<?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="1" name="Alt-Ergo" version="2.1.0" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="schorr_waite_via_recursion.mlw"/>
<theory name="SchorrWaite" proved="true">
 <goal name="black&#39;vc" expl="VC for black" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="black&#39;vc.0" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="2"/></proof>
  </goal>
  <goal name="black&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="17"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="schorr_waite&#39;vc" expl="VC for schorr_waite" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="schorr_waite&#39;vc.0" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="2"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.1" expl="exceptional postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="10"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="2"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="10"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.4" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="49"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="51"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="94"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.11" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="71"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.12" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="73"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.13" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="73"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.14" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="79"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.15" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="32"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.16" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="81"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.17" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="38"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="126"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.21" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="45"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.22" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="25"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.23" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.24" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.25" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="24"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.28" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.29" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="25"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.30" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="20"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.31" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.32" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.33" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="29"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.34" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.35" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.36" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="35"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.37" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="36"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.38" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="2"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.39" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="2"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.40" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="16"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.42" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.43" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="2"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.44" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="16"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.45" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.46" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.47" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.060000" steps="215"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.48" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="27"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.49" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="37"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.50" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="33"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.51" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="41"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.52" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="35"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.53" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="45"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.54" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="35"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.55" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="51"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.56" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="121"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.57" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="41"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.58" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="51"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.59" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.060000" steps="107"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.60" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="211"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.61" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="331"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.62" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.070000" steps="469"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.63" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="161"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.64" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="88"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.65" expl="loop invariant preservation" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.140000" steps="341"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.66" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.060000" steps="446"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.67" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="207"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.68" expl="loop invariant preservation" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.160000" steps="221"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.69" expl="loop invariant preservation" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.550000" steps="1198"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.70" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.240000" steps="889"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.71" expl="exceptional postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="53"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.72" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.050000" steps="117"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.73" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="37"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.74" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="47"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.75" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.070000" steps="103"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.76" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="208"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.77" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="215"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.78" expl="postcondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.230000" steps="529"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.79" expl="postcondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="1.076871" steps="3887"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.80" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="117"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.81" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.130000" steps="646"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.82" expl="exceptional postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="49"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.83" expl="out of loop bounds" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.84" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.85" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="51"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.86" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="118"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.87" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="40"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.88" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="45"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.89" expl="exceptional postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.90" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="46"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.91" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.92" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="2"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.93" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.94" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="16"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.95" expl="assertion" proved="true">
  <transf name="induction_pr" proved="true" >
   <goal name="schorr_waite&#39;vc.95.0" expl="assertion" proved="true">
   <transf name="simplify_trivial_quantification_in_goal" proved="true" >
    <goal name="schorr_waite&#39;vc.95.0.0" expl="assertion" proved="true">
    <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="schorr_waite&#39;vc.95.1" expl="assertion" proved="true">
   <transf name="simplify_trivial_quantification_in_goal" proved="true" >
    <goal name="schorr_waite&#39;vc.95.1.0" expl="assertion" proved="true">
    <proof prover="1"><result status="valid" time="0.080000" steps="230"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="schorr_waite&#39;vc.96" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="43"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.97" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="81"/></proof>
  </goal>
  <goal name="schorr_waite&#39;vc.98" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="29"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
