<?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="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.0.0" timelimit="36" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Alt-Ergo" version="2.3.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="insertion_sort.mlw"/>
<theory name="InsertionSort" proved="true">
 <goal name="insertion_sort&#39;vc" expl="VC for insertion_sort" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="insertion_sort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="12"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="7"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="7"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="135"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="32"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="12"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.7" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.9" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="42"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.10" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.88" steps="806"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.13" steps="190"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="108"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.15" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="25"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.16" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="11"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.13" steps="119"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="11547"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="6"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.20" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="test1&#39;vc" expl="VC for test1" proved="true">
 <proof prover="2"><result status="valid" time="0.00" steps="11"/></proof>
 </goal>
 <goal name="test2&#39;vc" expl="VC for test2" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="38"/></proof>
 </goal>
 <goal name="bench&#39;vc" expl="VC for bench" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="36"/></proof>
 </goal>
</theory>
<theory name="InsertionSortGen" proved="true">
 <goal name="insertion_sort&#39;vc" expl="VC for insertion_sort" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="insertion_sort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="12563"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="36385"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="36315"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="35853"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.04" steps="135"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="46050"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="37198"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.7" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="38520"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="38978"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.9" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="39011"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="55744"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.11" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="47949"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="48846"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.62" steps="808"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="70553"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="74248"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.16" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.01" steps="41"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.17" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="39380"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.03" steps="65757"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="48080"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="11856"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="35595"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.22" expl="out of loop bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="36997"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="InsertionSortSwaps" proved="true">
 <goal name="insertion_sort&#39;vc" expl="VC for insertion_sort" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="insertion_sort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="10209"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="11370"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="10379"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="9910"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="11422"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="10704"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="10718"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.7" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="10858"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.8" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="10294"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="10918"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="13541"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.10" steps="431"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="16690"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="10336"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="11321"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="10006"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.16" expl="out of loop bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="11858"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
