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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v2//EN" "http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="2">
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 <prover
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  id="0"
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  name="Alt-Ergo"
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  version="0.94"/>
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 <prover
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  id="1"
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  name="CVC3"
  version="2.2"/>
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 <prover
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  id="2"
  name="Coq"
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  version="8.3pl4"/>
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 <prover
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  id="3"
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  name="Z3"
  version="2.19"/>
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  name="../flag.mlw"
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  verified="true"
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  expanded="true">
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  <theory
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   name="Flag"
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   locfile="../flag.mlw"
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   loclnum="3" loccnumb="7" loccnume="11"
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   verified="true"
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   expanded="true">
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   <goal
    name="WP_parameter swap"
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    locfile="../flag.mlw"
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    loclnum="15" loccnumb="6" loccnume="10"
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    expl="VC for swap"
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    sum="f8309806995c23e0411a87500911c5fc"
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    proved="true"
    expanded="false"
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    shape="aexchangeV3V5V1V2Iainfix =V5asetV4V2agetV3V1FAainfix &lt;V2V0Aainfix &lt;=c0V2Iainfix =V4asetV3V1agetV3V2FAainfix &lt;V1V0Aainfix &lt;=c0V1Aainfix &lt;V2V0Aainfix &lt;=c0V2Aainfix &lt;V1V0Aainfix &lt;=c0V1Iainfix &lt;V2V0Aainfix &lt;=c0V2Aainfix &lt;V1V0Aainfix &lt;=c0V1FF">
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    <label
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     name="expl:VC for swap"/>
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    <proof
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     prover="0"
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     timelimit="10"
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     memlimit="0"
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     obsolete="false"
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     archived="false">
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     <result status="valid" time="0.01"/>
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    </proof>
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    <proof
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     prover="3"
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     timelimit="10"
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     memlimit="0"
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     obsolete="false"
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     archived="false">
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     <result status="valid" time="0.02"/>
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    </proof>
   </goal>
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   <goal
    name="WP_parameter dutch_flag"
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    locfile="../flag.mlw"
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    loclnum="24" loccnumb="6" loccnume="16"
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    expl="VC for dutch_flag"
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    sum="5ae146277eb89e5420ff6dd5da54f10f"
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    proved="true"
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    expanded="true"
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    shape="iainfix &lt;V5V4CagetV7V5aBlueainfix &lt;ainfix -V4V12ainfix -V4V5Aainfix &lt;=c0ainfix -V4V5Aapermut_subV2V9c0V1Aainfix =V0V1AamonochromeV10V4V1aRedAamonochromeV10V11V12aWhiteAamonochromeV10c0V11aBlueAainfix &lt;=V4V1Aainfix &lt;=V12V4Aainfix &lt;=V11V12Aainfix &lt;=c0V11Iainfix =V12ainfix +V5c1FIainfix =V11ainfix +V6c1FIaexchangeV7V9V6V5Lamk arrayV0V9FAainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhiteainfix &lt;ainfix -V4V13ainfix -V4V5Aainfix &lt;=c0ainfix -V4V5Aapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V13aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V13V4Aainfix &lt;=V6V13Aainfix &lt;=c0V6Iainfix =V13ainfix +V5c1FaRedainfix &lt;ainfix -V14V5ainfix -V4V5Aainfix &lt;=c0ainfix -V4V5Aapermut_subV2V15c0V1Aainfix =V0V1AamonochromeV16V14V1aRedAamonochromeV16V6V5aWhiteAamonochromeV16c0V6aBlueAainfix &lt;=V14V1Aainfix &lt;=V5V14Aainfix &lt;=V6V5Aainfix &lt;=c0V6IaexchangeV7V15V14V5Lamk arrayV0V15FAainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V14V0Aainfix &lt;=c0V14Iainfix =V14ainfix -V4c1FAainfix &lt;V5V0Aainfix &lt;=c0V5apermutV3V8AamonochromeV8V18V1aRedAamonochromeV8V17V18aWhiteAamonochromeV8c0V17aBlueEEIapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FAapermut_subV2V2c0V1Aainfix =V0V1AamonochromeV3V1V1aRedAamonochromeV3c0c0aWhiteAamonochromeV3c0c0aBlueAainfix &lt;=V1V1Aainfix &lt;=c0V1Aainfix &lt;=c0c0Aainfix &lt;=c0c0Iainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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    <label
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     name="expl:VC for dutch_flag"/>
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    <transf
     name="split_goal"
