<?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="32">

<source>andrews.out</source>

<heading><![CDATA[
FOF-Prover9 (32) version 2009-02A, February 2009.
Process 11202 was started by mccune on cleo,
Wed Feb 25 09:32:26 2009
The command was "/home/mccune/bin/fof-prover9 -f andrews.in".
]]></heading>

<proof number="1" length="7" max_count="4">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 7.
% Level of proof is 2.
% Maximum clause weight is 4.
% Given clauses 5.

]]></comments>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      q(c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      -q(c3)
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      q(c3)
    ]]></literal>
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      -q(c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      q(c3)
    ]]></literal>
    <justification jstring="[ur(6,b,3,a)].">
      <j1 rule="ur" parents="6 3"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -q(c3)
    ]]></literal>
    <justification jstring="[resolve(7,a,5,b)].">
      <j1 rule="resolve" parents="7 5"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(9,a,8,a)].">
      <j1 rule="resolve" parents="9 8"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(7,a,4,a)].">
      <j1 rule="resolve" parents="7 4"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <literal><![CDATA[
      -q(f2(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(5),unit_del(a,8),unit_del(b,8)].">
      <j1 rule="back_unit_del" parents="5"/>
      <j2 rule="unit_del" parents="8"/>
      <j2 rule="unit_del" parents="8"/>
    </justification>
  </clause>

</proof>

<proof number="4" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(8),unit_del(a,4)].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="unit_del" parents="4"/>
    </justification>
  </clause>

</proof>

<proof number="5" length="7" max_count="4">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 7.
% Level of proof is 2.
% Maximum clause weight is 4.
% Given clauses 5.

]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      p(c1)
    ]]></literal>
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      -p(c1)
    ]]></literal>
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -p(c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      p(c4)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      -p(c1)
    ]]></literal>
    <justification jstring="[resolve(4,a,2,b)].">
      <j1 rule="resolve" parents="4 2"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      p(c1)
    ]]></literal>
    <justification jstring="[ur(1,b,5,a)].">
      <j1 rule="ur" parents="1 5"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(7,a,6,a)].">
      <j1 rule="resolve" parents="7 6"/>
    </justification>
  </clause>

</proof>

<proof number="6" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(6,a,3,a)].">
      <j1 rule="resolve" parents="6 3"/>
    </justification>
  </clause>

</proof>

<proof number="7" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      q(f1(x))
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(5),unit_del(a,3),unit_del(b,3)].">
      <j1 rule="copy" parents="5"/>
      <j2 rule="unit_del" parents="3"/>
      <j2 rule="unit_del" parents="3"/>
    </justification>
  </clause>

</proof>

<proof number="8" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      q(f1(x))
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(5),unit_del(a,3),unit_del(b,3)].">
      <j1 rule="copy" parents="5"/>
      <j2 rule="unit_del" parents="3"/>
      <j2 rule="unit_del" parents="3"/>
    </justification>
  </clause>

</proof>

<proof number="9" length="7" max_count="4">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 7.
% Level of proof is 3.
% Maximum clause weight is 4.
% Given clauses 7.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      q(c1)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      -q(c3)
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      q(c3)
    ]]></literal>
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      -q(c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      q(c3)
    ]]></literal>
    <justification jstring="[resolve(7,b,4,a)].">
      <j1 rule="resolve" parents="7 4"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[back_unit_del(6),unit_del(a,10)].">
      <j1 rule="back_unit_del" parents="6"/>
      <j2 rule="unit_del" parents="10"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(11,a,9,a)].">
      <j1 rule="resolve" parents="11 9"/>
    </justification>
  </clause>

</proof>

<proof number="10" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <literal><![CDATA[
      p(f2(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(1),unit_del(a,8),unit_del(b,8)].">
      <j1 rule="back_unit_del" parents="1"/>
      <j2 rule="unit_del" parents="8"/>
      <j2 rule="unit_del" parents="8"/>
    </justification>
  </clause>

</proof>

<proof number="11" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <literal><![CDATA[
      -q(f4(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10" type="assumption">
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(6),unit_del(a,10),unit_del(b,10)].">
      <j1 rule="back_unit_del" parents="6"/>
      <j2 rule="unit_del" parents="10"/>
      <j2 rule="unit_del" parents="10"/>
    </justification>
  </clause>

</proof>

<proof number="12" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <literal><![CDATA[
      p(f2(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(1),unit_del(a,9),unit_del(b,9)].">
      <j1 rule="back_unit_del" parents="1"/>
      <j2 rule="unit_del" parents="9"/>
      <j2 rule="unit_del" parents="9"/>
    </justification>
  </clause>

</proof>

<proof number="13" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      -p(f1(x))
    ]]></literal>
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(2),unit_del(a,5),unit_del(b,5)].">
      <j1 rule="back_unit_del" parents="2"/>
      <j2 rule="unit_del" parents="5"/>
      <j2 rule="unit_del" parents="5"/>
    </justification>
  </clause>

</proof>

<proof number="14" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(8),unit_del(a,5)].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="unit_del" parents="5"/>
    </justification>
  </clause>

</proof>

<proof number="15" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      q(f3(x))
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(6),unit_del(a,4),unit_del(b,4)].">
      <j1 rule="copy" parents="6"/>
      <j2 rule="unit_del" parents="4"/>
      <j2 rule="unit_del" parents="4"/>
    </justification>
  </clause>

</proof>

<proof number="16" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      q(f3(x))
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(6),unit_del(a,4),unit_del(b,4)].">
      <j1 rule="copy" parents="6"/>
      <j2 rule="unit_del" parents="4"/>
      <j2 rule="unit_del" parents="4"/>
    </justification>
  </clause>

</proof>

<proof number="17" length="7" max_count="4">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 7.
% Level of proof is 2.
% Maximum clause weight is 4.
% Given clauses 4.

