<?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="Z3" version="4.6.0" timelimit="11" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.2.0" timelimit="11" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.5" timelimit="11" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="isqrt.mlw"/>
<theory name="Square" proved="true">
 <goal name="sqr_non_neg" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="869"/></proof>
 <proof prover="3" timelimit="5"><result status="valid" time="0.00" steps="2"/></proof>
 </goal>
 <goal name="sqr_increasing" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="1370"/></proof>
 </goal>
 <goal name="sqr_sum" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="2"/></proof>
 </goal>
</theory>
<theory name="Simple" proved="true">
 <goal name="isqrt&#39;vc" expl="VC for isqrt" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="101"/></proof>
 </goal>
 <goal name="main&#39;vc" expl="VC for main" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="12"/></proof>
 </goal>
</theory>
<theory name="NewtonMethod" proved="true">
 <goal name="sqrt&#39;vc" expl="VC for sqrt" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="sqrt&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="16"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.2" expl="check division by zero" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="8"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="10"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="13"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="17"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.8" expl="check division by zero" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.9" expl="check division by zero" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.10" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="sqrt&#39;vc.10.0" expl="VC for sqrt" proved="true">
   <proof prover="4"><result status="valid" time="0.01" steps="8099"/></proof>
   </goal>
   <goal name="sqrt&#39;vc.10.1" expl="VC for sqrt" proved="true">
   <proof prover="1"><result status="valid" time="0.03" steps="317"/></proof>
   </goal>
   <goal name="sqrt&#39;vc.10.2" expl="VC for sqrt" proved="true">
   <proof prover="3"><result status="valid" time="0.04" steps="30"/></proof>
   </goal>
   <goal name="sqrt&#39;vc.10.3" expl="VC for sqrt" proved="true">
   <proof prover="3"><result status="valid" time="0.01" steps="32"/></proof>
   </goal>
   <goal name="sqrt&#39;vc.10.4" expl="VC for sqrt" proved="true">
   <proof prover="3"><result status="valid" time="0.00" steps="30"/></proof>
   </goal>
   <goal name="sqrt&#39;vc.10.5" expl="VC for sqrt" proved="true">
   <proof prover="3"><result status="valid" time="0.00" steps="30"/></proof>
   </goal>
   <goal name="sqrt&#39;vc.10.6" expl="VC for sqrt" proved="true">
   <proof prover="3"><result status="valid" time="0.01" steps="32"/></proof>
   </goal>
   <goal name="sqrt&#39;vc.10.7" expl="VC for sqrt" proved="true">
   <proof prover="3"><result status="valid" time="0.00" steps="32"/></proof>
   </goal>
   <goal name="sqrt&#39;vc.10.8" expl="VC for sqrt" proved="true">
   <proof prover="3"><result status="valid" time="0.01" steps="40"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sqrt&#39;vc.11" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="26"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.10" steps="92"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="28"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="29"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="30"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="31"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.17" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="61"/></proof>
  </goal>
  <goal name="sqrt&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="5840"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
