<?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="Eprover" version="2.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.1.0" timelimit="15" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name=".."/><path name=".."/><path name="stdlib"/>
<path name="witness.mlw"/>
<theory name="Nat" proved="true">
 <goal name="witness&#39;vc" expl="VC for witness" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="witness&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3856"/></proof>
  </goal>
  <goal name="witness&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3685"/></proof>
  </goal>
  <goal name="witness&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3179"/></proof>
  </goal>
  <goal name="witness&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3429"/></proof>
  </goal>
  <goal name="witness&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="120"/></proof>
  </goal>
  <goal name="witness&#39;vc.5" expl="variant decrease" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="witness&#39;vc.5.0" expl="variant decrease" proved="true">
   <proof prover="2" timelimit="5"><result status="valid" time="0.020000" steps="3876"/></proof>
   </goal>
   <goal name="witness&#39;vc.5.1" expl="variant decrease" proved="true">
   <transf name="remove" proved="true" arg1="acc,well_founded,r">
    <goal name="witness&#39;vc.5.1.0" expl="variant decrease" proved="true">
    <proof prover="1"><result status="valid" time="0.360000"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="witness&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3931"/></proof>
  </goal>
  <goal name="witness&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="3653"/></proof>
  </goal>
  <goal name="witness&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3460"/></proof>
  </goal>
  <goal name="witness&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3238"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
