why3session.xml 59.4 KB
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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="4">
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<prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" memlimit="1000"/>
<prover id="1" name="Coq" version="8.4pl4" timelimit="10" memlimit="0"/>
<prover id="2" name="CVC3" version="2.4.1" timelimit="5" memlimit="1000"/>
<prover id="3" name="Eprover" version="1.6" timelimit="5" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.4" timelimit="5" memlimit="1000"/>
<prover id="5" name="Spass" version="3.7" timelimit="5" memlimit="1000"/>
<prover id="6" name="CVC3" version="2.2" timelimit="5" memlimit="1000"/>
<prover id="7" name="Alt-Ergo" version="0.95.2" timelimit="5" memlimit="4000"/>
<prover id="8" name="Vampire" version="0.6" timelimit="10" memlimit="1000"/>
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<file name="../vacid_0_red_black_trees.mlw" expanded="true">
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<theory name="RedBlackTree" sum="e16e6ca86bc8e9496342dc598e242252" expanded="true">
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 <goal name="memt_color">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="18"/></proof>
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 </goal>
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 <goal name="lt_leaf">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="4"/></proof>
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 </goal>
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 <goal name="gt_leaf">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.00" steps="4"/></proof>
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 </goal>
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 <goal name="lt_tree_node">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.00" steps="18"/></proof>
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 </goal>
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 <goal name="gt_tree_node">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="18"/></proof>
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 </goal>
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 <goal name="lt_node_lt">
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 <proof prover="1" edited="vacid_0_red_black_trees_WP_RedBlackTree_lt_node_lt_1.v"><result status="valid" time="0.79"/></proof>
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 </goal>
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 <goal name="gt_node_gt">
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 <proof prover="1" edited="vacid_0_red_black_trees_WP_RedBlackTree_gt_node_gt_1.v"><result status="valid" time="0.79"/></proof>
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 </goal>
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 <goal name="lt_left">
 <proof prover="6" timelimit="10" memlimit="0"><result status="valid" time="0.06"/></proof>
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 </goal>
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 <goal name="lt_right">
 <proof prover="6" timelimit="10" memlimit="0"><result status="valid" time="0.06"/></proof>
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 </goal>
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 <goal name="gt_left">
 <proof prover="6" timelimit="10" memlimit="0"><result status="valid" time="0.06"/></proof>
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 </goal>
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 <goal name="gt_right">
 <proof prover="6" timelimit="10" memlimit="0"><result status="valid" time="0.06"/></proof>
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 </goal>
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 <goal name="lt_tree_not_in">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.02" steps="3"/></proof>
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 </goal>
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 <goal name="lt_tree_trans">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="6"/></proof>
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 </goal>
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 <goal name="gt_tree_not_in">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="3"/></proof>
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 </goal>
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 <goal name="gt_tree_trans">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.02" steps="6"/></proof>
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 </goal>
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 <goal name="bst_Leaf">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.00" steps="2"/></proof>
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 </goal>
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 <goal name="bst_left">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.02" steps="13"/></proof>
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 </goal>
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 <goal name="bst_right">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.02" steps="13"/></proof>
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 </goal>
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 <goal name="bst_color">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.02" steps="47"/></proof>
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 </goal>
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 <goal name="rotate_left">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.15" steps="220"/></proof>
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 </goal>
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 <goal name="rotate_right">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.14" steps="264"/></proof>
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 </goal>
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 <goal name="rbtree_Leaf">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.02" steps="3"/></proof>
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 </goal>
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 <goal name="rbtree_Node1">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.05" steps="36"/></proof>
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 </goal>
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 <goal name="rbtree_left">
 <proof prover="3"><result status="valid" time="0.00"/></proof>
 <proof prover="5"><result status="valid" time="0.03"/></proof>
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 <proof prover="7"><result status="valid" time="0.02" steps="23"/></proof>
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 </goal>
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 <goal name="rbtree_right">
 <proof prover="3"><result status="valid" time="0.00"/></proof>
 <proof prover="5"><result status="valid" time="0.03"/></proof>
