why3session.xml 75.3 KB
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v2//EN" "http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
 <prover
  id="0"
  name="Alt-Ergo"
  version="0.95.2"/>
 <prover
  id="1"
  name="CVC3"
  version="2.4.1"/>
 <prover
  id="2"
  name="CVC4"
  version="1.3"/>
 <prover
  id="3"
  name="Eprover"
19
  version="1.6"/>
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 <prover
  id="4"
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  name="Eprover"
  version="1.8-001"/>
 <prover
  id="5"
  name="Vampire"
  version="0.6"/>
 <prover
  id="6"
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  name="Z3"
  version="4.3.1"/>
 <file
  name="../euler003.mlw"
  verified="true"
  expanded="true">
  <theory
   name="PrimeFactor"
   locfile="../euler003.mlw"
   loclnum="10" loccnumb="7" loccnume="18"
   verified="true"
   expanded="true">
   <goal
    name="WP_parameter smallest_divisor"
    locfile="../euler003.mlw"
    loclnum="19" loccnumb="8" loccnume="24"
    expl="VC for smallest_divisor"
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    sum="5148e7a4e729dac62919ff35357f7209"
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    proved="true"
    expanded="false"
    shape="iiNadividesV4V1Iainfix &lt;V4V3Aainfix &lt;=c2V4FAadividesV3V1Aainfix &lt;=V3V1Aainfix &lt;=V0V3INadividesV5V1Iainfix &lt;V5V3Aainfix &lt;=c2V5FAadividesV3V1Aainfix &lt;=V3V1Aainfix &lt;=V2V3FANadividesV6V1Iainfix &lt;V6V2Aainfix &lt;=c2V6FAainfix &lt;=V2V1Aainfix &lt;=c2V2Aainfix &lt;=c2V1Aainfix &lt;ainfix -V1V2ainfix -V1V0Aainfix &lt;=c0ainfix -V1V0Lainfix +V0c1NadividesV7V1Iainfix &lt;V7V0Aainfix &lt;=c2V7FAadividesV0V1Aainfix &lt;=V0V1Aainfix &lt;=V0V0ainfix =amodV1V0c0Aainfix &gt;=V0c2NadividesV8V1Iainfix &lt;V8V1Aainfix &lt;=c2V8FAadividesV1V1Aainfix &lt;=V1V1Aainfix &lt;=V0V1AfAainfix &lt;V10V1Aainfix &gt;=V10c2AfAainfix &gt;=ainfix *V0V9ainfix *V0V0Aainfix &gt;=V1ainfix *V0V9Iainfix &gt;=V10V0Aainfix =ainfix *V10V9V1AadividesV10V1Aainfix =ainfix *V10V9V1LadivV1V9Aainfix &gt;=V9V0IadividesV9V1Aainfix &lt;V9V1Aainfix &lt;=c2V9Fainfix &gt;ainfix *V0V0V1INadividesV11V1Iainfix &lt;V11V0Aainfix &lt;=c2V11FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
    <label
     name="expl:VC for smallest_divisor"/>
    <transf
     name="split_goal_wp"
     proved="true"
     expanded="false">
     <goal
      name="WP_parameter smallest_divisor.1"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="1. assertion"
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      sum="2bba7a26f99f92d3c4ea1dc601f609c1"
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      proved="true"
      expanded="false"
      shape="assertionfAainfix &lt;V3V1Aainfix &gt;=V3c2AfAainfix &gt;=ainfix *V0V2ainfix *V0V0Aainfix &gt;=V1ainfix *V0V2Iainfix &gt;=V3V0Aainfix =ainfix *V3V2V1AadividesV3V1Aainfix =ainfix *V3V2V1LadivV1V2Aainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <transf
       name="split_goal_wp"
       proved="true"
       expanded="false">
       <goal
        name="WP_parameter smallest_divisor.1.1"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="1. assertion"
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        sum="32824234b61f6f792ecbe86bcad17b68"
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        proved="true"
        expanded="false"
        shape="assertionainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV3V1Iainfix &lt;V3V0Aainfix &lt;=c2V3FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.2"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="2. assertion"
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        sum="824f47baa04cd3df43d9dcb51e99b3f6"
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        proved="true"
        expanded="false"
        shape="assertionainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.83"/>
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        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.3"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="3. assertion"
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        sum="5b7e581efce61165047735554f082451"
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        proved="true"
        expanded="false"
        shape="assertionadividesV3V1Iainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.4"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="4. assertion"
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        sum="5b47d7fcdac9483cf68d30335f421854"
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        proved="true"
        expanded="false"
        shape="assertionainfix =ainfix *V3V2V1IadividesV3V1Iainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.5"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="5. assertion"
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        sum="c70ecfb1ad31eed9528c50eefe156458"
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        proved="true"
        expanded="false"
        shape="assertionainfix &gt;=V1ainfix *V0V2Iainfix &gt;=V3V0Iainfix =ainfix *V3V2V1IadividesV3V1Iainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.04"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.6"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="6. assertion"
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        sum="9bf0bb7ab3f5f9467773de31ba944760"
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        proved="true"
        expanded="false"
        shape="assertionainfix &gt;=ainfix *V0V2ainfix *V0V0Iainfix &gt;=V3V0Iainfix =ainfix *V3V2V1IadividesV3V1Iainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
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         prover="6"
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         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.7"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="7. assertion"
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        sum="c7af7194a701d4309049824d3e1466dc"
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        proved="true"
        expanded="false"
