<?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="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.12.2" 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="0.000000" steps="12"/></proof>
  </goal>
  <goal name="list&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="12"/></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="0.000000" steps="18"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="823"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="405"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="410"/></proof>
  </goal>
  <goal name="list_concat&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.000000" steps="35"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="path_shorten" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
 </goal>
 <goal name="path_extend" proved="true">
 <proof prover="0"><result status="valid" time="0.010000"/></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="0.020000" steps="18"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="1293"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="880"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1528"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="20"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="20"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="22"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.10" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="25"/></proof>
  </goal>
  <goal name="no_cycle_to_null&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" 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="0.060000" steps="1478"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1130"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="1226"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="2048"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="8417"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1173"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.6" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="2271"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="13432"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1086"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.9" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1072"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.10" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1801"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="16928"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.12" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="1015"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.13" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="2620"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.14" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="1756"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.15" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1148"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.16" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="1062"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.17" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="1844"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.18" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="1659"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.19" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1069"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.20" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1072"/></proof>
  </goal>
  <goal name="jump_over&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="4913"/></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="0.030000" steps="1168"/></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="0.010000" steps="14"/></proof>
   </goal>
   <goal name="remove1&#39;vc.1.1" expl="loop invariant init" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" 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="0.000000" steps="28"/></proof>
  </goal>
  <goal name="remove1&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="47"/></proof>
  </goal>
  <goal name="remove1&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1234"/></proof>
  </goal>
  <goal name="remove1&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="20"/></proof>
  </goal>
  <goal name="remove1&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="20"/></proof>
  </goal>
  <goal name="remove1&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="22"/></proof>
  </goal>
  <goal name="remove1&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="22"/></proof>
  </goal>
  <goal name="remove1&#39;vc.9" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1377"/></proof>
  </goal>
  <goal name="remove1&#39;vc.10" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="32"/></proof>
  </goal>
  <goal name="remove1&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="36"/></proof>
  </goal>
  <goal name="remove1&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="39"/></proof>
  </goal>
  <goal name="remove1&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="97"/></proof>
  </goal>
  <goal name="remove1&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="1536"/></proof>
  </goal>
  <goal name="remove1&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="40"/></proof>
  </goal>
  <goal name="remove1&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="41"/></proof>
  </goal>
  <goal name="remove1&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="46"/></proof>
  </goal>
  <goal name="remove1&#39;vc.18" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.010000"/></proof>
  </goal>
  <goal name="remove1&#39;vc.19" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1373"/></proof>
  </goal>
  <goal name="remove1&#39;vc.20" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="2440"/></proof>
  </goal>
  <goal name="remove1&#39;vc.21" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="33"/></proof>
  </goal>
  <goal name="remove1&#39;vc.22" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="3742"/></proof>
  </goal>
  <goal name="remove1&#39;vc.23" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="1421"/></proof>
  </goal>
  <goal name="remove1&#39;vc.24" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="4064"/></proof>
  </goal>
  <goal name="remove1&#39;vc.25" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="32"/></proof>
  </goal>
  <goal name="remove1&#39;vc.26" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1412"/></proof>
  </goal>
  <goal name="remove1&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.010000" steps="7210"/></proof>
  </goal>
  <goal name="remove1&#39;vc.28" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="32"/></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="3" timelimit="10"><result status="valid" time="0.010000" steps="560"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="remove1&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.170000" steps="17712"/></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="0.010000" steps="14"/></proof>
  </goal>
  <goal name="remove2&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="16"/></proof>
  </goal>
  <goal name="remove2&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="remove2&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="20"/></proof>
  </goal>
  <goal name="remove2&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="remove2&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="remove2&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
  <proof prover="4"><result status="valid" time="0.020000" steps="1293"/></proof>
  </goal>
  <goal name="remove2&#39;vc.7" expl="loop variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="30"/></proof>
  </goal>
  <goal name="remove2&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="32"/></proof>
  </goal>
  <goal name="remove2&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="35"/></proof>
  </goal>
  <goal name="remove2&#39;vc.10" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="37"/></proof>
  </goal>
  <goal name="remove2&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="39"/></proof>
  </goal>
  <goal name="remove2&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="39"/></proof>
  </goal>
  <goal name="remove2&#39;vc.13" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="1289"/></proof>
  </goal>
  <goal name="remove2&#39;vc.14" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="26"/></proof>
  </goal>
  <goal name="remove2&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="3" timelimit="1"><result status="valid" time="0.010000" steps="12894"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
