<?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="Alt-Ergo" version="2.3.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.1.0" timelimit="1" 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="0.010000" steps="8357"/></proof>
  </goal>
  <goal name="dfs&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="12885"/></proof>
  </goal>
  <goal name="dfs&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="18715"/></proof>
  </goal>
  <goal name="dfs&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="14002"/></proof>
  </goal>
  <goal name="dfs&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="14048"/></proof>
  </goal>
  <goal name="dfs&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="8357"/></proof>
  </goal>
  <goal name="dfs&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="8357"/></proof>
  </goal>
  <goal name="dfs&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="16722"/></proof>
  </goal>
  <goal name="dfs&#39;vc.8" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="13131"/></proof>
  </goal>
  <goal name="dfs&#39;vc.9" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.160000" steps="23106"/></proof>
  </goal>
  <goal name="dfs&#39;vc.10" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.060000" steps="22825"/></proof>
  </goal>
  <goal name="dfs&#39;vc.11" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.060000" steps="17605"/></proof>
  </goal>
  <goal name="dfs&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="13247"/></proof>
  </goal>
  <goal name="dfs&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.337187" steps="50486"/></proof>
  </goal>
  <goal name="dfs&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="15433"/></proof>
  </goal>
  <goal name="dfs&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="18293"/></proof>
  </goal>
  <goal name="dfs&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="18648"/></proof>
  </goal>
  <goal name="dfs&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="8357"/></proof>
  </goal>
  <goal name="dfs&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.230000" steps="49759"/></proof>
  </goal>
  <goal name="dfs&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="16687"/></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="2.750000" steps="11689"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="dfs&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.070000" steps="18227"/></proof>
  </goal>
  <goal name="dfs&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="12776"/></proof>
  </goal>
  <goal name="dfs&#39;vc.23" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.070000" steps="18152"/></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="0.020000" steps="12295"/></proof>
    </goal>
    <goal name="dfs&#39;vc.24.0.1" expl="VC for dfs" proved="true">
    <proof prover="3"><result status="valid" time="0.040000" steps="12302"/></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="0.070000" steps="17958"/></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="0.040000" steps="14468"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="dfs&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="8357"/></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="0.040000" steps="14533"/></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="0.020000" steps="9828"/></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="0.040000" steps="13296"/></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="0.030000" steps="13975"/></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="0.020000" steps="10409"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="13187"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="8357"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="13057"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="14306"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="15782"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.7" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="16289"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="13087"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="16325"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.220000" steps="42172"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.11" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="8357"/></proof>
  </goal>
  <goal name="topo_order&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.080000" steps="20210"/></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="0.010000" steps="8281"/></proof>
  </goal>
  <goal name="create&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="13610"/></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="0.010000" steps="8281"/></proof>
  </goal>
  <goal name="dfs&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="12851"/></proof>
  </goal>
  <goal name="dfs&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="14028"/></proof>
  </goal>
  <goal name="dfs&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="14029"/></proof>
  </goal>
  <goal name="dfs&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="8281"/></proof>
  </goal>
  <goal name="dfs&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="12918"/></proof>
  </goal>
  <goal name="dfs&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="8281"/></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="0.040000" steps="16665"/></proof>
   </goal>
   <goal name="dfs&#39;vc.7.1" expl="VC for dfs" proved="true">
   <proof prover="3"><result status="valid" time="0.040000" steps="15344"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="dfs&#39;vc.8" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="13165"/></proof>
  </goal>
  <goal name="dfs&#39;vc.9" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.120000" steps="21745"/></proof>
  </goal>
  <goal name="dfs&#39;vc.10" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.060000" steps="21897"/></proof>
  </goal>
  <goal name="dfs&#39;vc.11" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.060000" steps="17674"/></proof>
  </goal>
  <goal name="dfs&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="13344"/></proof>
  </goal>
  <goal name="dfs&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.080000" steps="18616"/></proof>
  </goal>
  <goal name="dfs&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="18249"/></proof>
  </goal>
  <goal name="dfs&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="18744"/></proof>
  </goal>
  <goal name="dfs&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="18840"/></proof>
  </goal>
  <goal name="dfs&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="8281"/></proof>
  </goal>
  <goal name="dfs&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="16673"/></proof>
  </goal>
  <goal name="dfs&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="244"/></proof>
  </goal>
  <goal name="dfs&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.070000" steps="17831"/></proof>
  </goal>
  <goal name="dfs&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="18042"/></proof>
  </goal>
  <goal name="dfs&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="12082"/></proof>
  </goal>
  <goal name="dfs&#39;vc.23" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="12089"/></proof>
  </goal>
  <goal name="dfs&#39;vc.24" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="8281"/></proof>
  </goal>
  <goal name="dfs&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="12117"/></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="0.020000" steps="12557"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="12574"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="15589"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.190000" steps="51435"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="15358"/></proof>
  </goal>
  <goal name="add_edge&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="8281"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
