<?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="0" name="Z3" version="4.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Coq" version="8.11.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="warshall_algorithm.mlw"/>
<theory name="WarshallAlgorithm" proved="true">
 <goal name="weakening" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="weakening.0" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="weakening.1" proved="true">
  <proof prover="6"><result status="valid" time="0.01" steps="4686"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="decomposition" proved="true">
 <proof prover="1"><path name="warshall_algorithm_WarshallAlgorithm_decomposition_1.v"/><result status="valid" time="0.96"/></proof>
 </goal>
 <goal name="transitive_closure&#39;vc" expl="VC for transitive_closure" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="transitive_closure&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="34"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="33"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="50"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.3" expl="index in matrix bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.4" expl="index in matrix bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="19"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.5" expl="index in matrix bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.6" expl="index in matrix bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.7" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="transitive_closure&#39;vc.7.0" expl="loop invariant preservation" proved="true">
   <proof prover="3"><result status="valid" time="0.14" steps="292"/></proof>
   </goal>
   <goal name="transitive_closure&#39;vc.7.1" expl="loop invariant preservation" proved="true">
   <proof prover="3"><result status="valid" time="0.03" steps="163"/></proof>
   </goal>
   <goal name="transitive_closure&#39;vc.7.2" expl="loop invariant preservation" proved="true">
   <proof prover="0"><result status="valid" time="0.02" steps="29664"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="transitive_closure&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="65"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="23"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="transitive_closure&#39;vc.13" expl="out of loop bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="5"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
