<?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="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.1.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="pairing_heap_bin.mlw"/>
<theory name="Heap" proved="true">
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="2"><result status="valid" time="0.000000" 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="4"><result status="valid" time="0.000000" steps="40"/></proof>
 </goal>
 <goal name="size_empty" proved="true">
 <proof prover="4"><result status="valid" time="0.000000" steps="24"/></proof>
 </goal>
</theory>
<theory name="Occ" proved="true">
 <goal name="occ_nonneg&#39;vc" expl="VC for occ_nonneg" proved="true">
 <proof prover="3"><result status="valid" time="0.010000" steps="3571"/></proof>
 </goal>
</theory>
<theory name="PairingHeap" proved="true">
 <goal name="le_root_trans" proved="true">
 <proof prover="4"><result status="valid" time="0.000000" steps="36"/></proof>
 </goal>
 <goal name="le_root_tree_trans" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="le_root_tree_trans.0" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="68"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="mem_heap_tree&#39;vc" expl="VC for mem_heap_tree" proved="true">
 <proof prover="4"><result status="valid" time="0.030000" steps="304"/></proof>
 </goal>
 <goal name="mem_heap&#39;vc" expl="VC for mem_heap" proved="true">
 <proof prover="3"><result status="valid" time="0.040000" steps="8105"/></proof>
 </goal>
 <goal name="root_is_minimum" proved="true">
 <proof prover="4"><result status="valid" time="0.030000" steps="146"/></proof>
 </goal>
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="3"><result status="valid" time="0.010000" steps="4832"/></proof>
 </goal>
 <goal name="is_empty&#39;vc" expl="VC for is_empty" proved="true">
 <proof prover="4"><result status="valid" time="0.000000" steps="57"/></proof>
 </goal>
 <goal name="size&#39;vc" expl="VC for size" proved="true">
 <proof prover="0"><result status="valid" time="0.050000" steps="3984"/></proof>
 <proof prover="4"><result status="valid" time="0.000000" steps="10"/></proof>
 </goal>
 <goal name="merge&#39;vc" expl="VC for merge" proved="true">
 <proof prover="0"><result status="valid" time="0.100000" steps="20981"/></proof>
 <proof prover="3"><result status="valid" time="0.060000" steps="17884"/></proof>
 </goal>
 <goal name="insert&#39;vc" expl="VC for insert" proved="true">
 <proof prover="0"><result status="valid" time="0.090000" steps="7923"/></proof>
 <proof prover="3"><result status="valid" time="0.030000" steps="8006"/></proof>
 </goal>
 <goal name="find_min&#39;vc" expl="VC for find_min" proved="true">
 <proof prover="0"><result status="valid" time="0.050000" steps="4749"/></proof>
 <proof prover="4"><result status="valid" time="0.000000" steps="60"/></proof>
 </goal>
 <goal name="merge_pairs&#39;vc" expl="VC for merge_pairs" proved="true">
 <proof prover="0"><result status="valid" time="0.340000" steps="52495"/></proof>
 <proof prover="3"><result status="valid" time="0.270000" steps="46598"/></proof>
 </goal>
 <goal name="delete_min&#39;vc" expl="VC for delete_min" proved="true">
 <proof prover="0"><result status="valid" time="0.080000" steps="7778"/></proof>
 <proof prover="4"><result status="valid" time="0.020000" steps="261"/></proof>
 </goal>
</theory>
</file>
</why3session>
