<?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="Eprover" version="2.0" timelimit="10" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.8.6" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="list_removal.mlw"/>
<theory name="Top" proved="true">
 <goal name="list&#39;vc" expl="VC for list" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="list&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="16"/></proof>
  </goal>
  <goal name="list&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="16"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="list_concat&#39;vc" expl="VC for list_concat" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="list_concat&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="1938"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="1204"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="1209"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.6" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="list_concat&#39;vc.6.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.01" steps="35"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="path_shorten" proved="true">
 <proof prover="1"><result status="valid" time="0.00" steps="12"/></proof>
 </goal>
 <goal name="path_extend" proved="true">
 <proof prover="0"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="no_cycle_to_null&#39;vc" expl="VC for no_cycle_to_null" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="no_cycle_to_null&#39;vc.0" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="18"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="2408"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="1679"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="2637"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="20"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.10" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="25"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="jump_over&#39;vc" expl="VC for jump_over" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="jump_over&#39;vc.0" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="2593"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="1929"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="2136"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="3168"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="9617"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="1972"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.6" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="3391"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="3119"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="1885"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.9" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="1871"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.10" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="2728"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="15446"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.12" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="1814"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.13" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="3778"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.14" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="2881"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.15" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="2058"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.16" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="1861"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.17" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="2807"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.18" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="2588"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.19" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="1868"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.20" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="1871"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="6575"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="remove1&#39;vc" expl="VC for remove1" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="remove1&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="1967"/></proof>
  </goal>
  <goal name="remove1&#39;vc.1" expl="loop invariant init" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove1&#39;vc.1.0" expl="loop invariant init" proved="true">
   <proof prover="1"><result status="valid" time="0.01" steps="14"/></proof>
   </goal>
   <goal name="remove1&#39;vc.1.1" expl="loop invariant init" proved="true">
   <proof prover="1"><result status="valid" time="0.01" steps="14"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove1&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="28"/></proof>
  </goal>
  <goal name="remove1&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="47"/></proof>
  </goal>
  <goal name="remove1&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="2033"/></proof>
  </goal>
  <goal name="remove1&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="remove1&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="remove1&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="remove1&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="22"/></proof>
  </goal>
  <goal name="remove1&#39;vc.9" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="2199"/></proof>
  </goal>
  <goal name="remove1&#39;vc.10" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="34"/></proof>
  </goal>
  <goal name="remove1&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="38"/></proof>
  </goal>
  <goal name="remove1&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="41"/></proof>
  </goal>
  <goal name="remove1&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="99"/></proof>
  </goal>
  <goal name="remove1&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="2358"/></proof>
  </goal>
  <goal name="remove1&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="42"/></proof>
  </goal>
  <goal name="remove1&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="43"/></proof>
  </goal>
  <goal name="remove1&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="48"/></proof>
  </goal>
  <goal name="remove1&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="remove1&#39;vc.19" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="2217"/></proof>
  </goal>
  <goal name="remove1&#39;vc.20" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="3607"/></proof>
  </goal>
  <goal name="remove1&#39;vc.21" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="37"/></proof>
  </goal>
  <goal name="remove1&#39;vc.22" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="4930"/></proof>
  </goal>
  <goal name="remove1&#39;vc.23" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="2265"/></proof>
  </goal>
  <goal name="remove1&#39;vc.24" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="5253"/></proof>
  </goal>
  <goal name="remove1&#39;vc.25" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="remove1&#39;vc.26" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="2256"/></proof>
  </goal>
  <goal name="remove1&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="12529"/></proof>
  </goal>
  <goal name="remove1&#39;vc.28" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="36"/></proof>
  </goal>
  <goal name="remove1&#39;vc.29" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="remove1&#39;vc.29.0" expl="precondition" proved="true">
   <proof prover="2" timelimit="10"><result status="valid" time="0.03" steps="884"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove1&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="4" timelimit="5"><result status="valid" time="2.60" steps="285954"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="remove2&#39;vc" expl="VC for remove2" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="remove2&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="remove2&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="16"/></proof>
  </goal>
  <goal name="remove2&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="18"/></proof>
  </goal>
  <goal name="remove2&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="20"/></proof>
  </goal>
  <goal name="remove2&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="20"/></proof>
  </goal>
  <goal name="remove2&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="remove2&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="28"/></proof>
  <proof prover="4"><result status="valid" time="0.02" steps="2115"/></proof>
  </goal>
  <goal name="remove2&#39;vc.7" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="32"/></proof>
  </goal>
  <goal name="remove2&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="34"/></proof>
  </goal>
  <goal name="remove2&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="37"/></proof>
  </goal>
  <goal name="remove2&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="39"/></proof>
  </goal>
  <goal name="remove2&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.01" steps="41"/></proof>
  </goal>
  <goal name="remove2&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="41"/></proof>
  </goal>
  <goal name="remove2&#39;vc.13" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="2110"/></proof>
  </goal>
  <goal name="remove2&#39;vc.14" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.00" steps="28"/></proof>
  </goal>
  <goal name="remove2&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.02" steps="18057"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
