<?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="2" name="Z3" version="4.12.2" 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="0.020000" steps="2894"/></proof>
 <proof prover="5"><result status="valid" time="0.000000" steps="7"/></proof>
 </goal>
 <goal name="matches_right_extension" proved="true">
 <proof prover="5" timelimit="1"><result status="valid" time="0.010000" steps="25"/></proof>
 </goal>
 <goal name="matches_contradiction_at_first" proved="true">
 <proof prover="4"><result status="valid" time="0.040000"/></proof>
 </goal>
 <goal name="matches_contradiction_at_i" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="11815"/></proof>
 <proof prover="5"><result status="valid" time="0.000000" steps="23"/></proof>
 </goal>
 <goal name="matches_right_weakening" proved="true">
 <proof prover="2"><result status="valid" time="0.040000" steps="62390"/></proof>
 <proof prover="5"><result status="valid" time="0.000000" 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="0.350000"/></proof>
 </goal>
 <goal name="matches_sym" proved="true">
 <proof prover="0"><result status="valid" time="0.020000" steps="3820"/></proof>
 <proof prover="5"><result status="valid" time="0.000000" steps="7"/></proof>
 </goal>
 <goal name="matches_trans" proved="true">
 <proof prover="5" timelimit="1"><result status="valid" time="0.000000" steps="26"/></proof>
 </goal>
 <goal name="next_iteration" proved="true">
 <proof prover="0"><result status="valid" time="0.050000" steps="13698"/></proof>
 <proof prover="2" timelimit="5"><result status="valid" time="0.152996" steps="313134"/></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="0.449386"/></proof>
 </goal>
 <goal name="next_1_0" proved="true">
 <proof prover="0"><result status="valid" time="0.010000" steps="5199"/></proof>
 <proof prover="5"><result status="valid" time="0.000000" 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="0.020000" steps="4824"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="2"/></proof>
  </goal>
  <goal name="initnext&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="5871"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
  <goal name="initnext&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="5587"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="7"/></proof>
  </goal>
  <goal name="initnext&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="6521"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="11"/></proof>
  </goal>
  <goal name="initnext&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="5601"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" 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="0.000000" steps="20"/></proof>
  </goal>
  <goal name="initnext&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="7508"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="13"/></proof>
  </goal>
  <goal name="initnext&#39;vc.7" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="7504"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="13"/></proof>
  </goal>
  <goal name="initnext&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="7966"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="16"/></proof>
  </goal>
  <goal name="initnext&#39;vc.9" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="6515"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="19"/></proof>
  </goal>
  <goal name="initnext&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="8470"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" steps="19"/></proof>
  </goal>
  <goal name="initnext&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="9525"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" 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="0.040000" steps="8057"/></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="0.450000" steps="569"/></proof>
  </goal>
  <goal name="initnext&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="7855"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="16"/></proof>
  </goal>
  <goal name="initnext&#39;vc.15" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="6361"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="19"/></proof>
  </goal>
  <goal name="initnext&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="8264"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="19"/></proof>
  </goal>
  <goal name="initnext&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="9219"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" steps="35"/></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="0.460000"/></proof>
  </goal>
  <goal name="initnext&#39;vc.19" expl="loop invariant preservation" proved="true">
  <proof prover="5" timelimit="1"><result status="valid" time="0.220000" steps="412"/></proof>
  </goal>
  <goal name="initnext&#39;vc.20" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="7847"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="15"/></proof>
  </goal>
  <goal name="initnext&#39;vc.21" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="9914"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" steps="43"/></proof>
  </goal>
  <goal name="initnext&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="10002"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" steps="67"/></proof>
  </goal>
  <goal name="initnext&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.260000" steps="53316"/></proof>
  <proof prover="5"><result status="valid" time="0.030000" steps="89"/></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="0.560000"/></proof>
  </goal>
  <goal name="initnext&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="12824"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="29"/></proof>
  </goal>
  <goal name="initnext&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="8680"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="initnext&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="6076"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" 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="0.010000" steps="4550"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="1"/></proof>
  </goal>
  <goal name="kmp&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="6333"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
  <goal name="kmp&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="6583"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="kmp&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="5803"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="7"/></proof>
  </goal>
  <goal name="kmp&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="6840"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="19"/></proof>
  </goal>
  <goal name="kmp&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="6883"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="19"/></proof>
  </goal>
  <goal name="kmp&#39;vc.6" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="6515"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="12"/></proof>
  </goal>
  <goal name="kmp&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="7419"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="25"/></proof>
  </goal>
  <goal name="kmp&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="8392"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="26"/></proof>
  </goal>
  <goal name="kmp&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="9452"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
  <goal name="kmp&#39;vc.10" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.010000" steps="6402"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="12"/></proof>
  </goal>
  <goal name="kmp&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.030000" steps="7432"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="22"/></proof>
  </goal>
  <goal name="kmp&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="8304"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="28"/></proof>
  </goal>
  <goal name="kmp&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.080000" steps="9215"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="kmp&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="7344"/></proof>
  <proof prover="5"><result status="valid" time="0.000000" steps="21"/></proof>
  </goal>
  <goal name="kmp&#39;vc.15" expl="loop variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="9307"/></proof>
  <proof prover="5"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="kmp&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.040000" steps="9461"/></proof>
  <proof prover="5"><result status="valid" time="0.020000" steps="89"/></proof>
  </goal>
  <goal name="kmp&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.140000" steps="31904"/></proof>
  <proof prover="5"><result status="valid" time="0.020000" steps="77"/></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="0.142568" steps="272392"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="kmp&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.100000" steps="26920"/></proof>
  <proof prover="5"><result status="valid" time="0.020000" steps="82"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
