<?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="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Z3" version="4.5.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Coq" version="8.11.2" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="heapsort.mlw"/>
<theory name="HeapSort" proved="true">
 <goal name="min_of_sorted&#39;vc" expl="VC for min_of_sorted" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="min_of_sorted&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="10113"/></proof>
  </goal>
  <goal name="min_of_sorted&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="10085"/></proof>
  </goal>
  <goal name="min_of_sorted&#39;vc.2" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="11002"/></proof>
  </goal>
  <goal name="min_of_sorted&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.100000" steps="22559"/></proof>
  </goal>
 </transf>
 </goal>
 <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="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="7917"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="11820"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="11454"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.3" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="heapSort&#39;vc.3.0" expl="VC for heapSort" proved="true">
   <proof prover="0"><result status="valid" time="0.020000" steps="11954"/></proof>
   </goal>
   <goal name="heapSort&#39;vc.3.1" expl="VC for heapSort" proved="true">
   <proof prover="0"><result status="valid" time="0.020000" steps="11159"/></proof>
   </goal>
   <goal name="heapSort&#39;vc.3.2" expl="VC for heapSort" proved="true">
   <proof prover="1" timelimit="1"><result status="valid" time="0.010000" steps="13"/></proof>
   </goal>
   <goal name="heapSort&#39;vc.3.3" expl="VC for heapSort" proved="true">
   <proof prover="0"><result status="valid" time="0.060000" steps="13165"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="heapSort&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="14746"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.5" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="12463"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="13060"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1" timelimit="1"><result status="valid" time="0.030000" steps="111"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.8" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="heapSort&#39;vc.8.0" expl="VC for heapSort" proved="true">
   <proof prover="0"><result status="valid" time="0.020000" steps="13561"/></proof>
   </goal>
   <goal name="heapSort&#39;vc.8.1" expl="VC for heapSort" proved="true">
   <proof prover="0"><result status="valid" time="0.020000" steps="11935"/></proof>
   </goal>
   <goal name="heapSort&#39;vc.8.2" expl="VC for heapSort" proved="true">
   <proof prover="0"><result status="valid" time="0.020000" steps="12367"/></proof>
   </goal>
   <goal name="heapSort&#39;vc.8.3" expl="VC for heapSort" proved="true">
   <proof prover="0"><result status="valid" time="0.110000" steps="22513"/></proof>
   </goal>
   <goal name="heapSort&#39;vc.8.4" expl="VC for heapSort" proved="true">
   <proof prover="1" timelimit="1"><result status="valid" time="0.040000" steps="78"/></proof>
   </goal>
   <goal name="heapSort&#39;vc.8.5" expl="VC for heapSort" proved="true">
   <proof prover="1" timelimit="1"><result status="valid" time="0.030000" steps="93"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="heapSort&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="13427"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="10737"/></proof>
  </goal>
  <goal name="heapSort&#39;vc.11" expl="out of loop bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="14354"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
<file format="whyml" proved="true">
<path name=".."/><path name="heap.why"/>
<theory name="Heap" proved="true">
 <goal name="Parent_inf" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
 </goal>
 <goal name="Left_sup" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="3"/></proof>
 </goal>
 <goal name="Right_sup" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="3"/></proof>
 </goal>
 <goal name="Parent_right" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="9"/></proof>
 </goal>
 <goal name="Parent_left" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
 </goal>
 <goal name="Inf_parent" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
 </goal>
 <goal name="Child_parent" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="16"/></proof>
 </goal>
 <goal name="Parent_pos" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
 </goal>
 <goal name="Is_heap_when_no_element" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="4"/></proof>
 </goal>
 <goal name="Is_heap_sub" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="21"/></proof>
 </goal>
 <goal name="Is_heap_sub2" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="19"/></proof>
 </goal>
 <goal name="Is_heap_when_node_modified" proved="true">
 <proof prover="1"><result status="valid" time="0.150000" steps="360"/></proof>
 </goal>
 <goal name="Is_heap_add_last" proved="true">
 <proof prover="1"><result status="valid" time="0.050000" steps="180"/></proof>
 </goal>
 <goal name="Parent_inf_el" proved="true">
 <proof prover="2"><result status="valid" time="0.120000"/></proof>
 </goal>
 <goal name="Left_sup_el" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
 </goal>
 <goal name="Right_sup_el" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="12"/></proof>
 </goal>
 <goal name="is_heap_relation&#39;vc" expl="VC for is_heap_relation" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="is_heap_relation&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="is_heap_relation&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="is_heap_relation&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="is_heap_relation&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="9"/></proof>
  </goal>
  <goal name="is_heap_relation&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="31"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
<file format="whyml" proved="true">
<path name=".."/><path name="bag_of_integers.why"/>
<theory name="Bag_integers" proved="true">
 <goal name="Min_bag_union1" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
 </goal>
 <goal name="Min_bag_union2" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="16"/></proof>
 </goal>
</theory>
</file>
<file format="whyml" proved="true">
<path name=".."/><path name="test_harness.mlw"/>
<theory name="TestHarness" proved="true">
 <goal name="testHarness&#39;vc" expl="VC for testHarness" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="testHarness&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="1"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="2"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="10611"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="10843"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="11101"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1" timelimit="1"><result status="valid" time="0.010000" steps="81"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.6" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="34389"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.7" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="14955"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.8" expl="assertion" proved="true">
