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

<!DOCTYPE proofs SYSTEM "proof3.dtd">

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

<proofs number_of_proofs="1">

<source>RI_rezus.out</source>

<heading><![CDATA[
Prover9 (64) version Aug-2007, Aug 2007.
Process 24977 was started by veroff on titan,
Mon Dec  3 08:50:37 2007
The command was "prover9 -f RI_rezus.in".
]]></heading>

<proof number="1" length="119" max_count="98">

<comments><![CDATA[
% Proof 1 at 0.48 (+ 0.00) seconds: "Rezus".
% Length of proof is 119.
% Level of proof is 44.
% Maximum clause weight is 98.
% Given clauses 116.
]]></comments>

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

  <clause id="2" type="assumption">
    <literal><![CDATA[
      P(i(i(x,y),i(i(y,z),i(x,z))))
    ]]></literal>
    <attribute><![CDATA[
      label("B")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="4" type="assumption">
    <literal><![CDATA[
      P(i(x,x))
    ]]></literal>
    <attribute><![CDATA[
      label("I")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      P(i(i(x,i(x,y)),i(x,y)))
    ]]></literal>
    <attribute><![CDATA[
      label("W")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="assumption">
    <literal><![CDATA[
      -P(i(i(i(X,i(i(i(Y,Y),i(i(Z,Z),i(i(U,U),i(i(V,V),i(X,W))))),W)),i(i(i(i(i(V6,V7),i(i(V7,V8),i(V6,V8))),i(i(i(i(i(V9,i(V9,V10)),i(V9,V10)),i(i(i(V11,V12),i(i(V12,V13),i(V11,V13))),V14)),V14),V15)),V15),i(i(V16,i(i(i(V17,V17),i(i(V18,V18),i(i(V19,V19),i(i(V20,V20),i(V16,V21))))),V21)),V22))),V22))
    ]]></literal>
    <attribute><![CDATA[
      answer("Rezus")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8">
    <literal><![CDATA[
      P(i(x,i(i(y,i(x,z)),i(y,z))))
    ]]></literal>
    <justification jstring="[hyper(1,a,3,a,b,3,a)].">
      <j1 rule="hyper" parents="1 3 3"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      P(i(i(i(x,i(y,z)),u),i(i(y,i(x,z)),u)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,3,a)].">
      <j1 rule="hyper" parents="1 2 3"/>
    </justification>
  </clause>

  <clause id="10">
    <literal><![CDATA[
      P(i(i(x,y),i(i(z,x),i(z,y))))
    ]]></literal>
    <justification jstring="[hyper(1,a,3,a,b,2,a)].">
      <j1 rule="hyper" parents="1 3 2"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      P(i(x,i(i(x,y),y)))
    ]]></literal>
    <justification jstring="[hyper(1,a,3,a,b,4,a)].">
      <j1 rule="hyper" parents="1 3 4"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      P(i(x,i(i(x,i(x,y)),y)))
    ]]></literal>
    <justification jstring="[hyper(1,a,3,a,b,5,a)].">
      <j1 rule="hyper" parents="1 3 5"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      P(i(i(i(x,i(i(x,y),y)),z),z))
    ]]></literal>
    <justification jstring="[hyper(1,a,11,a,b,11,a)].">
      <j1 rule="hyper" parents="1 11 11"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      P(i(i(i(i(x,y),y),z),i(x,z)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,11,a)].">
      <j1 rule="hyper" parents="1 2 11"/>
    </justification>
  </clause>

  <clause id="17">
    <literal><![CDATA[
      P(i(i(i(x,x),y),y))
    ]]></literal>
    <justification jstring="[hyper(1,a,11,a,b,4,a)].">
      <j1 rule="hyper" parents="1 11 4"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      P(i(i(i(x,i(i(x,i(x,y)),y)),z),z))
    ]]></literal>
    <justification jstring="[hyper(1,a,11,a,b,12,a)].">
      <j1 rule="hyper" parents="1 11 12"/>
    </justification>
  </clause>

  <clause id="32">
    <literal><![CDATA[
      P(i(i(x,i(i(y,y),z)),i(x,z)))
    ]]></literal>
    <justification jstring="[hyper(1,a,17,a,b,8,a)].">
      <j1 rule="hyper" parents="1 17 8"/>
    </justification>
  </clause>

  <clause id="39">
    <literal><![CDATA[
      P(i(i(x,i(i(y,i(i(y,z),z)),u)),i(x,u)))
    ]]></literal>
    <justification jstring="[hyper(1,a,8,a,b,11,a)].">
      <j1 rule="hyper" parents="1 8 11"/>
    </justification>
  </clause>

  <clause id="49">
    <literal><![CDATA[
      P(i(i(x,y),i(x,i(i(y,z),z))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,11,a)].">
      <j1 rule="hyper" parents="1 10 11"/>
    </justification>
  </clause>

  <clause id="52">
    <literal><![CDATA[
      P(i(i(x,i(y,i(z,u))),i(x,i(z,i(y,u)))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,3,a)].">
      <j1 rule="hyper" parents="1 10 3"/>
    </justification>
  </clause>

