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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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<proofs number_of_proofs="1">

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

<heading><![CDATA[
Prover9 (32) version 2009-02A, February 2009.
Process 11195 was started by mccune on cleo,
Wed Feb 25 09:32:23 2009
The command was "/home/mccune/bin/prover9 -f xcb-reflex.in".
]]></heading>

<proof number="1" length="19" max_count="48">

<comments><![CDATA[
% Proof 1 at 2.64 (+ 0.06) seconds: Reflex.
% Length of proof is 19.
% Level of proof is 8.
% Maximum clause weight is 48.
% Given clauses 587.

]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      P(e(x,x))
    ]]></literal>
    <attribute><![CDATA[
      answer(Reflex)
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="2" type="assumption">
    <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="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      P(e(x,e(e(e(x,y),e(z,y)),z)))
    ]]></literal>
    <attribute><![CDATA[
      label(XCB)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4" type="deny">
    <literal><![CDATA[
      -P(e(c1,c1))
    ]]></literal>
    <attribute><![CDATA[
      answer(Reflex)
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="5">
    <literal><![CDATA[
      P(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),e(w,u)),w))
    ]]></literal>
    <justification jstring="[hyper(2,a,3,a,b,3,a)].">
      <j1 rule="hyper" parents="2 3 3"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      P(e(e(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),e(w,u)),w),v5),e(v6,v5)),v6))
    ]]></literal>
    <justification jstring="[hyper(2,a,3,a,b,5,a)].">
      <j1 rule="hyper" parents="2 3 5"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      P(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),w),e(u,w)))
    ]]></literal>
    <justification jstring="[hyper(2,a,5,a,b,3,a)].">
      <j1 rule="hyper" parents="2 5 3"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      P(e(e(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),e(w,u)),w),v5),v6),e(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(2,a,6,a,b,3,a)].">
      <j1 rule="hyper" parents="2 6 3"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      P(e(x,e(e(e(e(e(y,e(e(e(y,z),e(u,z)),u)),w),e(v5,w)),v5),x)))
    ]]></literal>
    <justification jstring="[hyper(2,a,7,a,b,7,a)].">
      <j1 rule="hyper" parents="2 7 7"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      P(e(e(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),w),e(u,w)),v5),e(v6,v5)),v6))
    ]]></literal>
    <justification jstring="[hyper(2,a,3,a,b,7,a)].">
      <j1 rule="hyper" parents="2 3 7"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      P(e(x,e(e(e(e(e(y,e(e(e(y,z),e(u,z)),u)),x),w),e(v5,w)),v5)))
    ]]></literal>
    <justification jstring="[hyper(2,a,7,a,b,3,a)].">
      <j1 rule="hyper" parents="2 7 3"/>
    </justification>
  </clause>

  <clause id="28">
    <literal><![CDATA[
      P(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),e(w,u)),w),e(e(e(e(v5,e(e(e(v5,v6),e(v7,v6)),v7)),v8),v9),e(v8,v9))))
    ]]></literal>
    <justification jstring="[hyper(2,a,10,a,b,7,a)].">
      <j1 rule="hyper" parents="2 10 7"/>
    </justification>
  </clause>

  <clause id="35">
    <literal><![CDATA[
      P(e(e(e(e(e(e(e(x,e(e(e(x,y),e(z,y)),z)),u),w),e(u,w)),v5),v6),e(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(2,a,11,a,b,3,a)].">
      <j1 rule="hyper" parents="2 11 3"/>
    </justification>
  </clause>

  <clause id="57">
    <literal><![CDATA[
      P(e(e(e(e(x,e(e(e(e(e(y,e(e(e(y,z),e(u,z)),u)),x),w),e(v5,w)),v5)),v6),e(v7,v6)),v7))
    ]]></literal>
    <justification jstring="[hyper(2,a,3,a,b,14,a)].">
      <j1 rule="hyper" parents="2 3 14"/>
    </justification>
  </clause>

  <clause id="141">
    <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,w),e(v5,w)),v5)),v6),v7),e(v6,v7)),v8),v9),e(v8,v9))),v10),e(v11,v10)),v11))
    ]]></literal>
    <justification jstring="[hyper(2,a,14,a,b,35,a)].">
      <j1 rule="hyper" parents="2 14 35"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      P(e(e(e(x,e(e(e(x,y),e(z,y)),z)),e(e(e(u,e(e(e(u,w),e(v5,w)),v5)),e(e(v6,e(e(e(v6,v7),e(v8,v7)),v8)),v9)),v10)),e(v9,v10)))
    ]]></literal>
    <justification jstring="[hyper(2,a,57,a,b,28,a)].">
      <j1 rule="hyper" parents="2 57 28"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      P(e(e(x,e(e(e(e(e(e(y,e(e(e(y,z),e(u,z)),u)),w),v5),e(w,v5)),e(e(e(v6,e(e(e(v6,v7),e(v8,v7)),v8)),v9),e(v10,v9))),v10)),x))
    ]]></literal>
    <justification jstring="[hyper(2,a,9,a,b,141,a)].">
      <j1 rule="hyper" parents="2 9 141"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      P(e(x,x))
    ]]></literal>
    <justification jstring="[hyper(2,a,262,a,b,589,a)].">
      <j1 rule="hyper" parents="2 262 589"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer(Reflex)
    ]]></attribute>
    <justification jstring="[resolve(1754,a,4,a)].">
      <j1 rule="resolve" parents="1754 4"/>
    </justification>
  </clause>

</proof>

</proofs>
