<?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="2">

<source>SET667+3.out</source>

<heading><![CDATA[
FOF-Prover9 (32) version August-2006A, August 2006.
Process 11286 was started by mccune on cleo.thornwood,
Sat Aug 12 20:59:29 2006
The command was "/home/mccune/bin/fof-prover9 -f SET667+3.in".
]]></heading>

<proof number="1" length="33" max_count="21">

<comments><![CDATA[
% Proof 1 at 0.13 (+ 0.01) seconds.
% Length of proof is 33.
% Level of proof is 7.
% Maximum clause weight is 21.
% Given clauses 263.
]]></comments>

  <clause id="2">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      ilf_type(A,binary_relation_type)
    ]]></literal>
    <literal><![CDATA[
      -relation_like(A)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,subset_type(cross_product(A,B)))
    ]]></literal>
    <literal><![CDATA[
      relation_like(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,binary_relation_type)
    ]]></literal>
    <literal><![CDATA[
      -member(ordered_pair(A,B),C)
    ]]></literal>
    <literal><![CDATA[
      member(A,domain_of(C))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -member(B,A)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,set_type)
    ]]></literal>
    <literal><![CDATA[
      member(ordered_pair(B,C),identity_relation_of(A))
    ]]></literal>
    <literal><![CDATA[
      C != B
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,relation_type(A,B))
    ]]></literal>
    <literal><![CDATA[
      ilf_type(C,subset_type(cross_product(A,B)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      subset(A,B)
    ]]></literal>
    <literal><![CDATA[
      member(f2(A,B),A)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      subset(A,B)
    ]]></literal>
    <literal><![CDATA[
      -member(f2(A,B),B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,set_type)
    ]]></literal>
    <literal><![CDATA[
      -member(C,A)
    ]]></literal>
    <literal><![CDATA[
      member(C,B)
    ]]></literal>
    <literal><![CDATA[
      -subset(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,relation_type(A,B))
    ]]></literal>
    <literal><![CDATA[
      domain(A,B,C) = domain_of(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      ilf_type(A,set_type)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      ilf_type(c5,relation_type(c2,c3))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="80">
    <literal><![CDATA[
      subset(identity_relation_of(c4),c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="81">
    <literal><![CDATA[
      -subset(c4,domain(c2,c3,c5))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="92">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,subset_type(cross_product(A,B)))
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,set_type)
    ]]></literal>
    <literal><![CDATA[
      ilf_type(C,binary_relation_type)
    ]]></literal>
    <justification jstring="[resolve(9,d,2,c)].">
      <j1 rule="resolve" parents="9 2"/>
    </justification>
  </clause>