        shape="assertionfIainfix &gt;=ainfix *V0V2ainfix *V0V0Aainfix &gt;=V1ainfix *V0V2Iainfix &gt;=V3V0Iainfix =ainfix *V3V2V1IadividesV3V1Iainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.8"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="8. assertion"
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        sum="15327381f18f815e96be50b120184254"
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        proved="true"
        expanded="false"
        shape="assertionainfix &gt;=V3c2IfAainfix &gt;=ainfix *V0V2ainfix *V0V0Aainfix &gt;=V1ainfix *V0V2Iainfix &gt;=V3V0Iainfix =ainfix *V3V2V1IadividesV3V1Iainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
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         prover="6"
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         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.9"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="9. assertion"
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        sum="3c395117a2f0534579537ffc48bded06"
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        proved="true"
        expanded="false"
        shape="assertionainfix &lt;V3V1Iainfix &gt;=V3c2IfAainfix &gt;=ainfix *V0V2ainfix *V0V0Aainfix &gt;=V1ainfix *V0V2Iainfix &gt;=V3V0Iainfix =ainfix *V3V2V1IadividesV3V1Iainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter smallest_divisor.1.10"
        locfile="../euler003.mlw"
        loclnum="19" loccnumb="8" loccnume="24"
        expl="10. assertion"
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        sum="985f2f140b6761460b28a6591be4b19c"
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        proved="true"
        expanded="false"
        shape="assertionfIainfix &lt;V3V1Iainfix &gt;=V3c2IfAainfix &gt;=ainfix *V0V2ainfix *V0V0Aainfix &gt;=V1ainfix *V0V2Iainfix &gt;=V3V0Iainfix =ainfix *V3V2V1IadividesV3V1Iainfix =ainfix *V3V2V1LadivV1V2Iainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
        <label
         name="expl:VC for smallest_divisor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.14"/>
        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.2"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="2. postcondition"
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      sum="072ce4e1079be7e064f9622f1293893f"
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      proved="true"
      expanded="false"
      shape="postconditionainfix &lt;=V1V1Aainfix &lt;=V0V1IfAainfix &lt;V3V1Aainfix &gt;=V3c2AfAainfix &gt;=ainfix *V0V2ainfix *V0V0Aainfix &gt;=V1ainfix *V0V2Iainfix &gt;=V3V0Aainfix =ainfix *V3V2V1AadividesV3V1Aainfix =ainfix *V3V2V1LadivV1V2Aainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.3"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="3. postcondition"
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      sum="c9b36f9ed2930619d137902fb18cb28c"
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      proved="true"
      expanded="false"
      shape="postconditionadividesV1V1IfAainfix &lt;V3V1Aainfix &gt;=V3c2AfAainfix &gt;=ainfix *V0V2ainfix *V0V0Aainfix &gt;=V1ainfix *V0V2Iainfix &gt;=V3V0Aainfix =ainfix *V3V2V1AadividesV3V1Aainfix =ainfix *V3V2V1LadivV1V2Aainfix &gt;=V2V0IadividesV2V1Aainfix &lt;V2V1Aainfix &lt;=c2V2FIainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.4"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="4. postcondition"
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      sum="f8f1bc3d2b3ec3c9ea3d3c43855ba896"
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      proved="true"
      expanded="false"
      shape="postconditionNadividesV2V1Iainfix &lt;V2V1Aainfix &lt;=c2V2FIfAainfix &lt;V4V1Aainfix &gt;=V4c2AfAainfix &gt;=ainfix *V0V3ainfix *V0V0Aainfix &gt;=V1ainfix *V0V3Iainfix &gt;=V4V0Aainfix =ainfix *V4V3V1AadividesV4V1Aainfix =ainfix *V4V3V1LadivV1V3Aainfix &gt;=V3V0IadividesV3V1Aainfix &lt;V3V1Aainfix &lt;=c2V3FIainfix &gt;ainfix *V0V0V1INadividesV5V1Iainfix &lt;V5V0Aainfix &lt;=c2V5FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.04"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.5"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="5. postcondition"
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      sum="0508f6c6aa14b4debc4e3b17955a5157"
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      proved="true"
      expanded="false"
      shape="postconditionainfix &lt;=V0V1Aainfix &lt;=V0V0Iainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV2V1Iainfix &lt;V2V0Aainfix &lt;=c2V2FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.6"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="6. postcondition"
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      sum="eb7beeda174cb0da13205390013b5614"
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      proved="true"
      expanded="false"
      shape="postconditionadividesV0V1Iainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV2V1Iainfix &lt;V2V0Aainfix &lt;=c2V2FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.7"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="7. postcondition"
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      sum="38a56fc12089a9862ea11d4a5aec077b"
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      proved="true"
      expanded="false"
      shape="postconditionNadividesV2V1Iainfix &lt;V2V0Aainfix &lt;=c2V2FIainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV3V1Iainfix &lt;V3V0Aainfix &lt;=c2V3FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.8"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="8. variant decrease"
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      sum="a34c36c9029a63eadc23b82fc9b92d44"
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      proved="true"
      expanded="false"
      shape="variant decreaseainfix &lt;ainfix -V1V2ainfix -V1V0Aainfix &lt;=c0ainfix -V1V0Lainfix +V0c1INainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV3V1Iainfix &lt;V3V0Aainfix &lt;=c2V3FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.9"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="9. precondition"
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      sum="33a7c63e98ce9dcd4b93f7aa808f8c23"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &lt;=c2V1Lainfix +V0c1INainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV3V1Iainfix &lt;V3V0Aainfix &lt;=c2V3FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.10"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="10. precondition"
