<?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="2.3.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="pairing_heap.mlw"/>
<theory name="Heap" proved="true">
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.00" steps="0"/></proof>
 </goal>
</theory>
<theory name="Size" proved="true">
 <goal name="size_nonneg&#39;vc" expl="VC for size_nonneg" proved="true">
 <proof prover="0"><result status="valid" time="0.00" steps="28"/></proof>
 </goal>
 <goal name="size_tree_nonneg&#39;vc" expl="VC for size_tree_nonneg" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="35"/></proof>
 </goal>
 <goal name="size_list_nonneg&#39;vc" expl="VC for size_list_nonneg" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="67"/></proof>
 </goal>
 <goal name="size_empty&#39;vc" expl="VC for size_empty" proved="true">
 <proof prover="0"><result status="valid" time="0.00" steps="46"/></proof>
 </goal>
</theory>
<theory name="Occ" proved="true">
 <goal name="occ_nonneg&#39;vc" expl="VC for occ_nonneg" proved="true">
 <proof prover="0"><result status="valid" time="0.00" steps="29"/></proof>
 </goal>
 <goal name="occ_tree_nonneg&#39;vc" expl="VC for occ_tree_nonneg" proved="true">
 <proof prover="0"><result status="valid" time="0.00" steps="26"/></proof>
 </goal>
 <goal name="occ_list_nonneg&#39;vc" expl="VC for occ_list_nonneg" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="63"/></proof>
 </goal>
</theory>
<theory name="PairingHeap" proved="true">
 <goal name="le_root_trans" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="63"/></proof>
 </goal>
 <goal name="le_roots_trans" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="le_roots_trans.0" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="124"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="heap&#39;vc" expl="VC for heap" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="10"/></proof>
 </goal>
 <goal name="heap_mem&#39;vc" expl="VC for heap_mem" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="205"/></proof>
 </goal>
 <goal name="heap_mem_tree&#39;vc" expl="VC for heap_mem_tree" proved="true">
 <proof prover="0"><result status="valid" time="0.06" steps="293"/></proof>
 </goal>
 <goal name="heap_mem_list&#39;vc" expl="VC for heap_mem_list" proved="true">
 <proof prover="0"><result status="valid" time="0.05" steps="468"/></proof>
 </goal>
 <goal name="root_is_minimum&#39;vc" expl="VC for root_is_minimum" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="root_is_minimum&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="root_is_minimum&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.58" steps="2560"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="40"/></proof>
 </goal>
 <goal name="is_empty&#39;vc" expl="VC for is_empty" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="57"/></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="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="merge&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="merge&#39;vc.2" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="merge&#39;vc.3" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="223"/></proof>
  </goal>
  <goal name="merge&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="225"/></proof>
  </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="0"><result status="valid" time="0.00" steps="20"/></proof>
   </goal>
   <goal name="merge&#39;vc.5.1" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.00" steps="20"/></proof>
   </goal>
   <goal name="merge&#39;vc.5.2" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.00" steps="20"/></proof>
   </goal>
   <goal name="merge&#39;vc.5.3" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="24"/></proof>
   </goal>
   <goal name="merge&#39;vc.5.4" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="24"/></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="0"><result status="valid" time="0.01" steps="23"/></proof>
   </goal>
   <goal name="merge&#39;vc.6.1" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="23"/></proof>
   </goal>
   <goal name="merge&#39;vc.6.2" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="23"/></proof>
   </goal>
   <goal name="merge&#39;vc.6.3" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.03" steps="243"/></proof>
   </goal>
   <goal name="merge&#39;vc.6.4" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.03" steps="245"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="insert&#39;vc" expl="VC for insert" proved="true">
 <proof prover="0"><result status="valid" time="0.04" steps="278"/></proof>
 </goal>
 <goal name="find_min&#39;vc" expl="VC for find_min" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="61"/></proof>
 </goal>
 <goal name="merge_pairs&#39;vc" expl="VC for merge_pairs" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="merge_pairs&#39;vc.0" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="16"/></proof>
  </goal>
  <goal name="merge_pairs&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="merge_pairs&#39;vc.2" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="merge_pairs&#39;vc.3" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="merge_pairs&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="23"/></proof>
  </goal>
  <goal name="merge_pairs&#39;vc.5" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="merge_pairs&#39;vc.6" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="merge_pairs&#39;vc.6.0" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.00" steps="20"/></proof>
   </goal>
   <goal name="merge_pairs&#39;vc.6.1" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="22"/></proof>
   </goal>
   <goal name="merge_pairs&#39;vc.6.2" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="34"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="merge_pairs&#39;vc.7" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="merge_pairs&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.03" steps="23"/></proof>
   </goal>
   <goal name="merge_pairs&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="77"/></proof>
   </goal>
   <goal name="merge_pairs&#39;vc.7.2" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.02" steps="200"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="delete_min&#39;vc" expl="VC for delete_min" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="delete_min&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="delete_min&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="55"/></proof>
  </goal>
  <goal name="delete_min&#39;vc.2" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="delete_min&#39;vc.2.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.04" steps="7519"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="delete_min&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="delete_min&#39;vc.3.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.05" steps="8113"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="delete_min&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.50" steps="3017"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Correct" proved="true">
 <goal name="Heap.TotalPreOrder.Refl" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="14"/></proof>
 </goal>
 <goal name="Heap.TotalPreOrder.Trans" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="18"/></proof>
 </goal>
 <goal name="Heap.TotalPreOrder.Total" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="16"/></proof>
 </goal>
 <goal name="Heap.min_def" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="90"/></proof>
 </goal>
 <goal name="Heap.empty&#39;refn&#39;vc" expl="VC for empty&#39;refn" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="43"/></proof>
 </goal>
 <goal name="Heap.is_empty&#39;refn&#39;vc" expl="VC for is_empty&#39;refn" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="26"/></proof>
 </goal>
 <goal name="Heap.merge&#39;refn&#39;vc" expl="VC for merge&#39;refn" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="85"/></proof>
 </goal>
 <goal name="Heap.insert&#39;refn&#39;vc" expl="VC for insert&#39;refn" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="69"/></proof>
 </goal>
 <goal name="Heap.find_min&#39;refn&#39;vc" expl="VC for find_min&#39;refn" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="17"/></proof>
 </goal>
 <goal name="Heap.delete_min&#39;refn&#39;vc" expl="VC for delete_min&#39;refn" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="115"/></proof>
 </goal>
</theory>
</file>
</why3session>