  <clause id="53">
    <literal><![CDATA[
      P(i(i(x,i(y,z)),i(x,i(i(z,u),i(y,u)))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,2,a)].">
      <j1 rule="hyper" parents="1 10 2"/>
    </justification>
  </clause>

  <clause id="59">
    <literal><![CDATA[
      P(i(x,i(i(i(i(x,y),y),z),z)))
    ]]></literal>
    <justification jstring="[hyper(1,a,14,a,b,15,a)].">
      <j1 rule="hyper" parents="1 14 15"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      P(i(x,i(i(y,z),i(i(x,y),z))))
    ]]></literal>
    <justification jstring="[hyper(1,a,15,a,b,2,a)].">
      <j1 rule="hyper" parents="1 15 2"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      P(i(i(x,i(y,i(i(z,z),u))),i(x,i(y,u))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,32,a)].">
      <j1 rule="hyper" parents="1 10 32"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      P(i(x,i(i(x,y),i(i(y,z),z))))
    ]]></literal>
    <justification jstring="[hyper(1,a,15,a,b,49,a)].">
      <j1 rule="hyper" parents="1 15 49"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      P(i(i(x,y),i(i(i(z,i(i(z,u),i(i(u,w),w))),x),y)))
    ]]></literal>
    <justification jstring="[hyper(1,a,68,a,b,79,a)].">
      <j1 rule="hyper" parents="1 68 79"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      P(i(i(i(x,i(i(x,y),i(i(y,z),z))),u),u))
    ]]></literal>
    <justification jstring="[hyper(1,a,11,a,b,79,a)].">
      <j1 rule="hyper" parents="1 11 79"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      P(i(i(x,i(i(y,i(i(y,z),i(i(z,u),u))),w)),i(x,w)))
    ]]></literal>
    <justification jstring="[hyper(1,a,8,a,b,79,a)].">
      <j1 rule="hyper" parents="1 8 79"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      P(i(i(i(i(i(i(i(x,i(i(x,i(x,y)),y)),z),z),u),u),w),w))
    ]]></literal>
    <justification jstring="[hyper(1,a,59,a,b,25,a)].">
      <j1 rule="hyper" parents="1 59 25"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      P(i(i(x,i(i(y,i(z,u)),w)),i(x,i(i(z,i(y,u)),w))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,9,a)].">
      <j1 rule="hyper" parents="1 10 9"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      P(i(i(x,i(y,i(z,i(u,w)))),i(x,i(y,i(u,i(z,w))))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,52,a)].">
      <j1 rule="hyper" parents="1 10 52"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      P(i(i(i(x,i(y,i(z,u))),w),i(i(x,i(z,i(y,u))),w)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,52,a)].">
      <j1 rule="hyper" parents="1 2 52"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      P(i(i(x,y),i(i(i(x,z),u),i(i(y,z),u))))
    ]]></literal>
    <justification jstring="[hyper(1,a,53,a,b,2,a)].">
      <j1 rule="hyper" parents="1 53 2"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      P(i(i(x,i(y,i(z,i(i(u,u),w)))),i(x,i(y,i(z,w)))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,73,a)].">
      <j1 rule="hyper" parents="1 10 73"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      P(i(i(i(x,i(y,z)),u),i(i(x,i(y,i(i(w,w),z))),u)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,73,a)].">
      <j1 rule="hyper" parents="1 2 73"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      P(i(i(i(i(x,i(y,i(z,u))),w),v5),i(i(i(x,i(z,i(y,u))),w),v5)))
    ]]></literal>
    <justification jstring="[hyper(1,a,248,a,b,52,a)].">
      <j1 rule="hyper" parents="1 248 52"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      P(i(i(i(i(i(x,i(y,z)),u),w),v5),i(i(i(i(y,i(x,z)),u),w),v5)))
    ]]></literal>
    <justification jstring="[hyper(1,a,248,a,b,9,a)].">
      <j1 rule="hyper" parents="1 248 9"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      P(i(i(i(i(x,y),z),u),i(i(i(i(i(w,i(i(w,v5),i(i(v5,v6),v6))),x),y),z),u)))
    ]]></literal>
    <justification jstring="[hyper(1,a,248,a,b,136,a)].">
      <j1 rule="hyper" parents="1 248 136"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      P(i(i(i(i(x,i(i(y,i(i(y,z),i(i(z,u),u))),w)),v5),v6),i(i(i(x,w),v5),v6)))
    ]]></literal>
    <justification jstring="[hyper(1,a,248,a,b,143,a)].">
      <j1 rule="hyper" parents="1 248 143"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      P(i(i(i(i(x,i(i(y,i(z,u)),w)),v5),v6),i(i(i(x,i(i(z,i(y,u)),w)),v5),v6)))
    ]]></literal>
    <justification jstring="[hyper(1,a,248,a,b,172,a)].">
      <j1 rule="hyper" parents="1 248 172"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      P(i(i(i(x,i(i(y,i(z,u)),w)),v5),i(i(x,i(i(z,i(y,u)),w)),v5)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,172,a)].">
