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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="3">
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 <prover
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  id="0"
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  name="Alt-Ergo"
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  version="0.95.1"/>
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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"
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  name="CVC3"
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  version="2.4.1"/>
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 <prover
  id="3"
  name="CVC4"
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  version="1.2"/>
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 <prover
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  id="4"
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  name="Coq"
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  version="8.4pl2"/>
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 <prover
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  id="5"
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  name="Eprover"
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  version="1.6"/>
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 <prover
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  id="6"
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  name="Gappa"
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  version="1.0.0"/>
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 <prover
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  id="7"
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  name="Spass"
  version="3.7"/>
 <prover
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  id="8"
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  name="Vampire"
  version="0.6"/>
 <prover
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  id="9"
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  name="Yices"
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  version="1.0.38"/>
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 <prover
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  id="10"
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  name="Z3"
  version="2.19"/>
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 <prover
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  id="11"
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  name="Z3"
  version="3.2"/>
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 <prover
  id="12"
  name="Z3"
  version="4.3.1"/>
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 <file
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  name="../test_harness.mlw"
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  verified="true"
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  expanded="false">
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  <theory
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   name="TestHarness"
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   locfile="../test_harness.mlw"
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   loclnum="2" loccnumb="7" loccnume="18"
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   verified="true"
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   expanded="false">
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   <goal
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    name="WP_parameter testHarness"
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    locfile="../test_harness.mlw"
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    loclnum="15" loccnumb="4" loccnume="15"
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    expl="VC for testHarness"
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    sum="b10d4cd4ff6369766e09633c7581dc5d"
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    proved="true"
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    expanded="false"
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    shape="ainfix =agetV3c2c42Aainfix =agetV3c1c42Aainfix =agetV3c1amin_bagaelementsV3c1c3Aainfix =agetV3c0c13Aainfix =agetV3c0amin_bagaelementsV3c0c3Aainfix =aelementsV3c0c3aunionasingletonc13aunionasingletonc42asingletonc42Aainfix &lt;=agetV3c1agetV3c2Aainfix &lt;=agetV3c0agetV3c1Iainfix =aelementsV3c0c3aelementsV2c0c3Aasorted_subV3c0c3Aainfix &lt;=c0c3FAainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FAainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FAainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FAainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Aainfix &gt;=c3c0">
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    <label
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     name="expl:VC for testHarness"/>
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    <transf
     name="split_goal"
     proved="true"
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     expanded="false">
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     <goal
      name="WP_parameter testHarness.1"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="1. precondition"
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      sum="a16436dad0c546c9ccc0c9fe78421fc4"
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      proved="true"
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      expanded="false"
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      shape="preconditionainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="6"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
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       prover="8"
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       timelimit="13"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="2.07"/>
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      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       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="10"
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       timelimit="3"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter testHarness.2"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="2. precondition"
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      sum="5c25f1b857ee62d1f85eabe842b01459"
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      proved="true"
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      expanded="false"
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      shape="preconditionainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="6"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       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="10"
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       timelimit="3"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter testHarness.3"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="3. precondition"
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      sum="fa916be5db3a7829c4d0deefef613c56"
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      proved="true"
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      expanded="false"
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      shape="preconditionainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="6"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
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      <proof
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       prover="10"
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       timelimit="3"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter testHarness.4"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="4. precondition"
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      sum="6e52bcf7508f93bf5bec382cc73a0031"
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      proved="true"
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      expanded="false"
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      shape="preconditionainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="6"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
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      <proof
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       prover="10"
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       timelimit="3"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter testHarness.5"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="5. precondition"
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      sum="bdbd9fef5720ff264f8616d9a7cc93c9"
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      proved="true"
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      expanded="false"
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      shape="preconditionainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FIainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="6"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
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      <proof
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       prover="10"
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       timelimit="3"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter testHarness.6"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="6. assertion"
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      sum="96d093e8fc0729a04b7cfc0c97d7cf2c"
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      proved="true"
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      expanded="false"
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      shape="assertionainfix &lt;=agetV3c1agetV3c2Aainfix &lt;=agetV3c0agetV3c1Iainfix =aelementsV3c0c3aelementsV2c0c3Aasorted_subV3c0c3Aainfix &lt;=c0c3FIainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FIainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter testHarness.7"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="7. assertion"
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      sum="7fe87d9275e955e41c57f6f32107e96b"
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      proved="true"
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      expanded="false"