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      sum="1ebcc1569c43a20bbc7807afd1d1c652"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &lt;=V2V1Aainfix &lt;=c2V2Lainfix +V0c1INainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV3V1Iainfix &lt;V3V0Aainfix &lt;=c2V3FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.24"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.11"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="11. precondition"
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      sum="941270a17df0ff50bf4e8e180ca13afd"
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      proved="true"
      expanded="false"
      shape="preconditionNadividesV3V1Iainfix &lt;V3V2Aainfix &lt;=c2V3FLainfix +V0c1INainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV4V1Iainfix &lt;V4V0Aainfix &lt;=c2V4FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.10"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.12"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="12. postcondition"
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      sum="b40e4752e90d7dcd4994487fa3610bf5"
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      proved="true"
      expanded="false"
      shape="postconditionainfix &lt;=V3V1Aainfix &lt;=V0V3INadividesV4V1Iainfix &lt;V4V3Aainfix &lt;=c2V4FAadividesV3V1Aainfix &lt;=V3V1Aainfix &lt;=V2V3FINadividesV5V1Iainfix &lt;V5V2Aainfix &lt;=c2V5FAainfix &lt;=V2V1Aainfix &lt;=c2V2Aainfix &lt;=c2V1Lainfix +V0c1INainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV6V1Iainfix &lt;V6V0Aainfix &lt;=c2V6FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.13"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="13. postcondition"
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      sum="b1cbb110b9806fab6ac5b82294c0c0d2"
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      proved="true"
      expanded="false"
      shape="postconditionadividesV3V1INadividesV4V1Iainfix &lt;V4V3Aainfix &lt;=c2V4FAadividesV3V1Aainfix &lt;=V3V1Aainfix &lt;=V2V3FINadividesV5V1Iainfix &lt;V5V2Aainfix &lt;=c2V5FAainfix &lt;=V2V1Aainfix &lt;=c2V2Aainfix &lt;=c2V1Lainfix +V0c1INainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV6V1Iainfix &lt;V6V0Aainfix &lt;=c2V6FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter smallest_divisor.14"
      locfile="../euler003.mlw"
      loclnum="19" loccnumb="8" loccnume="24"
      expl="14. postcondition"
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      sum="6e6d618d760df9e27364dd483b70c2f3"
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      proved="true"
      expanded="false"
      shape="postconditionNadividesV4V1Iainfix &lt;V4V3Aainfix &lt;=c2V4FINadividesV5V1Iainfix &lt;V5V3Aainfix &lt;=c2V5FAadividesV3V1Aainfix &lt;=V3V1Aainfix &lt;=V2V3FINadividesV6V1Iainfix &lt;V6V2Aainfix &lt;=c2V6FAainfix &lt;=V2V1Aainfix &lt;=c2V2Aainfix &lt;=c2V1Lainfix +V0c1INainfix =amodV1V0c0Aainfix &gt;=V0c2INainfix &gt;ainfix *V0V0V1INadividesV7V1Iainfix &lt;V7V0Aainfix &lt;=c2V7FAainfix &lt;=V0V1Aainfix &lt;=c2V0Aainfix &lt;=c2V1F">
      <label
       name="expl:VC for smallest_divisor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
    </transf>
   </goal>
   <goal
    name="WP_parameter largest_prime_factor"
    locfile="../euler003.mlw"
    loclnum="55" loccnumb="4" loccnume="24"
    expl="VC for largest_prime_factor"
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    sum="82f51dcf7c5c5cb1cf49fce71e24a4f3"
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    proved="true"
    expanded="false"
    shape="iNadividesV6V0AaprimeV6Iainfix &lt;=V6V0Aainfix &lt;V4V6FAadividesV4V0AaprimeV4ainfix &lt;V10V3Aainfix &lt;=c0V3AadividesV11V10Iainfix &gt;V11V8AadividesV11V0AaprimeV11FAadividesV12V0Aainfix &gt;=V12V8Iainfix &gt;=V12c2AadividesV12V10FAaprimeV8AadividesV8V0Aainfix &lt;=V8V0Aainfix &lt;=c2V8Aainfix &lt;=V10V0Aainfix &lt;=c1V10AadividesV13V10AacoprimeV7V13Aainfix &lt;V7V13Aainfix &lt;=c1V7AadividesV13V3Aainfix &gt;V13V4Iainfix &gt;V13V7AadividesV13V0AaprimeV13FAadividesV10V3Aainfix =ainfix *V10V7V3Iainfix =V10adivV3V7FIainfix =V9aConsV7V5FIainfix =V8V7FAaprimeV7INadividesV14V3Iainfix &lt;V14V7Aainfix &lt;=c2V14FAadividesV7V3Aainfix &lt;=V7V3Aainfix &lt;=V4V7FANadividesV15V3Iainfix &lt;V15V4Aainfix &lt;=c2V15FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Aainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3ainfix &gt;=V3c2IadividesV16V3Iainfix &gt;V16V4AadividesV16V0AaprimeV16FAadividesV17V0Aainfix &gt;=V17V4Iainfix &gt;=V17c2AadividesV17V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FAadividesV18adivV0V1Iainfix &gt;V18V1AadividesV18V0AaprimeV18FAadividesV19V0Aainfix &gt;=V19V1Iainfix &gt;=V19c2AadividesV19adivV0V1FAaprimeV1AadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1Aainfix &lt;=adivV0V1V0Aainfix &lt;=c1adivV0V1AadividesV20adivV0V1AacoprimeV1V20Iainfix &gt;V20V1AadividesV20V0AaprimeV20FAadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV21V0Iainfix &lt;V21V1Aainfix &lt;=c2V21FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FANadividesV22V0Iainfix &lt;V22c2Aainfix &lt;=c2V22FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
    <label
     name="expl:VC for largest_prime_factor"/>
    <transf
     name="split_goal_wp"
     proved="true"
     expanded="false">
     <goal
      name="WP_parameter largest_prime_factor.1"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="1. precondition"
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      sum="2184826c7f3607d95bb7562d42140d6f"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.2"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="2. precondition"
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      sum="15c1756fc611a6d7cc1eeb2c8f58f8e5"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &lt;=c2V0Aainfix &lt;=c2c2Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.3"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="3. precondition"
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      sum="a171a830f8892bd14bc7f8545888333d"
