<?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="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="hillel_challenge.mlw"/>
<theory name="Leftpad" proved="true">
 <goal name="leftpad&#39;vc" expl="VC for leftpad" proved="true">
 <proof prover="1"><result status="valid" time="0.400000" steps="628"/></proof>
 </goal>
</theory>
<theory name="Unique" proved="true">
 <goal name="unique&#39;vc" expl="VC for unique" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="unique&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="6369"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="4"/></proof>
  </goal>
  <goal name="unique&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="6324"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
  </goal>
  <goal name="unique&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="7551"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="unique&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="7580"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="43"/></proof>
  </goal>
  <goal name="unique&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="7463"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
  </goal>
  <goal name="unique&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="7375"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="16"/></proof>
  </goal>
  <goal name="unique&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="7387"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="unique&#39;vc.7" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="7496"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="unique&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="7744"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="unique&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="8818"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
  </goal>
  <goal name="unique&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="572"/></proof>
  </goal>
  <goal name="unique&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.150000" steps="721"/></proof>
  </goal>
  <goal name="unique&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="149"/></proof>
  </goal>
  <goal name="unique&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="7595"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="unique&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.140000" steps="19071"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="157"/></proof>
  </goal>
  <goal name="unique&#39;vc.15" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="x=a[i]">
   <goal name="unique&#39;vc.15.0" expl="true case (loop invariant preservation)" proved="true">
   <proof prover="0"><result status="valid" time="0.080000" steps="8290"/></proof>
   <proof prover="1"><result status="valid" time="0.010000" steps="27"/></proof>
   </goal>
   <goal name="unique&#39;vc.15.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="assert" proved="true" arg1="(mem x a (i+1) &lt;-&gt; mem x a i)">
    <goal name="unique&#39;vc.15.1.0" expl="asserted formula" proved="true">
    <proof prover="0"><result status="valid" time="0.080000" steps="8226"/></proof>
    <proof prover="1"><result status="valid" time="0.010000" steps="36"/></proof>
    </goal>
    <goal name="unique&#39;vc.15.1.1" expl="false case (loop invariant preservation)" proved="true">
    <proof prover="0"><result status="valid" time="0.060000" steps="7800"/></proof>
    <proof prover="1"><result status="valid" time="0.010000" steps="37"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="unique&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="8258"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="unique&#39;vc.17" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="7608"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
  <goal name="unique&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.150000" steps="18880"/></proof>
  <proof prover="3"><result status="valid" time="0.020000" steps="57431"/></proof>
  </goal>
  <goal name="unique&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="8629"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="unique&#39;vc.20" expl="out of loop bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="7025"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="7"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Fulcrum" proved="true">
 <goal name="fulcrum&#39;vc" expl="VC for fulcrum" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="fulcrum&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2897"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="7"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="2394"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.2" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="4287"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="19"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2924"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="2373"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="2375"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="7"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="4287"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="51"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2785"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="14"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="2765"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.9" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="2820"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="20"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="17403"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="50"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="7870"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="54"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3468"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="7010"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="4634"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="68"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="16400"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="46"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="6500"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="50"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3164"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="28"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2935"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.836304" steps="68971"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="35"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="2738"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="14"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3119"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="21"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.22" expl="out of loop bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="2680"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.23" expl="out of loop bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="6587"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="3"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="FulcrumNoOverflow" proved="true">
 <goal name="big&#39;vc" expl="VC for big" proved="true">
 <proof prover="0"><result status="valid" time="0.040000" steps="1772"/></proof>
 <proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
 </goal>
 <goal name="big_zero&#39;vc" expl="VC for big_zero" proved="true">
 <proof prover="0"><result status="valid" time="0.040000" steps="1955"/></proof>
 <proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
 </goal>
 <goal name="add_big&#39;vc" expl="VC for add_big" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="add_big&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="2761"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="48"/></proof>
  </goal>
  <goal name="add_big&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="2987"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="70"/></proof>
  </goal>
  <goal name="add_big&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3099"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="add_big&#39;vc.3" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3178"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="add_big&#39;vc.4" expl="type invariant" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3513"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="123"/></proof>
  </goal>
  <goal name="add_big&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2255"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="30"/></proof>
  </goal>
  <goal name="add_big&#39;vc.6" expl="type invariant" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="add_big&#39;vc.6.0" expl="type invariant" proved="true">
   <proof prover="0"><result status="valid" time="0.040000" steps="2844"/></proof>
   <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
   </goal>
   <goal name="add_big&#39;vc.6.1" expl="type invariant" proved="true">
   <proof prover="0"><result status="valid" time="0.050000" steps="2836"/></proof>
   <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
   </goal>
   <goal name="add_big&#39;vc.6.2" expl="type invariant" proved="true">
   <proof prover="0"><result status="valid" time="0.030000" steps="2122"/></proof>
   <proof prover="1"><result status="valid" time="0.010000" steps="12"/></proof>
   </goal>
   <goal name="add_big&#39;vc.6.3" expl="type invariant" proved="true">
   <proof prover="0"><result status="valid" time="0.050000" steps="2793"/></proof>
   <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
   </goal>
   <goal name="add_big&#39;vc.6.4" expl="type invariant" proved="true">
   <proof prover="0"><result status="valid" time="0.050000" steps="3060"/></proof>
   <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="add_big&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="2189"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="add_big&#39;vc.8" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="2670"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="16"/></proof>
  </goal>
  <goal name="add_big&#39;vc.9" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2882"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="64"/></proof>
  </goal>
  <goal name="add_big&#39;vc.10" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="2991"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="add_big&#39;vc.11" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3121"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="add_big&#39;vc.12" expl="type invariant" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3511"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="120"/></proof>
  </goal>
  <goal name="add_big&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2252"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="30"/></proof>
  </goal>