  <proof prover="1" timelimit="1"><result status="valid" time="0.040000" steps="104"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.9" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="15325"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.10" expl="assertion" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.090000" steps="22286"/></proof>
  </goal>
  <goal name="testHarness&#39;vc.11" expl="assertion" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.180000" steps="22339"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
<file format="whyml" proved="true">
<path name=".."/><path name="elements.why"/>
<theory name="Elements" proved="true">
 <goal name="Elements_singleton" proved="true">
 <proof prover="0"><result status="valid" time="0.030000" steps="6862"/></proof>
 </goal>
 <goal name="Elements_union" proved="true">
 <proof prover="5"><path name="elements_Elements_Elements_union_1.v"/><result status="valid" time="0.400000"/></proof>
 </goal>
 <goal name="Elements_add1" proved="true">
 <proof prover="5"><path name="elements_Elements_Elements_add1_1.v"/><result status="valid" time="0.330000"/></proof>
 </goal>
 <goal name="Elements_remove_last" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="9"/></proof>
 </goal>
 <goal name="Occ_elements" proved="true">
 <proof prover="5"><path name="elements_Elements_Occ_elements_1.v"/><result status="valid" time="0.340000"/></proof>
 </goal>
 <goal name="elements_set_outside&#39;vc" expl="VC for elements_set_outside" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="elements_set_outside&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="3"/></proof>
  </goal>
  <goal name="elements_set_outside&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="3"/></proof>
  </goal>
  <goal name="elements_set_outside&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="12663"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="Elements_set_inside" proved="true">
 <proof prover="5"><path name="elements_Elements_Elements_set_inside_1.v"/><result status="valid" time="0.543266"/></proof>
 </goal>
 <goal name="Elements_set_inside2" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="44"/></proof>
 </goal>
</theory>
</file>
<file format="whyml" proved="true">
<path name=".."/><path name="heap_implem.mlw"/>
<theory name="Implementation" proved="true">
 <goal name="is_heap_min&#39;vc" expl="VC for is_heap_min" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="is_heap_min&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4"/></proof>
  </goal>
  <goal name="is_heap_min&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4"/></proof>
  </goal>
  <goal name="is_heap_min&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="is_heap_min&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="1.166571" steps="699"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="create&#39;vc" expl="VC for create" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
 </goal>
 <goal name="insert&#39;vc" expl="VC for insert" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="insert&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="insert&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="5"/></proof>
  </goal>
  <goal name="insert&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="183"/></proof>
  </goal>
  <goal name="insert&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="78"/></proof>
  </goal>
  <goal name="insert&#39;vc.4" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="insert&#39;vc.4.0" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.130000" steps="46"/></proof>
   </goal>
   <goal name="insert&#39;vc.4.1" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.140000" steps="190"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="insert&#39;vc.5" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="24"/></proof>
  </goal>
  <goal name="insert&#39;vc.6" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="insert&#39;vc.6.0" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="30"/></proof>
   </goal>
   <goal name="insert&#39;vc.6.1" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="30"/></proof>
   </goal>
   <goal name="insert&#39;vc.6.2" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.030000" steps="62"/></proof>
   </goal>
   <goal name="insert&#39;vc.6.3" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.040000" steps="58"/></proof>
   </goal>
   <goal name="insert&#39;vc.6.4" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.790000" steps="608"/></proof>
   </goal>
   <goal name="insert&#39;vc.6.5" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="13"/></proof>
   </goal>
   <goal name="insert&#39;vc.6.6" expl="VC for insert" proved="true">
   <proof prover="0"><result status="valid" time="0.152173" steps="28121"/></proof>
   <proof prover="1"><result status="valid" time="0.420000" steps="496"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="insert&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="9"/></proof>
  </goal>
  <goal name="insert&#39;vc.8" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="65"/></proof>
  </goal>
  <goal name="insert&#39;vc.9" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="insert&#39;vc.9.0" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.150000" steps="228"/></proof>
   </goal>
   <goal name="insert&#39;vc.9.1" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="28"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="extractMin&#39;vc" expl="VC for extractMin" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="extractMin&#39;vc.0" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.330000" steps="646"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.2" expl="loop invariant init" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.2.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.2.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="1"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.2.2" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.040000" steps="101"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.2.3" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.240000" steps="378"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.2.4" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="146"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.4" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="17"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="1.190618" steps="806"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.6" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.6.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="20"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.6.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="106"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.6.2" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="1.032636" steps="660"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.7" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.7.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="12"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.7.