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      proved="true"
      expanded="false"
      shape="preconditionNadividesV1V0Iainfix &lt;V1c2Aainfix &lt;=c2V1FIainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.4"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="4. assertion"
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      sum="926db07d453cb0d3b6ec06ed7cb90533"
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      proved="true"
      expanded="false"
      shape="assertionadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV3V0Iainfix &lt;V3V1Aainfix &lt;=c2V3FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV4V0Iainfix &lt;V4c2Aainfix &lt;=c2V4FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <transf
       name="split_goal_wp"
       proved="true"
       expanded="false">
       <goal
        name="WP_parameter largest_prime_factor.4.1"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="1."
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        sum="c62addf15c2413f67ced057de113c5be"
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        proved="true"
        expanded="false"
        shape="ainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV3V0Iainfix &lt;V3V1Aainfix &lt;=c2V3FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV4V0Iainfix &lt;V4c2Aainfix &lt;=c2V4FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
643
         <result status="valid" time="0.85"/>
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        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.4.2"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="2."
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        sum="7e599979b410f30b3c85ae3cc56806db"
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        proved="true"
        expanded="false"
        shape="adividesadivV0V1V0Iainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV3V0Iainfix &lt;V3V1Aainfix &lt;=c2V3FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV4V0Iainfix &lt;V4c2Aainfix &lt;=c2V4FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.5"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="5. assertion"
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      sum="7512eb38350192b99784fa6cb4d42bd5"
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      proved="true"
      expanded="false"
      shape="assertionadividesV3adivV0V1AacoprimeV1V3Iainfix &gt;V3V1AadividesV3V0AaprimeV3FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV4V0Iainfix &lt;V4V1Aainfix &lt;=c2V4FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV5V0Iainfix &lt;V5c2Aainfix &lt;=c2V5FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="1.03"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.6"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="6. loop invariant init"
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      sum="20611831a17cb08e735c40b97f58d176"
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      proved="true"
      expanded="false"
      shape="loop invariant initainfix &lt;=adivV0V1V0Aainfix &lt;=c1adivV0V1IadividesV3adivV0V1AacoprimeV1V3Iainfix &gt;V3V1AadividesV3V0AaprimeV3FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV4V0Iainfix &lt;V4V1Aainfix &lt;=c2V4FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV5V0Iainfix &lt;V5c2Aainfix &lt;=c2V5FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
705
       <result status="valid" time="0.14"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.7"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="7. loop invariant init"
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      sum="35a6cc38a7b41bded0ca32c330868bb4"
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      proved="true"
      expanded="false"
      shape="loop invariant initainfix &lt;=V1V0Aainfix &lt;=c2V1IadividesV3adivV0V1AacoprimeV1V3Iainfix &gt;V3V1AadividesV3V0AaprimeV3FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV4V0Iainfix &lt;V4V1Aainfix &lt;=c2V4FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV5V0Iainfix &lt;V5c2Aainfix &lt;=c2V5FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.8"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="8. loop invariant init"
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      sum="c1d4a6d117eaa6333a354b15c8aae0fc"
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      proved="true"
      expanded="false"
      shape="loop invariant initadividesV1V0IadividesV3adivV0V1AacoprimeV1V3Iainfix &gt;V3V1AadividesV3V0AaprimeV3FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV4V0Iainfix &lt;V4V1Aainfix &lt;=c2V4FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV5V0Iainfix &lt;V5c2Aainfix &lt;=c2V5FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.9"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="9. loop invariant init"
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      sum="6303afbabc03135f1021dadba130bf7e"
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      proved="true"
      expanded="false"
      shape="loop invariant initaprimeV1IadividesV3adivV0V1AacoprimeV1V3Iainfix &gt;V3V1AadividesV3V0AaprimeV3FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV4V0Iainfix &lt;V4V1Aainfix &lt;=c2V4FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV5V0Iainfix &lt;V5c2Aainfix &lt;=c2V5FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.58"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.10"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="10. loop invariant init"
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      sum="e59ab4c97bb3f2e19e3107c35695b395"
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      proved="true"
      expanded="false"
      shape="loop invariant initadividesV3V0Aainfix &gt;=V3V1Iainfix &gt;=V3c2AadividesV3adivV0V1FIadividesV4adivV0V1AacoprimeV1V4Iainfix &gt;V4V1AadividesV4V0AaprimeV4FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV5V0Iainfix &lt;V5V1Aainfix &lt;=c2V5FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV6V0Iainfix &lt;V6c2Aainfix &lt;=c2V6FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.13"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.11"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="11. loop invariant init"