  <goal name="add_big&#39;vc.14" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3103"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="91"/></proof>
  </goal>
  <goal name="add_big&#39;vc.15" expl="type invariant" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3344"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="143"/></proof>
  </goal>
  <goal name="add_big&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2232"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_big&#39;vc" expl="VC for sub_big" proved="true">
 <proof prover="0"><result status="valid" time="0.060000" steps="5226"/></proof>
 <proof prover="1"><result status="valid" time="0.040000" steps="228"/></proof>
 </goal>
 <goal name="delta&#39;vc" expl="VC for delta" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="delta&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3156"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="69"/></proof>
  </goal>
  <goal name="delta&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3527"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="delta&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3599"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="28"/></proof>
  </goal>
  <goal name="delta&#39;vc.3" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3727"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="30"/></proof>
  </goal>
  <goal name="delta&#39;vc.4" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3814"/></proof>
  <proof prover="1"><result status="valid" time="0.050000" steps="156"/></proof>
  </goal>
  <goal name="delta&#39;vc.5" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="4125"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="123"/></proof>
  </goal>
  <goal name="delta&#39;vc.6" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="4426"/></proof>
  <proof prover="1"><result status="valid" time="0.050000" steps="209"/></proof>
  </goal>
  <goal name="delta&#39;vc.7" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3540"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="delta&#39;vc.8" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3707"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="96"/></proof>
  </goal>
  <goal name="delta&#39;vc.9" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="4064"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="110"/></proof>
  </goal>
  <goal name="delta&#39;vc.10" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3466"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="28"/></proof>
  </goal>
  <goal name="delta&#39;vc.11" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3786"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="139"/></proof>
  </goal>
  <goal name="delta&#39;vc.12" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3646"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="122"/></proof>
  </goal>
  <goal name="delta&#39;vc.13" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3592"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="30"/></proof>
  </goal>
  <goal name="delta&#39;vc.14" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3677"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="32"/></proof>
  </goal>
  <goal name="delta&#39;vc.15" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3807"/></proof>
  <proof prover="1"><result status="valid" time="0.050000" steps="147"/></proof>
  </goal>
  <goal name="delta&#39;vc.16" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="4035"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="119"/></proof>
  </goal>
  <goal name="delta&#39;vc.17" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="4384"/></proof>
  <proof prover="1"><result status="valid" time="0.040000" steps="196"/></proof>
  </goal>
  <goal name="delta&#39;vc.18" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3678"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="93"/></proof>
  </goal>
  <goal name="delta&#39;vc.19" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="4017"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="105"/></proof>
  </goal>
  <goal name="delta&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3180"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="31"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="big_lt&#39;vc" expl="VC for big_lt" proved="true">
 <proof prover="0"><result status="valid" time="0.050000" steps="3462"/></proof>
 <proof prover="1"><result status="valid" time="0.020000" steps="86"/></proof>
 </goal>
 <goal name="sum_bounds&#39;vc" expl="VC for sum_bounds" proved="true">
 <proof prover="0"><result status="valid" time="0.226502" steps="23913"/></proof>
 <proof prover="1"><result status="valid" time="1.270000" steps="1711"/></proof>
 </goal>
 <goal name="fulcrum&#39;vc" expl="VC for fulcrum" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="fulcrum&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3120"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2618"/></proof>
  <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3503"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2910"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="21"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="3967"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="53"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2873"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="6419"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="100"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.7" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="4137"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="74"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.8" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="4099"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2920"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="6232"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="30"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.11" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3140"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="30"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.12" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="2946"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="31"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.13" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="7079"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.14" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3305"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.15" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3513"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="60"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.16" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="5798"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="138"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.17" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3709"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="68"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.18" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="10357"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="151"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.19" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.150000" steps="16763"/></proof>
  <proof prover="1"><result status="valid" time="0.060000" steps="251"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.20" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="10775"/></proof>
  <proof prover="1"><result status="valid" time="0.110000" steps="354"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.21" expl="integer overflow" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="6600"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="88"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.22" expl="type invariant" proved="true">
  <proof prover="0"><result status="valid" time="0.070000" steps="6618"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="89"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3579"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="94"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.190000" steps="17473"/></proof>
  <proof prover="1"><result status="valid" time="0.120000" steps="303"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="1.896718" steps="99350"/></proof>
  <proof prover="1"><result status="valid" time="0.150000" steps="311"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.26" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3986"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="98"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="3.250007" steps="156969"/></proof>
  <proof prover="1"><result status="valid" time="0.030000" steps="102"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.28" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.057657" steps="8230"/></proof>
  <proof prover="1"><result status="valid" time="0.080000" steps="325"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3534"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="86"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.30" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.160000" steps="19693"/></proof>
  <proof prover="1"><result status="valid" time="0.120000" steps="276"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.31" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="1.231574" steps="60639"/></proof>
  <proof prover="1"><result status="valid" time="0.120000" steps="284"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.32" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="3867"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="90"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.33" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3609"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="91"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.34" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.226503" steps="20967"/></proof>
  <proof prover="1"><result status="valid" time="0.040000" steps="97"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.35" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3520"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="56"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.36" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="5735"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="63"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.37" expl="out of loop bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="3304"/></proof>
  <proof prover="1"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="fulcrum&#39;vc.38" expl="out of loop bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="16564"/></proof>
  <proof prover="1"><result status="valid" time="0.020000" steps="9"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