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="12"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.7.2" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="12"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.8" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="162"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.9" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="129"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="2.015429" steps="1095"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.11" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.11.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="27"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.11.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="59"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.11.2" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.740000" steps="568"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.12" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.12.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="19"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.12.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="19"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.12.2" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="19"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.13" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.14" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.14.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="22"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.14.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="23"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.14.2" expl="VC for extractMin" proved="true">
   <proof prover="0"><result status="valid" time="0.620000" steps="89144"/></proof>
   <proof prover="1"><result status="valid" time="5.119712" steps="1435"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.14.3" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.14.4" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="76"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.14.5" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.060000" steps="66"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="157"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.16" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="123"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.17" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="2.060000" steps="1087"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.18" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.18.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="25"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.18.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="56"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.18.2" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.750000" steps="565"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="17"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.20" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="20"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.21" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.21.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="20"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.21.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="21"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.21.2" expl="VC for extractMin" proved="true">
   <proof prover="0"><result status="valid" time="0.759772" steps="87950"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.21.3" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="20"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.21.4" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="74"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.21.5" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.040000" steps="61"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.22" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="152"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.23" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="32"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.24" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="2.350000" steps="1188"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.950000" steps="672"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="15"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.27" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="18"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.28" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.28.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="18"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.28.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="19"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.28.2" expl="VC for extractMin" proved="true">
   <proof prover="0"><result status="valid" time="0.390000" steps="67298"/></proof>
   <proof prover="1"><result status="valid" time="2.610000" steps="930"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.28.3" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="18"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.28.4" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="70"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.28.5" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.040000" steps="58"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.29" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="10"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.30" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.31" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="11"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.32" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
  </goal>
  <goal name="extractMin&#39;vc.33" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.33.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="11"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.33.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="11"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.33.2" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="extractMin&#39;vc.34" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="extractMin&#39;vc.34.0" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.020000" steps="15"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.34.1" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.030000" steps="26"/></proof>
   </goal>
   <goal name="extractMin&#39;vc.34.2" expl="VC for extractMin" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="23"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
</file>
<file format="whyml" proved="true">
<path name=".."/><path name="abstract_heap.mlw"/>
</file>
<file format="whyml" proved="true">
<path name=".."/><path name="heap_model.why"/>
<theory name="Model" proved="true">
 <goal name="Model_empty" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="5"/></proof>
 </goal>
 <goal name="Model_singleton" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
 </goal>
 <goal name="Model_set" proved="true">
 <proof prover="1"><result status="valid" time="0.300000" steps="336"/></proof>
 </goal>
 <goal name="Model_add_last" proved="true">
 <proof prover="0"><result status="valid" time="0.040000" steps="17240"/></proof>
 </goal>
</theory>
</file>
</why3session>
