<?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="2.2.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name=".."/><path name=".."/><path name="stdlib"/>
<path name="mach"/><path name="tagset.mlw"/>
<theory name="TagSetIntf" proved="true">
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <proof prover="1"><result status="valid" time="0.04" steps="18032"/></proof>
 </goal>
 <goal name="iterator&#39;vc" expl="VC for iterator" proved="true">
 <proof prover="1"><result status="valid" time="0.05" steps="18044"/></proof>
 </goal>
</theory>
<theory name="TagSet" proved="true">
 <goal name="iteration_state&#39;vc" expl="VC for iteration_state" proved="true">
 <proof prover="1"><result status="valid" time="0.07" steps="25183"/></proof>
 </goal>
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <proof prover="1"><result status="valid" time="0.03" steps="13863"/></proof>
 </goal>
 <goal name="create&#39;vc" expl="VC for create" proved="true">
 <proof prover="1"><result status="valid" time="0.09" steps="25398"/></proof>
 </goal>
 <goal name="mem&#39;vc" expl="VC for mem" proved="true">
 <proof prover="1"><result status="valid" time="0.11" steps="27187"/></proof>
 </goal>
 <goal name="max_tags&#39;vc" expl="VC for max_tags" proved="true">
 <proof prover="0"><result status="valid" time="0.04" steps="159"/></proof>
 <proof prover="1"><result status="valid" time="0.09" steps="22894"/></proof>
 <proof prover="2"><result status="valid" time="0.03"/></proof>
 </goal>
 <goal name="resize&#39;vc" expl="VC for resize" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="resize&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="16207"/></proof>
  </goal>
  <goal name="resize&#39;vc.1" expl="division by zero" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="14453"/></proof>
  </goal>
  <goal name="resize&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="17178"/></proof>
  </goal>
  <goal name="resize&#39;vc.3" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="18597"/></proof>
  </goal>
  <goal name="resize&#39;vc.4" expl="array creation size" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="15676"/></proof>
  </goal>
  <goal name="resize&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="20842"/></proof>
  </goal>
  <goal name="resize&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="17397"/></proof>
  </goal>
  <goal name="resize&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="18640"/></proof>
  </goal>
  <goal name="resize&#39;vc.8" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="24101"/></proof>
  </goal>
  <goal name="resize&#39;vc.9" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="27803"/></proof>
  </goal>
  <goal name="resize&#39;vc.10" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="28411"/></proof>
  </goal>
  <goal name="resize&#39;vc.11" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="28094"/></proof>
  </goal>
  <goal name="resize&#39;vc.12" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.11" steps="28020"/></proof>
  </goal>
  <goal name="resize&#39;vc.13" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="18982"/></proof>
  </goal>
  <goal name="resize&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="19062"/></proof>
  </goal>
  <goal name="resize&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="15337"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="add&#39;vc" expl="VC for add" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="add&#39;vc.0" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="14228"/></proof>
  </goal>
  <goal name="add&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="14464"/></proof>
  </goal>
  <goal name="add&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="17083"/></proof>
  </goal>
  <goal name="add&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="20543"/></proof>
  </goal>
  <goal name="add&#39;vc.4" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20864"/></proof>
  </goal>
  <goal name="add&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20964"/></proof>
  </goal>
  <goal name="add&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="21082"/></proof>
  </goal>
  <goal name="add&#39;vc.7" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="14978"/></proof>
  </goal>
  <goal name="add&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="15018"/></proof>
  </goal>
  <goal name="add&#39;vc.9" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="20176"/></proof>
  </goal>
  <goal name="add&#39;vc.10" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="26975"/></proof>
  </goal>
  <goal name="add&#39;vc.11" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="27880"/></proof>
  </goal>
  <goal name="add&#39;vc.12" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.11" steps="32966"/></proof>
  </goal>
  <goal name="add&#39;vc.13" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="33946"/></proof>
  </goal>
  <goal name="add&#39;vc.14" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="15960"/></proof>
  </goal>
  <goal name="add&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="15943"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="remove&#39;vc" expl="VC for remove" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="remove&#39;vc.0" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="14419"/></proof>
  </goal>
  <goal name="remove&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="17077"/></proof>
  </goal>
  <goal name="remove&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="20537"/></proof>
  </goal>
  <goal name="remove&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20858"/></proof>
  </goal>
  <goal name="remove&#39;vc.4" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20958"/></proof>
  </goal>
  <goal name="remove&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="21076"/></proof>
  </goal>
  <goal name="remove&#39;vc.6" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="14893"/></proof>
  </goal>
  <goal name="remove&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="14933"/></proof>
  </goal>
  <goal name="remove&#39;vc.8" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="19948"/></proof>
  </goal>
  <goal name="remove&#39;vc.9" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="26714"/></proof>
  </goal>
  <goal name="remove&#39;vc.10" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="27482"/></proof>
  </goal>
