<?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="2.4.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Z3" version="4.8.10" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="Alt-Ergo" version="2.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="fibonacci.mlw"/>
<theory name="FibonacciTest" proved="true">
 <goal name="isfib_2_1" proved="true">
 <proof prover="2" timelimit="5"><result status="valid" time="0.01" steps="1281"/></proof>
 <proof prover="4" timelimit="5"><result status="valid" time="0.00" steps="679"/></proof>
 </goal>
 <goal name="isfib_6_8" proved="true">
 <proof prover="2" timelimit="5"><result status="valid" time="0.01" steps="1821"/></proof>
 <proof prover="4" timelimit="5"><result status="valid" time="0.00" steps="1039"/></proof>
 </goal>
 <goal name="not_isfib_2_2" proved="true">
 <proof prover="2" timelimit="5"><result status="valid" time="0.01" steps="365"/></proof>
 <proof prover="3"><result status="valid" time="0.00" steps="5"/></proof>
 <proof prover="4" timelimit="5"><result status="valid" time="0.00" steps="376"/></proof>
 </goal>
</theory>
<theory name="FibonacciLinear" proved="true">
 <goal name="fib&#39;vc" expl="VC for fib" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="4794"/></proof>
 </goal>
</theory>
<theory name="FibonacciTailRecList" proved="true">
 <goal name="sum_fib&#39;vc" expl="VC for sum_fib" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="sum_fib&#39;vc.0" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="1.22" steps="8335"/></proof>
  </goal>
  <goal name="sum_fib&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.97" steps="8118"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sum_pow&#39;vc" expl="VC for sum_pow" proved="true">
 <transf name="split_all_full" proved="true" >
  <goal name="sum_pow&#39;vc.0" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.00" steps="35"/></proof>
  </goal>
  <goal name="sum_pow&#39;vc.1" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.01" steps="39"/></proof>
  </goal>
  <goal name="sum_pow&#39;vc.2" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.01" steps="95"/></proof>
  </goal>
  <goal name="sum_pow&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="5"><result status="valid" time="0.02" steps="15077"/></proof>
  </goal>
  <goal name="sum_pow&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.01" steps="54"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="pow_pos" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="pow_pos.0" proved="true">
  <transf name="induction" proved="true" arg1="x">
   <goal name="pow_pos.0.0" expl="base case" proved="true">
   <proof prover="5"><result status="valid" time="0.02" steps="15517"/></proof>
   </goal>
   <goal name="pow_pos.0.1" expl="recursive case" proved="true">
   <proof prover="5"><result status="valid" time="0.02" steps="16005"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="sum_fib_acc&#39;vc" expl="VC for sum_fib_acc" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="sum_fib_acc&#39;vc.0" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="2.52" steps="33488"/></proof>
  </goal>
  <goal name="sum_fib_acc&#39;vc.1" expl="variant decrease" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="sum_fib_acc&#39;vc.1.0" expl="variant decrease" proved="true">
   <proof prover="5"><result status="valid" time="0.02" steps="19082"/></proof>
   </goal>
   <goal name="sum_fib_acc&#39;vc.1.1" expl="variant decrease" proved="true">
   <proof prover="0"><result status="valid" time="0.03" steps="372"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sum_fib_acc&#39;vc.2" expl="precondition" proved="true">
  <transf name="assert" proved="true" arg1="(mem n l)">
   <goal name="sum_fib_acc&#39;vc.2.0" expl="asserted formula" proved="true">
   <proof prover="6"><result status="valid" time="0.01" steps="48"/></proof>
   </goal>
   <goal name="sum_fib_acc&#39;vc.2.1" expl="precondition" proved="true">
   <proof prover="6"><result status="valid" time="0.01" steps="50"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sum_fib_acc&#39;vc.3" expl="assertion" proved="true">
  <transf name="assert" proved="true" arg1="(u = x1 - 2 \/ mem u x)">
   <goal name="sum_fib_acc&#39;vc.3.0" expl="asserted formula" proved="true">
   <proof prover="6"><result status="valid" time="0.01" steps="47"/></proof>
   </goal>
   <goal name="sum_fib_acc&#39;vc.3.1" expl="assertion" proved="true">
   <transf name="destruct" proved="true" arg1="h">
    <goal name="sum_fib_acc&#39;vc.3.1.0" expl="assertion" proved="true">
    <proof prover="5"><result status="valid" time="0.02" steps="17799"/></proof>
    </goal>
    <goal name="sum_fib_acc&#39;vc.3.1.1" expl="assertion" proved="true">
    <transf name="assert" proved="true" arg1="(mem u l)">
     <goal name="sum_fib_acc&#39;vc.3.1.1.0" expl="asserted formula" proved="true">
     <proof prover="1"><result status="valid" time="0.03" steps="4419"/></proof>
     </goal>
     <goal name="sum_fib_acc&#39;vc.3.1.1.1" expl="assertion" proved="true">
     <proof prover="5"><result status="valid" time="0.02" steps="18411"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="sum_fib_acc&#39;vc.4" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.03" steps="5479"/></proof>
  </goal>
  <goal name="sum_fib_acc&#39;vc.5" expl="variant decrease" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="sum_fib_acc&#39;vc.5.0" expl="variant decrease" proved="true">
   <proof prover="5"><result status="valid" time="0.01" steps="19058"/></proof>
   </goal>
   <goal name="sum_fib_acc&#39;vc.5.1" expl="variant decrease" proved="true">
   <proof prover="1"><result status="valid" time="0.05" steps="9472"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sum_fib_acc&#39;vc.6" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.03" steps="19232"/></proof>
  </goal>
  <goal name="sum_fib_acc&#39;vc.7" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="sum_fib_acc&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="5" timelimit="1"><result status="valid" time="0.01" steps="37534"/></proof>
   </goal>
   <goal name="sum_fib_acc&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.03" steps="8079"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="fib&#39;vc" expl="VC for fib" proved="true">
 <proof prover="1"><result status="valid" time="0.04" steps="6230"/></proof>
 </goal>
</theory>
<theory name="FibRecGhost" proved="true">
