<?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>3.4.out</source>

<heading><![CDATA[
Prover9 (64) version Aug-2007, Aug 2007.
Process 32400 was started by veroff on io,
Mon Jan 21 11:14:49 2008
The command was "prover9 -f 3.4.in".
]]></heading>

<proof number="1" length="6" max_count="9">

<comments><![CDATA[
% Proof 1 at 0.02 (+ 0.01) seconds: "(BCK5)".
% Length of proof is 6.
% Level of proof is 2.
% Maximum clause weight is 9.
% Given clauses 38.
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      x => ((x => y) => y) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("(BCK5)")
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="35" type="assumption">
    <literal><![CDATA[
      x ^ ((x => y) => y) = x
    ]]></literal>
    <attribute><![CDATA[
      label("(3.7)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="42" type="assumption">
    <literal><![CDATA[
      (x ^ y) => y = 1
    ]]></literal>
    <attribute><![CDATA[
      label("(3.11)")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="48" type="deny">
    <literal><![CDATA[
      c1 => ((c1 => c2) => c2) != 1
    ]]></literal>
    <attribute><![CDATA[
      label("(BCK5)")
    ]]></attribute>
    <attribute><![CDATA[
      answer("(BCK5)")
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      x => ((x => y) => y) = 1
    ]]></literal>
    <justification jstring="[para(35(a,1),42(a,1,1))].">
      <j1 rule="para" parents="35 42"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("(BCK5)")
    ]]></attribute>
    <justification jstring="[resolve(589,a,48,a)].">
      <j1 rule="resolve" parents="589 48"/>
    </justification>
  </clause>

</proof>

</proofs>
