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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v2//EN" "http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="2">
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 <prover
  id="0"
  name="Alt-Ergo"
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  version="0.93.1"/>
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 <prover
  id="1"
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  name="Alt-Ergo"
  version="0.94"/>
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 <prover
  id="2"
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  name="Alt-Ergo"
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  version="0.95"/>
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 <prover
  id="3"
  name="CVC3"
  version="2.2"/>
 <prover
  id="4"
  name="CVC3"
  version="2.4.1"/>
 <prover
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  id="5"
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  name="Coq"
  version="8.3pl4"/>
 <prover
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  id="6"
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  name="Z3"
  version="2.19"/>
 <prover
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  id="7"
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  name="Z3"
  version="3.2"/>
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 <prover
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  id="8"
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  name="Z3"
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  version="4.2"/>
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 <file
  name="../alphaBeta.mlw"
  verified="false"
  expanded="true">
  <theory
   name="TwoPlayerGame"
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   locfile="../alphaBeta.mlw"
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   loclnum="2" loccnumb="7" loccnume="20"
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   verified="true"
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   expanded="false">
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   <goal
    name="Test"
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    locfile="../alphaBeta.mlw"
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    loclnum="76" loccnumb="7" loccnume="11"
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    sum="610608283a85bf303ebe1a84cfcfc086"
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    proved="true"
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    expanded="false"
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    shape="ainfix &lt;=aprefix -aposition_valueado_moveV0V1aminmaxV0c1IamemV1V2Lalegal_movesV0F">
    <proof
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     prover="5"
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     timelimit="10"
     memlimit="1000"
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     edited="alphaBeta_TwoPlayerGame_Test_1.v"
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     obsolete="false"
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     archived="false">
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     <result status="valid" time="0.51"/>
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    </proof>
    <proof
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     prover="6"
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     timelimit="10"
     memlimit="1000"
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     obsolete="false"
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     archived="false">
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     <result status="valid" time="0.03"/>
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    </proof>
    <proof
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     prover="7"
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     timelimit="10"
     memlimit="1000"
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     obsolete="false"
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     archived="false">
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     <result status="valid" time="0.05"/>
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    </proof>
   </goal>
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   <goal
    name="minmax_bound"
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    locfile="../alphaBeta.mlw"
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    loclnum="82" loccnumb="8" loccnume="20"
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    sum="09da0270a2e52b38705869d9ac120b60"
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    proved="true"
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    expanded="false"
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    shape="ainfix &lt;aminmaxV0V1ainfinityAainfix &lt;aprefix -ainfinityaminmaxV0V1Iainfix &gt;=V1c0F">
    <proof
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     prover="5"
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     timelimit="3"
     memlimit="1000"
     edited="alphaBeta_TwoPlayerGame_minmax_bound_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.80"/>
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    </proof>
   </goal>
   <goal
    name="minmax_nomove"
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    locfile="../alphaBeta.mlw"
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    loclnum="86" loccnumb="8" loccnume="21"
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    sum="31d04b93aaada3edf39c7cebc00b7339"
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    proved="true"
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    expanded="false"
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    shape="ainfix =aminmaxV0V1aposition_valueV0Iainfix =alegal_movesV0aNilAainfix &gt;=V1c0F">
    <proof
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     prover="0"
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     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.09"/>
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    </proof>
    <proof
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     prover="1"
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     timelimit="3"
     memlimit="1000"
     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="2"
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     timelimit="3"
     memlimit="1000"
     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="3"
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     timelimit="3"
     memlimit="1000"
     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="4"
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     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.01"/>
    </proof>
    <proof
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     prover="6"
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     timelimit="3"
     memlimit="1000"
     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="7"
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     timelimit="3"
     memlimit="1000"
     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="8"
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     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.02"/>
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    </proof>
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   </goal>
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  </theory>
  <theory
   name="AlphaBeta"
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   locfile="../alphaBeta.mlw"
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   loclnum="99" loccnumb="7" loccnume="16"
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   verified="false"
   expanded="true">
   <goal
    name="WP_parameter move_value_alpha_beta"
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    locfile="../alphaBeta.mlw"
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    loclnum="109" loccnumb="10" loccnume="31"
