<?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="3" name="Z3" version="4.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.0.0" 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_maximum_sum_submatrix.mlw"/>
<theory name="Kadane2D" proved="true">
 <goal name="maximum_submatrix&#39;vc" expl="VC for maximum_submatrix" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="maximum_submatrix&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="3"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="6"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="12"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="8"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="16"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="45069"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.11" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.12" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="34"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.13" expl="index in matrix bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="32"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="31"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.15" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="31"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="138"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="98"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.18" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="1.76" steps="852"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.19" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="maximum_submatrix&#39;vc.19.0" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.34" steps="314"/></proof>
   </goal>
   <goal name="maximum_submatrix&#39;vc.19.1" expl="VC for maximum_submatrix" proved="true">
   <proof prover="4"><result status="valid" time="0.01" steps="52"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="maximum_submatrix&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="40"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="43"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="46"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.05" steps="24273"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="57"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="35"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.26" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="35"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="35"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.28" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.05" steps="22506"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="44"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.30" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="27"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.31" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="25"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.32" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="25"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.33" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="25"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.34" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="41551"/></proof>
  <proof prover="5"><result status="valid" time="0.03" steps="14903"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.35" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="maximum_submatrix&#39;vc.36" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="maximum_submatrix&#39;vc.36.0" expl="VC for maximum_submatrix" proved="true">
   <proof prover="4"><result status="valid" time="0.00" steps="12"/></proof>
   </goal>
   <goal name="maximum_submatrix&#39;vc.36.1" expl="VC for maximum_submatrix" proved="true">
   <proof prover="4"><result status="valid" time="0.01" steps="12"/></proof>
   </goal>
   <goal name="maximum_submatrix&#39;vc.36.2" expl="VC for maximum_submatrix" proved="true">
   <proof prover="4"><result status="valid" time="0.00" steps="12"/></proof>
   </goal>
   <goal name="maximum_submatrix&#39;vc.36.3" expl="VC for maximum_submatrix" proved="true">
   <proof prover="4"><result status="valid" time="0.01" steps="12"/></proof>
   </goal>
   <goal name="maximum_submatrix&#39;vc.36.4" expl="VC for maximum_submatrix" proved="true">
   <proof prover="4"><result status="valid" time="0.00" steps="12"/></proof>
   </goal>
   <goal name="maximum_submatrix&#39;vc.36.5" expl="VC for maximum_submatrix" proved="true">
   <proof prover="4"><result status="valid" time="0.01" steps="12"/></proof>
   </goal>
   <goal name="maximum_submatrix&#39;vc.36.6" expl="VC for maximum_submatrix" proved="true">
   <proof prover="4"><result status="valid" time="0.00" steps="12"/></proof>
   </goal>
   <goal name="maximum_submatrix&#39;vc.36.7" expl="VC for maximum_submatrix" proved="true">
   <proof prover="3"><result status="valid" time="0.02" steps="264647"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="maximum_submatrix&#39;vc.37" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="4"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
