# Generated with http://www.agfa.com/w3c/euler/#R3588 on 29 Sep 2003 22:06:15 GMT
{
 (
 <http://www.agfa.com/w3c/euler/rdfs-rules.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.agfa.com/w3c/euler/graph.axiom.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.lemma.n3>.<http://www.w3.org/2000/10/swap/log#semantics>
}
<http://www.w3.org/2000/10/swap/reason#because>
{
@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 iw: <http://www.ksl.stanford.edu/software/IW/spec/iw#>.
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>.

 {
  <http://www.agfa.com/w3c/euler/owl-rules#owl2t1>. 
  :route a owl:TransitiveProperty. 
   {
    <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
     {[iw:Variable "?P"] = :twoway. 
      [iw:Variable "?P"] rdfs:subPropertyOf :route} =>
    {:twoway rdfs:subPropertyOf :route}. 
     {
      <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
       {[iw:Variable "?P"] = :oneway. 
        [iw:Variable "?P"] rdfs:subPropertyOf :twoway} =>
      {:oneway rdfs:subPropertyOf :twoway}. 
       {[iw:Variable "?S"] = :angers. 
        [iw:Variable "?P"] = :oneway.
        [iw:Variable "?O"] = :nantes. 
        [iw:Variable "?S"] [iw:Variable "?P"] [iw:Variable "?O"]} =>
      {:angers :oneway :nantes}. 
      [iw:Variable "?S"] = :angers. 
      [iw:Variable ":twoway"] = :twoway.
      [iw:Variable "?O"] = :nantes. 
      [iw:Variable "?S"] [iw:Variable ":twoway"] [iw:Variable "?O"]} =>
    {:angers :twoway :nantes}. 
    [iw:Variable "?X"] = :angers. 
    [iw:Variable "?O"] = :nantes. 
    [iw:Variable "?X"] :route [iw:Variable "?O"]} =>
  {:angers :route :nantes}. 
   {
    <http://www.agfa.com/w3c/euler/owl-rules#owl2t1>. 
    :route a owl:TransitiveProperty. 
     {
      <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
       {[iw:Variable "?P"] = :twoway. 
        [iw:Variable "?P"] rdfs:subPropertyOf :route} =>
      {:twoway rdfs:subPropertyOf :route}. 
       {
        <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
         {[iw:Variable "?P"] = :oneway. 
          [iw:Variable "?P"] rdfs:subPropertyOf :twoway} =>
        {:oneway rdfs:subPropertyOf :twoway}. 
         {[iw:Variable "?S"] = :lemans. 
          [iw:Variable "?P"] = :oneway.
          [iw:Variable "?O"] = :angers. 
          [iw:Variable "?S"] [iw:Variable "?P"] [iw:Variable "?O"]} =>
        {:lemans :oneway :angers}. 
        [iw:Variable "?S"] = :lemans. 
        [iw:Variable ":twoway"] = :twoway.
        [iw:Variable "?O"] = :angers. 
        [iw:Variable "?S"] [iw:Variable ":twoway"] [iw:Variable "?O"]} =>
      {:lemans :twoway :angers}. 
      [iw:Variable "?X"] = :lemans. 
      [iw:Variable "?O"] = :angers. 
      [iw:Variable "?X"] :route [iw:Variable "?O"]} =>
    {:lemans :route :angers}. 
     {
      <http://www.agfa.com/w3c/euler/owl-rules#owl2t1>. 
      :route a owl:TransitiveProperty. 
       {
        <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
         {[iw:Variable "?P"] = :twoway. 
          [iw:Variable "?P"] rdfs:subPropertyOf :route} =>
        {:twoway rdfs:subPropertyOf :route}. 
         {
          <http://www.agfa.com/w3c/euler/owl-rules#owl1s1>. 
          :twoway a owl:SymmetricProperty. 
           {
            <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
             {[iw:Variable "?P"] = :oneway. 
              [iw:Variable "?P"] rdfs:subPropertyOf :twoway} =>
            {:oneway rdfs:subPropertyOf :twoway}. 
             {[iw:Variable "?S"] = :lemans. 
              [iw:Variable "?P"] = :oneway.
              [iw:Variable "?O"] = :tours. 
              [iw:Variable "?S"] [iw:Variable "?P"] [iw:Variable "?O"]} =>
            {:lemans :oneway :tours}. 
            [iw:Variable "?S"] = :lemans. 
            [iw:Variable "?O"] = :tours. 
            [iw:Variable "?S"] :twoway [iw:Variable "?O"]} =>
          {:lemans :twoway :tours}. 
          [iw:Variable "?S"] = :tours. 
          [iw:Variable ":twoway"] = :twoway.
          [iw:Variable "?O"] = :lemans. 
          [iw:Variable "?S"] [iw:Variable ":twoway"] [iw:Variable "?O"]} =>
        {:tours :twoway :lemans}. 
        [iw:Variable "?X"] = :tours. 
