<?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="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.8.4" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Coq" version="8.11.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Eprover" version="2.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="kmp.mlw"/>
<theory name="KnuthMorrisPratt" proved="true">
 <goal name="matches_empty" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="3422"/></proof>
 <proof prover="5"><result status="valid" time="0.00" steps="7"/></proof>
 </goal>
 <goal name="matches_right_extension" proved="true">
 <proof prover="5" timelimit="1"><result status="valid" time="0.01" steps="25"/></proof>
 </goal>
 <goal name="matches_contradiction_at_first" proved="true">
 <proof prover="4"><result status="valid" time="0.04"/></proof>
 </goal>
 <goal name="matches_contradiction_at_i" proved="true">
 <proof prover="1"><result status="valid" time="0.01" steps="12083"/></proof>
 <proof prover="5"><result status="valid" time="0.00" steps="23"/></proof>
 </goal>
 <goal name="matches_right_weakening" proved="true">
 <proof prover="1"><result status="valid" time="0.42" steps="1602156"/></proof>
 <proof prover="5"><result status="valid" time="0.00" steps="21"/></proof>
 </goal>
 <goal name="matches_left_weakening" proved="true">
 <proof prover="3"><path name="kmp_WP_KnuthMorrisPratt_matches_left_weakening_1.v"/><result status="valid" time="0.35"/></proof>
 </goal>
 <goal name="matches_sym" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="4112"/></proof>
 <proof prover="5"><result status="valid" time="0.00" steps="7"/></proof>
 </goal>
 <goal name="matches_trans" proved="true">
 <proof prover="5" timelimit="1"><result status="valid" time="0.00" steps="26"/></proof>
 </goal>
 <goal name="next_iteration" proved="true">
 <proof prover="0"><result status="valid" time="0.05" steps="14222"/></proof>
 <proof prover="1" timelimit="5"><result status="valid" time="0.02" steps="54610"/></proof>
 </goal>
 <goal name="next_is_maximal" proved="true">
 <proof prover="3"><path name="kmp_WP_KnuthMorrisPratt_next_is_maximal_1.v"/><result status="valid" time="0.31"/></proof>
 </goal>
 <goal name="next_1_0" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="5727"/></proof>
 <proof prover="5"><result status="valid" time="0.00" steps="8"/></proof>
 </goal>
 <goal name="initnext&#39;vc" expl="VC for initnext" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="initnext&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="5352"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="2"/></proof>
  </goal>
  <goal name="initnext&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="6476"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="4"/></proof>
  </goal>
  <goal name="initnext&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="6033"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="7"/></proof>
  </goal>
  <goal name="initnext&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="7045"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="11"/></proof>
  </goal>
  <goal name="initnext&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="6047"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="initnext&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="5" timelimit="1"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="initnext&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="8033"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="initnext&#39;vc.7" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="8029"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="initnext&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="8331"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="16"/></proof>
  </goal>
  <goal name="initnext&#39;vc.9" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="6813"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="19"/></proof>
  </goal>
  <goal name="initnext&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="8836"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="19"/></proof>
  </goal>
  <goal name="initnext&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="9890"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="38"/></proof>
  </goal>
  <goal name="initnext&#39;vc.12" expl="loop invariant preservation" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="initnext&#39;vc.12.0" expl="loop invariant preservation" proved="true">
   <transf name="instantiate" proved="true" arg1="LoopInvariant3" arg2="(z-1)">
    <goal name="initnext&#39;vc.12.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="6"><result status="valid" time="0.04" steps="8926"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="initnext&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="5" timelimit="1"><result status="valid" time="0.45" steps="569"/></proof>
  </goal>
  <goal name="initnext&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="8221"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="17"/></proof>
  </goal>
  <goal name="initnext&#39;vc.15" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="6659"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="initnext&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="8630"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="initnext&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="9584"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="36"/></proof>
  </goal>
  <goal name="initnext&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="3"><path name="kmp_KnuthMorrisPratt_VC_initnext_1.v"/><result status="valid" time="0.46"/></proof>
  </goal>
  <goal name="initnext&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="5" timelimit="1"><result status="valid" time="0.22" steps="413"/></proof>
  </goal>
  <goal name="initnext&#39;vc.20" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="8213"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="16"/></proof>
  </goal>
  <goal name="initnext&#39;vc.21" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="10280"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="44"/></proof>
  </goal>
  <goal name="initnext&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="10368"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="68"/></proof>
  </goal>
  <goal name="initnext&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.26" steps="53680"/></proof>
  <proof prover="5"><result status="valid" time="0.03" steps="90"/></proof>
  </goal>
  <goal name="initnext&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="3"><path name="kmp_KnuthMorrisPratt_VC_initnext_2.v"/><result status="valid" time="0.56"/></proof>
  </goal>
  <goal name="initnext&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="13190"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="30"/></proof>
  </goal>
  <goal name="initnext&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="9205"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="20"/></proof>
  </goal>
  <goal name="initnext&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="6681"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="4"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="kmp&#39;vc" expl="VC for kmp" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="kmp&#39;vc.0" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="4791"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="1"/></proof>
  </goal>
  <goal name="kmp&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="6938"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="4"/></proof>
  </goal>
  <goal name="kmp&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="7188"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="8"/></proof>
  </goal>
  <goal name="kmp&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="6329"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="7"/></proof>
  </goal>
  <goal name="kmp&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="7349"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="kmp&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="7390"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="kmp&#39;vc.6" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="6779"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="kmp&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="7766"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="21"/></proof>
  </goal>
  <goal name="kmp&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="8660"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="27"/></proof>
  </goal>
  <goal name="kmp&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="9712"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="30"/></proof>
  </goal>
  <goal name="kmp&#39;vc.10" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="6662"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="14"/></proof>
  </goal>
  <goal name="kmp&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="7738"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="14"/></proof>
  </goal>
  <goal name="kmp&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="8558"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="30"/></proof>
  </goal>
  <goal name="kmp&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.08" steps="9452"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="kmp&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="7676"/></proof>
  <proof prover="5"><result status="valid" time="0.00" steps="13"/></proof>
  </goal>
  <goal name="kmp&#39;vc.15" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="9638"/></proof>
  <proof prover="5"><result status="valid" time="0.01" steps="37"/></proof>
  </goal>
  <goal name="kmp&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="9793"/></proof>
  <proof prover="5"><result status="valid" time="0.02" steps="84"/></proof>
  </goal>
  <goal name="kmp&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.14" steps="32226"/></proof>
  <proof prover="5"><result status="valid" time="0.02" steps="79"/></proof>
  </goal>
  <goal name="kmp&#39;vc.18" expl="loop invariant preservation" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="kmp&#39;vc.18.0" expl="loop invariant preservation" proved="true">
   <transf name="instantiate" proved="true" arg1="LoopInvariant2" arg2="(k-1)">
    <goal name="kmp&#39;vc.18.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="2"><result status="valid" time="0.06" steps="135038"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="kmp&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.10" steps="27430"/></proof>
  <proof prover="5"><result status="valid" time="0.02" steps="76"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
