<?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="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Z3" version="4.12.2" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Alt-Ergo" version="2.3.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="insertion_sort.mlw"/>
<theory name="InsertionSort" proved="true">
 <goal name="insertion_sort&#39;vc" expl="VC for insertion_sort" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="insertion_sort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="40195"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="34905"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="34546"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.120000" steps="324"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="40055"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="36351"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="37455"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.7" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="38111"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="38094"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.9" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="54790"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.10" expl="loop variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="18926"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="48981"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="13813"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="77551"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="53607"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.15" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="41846"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.16" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="38242"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="58659"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="9772"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="34569"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.20" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="35187"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="test1&#39;vc" expl="VC for test1" proved="true">
 <proof prover="4"><result status="valid" time="0.010000" steps="47092"/></proof>
 </goal>
 <goal name="test2&#39;vc" expl="VC for test2" proved="true">
 <proof prover="4"><result status="valid" time="0.020000" steps="54042"/></proof>
 </goal>
 <goal name="bench&#39;vc" expl="VC for bench" proved="true">
 <proof prover="4"><result status="valid" time="0.010000" steps="34017"/></proof>
 </goal>
</theory>
<theory name="InsertionSortGen" proved="true">
 <goal name="insertion_sort&#39;vc" expl="VC for insertion_sort" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="insertion_sort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="10222"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="35823"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="36071"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="35702"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.090000" steps="310"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="78"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="37403"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.7" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="38484"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="39075"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.9" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="39054"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.10" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="58822"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.11" expl="loop variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="19388"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="49966"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="13305"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="64724"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="56207"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.16" expl="assertion" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.010000" steps="67"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.17" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="39159"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="4" timelimit="5"><result status="valid" time="0.020000" steps="55184"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="19456"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="10081"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="35713"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.22" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="36331"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="InsertionSortSwaps" proved="true">
 <goal name="insertion_sort&#39;vc" expl="VC for insertion_sort" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="insertion_sort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="8732"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="9599"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="8919"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="8643"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="9869"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="9233"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="9247"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.7" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="9432"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.8" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="9027"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="9505"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.060000" steps="11686"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.100000" steps="467"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="12563"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="9138"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="9768"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="8739"/></proof>
  </goal>
  <goal name="insertion_sort&#39;vc.16" expl="out of loop bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.050000" steps="10088"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
