<?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="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.4" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Spass" version="3.9" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.5.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Coq" version="8.11.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC5" version="1.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="8" name="Alt-Ergo" version="2.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="vacid_0_red_black_trees.mlw"/>
<theory name="RedBlackTree" proved="true">
 <goal name="memt_color" proved="true">
 <proof prover="0"><result status="valid" time="0.00" steps="21"/></proof>
 </goal>
 <goal name="lt_leaf" proved="true">
 <proof prover="4"><result status="valid" time="0.00" steps="696"/></proof>
 </goal>
 <goal name="gt_leaf" proved="true">
 <proof prover="4"><result status="valid" time="0.00" steps="724"/></proof>
 </goal>
 <goal name="lt_tree_node" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="1607"/></proof>
 </goal>
 <goal name="gt_tree_node" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="1981"/></proof>
 </goal>
 <goal name="lt_node_lt" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="gt_node_gt" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="lt_left" proved="true">
 <proof prover="3"><result status="valid" time="0.01" steps="4206"/></proof>
 </goal>
 <goal name="lt_right" proved="true">
 <proof prover="3"><result status="valid" time="0.01" steps="4613"/></proof>
 </goal>
 <goal name="gt_left" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="5004"/></proof>
 </goal>
 <goal name="gt_right" proved="true">
 <proof prover="3"><result status="valid" time="0.01" steps="5380"/></proof>
 </goal>
 <goal name="lt_tree_not_in" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3128"/></proof>
 </goal>
 <goal name="lt_tree_trans" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3579"/></proof>
 </goal>
 <goal name="gt_tree_not_in" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="3684"/></proof>
 </goal>
 <goal name="gt_tree_trans" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="4148"/></proof>
 </goal>
 <goal name="bst_Leaf" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="4298"/></proof>
 </goal>
 <goal name="bst_left" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="4704"/></proof>
 </goal>
 <goal name="bst_right" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="4788"/></proof>
 </goal>
 <goal name="bst_color" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="4905"/></proof>
 </goal>
 <goal name="rotate_left" proved="true">
 <proof prover="8"><result status="valid" time="0.02" steps="160"/></proof>
 </goal>
 <goal name="rotate_right" proved="true">
 <proof prover="8"><result status="valid" time="0.02" steps="164"/></proof>
 </goal>
 <goal name="rbtree_Leaf" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="5285"/></proof>
 </goal>
 <goal name="rbtree_Node1" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="5474"/></proof>
 </goal>
 <goal name="rbtree_left" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="6016"/></proof>
 </goal>
 <goal name="rbtree_right" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="6203"/></proof>
 </goal>
 <goal name="find&#39;vc" expl="VC for find" proved="true">
 <proof prover="4"><result status="valid" time="0.13" steps="25584"/></proof>
 </goal>
 <goal name="rbtree_almost_rbtree" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="6477"/></proof>
 </goal>
 <goal name="rbtree_almost_rbtree_ex" proved="true">
 <proof prover="4"><result status="valid" time="0.03" steps="10730"/></proof>
 </goal>
 <goal name="almost_rbtree_rbtree_black" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="7200"/></proof>
 </goal>
 <goal name="lbalance&#39;vc" expl="VC for lbalance" proved="true">
 <proof prover="1"><result status="valid" time="0.60"/></proof>
 </goal>
 <goal name="rbalance&#39;vc" expl="VC for rbalance" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="rbalance&#39;vc.0" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="rbalance&#39;vc.0.0" expl="postcondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="rbalance&#39;vc.0.0.0" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.31"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.1" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.35"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.2" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="1.13"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.3" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.35"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.4" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.13"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.5" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.30"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.6" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.30"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.7" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.35"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.8" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.32"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.9" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.28"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.10" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.14"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.11" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.27"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.12" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.27"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.13" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.30"/></proof>