 <goal name="fib_aux&#39;vc" expl="VC for fib_aux" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="2907"/></proof>
 </goal>
 <goal name="fib&#39;vc" expl="VC for fib" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="4"/></proof>
 </goal>
 <goal name="test42&#39;vc" expl="VC for test42" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="3"/></proof>
 </goal>
</theory>
<theory name="FibRecNoGhost" proved="true">
 <goal name="fib_aux&#39;vc" expl="VC for fib_aux" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="10459"/></proof>
 </goal>
 <goal name="fib&#39;vc" expl="VC for fib" proved="true">
 <proof prover="2"><result status="valid" time="0.19" steps="549611"/></proof>
 </goal>
</theory>
<theory name="SmallestFibAbove" proved="true">
 <goal name="smallest_fib_above&#39;vc" expl="VC for smallest_fib_above" proved="true">
 <proof prover="4"><result status="valid" time="0.04" steps="5188"/></proof>
 </goal>
</theory>
<theory name="Zeckendorf" proved="true">
 <goal name="fib_nonneg&#39;vc" expl="VC for fib_nonneg" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="20"/></proof>
 </goal>
 <goal name="fib_increasing&#39;vc" expl="VC for fib_increasing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="6303"/></proof>
 </goal>
 <goal name="greatest_fib&#39;vc" expl="VC for greatest_fib" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="20179"/></proof>
 </goal>
 <goal name="zeckendorf&#39;vc" expl="VC for zeckendorf" proved="true">
 <proof prover="4"><result status="valid" time="0.23" steps="29213"/></proof>
 </goal>
 <goal name="zeckendorf_fast&#39;vc" expl="VC for zeckendorf_fast" proved="true">
 <proof prover="4"><result status="valid" time="0.66" steps="63532"/></proof>
 </goal>
 <goal name="zeckendorf_unique&#39;vc" expl="VC for zeckendorf_unique" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="zeckendorf_unique&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="8637"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="4765"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10519"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="4904"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="4961"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="11653"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="14384"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="7961"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="2823"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="9199"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="9404"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.11" expl="unreachable point" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="13623"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.12" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2823"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.13" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="9199"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.14" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="9404"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.15" expl="unreachable point" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="13623"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2748"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.17" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="9341"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.18" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="9429"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10915"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="12240"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.21" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="12452"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.22" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="18401"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.23" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="11693"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.24" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="30232"/></proof>
  </goal>
  <goal name="zeckendorf_unique&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="34152"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Mat22" proved="true">
 <goal name="Assoc" proved="true">
 <proof prover="3"><result status="valid" time="0.03" steps="2"/></proof>
 </goal>
 <goal name="Unit_def_l" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="2"/></proof>
 </goal>
 <goal name="Unit_def_r" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="2"/></proof>
 </goal>
</theory>
<theory name="FibonacciLogarithmic" proved="true">
 <goal name="logfib&#39;vc" expl="VC for logfib" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="logfib&#39;vc.0" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="9"/></proof>
  </goal>
  <goal name="logfib&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="logfib&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="11"/></proof>
  </goal>
  <goal name="logfib&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="4"/></proof>
  </goal>
  <goal name="logfib&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="8"/></proof>
  </goal>
  <goal name="logfib&#39;vc.5" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="logfib&#39;vc.6" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="10"/></proof>
  </goal>
  <goal name="logfib&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.29" steps="95"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="fib_m&#39;vc" expl="VC for fib_m" proved="true">
 <proof prover="6"><result status="valid" time="0.10" steps="1017"/></proof>
 </goal>
 <goal name="fibo&#39;vc" expl="VC for fibo" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="7"/></proof>
 </goal>
 <goal name="test0&#39;vc" expl="VC for test0" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="3"/></proof>
 </goal>
 <goal name="test1&#39;vc" expl="VC for test1" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="3"/></proof>
 </goal>
 <goal name="test7&#39;vc" expl="VC for test7" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="3"/></proof>
 </goal>
 <goal name="test42&#39;vc" expl="VC for test42" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="3"/></proof>
 </goal>
 <goal name="test2014&#39;vc" expl="VC for test2014" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="3"/></proof>
 </goal>
</theory>
</file>
</why3session>