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     proved="true"
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     expanded="true">
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     <goal
      name="WP_parameter dutch_flag.1"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="1. loop invariant init"
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      sum="d1a657d49930c65578430bfca9eaec6d"
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      proved="true"
      expanded="false"
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      shape="ainfix &lt;=V1V1Aainfix &lt;=c0V1Aainfix &lt;=c0c0Aainfix &lt;=c0c0Iainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
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     </goal>
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     <goal
      name="WP_parameter dutch_flag.2"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="2. loop invariant init"
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      sum="60c49b52aa952f5ad8f2cc8ebaf5e940"
      proved="true"
      expanded="false"
      shape="amonochromeV3c0c0aBlueIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.3"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="3. loop invariant init"
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      sum="600f13fe995c9fa18690f3b5fbdf99b3"
      proved="true"
      expanded="false"
      shape="amonochromeV3c0c0aWhiteIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.4"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="4. loop invariant init"
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      sum="4908a7ca332703dbc3e93ddaf1273068"
      proved="true"
      expanded="false"
      shape="amonochromeV3V1V1aRedIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.5"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="5. loop invariant init"
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      sum="d95ce012ec5eab914d34fb90f8e13d61"
      proved="true"
      expanded="false"
      shape="ainfix =V0V1Iainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.6"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="6. loop invariant init"
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      sum="f7cb15e482c7dad1f8c9732a69bd5481"
      proved="true"
      expanded="false"
      shape="apermut_subV2V2c0V1Iainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.7"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="7. precondition"
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      sum="2c72f24129cde85d10df285ebb28968d"
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      proved="true"
      expanded="false"
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      shape="ainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
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     </goal>
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     <goal
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      name="WP_parameter dutch_flag.8"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="8. precondition"
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      sum="af049d27d376d45225225634d10919c9"
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      proved="true"
      expanded="false"
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      shape="CagetV7V5aBlueainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhitetaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
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       prover="0"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
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      <proof
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       prover="1"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
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      <proof
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       prover="3"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
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     </goal>
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     <goal
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      name="WP_parameter dutch_flag.9"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="9. loop invariant preservation"
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      sum="0657b0f6faddf3df44557be3bf2f7ddb"
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      proved="true"
      expanded="false"
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      shape="CagetV7V5aBlueainfix &lt;=V4V1Aainfix &lt;=V12V4Aainfix &lt;=V11V12Aainfix &lt;=c0V11Iainfix =V12ainfix +V5c1FIainfix =V11ainfix +V6c1FIaexchangeV7V9V6V5Lamk arrayV0V9FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhitetaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
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     </goal>
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     <goal
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      name="WP_parameter dutch_flag.10"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="10. loop invariant preservation"
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      sum="7593fd042a5b211b7e1c236cef12acc7"
      proved="true"
      expanded="true"
      shape="CagetV7V5aBlueamonochromeV10c0V11aBlueIainfix =V12ainfix +V5c1FIainfix =V11ainfix +V6c1FIaexchangeV7V9V6V5Lamk arrayV0V9FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhitetaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       edited="flag_WP_Flag_WP_parameter_dutch_flag_1.v"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.54"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.11"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="11. loop invariant preservation"
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      sum="23f53b92827b703ebe1fc0cd80649695"
      proved="true"
      expanded="true"
      shape="CagetV7V5aBlueamonochromeV10V11V12aWhiteIainfix =V12ainfix +V5c1FIainfix =V11ainfix +V6c1FIaexchangeV7V9V6V5Lamk arrayV0V9FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhitetaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       edited="flag_WP_Flag_WP_parameter_dutch_flag_4.v"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.55"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.12"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="12. loop invariant preservation"