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      shape="assertionainfix =aelementsV3c0c3aunionasingletonc13aunionasingletonc42asingletonc42Iainfix &lt;=agetV3c1agetV3c2Aainfix &lt;=agetV3c0agetV3c1Iainfix =aelementsV3c0c3aelementsV2c0c3Aasorted_subV3c0c3Aainfix &lt;=c0c3FIainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FIainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="10"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.06"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter testHarness.8"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="8. assertion"
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      sum="d004e2afdbd6c644404fc8c0144adc08"
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      proved="true"
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      expanded="false"
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      shape="assertionainfix =agetV3c0amin_bagaelementsV3c0c3Iainfix =aelementsV3c0c3aunionasingletonc13aunionasingletonc42asingletonc42Iainfix &lt;=agetV3c1agetV3c2Aainfix &lt;=agetV3c0agetV3c1Iainfix =aelementsV3c0c3aelementsV2c0c3Aasorted_subV3c0c3Aainfix &lt;=c0c3FIainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FIainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.04"/>
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      </proof>
      <proof
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       prover="10"
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       timelimit="12"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter testHarness.9"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="9. assertion"
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      sum="7cd044245e5ed06afc2ff92d88bcc11c"
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      proved="true"
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      expanded="false"
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      shape="assertionainfix =agetV3c0c13Iainfix =agetV3c0amin_bagaelementsV3c0c3Iainfix =aelementsV3c0c3aunionasingletonc13aunionasingletonc42asingletonc42Iainfix &lt;=agetV3c1agetV3c2Aainfix &lt;=agetV3c0agetV3c1Iainfix =aelementsV3c0c3aelementsV2c0c3Aasorted_subV3c0c3Aainfix &lt;=c0c3FIainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FIainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.10"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.04"/>
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      </proof>
      <proof
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       prover="10"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.06"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter testHarness.10"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="10. assertion"
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      sum="eeac666577c986b377bbed9a049c2758"
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      proved="true"
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      expanded="false"
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      shape="assertionainfix =agetV3c1amin_bagaelementsV3c1c3Iainfix =agetV3c0c13Iainfix =agetV3c0amin_bagaelementsV3c0c3Iainfix =aelementsV3c0c3aunionasingletonc13aunionasingletonc42asingletonc42Iainfix &lt;=agetV3c1agetV3c2Aainfix &lt;=agetV3c0agetV3c1Iainfix =aelementsV3c0c3aelementsV2c0c3Aasorted_subV3c0c3Aainfix &lt;=c0c3FIainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FIainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter testHarness.11"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="11. assertion"
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      sum="cb7bc18118a1f59f024056c439429988"
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      proved="true"
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      expanded="false"
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      shape="assertionainfix =agetV3c1c42Iainfix =agetV3c1amin_bagaelementsV3c1c3Iainfix =agetV3c0c13Iainfix =agetV3c0amin_bagaelementsV3c0c3Iainfix =aelementsV3c0c3aunionasingletonc13aunionasingletonc42asingletonc42Iainfix &lt;=agetV3c1agetV3c2Aainfix &lt;=agetV3c0agetV3c1Iainfix =aelementsV3c0c3aelementsV2c0c3Aasorted_subV3c0c3Aainfix &lt;=c0c3FIainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FIainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.05"/>
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      </proof>
      <proof
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       prover="10"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.04"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter testHarness.12"
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      locfile="../test_harness.mlw"
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      loclnum="15" loccnumb="4" loccnume="15"
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      expl="12. assertion"
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      sum="7c7c15fb2d9c2653f70a38169169710f"
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      proved="true"
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      expanded="false"
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      shape="assertionainfix =agetV3c2c42Iainfix =agetV3c1c42Iainfix =agetV3c1amin_bagaelementsV3c1c3Iainfix =agetV3c0c13Iainfix =agetV3c0amin_bagaelementsV3c0c3Iainfix =aelementsV3c0c3aunionasingletonc13aunionasingletonc42asingletonc42Iainfix &lt;=agetV3c1agetV3c2Aainfix &lt;=agetV3c0agetV3c1Iainfix =aelementsV3c0c3aelementsV2c0c3Aasorted_subV3c0c3Aainfix &lt;=c0c3FIainfix &gt;=c3c0Iainfix =V2asetV1c2c42Aainfix &lt;=c0c3FIainfix &lt;c2c3Aainfix &lt;=c0c2Iainfix =V1asetV0c1c13Aainfix &lt;=c0c3FIainfix &lt;c1c3Aainfix &lt;=c0c1Iainfix =V0asetaconstc0c0c42Aainfix &lt;=c0c3FIainfix &lt;c0c3Aainfix &lt;=c0c0Iainfix &lt;=c0c3Iainfix &gt;=c3c0">
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      <label
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       name="expl:VC for testHarness"/>
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      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.06"/>
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      </proof>
      <proof
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       prover="10"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.04"/>
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      </proof>
     </goal>
    </transf>
   </goal>
  </theory>
 </file>
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 <file
  name="../elements.why"
  verified="true"
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  expanded="false">
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  <theory
   name="Elements"
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   locfile="../elements.why"
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   loclnum="1" loccnumb="7" loccnume="15"
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   verified="true"
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   expanded="false">
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   <goal
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    name="Elements_singleton"
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    locfile="../elements.why"
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    loclnum="19" loccnumb="6" loccnume="24"
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    sum="fd7213192d40d6a2c3748d0c1910da5e"
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    proved="true"
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    expanded="false"
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    shape="ainfix =aelementsV0V1V2asingletonamixfix []V0V1Iainfix =V2ainfix +V1c1F">
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    <proof
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     prover="10"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.02"/>
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    </proof>
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   </goal>
   <goal
    name="Elements_union"
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    locfile="../elements.why"
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    loclnum="23" loccnumb="6" loccnume="20"
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    sum="648b7ea62cdb3d21fca4bbe73fb2b0fe"
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    proved="true"
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    expanded="false"
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    shape="ainfix =aelementsV0V1V3aunionaelementsV0V1V2aelementsV0V2V3Iainfix &lt;=V2V3Aainfix &lt;=V1V2F">
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    <proof
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     prover="4"
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     timelimit="5"
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     memlimit="0"
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     edited="elements_Elements_Elements_union_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.28"/>
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    </proof>
   </goal>
   <goal
    name="Elements_add1"
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    locfile="../elements.why"
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    loclnum="27" loccnumb="6" loccnume="19"
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    sum="ef60acbbed9eb5b22b2aa8b53dbe5ff0"
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    proved="true"
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    expanded="false"
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    shape="ainfix =aelementsV0V1V2aaddamixfix []V0V1aelementsV0ainfix +V1c1V2Iainfix &lt;V1V2F">
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    <proof
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     prover="4"
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     timelimit="5"
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     memlimit="0"
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     edited="elements_Elements_Elements_add1_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.08"/>
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    </proof>
    <proof
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     prover="9"
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     timelimit="10"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.00"/>