<?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="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.4.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="7" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="skew_heaps.mlw"/>
<theory name="Heap" proved="true">
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="5"><result status="valid" time="0.000000" steps="0"/></proof>
 </goal>
</theory>
<theory name="SkewHeaps" proved="true">
 <goal name="root_is_min&#39;vc" expl="VC for root_is_min" proved="true">
 <proof prover="1"><result status="valid" time="8.661145" steps="52876"/></proof>
 </goal>
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="21"/></proof>
 </goal>
 <goal name="get_min&#39;vc" expl="VC for get_min" proved="true">
 <proof prover="7"><result status="valid" time="0.000000" steps="35"/></proof>
 </goal>
 <goal name="merge&#39;vc" expl="VC for merge" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="merge&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="5468"/></proof>
  </goal>
  <goal name="merge&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="3730"/></proof>
  </goal>
  <goal name="merge&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="5524"/></proof>
  </goal>
  <goal name="merge&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="3734"/></proof>
  </goal>
  <goal name="merge&#39;vc.4" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="merge&#39;vc.4.0" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.030000" steps="3702"/></proof>
   </goal>
   <goal name="merge&#39;vc.4.1" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.040000" steps="4003"/></proof>
   </goal>
   <goal name="merge&#39;vc.4.2" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.040000" steps="4003"/></proof>
   </goal>
   <goal name="merge&#39;vc.4.3" expl="postcondition" proved="true">
   <proof prover="6"><result status="valid" time="1.010611" steps="92499"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="merge&#39;vc.5" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="merge&#39;vc.5.0" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.050000" steps="3927"/></proof>
   </goal>
   <goal name="merge&#39;vc.5.1" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.030000" steps="4214"/></proof>
   </goal>
   <goal name="merge&#39;vc.5.2" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.040000" steps="4214"/></proof>
   </goal>
   <goal name="merge&#39;vc.5.3" expl="postcondition" proved="true">
   <proof prover="6"><result status="valid" time="0.040000" steps="9977"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="merge&#39;vc.6" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="merge&#39;vc.6.0" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.040000" steps="3938"/></proof>
   </goal>
   <goal name="merge&#39;vc.6.1" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.030000" steps="4211"/></proof>
   </goal>
   <goal name="merge&#39;vc.6.2" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.040000" steps="4211"/></proof>
   </goal>
   <goal name="merge&#39;vc.6.3" expl="postcondition" proved="true">
   <proof prover="6"><result status="valid" time="0.050000" steps="5100"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="add&#39;vc" expl="VC for add" proved="true">
 <proof prover="7"><result status="valid" time="0.020000" steps="158"/></proof>
 </goal>
 <goal name="remove_min&#39;vc" expl="VC for remove_min" proved="true">
 <proof prover="7"><result status="valid" time="0.020000" steps="260"/></proof>
 </goal>
</theory>
<theory name="HeapSort" proved="true">
 <goal name="heapsort&#39;vc" expl="VC for heapsort" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="heapsort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="34"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.3" expl="precondition" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.4" expl="assertion" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="36"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="7"><result status="valid" time="0.190000" steps="318"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="60718"/></proof>
  <proof prover="4"><result status="valid" time="0.070000" steps="15941"/></proof>
  <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="7"><result status="valid" time="0.080000" steps="70"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.11" expl="precondition" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="30"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.12" expl="index in array bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="30"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.13" expl="precondition" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="30"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.253648" steps="370541"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="7"><result status="valid" time="0.020000" steps="50"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.100000" steps="29125"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="1.257167" steps="134229"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="68"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="7"><result status="valid" time="0.030000" steps="116"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.20" expl="out of loop bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="heapsort&#39;vc.21" expl="out of loop bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
