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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="5">
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<prover id="0" name="Eprover" version="1.9.1-001" timelimit="5" steplimit="0" memlimit="2000"/>
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<prover id="1" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="2" name="Alt-Ergo" version="2.2.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="3" name="Z3" version="4.5.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="5" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
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<file name="../verifythis_2018_array_based_queuing_lock_2.mlw" proved="true">
<theory name="ABQL" proved="true">
 <goal name="VC tick" expl="VC for tick" proved="true">
 <proof prover="3"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC fetch_and_add" expl="VC for fetch_and_add" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="VC fetch_and_add.0" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
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   <goal name="VC fetch_and_add.0.0" expl="assertion" proved="true">
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   <transf name="subst" proved="true" arg1="a">
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    <goal name="VC fetch_and_add.0.0.0" expl="assertion" proved="true">
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    <transf name="apply" proved="true" arg1="Div_mod">
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     <goal name="VC fetch_and_add.0.0.0.0" expl="apply premises" proved="true">
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     <proof prover="3"><result status="valid" time="0.02"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="VC fetch_and_add.0.1" expl="VC for fetch_and_add" proved="true">
   <proof prover="3"><result status="valid" time="0.01"/></proof>
   </goal>
   <goal name="VC fetch_and_add.0.2" expl="VC for fetch_and_add" proved="true">
   <proof prover="3"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="VC fetch_and_add.0.3" expl="VC for fetch_and_add" proved="true">
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   <proof prover="4"><result status="valid" time="0.00" steps="6"/></proof>
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   </goal>
   <goal name="VC fetch_and_add.0.4" expl="VC for fetch_and_add" proved="true">
   <proof prover="3"><result status="valid" time="0.02"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC fetch_and_add.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC fetch_and_add.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC fetch_and_add.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC fetch_and_add.4" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="Sorted.Transitive.Trans" proved="true">
 <proof prover="3"><result status="valid" time="0.03"/></proof>
 </goal>
 <goal name="VC last_push" expl="VC for last_push" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="VC last_push.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC last_push.1" expl="postcondition" proved="true">
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  <proof prover="1"><result status="valid" time="0.18"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC consecutive_last_push" expl="VC for consecutive_last_push" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="VC consecutive_last_push.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC consecutive_last_push.1" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="75"/></proof>
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  </goal>
  <goal name="VC consecutive_last_push.2" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.23" steps="163"/></proof>
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  </goal>
  <goal name="VC consecutive_last_push.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.47"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="hd_push" proved="true">
 <proof prover="3"><result status="valid" time="0.17"/></proof>
 </goal>
 <goal name="VC consecutive_implies_sorted" expl="VC for consecutive_implies_sorted" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="VC consecutive_implies_sorted.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC consecutive_implies_sorted.1" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="75"/></proof>
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  </goal>
  <goal name="VC consecutive_implies_sorted.2" expl="postcondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="51"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC numof_equiv" expl="VC for numof_equiv" proved="true">
 <proof prover="3"><result status="valid" time="0.35"/></proof>
 </goal>
 <goal name="VC numof_add" expl="VC for numof_add" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="VC numof_add.0" expl="assertion" proved="true">
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  <proof prover="4"><result status="valid" time="0.07" steps="157"/></proof>
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  </goal>
  <goal name="VC numof_add.1" expl="assertion" proved="true">
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  <proof prover="4"><result status="valid" time="0.15" steps="251"/></proof>
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  </goal>
  <goal name="VC numof_add.2" expl="assertion" proved="true">
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  <proof prover="4"><result status="valid" time="0.08" steps="226"/></proof>
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  </goal>
  <goal name="VC numof_add.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.44"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="mod_diff" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="mod_diff.0" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="mod_diff.1" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="mod_diff.2" proved="true">
