<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.0.0" timelimit="16" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml">
<path name=".."/><path name=".."/><path name=".."/><path name="stdlib"/>
<path name="pigeon.mlw"/>
<theory name="Pigeonhole" proved="true">
 <goal name="pigeonhole&#39;vc" expl="VC for pigeonhole" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="pigeonhole&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="431"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="628"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="1459"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.3" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="1591"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="792"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="10"/></proof>
  <proof prover="3"><result status="valid" time="0.01" steps="1256"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="2124"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="8727"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.8" expl="out of loop bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="8"/></proof>
  <proof prover="3"><result status="valid" time="0.01" steps="1335"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="904"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="4"/></proof>
  <proof prover="3"><result status="valid" time="0.01" steps="511"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.11" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="1716"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.12" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="738"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="805"/></proof>
  </goal>
  <goal name="pigeonhole&#39;vc.14" expl="out of loop bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="611"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="ListAndSet">
 <goal name="corner">
 </goal>
 <goal name="pigeon_0" proved="true">
 <transf name="unfold" proved="true" arg1="pigeon_set">
  <goal name="pigeon_0.0" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="pigeon_0.0.0" proved="true">
   <transf name="destruct_term" proved="true" arg1="l">
    <goal name="pigeon_0.0.0.0" proved="true">
    <transf name="assert" proved="true" arg1="(mem x1 empty)">
     <goal name="pigeon_0.0.0.0.0" expl="asserted formula" proved="true">
     <proof prover="2"><result status="valid" time="0.06" steps="14434"/></proof>
     </goal>
     <goal name="pigeon_0.0.0.0.1" proved="true">
     <proof prover="2"><result status="valid" time="0.05" steps="13666"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="pigeon_0.0.0.1" proved="true">
    <proof prover="2"><result status="valid" time="0.04" steps="13607"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="pigeon_1">
 </goal>
 <goal name="pigeon_2" proved="true">
 <proof prover="2"><result status="valid" time="0.05" steps="9412"/></proof>
 </goal>
 <goal name="pigeonhole" proved="true">
 <proof prover="0"><result status="valid" time="0.84" steps="1633487"/></proof>
 </goal>
</theory>
</file>
</why3session>