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      sum="cacdebae799771db6234243898930231"
      proved="true"
      expanded="true"
      shape="CagetV7V5aBlueamonochromeV10V4V1aRedIainfix =V12ainfix +V5c1FIainfix =V11ainfix +V6c1FIaexchangeV7V9V6V5Lamk arrayV0V9FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhitetaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.22"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.13"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="13. loop invariant preservation"
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      sum="6a64f49d60b2f2ac1cb24832adc1e30e"
      proved="true"
      expanded="false"
      shape="CagetV7V5aBlueainfix =V0V1Iainfix =V12ainfix +V5c1FIainfix =V11ainfix +V6c1FIaexchangeV7V9V6V5Lamk arrayV0V9FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhitetaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.14"
353
      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="14. loop invariant preservation"
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      sum="033516e53b31886e83df1755549b8cc5"
      proved="true"
      expanded="true"
      shape="CagetV7V5aBlueapermut_subV2V9c0V1Iainfix =V12ainfix +V5c1FIainfix =V11ainfix +V6c1FIaexchangeV7V9V6V5Lamk arrayV0V9FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhitetaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="35"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="29.31"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.15"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="15. loop variant decrease"
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      sum="5bcef5d37280672dee15b4480e144c35"
377 378
      proved="true"
      expanded="false"
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      shape="CagetV7V5aBlueainfix &lt;ainfix -V4V12ainfix -V4V5Aainfix &lt;=c0ainfix -V4V5Iainfix =V12ainfix +V5c1FIainfix =V11ainfix +V6c1FIaexchangeV7V9V6V5Lamk arrayV0V9FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V6V0Aainfix &lt;=c0V6aWhitetaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
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       prover="0"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
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     <goal
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      name="WP_parameter dutch_flag.16"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="16. loop invariant preservation"
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      sum="1544b6e827d29a6854e6b758a707acda"
397 398
      proved="true"
      expanded="false"
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      shape="CagetV7V5aBluetaWhiteainfix &lt;=V4V1Aainfix &lt;=V9V4Aainfix &lt;=V6V9Aainfix &lt;=c0V6Iainfix =V9ainfix +V5c1FaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
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     </goal>
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     <goal
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      name="WP_parameter dutch_flag.17"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="17. loop invariant preservation"
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      sum="61256c450d2873918ed358799e055d14"
      proved="true"
      expanded="false"
      shape="CagetV7V5aBluetaWhiteamonochromeV8c0V6aBlueIainfix =V9ainfix +V5c1FaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.18"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="18. loop invariant preservation"
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      sum="c847fa95bb7b834d85fcec004cf5eed6"
      proved="true"
      expanded="false"
      shape="CagetV7V5aBluetaWhiteamonochromeV8V6V9aWhiteIainfix =V9ainfix +V5c1FaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.19"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="19. loop invariant preservation"
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      sum="60d5b7aae43debe55ebdb37c4eb22db9"
      proved="true"
      expanded="false"
      shape="CagetV7V5aBluetaWhiteamonochromeV8V4V1aRedIainfix =V9ainfix +V5c1FaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.20"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="20. loop invariant preservation"
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      sum="174213324b547d6f318516a0c799b42b"
      proved="true"
      expanded="false"
      shape="CagetV7V5aBluetaWhiteainfix =V0V1Iainfix =V9ainfix +V5c1FaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.21"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="21. loop invariant preservation"
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      sum="21066d148a0d31374c0bb247f59bf538"
      proved="true"
      expanded="false"
      shape="CagetV7V5aBluetaWhiteapermut_subV2V7c0V1Iainfix =V9ainfix +V5c1FaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.22"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="22. loop variant decrease"
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      sum="77b0dd8e82b2aa50827e64fae6bac7dd"
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      proved="true"
      expanded="false"
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      shape="CagetV7V5aBluetaWhiteainfix &lt;ainfix -V4V9ainfix -V4V5Aainfix &lt;=c0ainfix -V4V5Iainfix =V9ainfix +V5c1FaRedtIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
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     </goal>
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     <goal
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      name="WP_parameter dutch_flag.23"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="23. precondition"
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      sum="a88eb7559ec50873874e71857f06d919"
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      proved="true"
      expanded="false"
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      shape="CagetV7V5aBluetaWhitetaRedainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V9V0Aainfix &lt;=c0V9Iainfix =V9ainfix -V4c1FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
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       prover="0"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.00"/>
