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<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="50">

<source>ALG189+1.out</source>

<heading><![CDATA[
FOF-Prover9 (32) version 2008-05A, May 2008.
Process 21754 was started by mccune on cleo,
Wed May  7 22:14:44 2008
The command was "/home/mccune/LADR/bin/fof-prover9 -f ALG189+1.in".
]]></heading>

<proof number="1" length="3" max_count="7">

<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="11" type="assumption">
    <literal><![CDATA[
      op(e0,e0) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e0),e0) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([11(3),11(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="11 11"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="12" type="assumption">
    <literal><![CDATA[
      op(e0,e1) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27" type="assumption">
    <literal><![CDATA[
      op(e3,e1) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e1),e1) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([12(3),27(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="12 27"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="3" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="13" type="assumption">
    <literal><![CDATA[
      op(e0,e2) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      op(e4,e2) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e2),e2) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([13(3),33(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="13 33"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="14" type="assumption">
    <literal><![CDATA[
      op(e0,e3) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24" type="assumption">
    <literal><![CDATA[
      op(e2,e3) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e3),e3) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([14(3),24(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="14 24"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="15" type="assumption">
    <literal><![CDATA[
      op(e0,e4) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20" type="assumption">
    <literal><![CDATA[
      op(e1,e4) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e4),e4) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([15(3),20(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="15 20"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="6" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="16" type="assumption">
    <literal><![CDATA[
      op(e1,e0) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21" type="assumption">
    <literal><![CDATA[
      op(e2,e0) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e0),e0) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([16(3),21(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="16 21"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

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

<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="17" type="assumption">
    <literal><![CDATA[
      op(e1,e1) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e1),e1) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([17(3),17(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="17 17"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="8" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="18" type="assumption">
    <literal><![CDATA[
      op(e1,e2) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      op(e3,e2) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e2),e2) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([18(3),28(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="18 28"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="19" type="assumption">
    <literal><![CDATA[
      op(e1,e3) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      op(e4,e3) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e3),e3) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([19(3),34(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="19 34"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="10" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="15" type="assumption">
    <literal><![CDATA[
      op(e0,e4) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20" type="assumption">
    <literal><![CDATA[
      op(e1,e4) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e4),e4) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([20(3),15(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="20 15"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="11" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="16" type="assumption">
    <literal><![CDATA[
      op(e1,e0) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21" type="assumption">
    <literal><![CDATA[
      op(e2,e0) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e0),e0) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([21(3),16(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="21 16"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="12" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="22" type="assumption">
    <literal><![CDATA[
      op(e2,e1) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="32" type="assumption">
    <literal><![CDATA[
      op(e4,e1) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e1),e1) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([22(3),32(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="22 32"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="13" length="3" max_count="7">

<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="23" type="assumption">
    <literal><![CDATA[
      op(e2,e2) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e2),e2) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([23(3),23(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="23 23"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="14" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="14" type="assumption">
    <literal><![CDATA[
      op(e0,e3) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24" type="assumption">
    <literal><![CDATA[
      op(e2,e3) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e3),e3) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([24(3),14(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="24 14"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="15" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="25" type="assumption">
    <literal><![CDATA[
      op(e2,e4) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      op(e3,e4) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e4),e4) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([25(3),30(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="25 30"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="16" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="26" type="assumption">
    <literal><![CDATA[
      op(e3,e0) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31" type="assumption">
    <literal><![CDATA[
      op(e4,e0) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e0),e0) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([26(3),31(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="26 31"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="12" type="assumption">
    <literal><![CDATA[
      op(e0,e1) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27" type="assumption">
    <literal><![CDATA[
      op(e3,e1) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e1),e1) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([27(3),12(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="27 12"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

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

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="18" type="assumption">
    <literal><![CDATA[
      op(e1,e2) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      op(e3,e2) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e2),e2) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([28(3),18(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="28 18"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="19" length="3" max_count="7">

<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="29" type="assumption">
    <literal><![CDATA[
      op(e3,e3) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e3),e3) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([29(3),29(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="29 29"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="20" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="25" type="assumption">
    <literal><![CDATA[
      op(e2,e4) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      op(e3,e4) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e4),e4) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([30(3),25(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="30 25"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="21" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="26" type="assumption">
    <literal><![CDATA[
      op(e3,e0) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31" type="assumption">
    <literal><![CDATA[
      op(e4,e0) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e0),e0) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([31(3),26(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="31 26"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="22" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="22" type="assumption">
    <literal><![CDATA[
      op(e2,e1) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="32" type="assumption">
    <literal><![CDATA[
      op(e4,e1) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e1),e1) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([32(3),22(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="32 22"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="23" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="13" type="assumption">
    <literal><![CDATA[
      op(e0,e2) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      op(e4,e2) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e2),e2) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([33(3),13(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="33 13"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="24" length="4" max_count="7">