  <proof prover="3"><result status="valid" time="0.15"/></proof>
  </goal>
  <goal name="mod_diff.3" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="14"/></proof>
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  </goal>
  <goal name="mod_diff.4" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="mod_diff.5" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC main" expl="VC for main" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="VC main.0" expl="array creation size" proved="true">
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  <proof prover="3"><result status="valid" time="0.14"/></proof>
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  </goal>
  <goal name="VC main.1" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.18"/></proof>
  </goal>
  <goal name="VC main.2" expl="precondition" proved="true">
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  <proof prover="3"><result status="valid" time="0.30"/></proof>
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  </goal>
  <goal name="VC main.3" expl="array creation size" proved="true">
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  <proof prover="3"><result status="valid" time="0.02"/></proof>
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  </goal>
  <goal name="VC main.4" expl="array creation size" proved="true">
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  <proof prover="3"><result status="valid" time="0.05"/></proof>
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  </goal>
  <goal name="VC main.5" expl="array creation size" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="16"/></proof>
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  </goal>
  <goal name="VC main.6" expl="safety" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="31"/></proof>
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  </goal>
  <goal name="VC main.7" expl="loop invariant init" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
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  </goal>
  <goal name="VC main.8" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC main.9" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC main.10" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC main.11" expl="loop invariant init" proved="true">
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  <proof prover="4"><result status="valid" time="0.10" steps="113"/></proof>
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  </goal>
  <goal name="VC main.12" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC main.13" expl="loop invariant init" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.03" steps="58"/></proof>
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  </goal>
  <goal name="VC main.14" expl="loop invariant init" proved="true">
  <transf name="split_vc" proved="true" >
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   <goal name="VC main.14.0" expl="loop invariant init" proved="true">
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   <proof prover="4" memlimit="2000"><result status="valid" time="0.02" steps="46"/></proof>
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   </goal>
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   <goal name="VC main.14.1" expl="loop invariant init" proved="true">
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   <proof prover="4"><result status="valid" time="0.02" steps="47"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC main.15" expl="loop invariant init" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="31"/></proof>
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  </goal>
  <goal name="VC main.16" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC main.17" expl="loop invariant init" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="33"/></proof>
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  </goal>
  <goal name="VC main.18" expl="loop invariant init" proved="true">
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  <proof prover="4"><result status="valid" time="0.12" steps="20"/></proof>
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  </goal>
  <goal name="VC main.19" expl="loop invariant init" proved="true">
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  <proof prover="4"><result status="valid" time="0.16" steps="142"/></proof>
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  </goal>
  <goal name="VC main.20" expl="loop invariant init" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="29"/></proof>
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  </goal>
  <goal name="VC main.21" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC main.22" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC main.23" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC main.24" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC main.25" expl="liveness" proved="true">
  <transf name="right" proved="true" >
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   <goal name="VC main.25.0" expl="right case" proved="true">
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   <transf name="split_vc" proved="true" >
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    <goal name="VC main.25.0.0" expl="right case" proved="true">
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    <transf name="exists" proved="true" arg1="0">
     <goal name="VC main.25.0.0.0" proved="true">
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     <proof prover="4"><result status="valid" time="0.01" steps="29"/></proof>
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     </goal>
    </transf>
    </goal>
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    <goal name="VC main.25.0.1" expl="right case" proved="true">