  <clause id="93">
    <literal><![CDATA[
      -ilf_type(A,subset_type(cross_product(B,C)))
    ]]></literal>
    <literal><![CDATA[
      ilf_type(A,binary_relation_type)
    ]]></literal>
    <justification jstring="[copy(92),unit_del(a,78),unit_del(b,78),unit_del(d,78)].">
      <j1 rule="copy" parents="92"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="106">
    <literal><![CDATA[
      -member(A,B)
    ]]></literal>
    <literal><![CDATA[
      member(ordered_pair(A,A),identity_relation_of(B))
    ]]></literal>
    <justification jstring="[factor(15,b,d),xx(e),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="factor" parents="15"/>
      <j2 rule="xx"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      -ilf_type(A,relation_type(B,C))
    ]]></literal>
    <literal><![CDATA[
      domain(B,C,A) = domain_of(A)
    ]]></literal>
    <justification jstring="[back_unit_del(74),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="74"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      -member(A,B)
    ]]></literal>
    <literal><![CDATA[
      member(A,C)
    ]]></literal>
    <literal><![CDATA[
      -subset(B,C)
    ]]></literal>
    <justification jstring="[back_unit_del(25),unit_del(a,78),unit_del(b,78),unit_del(c,78)].">
      <j1 rule="back_unit_del" parents="25"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      subset(A,B)
    ]]></literal>
    <literal><![CDATA[
      -member(f2(A,B),B)
    ]]></literal>
    <justification jstring="[back_unit_del(24),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="24"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      subset(A,B)
    ]]></literal>
    <literal><![CDATA[
      member(f2(A,B),A)
    ]]></literal>
    <justification jstring="[back_unit_del(23),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="23"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      -ilf_type(A,relation_type(B,C))
    ]]></literal>
    <literal><![CDATA[
      ilf_type(A,subset_type(cross_product(B,C)))
    ]]></literal>
    <justification jstring="[back_unit_del(20),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="20"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      -ilf_type(A,binary_relation_type)
    ]]></literal>
    <literal><![CDATA[
      -member(ordered_pair(B,C),A)
    ]]></literal>
    <literal><![CDATA[
      member(B,domain_of(A))
    ]]></literal>
    <justification jstring="[back_unit_del(11),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="11"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      domain(c2,c3,c5) = domain_of(c5)
    ]]></literal>
    <justification jstring="[resolve(151,a,79,a)].">
      <j1 rule="resolve" parents="151 79"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      -subset(c4,domain_of(c5))
    ]]></literal>
    <justification jstring="[back_rewrite(81),rewrite(192(5))].">
      <j1 rule="back_rewrite" parents="81"/>
      <j2 rule="rewrite" parents="192"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      -member(A,identity_relation_of(c4))
    ]]></literal>
    <literal><![CDATA[
      member(A,c5)
    ]]></literal>
    <justification jstring="[resolve(173,c,80,a)].">
      <j1 rule="resolve" parents="173 80"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      ilf_type(c5,subset_type(cross_product(c2,c3)))
    ]]></literal>
    <justification jstring="[resolve(177,a,79,a)].">
      <j1 rule="resolve" parents="177 79"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      member(f2(c4,domain_of(c5)),c4)
    ]]></literal>
    <justification jstring="[resolve(194,a,175,a)].">
      <j1 rule="resolve" parents="194 175"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      -member(f2(c4,domain_of(c5)),domain_of(c5))
    ]]></literal>
    <justification jstring="[ur(174,a,194,a)].">
      <j1 rule="ur" parents="174 194"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      ilf_type(c5,binary_relation_type)
    ]]></literal>
    <justification jstring="[resolve(238,a,93,a)].">
      <j1 rule="resolve" parents="238 93"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      -member(ordered_pair(f2(c4,domain_of(c5)),A),c5)
    ]]></literal>
    <justification jstring="[ur(184,a,365,a,c,259,a)].">
      <j1 rule="ur" parents="184 365 259"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      member(ordered_pair(f2(c4,domain_of(c5)),f2(c4,domain_of(c5))),identity_relation_of(c4))
    ]]></literal>
    <justification jstring="[resolve(258,a,106,a)].">
      <j1 rule="resolve" parents="258 106"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      -member(ordered_pair(f2(c4,domain_of(c5)),A),identity_relation_of(c4))
    ]]></literal>
    <justification jstring="[ur(231,b,397,a)].">
      <j1 rule="ur" parents="231 397"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(1557,a,454,a)].">
      <j1 rule="resolve" parents="1557 454"/>
    </justification>
  </clause>

</proof>

<proof number="2" length="33" max_count="21">

<comments><![CDATA[
% Proof 1 at 0.12 (+ 0.01) seconds.
% Length of proof is 33.
% Level of proof is 7.
% Maximum clause weight is 21.
% Given clauses 263.
]]></comments>

  <clause id="2">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      ilf_type(A,binary_relation_type)
    ]]></literal>
    <literal><![CDATA[
      -relation_like(A)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,subset_type(cross_product(A,B)))
    ]]></literal>
    <literal><![CDATA[
      relation_like(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,binary_relation_type)
    ]]></literal>
    <literal><![CDATA[
      -member(ordered_pair(A,B),C)
    ]]></literal>
    <literal><![CDATA[
      member(B,range_of(C))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="15">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -member(B,A)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,set_type)
    ]]></literal>
    <literal><![CDATA[
      member(ordered_pair(B,C),identity_relation_of(A))
    ]]></literal>
    <literal><![CDATA[
      C != B
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,relation_type(A,B))
    ]]></literal>
    <literal><![CDATA[
      ilf_type(C,subset_type(cross_product(A,B)))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="23">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      subset(A,B)
    ]]></literal>
    <literal><![CDATA[
      member(f2(A,B),A)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      subset(A,B)
    ]]></literal>
    <literal><![CDATA[
      -member(f2(A,B),B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,set_type)
    ]]></literal>
    <literal><![CDATA[
      -member(C,A)
    ]]></literal>
    <literal><![CDATA[
      member(C,B)
    ]]></literal>
    <literal><![CDATA[
      -subset(A,B)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,relation_type(A,B))
    ]]></literal>
    <literal><![CDATA[
      range(A,B,C) = range_of(C)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      ilf_type(A,set_type)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      ilf_type(c5,relation_type(c2,c3))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="80">
    <literal><![CDATA[
      subset(identity_relation_of(c4),c5)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="81">
    <literal><![CDATA[
      -subset(c4,range(c2,c3,c5))
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="92">
    <literal><![CDATA[
      -ilf_type(A,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(B,set_type)
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,subset_type(cross_product(A,B)))
    ]]></literal>
    <literal><![CDATA[
      -ilf_type(C,set_type)
    ]]></literal>
    <literal><![CDATA[
      ilf_type(C,binary_relation_type)
    ]]></literal>
    <justification jstring="[resolve(9,d,2,c)].">
      <j1 rule="resolve" parents="9 2"/>
    </justification>
  </clause>