        [iw:Variable "?O"] = :lemans. 
        [iw:Variable "?X"] :route [iw:Variable "?O"]} =>
      {:tours :route :lemans}. 
       {
        <http://www.agfa.com/w3c/euler/owl-rules#owl2t1>. 
        :route a owl:TransitiveProperty. 
         {
          <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
           {[iw:Variable "?P"] = :twoway. 
            [iw:Variable "?P"] rdfs:subPropertyOf :route} =>
          {:twoway rdfs:subPropertyOf :route}. 
           {
            <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
             {[iw:Variable "?P"] = :oneway. 
              [iw:Variable "?P"] rdfs:subPropertyOf :twoway} =>
            {:oneway rdfs:subPropertyOf :twoway}. 
             {[iw:Variable "?S"] = :blois. 
              [iw:Variable "?P"] = :oneway.
              [iw:Variable "?O"] = :tours. 
              [iw:Variable "?S"] [iw:Variable "?P"] [iw:Variable "?O"]} =>
            {:blois :oneway :tours}. 
            [iw:Variable "?S"] = :blois. 
            [iw:Variable ":twoway"] = :twoway.
            [iw:Variable "?O"] = :tours. 
            [iw:Variable "?S"] [iw:Variable ":twoway"] [iw:Variable "?O"]} =>
          {:blois :twoway :tours}. 
          [iw:Variable "?X"] = :blois. 
          [iw:Variable "?O"] = :tours. 
          [iw:Variable "?X"] :route [iw:Variable "?O"]} =>
        {:blois :route :tours}. 
         {
          <http://www.agfa.com/w3c/euler/owl-rules#owl2t1>. 
          :route a owl:TransitiveProperty. 
           {
            <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
             {[iw:Variable "?P"] = :twoway. 
              [iw:Variable "?P"] rdfs:subPropertyOf :route} =>
            {:twoway rdfs:subPropertyOf :route}. 
             {
              <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
               {[iw:Variable "?P"] = :oneway. 
                [iw:Variable "?P"] rdfs:subPropertyOf :twoway} =>
              {:oneway rdfs:subPropertyOf :twoway}. 
               {[iw:Variable "?S"] = :orleans. 
                [iw:Variable "?P"] = :oneway.
                [iw:Variable "?O"] = :blois. 
                [iw:Variable "?S"] [iw:Variable "?P"] [iw:Variable "?O"]} =>
              {:orleans :oneway :blois}. 
              [iw:Variable "?S"] = :orleans. 
              [iw:Variable ":twoway"] = :twoway.
              [iw:Variable "?O"] = :blois. 
              [iw:Variable "?S"] [iw:Variable ":twoway"] [iw:Variable "?O"]} =>
            {:orleans :twoway :blois}. 
            [iw:Variable "?X"] = :orleans. 
            [iw:Variable "?O"] = :blois. 
            [iw:Variable "?X"] :route [iw:Variable "?O"]} =>
          {:orleans :route :blois}. 
           {
            <http://www.agfa.com/w3c/euler/owl-rules#owl2t1>. 
            :route a owl:TransitiveProperty. 
             {
              <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
               {[iw:Variable "?P"] = :twoway. 
                [iw:Variable "?P"] rdfs:subPropertyOf :route} =>
              {:twoway rdfs:subPropertyOf :route}. 
               {
                <http://www.agfa.com/w3c/euler/owl-rules#owl1s1>. 
                :twoway a owl:SymmetricProperty. 
                 {
                  <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
                   {[iw:Variable "?P"] = :oneway. 
                    [iw:Variable "?P"] rdfs:subPropertyOf :twoway} =>
                  {:oneway rdfs:subPropertyOf :twoway}. 
                   {[iw:Variable "?S"] = :orleans. 
                    [iw:Variable "?P"] = :oneway.
                    [iw:Variable "?O"] = :bourges. 
                    [iw:Variable "?S"] [iw:Variable "?P"] [iw:Variable "?O"]} =>
                  {:orleans :oneway :bourges}. 
                  [iw:Variable "?S"] = :orleans. 
                  [iw:Variable "?O"] = :bourges. 
                  [iw:Variable "?S"] :twoway [iw:Variable "?O"]} =>
                {:orleans :twoway :bourges}. 
                [iw:Variable "?S"] = :bourges. 
                [iw:Variable ":twoway"] = :twoway.
                [iw:Variable "?O"] = :orleans. 
                [iw:Variable "?S"] [iw:Variable ":twoway"] [iw:Variable "?O"]} =>
              {:bourges :twoway :orleans}. 
              [iw:Variable "?X"] = :bourges. 
              [iw:Variable "?O"] = :orleans. 
              [iw:Variable "?X"] :route [iw:Variable "?O"]} =>
            {:bourges :route :orleans}. 
             {
              <http://www.agfa.com/w3c/euler/owl-rules#owl2t1>. 
              :route a owl:TransitiveProperty. 