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    <proof prover="3"><result status="valid" time="0.02"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="VC main.26" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC main.27" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC main.28" expl="safety" proved="true">
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  <proof prover="4"><result status="valid" time="0.05" steps="118"/></proof>
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  </goal>
  <goal name="VC main.29" expl="loop invariant preservation" proved="true">
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  <proof prover="3"><result status="valid" time="0.02"/></proof>
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  </goal>
  <goal name="VC main.30" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.32" steps="348"/></proof>
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  </goal>
  <goal name="VC main.31" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="54"/></proof>
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  </goal>
  <goal name="VC main.32" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.33" steps="972"/></proof>
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  </goal>
  <goal name="VC main.33" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.04" steps="86"/></proof>
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  </goal>
  <goal name="VC main.34" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.06" steps="59"/></proof>
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  </goal>
  <goal name="VC main.35" expl="loop invariant preservation" proved="true">
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  <transf name="split_all_full" proved="true" >
   <goal name="VC main.35.0" expl="VC for main" proved="true">
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   <proof prover="4" timelimit="10" memlimit="4000"><result status="valid" time="0.06" steps="80"/></proof>
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   </goal>
  </transf>
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  </goal>
  <goal name="VC main.36" expl="loop invariant preservation" proved="true">
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  <transf name="case" proved="true" arg1="(th=th1)">
   <goal name="VC main.36.0" expl="true case (loop invariant preservation)" proved="true">
   <proof prover="4"><result status="valid" time="0.04" steps="86"/></proof>
   </goal>
   <goal name="VC main.36.1" expl="false case (loop invariant preservation)" proved="true">
   <proof prover="4" memlimit="2000"><result status="valid" time="0.12" steps="313"/></proof>
   </goal>
  </transf>
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  </goal>
  <goal name="VC main.37" expl="loop invariant preservation" proved="true">
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  <transf name="split_vc" proved="true" >
   <goal name="VC main.37.0" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="43"/></proof>
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   </goal>
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   <goal name="VC main.37.1" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.25" steps="667"/></proof>
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   </goal>
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   <goal name="VC main.37.2" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.05" steps="136"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC main.38" expl="loop invariant preservation" proved="true">
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  <proof prover="3"><result status="valid" time="0.05"/></proof>
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  </goal>
  <goal name="VC main.39" expl="loop invariant preservation" proved="true">
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  <proof prover="0" timelimit="10" memlimit="1000"><result status="valid" time="1.63"/></proof>
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  <transf name="split_all_full" proved="true" >
   <goal name="VC main.39.0" expl="VC for main" proved="true">
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   <proof prover="5"><result status="valid" time="0.18"/></proof>
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   </goal>
   <goal name="VC main.39.1" expl="VC for main" proved="true">
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   <transf name="introduce_premises" proved="true" >
    <goal name="VC main.39.1.0" expl="VC for main" proved="true">
    <proof prover="2" timelimit="30" memlimit="4000"><result status="valid" time="1.14" steps="1064"/></proof>
    </goal>
   </transf>
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   </goal>
  </transf>
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  </goal>
  <goal name="VC main.40" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.02" steps="34"/></proof>
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  </goal>
  <goal name="VC main.41" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="140"/></proof>
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  </goal>
  <goal name="VC main.42" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.03" steps="50"/></proof>
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  </goal>
  <goal name="VC main.43" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.04" steps="47"/></proof>
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  </goal>
  <goal name="VC main.44" expl="loop invariant preservation" proved="true">
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  <proof prover="3"><result status="valid" time="0.02"/></proof>
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  </goal>
  <goal name="VC main.45" expl="loop invariant preservation" proved="true">
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  <transf name="split_vc" proved="true" >
