<?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="1">

<source>xcb-reflex.out</source>

<heading><![CDATA[
Prover9 (32) version June-2006C, June 2006.
Process 13072 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:08 2006
The command was "/home/mccune/bin/prover9 -f xcb-reflex.in".
]]></heading>

<proof number="1" length="18" max_count="48">

<comments><![CDATA[
% Proof 1 at 2.98 (+ 0.04) seconds: Reflex.
% Length of proof is 18.
% Level of proof is 8.
% Maximum clause weight is 48.
% Given clauses 587.
]]></comments>

  <clause id="1">
    <literal><![CDATA[
      - P(e(x,y))
    ]]></literal>
    <literal><![CDATA[
      - P(x)
    ]]></literal>
    <literal><![CDATA[
      P(y)
    ]]></literal>
    <attribute><![CDATA[
      label(condensed_detachment)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="4">
    <literal><![CDATA[
      P(e(x,e(e(e(x,y),e(z,y)),z)))
    ]]></literal>
    <attribute><![CDATA[
      label(XCB)
    ]]></attribute>
    <justification jstring="[input].">
      <j1 rule="input"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      - P(e(c1,c1))
    ]]></literal>
    <attribute><![CDATA[
      answer(Reflex)
    ]]></attribute>
    <justification jstring="[clausify].">
      <j1 rule="clausify"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      P(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),e(v,u)),v))
    ]]></literal>
    <justification jstring="[hyper(1,a,4,a,b,4,a)].">
      <j1 rule="hyper" parents="1 4 4"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      P(e(e(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),e(v,u)),v),w),e(v6,w)),v6))
    ]]></literal>
    <justification jstring="[hyper(1,a,4,a,b,6,a)].">
      <j1 rule="hyper" parents="1 4 6"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      P(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),v),e(u,v)))
    ]]></literal>
    <justification jstring="[hyper(1,a,6,a,b,4,a)].">
      <j1 rule="hyper" parents="1 6 4"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      P(e(e(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),e(v,u)),v),w),v6),e(w,v6)))
    ]]></literal>
    <justification jstring="[hyper(1,a,7,a,b,4,a)].">
      <j1 rule="hyper" parents="1 7 4"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      P(e(x,e(e(e(e(e(y,e(e(e(y,z),e(u,z)),u)),v),e(w,v)),w),x)))
    ]]></literal>
    <justification jstring="[hyper(1,a,8,a,b,8,a)].">
      <j1 rule="hyper" parents="1 8 8"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      P(e(e(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),v),e(u,v)),w),e(v6,w)),v6))
    ]]></literal>
    <justification jstring="[hyper(1,a,4,a,b,8,a)].">
      <j1 rule="hyper" parents="1 4 8"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      P(e(x,e(e(e(e(e(y,e(e(e(y,z),e(u,z)),u)),x),v),e(w,v)),w)))
    ]]></literal>
    <justification jstring="[hyper(1,a,8,a,b,4,a)].">
      <j1 rule="hyper" parents="1 8 4"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      P(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),e(v,u)),v),e(e(e(e(w,e(e(e(w,v6),e(v7,v6)),v7)),v8),v9),e(v8,v9))))
    ]]></literal>
    <justification jstring="[hyper(1,a,11,a,b,8,a)].">
      <j1 rule="hyper" parents="1 11 8"/>
    </justification>
  </clause>

  <clause id="36">
    <literal><![CDATA[
      P(e(e(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),v),e(u,v)),w),v6),e(w,v6)))
    ]]></literal>
    <justification jstring="[hyper(1,a,12,a,b,4,a)].">
      <j1 rule="hyper" parents="1 12 4"/>
    </justification>
  </clause>

  <clause id="58">
    <literal><![CDATA[
      P(e(e(e(e(x,e(e(e(e(e(y,e(e(e(y,z),e(u,z)),u)),x),v),e(w,v)),w)),v6),e(v7,v6)),v7))
    ]]></literal>
    <justification jstring="[hyper(1,a,4,a,b,15,a)].">
      <j1 rule="hyper" parents="1 4 15"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      P(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),e(e(e(e(e(e(e(u,e(e(e(u,v),e(w,v)),w)),v6),v7),e(v6,v7)),v8),v9),e(v8,v9))),v10),e(v11,v10)),v11))
    ]]></literal>
    <justification jstring="[hyper(1,a,15,a,b,36,a)].">
      <j1 rule="hyper" parents="1 15 36"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      P(e(e(e(x,e(e(e(x,y),e(z,y)),z)),e(e(e(u,e(e(e(u,v),e(w,v)),w)),e(e(v6,e(e(e(v6,v7),e(v8,v7)),v8)),v9)),v10)),e(v9,v10)))
    ]]></literal>
    <justification jstring="[hyper(1,a,58,a,b,29,a)].">
      <j1 rule="hyper" parents="1 58 29"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      P(e(e(x,e(e(e(e(e(e(y,e(e(e(y,z),e(u,z)),u)),v),w),e(v,w)),e(e(e(v6,e(e(e(v6,v7),e(v8,v7)),v8)),v9),e(v10,v9))),v10)),x))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,142,a)].">
      <j1 rule="hyper" parents="1 10 142"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      P(e(x,x))
    ]]></literal>
    <justification jstring="[hyper(1,a,263,a,b,590,a)].">
      <j1 rule="hyper" parents="1 263 590"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Reflex)
    ]]></attribute>
    <justification jstring="[resolve(1755,a,5,a)].">
      <j1 rule="resolve" parents="1755 5"/>
    </justification>
  </clause>

</proof>

</proofs>
