<?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="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.5.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="verifythis_2017_pair_insertion_sort.mlw"/>
<theory name="Challenge1" proved="true">
 <goal name="pair_insertion_sort&#39;vc" expl="VC for pair_insertion_sort" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="pair_insertion_sort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="3"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="5"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="6"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="6"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="19"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="11"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="11"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.30" steps="271"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.11" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="14"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.12" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.14" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="47"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="117"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.16" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.36" steps="451"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.17" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.22" steps="198"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="199"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.24" steps="205"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.14" steps="168"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.10"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.24" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.25" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.26" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="54"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.27" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="66"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.28" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="102"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.29" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="80"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.30" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.38" steps="430"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.31" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.32" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.33" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.34" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="67"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.35" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="27"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.36" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="27"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.37" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="159"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.38" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="152"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.39" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.14" steps="167"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.40" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="121"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.41" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="36722"/></proof>
  <proof prover="5"><result status="valid" time="0.09" steps="27219"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.42" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="20"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.43" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.44" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.45" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.14" steps="214"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.46" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="26"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.47" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="40"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.48" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="8"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.49" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.50" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="12"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.51" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.52" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.53" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.42" steps="278"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.54" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.55" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="14"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.56" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="14"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.57" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="72"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.58" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="188"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.59" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.47" steps="606"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.60" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="21"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.61" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.62" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.27" steps="244"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.63" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.28" steps="239"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.64" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.32" steps="253"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.65" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.12" steps="211"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.66" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.11"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.67" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="12"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.68" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.69" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="91"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.70" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="109"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.71" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.20" steps="196"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.72" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="167"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.73" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.44" steps="618"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.74" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="20"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.75" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="21"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.76" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.77" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="92"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.78" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="26"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.79" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="26"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.80" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="220"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.81" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="198"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.82" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="215"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.83" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="164"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.84" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="2.13" steps="1034"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.85" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="19"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.86" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="23"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.87" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="23"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.88" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.25" steps="303"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.89" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="25"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.90" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="7"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.91" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="7"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.92" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="17"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.93" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="11"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.94" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.95" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.96" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="235"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.97" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="12"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.98" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.99" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.100" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="40"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.101" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.102" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.103" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="118"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.104" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="112"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.105" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="127"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.106" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="84"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.107" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.84" steps="658"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.108" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="11"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.109" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="161"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.110" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.111" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="pair_insertion_sort&#39;vc.112" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