   <goal name="VC main.45.0" expl="loop invariant preservation" proved="true">
   <proof prover="4" memlimit="2000"><result status="valid" time="0.10" steps="37"/></proof>
   </goal>
   <goal name="VC main.45.1" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.04" steps="52"/></proof>
   </goal>
   <goal name="VC main.45.2" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.05" steps="48"/></proof>
   </goal>
   <goal name="VC main.45.3" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.05" steps="47"/></proof>
   </goal>
   <goal name="VC main.45.4" expl="loop invariant preservation" proved="true">
   <proof prover="4" memlimit="2000"><result status="valid" time="0.10" steps="69"/></proof>
   </goal>
   <goal name="VC main.45.5" expl="loop invariant preservation" proved="true">
   <proof prover="4" memlimit="2000"><result status="valid" time="0.11" steps="36"/></proof>
   </goal>
   <goal name="VC main.45.6" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.10" steps="100"/></proof>
   </goal>
  </transf>
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  </goal>
  <goal name="VC main.46" expl="loop invariant preservation" proved="true">
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  <proof prover="3"><result status="valid" time="0.04"/></proof>
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  </goal>
  <goal name="VC main.47" expl="liveness" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.06" steps="177"/></proof>
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  </goal>
  <goal name="VC main.48" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
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   <goal name="VC main.48.0" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.02" steps="33"/></proof>
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   </goal>
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   <goal name="VC main.48.1" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.02" steps="33"/></proof>
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   </goal>
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   <goal name="VC main.48.2" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.01" steps="38"/></proof>
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   </goal>
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   <goal name="VC main.48.3" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.05" steps="47"/></proof>
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   </goal>
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   <goal name="VC main.48.4" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.02" steps="47"/></proof>
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   </goal>
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   <goal name="VC main.48.5" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.07" steps="118"/></proof>
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   </goal>
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   <goal name="VC main.48.6" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.13" steps="115"/></proof>
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   </goal>
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   <goal name="VC main.48.7" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.03" steps="54"/></proof>
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   </goal>
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   <goal name="VC main.48.8" expl="assertion" proved="true">
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   <proof prover="4"><result status="valid" time="0.06" steps="148"/></proof>
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   </goal>
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   <goal name="VC main.48.9" expl="assertion" proved="true">
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   <proof prover="3"><result status="valid" time="0.03"/></proof>
   </goal>
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   <goal name="VC main.48.10" expl="assertion" proved="true">
401
   <proof prover="4"><result status="valid" time="0.03" steps="104"/></proof>
402
   </goal>
403
   <goal name="VC main.48.11" expl="assertion" proved="true">
404
   <proof prover="4"><result status="valid" time="0.29" steps="328"/></proof>
405
   </goal>
406
   <goal name="VC main.48.12" expl="assertion" proved="true">
407
   <proof prover="4"><result status="valid" time="0.02" steps="52"/></proof>
408
   </goal>
409
   <goal name="VC main.48.13" expl="assertion" proved="true">
410
   <proof prover="4"><result status="valid" time="0.02" steps="52"/></proof>
411
   </goal>
412
   <goal name="VC main.48.14" expl="assertion" proved="true">
413
   <proof prover="4"><result status="valid" time="0.10" steps="246"/></proof>
414
   </goal>
415
   <goal name="VC main.48.15" expl="assertion" proved="true">
416
   <proof prover="4"><result status="valid" time="0.17" steps="134"/></proof>
417
   </goal>
418
   <goal name="VC main.48.16" expl="assertion" proved="true">
419
   <proof prover="4"><result status="valid" time="0.02" steps="46"/></proof>
420
   </goal>
421
   <goal name="VC main.48.17" expl="assertion" proved="true">
422
   <proof prover="4"><result status="valid" time="0.01" steps="36"/></proof>
423
   </goal>
424
   <goal name="VC main.48.18" expl="assertion" proved="true">
425
   <proof prover="4"><result status="valid" time="0.02" steps="40"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC main.49" expl="assertion" proved="true">
430
  <proof prover="4"><result status="valid" time="0.04" steps="144"/></proof>
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  </goal>
