<?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="4.12.2" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.4.1" 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="0.020000" steps="2763"/></proof>
  </goal>
  <goal name="mex&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4265"/></proof>
  </goal>
  <goal name="mex&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="4003"/></proof>
  </goal>
  <goal name="mex&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4136"/></proof>
  </goal>
  <goal name="mex&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="4410"/></proof>
  </goal>
  <goal name="mex&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="20950"/></proof>
  </goal>
  <goal name="mex&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="23903"/></proof>
  </goal>
  <goal name="mex&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="19970"/></proof>
  </goal>
  <goal name="mex&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="21114"/></proof>
  </goal>
  <goal name="mex&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4099"/></proof>
  </goal>
  <goal name="mex&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4188"/></proof>
  </goal>
  <goal name="mex&#39;vc.11" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4334"/></proof>
  </goal>
  <goal name="mex&#39;vc.12" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="4693"/></proof>
  </goal>
  <goal name="mex&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="4686"/></proof>
  </goal>
  <goal name="mex&#39;vc.14" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4583"/></proof>
  </goal>
  <goal name="mex&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="4930"/></proof>
  </goal>
  <goal name="mex&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.050000" steps="6737"/></proof>
  </goal>
  <goal name="mex&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="5266"/></proof>
  </goal>
  <goal name="mex&#39;vc.18" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4581"/></proof>
  </goal>
  <goal name="mex&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="4918"/></proof>
  </goal>
  <goal name="mex&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="7598"/></proof>
  </goal>
  <goal name="mex&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="6054"/></proof>
  </goal>
  <goal name="mex&#39;vc.22" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4540"/></proof>
  </goal>
  <goal name="mex&#39;vc.23" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="5571"/></proof>
  </goal>
  <goal name="mex&#39;vc.24" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4731"/></proof>
  </goal>
  <goal name="mex&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="26761"/></proof>
  </goal>
  <goal name="mex&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="7155"/></proof>
  </goal>
  <goal name="mex&#39;vc.27" expl="out of loop bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="9411"/></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="0.030000" steps="6504"/></proof>
  </goal>
  <goal name="mex&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="5942"/></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="0.010000" steps="6545"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mex&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="6495"/></proof>
  </goal>
  <goal name="mex&#39;vc.4" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="7142"/></proof>
  </goal>
  <goal name="mex&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="6702"/></proof>
  </goal>
  <goal name="mex&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="6775"/></proof>
  </goal>
  <goal name="mex&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="27577"/></proof>
  </goal>
  <goal name="mex&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="6664"/></proof>
  </goal>
  <goal name="mex&#39;vc.9" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="7237"/></proof>
  </goal>
  <goal name="mex&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="6822"/></proof>
  </goal>
  <goal name="mex&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.220000" steps="33436"/></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="0"><result status="valid" time="0.020000" steps="42268"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mex&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="6627"/></proof>
  </goal>
  <goal name="mex&#39;vc.14" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="7228"/></proof>
  </goal>
  <goal name="mex&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="6813"/></proof>
  </goal>
  <goal name="mex&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="6876"/></proof>
  </goal>
  <goal name="mex&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="8987"/></proof>
  </goal>
  <goal name="mex&#39;vc.18" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="6728"/></proof>
  </goal>
  <goal name="mex&#39;vc.19" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.300000" steps="53277"/></proof>
  </goal>
  <goal name="mex&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="6377"/></proof>
  </goal>
  <goal name="mex&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.150000" steps="24519"/></proof>
  </goal>
  <goal name="mex&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="15160"/></proof>
  </goal>
  <goal name="mex&#39;vc.23" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="427"/></proof>
  </goal>
  <goal name="mex&#39;vc.24" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="6444"/></proof>
  </goal>
  <goal name="mex&#39;vc.25" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="6824"/></proof>
  </goal>
  <goal name="mex&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="6883"/></proof>
  </goal>
  <goal name="mex&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="8279"/></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="0.020000" steps="7783"/></proof>
    </goal>
    <goal name="mex&#39;vc.28.0.1" expl="asserted formula" proved="true">
    <proof prover="1"><result status="valid" time="0.020000" steps="8347"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="mex&#39;vc.28.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="6988"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mex&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="7605"/></proof>
  </goal>
  <goal name="mex&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="6763"/></proof>
  </goal>
  <goal name="mex&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="8122"/></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="0.030000" steps="7540"/></proof>
    </goal>
    <goal name="mex&#39;vc.32.0.1" expl="asserted formula" proved="true">
    <proof prover="1"><result status="valid" time="0.030000" steps="7791"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="mex&#39;vc.32.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="6877"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mex&#39;vc.33" expl="out of loop bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="6789"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