<comments><![CDATA[
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 4.
% Level of proof is 1.
% Maximum clause weight is 5.
% Given clauses 0.
]]></comments>

  <clause id="19" type="assumption">
    <literal><![CDATA[
      op(e1,e3) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      op(e4,e3) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e3),e3) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([34(3),19(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="34 19"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="25" length="3" max_count="7">

<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="35" type="assumption">
    <literal><![CDATA[
      op(e4,e4) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e4),e4) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([35(3),35(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="35 35"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="26" length="3" max_count="9">

<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="11" type="assumption">
    <literal><![CDATA[
      op(e0,e0) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e0),op(e0,e0)) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([11(3),11(4),11(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="11 11 11"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="27" length="5" max_count="9">

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

  <clause id="12" type="assumption">
    <literal><![CDATA[
      op(e0,e1) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="16" type="assumption">
    <literal><![CDATA[
      op(e1,e0) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24" type="assumption">
    <literal><![CDATA[
      op(e2,e3) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e0),op(e0,e1)) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([16(3),12(4),24(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="16 12 24"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="28" length="5" max_count="9">

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

  <clause id="13" type="assumption">
    <literal><![CDATA[
      op(e0,e2) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20" type="assumption">
    <literal><![CDATA[
      op(e1,e4) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21" type="assumption">
    <literal><![CDATA[
      op(e2,e0) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e0),op(e0,e2)) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([21(3),13(4),20(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="21 13 20"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="29" length="5" max_count="9">

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

  <clause id="14" type="assumption">
    <literal><![CDATA[
      op(e0,e3) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26" type="assumption">
    <literal><![CDATA[
      op(e3,e0) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      op(e4,e2) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e0),op(e0,e3)) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([26(3),14(4),33(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="26 14 33"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="30" length="5" max_count="9">

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

  <clause id="15" type="assumption">
    <literal><![CDATA[
      op(e0,e4) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27" type="assumption">
    <literal><![CDATA[
      op(e3,e1) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31" type="assumption">
    <literal><![CDATA[
      op(e4,e0) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e0),op(e0,e4)) != e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([31(3),15(4),27(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="31 15 27"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="31" length="5" max_count="9">

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

  <clause id="12" type="assumption">
    <literal><![CDATA[
      op(e0,e1) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="16" type="assumption">
    <literal><![CDATA[
      op(e1,e0) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      op(e3,e2) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e1),op(e1,e0)) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([12(3),16(4),28(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="12 16 28"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="32" length="3" max_count="9">

<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="17" type="assumption">
    <literal><![CDATA[
      op(e1,e1) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e1),op(e1,e1)) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([17(3),17(4),17(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="17 17 17"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="33" length="5" max_count="9">

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

  <clause id="18" type="assumption">
    <literal><![CDATA[
      op(e1,e2) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22" type="assumption">
    <literal><![CDATA[
      op(e2,e1) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      op(e4,e3) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e1),op(e1,e2)) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([22(3),18(4),34(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="22 18 34"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="34" length="5" max_count="9">

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

  <clause id="15" type="assumption">
    <literal><![CDATA[
      op(e0,e4) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="19" type="assumption">
    <literal><![CDATA[
      op(e1,e3) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27" type="assumption">
    <literal><![CDATA[
      op(e3,e1) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e1),op(e1,e3)) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([27(3),19(4),15(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="27 19 15"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="35" length="5" max_count="9">

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

  <clause id="20" type="assumption">
    <literal><![CDATA[
      op(e1,e4) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21" type="assumption">
    <literal><![CDATA[
      op(e2,e0) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="32" type="assumption">
    <literal><![CDATA[
      op(e4,e1) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e1),op(e1,e4)) != e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([32(3),20(4),21(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="32 20 21"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="36" length="5" max_count="9">

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

  <clause id="13" type="assumption">
    <literal><![CDATA[
      op(e0,e2) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="21" type="assumption">
    <literal><![CDATA[
      op(e2,e0) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="32" type="assumption">
    <literal><![CDATA[
      op(e4,e1) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e2),op(e2,e0)) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([13(3),21(4),32(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="13 21 32"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="37" length="5" max_count="9">