  <goal name="VC main.50" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC main.51" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC main.52" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC main.53" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC main.54" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC main.55" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
449
   <goal name="VC main.55.0" expl="assertion" proved="true">
450
   <proof prover="4"><result status="valid" time="0.04" steps="109"/></proof>
451
   </goal>
452
   <goal name="VC main.55.1" expl="assertion" proved="true">
453
   <proof prover="4"><result status="valid" time="0.39" steps="248"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC main.56" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
459
   <goal name="VC main.56.0" expl="assertion" proved="true">
460
   <proof prover="4"><result status="valid" time="0.03" steps="114"/></proof>
461
   </goal>
462
   <goal name="VC main.56.1" expl="assertion" proved="true">
463
   <proof prover="4"><result status="valid" time="0.08" steps="125"/></proof>
464
   </goal>
465
   <goal name="VC main.56.2" expl="assertion" proved="true">
466
   <proof prover="4"><result status="valid" time="0.04" steps="49"/></proof>
467
   </goal>
468
   <goal name="VC main.56.3" expl="assertion" proved="true">
469
   <proof prover="4"><result status="valid" time="0.07" steps="50"/></proof>
470
   </goal>
471
   <goal name="VC main.56.4" expl="assertion" proved="true">
472
   <proof prover="4"><result status="valid" time="0.10" steps="197"/></proof>
473
   </goal>
474
   <goal name="VC main.56.5" expl="assertion" proved="true">
475
   <proof prover="4"><result status="valid" time="0.11" steps="205"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC main.57" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
481 482
   <goal name="VC main.57.0" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.01"/></proof>
483
   </goal>
484
   <goal name="VC main.57.1" expl="assertion" proved="true">
485
   <transf name="rewrite" proved="true" arg1="H">
486
    <goal name="VC main.57.1.0" expl="assertion" proved="true">
487
    <transf name="apply" proved="true" arg1="consecutive_last_push">
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488
     <goal name="VC main.57.1.0.0" expl="apply premises" proved="true">
489
     <proof prover="3"><result status="valid" time="0.01"/></proof>
490
     </goal>
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491
     <goal name="VC main.57.1.0.1" expl="apply premises" proved="true">
492
     <proof prover="3"><result status="valid" time="0.03"/></proof>
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     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="VC main.58" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
502
   <goal name="VC main.58.0" expl="assertion" proved="true">
503
   <proof prover="4"><result status="valid" time="0.08" steps="49"/></proof>
504
   </goal>
505
   <goal name="VC main.58.1" expl="assertion" proved="true">
506
   <proof prover="4"><result status="valid" time="0.41" steps="593"/></proof>
507
   </goal>
508
   <goal name="VC main.58.2" expl="assertion" proved="true">
509
   <proof prover="4"><result status="valid" time="0.19" steps="271"/></proof>
510
   </goal>
511
   <goal name="VC main.58.3" expl="assertion" proved="true">
512
   <proof prover="4"><result status="valid" time="0.03" steps="61"/></proof>
513
   </goal>
514
   <goal name="VC main.58.4" expl="assertion" proved="true">
515
   <proof prover="4"><result status="valid" time="0.12" steps="138"/></proof>
516
   </goal>
517
   <goal name="VC main.58.5" expl="assertion" proved="true">
518
   <proof prover="4"><result status="valid" time="0.02" steps="50"/></proof>
519
   </goal>
520
   <goal name="VC main.58.6" expl="assertion" proved="true">
521
   <proof prover="4"><result status="valid" time="0.03" steps="59"/></proof>
522
   </goal>
523
   <goal name="VC main.58.7" expl="assertion" proved="true">
524
   <proof prover="4"><result status="valid" time="0.08" steps="282"/></proof>
525 526 527 528 529
   </goal>
  </transf>
  </goal>
  <goal name="VC main.59" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
530
   <goal name="VC main.59.0" expl="assertion" proved="true">
531
   <proof prover="4"><result status="valid" time="0.12" steps="52"/></proof>
532
   </goal>
533
   <goal name="VC main.59.1" expl="assertion" proved="true">
534
   <proof prover="4"><result status="valid" time="0.03" steps="57"/></proof>
535
   </goal>
536
   <goal name="VC main.59.2" expl="assertion" proved="true">
537
   <proof prover="4"><result status="valid" time="0.08" steps="162"/></proof>
538
   </goal>
539
   <goal name="VC main.59.3" expl="assertion" proved="true">
540
   <proof prover="4"><result status="valid" time="0.03" steps="57"/></proof>
541
   </goal>
542
   <goal name="VC main.59.4" expl="assertion" proved="true">
543
   <proof prover="4"><result status="valid" time="0.04" steps="51"/></proof>
544
   </goal>
545
   <goal name="VC main.59.5" expl="assertion" proved="true">
546 547
   <proof prover="0"><result status="valid" time="0.03"/></proof>
   </goal>
548
   <goal name="VC main.59.6" expl="assertion" proved="true">
549
   <proof prover="4"><result status="valid" time="0.10" steps="336"/></proof>
550
   </goal>
551
   <goal name="VC main.59.7" expl="assertion" proved="true">
552
   <proof prover="4"><result status="valid" time="0.02" steps="51"/></proof>
553 554
   </goal>
   <goal name="VC main.59.8" expl="assertion" proved="true">
555
   <proof prover="0"><result status="valid" time="0.04"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC main.60" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
561 562
   <goal name="VC main.60.0" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.08"/></proof>
563
   </goal>
564
   <goal name="VC main.60.1" expl="assertion" proved="true">
565
   <proof prover="4"><result status="valid" time="0.60" steps="814"/></proof>
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   </goal>
567