    </goal>
    <goal name="rbalance&#39;vc.0.0.14" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="0.50"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="rbalance&#39;vc.0.1" expl="postcondition" proved="true">
   <proof prover="6"><result status="valid" time="0.14" steps="28235"/></proof>
   </goal>
   <goal name="rbalance&#39;vc.0.2" expl="postcondition" proved="true">
   <proof prover="6"><result status="valid" time="0.67" steps="88323"/></proof>
   </goal>
   <goal name="rbalance&#39;vc.0.3" expl="postcondition" proved="true">
   <proof prover="6"><result status="valid" time="0.12" steps="18742"/></proof>
   </goal>
   <goal name="rbalance&#39;vc.0.4" expl="postcondition" proved="true">
   <proof prover="6"><result status="valid" time="0.10" steps="14817"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="insert&#39;vc" expl="VC for insert" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="insert&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="6594"/></proof>
  </goal>
  <goal name="insert&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7635"/></proof>
  </goal>
  <goal name="insert&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="6651"/></proof>
  </goal>
  <goal name="insert&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7710"/></proof>
  </goal>
  <goal name="insert&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="6594"/></proof>
  </goal>
  <goal name="insert&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7599"/></proof>
  </goal>
  <goal name="insert&#39;vc.6" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="30646"/></proof>
  </goal>
  <goal name="insert&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="6651"/></proof>
  </goal>
  <goal name="insert&#39;vc.8" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7674"/></proof>
  </goal>
  <goal name="insert&#39;vc.9" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="32487"/></proof>
  </goal>
  <goal name="insert&#39;vc.10" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="insert&#39;vc.10.0" expl="VC for insert" proved="true">
   <proof prover="4"><result status="valid" time="0.94" steps="118187"/></proof>
   </goal>
   <goal name="insert&#39;vc.10.1" expl="VC for insert" proved="true">
   <proof prover="8"><result status="valid" time="0.99" steps="9880"/></proof>
   </goal>
   <goal name="insert&#39;vc.10.2" expl="VC for insert" proved="true">
   <proof prover="4"><result status="valid" time="0.30" steps="77791"/></proof>
   </goal>
   <goal name="insert&#39;vc.10.3" expl="VC for insert" proved="true">
   <proof prover="4"><result status="valid" time="0.05" steps="18201"/></proof>
   </goal>
   <goal name="insert&#39;vc.10.4" expl="VC for insert" proved="true">
   <proof prover="1"><result status="valid" time="0.62"/></proof>
   </goal>
   <goal name="insert&#39;vc.10.5" expl="VC for insert" proved="true">
   <proof prover="4"><result status="valid" time="0.28" steps="50727"/></proof>
   </goal>
   <goal name="insert&#39;vc.10.6" expl="VC for insert" proved="true">
   <proof prover="0" timelimit="1"><result status="valid" time="0.24" steps="795"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="add&#39;vc" expl="VC for add" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="add&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="6080"/></proof>
  </goal>
  <goal name="add&#39;vc.1" expl="unreachable point" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7169"/></proof>
  </goal>
  <goal name="add&#39;vc.2" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="add&#39;vc.2.0" expl="VC for add" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="7540"/></proof>
   </goal>
   <goal name="add&#39;vc.2.1" expl="VC for add" proved="true">
   <proof prover="5"><path name="vacid_0_red_black_trees_RedBlackTree_VC_add_1.v"/><result status="valid" time="0.32"/></proof>
   </goal>
   <goal name="add&#39;vc.2.2" expl="VC for add" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="7566"/></proof>
   </goal>
   <goal name="add&#39;vc.2.3" expl="VC for add" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="9524"/></proof>
   </goal>
   <goal name="add&#39;vc.2.4" expl="VC for add" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="9559"/></proof>
   </goal>
   <goal name="add&#39;vc.2.5" expl="VC for add" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="9929"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Vacid0" proved="true">
 <goal name="create&#39;vc" expl="VC for create" proved="true">
 <proof prover="4"><result status="valid" time="0.03" steps="7961"/></proof>
 </goal>
 <goal name="replace&#39;vc" expl="VC for replace" proved="true">
 <proof prover="4"><result status="valid" time="0.04" steps="10469"/></proof>
 </goal>
 <goal name="lookup&#39;vc" expl="VC for lookup" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="7423"/></proof>
 </goal>
 <goal name="remove&#39;vc" expl="VC for remove" proved="true">
 <proof prover="4"><result status="valid" time="0.02" steps="7814"/></proof>
 </goal>
</theory>
</file>
</why3session>
