<?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="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="quicksort.mlw"/>
<theory name="Quicksort" proved="true">
 <goal name="quick_rec&#39;vc" expl="VC for quick_rec" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="quick_rec&#39;vc.0" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="19"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="21"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="45"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.7" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="48"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="194"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="486"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="477"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="58"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="50"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="52"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="22"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="30"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.17" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.065213" steps="523"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.18" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.20" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.115621" steps="743"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.21" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.22" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="50"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.23" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.210000" steps="875"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.24" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="125"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.110000" steps="578"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="132"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.27" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.28" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="15"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.29" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="quicksort&#39;vc" expl="VC for quicksort" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="62"/></proof>
 </goal>
</theory>
<theory name="Shuffle" proved="true">
 <goal name="shuffle&#39;vc" expl="VC for shuffle" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="86"/></proof>
 </goal>
</theory>
<theory name="QuicksortWithShuffle" proved="true">
 <goal name="qs&#39;vc" expl="VC for qs" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="26"/></proof>
 </goal>
</theory>
<theory name="Quicksort3way" proved="true">
 <goal name="quick_rec&#39;vc" expl="VC for quick_rec" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="quick_rec&#39;vc.0" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="10"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="22"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="24"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="49"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="34"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.8" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="61"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.9" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="335"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="368"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="268"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="53"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.15" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.17" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="63"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.18" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="257"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="260"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="331"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="53"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.24" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="12"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.26" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="48"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="50"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.28" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="52"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="12"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.30" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="86"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.31" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.32" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.33" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="208"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.34" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="36"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.35" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.36" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="366"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.37" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="108"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="326"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.39" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="115"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.40" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="15"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="quicksort&#39;vc" expl="VC for quicksort" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="62"/></proof>
 </goal>
 <goal name="qs&#39;vc" expl="VC for qs" proved="true">
 <proof prover="2"><result status="valid" time="0.000000" steps="26"/></proof>
 </goal>
</theory>
<theory name="Test" proved="true">
 <goal name="test1&#39;vc" expl="VC for test1" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="10"/></proof>
 </goal>
 <goal name="test2&#39;vc" expl="VC for test2" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="91"/></proof>
 </goal>
 <goal name="bench&#39;vc" expl="VC for bench" proved="true">
 <proof prover="2"><result status="valid" time="0.000000" steps="2"/></proof>
 </goal>
</theory>
<theory name="Traditional" proved="true">
 <goal name="quick_rec&#39;vc" expl="VC for quick_rec" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="quick_rec&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="15"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="29"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="10"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="25"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.11" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="28"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.12" expl="loop invariant init" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="quick_rec&#39;vc.12.0" expl="loop invariant init" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="34"/></proof>
   </goal>
   <goal name="quick_rec&#39;vc.12.1" expl="loop invariant init" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="34"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="quick_rec&#39;vc.13" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="42"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.15" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.16" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.17" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.18" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.19" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.22" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.23" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.26" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.28" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="9614"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.30" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.31" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.32" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="52"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.33" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="42"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.34" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="46"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.35" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="46"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.36" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="52"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.37" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="52"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.110000" steps="411"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.39" expl="postcondition" proved="true">
  <transf name="apply" proved="true" arg1="permut_sub_trans" arg2="with" arg3="a2">
   <goal name="quick_rec&#39;vc.39.0" expl="apply premises" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="60"/></proof>
   </goal>
   <goal name="quick_rec&#39;vc.39.1" expl="apply premises" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="60"/></proof>
   </goal>
   <goal name="quick_rec&#39;vc.39.2" expl="apply premises" proved="true">
   <transf name="apply" proved="true" arg1="permut_sub_trans" arg2="with" arg3="a3">
    <goal name="quick_rec&#39;vc.39.2.0" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="60"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.39.2.1" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="60"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.39.2.2" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="60"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.39.2.3" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.020000" steps="62"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="quick_rec&#39;vc.39.3" expl="apply premises" proved="true">
   <transf name="apply" proved="true" arg1="permut_sub_trans" arg2="with" arg3="a1">
    <goal name="quick_rec&#39;vc.39.3.0" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="60"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.39.3.1" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.020000" steps="60"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.39.3.2" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.020000" steps="62"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.39.3.3" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.020000" steps="62"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="quick_rec&#39;vc.40" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.41" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.42" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.43" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.44" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.45" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.46" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.47" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.48" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.49" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="34"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.50" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="42"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.51" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.52" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.53" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.54" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.55" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.56" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.57" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.58" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.59" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.60" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.61" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.62" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.63" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.64" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.65" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.66" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.67" expl="loop invariant preservation" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="quick_rec&#39;vc.67.0" expl="loop invariant preservation" proved="true">
   <proof prover="3"><result status="valid" time="0.040000" steps="9845"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="quick_rec&#39;vc.68" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="38"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.69" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="42"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.70" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="42"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.71" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="50"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.72" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.73" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.74" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.75" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="50"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.76" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="50"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.77" expl="postcondition" proved="true">
  <proof prover="0" timelimit="10" memlimit="4000"><result status="valid" time="1.972487" steps="4398"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.78" expl="postcondition" proved="true">
  <transf name="apply" proved="true" arg1="permut_sub_trans" arg2="with" arg3="a2">
   <goal name="quick_rec&#39;vc.78.0" expl="apply premises" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="58"/></proof>
   </goal>
   <goal name="quick_rec&#39;vc.78.1" expl="apply premises" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="58"/></proof>
   </goal>
   <goal name="quick_rec&#39;vc.78.2" expl="apply premises" proved="true">
   <transf name="apply" proved="true" arg1="permut_sub_trans" arg2="with" arg3="a3">
    <goal name="quick_rec&#39;vc.78.2.0" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="58"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.78.2.1" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="58"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.78.2.2" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="58"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.78.2.3" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.020000" steps="60"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="quick_rec&#39;vc.78.3" expl="apply premises" proved="true">
   <transf name="apply" proved="true" arg1="permut_sub_trans" arg2="with" arg3="a1">
    <goal name="quick_rec&#39;vc.78.3.0" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.020000" steps="58"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.78.3.1" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="58"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.78.3.2" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="60"/></proof>
    </goal>
    <goal name="quick_rec&#39;vc.78.3.3" expl="apply premises" proved="true">
    <proof prover="0"><result status="valid" time="0.010000" steps="60"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="quick_rec&#39;vc.79" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.80" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.81" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.82" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="259"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.83" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="48"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.84" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="262"/></proof>
  </goal>
  <goal name="quick_rec&#39;vc.85" expl="loop invariant preservation" proved="true">
  <transf name="apply" proved="true" arg1="permut_sub_trans" arg2="with" arg3="a1">
   <goal name="quick_rec&#39;vc.85.0" expl="apply premises" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="52"/></proof>
   </goal>
   <goal name="quick_rec&#39;vc.85.1" expl="apply premises" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="52"/></proof>
   </goal>
   <goal name="quick_rec&#39;vc.85.2" expl="apply premises" proved="true">
   <proof prover="0"><result status="valid" time="0.010000" steps="52"/></proof>
   </goal>
   <goal name="quick_rec&#39;vc.85.3" expl="apply premises" proved="true">
   <proof prover="0"><result status="valid" time="0.020000" steps="54"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="quick_rec&#39;vc.86" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="196"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="quicksort&#39;vc" expl="VC for quicksort" proved="true">
 <proof prover="0"><result status="valid" time="0.010000" steps="62"/></proof>
 </goal>
</theory>
</file>
</why3session>