   <goal name="VC main.60.2" expl="assertion" proved="true">
568
   <proof prover="4"><result status="valid" time="0.03" steps="64"/></proof>
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   </goal>
570
   <goal name="VC main.60.3" expl="assertion" proved="true">
571
   <proof prover="4"><result status="valid" time="0.04" steps="50"/></proof>
572
   </goal>
573
   <goal name="VC main.60.4" expl="assertion" proved="true">
574
   <proof prover="4"><result status="valid" time="0.03" steps="57"/></proof>
575
   </goal>
576
   <goal name="VC main.60.5" expl="assertion" proved="true">
577
   <proof prover="4"><result status="valid" time="0.04" steps="66"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC main.61" expl="safety" proved="true">
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  <proof prover="4"><result status="valid" time="0.53" steps="744"/></proof>
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  </goal>
  <goal name="VC main.62" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC main.63" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="(b = tick.b1)">
   <goal name="VC main.63.0" expl="true case (loop invariant preservation)" proved="true">
590
   <proof prover="4"><result status="valid" time="0.25" steps="369"/></proof>
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   </goal>
   <goal name="VC main.63.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="replace" proved="true" arg1="owners[b]" arg2="owners1[b]">
    <goal name="VC main.63.1.0" expl="false case (loop invariant preservation)" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="VC main.63.1.0.0" expl="VC for main" proved="true">
     <proof prover="3"><result status="valid" time="0.07"/></proof>
     </goal>
     <goal name="VC main.63.1.0.1" expl="VC for main" proved="true">
     <proof prover="3"><result status="valid" time="0.04"/></proof>
     </goal>
     <goal name="VC main.63.1.0.2" expl="VC for main" proved="true">
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     <proof prover="4"><result status="valid" time="0.24" steps="346"/></proof>
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     </goal>
     <goal name="VC main.63.1.0.3" expl="VC for main" proved="true">
     <transf name="assert" proved="true" arg1="( x1 &lt;&gt; th )">
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607
      <goal name="VC main.63.1.0.3.0" expl="asserted formula" proved="true">
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      <proof prover="3"><result status="valid" time="0.08"/></proof>
      </goal>
      <goal name="VC main.63.1.0.3.1" expl="VC for main" proved="true">
      <transf name="replace" proved="true" arg1="memo[x1]" arg2="memo1[x1]" arg3="in" arg4="H">
       <goal name="VC main.63.1.0.3.1.0" expl="VC for main" proved="true">
       <proof prover="3"><result status="valid" time="0.06"/></proof>
       </goal>
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615
       <goal name="VC main.63.1.0.3.1.1" expl="equality hypothesis" proved="true">
616
       <proof prover="4"><result status="valid" time="0.05" steps="70"/></proof>
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       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
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624
    <goal name="VC main.63.1.1" expl="equality hypothesis" proved="true">
625
    <proof prover="4"><result status="valid" time="0.04" steps="51"/></proof>
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    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="VC main.64" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.30" steps="734"/></proof>
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  </goal>
  <goal name="VC main.65" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.62" steps="1711"/></proof>
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  </goal>
  <goal name="VC main.66" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC main.67" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.18" steps="244"/></proof>
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  </goal>
  <goal name="VC main.68" expl="loop invariant preservation" proved="true">
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  <transf name="split_all_full" proved="true" >
   <goal name="VC main.68.0" expl="VC for main" proved="true">
   <proof prover="4" timelimit="10" memlimit="4000"><result status="valid" time="0.63" steps="363"/></proof>
   </goal>
  </transf>
649 650
  </goal>
  <goal name="VC main.69" expl="loop invariant preservation" proved="true">
651
  <proof prover="4" memlimit="2000"><result status="valid" time="0.88" steps="1246"/></proof>
652 653
  </goal>
  <goal name="VC main.70" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="3.65" steps="1852"/></proof>
655 656 657 658
  </goal>
  <goal name="VC main.71" expl="loop invariant preservation" proved="true">
  <transf name="case" proved="true" arg1="th=th1">
   <goal name="VC main.71.0" expl="true case (loop invariant preservation)" proved="true">
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   <proof prover="2"><result status="valid" time="0.11" steps="320"/></proof>
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   </goal>
   <goal name="VC main.71.1" expl="false case (loop invariant preservation)" proved="true">
   <transf name="replace" proved="true" arg1="memo[th]" arg2="memo1[th]">
    <goal name="VC main.71.1.0" expl="false case (loop invariant preservation)" proved="true">
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    <proof prover="5"><result status="valid" time="0.31"/></proof>
665
    </goal>
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666
    <goal name="VC main.71.1.1" expl="equality hypothesis" proved="true">
667
    <proof prover="2"><result status="valid" time="0.05" steps="107"/></proof>
