<?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="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="priority_queue.mlw"/>
<theory name="PQueue" proved="true">
 <goal name="balancing&#39;vc" expl="VC for balancing" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="4"/></proof>
 </goal>
 <goal name="M.assoc_m&#39;vc" expl="VC for assoc_m" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="assoc_m&#39;vc.0" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="11118"/></proof>
  </goal>
  <goal name="assoc_m&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="11118"/></proof>
  </goal>
  <goal name="assoc_m&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="11118"/></proof>
  </goal>
  <goal name="assoc_m&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="11118"/></proof>
  </goal>
  <goal name="assoc_m&#39;vc.4" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="11118"/></proof>
  </goal>
  <goal name="assoc_m&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="11118"/></proof>
  </goal>
  <goal name="assoc_m&#39;vc.6" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="11118"/></proof>
  </goal>
  <goal name="assoc_m&#39;vc.7" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="assoc_m&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.06" steps="12131"/></proof>
   </goal>
   <goal name="assoc_m&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.06" steps="12385"/></proof>
   </goal>
   <goal name="assoc_m&#39;vc.7.2" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.06" steps="12401"/></proof>
   </goal>
   <goal name="assoc_m&#39;vc.7.3" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.05" steps="12969"/></proof>
   </goal>
   <goal name="assoc_m&#39;vc.7.4" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.06" steps="12394"/></proof>
   </goal>
   <goal name="assoc_m&#39;vc.7.5" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.06" steps="12425"/></proof>
   </goal>
   <goal name="assoc_m&#39;vc.7.6" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.03" steps="12455"/></proof>
   </goal>
   <goal name="assoc_m&#39;vc.7.7" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.06" steps="17939"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="M.neutral_m&#39;vc" expl="VC for neutral_m" proved="true">
 <proof prover="1"><result status="valid" time="0.04" steps="12412"/></proof>
 </goal>
 <goal name="M.assoc" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="5"/></proof>
 </goal>
 <goal name="M.neutral" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
 </goal>
 <goal name="M.M.assoc" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="5"/></proof>
 </goal>
 <goal name="M.M.neutral" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
 </goal>
 <goal name="M.zero&#39;vc" expl="VC for zero" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="4"/></proof>
 </goal>
 <goal name="M.op&#39;vc" expl="VC for op" proved="true">
 <proof prover="4" timelimit="5"><result status="valid" time="0.01" steps="58"/></proof>
 </goal>
 <goal name="monoid_sum_is_min&#39;vc" expl="VC for monoid_sum_is_min" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="monoid_sum_is_min&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="6"/></proof>
  </goal>
  <goal name="monoid_sum_is_min&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="22"/></proof>
  </goal>
  <goal name="monoid_sum_is_min&#39;vc.2" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="8"/></proof>
  </goal>
  <goal name="monoid_sum_is_min&#39;vc.3" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="43"/></proof>
  </goal>
  <goal name="monoid_sum_is_min&#39;vc.4" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="monoid_sum_is_min&#39;vc.4.0" expl="VC for monoid_sum_is_min" proved="true">
   <proof prover="1"><result status="valid" time="0.09" steps="27405"/></proof>
   </goal>
   <goal name="monoid_sum_is_min&#39;vc.4.1" expl="VC for monoid_sum_is_min" proved="true">
   <proof prover="1"><result status="valid" time="2.08" steps="173173"/></proof>
   </goal>
   <goal name="monoid_sum_is_min&#39;vc.4.2" expl="VC for monoid_sum_is_min" proved="true">
   <proof prover="1"><result status="valid" time="0.10" steps="29055"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="selected_is_min&#39;vc" expl="VC for selected_is_min" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="selected_is_min&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="6"/></proof>
  </goal>
  <goal name="selected_is_min&#39;vc.1" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="selected_is_min&#39;vc.1.0" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.64" steps="1705"/></proof>
   </goal>
   <goal name="selected_is_min&#39;vc.1.1" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.84" steps="132427"/></proof>
   </goal>
   <goal name="selected_is_min&#39;vc.1.2" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.27" steps="58807"/></proof>
   </goal>
