<?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="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.4.2" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="random_access_list.mlw"/>
<theory name="RandomAccessList" proved="true">
 <goal name="length_flatten&#39;vc" expl="VC for length_flatten" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="length_flatten&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="31"/></proof>
  </goal>
  <goal name="length_flatten&#39;vc.1" expl="postcondition" proved="true">
  <transf name="unfold" proved="true" arg1="flatten">
   <goal name="length_flatten&#39;vc.1.0" expl="postcondition" proved="true">
   <proof prover="5"><result status="valid" time="0.010000" steps="23541"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="size&#39;vc" expl="VC for size" proved="true">
 <proof prover="1"><result status="valid" time="0.020000" steps="191"/></proof>
 </goal>
 <goal name="cons&#39;vc" expl="VC for cons" proved="true">
 <proof prover="1"><result status="valid" time="0.030000" steps="247"/></proof>
 </goal>
 <goal name="nth_flatten&#39;vc" expl="VC for nth_flatten" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="nth_flatten&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="41"/></proof>
  </goal>
  <goal name="nth_flatten&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="10"/></proof>
  </goal>
  <goal name="nth_flatten&#39;vc.2" expl="postcondition" proved="true">
  <transf name="destruct_term_subst" proved="true" arg1="l">
   <goal name="nth_flatten&#39;vc.2.0" expl="postcondition" proved="true">
   <transf name="case" proved="true" arg1="(i = 0)">
    <goal name="nth_flatten&#39;vc.2.0.0" expl="true case (postcondition)" proved="true">
    <transf name="subst" proved="true" arg1="i">
     <goal name="nth_flatten&#39;vc.2.0.0.0" expl="true case (postcondition)" proved="true">
     <transf name="destruct_term_subst" proved="true" arg1="x1">
      <goal name="nth_flatten&#39;vc.2.0.0.0.0" expl="true case (postcondition)" proved="true">
      <transf name="compute_in_goal" proved="true" >
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="nth_flatten&#39;vc.2.0.1" expl="false case (postcondition)" proved="true">
    <transf name="replace" proved="true" arg1="(nth i (Cons x1 x))" arg2="(nth (i - 1) x)">
     <goal name="nth_flatten&#39;vc.2.0.1.0" expl="false case (postcondition)" proved="true">
     <transf name="destruct_term_subst" proved="true" arg1="x1">
      <goal name="nth_flatten&#39;vc.2.0.1.0.0" expl="false case (postcondition)" proved="true">
      <transf name="replace" proved="true" arg1="(2 * i)" arg2="((2 * (i - 1) + 1) + 1)">
       <goal name="nth_flatten&#39;vc.2.0.1.0.0.0" expl="false case (postcondition)" proved="true">
       <transf name="destruct_term_subst" proved="true" arg1="(nth (i - 1) x)">
        <goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0" expl="false case (postcondition)" proved="true">
        <transf name="destruct_term_subst" proved="true" arg1="x">
         <goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0" expl="false case (postcondition)" proved="true">
         <transf name="replace" proved="true" arg1="(nth (i - 1) x2)" arg2="(Some (x1, x))">
          <goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.0" expl="false case (postcondition)" proved="true">
          <transf name="assert" proved="true" arg1="(match Some (x1, x) with None -&gt; false | Some (x0, x11) -&gt; Some x0 = nth (2 * (i - 1)) (flatten x2) /\ Some x11 = nth ((2 * (i - 1)) + 1) (flatten x2) end)">
           <goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.0.0" expl="asserted formula" proved="true">
           <proof prover="1"><result status="valid" time="0.010000" steps="57"/></proof>
           </goal>
           <goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.0.1" expl="false case (postcondition)" proved="true">
           <transf name="unfold" proved="true" arg1="flatten">
            <goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.0.1.0" expl="false case (postcondition)" proved="true">
            <proof prover="1"><result status="valid" time="0.020000" steps="96"/></proof>
            </goal>
           </transf>
           </goal>
          </transf>
          </goal>
          <goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.1" expl="equality hypothesis" proved="true">
          <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
          </goal>
         </transf>
         </goal>
        </transf>
        </goal>
        <goal name="nth_flatten&#39;vc.2.0.1.0.0.0.1" expl="false case (postcondition)" proved="true">
        <proof prover="1"><result status="valid" time="0.000000" steps="10"/></proof>
        </goal>
       </transf>
       </goal>
       <goal name="nth_flatten&#39;vc.2.0.1.0.0.1" expl="equality hypothesis" proved="true">
       <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
     <goal name="nth_flatten&#39;vc.2.0.1.1" expl="equality hypothesis" proved="true">
     <proof prover="1"><result status="valid" time="0.010000" steps="13"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="nth_flatten&#39;vc.2.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="7"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="lookup&#39;vc" expl="VC for lookup" proved="true">
 <proof prover="1"><result status="valid" time="0.180000" steps="693"/></proof>
 </goal>
 <goal name="tail&#39;vc" expl="VC for tail" proved="true">
 <proof prover="2"><result status="valid" time="0.200000" steps="36637"/></proof>
 </goal>
 <goal name="update&#39;vc" expl="VC for update" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="update&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
  </goal>
  <goal name="update&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="update&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="33"/></proof>