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    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="VC main.72" expl="loop invariant preservation" proved="true">
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674 675
  <transf name="split_all_full" proved="true" >
   <goal name="VC main.72.0" expl="VC for main" proved="true">
676
   <proof prover="5"><result status="valid" time="0.17"/></proof>
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677 678
   </goal>
   <goal name="VC main.72.1" expl="VC for main" proved="true">
679
   <proof prover="2" timelimit="10" memlimit="4000"><result status="valid" time="8.67" steps="3776"/></proof>
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   </goal>
  </transf>
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  </goal>
  <goal name="VC main.73" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.11" steps="47"/></proof>
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  </goal>
  <goal name="VC main.74" expl="loop invariant preservation" proved="true">
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  <transf name="split_all_full" proved="true" >
   <goal name="VC main.74.0" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.04" steps="59"/></proof>
   </goal>
  </transf>
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  </goal>
  <goal name="VC main.75" expl="loop invariant preservation" proved="true">
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  <transf name="split_vc" proved="true" >
   <goal name="VC main.75.0" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.52" steps="298"/></proof>
   </goal>
   <goal name="VC main.75.1" expl="loop invariant preservation" proved="true">
   <proof prover="4" memlimit="2000"><result status="valid" time="0.30" steps="301"/></proof>
   </goal>
  </transf>
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  </goal>
  <goal name="VC main.76" expl="loop invariant preservation" proved="true">
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  <proof prover="3"><result status="valid" time="0.01"/></proof>
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  </goal>
  <goal name="VC main.77" expl="loop invariant preservation" proved="true">
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  <transf name="split_all_full" proved="true" >
   <goal name="VC main.77.0" expl="VC for main" proved="true">
   <proof prover="4" timelimit="10" memlimit="4000"><result status="valid" time="0.03" steps="57"/></proof>
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   </goal>
  </transf>
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  </goal>
  <goal name="VC main.78" expl="loop invariant preservation" proved="true">
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  <transf name="split_vc" proved="true" >
   <goal name="VC main.78.0" expl="loop invariant preservation" proved="true">
   <transf name="split_all_full" proved="true" >
    <goal name="VC main.78.0.0" expl="loop invariant preservation" proved="true">
    <proof prover="4" timelimit="10" memlimit="4000"><result status="valid" time="0.08" steps="51"/></proof>
    </goal>
   </transf>
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   </goal>
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   <goal name="VC main.78.1" expl="loop invariant preservation" proved="true">
   <proof prover="3"><result status="valid" time="0.03"/></proof>
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   </goal>
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   <goal name="VC main.78.2" expl="loop invariant preservation" proved="true">
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726
   <proof prover="3"><result status="valid" time="0.01"/></proof>
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   </goal>
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   <goal name="VC main.78.3" expl="loop invariant preservation" proved="true">
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729
   <proof prover="3"><result status="valid" time="0.04"/></proof>
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   </goal>
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   <goal name="VC main.78.4" expl="loop invariant preservation" proved="true">
   <transf name="split_all_full" proved="true" >
    <goal name="VC main.78.4.0" expl="loop invariant preservation" proved="true">
    <proof prover="4" timelimit="10" memlimit="4000"><result status="valid" time="0.04" steps="123"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="VC main.78.5" expl="loop invariant preservation" proved="true">
   <transf name="split_all_full" proved="true" >
    <goal name="VC main.78.5.0" expl="loop invariant preservation" proved="true">
    <proof prover="4" timelimit="10" memlimit="4000"><result status="valid" time="0.05" steps="49"/></proof>
    </goal>
   </transf>
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   </goal>
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   <goal name="VC main.78.6" expl="loop invariant preservation" proved="true">
   <proof prover="4"><result status="valid" time="0.06" steps="195"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC main.79" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.13" steps="219"/></proof>
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  </goal>
  <goal name="VC main.80" expl="liveness" proved="true">
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  <transf name="split_all_full" proved="true" >
   <goal name="VC main.80.0" expl="liveness" proved="true">
   <proof prover="4" memlimit="2000"><result status="valid" time="0.03" steps="52"/></proof>
   </goal>
   <goal name="VC main.80.1" expl="liveness" proved="true">
   <proof prover="3"><result status="valid" time="0.01"/></proof>
   </goal>
   <goal name="VC main.80.2" expl="liveness" proved="true">
   <proof prover="4" memlimit="2000"><result status="valid" time="0.12" steps="54"/></proof>
   </goal>