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 <proof prover="7"><result status="valid" time="0.02" steps="27"/></proof>
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 </goal>
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 <goal name="WP_parameter find" expl="VC for find">
 <transf name="split_goal_wp">
  <goal name="WP_parameter find.1" expl="1. exceptional postcondition">
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  <proof prover="7"><result status="valid" time="0.01" steps="6"/></proof>
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  </goal>
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  <goal name="WP_parameter find.2" expl="2. postcondition">
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  <proof prover="7"><result status="valid" time="0.02" steps="7"/></proof>
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  </goal>
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  <goal name="WP_parameter find.3" expl="3. variant decrease">
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  <proof prover="7"><result status="valid" time="0.02" steps="24"/></proof>
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  </goal>
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  <goal name="WP_parameter find.4" expl="4. precondition">
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  <proof prover="7"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
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  <goal name="WP_parameter find.5" expl="5. postcondition">
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  <proof prover="7"><result status="valid" time="0.01" steps="10"/></proof>
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  </goal>
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  <goal name="WP_parameter find.6" expl="6. exceptional postcondition">
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  <proof prover="7"><result status="valid" time="0.02" steps="21"/></proof>
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  </goal>
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  <goal name="WP_parameter find.7" expl="7. variant decrease">
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  <proof prover="7"><result status="valid" time="0.02" steps="18"/></proof>
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  </goal>
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  <goal name="WP_parameter find.8" expl="8. precondition">
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  <proof prover="7"><result status="valid" time="0.02" steps="14"/></proof>
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  </goal>
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  <goal name="WP_parameter find.9" expl="9. postcondition">
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  <proof prover="7"><result status="valid" time="0.02" steps="11"/></proof>
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  </goal>
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  <goal name="WP_parameter find.10" expl="10. exceptional postcondition">
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  <proof prover="7"><result status="valid" time="0.02" steps="21"/></proof>
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  </goal>
 </transf>
 </goal>
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 <goal name="rbtree_almost_rbtree">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.03" steps="49"/></proof>
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 </goal>
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 <goal name="rbtree_almost_rbtree_ex">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="6"/></proof>
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 </goal>
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 <goal name="almost_rbtree_rbtree_black">
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 <proof prover="7" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="14"/></proof>
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 </goal>
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 <goal name="WP_parameter lbalance" expl="VC for lbalance">
 <transf name="split_goal_wp">
  <goal name="WP_parameter lbalance.1" expl="1. postcondition">
  <transf name="split_goal_wp">
   <goal name="WP_parameter lbalance.1.1" expl="1.">
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   <proof prover="7" timelimit="12" memlimit="0"><result status="valid" time="0.88" steps="750"/></proof>
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   </goal>
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   <goal name="WP_parameter lbalance.1.2" expl="2.">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
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   </goal>
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   <goal name="WP_parameter lbalance.1.3" expl="3.">
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   <proof prover="7" timelimit="100" memlimit="0"><result status="valid" time="0.31" steps="231"/></proof>
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   </goal>
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   <goal name="WP_parameter lbalance.1.4" expl="4.">
   <proof prover="2" memlimit="0"><result status="valid" time="0.09"/></proof>
   <proof prover="4"><result status="valid" time="0.05"/></proof>
   <proof prover="6" memlimit="0"><result status="valid" time="0.06"/></proof>
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   <proof prover="7" timelimit="8" memlimit="0"><result status="valid" time="0.26" steps="194"/></proof>
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   </goal>
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   <goal name="WP_parameter lbalance.1.5" expl="5.">
   <proof prover="4"><result status="valid" time="0.03"/></proof>
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   <proof prover="7" timelimit="6" memlimit="0"><result status="valid" time="1.11" steps="1184"/></proof>
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   </goal>
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  </transf>
  </goal>
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  <goal name="WP_parameter lbalance.2" expl="2. postcondition">
  <transf name="split_goal_wp">
   <goal name="WP_parameter lbalance.2.1" expl="1.">
   <proof prover="2" memlimit="0"><result status="valid" time="0.02"/></proof>
   <proof prover="4"><result status="valid" time="0.01"/></proof>
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   <proof prover="6" memlimit="0"><result status="valid" time="0.02"/></proof>
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   <proof prover="7" memlimit="0"><result status="valid" time="0.02" steps="20"/></proof>
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   </goal>
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   <goal name="WP_parameter lbalance.2.2" expl="2.">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