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      sum="5855c54ed35d9657778f3cdd15338b75"
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      proved="true"
      expanded="false"
      shape="loop invariant initadividesV3adivV0V1Iainfix &gt;V3V1AadividesV3V0AaprimeV3FIadividesV4adivV0V1AacoprimeV1V4Iainfix &gt;V4V1AadividesV4V0AaprimeV4FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV5V0Iainfix &lt;V5V1Aainfix &lt;=c2V5FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV6V0Iainfix &lt;V6c2Aainfix &lt;=c2V6FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.10"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.12"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="12. assertion"
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      sum="fc5d0a3abed8d14a15aca3e9e174f922"
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      proved="true"
      expanded="false"
      shape="assertionainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV6V3Iainfix &gt;V6V4AadividesV6V0AaprimeV6FAadividesV7V0Aainfix &gt;=V7V4Iainfix &gt;=V7c2AadividesV7V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV8adivV0V1AacoprimeV1V8Iainfix &gt;V8V1AadividesV8V0AaprimeV8FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV9V0Iainfix &lt;V9V1Aainfix &lt;=c2V9FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV10V0Iainfix &lt;V10c2Aainfix &lt;=c2V10FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <transf
       name="split_goal_wp"
       proved="true"
       expanded="false">
       <goal
        name="WP_parameter largest_prime_factor.12.1"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="1."
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        sum="341fc55dda37c16291149404e27e2268"
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        proved="true"
        expanded="false"
        shape="adividesV3V3Iainfix &gt;=V3c2IadividesV6V3Iainfix &gt;V6V4AadividesV6V0AaprimeV6FAadividesV7V0Aainfix &gt;=V7V4Iainfix &gt;=V7c2AadividesV7V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV8adivV0V1AacoprimeV1V8Iainfix &gt;V8V1AadividesV8V0AaprimeV8FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV9V0Iainfix &lt;V9V1Aainfix &lt;=c2V9FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV10V0Iainfix &lt;V10c2Aainfix &lt;=c2V10FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.12.2"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="2."
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        sum="443f3bfc28ccbf4125ab6ec6161338dc"
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        proved="true"
        expanded="false"
        shape="ainfix &gt;=V3c2IadividesV3V3Iainfix &gt;=V3c2IadividesV6V3Iainfix &gt;V6V4AadividesV6V0AaprimeV6FAadividesV7V0Aainfix &gt;=V7V4Iainfix &gt;=V7c2AadividesV7V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV8adivV0V1AacoprimeV1V8Iainfix &gt;V8V1AadividesV8V0AaprimeV8FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV9V0Iainfix &lt;V9V1Aainfix &lt;=c2V9FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV10V0Iainfix &lt;V10c2Aainfix &lt;=c2V10FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.12.3"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="3."
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        sum="0bdd93529eb2f83a1339c024c300d5cb"
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        proved="true"
        expanded="false"
        shape="ainfix &gt;=V3V4Iainfix &gt;=V3c2IadividesV3V3Iainfix &gt;=V3c2IadividesV6V3Iainfix &gt;V6V4AadividesV6V0AaprimeV6FAadividesV7V0Aainfix &gt;=V7V4Iainfix &gt;=V7c2AadividesV7V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV8adivV0V1AacoprimeV1V8Iainfix &gt;V8V1AadividesV8V0AaprimeV8FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV9V0Iainfix &lt;V9V1Aainfix &lt;=c2V9FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV10V0Iainfix &lt;V10c2Aainfix &lt;=c2V10FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="2"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.04"/>
        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.13"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="13. precondition"
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      sum="7aa295f86d8f09d3837ae5926f9154f8"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV6V3Iainfix &gt;V6V4AadividesV6V0AaprimeV6FAadividesV7V0Aainfix &gt;=V7V4Iainfix &gt;=V7c2AadividesV7V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV8adivV0V1AacoprimeV1V8Iainfix &gt;V8V1AadividesV8V0AaprimeV8FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV9V0Iainfix &lt;V9V1Aainfix &lt;=c2V9FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV10V0Iainfix &lt;V10c2Aainfix &lt;=c2V10FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.14"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="14. precondition"
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      sum="bc1dac1b80f66c7311bd1733957589e7"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &lt;=V4V3Aainfix &lt;=c2V4Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV6V3Iainfix &gt;V6V4AadividesV6V0AaprimeV6FAadividesV7V0Aainfix &gt;=V7V4Iainfix &gt;=V7c2AadividesV7V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV8adivV0V1AacoprimeV1V8Iainfix &gt;V8V1AadividesV8V0AaprimeV8FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV9V0Iainfix &lt;V9V1Aainfix &lt;=c2V9FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV10V0Iainfix &lt;V10c2Aainfix &lt;=c2V10FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.15"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="15. precondition"
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      sum="cea6c5f40c7cbdeedf5ae6e1e8eaa172"
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      proved="true"
      expanded="false"
      shape="preconditionNadividesV6V3Iainfix &lt;V6V4Aainfix &lt;=c2V6FIainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV7V3Iainfix &gt;V7V4AadividesV7V0AaprimeV7FAadividesV8V0Aainfix &gt;=V8V4Iainfix &gt;=V8c2AadividesV8V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV9adivV0V1AacoprimeV1V9Iainfix &gt;V9V1AadividesV9V0AaprimeV9FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV10V0Iainfix &lt;V10V1Aainfix &lt;=c2V10FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV11V0Iainfix &lt;V11c2Aainfix &lt;=c2V11FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.10"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.16"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="16. assertion"