   <goal name="VC main.80.3" expl="liveness" proved="true">
   <proof prover="4" memlimit="2000"><result status="valid" time="0.02" steps="54"/></proof>
   </goal>
  </transf>
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  </goal>
  <goal name="VC main.81" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC main.82" expl="unreachable point" proved="true">
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  <proof prover="4"><result status="valid" time="0.05" steps="110"/></proof>
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  </goal>
  <goal name="VC main.83" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC main.84" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC main.85" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC main.86" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC main.87" expl="assertion" proved="true">
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  <proof prover="4"><result status="valid" time="0.70" steps="731"/></proof>
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  </goal>
  <goal name="VC main.88" expl="fairness" proved="true">
  <transf name="split_vc" proved="true" >
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   <goal name="VC main.88.0" expl="fairness" proved="true">
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   <proof prover="3"><result status="valid" time="0.04"/></proof>
   </goal>
795 796 797 798
   <goal name="VC main.88.1" expl="fairness" proved="true">
   <proof prover="3"><result status="valid" time="0.05"/></proof>
   </goal>
   <goal name="VC main.88.2" expl="fairness" proved="true">
799
   <proof prover="4"><result status="valid" time="0.12" steps="268"/></proof>
800
   </goal>
801
   <goal name="VC main.88.3" expl="fairness" proved="true">
802
   <proof prover="4"><result status="valid" time="0.33" steps="424"/></proof>
803 804 805 806 807
   </goal>
  </transf>
  </goal>
  <goal name="VC main.89" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
808
   <goal name="VC main.89.0" expl="assertion" proved="true">
809
   <proof prover="4"><result status="valid" time="0.48" steps="1060"/></proof>
810
   </goal>
811
   <goal name="VC main.89.1" expl="assertion" proved="true">
812
   <proof prover="4"><result status="valid" time="0.10" steps="41"/></proof>
813
   </goal>
814
   <goal name="VC main.89.2" expl="assertion" proved="true">
815
   <proof prover="4"><result status="valid" time="1.22" steps="803"/></proof>
816
   </goal>
817
   <goal name="VC main.89.3" expl="assertion" proved="true">
818
   <proof prover="4" memlimit="2000"><result status="valid" time="0.07" steps="154"/></proof>
819
   </goal>
820
   <goal name="VC main.89.4" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
821
   <proof prover="3"><result status="valid" time="0.04"/></proof>
822
   </goal>
823
   <goal name="VC main.89.5" expl="assertion" proved="true">
824
   <proof prover="4"><result status="valid" time="0.04" steps="65"/></proof>
825
   </goal>
826 827
   <goal name="VC main.89.6" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.08"/></proof>
828
   </goal>
829
   <goal name="VC main.89.7" expl="assertion" proved="true">
830
   <proof prover="4"><result status="valid" time="0.03" steps="109"/></proof>
831
   </goal>
832
   <goal name="VC main.89.8" expl="assertion" proved="true">
833
   <proof prover="4" memlimit="2000"><result status="valid" time="0.02" steps="46"/></proof>
834 835 836 837 838
   </goal>
  </transf>
  </goal>
  <goal name="VC main.90" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
839
   <goal name="VC main.90.0" expl="assertion" proved="true">
840
   <proof prover="4"><result status="valid" time="0.02" steps="44"/></proof>
841
   </goal>
842
   <goal name="VC main.90.1" expl="assertion" proved="true">
843
   <proof prover="4"><result status="valid" time="0.05" steps="44"/></proof>
844
   </goal>
845
   <goal name="VC main.90.2" expl="assertion" proved="true">
846
   <proof prover="4"><result status="valid" time="0.02" steps="50"/></proof>
847
   </goal>
848
   <goal name="VC main.90.3" expl="assertion" proved="true">
849
   <proof prover="4"><result status="valid" time="0.02" steps="46"/></proof>
850
   </goal>
851
   <goal name="VC main.90.4" expl="assertion" proved="true">
852
   <proof prover="4"><result status="valid" time="0.11" steps="91"/></proof>
853
   </goal>
854
   <goal name="VC main.90.5" expl="assertion" proved="true">
855
   <proof prover="4"><result status="valid" time="0.05" steps="120"/></proof>
856
   </goal>
857
   <goal name="VC main.90.6" expl="assertion" proved="true">
858
   <proof prover="4"><result status="valid" time="0.13" steps="131"/></proof>
859
   </goal>
860
   <goal name="VC main.90.7" expl="assertion" proved="true">
861
   <proof prover="4"><result status="valid" time="0.03" steps="54"/></proof>
862 863 864 865 866
   </goal>
  </transf>
  </goal>
  <goal name="VC main.91" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
867
   <goal name="VC main.91.0" expl="assertion" proved="true">
868
   <proof prover="4"><result status="valid" time="0.23" steps="280"/></proof>
869
   </goal>
870
   <goal name="VC main.91.1" expl="assertion" proved="true">
871
   <proof prover="4"><result status="valid" time="0.02" steps="43"/></proof>
872
   </goal>
873
   <goal name="VC main.91.2" expl="assertion" proved="true">
874
   <proof prover="4"><result status="valid" time="1.69" steps="1514"/></proof>
875
   </goal>
876
   <goal name="VC main.91.3" expl="assertion" proved="true">
877
   <proof prover="4"><result status="valid" time="0.60" steps="634"/></proof>
878
   </goal>
879
   <goal name="VC main.91.4" expl="assertion" proved="true">
880
   <proof prover="4"><result status="valid" time="0.02" steps="48"/></proof>
881
   </goal>
882
   <goal name="VC main.91.5" expl="assertion" proved="true">
883
   <proof prover="4"><result status="valid" time="0.02" steps="47"/></proof>