   <goal name="selected_is_min&#39;vc.1.3" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="9"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="selected_is_min&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="23"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="selected_part&#39;vc" expl="VC for selected_part" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="selected_part&#39;vc.0" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="selected_part&#39;vc.0.0" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.20" steps="986"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.1" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="183"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.2" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="10"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.3" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.06" steps="158"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.4" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="147"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.5" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="10"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.6" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.09" steps="250"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.7" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.65" steps="2063"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.8" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="33"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.9" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.21" steps="891"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.10" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.17" steps="848"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.11" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="23"/></proof>
   </goal>
   <goal name="selected_part&#39;vc.0.12" expl="VC for selected_part" proved="true">
   <proof prover="4"><result status="valid" time="0.80" steps="1959"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="Sel.M.assoc" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="5"/></proof>
 </goal>
 <goal name="Sel.M.neutral" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
 </goal>
 <goal name="Sel.M.zero&#39;refn&#39;vc" expl="VC for zero&#39;refn" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="4"/></proof>
 </goal>
 <goal name="Sel.M.op&#39;refn&#39;vc" expl="VC for op&#39;refn" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="4"/></proof>
 </goal>
 <goal name="Sel.M.agg_empty" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
 </goal>
 <goal name="Sel.M.agg_sing" proved="true">
 <proof prover="1"><result status="valid" time="0.08" steps="20157"/></proof>
 </goal>
 <goal name="Sel.M.agg_cat" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="5"/></proof>
 </goal>
 <goal name="Sel.balancing&#39;refn&#39;vc" expl="VC for balancing&#39;refn" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="4"/></proof>
 </goal>
 <goal name="Sel.selection_empty" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="9"/></proof>
 </goal>
 <goal name="Sel.selected_part&#39;refn&#39;vc" expl="VC for selected_part&#39;refn" proved="true">
 <proof prover="4"><result status="valid" time="0.04" steps="257"/></proof>
 </goal>
 <goal name="to_bag&#39;vc" expl="VC for to_bag" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="6"/></proof>
 </goal>
 <goal name="to_bag_mem&#39;vc" expl="VC for to_bag_mem" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="to_bag_mem&#39;vc.0" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="to_bag_mem&#39;vc.0.0" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="39"/></proof>
   </goal>
   <goal name="to_bag_mem&#39;vc.0.1" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="69"/></proof>
   </goal>
   <goal name="to_bag_mem&#39;vc.0.2" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.04" steps="189"/></proof>
   </goal>
   <goal name="to_bag_mem&#39;vc.0.3" expl="VC for to_bag_mem" proved="true">
   <proof prover="4"><result status="valid" time="0.24" steps="559"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="to_bag_mem&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4" timelimit="10"><result status="valid" time="0.04" steps="189"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="get_minimum_index&#39;vc" expl="VC for get_minimum_index" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="get_minimum_index&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="51"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="30"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="8"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.3" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.17" steps="203"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.4" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.23" steps="348"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="115"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="16"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.22" steps="320"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="17"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.10" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.70" steps="1347"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="13"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="60"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="14"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="36"/></proof>
  </goal>
  <goal name="get_minimum_index&#39;vc.15" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="27"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="split_gives_minimum&#39;vc" expl="VC for split_gives_minimum" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="split_gives_minimum&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="47"/></proof>
  </goal>
  <goal name="split_gives_minimum&#39;vc.1" expl="unreachable point" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="11"/></proof>
  </goal>
  <goal name="split_gives_minimum&#39;vc.2" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="221"/></proof>
  </goal>
  <goal name="split_gives_minimum&#39;vc.3" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.15" steps="144"/></proof>