               {
                <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
                 {[iw:Variable "?P"] = :twoway. 
                  [iw:Variable "?P"] rdfs:subPropertyOf :route} =>
                {:twoway rdfs:subPropertyOf :route}. 
                 {
                  <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
                   {[iw:Variable "?P"] = :oneway. 
                    [iw:Variable "?P"] rdfs:subPropertyOf :twoway} =>
                  {:oneway rdfs:subPropertyOf :twoway}. 
                   {[iw:Variable "?S"] = :orleans. 
                    [iw:Variable "?P"] = :oneway.
                    [iw:Variable "?O"] = :bourges. 
                    [iw:Variable "?S"] [iw:Variable "?P"] [iw:Variable "?O"]} =>
                  {:orleans :oneway :bourges}. 
                  [iw:Variable "?S"] = :orleans. 
                  [iw:Variable ":twoway"] = :twoway.
                  [iw:Variable "?O"] = :bourges. 
                  [iw:Variable "?S"] [iw:Variable ":twoway"] [iw:Variable "?O"]} =>
                {:orleans :twoway :bourges}. 
                [iw:Variable "?X"] = :orleans. 
                [iw:Variable "?O"] = :bourges. 
                [iw:Variable "?X"] :route [iw:Variable "?O"]} =>
              {:orleans :route :bourges}. 
               {
                <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
                 {[iw:Variable "?P"] = :twoway. 
                  [iw:Variable "?P"] rdfs:subPropertyOf :route} =>
                {:twoway rdfs:subPropertyOf :route}. 
                 {
                  <http://www.agfa.com/w3c/euler/owl-rules#owl1s1>. 
                  :twoway a owl:SymmetricProperty. 
                   {
                    <http://www.agfa.com/w3c/euler/owl-rules#owl1s1>. 
                    :twoway a owl:SymmetricProperty. 
                     {
                      <http://www.agfa.com/w3c/euler/rdfs-rules#rdfs7>. 
                       {[iw:Variable "?P"] = :oneway. 
                        [iw:Variable "?P"] rdfs:subPropertyOf :twoway} =>
                      {:oneway rdfs:subPropertyOf :twoway}. 
                       {[iw:Variable "?S"] = :parijs. 
                        [iw:Variable "?P"] = :oneway.
                        [iw:Variable "?O"] = :orleans. 
                        [iw:Variable "?S"] [iw:Variable "?P"] [iw:Variable "?O"]} =>
                      {:parijs :oneway :orleans}. 
                      [iw:Variable "?S"] = :parijs. 
                      [iw:Variable "?O"] = :orleans. 
                      [iw:Variable "?S"] :twoway [iw:Variable "?O"]} =>
                    {:parijs :twoway :orleans}. 
                    [iw:Variable "?S"] = :orleans. 
                    [iw:Variable "?O"] = :parijs. 
                    [iw:Variable "?S"] :twoway [iw:Variable "?O"]} =>
                  {:orleans :twoway :parijs}. 
                  [iw:Variable "?S"] = :parijs. 
                  [iw:Variable ":twoway"] = :twoway.
                  [iw:Variable "?O"] = :orleans. 
                  [iw:Variable "?S"] [iw:Variable ":twoway"] [iw:Variable "?O"]} =>
                {:parijs :twoway :orleans}. 
                [iw:Variable "?S"] = :parijs. 
                [iw:Variable "?X"] = :orleans. 
                [iw:Variable "?S"] :route [iw:Variable "?X"]} =>
              {:parijs :route :orleans}. 
              [iw:Variable "?S"] = :parijs. 
              [iw:Variable "?X"] = :bourges. 
              [iw:Variable "?S"] :route [iw:Variable "?X"]} =>
            {:parijs :route :bourges}. 
            [iw:Variable "?S"] = :parijs. 
            [iw:Variable "?X"] = :orleans. 
            [iw:Variable "?S"] :route [iw:Variable "?X"]} =>
          {:parijs :route :orleans}. 
          [iw:Variable "?S"] = :parijs. 
          [iw:Variable "?X"] = :blois. 
          [iw:Variable "?S"] :route [iw:Variable "?X"]} =>
        {:parijs :route :blois}. 
        [iw:Variable "?S"] = :parijs. 
        [iw:Variable "?X"] = :tours. 
        [iw:Variable "?S"] :route [iw:Variable "?X"]} =>
      {:parijs :route :tours}. 
      [iw:Variable "?S"] = :parijs. 
      [iw:Variable "?X"] = :lemans. 
      [iw:Variable "?S"] :route [iw:Variable "?X"]} =>
    {:parijs :route :lemans}. 
    [iw:Variable "?S"] = :parijs. 
    [iw:Variable "?X"] = :angers. 
    [iw:Variable "?S"] :route [iw:Variable "?X"]} =>
  {:parijs :route :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>.
# Proof found for http://www.agfa.com/w3c/euler/graph.lemma.n3 in 2830 steps (6431 steps/sec) using 1 engine
}.