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      sum="870fd789c9f4fe3049ed7b246b2cbe74"
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      proved="true"
      expanded="false"
      shape="assertionaprimeV6INadividesV7V3Iainfix &lt;V7V6Aainfix &lt;=c2V7FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV8V3Iainfix &lt;V8V4Aainfix &lt;=c2V8FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV9V3Iainfix &gt;V9V4AadividesV9V0AaprimeV9FAadividesV10V0Aainfix &gt;=V10V4Iainfix &gt;=V10c2AadividesV10V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV11adivV0V1AacoprimeV1V11Iainfix &gt;V11V1AadividesV11V0AaprimeV11FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV12V0Iainfix &lt;V12V1Aainfix &lt;=c2V12FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV13V0Iainfix &lt;V13c2Aainfix &lt;=c2V13FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="2.83"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.17"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="17. assertion"
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      sum="bca106f688e018fdc712421509bd4190"
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      proved="true"
      expanded="false"
      shape="assertionadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV10V3Iainfix &lt;V10V6Aainfix &lt;=c2V10FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV11V3Iainfix &lt;V11V4Aainfix &lt;=c2V11FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV12V3Iainfix &gt;V12V4AadividesV12V0AaprimeV12FAadividesV13V0Aainfix &gt;=V13V4Iainfix &gt;=V13c2AadividesV13V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV14adivV0V1AacoprimeV1V14Iainfix &gt;V14V1AadividesV14V0AaprimeV14FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV15V0Iainfix &lt;V15V1Aainfix &lt;=c2V15FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV16V0Iainfix &lt;V16c2Aainfix &lt;=c2V16FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <transf
       name="split_goal_wp"
       proved="true"
       expanded="false">
       <goal
        name="WP_parameter largest_prime_factor.17.1"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="1."
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        sum="66180f2f3c4519a6296ee16cb9006037"
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        proved="true"
        expanded="false"
        shape="ainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV10V3Iainfix &lt;V10V6Aainfix &lt;=c2V10FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV11V3Iainfix &lt;V11V4Aainfix &lt;=c2V11FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV12V3Iainfix &gt;V12V4AadividesV12V0AaprimeV12FAadividesV13V0Aainfix &gt;=V13V4Iainfix &gt;=V13c2AadividesV13V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV14adivV0V1AacoprimeV1V14Iainfix &gt;V14V1AadividesV14V0AaprimeV14FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV15V0Iainfix &lt;V15V1Aainfix &lt;=c2V15FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV16V0Iainfix &lt;V16c2Aainfix &lt;=c2V16FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
997
         <result status="valid" time="2.92"/>
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        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.17.2"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="2."
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        sum="88737e93d547b633ad2d343d053ae3eb"
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        proved="true"
        expanded="false"
        shape="adividesV9V3Iainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV10V3Iainfix &lt;V10V6Aainfix &lt;=c2V10FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV11V3Iainfix &lt;V11V4Aainfix &lt;=c2V11FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV12V3Iainfix &gt;V12V4AadividesV12V0AaprimeV12FAadividesV13V0Aainfix &gt;=V13V4Iainfix &gt;=V13c2AadividesV13V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV14adivV0V1AacoprimeV1V14Iainfix &gt;V14V1AadividesV14V0AaprimeV14FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV15V0Iainfix &lt;V15V1Aainfix &lt;=c2V15FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV16V0Iainfix &lt;V16c2Aainfix &lt;=c2V16FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.04"/>
        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.18"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="18. assertion"
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      sum="fe2600ea387143bc46154547cd58a3d9"
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      proved="true"
      expanded="false"
      shape="assertionadividesV10V9AacoprimeV6V10Aainfix &lt;V6V10Aainfix &lt;=c1V6AadividesV10V3Aainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <transf
       name="split_goal_wp"
       proved="true"
       expanded="false">
       <goal
        name="WP_parameter largest_prime_factor.18.1"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="1. assertion"
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        sum="abb143dd3542dda1f1936144c7e790c4"
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        proved="true"
        expanded="false"
        shape="assertionainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.18.2"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="2. assertion"
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        sum="e5fb8d92667f1960b6966f2539a581f9"
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        proved="true"
        expanded="false"
        shape="assertionadividesV10V3Iainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.11"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.18.3"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="3. assertion"
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        sum="610c00ed6f5170d022c19af29b8e3e67"
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        proved="true"
