<?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="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.2.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Z3" version="4.5.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC4" version="1.4" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="7" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="8" name="Z3" version="4.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="9" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="10" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="11" name="CVC4" version="1.7" timelimit="10" steplimit="0" memlimit="4000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="queens_bv.mlw"/>
<theory name="Solution" proved="true">
 <goal name="partial_solution_eq_prefix" proved="true">
 <proof prover="10"><result status="valid" time="0.03" steps="51"/></proof>
 </goal>
 <goal name="no_duplicate" proved="true">
 <proof prover="1"><result status="valid" time="0.02"/></proof>
 <proof prover="3"><result status="valid" time="0.03"/></proof>
 </goal>
</theory>
<theory name="BitsSpec" proved="true">
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <proof prover="7"><result status="valid" time="0.03"/></proof>
 </goal>
</theory>
<theory name="Bits" proved="true">
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <proof prover="7"><result status="valid" time="0.03"/></proof>
 </goal>
 <goal name="empty&#39;vc" expl="VC for empty" proved="true">
 <proof prover="10"><result status="valid" time="0.03" steps="96"/></proof>
 </goal>
 <goal name="is_empty&#39;vc" expl="VC for is_empty" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="is_empty&#39;vc.0" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="is_empty&#39;vc.0.0" expl="assertion" proved="true">
   <proof prover="10" timelimit="1"><result status="valid" time="0.10" steps="119"/></proof>
   </goal>
   <goal name="is_empty&#39;vc.0.1" expl="VC for is_empty" proved="true">
   <proof prover="10" timelimit="1"><result status="valid" time="0.06" steps="89"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="is_empty&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="10" timelimit="1"><result status="valid" time="0.05" steps="81"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="remove_singleton&#39;vc" expl="VC for remove_singleton" proved="true">
 <proof prover="10"><result status="valid" time="0.42" steps="803"/></proof>
 </goal>
 <goal name="add_singleton&#39;vc" expl="VC for add_singleton" proved="true">
 <proof prover="6"><result status="valid" time="0.08"/></proof>
 </goal>
 <goal name="mul2&#39;vc" expl="VC for mul2" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="mul2&#39;vc.0" expl="precondition" proved="true">
  <proof prover="10" timelimit="1"><result status="valid" time="0.32" steps="460"/></proof>
  </goal>
  <goal name="mul2&#39;vc.1" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="mul2&#39;vc.1.0" expl="postcondition" proved="true">
   <proof prover="10"><result status="valid" time="0.04" steps="77"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="div2&#39;vc" expl="VC for div2" proved="true">
 <proof prover="10"><result status="valid" time="0.14" steps="223"/></proof>
 </goal>
 <goal name="diff&#39;vc" expl="VC for diff" proved="true">
 <proof prover="10"><result status="valid" time="0.24" steps="676"/></proof>
 </goal>
 <goal name="rightmost_bit_trick&#39;vc" expl="VC for rightmost_bit_trick" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="rightmost_bit_trick&#39;vc.0" expl="assertion" proved="true">
  <proof prover="10" timelimit="1"><result status="valid" time="0.24" steps="408"/></proof>
  </goal>
  <goal name="rightmost_bit_trick&#39;vc.1" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.08"/></proof>
  </goal>
  <goal name="rightmost_bit_trick&#39;vc.2" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="rightmost_bit_trick&#39;vc.3" expl="assertion" proved="true">
  <proof prover="10" timelimit="1"><result status="valid" time="0.05" steps="148"/></proof>
  </goal>
  <goal name="rightmost_bit_trick&#39;vc.4" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.21"/></proof>
  </goal>
  <goal name="rightmost_bit_trick&#39;vc.5" expl="assertion" proved="true">
  <proof prover="5"><result status="valid" time="0.08" steps="135106"/></proof>
  </goal>
  <goal name="rightmost_bit_trick&#39;vc.6" expl="precondition" proved="true">
  <proof prover="10"><result status="valid" time="0.19" steps="490"/></proof>
  </goal>
  <goal name="rightmost_bit_trick&#39;vc.7" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="rightmost_bit_trick&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="10"><result status="valid" time="0.05" steps="84"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="below&#39;vc" expl="VC for below" proved="true">
 <proof prover="6"><result status="valid" time="0.06"/></proof>
 </goal>
</theory>
<theory name="NQueensBits" proved="true">
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="t&#39;vc.0" expl="assertion" proved="true">
  <proof prover="10" timelimit="10" memlimit="4000"><result status="valid" time="0.56" steps="791"/></proof>
  </goal>
  <goal name="t&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="1.13"/></proof>
  </goal>
  <goal name="t&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="t&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.10"/></proof>
  </goal>
  <goal name="t&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="t&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="10"><result status="valid" time="0.03" steps="86"/></proof>
  </goal>
