<?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="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Z3" version="4.8.10" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="huffman_with_two_queues.mlw"/>
<theory name="Top" proved="true">
 <goal name="add_last" proved="true">
 <proof prover="1"><result status="valid" time="0.02" steps="59"/></proof>
 </goal>
 <goal name="sorted_tail" proved="true">
 <proof prover="1"><result status="valid" time="0.07" steps="78"/></proof>
 <proof prover="4"><result status="valid" time="0.69" steps="75047"/></proof>
 </goal>
 <goal name="sorted_tail_tail" proved="true">
 <proof prover="1"><result status="valid" time="0.06" steps="82"/></proof>
 <proof prover="4"><result status="valid" time="0.58" steps="69528"/></proof>
 </goal>
 <goal name="huffman_coding&#39;vc" expl="VC for huffman_coding" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="huffman_coding&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="6"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14506"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="19"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="18142"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="8"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14254"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="46"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="18146"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="16"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14644"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="16"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14726"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="17"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14785"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="24"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="15395"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.8" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="70"/></proof>
  <proof prover="4"><result status="valid" time="0.13" steps="25061"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="30"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="18099"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="32"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18316"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="34"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18176"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="84"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="18299"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="3.12" steps="1241"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15284"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="35"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15337"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.16" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="22"/></proof>
  <proof prover="4"><result status="valid" time="0.07" steps="15278"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.17" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="74"/></proof>
  <proof prover="4"><result status="valid" time="0.12" steps="24796"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="34"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18099"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="17872"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="32"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15026"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.21" expl="loop invariant preservation" proved="true">
  <transf name="assert" proved="true" arg1="(sorted y1[2..])">
   <goal name="huffman_coding&#39;vc.21.0" expl="asserted formula" proved="true">
   <transf name="assert" proved="true" arg1="(length y1 &gt;= 2)">
    <goal name="huffman_coding&#39;vc.21.0.0" expl="asserted formula" proved="true">
    <proof prover="1"><result status="valid" time="0.01" steps="32"/></proof>
    <proof prover="4"><result status="valid" time="0.07" steps="15423"/></proof>
    </goal>
    <goal name="huffman_coding&#39;vc.21.0.1" expl="asserted formula" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="huffman_coding&#39;vc.21.0.1.0" expl="asserted formula" proved="true">
     <proof prover="1"><result status="valid" time="0.02" steps="40"/></proof>
     <proof prover="4"><result status="valid" time="0.10" steps="19983"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="huffman_coding&#39;vc.21.1" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.24" steps="188"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="34"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15125"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="34"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15194"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="2.72" steps="1056"/></proof>
  <proof prover="4"><result status="valid" time="1.62" steps="202281"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.25" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="34"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15078"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.26" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="107"/></proof>
  <proof prover="4"><result status="valid" time="0.13" steps="24822"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="40"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18326"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.28" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="42"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18490"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="44"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18398"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.30" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="76"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18492"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.31" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="2.91" steps="2569"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.32" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.21" steps="520493"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.33" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.42" steps="261"/></proof>
  <proof prover="4"><result status="valid" time="0.32" steps="57146"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.34" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="28"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17445"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.35" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17841"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.36" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="378"/></proof>
  <proof prover="4"><result status="valid" time="0.14" steps="27023"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.37" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="37"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18529"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.38" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.38.0" expl="loop invariant preservation" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="huffman_coding&#39;vc.38.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="1"><result status="valid" time="0.03" steps="95"/></proof>
    <proof prover="4"><result status="valid" time="0.11" steps="21144"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.39" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="45"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18626"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.40" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.40.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.53" steps="677"/></proof>
   <proof prover="4"><result status="valid" time="1.86" steps="221939"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.41" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="1.95" steps="1736"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.42" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.68" steps="565"/></proof>
  <proof prover="4"><result status="valid" time="2.00" steps="236678"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.43" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.73" steps="515"/></proof>
  <proof prover="4"><result status="valid" time="2.53" steps="291682"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.44" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="30"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="14987"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.45" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="102"/></proof>
  <proof prover="4"><result status="valid" time="0.12" steps="25034"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.46" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="39"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="18283"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.47" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.47.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.02" steps="41"/></proof>
   <proof prover="4"><result status="valid" time="0.09" steps="20451"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.48" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="40"/></proof>
  <proof prover="4"><result status="valid" time="0.06" steps="15080"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.49" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.49.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.30" steps="258"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.50" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.31" steps="192"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.51" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="1.59" steps="1183"/></proof>
  <proof prover="4"><result status="valid" time="1.19" steps="168412"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.52" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="2.21" steps="1607"/></proof>
  <proof prover="4"><result status="valid" time="1.30" steps="170097"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.53" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="28"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17443"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.54" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="17858"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.55" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="379"/></proof>
  <proof prover="4"><result status="valid" time="0.13" steps="27097"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.56" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="37"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="18603"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.57" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.57.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.02" steps="85"/></proof>
   <proof prover="4"><result status="valid" time="0.09" steps="21175"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.58" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="45"/></proof>
  <proof prover="4"><result status="valid" time="0.08" steps="18695"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.59" expl="loop invariant preservation" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="huffman_coding&#39;vc.59.0" expl="loop invariant preservation" proved="true">
   <proof prover="1"><result status="valid" time="0.53" steps="671"/></proof>
   <proof prover="4"><result status="valid" time="1.74" steps="218405"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="huffman_coding&#39;vc.60" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="1.88" steps="2015"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.61" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.62" steps="565"/></proof>
  <proof prover="4"><result status="valid" time="1.52" steps="226914"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.62" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="1.40" steps="1684"/></proof>
  </goal>
  <goal name="huffman_coding&#39;vc.63" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.19" steps="323"/></proof>
  <proof prover="4"><result status="valid" time="0.14" steps="26192"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