  </goal>
  <goal name="update&#39;vc.3" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="update&#39;vc.4" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
  </goal>
  <goal name="update&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="update&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="46"/></proof>
  </goal>
  <goal name="update&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="update&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="update&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.060000" steps="209"/></proof>
  </goal>
  <goal name="update&#39;vc.10" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="73"/></proof>
  </goal>
  <goal name="update&#39;vc.11" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="update&#39;vc.11.0" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.080000" steps="95"/></proof>
   </goal>
   <goal name="update&#39;vc.11.1" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.120000" steps="307"/></proof>
   </goal>
   <goal name="update&#39;vc.11.2" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.250000" steps="2659"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="update&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.140000" steps="1314"/></proof>
  </goal>
  <goal name="update&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="481"/></proof>
  </goal>
  <goal name="update&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="655"/></proof>
  </goal>
  <goal name="update&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.060000" steps="306"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="RAL" proved="true">
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
 </goal>
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="1"/></proof>
 </goal>
 <goal name="size&#39;vc" expl="VC for size" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="2"/></proof>
 </goal>
 <goal name="cons&#39;vc" expl="VC for cons" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="16"/></proof>
 </goal>
 <goal name="lookup&#39;vc" expl="VC for lookup" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="9"/></proof>
 </goal>
</theory>
<theory name="RandomAccessListWithSeq" proved="true">
 <goal name="cons_flatten" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="cons_flatten.0" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
  <goal name="cons_flatten.1" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="cons_flatten.2" proved="true">
  <proof prover="1"><result status="valid" time="0.060000" steps="104"/></proof>
  </goal>
  <goal name="cons_flatten.3" proved="true">
  <proof prover="1"><result status="valid" time="0.600000" steps="1541"/></proof>
  </goal>
  <goal name="cons_flatten.4" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="79"/></proof>
  </goal>
  <goal name="cons_flatten.5" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="4"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="size&#39;vc" expl="VC for size" proved="true">
 <proof prover="1"><result status="valid" time="0.030000" steps="139"/></proof>
 </goal>
 <goal name="cons&#39;vc" expl="VC for cons" proved="true">
 <proof prover="1"><result status="valid" time="0.050000" steps="339"/></proof>
 </goal>
 <goal name="lookup&#39;vc" expl="VC for lookup" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="lookup&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
  </goal>
  <goal name="lookup&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="lookup&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="lookup&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="lookup&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="130"/></proof>
  </goal>
  <goal name="lookup&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="67"/></proof>
  </goal>
  <goal name="lookup&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="lookup&#39;vc.7" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="lookup&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="48"/></proof>
   </goal>
   <goal name="lookup&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.010000" steps="131"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="tail&#39;vc" expl="VC for tail" proved="true">
 <proof prover="1"><result status="valid" time="0.110000" steps="584"/></proof>
 </goal>
 <goal name="aux&#39;vc" expl="VC for aux" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="0"/></proof>
 </goal>
 <goal name="fupdate&#39;vc" expl="VC for fupdate" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="fupdate&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
  </goal>
  <goal name="fupdate&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="fupdate&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="fupdate&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
  </goal>
  <goal name="fupdate&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="130"/></proof>
  </goal>
  <goal name="fupdate&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="67"/></proof>
  </goal>
  <goal name="fupdate&#39;vc.6" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="1.510000" steps="2260"/></proof>
  </goal>
  <goal name="fupdate&#39;vc.7" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="fupdate&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.030000" steps="281"/></proof>
   </goal>
   <goal name="fupdate&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.030000" steps="184"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="f&#39;vc" expl="VC for f" proved="true">
 <proof prover="0"><result status="valid" time="0.010000" steps="0"/></proof>
 </goal>
 <goal name="update&#39;vc" expl="VC for update" proved="true">
 <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
 </goal>
</theory>
</file>
</why3session>