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      </proof>
     </goal>
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     <goal
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      name="WP_parameter dutch_flag.24"
553
      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="24. loop invariant preservation"
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      sum="7f191d496b9bf579e736b0ee668fd3fe"
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      proved="true"
      expanded="false"
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      shape="CagetV7V5aBluetaWhitetaRedainfix &lt;=V9V1Aainfix &lt;=V5V9Aainfix &lt;=V6V5Aainfix &lt;=c0V6IaexchangeV7V10V9V5Lamk arrayV0V10FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V9V0Aainfix &lt;=c0V9Iainfix =V9ainfix -V4c1FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
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     </goal>
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     <goal
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      name="WP_parameter dutch_flag.25"
573
      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="25. loop invariant preservation"
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      sum="c6e2b98ed3259712610485a9ed5c5b1a"
      proved="true"
      expanded="true"
      shape="CagetV7V5aBluetaWhitetaRedamonochromeV11c0V6aBlueIaexchangeV7V10V9V5Lamk arrayV0V10FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V9V0Aainfix &lt;=c0V9Iainfix =V9ainfix -V4c1FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.24"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.26"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="26. loop invariant preservation"
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      sum="873b89028a331695f76353e5e5a1fa39"
      proved="true"
      expanded="true"
      shape="CagetV7V5aBluetaWhitetaRedamonochromeV11V6V5aWhiteIaexchangeV7V10V9V5Lamk arrayV0V10FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V9V0Aainfix &lt;=c0V9Iainfix =V9ainfix -V4c1FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.53"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.27"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="27. loop invariant preservation"
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      sum="8b4dabe7942ce4ed0e164d15bc002e39"
      proved="true"
      expanded="true"
      shape="CagetV7V5aBluetaWhitetaRedamonochromeV11V9V1aRedIaexchangeV7V10V9V5Lamk arrayV0V10FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V9V0Aainfix &lt;=c0V9Iainfix =V9ainfix -V4c1FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="1.41"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.28"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="28. loop invariant preservation"
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      sum="0af70edc9ee11fa99a88ca3aac26ee1c"
      proved="true"
      expanded="false"
      shape="CagetV7V5aBluetaWhitetaRedainfix =V0V1IaexchangeV7V10V9V5Lamk arrayV0V10FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V9V0Aainfix &lt;=c0V9Iainfix =V9ainfix -V4c1FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.29"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="29. loop invariant preservation"
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      sum="99bef21228fe186dc80e6b5f1c93b971"
      proved="true"
      expanded="true"
      shape="CagetV7V5aBluetaWhitetaRedapermut_subV2V10c0V1IaexchangeV7V10V9V5Lamk arrayV0V10FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V9V0Aainfix &lt;=c0V9Iainfix =V9ainfix -V4c1FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="35"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="27.59"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.30"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="30. loop variant decrease"
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      sum="e969d35ed6cc51271379485651208795"
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      proved="true"
      expanded="false"
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      shape="CagetV7V5aBluetaWhitetaRedainfix &lt;ainfix -V9V5ainfix -V4V5Aainfix &lt;=c0ainfix -V4V5IaexchangeV7V10V9V5Lamk arrayV0V10FIainfix &lt;V5V0Aainfix &lt;=c0V5Aainfix &lt;V9V0Aainfix &lt;=c0V9Iainfix =V9ainfix -V4c1FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix &lt;V5V4Iapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
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     </goal>
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     <goal
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      name="WP_parameter dutch_flag.31"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="31. postcondition"
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      sum="66bc19d0ba588dd2ff0e5413b36093cb"
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      proved="true"
      expanded="false"
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      shape="amonochromeV8V10V1aRedAamonochromeV8V9V10aWhiteAamonochromeV8c0V9aBlueEEIainfix &lt;V5V4NIapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
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      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter dutch_flag.32"
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      locfile="../flag.mlw"
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      loclnum="24" loccnumb="6" loccnume="16"
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      expl="32. postcondition"
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      sum="e982feef64a35c17c4161814cc92a90e"
      proved="true"
      expanded="false"
      shape="apermutV3V8Iainfix &lt;V5V4NIapermut_subV2V7c0V1Aainfix =V0V1AamonochromeV8V4V1aRedAamonochromeV8V6V5aWhiteAamonochromeV8c0V6aBlueAainfix &lt;=V4V1Aainfix &lt;=V5V4Aainfix &lt;=V6V5Aainfix &lt;=c0V6Lamk arrayV0V7FIainfix =V0V1Aainfix &lt;=c0V1Lamk arrayV0V2FF">
      <label
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       name="expl:VC for dutch_flag"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
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     </goal>
    </transf>
   </goal>
  </theory>
 </file>
</why3session>