  <clause id="93">
    <literal><![CDATA[
      -ilf_type(A,subset_type(cross_product(B,C)))
    ]]></literal>
    <literal><![CDATA[
      ilf_type(A,binary_relation_type)
    ]]></literal>
    <justification jstring="[copy(92),unit_del(a,78),unit_del(b,78),unit_del(d,78)].">
      <j1 rule="copy" parents="92"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="106">
    <literal><![CDATA[
      -member(A,B)
    ]]></literal>
    <literal><![CDATA[
      member(ordered_pair(A,A),identity_relation_of(B))
    ]]></literal>
    <justification jstring="[factor(15,b,d),xx(e),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="factor" parents="15"/>
      <j2 rule="xx"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      -ilf_type(A,relation_type(B,C))
    ]]></literal>
    <literal><![CDATA[
      range(B,C,A) = range_of(A)
    ]]></literal>
    <justification jstring="[back_unit_del(76),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="76"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      -member(A,B)
    ]]></literal>
    <literal><![CDATA[
      member(A,C)
    ]]></literal>
    <literal><![CDATA[
      -subset(B,C)
    ]]></literal>
    <justification jstring="[back_unit_del(25),unit_del(a,78),unit_del(b,78),unit_del(c,78)].">
      <j1 rule="back_unit_del" parents="25"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      subset(A,B)
    ]]></literal>
    <literal><![CDATA[
      -member(f2(A,B),B)
    ]]></literal>
    <justification jstring="[back_unit_del(24),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="24"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      subset(A,B)
    ]]></literal>
    <literal><![CDATA[
      member(f2(A,B),A)
    ]]></literal>
    <justification jstring="[back_unit_del(23),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="23"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      -ilf_type(A,relation_type(B,C))
    ]]></literal>
    <literal><![CDATA[
      ilf_type(A,subset_type(cross_product(B,C)))
    ]]></literal>
    <justification jstring="[back_unit_del(20),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="20"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      -ilf_type(A,binary_relation_type)
    ]]></literal>
    <literal><![CDATA[
      -member(ordered_pair(B,C),A)
    ]]></literal>
    <literal><![CDATA[
      member(C,range_of(A))
    ]]></literal>
    <justification jstring="[back_unit_del(12),unit_del(a,78),unit_del(b,78)].">
      <j1 rule="back_unit_del" parents="12"/>
      <j2 rule="unit_del" parents="78"/>
      <j2 rule="unit_del" parents="78"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      range(c2,c3,c5) = range_of(c5)
    ]]></literal>
    <justification jstring="[resolve(149,a,79,a)].">
      <j1 rule="resolve" parents="149 79"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      -subset(c4,range_of(c5))
    ]]></literal>
    <justification jstring="[back_rewrite(81),rewrite(189(5))].">
      <j1 rule="back_rewrite" parents="81"/>
      <j2 rule="rewrite" parents="189"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      -member(A,identity_relation_of(c4))
    ]]></literal>
    <literal><![CDATA[
      member(A,c5)
    ]]></literal>
    <justification jstring="[resolve(173,c,80,a)].">
      <j1 rule="resolve" parents="173 80"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      ilf_type(c5,subset_type(cross_product(c2,c3)))
    ]]></literal>
    <justification jstring="[resolve(177,a,79,a)].">
      <j1 rule="resolve" parents="177 79"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      member(f2(c4,range_of(c5)),c4)
    ]]></literal>
    <justification jstring="[resolve(191,a,175,a)].">
      <j1 rule="resolve" parents="191 175"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      -member(f2(c4,range_of(c5)),range_of(c5))
    ]]></literal>
    <justification jstring="[ur(174,a,191,a)].">
      <j1 rule="ur" parents="174 191"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      ilf_type(c5,binary_relation_type)
    ]]></literal>
    <justification jstring="[resolve(238,a,93,a)].">
      <j1 rule="resolve" parents="238 93"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      -member(ordered_pair(A,f2(c4,range_of(c5))),c5)
    ]]></literal>
    <justification jstring="[ur(183,a,365,a,c,259,a)].">
      <j1 rule="ur" parents="183 365 259"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      member(ordered_pair(f2(c4,range_of(c5)),f2(c4,range_of(c5))),identity_relation_of(c4))
    ]]></literal>
    <justification jstring="[resolve(258,a,106,a)].">
      <j1 rule="resolve" parents="258 106"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      -member(ordered_pair(A,f2(c4,range_of(c5))),identity_relation_of(c4))
    ]]></literal>
    <justification jstring="[ur(231,b,397,a)].">
      <j1 rule="ur" parents="231 397"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      $F
    ]]></literal>
    <justification jstring="[resolve(1557,a,454,a)].">
      <j1 rule="resolve" parents="1557 454"/>
    </justification>
  </clause>

</proof>

</proofs>