  <goal name="t&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.06"/></proof>
  </goal>
  <goal name="t&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="t&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="t&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="t&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="t&#39;vc.11" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="t&#39;vc.12" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.50"/></proof>
  </goal>
  <goal name="t&#39;vc.13" expl="assertion" proved="true">
  <proof prover="5"><result status="valid" time="0.04" steps="77086"/></proof>
  </goal>
  <goal name="t&#39;vc.14" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.16"/></proof>
  </goal>
  <goal name="t&#39;vc.15" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.07"/></proof>
  </goal>
  <goal name="t&#39;vc.16" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.24"/></proof>
  </goal>
  <goal name="t&#39;vc.17" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.82"/></proof>
  </goal>
  <goal name="t&#39;vc.18" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.13"/></proof>
  </goal>
  <goal name="t&#39;vc.19" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="t&#39;vc.19.0" expl="assertion" proved="true">
   <proof prover="8"><result status="valid" time="1.01"/></proof>
   </goal>
   <goal name="t&#39;vc.19.1" expl="assertion" proved="true">
   <proof prover="10" timelimit="10" memlimit="4000"><result status="valid" time="1.46" steps="1515"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="t&#39;vc.20" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.40" steps="73660"/></proof>
  </goal>
  <goal name="t&#39;vc.21" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="t&#39;vc.21.0" expl="assertion" proved="true">
   <proof prover="10" timelimit="1"><result status="valid" time="0.28" steps="482"/></proof>
   </goal>
   <goal name="t&#39;vc.21.1" expl="assertion" proved="true">
   <proof prover="10" timelimit="10" memlimit="4000"><result status="valid" time="1.10" steps="1141"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="t&#39;vc.22" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.19"/></proof>
  </goal>
  <goal name="t&#39;vc.23" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.20"/></proof>
  </goal>
  <goal name="t&#39;vc.24" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.20"/></proof>
  </goal>
  <goal name="t&#39;vc.25" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.23"/></proof>
  </goal>
  <goal name="t&#39;vc.26" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.22"/></proof>
  </goal>
  <goal name="t&#39;vc.27" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.14"/></proof>
  </goal>
  <goal name="t&#39;vc.28" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.11"/></proof>
  </goal>
  <goal name="t&#39;vc.29" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.08"/></proof>
  </goal>
  <goal name="t&#39;vc.30" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06"/></proof>
  </goal>
  <goal name="t&#39;vc.31" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.00"/></proof>
  </goal>
  <goal name="t&#39;vc.32" expl="precondition" proved="true">
  <proof prover="3" timelimit="30"><result status="valid" time="6.86"/></proof>
  </goal>
  <goal name="t&#39;vc.33" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.13"/></proof>
  </goal>
  <goal name="t&#39;vc.34" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.27"/></proof>
  </goal>
  <goal name="t&#39;vc.35" expl="assertion" proved="true">
  <transf name="split_all_full" proved="true" >
   <goal name="t&#39;vc.35.0" expl="assertion" proved="true">
   <transf name="split_all_full" proved="true" >
    <goal name="t&#39;vc.35.0.0" expl="assertion" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="t&#39;vc.35.0.0.0" expl="assertion" proved="true">
     <proof prover="11"><result status="valid" time="0.08" steps="23461"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="t&#39;vc.35.0.1" expl="assertion" proved="true">
    <proof prover="4" timelimit="10" memlimit="4000"><result status="valid" time="8.18" steps="638665"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="t&#39;vc.35.1" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.50" steps="101127"/></proof>
   </goal>
   <goal name="t&#39;vc.35.2" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.10" steps="34825"/></proof>
   </goal>
   <goal name="t&#39;vc.35.3" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.05" steps="110759"/></proof>
   </goal>
   <goal name="t&#39;vc.35.4" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.22" steps="56581"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="t&#39;vc.36" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.23"/></proof>
  </goal>
  <goal name="t&#39;vc.37" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.19" steps="51916"/></proof>
  </goal>
  <goal name="t&#39;vc.38" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.24"/></proof>
  </goal>
  <goal name="t&#39;vc.39" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="1.31"/></proof>
  </goal>
  <goal name="t&#39;vc.40" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.12"/></proof>
  </goal>
  <goal name="t&#39;vc.41" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.15"/></proof>
  </goal>
  <goal name="t&#39;vc.42" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.37"/></proof>
  </goal>
  <goal name="t&#39;vc.43" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="t&#39;vc.43.0" expl="loop invariant preservation" proved="true">
   <proof prover="3" timelimit="60"><result status="valid" time="0.23"/></proof>