      <j1 rule="hyper" parents="1 2 172"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      P(i(i(x,i(y,i(z,i(u,i(w,v5))))),i(x,i(y,i(z,i(w,i(u,v5)))))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,208,a)].">
      <j1 rule="hyper" parents="1 10 208"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      P(i(i(i(x,i(y,i(z,i(u,w)))),v5),i(i(x,i(y,i(u,i(z,w)))),v5)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,208,a)].">
      <j1 rule="hyper" parents="1 2 208"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      P(i(i(i(x,i(y,i(z,u))),w),i(i(z,i(x,i(y,u))),w)))
    ]]></literal>
    <justification jstring="[hyper(1,a,172,a,b,211,a)].">
      <j1 rule="hyper" parents="1 172 211"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      P(i(i(x,i(i(y,i(z,i(u,w))),v5)),i(x,i(i(y,i(u,i(z,w))),v5))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,211,a)].">
      <j1 rule="hyper" parents="1 10 211"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      P(i(i(x,i(y,i(z,i(u,i(i(w,w),v5))))),i(x,i(y,i(z,i(u,v5))))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,262,a)].">
      <j1 rule="hyper" parents="1 10 262"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      P(i(i(x,i(i(y,i(z,u)),w)),i(x,i(i(y,i(z,i(i(v5,v5),u))),w))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,264,a)].">
      <j1 rule="hyper" parents="1 10 264"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      P(i(i(i(i(i(i(i(x,i(i(x,i(x,y)),y)),z),z),u),u),w),i(i(w,v5),v5)))
    ]]></literal>
    <justification jstring="[hyper(1,a,141,a,b,160,a)].">
      <j1 rule="hyper" parents="1 141 160"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      P(i(i(i(i(i(i(x,i(y,i(z,u))),w),v5),v6),v7),i(i(i(i(i(x,i(z,i(y,u))),w),v5),v6),v7)))
    ]]></literal>
    <justification jstring="[hyper(1,a,248,a,b,303,a)].">
      <j1 rule="hyper" parents="1 248 303"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      P(i(i(x,i(i(i(i(y,i(z,u)),w),v5),v6)),i(x,i(i(i(i(z,i(y,u)),w),v5),v6))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,312,a)].">
      <j1 rule="hyper" parents="1 10 312"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      P(i(i(i(i(i(i(x,i(y,z)),u),w),v5),v6),i(i(i(i(i(y,i(x,z)),u),w),v5),v6)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,312,a)].">
      <j1 rule="hyper" parents="1 2 312"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      P(i(i(x,i(i(y,i(i(z,i(u,w)),v5)),v6)),i(x,i(i(y,i(i(u,i(z,w)),v5)),v6))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,384,a)].">
      <j1 rule="hyper" parents="1 10 384"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      P(i(i(i(x,i(y,i(z,i(u,i(w,v5))))),v6),i(i(x,i(y,i(z,i(w,i(u,v5))))),v6)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,416,a)].">
      <j1 rule="hyper" parents="1 2 416"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      P(i(i(x,i(i(y,i(z,i(u,i(w,v5)))),v6)),i(x,i(i(y,i(z,i(w,i(u,v5)))),v6))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,418,a)].">
      <j1 rule="hyper" parents="1 10 418"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      P(i(i(i(i(x,i(i(y,i(z,i(u,w))),v5)),v6),v7),i(i(i(x,i(i(y,i(u,i(z,w))),v5)),v6),v7)))
    ]]></literal>
    <justification jstring="[hyper(1,a,248,a,b,450,a)].">
      <j1 rule="hyper" parents="1 248 450"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      P(i(i(i(x,i(i(y,i(z,i(u,w))),v5)),v6),i(i(x,i(i(y,i(u,i(z,w))),v5)),v6)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,450,a)].">
      <j1 rule="hyper" parents="1 2 450"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      P(i(i(i(x,i(y,i(z,i(u,w)))),v5),i(i(x,i(y,i(z,i(u,i(i(v6,v6),w))))),v5)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,482,a)].">
      <j1 rule="hyper" parents="1 2 482"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      P(i(i(i(x,i(i(y,i(z,i(i(u,u),w))),v5)),v6),i(i(x,i(i(y,i(z,w)),v5)),v6)))
    ]]></literal>
    <justification jstring="[hyper(1,a,2,a,b,518,a)].">
      <j1 rule="hyper" parents="1 2 518"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      P(i(i(i(i(i(i(i(x,i(i(x,i(x,y)),y)),i(i(z,i(i(z,u),i(i(u,w),w))),v5)),v5),v6),v6),v7),v7))
    ]]></literal>
    <justification jstring="[hyper(1,a,580,a,b,347,a)].">
      <j1 rule="hyper" parents="1 580 347"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      P(i(i(x,i(i(i(y,i(i(z,i(u,w)),v5)),v6),v7)),i(x,i(i(i(y,i(i(u,i(z,w)),v5)),v6),v7))))
    ]]></literal>
    <justification jstring="[hyper(1,a,10,a,b,368,a)].">
      <j1 rule="hyper" parents="1 10 368"/>
    </justification>
  </clause>

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</proof>

</proofs>