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   <proof prover="7" timelimit="120"><result status="valid" time="0.02" steps="45"/></proof>
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   <metas>
    <ts_pos name="key" arity="0" id="376"
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     ip_theory="RedBlackTree">
     <ip_qualid name="key"/>
    </ts_pos>
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    <ts_pos name="value" arity="0" id="377"
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     ip_theory="RedBlackTree">
     <ip_qualid name="value"/>
    </ts_pos>
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    <ls_pos name="zero" id="460"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="zero"/>
    </ls_pos>
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    <ls_pos name="one" id="461"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="one"/>
    </ls_pos>
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    <ls_pos name="infix &lt;" id="462"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="infix &lt;"/>
    </ls_pos>
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    <ls_pos name="infix &gt;" id="465"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="infix &gt;"/>
    </ls_pos>
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    <ls_pos name="infix &lt;=" id="474"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="infix &lt;="/>
    </ls_pos>
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    <ls_pos name="infix +" id="1631"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="infix +"/>
    </ls_pos>
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    <ls_pos name="prefix -" id="1632"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="prefix -"/>
    </ls_pos>
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    <ls_pos name="infix *" id="1633"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="infix *"/>
    </ls_pos>
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    <ls_pos name="infix &gt;=" id="1701"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="infix &gt;="/>
    </ls_pos>
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    <pr_pos name="memt_color" id="434"
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     ip_theory="RedBlackTree">
     <ip_qualid name="memt_color"/>
    </pr_pos>
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    <pr_pos name="Assoc" id="1634"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="CommutativeGroup"/>
     <ip_qualid name="Assoc"/>
    </pr_pos>
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    <pr_pos name="Unit_def_l" id="1641"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="CommutativeGroup"/>
     <ip_qualid name="Unit_def_l"/>
    </pr_pos>
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    <pr_pos name="Unit_def_r" id="1644"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="CommutativeGroup"/>
     <ip_qualid name="Unit_def_r"/>
    </pr_pos>
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    <pr_pos name="Inv_def_l" id="1647"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="CommutativeGroup"/>
     <ip_qualid name="Inv_def_l"/>
    </pr_pos>
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    <pr_pos name="Inv_def_r" id="1650"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="CommutativeGroup"/>
     <ip_qualid name="Inv_def_r"/>
    </pr_pos>
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    <pr_pos name="Comm" id="1653"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="CommutativeGroup"/>
     <ip_qualid name="Comm"/>
     <ip_qualid name="Comm"/>
    </pr_pos>
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    <pr_pos name="Assoc" id="1658"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Assoc"/>
     <ip_qualid name="Assoc"/>
    </pr_pos>
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    <pr_pos name="Mul_distr_l" id="1665"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Mul_distr_l"/>
    </pr_pos>
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    <pr_pos name="Mul_distr_r" id="1672"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Mul_distr_r"/>
    </pr_pos>
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    <pr_pos name="Comm" id="1690"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Comm"/>
     <ip_qualid name="Comm"/>
    </pr_pos>
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    <pr_pos name="Unitary" id="1695"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Unitary"/>
    </pr_pos>
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    <pr_pos name="NonTrivialRing" id="1698"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="NonTrivialRing"/>
    </pr_pos>
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    <pr_pos name="Refl" id="1710"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Refl"/>
    </pr_pos>
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    <pr_pos name="Trans" id="1713"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Trans"/>
    </pr_pos>
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    <pr_pos name="Antisymm" id="1720"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Antisymm"/>
    </pr_pos>
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    <pr_pos name="Total" id="1725"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="Total"/>
    </pr_pos>
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    <pr_pos name="ZeroLessOne" id="1730"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="ZeroLessOne"/>
    </pr_pos>
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    <pr_pos name="CompatOrderAdd" id="1731"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="CompatOrderAdd"/>
    </pr_pos>
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    <pr_pos name="CompatOrderMult" id="1738"
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     ip_theory="Int">
     <ip_library name="int"/>
     <ip_qualid name="CompatOrderMult"/>
    </pr_pos>
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    <pr_pos name="lt_leaf" id="2446"
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     ip_theory="RedBlackTree">
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    <goal name="WP_parameter lbalance.2.2" expl="2.">
    <transf name="eliminate_builtin">
     <goal name="WP_parameter lbalance.2.2.1" expl="1.">
     <proof prover="2" timelimit="10"><result status="valid" time="0.01"/></proof>
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     <proof prover="7" timelimit="120"><result status="valid" time="0.02" steps="57"/></proof>
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     </goal>
    </transf>
    </goal>
   </metas>
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   </goal>
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   <goal name="WP_parameter lbalance.2.3" expl="3.">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