]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      p(c1)
    ]]></literal>
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      -p(c1)
    ]]></literal>
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -p(c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      p(c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -p(c1)
    ]]></literal>
    <justification jstring="[resolve(4,a,2,b)].">
      <j1 rule="resolve" parents="4 2"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      p(c1)
    ]]></literal>
    <justification jstring="[ur(1,b,7,a)].">
      <j1 rule="ur" parents="1 7"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(10,a,9,a)].">
      <j1 rule="resolve" parents="10 9"/>
    </justification>
  </clause>

</proof>

<proof number="18" length="7" max_count="4">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 7.
% Level of proof is 2.
% Maximum clause weight is 4.
% Given clauses 5.

]]></comments>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      q(c2)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      -q(c4)
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      q(c4)
    ]]></literal>
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      -q(c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      q(c4)
    ]]></literal>
    <justification jstring="[ur(6,b,3,a)].">
      <j1 rule="ur" parents="6 3"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -q(c4)
    ]]></literal>
    <justification jstring="[resolve(8,a,5,b)].">
      <j1 rule="resolve" parents="8 5"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(10,a,9,a)].">
      <j1 rule="resolve" parents="10 9"/>
    </justification>
  </clause>

</proof>

<proof number="19" length="7" max_count="4">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 7.
% Level of proof is 3.
% Maximum clause weight is 4.
% Given clauses 4.

]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      p(c1)
    ]]></literal>
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      -p(c1)
    ]]></literal>
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -p(c3)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      p(c4)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      -p(c1)
    ]]></literal>
    <justification jstring="[ur(2,b,4,a)].">
      <j1 rule="ur" parents="2 4"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[back_unit_del(1),unit_del(a,10)].">
      <j1 rule="back_unit_del" parents="1"/>
      <j2 rule="unit_del" parents="10"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(11,a,8,a)].">
      <j1 rule="resolve" parents="11 8"/>
    </justification>
  </clause>

</proof>

<proof number="20" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <literal><![CDATA[
      -q(f2(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(5),unit_del(a,9),unit_del(b,9)].">
      <j1 rule="back_unit_del" parents="5"/>
      <j2 rule="unit_del" parents="9"/>
      <j2 rule="unit_del" parents="9"/>
    </justification>
  </clause>

</proof>

<proof number="21" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(5,a,3,a)].">
      <j1 rule="resolve" parents="5 3"/>
    </justification>
  </clause>

</proof>

<proof number="22" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(5,a,4,a)].">
      <j1 rule="resolve" parents="5 4"/>
    </justification>
  </clause>

</proof>

<proof number="23" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      q(f1(x))
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(5),unit_del(a,3),unit_del(b,3)].">
      <j1 rule="copy" parents="5"/>
      <j2 rule="unit_del" parents="3"/>
      <j2 rule="unit_del" parents="3"/>
    </justification>
  </clause>

</proof>

<proof number="24" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      q(f1(x))
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(5),unit_del(a,3),unit_del(b,3)].">
      <j1 rule="copy" parents="5"/>
      <j2 rule="unit_del" parents="3"/>
      <j2 rule="unit_del" parents="3"/>
    </justification>
  </clause>

</proof>

<proof number="25" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      -p(f1(x))
    ]]></literal>
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(2),unit_del(a,5),unit_del(b,5)].">
      <j1 rule="back_unit_del" parents="2"/>
      <j2 rule="unit_del" parents="5"/>
      <j2 rule="unit_del" parents="5"/>
    </justification>
  </clause>

</proof>

<proof number="26" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(8),unit_del(a,5)].">
      <j1 rule="copy" parents="8"/>
      <j2 rule="unit_del" parents="5"/>
    </justification>
  </clause>

</proof>

<proof number="27" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      -p(f1(x))
    ]]></literal>
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(2),unit_del(a,5),unit_del(b,5)].">
      <j1 rule="back_unit_del" parents="2"/>
      <j2 rule="unit_del" parents="5"/>
      <j2 rule="unit_del" parents="5"/>
    </justification>
  </clause>

</proof>

<proof number="28" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(9),unit_del(a,5)].">
      <j1 rule="copy" parents="9"/>
      <j2 rule="unit_del" parents="5"/>
    </justification>
  </clause>

</proof>

<proof number="29" length="3" max_count="2">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(9),unit_del(a,4)].">
      <j1 rule="copy" parents="9"/>
      <j2 rule="unit_del" parents="4"/>
    </justification>
  </clause>

</proof>

<proof number="30" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.

]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      p(x)
    ]]></literal>
    <literal><![CDATA[
      p(f2(x))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      -p(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[back_unit_del(1),unit_del(a,8),unit_del(b,8)].">
      <j1 rule="back_unit_del" parents="1"/>
      <j2 rule="unit_del" parents="8"/>
      <j2 rule="unit_del" parents="8"/>
    </justification>
  </clause>

</proof>

<proof number="31" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      q(f3(x))
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(6),unit_del(a,4),unit_del(b,4)].">
      <j1 rule="copy" parents="6"/>
      <j2 rule="unit_del" parents="4"/>
      <j2 rule="unit_del" parents="4"/>
    </justification>
  </clause>

</proof>

<proof number="32" length="3" max_count="5">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 3.
% Level of proof is 1.
% Maximum clause weight is 2.
% Given clauses 0.

]]></comments>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      -q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      q(f3(x))
    ]]></literal>
    <literal><![CDATA[
      q(x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="7">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(6),unit_del(a,4),unit_del(b,4)].">
      <j1 rule="copy" parents="6"/>
      <j2 rule="unit_del" parents="4"/>
      <j2 rule="unit_del" parents="4"/>
    </justification>
  </clause>

</proof>

</proofs>