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

  <clause id="18" type="assumption">
    <literal><![CDATA[
      op(e1,e2) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22" type="assumption">
    <literal><![CDATA[
      op(e2,e1) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      op(e3,e4) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e2),op(e2,e1)) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([18(3),22(4),30(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="18 22 30"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="38" length="3" max_count="9">

<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="23" type="assumption">
    <literal><![CDATA[
      op(e2,e2) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e2),op(e2,e2)) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([23(3),23(4),23(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="23 23 23"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="39" length="5" max_count="9">

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

  <clause id="16" type="assumption">
    <literal><![CDATA[
      op(e1,e0) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24" type="assumption">
    <literal><![CDATA[
      op(e2,e3) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      op(e3,e2) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e2),op(e2,e3)) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([28(3),24(4),16(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="28 24 16"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="40" length="5" max_count="9">

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

  <clause id="14" type="assumption">
    <literal><![CDATA[
      op(e0,e3) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25" type="assumption">
    <literal><![CDATA[
      op(e2,e4) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      op(e4,e2) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e2),op(e2,e4)) != e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([33(3),25(4),14(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="33 25 14"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="41" length="5" max_count="9">

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

  <clause id="14" type="assumption">
    <literal><![CDATA[
      op(e0,e3) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25" type="assumption">
    <literal><![CDATA[
      op(e2,e4) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26" type="assumption">
    <literal><![CDATA[
      op(e3,e0) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e3),op(e3,e0)) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([14(3),26(4),25(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="14 26 25"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="42" length="5" max_count="9">

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

  <clause id="19" type="assumption">
    <literal><![CDATA[
      op(e1,e3) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27" type="assumption">
    <literal><![CDATA[
      op(e3,e1) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31" type="assumption">
    <literal><![CDATA[
      op(e4,e0) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e3),op(e3,e1)) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([19(3),27(4),31(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="19 27 31"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="43" length="5" max_count="9">

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

  <clause id="12" type="assumption">
    <literal><![CDATA[
      op(e0,e1) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24" type="assumption">
    <literal><![CDATA[
      op(e2,e3) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      op(e3,e2) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e3),op(e3,e2)) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([24(3),28(4),12(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="24 28 12"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="44" length="3" max_count="9">

<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="29" type="assumption">
    <literal><![CDATA[
      op(e3,e3) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e3),op(e3,e3)) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([29(3),29(4),29(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="29 29 29"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="45" length="5" max_count="9">

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

  <clause id="18" type="assumption">
    <literal><![CDATA[
      op(e1,e2) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      op(e3,e4) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      op(e4,e3) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e3),op(e3,e4)) != e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([34(3),30(4),18(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="34 30 18"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="46" length="5" max_count="9">

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

  <clause id="15" type="assumption">
    <literal><![CDATA[
      op(e0,e4) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="19" type="assumption">
    <literal><![CDATA[
      op(e1,e3) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31" type="assumption">
    <literal><![CDATA[
      op(e4,e0) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e0,e4),op(e4,e0)) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([15(3),31(4),19(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="15 31 19"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="47" length="5" max_count="9">

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

  <clause id="13" type="assumption">
    <literal><![CDATA[
      op(e0,e2) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20" type="assumption">
    <literal><![CDATA[
      op(e1,e4) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="32" type="assumption">
    <literal><![CDATA[
      op(e4,e1) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e1,e4),op(e4,e1)) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([20(3),32(4),13(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="20 32 13"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="48" length="5" max_count="9">

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

  <clause id="25" type="assumption">
    <literal><![CDATA[
      op(e2,e4) = e3
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26" type="assumption">
    <literal><![CDATA[
      op(e3,e0) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      op(e4,e2) = e0
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e2,e4),op(e4,e2)) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([25(3),33(4),26(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="25 33 26"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="49" length="5" max_count="9">

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

  <clause id="22" type="assumption">
    <literal><![CDATA[
      op(e2,e1) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      op(e3,e4) = e2
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      op(e4,e3) = e1
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e3,e4),op(e4,e3)) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([30(3),34(4),22(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="30 34 22"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

<proof number="50" length="3" max_count="9">

<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="35" type="assumption">
    <literal><![CDATA[
      op(e4,e4) = e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      op(op(e4,e4),op(e4,e4)) != e4
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[copy(36),rewrite([35(3),35(4),35(3)]),xx(a)].">
      <j1 rule="copy" parents="36"/>
      <j2 rule="rewrite" parents="35 35 35"/>
      <j2 rule="xx"/>
    </justification>
  </clause>

</proof>

</proofs>