  <goal name="remove&#39;vc.11" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.10" steps="31117"/></proof>
  </goal>
  <goal name="remove&#39;vc.12" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.13" steps="32580"/></proof>
  </goal>
  <goal name="remove&#39;vc.13" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="15850"/></proof>
  </goal>
  <goal name="remove&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="19534"/></proof>
  </goal>
  <goal name="remove&#39;vc.15" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="16968"/></proof>
  </goal>
  <goal name="remove&#39;vc.16" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20420"/></proof>
  </goal>
  <goal name="remove&#39;vc.17" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20741"/></proof>
  </goal>
  <goal name="remove&#39;vc.18" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20841"/></proof>
  </goal>
  <goal name="remove&#39;vc.19" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20959"/></proof>
  </goal>
  <goal name="remove&#39;vc.20" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="14497"/></proof>
  </goal>
  <goal name="remove&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="14913"/></proof>
  </goal>
  <goal name="remove&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.05" steps="75"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="iterator&#39;vc" expl="VC for iterator" proved="true">
 <proof prover="1"><result status="valid" time="0.11" steps="28972"/></proof>
 </goal>
 <goal name="Iterator.create&#39;vc" expl="VC for create" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="create&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="16915"/></proof>
  </goal>
  <goal name="create&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="17546"/></proof>
  </goal>
  <goal name="create&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="17665"/></proof>
  </goal>
  <goal name="create&#39;vc.3" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="20730"/></proof>
  </goal>
  <goal name="create&#39;vc.4" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="18958"/></proof>
  </goal>
  <goal name="create&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="18991"/></proof>
  </goal>
  <goal name="create&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="20522"/></proof>
  </goal>
  <goal name="create&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="23783"/></proof>
  </goal>
  <goal name="create&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="19599"/></proof>
  </goal>
  <goal name="create&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="22828"/></proof>
  </goal>
  <goal name="create&#39;vc.10" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="23188"/></proof>
  </goal>
  <goal name="create&#39;vc.11" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.13" steps="33304"/></proof>
  </goal>
  <goal name="create&#39;vc.12" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="create&#39;vc.12.0" expl="precondition" proved="true">
   <proof prover="1"><result status="valid" time="0.04" steps="21898"/></proof>
   </goal>
   <goal name="create&#39;vc.12.1" expl="precondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="create&#39;vc.12.1.0" expl="precondition" proved="true">
    <proof prover="1"><result status="valid" time="0.07" steps="26241"/></proof>
    </goal>
    <goal name="create&#39;vc.12.1.1" expl="precondition" proved="true">
    <proof prover="1"><result status="valid" time="0.06" steps="25374"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="create&#39;vc.12.2" expl="precondition" proved="true">
   <proof prover="1"><result status="valid" time="0.12" steps="28455"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="create&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="18226"/></proof>
  </goal>
  <goal name="create&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="18229"/></proof>
  </goal>
  <goal name="create&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="18232"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="Iterator.is_empty&#39;vc" expl="VC for is_empty" proved="true">
 <proof prover="2"><result status="valid" time="0.17"/></proof>
 </goal>
 <goal name="Iterator.next&#39;vc" expl="VC for next" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="next&#39;vc.0" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="109"/></proof>
  </goal>
  <goal name="next&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="17921"/></proof>
  </goal>
  <goal name="next&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="18027"/></proof>
  </goal>
  <goal name="next&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="16215"/></proof>
  </goal>
  <goal name="next&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="19051"/></proof>
  </goal>
  <goal name="next&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="21390"/></proof>
  </goal>
  <goal name="next&#39;vc.6" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="21969"/></proof>
  </goal>
  <goal name="next&#39;vc.7" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="19450"/></proof>
  </goal>
  <goal name="next&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="19517"/></proof>
  </goal>
  <goal name="next&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="21654"/></proof>
  </goal>
  <goal name="next&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="22140"/></proof>
  </goal>
  <goal name="next&#39;vc.11" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.12" steps="33676"/></proof>
  </goal>
  <goal name="next&#39;vc.12" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="23680"/></proof>
  </goal>
  <goal name="next&#39;vc.13" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="24856"/></proof>
  </goal>
  <goal name="next&#39;vc.14" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="25321"/></proof>
  </goal>
  <goal name="next&#39;vc.15" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.23" steps="46966"/></proof>
  </goal>
  <goal name="next&#39;vc.16" expl="type invariant" proved="true">
  <proof prover="1"><result status="valid" time="0.13" steps="32757"/></proof>
  </goal>
  <goal name="next&#39;vc.17" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.12" steps="28587"/></proof>
  </goal>
  <goal name="next&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20964"/></proof>
  </goal>
  <goal name="next&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.04" steps="20975"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
