<?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="Coq" version="8.11.2" timelimit="0" steplimit="0" memlimit="0"/>
<prover id="3" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="8" name="Eprover" version="2.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="9" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="vstte12_bfs.mlw"/>
<theory name="Graph" proved="true">
 <goal name="path_nonneg" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="path_nonneg.0" proved="true">
  <proof prover="9"><result status="valid" time="0.00" steps="4"/></proof>
  </goal>
  <goal name="path_nonneg.1" proved="true">
  <proof prover="6"><result status="valid" time="0.00" steps="9455"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="path_inversion" proved="true">
 <transf name="inversion_pr" proved="true" >
  <goal name="path_inversion.0" proved="true">
  <proof prover="9"><result status="valid" time="0.00" steps="4"/></proof>
  </goal>
  <goal name="path_inversion.1" proved="true">
  <proof prover="9"><result status="valid" time="0.00" steps="7"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="path_closure" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="path_closure.0" proved="true">
  <proof prover="9"><result status="valid" time="0.00" steps="5"/></proof>
  </goal>
  <goal name="path_closure.1" proved="true">
  <proof prover="6"><result status="valid" time="0.01" steps="9965"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="BFS" proved="true">
 <goal name="B.eq&#39;refn&#39;vc" expl="VC for eq&#39;refn" proved="true">
 <proof prover="3"><result status="valid" time="0.02" steps="6347"/></proof>
 </goal>
 <goal name="fill_next&#39;vc" expl="VC for fill_next" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="fill_next&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="77"/></proof>
  </goal>
  <goal name="fill_next&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="1"/></proof>
  </goal>
  <goal name="fill_next&#39;vc.2" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="56"/></proof>
  </goal>
  <goal name="fill_next&#39;vc.3" expl="loop invariant preservation" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="fill_next&#39;vc.3.0" expl="loop invariant preservation" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="fill_next&#39;vc.3.0.0" expl="loop invariant preservation" proved="true">
    <transf name="split_goal_right" proved="true" >
     <goal name="fill_next&#39;vc.3.0.0.0" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.03" steps="54"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.1" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.01" steps="24"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.2" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.03" steps="53"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.3" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.04" steps="132"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.4" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.01" steps="75"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.5" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.37" steps="1163"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.6" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.01" steps="81"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.7" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.02" steps="90"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.8" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.11" steps="49"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.9" expl="VC for fill_next" proved="true">
     <proof prover="9"><result status="valid" time="0.01" steps="192"/></proof>
     </goal>
     <goal name="fill_next&#39;vc.3.0.0.10" expl="VC for fill_next" proved="true">
     <proof prover="8"><result status="valid" time="0.42"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="fill_next&#39;vc.4" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="38"/></proof>
  </goal>
  <goal name="fill_next&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.15" steps="744"/></proof>
  </goal>
  <goal name="fill_next&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.09" steps="219"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="bfs&#39;vc" expl="VC for bfs" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="bfs&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.04" steps="268"/></proof>
  </goal>
  <goal name="bfs&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.00" steps="1"/></proof>
  </goal>
  <goal name="bfs&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="20"/></proof>
  </goal>
  <goal name="bfs&#39;vc.3" expl="precondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="bfs&#39;vc.3.0" expl="VC for bfs" proved="true">
   <proof prover="9"><result status="valid" time="0.02" steps="130"/></proof>
   </goal>
   <goal name="bfs&#39;vc.3.1" expl="VC for bfs" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="20"/></proof>
   </goal>
   <goal name="bfs&#39;vc.3.2" expl="VC for bfs" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="bfs&#39;vc.3.2.0" expl="VC for bfs" proved="true">
    <transf name="inline_goal" proved="true" >
     <goal name="bfs&#39;vc.3.2.0.0" expl="VC for bfs" proved="true">
     <proof prover="8"><result status="valid" time="0.34"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="bfs&#39;vc.4" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="bfs&#39;vc.4.0" expl="VC for bfs" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="bfs&#39;vc.4.0.0" expl="VC for bfs" proved="true">
    <transf name="inline_goal" proved="true" >
     <goal name="bfs&#39;vc.4.0.0.0" expl="VC for bfs" proved="true">
     <transf name="split_goal_right" proved="true" >
      <goal name="bfs&#39;vc.4.0.0.0.0" expl="VC for bfs" proved="true">
      <proof prover="9"><result status="valid" time="0.01" steps="28"/></proof>
      </goal>
      <goal name="bfs&#39;vc.4.0.0.0.1" expl="VC for bfs" proved="true">
      <proof prover="9"><result status="valid" time="0.01" steps="35"/></proof>
      </goal>
      <goal name="bfs&#39;vc.4.0.0.0.2" expl="VC for bfs" proved="true">
      <proof prover="9"><result status="valid" time="0.02" steps="85"/></proof>
      </goal>
      <goal name="bfs&#39;vc.4.0.0.0.3" expl="VC for bfs" proved="true">
      <proof prover="9"><result status="valid" time="0.02" steps="108"/></proof>
      </goal>
      <goal name="bfs&#39;vc.4.0.0.0.4" expl="VC for bfs" proved="true">
      <transf name="inline_all" proved="true" >
       <goal name="bfs&#39;vc.4.0.0.0.4.0" expl="VC for bfs" proved="true">
       <proof prover="3"><result status="valid" time="0.21" steps="38158"/></proof>
       </goal>
      </transf>
      </goal>
      <goal name="bfs&#39;vc.4.0.0.0.5" expl="VC for bfs" proved="true">
      <proof prover="9"><result status="valid" time="0.02" steps="131"/></proof>
      </goal>
      <goal name="bfs&#39;vc.4.0.0.0.6" expl="VC for bfs" proved="true">
      <proof prover="9"><result status="valid" time="0.00" steps="60"/></proof>
      </goal>
      <goal name="bfs&#39;vc.4.0.0.0.7" expl="VC for bfs" proved="true">
      <proof prover="9"><result status="valid" time="0.02" steps="36"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="bfs&#39;vc.4.1" expl="VC for bfs" proved="true">
   <proof prover="9"><result status="valid" time="0.00" steps="34"/></proof>
   </goal>
   <goal name="bfs&#39;vc.4.2" expl="VC for bfs" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="bfs&#39;vc.4.2.0" expl="VC for bfs" proved="true">
    <transf name="inline_goal" proved="true" >
     <goal name="bfs&#39;vc.4.2.0.0" expl="VC for bfs" proved="true">
     <proof prover="8"><result status="valid" time="0.10"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="bfs&#39;vc.4.3" expl="VC for bfs" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="24"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="bfs&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="51"/></proof>
  </goal>
  <goal name="bfs&#39;vc.6" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="18"/></proof>
  </goal>
  <goal name="bfs&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="1"><path name="vstte12_bfs_BFS_VC_bfs_1.v"/><result status="valid" time="0.34"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