   <proof prover="6" timelimit="8" memlimit="0"><result status="valid" time="0.04"/></proof>
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   <proof prover="7" memlimit="0"><result status="valid" time="0.03" steps="62"/></proof>
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   </goal>
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   <goal name="WP_parameter lbalance.2.4" expl="4.">
   <proof prover="2" memlimit="0"><result status="valid" time="0.03"/></proof>
   <proof prover="4"><result status="valid" time="0.01"/></proof>
   <proof prover="6" memlimit="0"><result status="valid" time="0.02"/></proof>
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   <proof prover="7" memlimit="0"><result status="valid" time="0.02" steps="64"/></proof>
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   </goal>
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   <goal name="WP_parameter lbalance.2.5" expl="5.">
   <proof prover="2" memlimit="0"><result status="valid" time="0.01"/></proof>
   <proof prover="4"><result status="valid" time="0.01"/></proof>
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   <proof prover="6" memlimit="0"><result status="valid" time="0.01"/></proof>
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   <proof prover="7" memlimit="0"><result status="valid" time="0.01" steps="21"/></proof>
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   </goal>
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  </transf>
  </goal>
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  <goal name="WP_parameter lbalance.3" expl="3. postcondition">
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  <proof prover="0"><result status="valid" time="2.06" steps="2335"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.4" expl="4. postcondition">
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  <proof prover="4"><result status="valid" time="0.04"/></proof>
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  <proof prover="7" memlimit="1000"><result status="valid" time="0.08" steps="215"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.5" expl="5. postcondition">
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  <proof prover="0"><result status="valid" time="0.82" steps="1403"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.6" expl="6. postcondition">
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  <proof prover="4"><result status="valid" time="0.04"/></proof>
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  <proof prover="7" memlimit="1000"><result status="valid" time="0.07" steps="159"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.7" expl="7. postcondition">
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  <proof prover="0"><result status="valid" time="1.39" steps="1863"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.8" expl="8. postcondition">
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  <proof prover="4"><result status="valid" time="0.04"/></proof>
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  <proof prover="7" memlimit="1000"><result status="valid" time="0.09" steps="215"/></proof>
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  </goal>
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  <goal name="WP_parameter lbalance.9" expl="9. postcondition">
  <transf name="split_goal_wp">
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   <goal name="WP_parameter lbalance.9.1" expl="1.">
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   <proof prover="4"><result status="valid" time="0.01"/></proof>
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   <proof prover="7" memlimit="1000"><result status="valid" time="0.02" steps="19"/></proof>
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   </goal>
   <goal name="WP_parameter lbalance.9.2" expl="2.">
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   <proof prover="4"><result status="timeout" time="5.03"/></proof>
   <proof prover="7" memlimit="1000"><result status="valid" time="0.34" steps="304"/></proof>
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   </goal>
   <goal name="WP_parameter lbalance.9.3" expl="3.">
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   <proof prover="4"><result status="valid" time="0.02"/></proof>
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   <proof prover="7" memlimit="1000"><result status="valid" time="0.03" steps="61"/></proof>
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   </goal>
   <goal name="WP_parameter lbalance.9.4" expl="4.">
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   <proof prover="4"><result status="valid" time="0.02"/></proof>
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   <proof prover="7" memlimit="1000"><result status="valid" time="0.03" steps="63"/></proof>
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   </goal>
   <goal name="WP_parameter lbalance.9.5" expl="5.">
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   <proof prover="4"><result status="valid" time="0.01"/></proof>
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   <proof prover="7" memlimit="1000"><result status="valid" time="0.02" steps="20"/></proof>
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   </goal>
  </transf>
  </goal>
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  <goal name="WP_parameter lbalance.10" expl="10. postcondition">
  <transf name="split_goal_wp">
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   <goal name="WP_parameter lbalance.10.1" expl="1.">
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   <proof prover="4"><result status="valid" time="0.01"/></proof>
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   <proof prover="7" memlimit="1000"><result status="valid" time="0.02" steps="18"/></proof>
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   </goal>
   <goal name="WP_parameter lbalance.10.2" expl="2.">
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   <proof prover="4"><result status="timeout" time="5.03"/></proof>
   <proof prover="7" memlimit="1000"><result status="valid" time="0.12" steps="169"/></proof>
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   </goal>
   <goal name="WP_parameter lbalance.10.3" expl="3.">
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   <proof prover="4"><result status="valid" time="0.03"/></proof>
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   <proof prover="7" memlimit="1000"><result status="valid" time="0.04" steps="48"/></proof>
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   </goal>
   <goal name="WP_parameter lbalance.10.4" expl="4.">
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   <proof prover="4"><result status="valid" time="0.02"/></proof>
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   <proof prover="7" memlimit="1000"><result status="valid" time="0.02" steps="50"/></proof>