        expanded="false"
        shape="assertionainfix &lt;=c1V6IadividesV10V3Iainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.18.4"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="4. assertion"
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        sum="d37e23b0e084c081e42151378ca73d73"
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        proved="true"
        expanded="false"
        shape="assertionainfix &lt;V6V10IadividesV10V3Iainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.18.5"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="5. assertion"
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        sum="1d781e28d1b0113718384cde0c8bc7b7"
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        proved="true"
        expanded="false"
        shape="assertionacoprimeV6V10Iainfix &lt;V6V10Aainfix &lt;=c1V6IadividesV10V3Iainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="1"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.89"/>
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        </proof>
       </goal>
       <goal
        name="WP_parameter largest_prime_factor.18.6"
        locfile="../euler003.mlw"
        loclnum="55" loccnumb="4" loccnume="24"
        expl="6. assertion"
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        sum="1acbe165c3d2b63850cc877ff55df79b"
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        proved="true"
        expanded="false"
        shape="assertionadividesV10V9IacoprimeV6V10Iainfix &lt;V6V10Aainfix &lt;=c1V6IadividesV10V3Iainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
        <label
         name="expl:VC for largest_prime_factor"/>
        <proof
         prover="3"
         timelimit="5"
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         memlimit="4000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.34"/>
        </proof>
        <proof
         prover="4"
         timelimit="5"
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         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.61"/>
        </proof>
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        <proof
         prover="5"
         timelimit="5"
         memlimit="4000"
         obsolete="false"
         archived="false">
         <result status="valid" time="2.73"/>
        </proof>
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       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.19"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="19. loop invariant preservation"
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      sum="abbb138ad42bff9112723c08c9931fb0"
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      proved="true"
      expanded="false"
      shape="loop invariant preservationainfix &lt;=V9V0Aainfix &lt;=c1V9IadividesV10V9AacoprimeV6V10Aainfix &lt;V6V10Aainfix &lt;=c1V6AadividesV10V3Aainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
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       prover="6"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.20"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="20. loop invariant preservation"
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      sum="259a077bba0d316d3646f0b5ba270678"
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      proved="true"
      expanded="false"
      shape="loop invariant preservationainfix &lt;=V7V0Aainfix &lt;=c2V7IadividesV10V9AacoprimeV6V10Aainfix &lt;V6V10Aainfix &lt;=c1V6AadividesV10V3Aainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.05"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.21"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="21. loop invariant preservation"
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      sum="fe9c86189e6e7cd0a6d209eda7dfe879"
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      proved="true"
      expanded="false"
      shape="loop invariant preservationadividesV7V0IadividesV10V9AacoprimeV6V10Aainfix &lt;V6V10Aainfix &lt;=c1V6AadividesV10V3Aainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.17"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.22"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="22. loop invariant preservation"
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      sum="b489e4d5da80bc5b1902ed027e2cec8d"
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      proved="true"
      expanded="false"
      shape="loop invariant preservationaprimeV7IadividesV10V9AacoprimeV6V10Aainfix &lt;V6V10Aainfix &lt;=c1V6AadividesV10V3Aainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.06"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.23"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="23. loop invariant preservation"
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      sum="3d7bfbb426a15cd2f47ec9f48953f3dd"
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      proved="true"
      expanded="false"
      shape="loop invariant preservationadividesV10V0Aainfix &gt;=V10V7Iainfix &gt;=V10c2AadividesV10V9FIadividesV11V9AacoprimeV6V11Aainfix &lt;V6V11Aainfix &lt;=c1V6AadividesV11V3Aainfix &gt;V11V4Iainfix &gt;V11V6AadividesV11V0AaprimeV11FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV12V3Iainfix &lt;V12V6Aainfix &lt;=c2V12FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV13V3Iainfix &lt;V13V4Aainfix &lt;=c2V13FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV14V3Iainfix &gt;V14V4AadividesV14V0AaprimeV14FAadividesV15V0Aainfix &gt;=V15V4Iainfix &gt;=V15c2AadividesV15V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV16adivV0V1AacoprimeV1V16Iainfix &gt;V16V1AadividesV16V0AaprimeV16FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV17V0Iainfix &lt;V17V1Aainfix &lt;=c2V17FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV18V0Iainfix &lt;V18c2Aainfix &lt;=c2V18FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.20"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.24"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="24. loop invariant preservation"
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      sum="0484bacdcf482242cb182494ebf8119a"
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      proved="true"
      expanded="false"
