<?xml version="1.0" encoding="ISO-8859-1"?>

<!DOCTYPE proofs SYSTEM "proof3.dtd">

<?xml-stylesheet type="text/xsl" href="proof3.xsl"?>

<proofs number_of_proofs="2">

<source>GEO146+1.out</source>

<heading><![CDATA[
FOF-Prover9 (32) version March-2007, March 2007.
Process 20920 was started by mccune on cleo,
Mon Mar 19 17:01:17 2007
The command was "/home/mccune/bin/fof-prover9 -f GEO146+1.in".
]]></heading>

<proof number="1" length="8" max_count="12">

<comments><![CDATA[
% Proof 1 at 2.10 (+ 0.01) seconds.
% Length of proof is 8.
% Level of proof is 3.
% Maximum clause weight is 12.
% Given clauses 477.
]]></comments>

  <clause id="204" type="assumption">
    <literal><![CDATA[
      connect(A,B,C)
    ]]></literal>
    <literal><![CDATA[
      -once(at_the_same_time(at(A,C),at(B,C)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="205" type="assumption">
    <literal><![CDATA[
      once(at_the_same_time(at(A,B),at(C,B)))
    ]]></literal>
    <literal><![CDATA[
      -connect(A,C,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="206" type="assumption">
    <literal><![CDATA[
      once(at_the_same_time(A,B))
    ]]></literal>
    <literal><![CDATA[
      -once(at_the_same_time(B,A))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="218" type="assumption">
    <literal><![CDATA[
      connect(c1,c2,c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="219" type="assumption">
    <literal><![CDATA[
      -connect(c2,c1,c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      once(at_the_same_time(at(c1,c3),at(c2,c3)))
    ]]></literal>
    <justification jstring="[resolve(218,a,205,b)].">
      <j1 rule="resolve" parents="218 205"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      once(at_the_same_time(at(c2,c3),at(c1,c3)))
    ]]></literal>
    <justification jstring="[resolve(569,a,206,b)].">
      <j1 rule="resolve" parents="569 206"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(3571,a,204,b),unit_del(a,219)].">
      <j1 rule="resolve" parents="3571 204"/>
      <j2 rule="unit_del" parents="219"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="8" max_count="12">

<comments><![CDATA[
% Proof 1 at 2.10 (+ 0.01) seconds.
% Length of proof is 8.
% Level of proof is 3.
% Maximum clause weight is 12.
% Given clauses 477.
]]></comments>

  <clause id="204" type="assumption">
    <literal><![CDATA[
      connect(A,B,C)
    ]]></literal>
    <literal><![CDATA[
      -once(at_the_same_time(at(A,C),at(B,C)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="205" type="assumption">
    <literal><![CDATA[
      once(at_the_same_time(at(A,B),at(C,B)))
    ]]></literal>
    <literal><![CDATA[
      -connect(A,C,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="206" type="assumption">
    <literal><![CDATA[
      once(at_the_same_time(A,B))
    ]]></literal>
    <literal><![CDATA[
      -once(at_the_same_time(B,A))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="218" type="assumption">
    <literal><![CDATA[
      -connect(c1,c2,c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="219" type="assumption">
    <literal><![CDATA[
      connect(c2,c1,c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      once(at_the_same_time(at(c2,c3),at(c1,c3)))
    ]]></literal>
    <justification jstring="[resolve(219,a,205,b)].">
      <j1 rule="resolve" parents="219 205"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      once(at_the_same_time(at(c1,c3),at(c2,c3)))
    ]]></literal>
    <justification jstring="[resolve(569,a,206,b)].">
      <j1 rule="resolve" parents="569 206"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(3571,a,204,b),unit_del(a,218)].">
      <j1 rule="resolve" parents="3571 204"/>
      <j2 rule="unit_del" parents="218"/>
    </justification>
  </clause>

</proof>

</proofs>
