<?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="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.12.2" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="min_max.mlw"/>
<theory name="Top" proved="true">
 <goal name="min_max&#39;vc" expl="VC for min_max" proved="true">
 <proof prover="2"><result status="valid" time="0.080000" steps="291"/></proof>
 </goal>
 <goal name="a_better_min_max&#39;vc" expl="VC for a_better_min_max" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="a_better_min_max&#39;vc.0" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.2" expl="check modulo by zero" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="2"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="6"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="54"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="543"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.9" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="62"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.10" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="55"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.11" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="68"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.12" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="61"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="61"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="68"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.15" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="23045"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="120"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.408187" steps="39363"/></proof>
  </goal>
  <goal name="a_better_min_max&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="126"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="divide_and_conquer&#39;vc" expl="VC for divide_and_conquer" proved="true">
 <proof prover="2"><result status="valid" time="0.370000" steps="989"/></proof>
 </goal>
 <goal name="a_similar_min_max&#39;vc" expl="VC for a_similar_min_max" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="11"/></proof>
 </goal>
</theory>
</file>
</why3session>
