<?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="1" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="mex.mlw"/>
<theory name="MexArray" proved="true">
 <goal name="mex&#39;vc" expl="VC for mex" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="mex&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="3133"/></proof>
  </goal>
  <goal name="mex&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="4891"/></proof>
  </goal>
  <goal name="mex&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="4528"/></proof>
  </goal>
  <goal name="mex&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="4691"/></proof>
  </goal>
  <goal name="mex&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="5056"/></proof>
  </goal>
  <goal name="mex&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="127"/></proof>
  </goal>
  <goal name="mex&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="46"/></proof>
  </goal>
  <goal name="mex&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="32"/></proof>
  </goal>
  <goal name="mex&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="39"/></proof>
  </goal>
  <goal name="mex&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="4654"/></proof>
  </goal>
  <goal name="mex&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="4743"/></proof>
  </goal>
  <goal name="mex&#39;vc.11" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="4889"/></proof>
  </goal>
  <goal name="mex&#39;vc.12" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="5356"/></proof>
  </goal>
  <goal name="mex&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="5350"/></proof>
  </goal>
  <goal name="mex&#39;vc.14" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="5172"/></proof>
  </goal>
  <goal name="mex&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="5623"/></proof>
  </goal>
  <goal name="mex&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="7454"/></proof>
  </goal>
  <goal name="mex&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="5967"/></proof>
  </goal>
  <goal name="mex&#39;vc.18" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="5171"/></proof>
  </goal>
  <goal name="mex&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="5608"/></proof>
  </goal>
  <goal name="mex&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="8311"/></proof>
  </goal>
  <goal name="mex&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="6767"/></proof>
  </goal>
  <goal name="mex&#39;vc.22" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="5116"/></proof>
  </goal>
  <goal name="mex&#39;vc.23" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="6211"/></proof>
  </goal>
  <goal name="mex&#39;vc.24" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="5286"/></proof>
  </goal>
  <goal name="mex&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="92"/></proof>
  </goal>
  <goal name="mex&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="7831"/></proof>
  </goal>
  <goal name="mex&#39;vc.27" expl="out of loop bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="9766"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="MexArrayInPlace" proved="true">
 <goal name="mex&#39;vc" expl="VC for mex" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="mex&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="6874"/></proof>
  </goal>
  <goal name="mex&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="6252"/></proof>
  </goal>
  <goal name="mex&#39;vc.2" expl="loop invariant init" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="mex&#39;vc.2.0" expl="loop invariant init" proved="true">
   <proof prover="1"><result status="valid" time="0.01" steps="6806"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mex&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="6861"/></proof>
  </goal>
  <goal name="mex&#39;vc.4" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="7485"/></proof>
  </goal>
  <goal name="mex&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="7049"/></proof>
  </goal>
  <goal name="mex&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="7135"/></proof>
  </goal>
  <goal name="mex&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="28474"/></proof>
  </goal>
  <goal name="mex&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="6994"/></proof>
  </goal>
  <goal name="mex&#39;vc.9" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="7566"/></proof>
  </goal>
  <goal name="mex&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="7135"/></proof>
  </goal>
  <goal name="mex&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.22" steps="33763"/></proof>
  </goal>
  <goal name="mex&#39;vc.12" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="mex&#39;vc.12.0" expl="loop invariant preservation" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="80"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mex&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="6961"/></proof>
  </goal>
  <goal name="mex&#39;vc.14" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="7579"/></proof>
  </goal>
  <goal name="mex&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="7153"/></proof>
  </goal>
  <goal name="mex&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="7228"/></proof>
  </goal>
  <goal name="mex&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="9339"/></proof>
  </goal>
  <goal name="mex&#39;vc.18" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="7080"/></proof>
  </goal>
  <goal name="mex&#39;vc.19" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.30" steps="53687"/></proof>
  </goal>
  <goal name="mex&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="6688"/></proof>
  </goal>
  <goal name="mex&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="24873"/></proof>
  </goal>
  <goal name="mex&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="15514"/></proof>
  </goal>
  <goal name="mex&#39;vc.23" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.14" steps="391249"/></proof>
  </goal>
  <goal name="mex&#39;vc.24" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="6753"/></proof>
  </goal>
  <goal name="mex&#39;vc.25" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="7190"/></proof>
  </goal>
  <goal name="mex&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="7276"/></proof>
  </goal>
  <goal name="mex&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="8672"/></proof>
  </goal>
  <goal name="mex&#39;vc.28" expl="postcondition" proved="true">
  <transf name="assert" proved="true" arg1="(mem x a)">
   <goal name="mex&#39;vc.28.0" expl="asserted formula" proved="true">
   <transf name="assert" proved="true" arg1="(a[x] = x)">
    <goal name="mex&#39;vc.28.0.0" expl="asserted formula" proved="true">
    <proof prover="1"><result status="valid" time="0.02" steps="8176"/></proof>
    </goal>
    <goal name="mex&#39;vc.28.0.1" expl="asserted formula" proved="true">
    <proof prover="1"><result status="valid" time="0.02" steps="8740"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="mex&#39;vc.28.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.02" steps="7381"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mex&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="8000"/></proof>
  </goal>
  <goal name="mex&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="7120"/></proof>
  </goal>
  <goal name="mex&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="8489"/></proof>
  </goal>
  <goal name="mex&#39;vc.32" expl="postcondition" proved="true">
  <transf name="assert" proved="true" arg1="(mem x a)">
   <goal name="mex&#39;vc.32.0" expl="asserted formula" proved="true">
   <transf name="assert" proved="true" arg1="(a[x] = x)">
    <goal name="mex&#39;vc.32.0.0" expl="asserted formula" proved="true">
    <proof prover="1"><result status="valid" time="0.03" steps="7906"/></proof>
    </goal>
    <goal name="mex&#39;vc.32.0.1" expl="asserted formula" proved="true">
    <proof prover="1"><result status="valid" time="0.03" steps="8157"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="mex&#39;vc.32.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.02" steps="7243"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mex&#39;vc.33" expl="out of loop bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="7157"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