      shape="loop invariant preservationadividesV10V9Iainfix &gt;V10V7AadividesV10V0AaprimeV10FIadividesV11V9AacoprimeV6V11Aainfix &lt;V6V11Aainfix &lt;=c1V6AadividesV11V3Aainfix &gt;V11V4Iainfix &gt;V11V6AadividesV11V0AaprimeV11FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV12V3Iainfix &lt;V12V6Aainfix &lt;=c2V12FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV13V3Iainfix &lt;V13V4Aainfix &lt;=c2V13FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV14V3Iainfix &gt;V14V4AadividesV14V0AaprimeV14FAadividesV15V0Aainfix &gt;=V15V4Iainfix &gt;=V15c2AadividesV15V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV16adivV0V1AacoprimeV1V16Iainfix &gt;V16V1AadividesV16V0AaprimeV16FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV17V0Iainfix &lt;V17V1Aainfix &lt;=c2V17FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV18V0Iainfix &lt;V18c2Aainfix &lt;=c2V18FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.11"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.25"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="25. loop variant decrease"
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      sum="35d2e7ab69d5da424ce7b761a2088c97"
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      proved="true"
      expanded="false"
      shape="loop variant decreaseainfix &lt;V9V3Aainfix &lt;=c0V3IadividesV10V9AacoprimeV6V10Aainfix &lt;V6V10Aainfix &lt;=c1V6AadividesV10V3Aainfix &gt;V10V4Iainfix &gt;V10V6AadividesV10V0AaprimeV10FIadividesV9V3Aainfix =ainfix *V9V6V3Iainfix =V9adivV3V6FIainfix =V8aConsV6V5FIainfix =V7V6FIaprimeV6INadividesV11V3Iainfix &lt;V11V6Aainfix &lt;=c2V11FAadividesV6V3Aainfix &lt;=V6V3Aainfix &lt;=V4V6FINadividesV12V3Iainfix &lt;V12V4Aainfix &lt;=c2V12FAainfix &lt;=V4V3Aainfix &lt;=c2V4Aainfix &lt;=c2V3Iainfix &gt;=V3V4Aainfix &gt;=V3c2AadividesV3V3Iainfix &gt;=V3c2IadividesV13V3Iainfix &gt;V13V4AadividesV13V0AaprimeV13FAadividesV14V0Aainfix &gt;=V14V4Iainfix &gt;=V14c2AadividesV14V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV15adivV0V1AacoprimeV1V15Iainfix &gt;V15V1AadividesV15V0AaprimeV15FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV16V0Iainfix &lt;V16V1Aainfix &lt;=c2V16FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV17V0Iainfix &lt;V17c2Aainfix &lt;=c2V17FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.07"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.26"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="26. postcondition"
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      sum="0d16456924d603a92dcb52926bd54d9c"
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      proved="true"
      expanded="false"
      shape="postconditionaprimeV4INainfix &gt;=V3c2IadividesV6V3Iainfix &gt;V6V4AadividesV6V0AaprimeV6FAadividesV7V0Aainfix &gt;=V7V4Iainfix &gt;=V7c2AadividesV7V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV8adivV0V1AacoprimeV1V8Iainfix &gt;V8V1AadividesV8V0AaprimeV8FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV9V0Iainfix &lt;V9V1Aainfix &lt;=c2V9FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV10V0Iainfix &lt;V10c2Aainfix &lt;=c2V10FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.27"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="27. postcondition"
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      sum="830dd87ff41b4dae93a5d0dc03eab493"
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      proved="true"
      expanded="false"
      shape="postconditionadividesV4V0INainfix &gt;=V3c2IadividesV6V3Iainfix &gt;V6V4AadividesV6V0AaprimeV6FAadividesV7V0Aainfix &gt;=V7V4Iainfix &gt;=V7c2AadividesV7V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV8adivV0V1AacoprimeV1V8Iainfix &gt;V8V1AadividesV8V0AaprimeV8FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV9V0Iainfix &lt;V9V1Aainfix &lt;=c2V9FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV10V0Iainfix &lt;V10c2Aainfix &lt;=c2V10FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.04"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter largest_prime_factor.28"
      locfile="../euler003.mlw"
      loclnum="55" loccnumb="4" loccnume="24"
      expl="28. postcondition"
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      sum="22bbada92b8039038dbebb13aaad9748"
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      proved="true"
      expanded="false"
      shape="postconditionNadividesV6V0AaprimeV6Iainfix &lt;=V6V0Aainfix &lt;V4V6FINainfix &gt;=V3c2IadividesV7V3Iainfix &gt;V7V4AadividesV7V0AaprimeV7FAadividesV8V0Aainfix &gt;=V8V4Iainfix &gt;=V8c2AadividesV8V3FAaprimeV4AadividesV4V0Aainfix &lt;=V4V0Aainfix &lt;=c2V4Aainfix &lt;=V3V0Aainfix &lt;=c1V3FIadividesV9adivV0V1AacoprimeV1V9Iainfix &gt;V9V1AadividesV9V0AaprimeV9FIadividesadivV0V1V0Aainfix =ainfix *adivV0V1V1V0Iainfix =V2aConsV1aNilFINadividesV10V0Iainfix &lt;V10V1Aainfix &lt;=c2V10FAadividesV1V0Aainfix &lt;=V1V0Aainfix &lt;=c2V1FINadividesV11V0Iainfix &lt;V11c2Aainfix &lt;=c2V11FAainfix &lt;=c2V0Aainfix &lt;=c2c2Aainfix &lt;=c2V0Iainfix &lt;=c2V0F">
      <label
       name="expl:VC for largest_prime_factor"/>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.13"/>
      </proof>
     </goal>
    </transf>
   </goal>
   <goal
    name="WP_parameter test"
    locfile="../euler003.mlw"
    loclnum="97" loccnumb="4" loccnume="8"
    expl="VC for test"
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    sum="1f68094bf108787ce2e89cff937f2ec2"
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    proved="true"
    expanded="false"
    shape="ainfix &lt;=c2c13195">
    <label
     name="expl:VC for test"/>
    <proof
     prover="0"
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.02"/>
    </proof>
   </goal>
   <goal
    name="WP_parameter solve"
    locfile="../euler003.mlw"
    loclnum="100" loccnumb="4" loccnume="9"
    expl="VC for solve"
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    sum="e2142f24f78c2821c235ee6b07a99a22"
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    proved="true"
    expanded="false"
    shape="ainfix &lt;=c2c600851475143">
    <label
     name="expl:VC for solve"/>
    <proof
     prover="0"
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.01"/>
    </proof>
   </goal>
  </theory>
 </file>
</why3session>