   <proof prover="6" timelimit="60"><result status="valid" time="0.25"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="t&#39;vc.44" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.29"/></proof>
  </goal>
  <goal name="t&#39;vc.45" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="t&#39;vc.45.0" expl="loop invariant preservation" proved="true">
   <proof prover="10" timelimit="1"><result status="valid" time="0.08" steps="198"/></proof>
   </goal>
   <goal name="t&#39;vc.45.1" expl="loop invariant preservation" proved="true">
   <proof prover="4" timelimit="30"><result status="valid" time="7.06" steps="593142"/></proof>
   </goal>
   <goal name="t&#39;vc.45.2" expl="loop invariant preservation" proved="true">
   <proof prover="3" timelimit="1"><result status="valid" time="0.89"/></proof>
   </goal>
   <goal name="t&#39;vc.45.3" expl="loop invariant preservation" proved="true">
   <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="5.23"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="t&#39;vc.46" expl="loop invariant preservation" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="t&#39;vc.46.0" expl="loop invariant preservation" proved="true">
   <proof prover="3"><result status="valid" time="1.14"/></proof>
   </goal>
   <goal name="t&#39;vc.46.1" expl="loop invariant preservation" proved="true">
   <proof prover="3"><result status="valid" time="0.12"/></proof>
   </goal>
   <goal name="t&#39;vc.46.2" expl="loop invariant preservation" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="t&#39;vc.46.2.0" expl="loop invariant preservation" proved="true">
    <transf name="case" proved="true" arg1="(u[k] &lt;= min1)">
     <goal name="t&#39;vc.46.2.0.0" expl="true case (loop invariant preservation)" proved="true">
     <transf name="assert" proved="true" arg1="(eq_prefix col2 u k)">
      <goal name="t&#39;vc.46.2.0.0.0" expl="asserted formula" proved="true">
      <proof prover="2"><result status="valid" time="0.17" steps="655"/></proof>
      </goal>
      <goal name="t&#39;vc.46.2.0.0.1" expl="true case (loop invariant preservation)" proved="true">
      <proof prover="2"><result status="valid" time="0.45" steps="1254"/></proof>
      </goal>
     </transf>
     </goal>
     <goal name="t&#39;vc.46.2.0.1" expl="false case (loop invariant preservation)" proved="true">
     <proof prover="3" timelimit="30"><result status="valid" time="0.90"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="t&#39;vc.47" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.21"/></proof>
  </goal>
  <goal name="t&#39;vc.48" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.19"/></proof>
  </goal>
  <goal name="t&#39;vc.49" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.17"/></proof>
  </goal>
  <goal name="t&#39;vc.50" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07"/></proof>
  </goal>
  <goal name="t&#39;vc.51" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07"/></proof>
  </goal>
  <goal name="t&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="t&#39;vc.53" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07"/></proof>
  </goal>
  <goal name="t&#39;vc.54" expl="postcondition" proved="true">
  <proof prover="10"><result status="valid" time="0.04" steps="90"/></proof>
  </goal>
  <goal name="t&#39;vc.55" expl="postcondition" proved="true">
  <proof prover="10"><result status="valid" time="0.04" steps="90"/></proof>
  </goal>
  <goal name="t&#39;vc.56" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07"/></proof>
  </goal>
  <goal name="t&#39;vc.57" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08"/></proof>
  </goal>
  <goal name="t&#39;vc.58" expl="postcondition" proved="true">
  <proof prover="5"><result status="valid" time="0.02" steps="35755"/></proof>
  </goal>
  <goal name="t&#39;vc.59" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="t&#39;vc.60" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06"/></proof>
  </goal>
  <goal name="t&#39;vc.61" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="queens&#39;vc" expl="VC for queens" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="queens&#39;vc.0" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="queens&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.10"/></proof>
  </goal>
  <goal name="queens&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.10"/></proof>
  </goal>
  <goal name="queens&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.10"/></proof>
  </goal>
  <goal name="queens&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.09"/></proof>
  </goal>
  <goal name="queens&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08"/></proof>
  </goal>
  <goal name="queens&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08"/></proof>
  </goal>
  <goal name="queens&#39;vc.7" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.10"/></proof>
  </goal>
  <goal name="queens&#39;vc.8" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.12"/></proof>
  </goal>
  <goal name="queens&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="queens&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08"/></proof>
  </goal>
  <goal name="queens&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.51"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="test8&#39;vc" expl="VC for test8" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="test8&#39;vc.0" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="test8&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05"/></proof>
  </goal>
  <goal name="test8&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
