<?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="2" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="mergesort_queue.mlw"/>
<theory name="MergesortQueue" proved="true">
 <goal name="TO.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="6"/></proof>
 </goal>
 <goal name="TO.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="10"/></proof>
 </goal>
 <goal name="TO.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="8"/></proof>
 </goal>
 <goal name="merge&#39;vc" expl="VC for merge" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="merge&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="36"/></proof>
  </goal>
  <goal name="merge&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="32"/></proof>
  </goal>
  <goal name="merge&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="34"/></proof>
  </goal>
  <goal name="merge&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="merge&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="51"/></proof>
  </goal>
  <goal name="merge&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="merge&#39;vc.6" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="104"/></proof>
  </goal>
  <goal name="merge&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.19" steps="783"/></proof>
  </goal>
  <goal name="merge&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="93"/></proof>
  </goal>
  <goal name="merge&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="449"/></proof>
  </goal>
  <goal name="merge&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="95"/></proof>
  </goal>
  <goal name="merge&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="128"/></proof>
  </goal>
  <goal name="merge&#39;vc.12" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="merge&#39;vc.13" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="104"/></proof>
  </goal>
  <goal name="merge&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.20" steps="751"/></proof>
  </goal>
  <goal name="merge&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="431"/></proof>
  </goal>
  <goal name="merge&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="95"/></proof>
  </goal>
  <goal name="merge&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="95"/></proof>
  </goal>
  <goal name="merge&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="128"/></proof>
  </goal>
  <goal name="merge&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="merge&#39;vc.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="merge&#39;vc.21" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="32"/></proof>
  </goal>
  <goal name="merge&#39;vc.22" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="110"/></proof>
  </goal>
  <goal name="merge&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.18" steps="870"/></proof>
  </goal>
  <goal name="merge&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.12" steps="436"/></proof>
  </goal>
  <goal name="merge&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="2.77" steps="11111"/></proof>
  </goal>
  <goal name="merge&#39;vc.26" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="100"/></proof>
  </goal>
  <goal name="merge&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="138"/></proof>
  </goal>
  <goal name="merge&#39;vc.28" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="32"/></proof>
  </goal>
  <goal name="merge&#39;vc.29" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="114"/></proof>
  </goal>
  <goal name="merge&#39;vc.30" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.62" steps="3139"/></proof>
  </goal>
  <goal name="merge&#39;vc.31" expl="loop invariant preservation" proved="true">
  <proof prover="6"><result status="valid" time="0.50" steps="81968"/></proof>
  </goal>
  <goal name="merge&#39;vc.32" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="760"/></proof>
  </goal>
  <goal name="merge&#39;vc.33" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="105"/></proof>
  </goal>
  <goal name="merge&#39;vc.34" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="142"/></proof>
  </goal>
  <goal name="merge&#39;vc.35" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="merge&#39;vc.36" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="merge&#39;vc.37" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.21" steps="49978"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="mergesort&#39;vc" expl="VC for mergesort" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="mergesort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="49"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="20"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.5" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="237"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.45" steps="1948"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="245"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="41"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.9" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="34"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="281"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="81"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="50"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.13" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="20"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.14" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.28" steps="386"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.15" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.16" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.17" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="1.52" steps="440826"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.19" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="294"/></proof>
  </goal>
  <goal name="mergesort&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="185"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