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   </goal>
   <goal name="WP_parameter lbalance.10.5" expl="5.">
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   <proof prover="4"><result status="valid" time="0.01"/></proof>
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   <proof prover="7" memlimit="1000"><result status="valid" time="0.01" steps="19"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="WP_parameter lbalance.11" expl="11. postcondition">
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  <proof prover="0"><result status="valid" time="0.71" steps="1172"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.12" expl="12. postcondition">
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  <proof prover="4"><result status="valid" time="0.04"/></proof>
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  <proof prover="7" memlimit="1000"><result status="valid" time="0.07" steps="159"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.13" expl="13. postcondition">
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  <proof prover="4"><result status="timeout" time="6.01"/></proof>
  <proof prover="7" memlimit="1000"><result status="valid" time="2.57" steps="763"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.14" expl="14. postcondition">
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  <proof prover="4"><result status="timeout" time="5.06"/></proof>
  <proof prover="7" memlimit="1000"><result status="valid" time="0.18" steps="202"/></proof>
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  </goal>
  <goal name="WP_parameter lbalance.15" expl="15. postcondition">
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  <proof prover="4"><result status="valid" time="0.02"/></proof>
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  <proof prover="7" memlimit="1000"><result status="valid" time="0.02" steps="52"/></proof>
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  </goal>
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 </transf>
 </goal>
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 <goal name="WP_parameter rbalance" expl="VC for rbalance">
 <transf name="split_goal_wp">
  <goal name="WP_parameter rbalance.1" expl="1. postcondition">
  <transf name="split_goal_wp">
   <goal name="WP_parameter rbalance.1.1" expl="1.">
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   <proof prover="7" timelimit="14" memlimit="0"><result status="valid" time="0.93" steps="807"/></proof>
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   </goal>
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   <goal name="WP_parameter rbalance.1.2" expl="2.">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
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   </goal>
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   <goal name="WP_parameter rbalance.1.3" expl="3.">
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   <proof prover="7" timelimit="100" memlimit="0"><result status="valid" time="0.96" steps="524"/></proof>
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   </goal>
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   <goal name="WP_parameter rbalance.1.4" expl="4.">
   <proof prover="2" memlimit="0"><result status="valid" time="0.10"/></proof>
   <proof prover="4"><result status="valid" time="0.13"/></proof>
   <proof prover="6" memlimit="0"><result status="valid" time="0.06"/></proof>
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   <proof prover="7" timelimit="7" memlimit="0"><result status="valid" time="0.36" steps="222"/></proof>
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   </goal>
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   <goal name="WP_parameter rbalance.1.5" expl="5.">
   <proof prover="4"><result status="valid" time="0.04"/></proof>
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   <proof prover="7" timelimit="6" memlimit="0"><result status="valid" time="1.64" steps="1572"/></proof>
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   </goal>
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  </transf>
  </goal>
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  <goal name="WP_parameter rbalance.2" expl="2. postcondition">
  <proof prover="4"><result status="valid" time="0.04"/></proof>
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  <proof prover="7" timelimit="120"><result status="valid" time="0.08" steps="215"/></proof>
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  <metas>
   <ts_pos name="key" arity="0" id="376"
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    ip_theory="RedBlackTree">
    <ip_qualid name="key"/>
   </ts_pos>
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   <ts_pos name="value" arity="0" id="377"
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    ip_theory="RedBlackTree">
    <ip_qualid name="value"/>
   </ts_pos>
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   <ls_pos name="zero" id="460"
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    ip_theory="Int">
    <ip_library name="int"/>
    <ip_qualid name="zero"/>
   </ls_pos>
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   <ls_pos name="one" id="461"
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    ip_theory="Int">
    <ip_library name="int"/>
    <ip_qualid name="one"/>
   </ls_pos>
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   <ls_pos name="infix &lt;" id="462"
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    ip_theory="Int">
    <ip_library name="int"/>
    <ip_qualid name="infix &lt;"/>
   </ls_pos>
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   <ls_pos name="infix &gt;" id="465"
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    ip_theory="Int">
    <ip_library name="int"/>
    <ip_qualid name="infix &gt;"/>
   </ls_pos>
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   <ls_pos name="infix &lt;=" id="474"
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    ip_theory="Int">
    <ip_library name="int"/>
    <ip_qualid name="infix &lt;="/>
   </ls_pos>
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   <ls_pos name="infix +" id="1631"
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    ip_theory="Int">
    <ip_library name="int"/>
    <ip_qualid name="infix +"/>
   </ls_pos>
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   <ls_pos name="prefix -" id="1632"
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    ip_theory="Int">
    <ip_library name="int"/>
    <ip_qualid name="prefix -"/>
   </ls_pos>
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   <ls_pos name="infix *" id="1633"
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    ip_theory="Int">
    <ip_library name="int"/>
    <ip_qualid name="infix *"/>
   </ls_pos>
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   <ls_pos name="infix &gt;=" id="1701"