<?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="Alt-Ergo" version="2.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.3.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="topological_sorting.mlw"/>
<theory name="Static" proved="true">
 <goal name="dfs&#39;vc" expl="VC for dfs" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="dfs&#39;vc.0" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="8619"/></proof>
  </goal>
  <goal name="dfs&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13147"/></proof>
  </goal>
  <goal name="dfs&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="19039"/></proof>
  </goal>
  <goal name="dfs&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="14326"/></proof>
  </goal>
  <goal name="dfs&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="14372"/></proof>
  </goal>
  <goal name="dfs&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="8619"/></proof>
  </goal>
  <goal name="dfs&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="8619"/></proof>
  </goal>
  <goal name="dfs&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="17045"/></proof>
  </goal>
  <goal name="dfs&#39;vc.8" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13393"/></proof>
  </goal>
  <goal name="dfs&#39;vc.9" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.16" steps="23429"/></proof>
  </goal>
  <goal name="dfs&#39;vc.10" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="23148"/></proof>
  </goal>
  <goal name="dfs&#39;vc.11" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="17928"/></proof>
  </goal>
  <goal name="dfs&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13509"/></proof>
  </goal>
  <goal name="dfs&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.21" steps="50811"/></proof>
  </goal>
  <goal name="dfs&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="15756"/></proof>
  </goal>
  <goal name="dfs&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="18616"/></proof>
  </goal>
  <goal name="dfs&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="18971"/></proof>
  </goal>
  <goal name="dfs&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="8619"/></proof>
  </goal>
  <goal name="dfs&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.23" steps="50083"/></proof>
  </goal>
  <goal name="dfs&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="17010"/></proof>
  </goal>
  <goal name="dfs&#39;vc.20" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="dfs&#39;vc.20.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="2.85" steps="13071"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="dfs&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07" steps="18552"/></proof>
  </goal>
  <goal name="dfs&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="13100"/></proof>
  </goal>
  <goal name="dfs&#39;vc.23" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07" steps="18476"/></proof>
  </goal>
  <goal name="dfs&#39;vc.24" expl="postcondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="dfs&#39;vc.24.0" expl="postcondition" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="dfs&#39;vc.24.0.0" expl="VC for dfs" proved="true">
    <proof prover="3"><result status="valid" time="0.02" steps="12557"/></proof>
    </goal>
    <goal name="dfs&#39;vc.24.0.1" expl="VC for dfs" proved="true">
    <proof prover="3"><result status="valid" time="0.04" steps="12564"/></proof>
    </goal>
    <goal name="dfs&#39;vc.24.0.2" expl="VC for dfs" proved="true">
    <transf name="inline_goal" proved="true" >
     <goal name="dfs&#39;vc.24.0.2.0" expl="VC for dfs" proved="true">
     <proof prover="3"><result status="valid" time="0.07" steps="18286"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="dfs&#39;vc.24.0.3" expl="VC for dfs" proved="true">
    <proof prover="3"><result status="valid" time="0.04" steps="14792"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="dfs&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="8619"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="topo_order&#39;vc" expl="VC for topo_order" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="topo_order&#39;vc.0" expl="loop invariant init" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="topo_order&#39;vc.0.0" expl="loop invariant init" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="topo_order&#39;vc.0.0.0" expl="VC for topo_order" proved="true">
    <proof prover="3"><result status="valid" time="0.04" steps="14857"/></proof>
    </goal>
    <goal name="topo_order&#39;vc.0.0.1" expl="VC for topo_order" proved="true">
    <proof prover="3"><result status="valid" time="0.02" steps="10089"/></proof>
    </goal>
    <goal name="topo_order&#39;vc.0.0.2" expl="VC for topo_order" proved="true">
    <proof prover="3"><result status="valid" time="0.04" steps="13561"/></proof>
    </goal>
    <goal name="topo_order&#39;vc.0.0.3" expl="VC for topo_order" proved="true">
    <proof prover="3"><result status="valid" time="0.03" steps="14305"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="topo_order&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="10732"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="13470"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="8619"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13319"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="14635"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="16109"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.7" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="16616"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13349"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="16652"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.22" steps="42499"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.11" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="8619"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="20535"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Online_Basic" proved="true">
 <goal name="create&#39;vc" expl="VC for create" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="create&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="8584"/></proof>
  </goal>
  <goal name="create&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="13944"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="dfs&#39;vc" expl="VC for dfs" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="dfs&#39;vc.0" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="8584"/></proof>
  </goal>
  <goal name="dfs&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13154"/></proof>
  </goal>
  <goal name="dfs&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="14363"/></proof>
  </goal>
  <goal name="dfs&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="14364"/></proof>
  </goal>
  <goal name="dfs&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="8584"/></proof>
  </goal>
  <goal name="dfs&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13220"/></proof>
  </goal>
  <goal name="dfs&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="8584"/></proof>
  </goal>
  <goal name="dfs&#39;vc.7" expl="variant decrease" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="dfs&#39;vc.7.0" expl="VC for dfs" proved="true">
   <proof prover="3"><result status="valid" time="0.04" steps="16999"/></proof>
   </goal>
   <goal name="dfs&#39;vc.7.1" expl="VC for dfs" proved="true">
   <proof prover="3"><result status="valid" time="0.04" steps="15678"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="dfs&#39;vc.8" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13468"/></proof>
  </goal>
  <goal name="dfs&#39;vc.9" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.12" steps="22079"/></proof>
  </goal>
  <goal name="dfs&#39;vc.10" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="22231"/></proof>
  </goal>
  <goal name="dfs&#39;vc.11" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="18008"/></proof>
  </goal>
  <goal name="dfs&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13647"/></proof>
  </goal>
  <goal name="dfs&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="18950"/></proof>
  </goal>
  <goal name="dfs&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="18583"/></proof>
  </goal>
  <goal name="dfs&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="19078"/></proof>
  </goal>
  <goal name="dfs&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="19174"/></proof>
  </goal>
  <goal name="dfs&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="8584"/></proof>
  </goal>
  <goal name="dfs&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="17007"/></proof>
  </goal>
  <goal name="dfs&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.05" steps="126"/></proof>
  </goal>
  <goal name="dfs&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07" steps="18167"/></proof>
  </goal>
  <goal name="dfs&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="18378"/></proof>
  </goal>
  <goal name="dfs&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="12385"/></proof>
  </goal>
  <goal name="dfs&#39;vc.23" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="12392"/></proof>
  </goal>
  <goal name="dfs&#39;vc.24" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="8584"/></proof>
  </goal>
  <goal name="dfs&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="12419"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="add_edge&#39;vc" expl="VC for add_edge" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="add_edge&#39;vc.0" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="12860"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="12877"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="15923"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.19" steps="51769"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="15692"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="8584"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