  </goal>
  <goal name="split_gives_minimum&#39;vc.4" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.52" steps="117465"/></proof>
  </goal>
  <goal name="split_gives_minimum&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.31" steps="584"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="correction&#39;vc" expl="VC for correction" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="correction&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="13"/></proof>
  </goal>
  <goal name="correction&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.26" steps="418"/></proof>
  </goal>
  <goal name="correction&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="84"/></proof>
  </goal>
  <goal name="correction&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4" timelimit="20"><result status="valid" time="2.53" steps="1306"/></proof>
  </goal>
  <goal name="correction&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="38"/></proof>
  </goal>
  <goal name="correction&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="7"/></proof>
  </goal>
  <goal name="correction&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="18"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
 </goal>
 <goal name="singleton&#39;vc" expl="VC for singleton" proved="true">
 <proof prover="4"><result status="valid" time="0.03" steps="85"/></proof>
 </goal>
 <goal name="is_empty&#39;vc" expl="VC for is_empty" proved="true">
 <proof prover="4"><result status="valid" time="0.04" steps="125"/></proof>
 </goal>
 <goal name="merge&#39;vc" expl="VC for merge" proved="true">
 <proof prover="4"><result status="valid" time="0.48" steps="993"/></proof>
 </goal>
 <goal name="remove_count&#39;vc" expl="VC for remove_count" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="remove_count&#39;vc.0" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="72"/></proof>
  </goal>
  <goal name="remove_count&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="1" timelimit="10"><result status="valid" time="0.83" steps="195278"/></proof>
  </goal>
  <goal name="remove_count&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="1" timelimit="10"><result status="valid" time="0.22" steps="49761"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="extract_min&#39;vc" expl="VC for extract_min" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="extract_min&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="21"/></proof>
  </goal>
  <goal name="extract_min&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="extract_min&#39;vc.2" expl="unreachable point" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="15"/></proof>
  </goal>
  <goal name="extract_min&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extract_min&#39;vc.3.0" expl="VC for extract_min" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="22"/></proof>
   </goal>
   <goal name="extract_min&#39;vc.3.1" expl="VC for extract_min" proved="true">
   <proof prover="4"><result status="valid" time="0.04" steps="24"/></proof>
   </goal>
   <goal name="extract_min&#39;vc.3.2" expl="VC for extract_min" proved="true">
   <proof prover="4"><result status="valid" time="0.12" steps="106"/></proof>
   </goal>
   <goal name="extract_min&#39;vc.3.3" expl="VC for extract_min" proved="true">
   <proof prover="3"><result status="valid" time="0.06"/></proof>
   </goal>
   <goal name="extract_min&#39;vc.3.4" expl="VC for extract_min" proved="true">
   <proof prover="4"><result status="valid" time="0.06" steps="55"/></proof>
   </goal>
   <goal name="extract_min&#39;vc.3.5" expl="VC for extract_min" proved="true">
   <proof prover="3"><result status="valid" time="0.06"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="min&#39;vc" expl="VC for min" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="min&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="13"/></proof>
  </goal>
  <goal name="min&#39;vc.1" expl="unreachable point" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="11"/></proof>
  </goal>
  <goal name="min&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.15" steps="165"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="pop_min&#39;vc" expl="VC for pop_min" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="pop_min&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="13"/></proof>
  </goal>
  <goal name="pop_min&#39;vc.1" expl="unreachable point" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="11"/></proof>
  </goal>
  <goal name="pop_min&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="11"/></proof>
  </goal>
  <goal name="pop_min&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="pop_min&#39;vc.3.0" expl="VC for pop_min" proved="true">
   <proof prover="4"><result status="valid" time="0.12" steps="77"/></proof>
   </goal>
   <goal name="pop_min&#39;vc.3.1" expl="VC for pop_min" proved="true">
   <proof prover="4" timelimit="5"><result status="valid" time="1.03" steps="614"/></proof>
   </goal>
   <goal name="pop_min&#39;vc.3.2" expl="VC for pop_min" proved="true">
   <proof prover="4" timelimit="20"><result status="valid" time="5.97" steps="2292"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="add&#39;vc" expl="VC for add" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="add&#39;vc.0" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="81"/></proof>
  </goal>
  <goal name="add&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4" timelimit="20"><result status="valid" time="0.77" steps="1268"/></proof>
  </goal>
  <goal name="add&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
