<?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="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.12.2" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="verifythis_2021_shearsort_modified.mlw"/>
<theory name="Top" proved="true">
 <goal name="inv_nonneg&#39;vc" expl="VC for inv_nonneg" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="inv_nonneg&#39;vc.0" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="10968"/></proof>
  </goal>
  <goal name="inv_nonneg&#39;vc.1" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.305503" steps="39502"/></proof>
  </goal>
  <goal name="inv_nonneg&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="188866"/></proof>
  </goal>
  <goal name="inv_nonneg&#39;vc.3" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="inv_nonneg&#39;vc.3.0" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.060000" steps="11509"/></proof>
   </goal>
   <goal name="inv_nonneg&#39;vc.3.1" expl="assertion" proved="true">
   <transf name="unfold" proved="true" arg1="inversions">
    <goal name="inv_nonneg&#39;vc.3.1.0" expl="assertion" proved="true">
    <transf name="apply" proved="true" arg1="sum_le">
     <goal name="inv_nonneg&#39;vc.3.1.0.0" expl="apply premises" proved="true">
     <transf name="split_vc" proved="true" >
      <goal name="inv_nonneg&#39;vc.3.1.0.0.0" expl="apply premises" proved="true">
      <transf name="compute_specified" proved="true" >
       <goal name="inv_nonneg&#39;vc.3.1.0.0.0.0" expl="apply premises" proved="true">
       <proof prover="1"><result status="valid" time="0.179659" steps="356131"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="inv_nonneg&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="10855"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="shearsort&#39;vc" expl="VC for shearsort" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="shearsort&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="7261"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="7805"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="8138"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="7826"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="7947"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.5" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="8229"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.6" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(k=i)">
   <goal name="shearsort&#39;vc.6.0" expl="true case (loop invariant preservation)" proved="true">
   <proof prover="0" timelimit="5"><result status="valid" time="0.060000" steps="11277"/></proof>
   </goal>
   <goal name="shearsort&#39;vc.6.1" expl="false case (loop invariant preservation)" proved="true">
   <proof prover="0" timelimit="5"><result status="valid" time="2.344945" steps="228628"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="shearsort&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="12343"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="11267"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="7981"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="8153"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.11" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="8571"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.12" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="8187"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.13" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="8190"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.14" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="11445"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="11469"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.16" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(l = j)">
   <goal name="shearsort&#39;vc.16.0" expl="true case (loop invariant preservation)" proved="true">
   <proof prover="0" timelimit="5"><result status="valid" time="0.060000" steps="11999"/></proof>
   </goal>
   <goal name="shearsort&#39;vc.16.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="unfold" proved="true" arg1="sorted_column">
    <goal name="shearsort&#39;vc.16.1.0" expl="VC for shearsort" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="shearsort&#39;vc.16.1.0.0" expl="VC for shearsort" proved="true">
     <proof prover="0"><result status="valid" time="0.040000" steps="11561"/></proof>
     </goal>
     <goal name="shearsort&#39;vc.16.1.0.1" expl="VC for shearsort" proved="true">
     <proof prover="0"><result status="valid" time="0.040000" steps="12018"/></proof>
     </goal>
     <goal name="shearsort&#39;vc.16.1.0.2" expl="VC for shearsort" proved="true">
     <transf name="rewrite" proved="true" arg1="Ensures5">
      <goal name="shearsort&#39;vc.16.1.0.2.0" expl="VC for shearsort" proved="true">
      <transf name="unfold" proved="true" arg1="sorted_column" arg2="in" arg3="LoopInvariant4">
       <goal name="shearsort&#39;vc.16.1.0.2.0.0" expl="VC for shearsort" proved="true">
       <proof prover="0"><result status="valid" time="0.200000" steps="29120"/></proof>
       </goal>
      </transf>
      </goal>
      <goal name="shearsort&#39;vc.16.1.0.2.1" expl="rewrite premises" proved="true">
      <proof prover="0"><result status="valid" time="0.050000" steps="12084"/></proof>
      </goal>
      <goal name="shearsort&#39;vc.16.1.0.2.2" expl="rewrite premises" proved="true">
      <proof prover="0"><result status="valid" time="0.050000" steps="12090"/></proof>
      </goal>
      <goal name="shearsort&#39;vc.16.1.0.2.3" expl="rewrite premises" proved="true">
      <proof prover="0"><result status="valid" time="0.040000" steps="11607"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="shearsort&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="12872"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="12015"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="12040"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="13491"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.21" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(l = j)">
