01/rdf-schema#subPropertyOf>
                      :path. {<http://www.agfa.com/w3c/euler/rdfs-rules#rdfs6>  . :oneway <http://www.w3.org/2000/01/rdf-schema#subPropertyOf>
                          :twoway. {?S = :chartres. ?O =
                              :lemans. ?S :oneway ?O}  => {:chartres :oneway
                                  :lemans} . ?S =
                              :chartres. ?O = :lemans. ?S :twoway
                                  ?O}  =>
                                  {:chartres :twoway
                                      :lemans} . ?X =
                          :chartres. ?O = :lemans. ?X :path
                              ?O}  =>
                              {:chartres :path
                                  :lemans} . {<http://www.agfa.com/w3c/euler/rdfs-rules#rdfs6> 
                      . :twoway <http://www.w3.org/2000/01/rdf-schema#subPropertyOf> :path. {<http://www.agfa.com/w3c/euler/rdfs-rules#rdfs6> 
                          . :oneway <http://www.w3.org/2000/01/rdf-schema#subPropertyOf> :twoway. {?S =
                              :parijs. ?O = :chartres. ?S :oneway
                                  ?O}  =>
                                  {:parijs :oneway
                                      :chartres} . ?S = :parijs. ?O =
                                  :chartres. ?S :twoway ?O}  => {:parijs :twoway
                                      :chartres} . ?S = :parijs. ?X =
                              :chartres. ?S :path ?X}  => {:parijs :path
                                  :chartres} . ?S = :parijs. ?X =
                          :lemans. ?S :path ?X}  => {:parijs :path
                              :lemans} . ?S =
                  :parijs. ?X = :angers. ?S :path
                      ?X}  =>
                      {:parijs :path
                          :angers} }  =>
          {:parijs :route
              :nantes} . 
<http://www.agfa.com/w3c/euler/graph#path> <http://www.w3.org/2002/07/owl#sameAs> <http://www.agfa.com/w3c/euler/graph#route>. 
<http://www.agfa.com/w3c/euler/graph#parijs> <http://www.w3.org/2002/07/owl#sameAs> <http://www.agfa.com/w3c/euler/graph#paris>. 

<http://www.agfa.com/w3c/euler/graph#path> <http://www.w3.org/2002/07/owl#sameAs> <http://www.agfa.com/w3c/euler/graph#route>.
<http://www.agfa.com/w3c/euler/graph#parijs> <http://www.w3.org/2002/07/owl#sameAs> <http://www.agfa.com/w3c/euler/graph#paris>.

# Proof found for http://www.agfa.com/w3c/euler/graph.proof.n3 in 6 steps (6000 steps/sec) using 1 engine}