   <goal name="shearsort&#39;vc.21.0" expl="true case (loop invariant preservation)" proved="true">
   <proof prover="0"><result status="valid" time="0.030000" steps="12024"/></proof>
   </goal>
   <goal name="shearsort&#39;vc.21.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="unfold" proved="true" arg1="sorted_column">
    <goal name="shearsort&#39;vc.21.1.0" expl="VC for shearsort" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="shearsort&#39;vc.21.1.0.0" expl="VC for shearsort" proved="true">
     <proof prover="0"><result status="valid" time="0.030000" steps="11558"/></proof>
     </goal>
     <goal name="shearsort&#39;vc.21.1.0.1" expl="VC for shearsort" proved="true">
     <proof prover="0"><result status="valid" time="0.050000" steps="11996"/></proof>
     </goal>
     <goal name="shearsort&#39;vc.21.1.0.2" expl="VC for shearsort" proved="true">
     <transf name="rewrite" proved="true" arg1="Ensures5">
      <goal name="shearsort&#39;vc.21.1.0.2.0" expl="VC for shearsort" proved="true">
      <transf name="rewrite" proved="true" arg1="Ensures5">
       <goal name="shearsort&#39;vc.21.1.0.2.0.0" expl="VC for shearsort" proved="true">
       <transf name="unfold" proved="true" arg1="sorted_column" arg2="in" arg3="LoopInvariant4">
        <goal name="shearsort&#39;vc.21.1.0.2.0.0.0" expl="VC for shearsort" proved="true">
        <proof prover="0"><result status="valid" time="0.080000" steps="16773"/></proof>
        </goal>
       </transf>
       </goal>
       <goal name="shearsort&#39;vc.21.1.0.2.0.1" expl="rewrite premises" proved="true">
       <proof prover="0"><result status="valid" time="0.060000" steps="12047"/></proof>
       </goal>
       <goal name="shearsort&#39;vc.21.1.0.2.0.2" expl="rewrite premises" proved="true">
       <proof prover="0"><result status="valid" time="0.060000" steps="12068"/></proof>
       </goal>
       <goal name="shearsort&#39;vc.21.1.0.2.0.3" expl="rewrite premises" proved="true">
       <proof prover="0"><result status="valid" time="0.040000" steps="11604"/></proof>
       </goal>
      </transf>
      </goal>
      <goal name="shearsort&#39;vc.21.1.0.2.1" expl="rewrite premises" proved="true">
      <proof prover="0"><result status="valid" time="0.060000" steps="12062"/></proof>
      </goal>
      <goal name="shearsort&#39;vc.21.1.0.2.2" expl="rewrite premises" proved="true">
      <proof prover="0"><result status="valid" time="0.060000" steps="12068"/></proof>
      </goal>
      <goal name="shearsort&#39;vc.21.1.0.2.3" expl="rewrite premises" proved="true">
      <proof prover="0"><result status="valid" time="0.050000" steps="11604"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="shearsort&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="12835"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="11994"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="12030"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="0" timelimit="5"><result status="valid" time="1.661281" steps="180046"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.26" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="12400"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.27" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="12589"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.28" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="11224"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.29" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="shearsort&#39;vc.29.0" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.241251" steps="26110"/></proof>
   </goal>
   <goal name="shearsort&#39;vc.29.1" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.070000" steps="16181"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="shearsort&#39;vc.30" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.190000" steps="23833"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.31" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.160000" steps="27373"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.32" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="shearsort&#39;vc.32.0" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.080000" steps="17068"/></proof>
   </goal>
   <goal name="shearsort&#39;vc.32.1" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.080000" steps="17092"/></proof>
   </goal>
   <goal name="shearsort&#39;vc.32.2" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.100000" steps="17361"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="shearsort&#39;vc.33" expl="postcondition" proved="true">
  <proof prover="0" timelimit="5"><result status="valid" time="0.710051" steps="74410"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.34" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.164761" steps="16945"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.35" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.050000" steps="12160"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.36" expl="loop variant decrease" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="shearsort&#39;vc.36.0" expl="loop variant decrease" proved="true">
   <proof prover="0"><result status="valid" time="0.050000" steps="11873"/></proof>
   </goal>
   <goal name="shearsort&#39;vc.36.1" expl="loop variant decrease" proved="true">
   <proof prover="0"><result status="valid" time="0.050000" steps="11428"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="shearsort&#39;vc.37" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="11575"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.38" expl="out of loop bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="11862"/></proof>
  </goal>
  <goal name="shearsort&#39;vc.39" expl="out of loop bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.090000" steps="19212"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