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    expl="VC for move_value_alpha_beta"
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    sum="f2b2c50e29db1fb27fd1056697ca29b4"
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    proved="true"
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    expanded="false"
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    shape="iainfix &lt;V6aprefix -V0Aainfix &lt;aprefix -V1V6ainfix =aprefix -V5aprefix -V6iainfix &lt;=V6aprefix -V1ainfix &gt;=aprefix -V5V1ainfix &lt;=aprefix -V5V0Laminmaxado_moveV2V4ainfix -V3c1Iiainfix &lt;aminmaxado_moveV2V4ainfix -V3c1aprefix -V0Aainfix &lt;aprefix -V1aminmaxado_moveV2V4ainfix -V3c1ainfix =V5aminmaxado_moveV2V4ainfix -V3c1iainfix &lt;=aminmaxado_moveV2V4ainfix -V3c1aprefix -V1ainfix &lt;=V5aprefix -V1ainfix &gt;=V5aprefix -V0FAainfix &gt;=ainfix -V3c1c0Iainfix &gt;=V3c1F">
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    <label
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     name="expl:VC for move_value_alpha_beta"/>
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    <transf
     name="split_goal_wp"
     proved="true"
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     expanded="false">
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     <goal
      name="WP_parameter move_value_alpha_beta.1"
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      locfile="../alphaBeta.mlw"
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      loclnum="109" loccnumb="10" loccnume="31"
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      expl="1. precondition"
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      sum="a2e31407b2d98a26cdc1eecfe67f4a18"
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      proved="true"
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      expanded="false"
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      shape="ainfix &gt;=ainfix -V3c1c0Iainfix &gt;=V3c1F">
      <label
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       name="expl:VC for move_value_alpha_beta"/>
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      <proof
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       prover="0"
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       timelimit="3"
       memlimit="1000"
       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"
       memlimit="1000"
       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="2"
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       timelimit="3"
       memlimit="1000"
       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="3"
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       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.00"/>
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      </proof>
      <proof
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       prover="4"
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       timelimit="3"
       memlimit="1000"
       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="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
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       prover="7"
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       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.00"/>
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      </proof>
      <proof
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       prover="8"
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       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.00"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter move_value_alpha_beta.2"
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      locfile="../alphaBeta.mlw"
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      loclnum="109" loccnumb="10" loccnume="31"
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      expl="2. postcondition"
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      sum="f7d37657adac949f80acee2dacdbf903"
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      proved="true"
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      expanded="false"
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      shape="iainfix &lt;V6aprefix -V0Aainfix &lt;aprefix -V1V6ainfix =aprefix -V5aprefix -V6iainfix &lt;=V6aprefix -V1ainfix &gt;=aprefix -V5V1ainfix &lt;=aprefix -V5V0Laminmaxado_moveV2V4ainfix -V3c1Iiainfix &lt;aminmaxado_moveV2V4ainfix -V3c1aprefix -V0Aainfix &lt;aprefix -V1aminmaxado_moveV2V4ainfix -V3c1ainfix =V5aminmaxado_moveV2V4ainfix -V3c1iainfix &lt;=aminmaxado_moveV2V4ainfix -V3c1aprefix -V1ainfix &lt;=V5aprefix -V1ainfix &gt;=V5aprefix -V0FIainfix &gt;=ainfix -V3c1c0Iainfix &gt;=V3c1F">
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      <label
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       name="expl:VC for move_value_alpha_beta"/>
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      <transf
       name="split_goal_wp"
       proved="true"
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       expanded="false">
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       <goal
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        name="WP_parameter move_value_alpha_beta.2.1"
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        locfile="../alphaBeta.mlw"
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        loclnum="109" loccnumb="10" loccnume="31"
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        expl="1. postcondition"
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        sum="3fe99f92c30fc7fdd5b8fa12275d56ad"
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        proved="true"
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        expanded="false"
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        shape="ainfix =aprefix -V5aprefix -V6Iainfix &lt;V6aprefix -V0Aainfix &lt;aprefix -V1V6Laminmaxado_moveV2V4ainfix -V3c1Iiainfix &lt;aminmaxado_moveV2V4ainfix -V3c1aprefix -V0Aainfix &lt;aprefix -V1aminmaxado_moveV2V4ainfix -V3c1ainfix =V5aminmaxado_moveV2V4ainfix -V3c1iainfix &lt;=aminmaxado_moveV2V4ainfix -V3c1aprefix -V1ainfix &lt;=V5aprefix -V1ainfix &gt;=V5aprefix -V0FIainfix &gt;=ainfix -V3c1c0Iainfix &gt;=V3c1F">
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        <label
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         name="expl:VC for move_value_alpha_beta"/>
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        <proof
         prover="0"
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.01"/>
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        </proof>
       </goal>
       <goal
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        name="WP_parameter move_value_alpha_beta.2.2"
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        locfile="../alphaBeta.mlw"
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        loclnum="109" loccnumb="10" loccnume="31"
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        expl="2. postcondition"
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        sum="bce92f52b1606bc59d69750f380be885"
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        proved="true"
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        expanded="false"
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        shape="ainfix &gt;=aprefix -V5V1Iainfix &lt;=V6aprefix -V1Iainfix &lt;V6aprefix -V0Aainfix &lt;aprefix -V1V6NLaminmaxado_moveV2V4ainfix -V3c1Iiainfix &lt;aminmaxado_moveV2V4ainfix -V3c1aprefix -V0Aainfix &lt;aprefix -V1aminmaxado_moveV2V4ainfix -V3c1ainfix =V5aminmaxado_moveV2V4ainfix -V3c1iainfix &lt;=aminmaxado_moveV2V4ainfix -V3c1aprefix -V1ainfix &lt;=V5aprefix -V1ainfix &gt;=V5aprefix -V0FIainfix &gt;=ainfix -V3c1c0Iainfix &gt;=V3c1F">
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        <label
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         name="expl:VC for move_value_alpha_beta"/>
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        <proof
         prover="0"
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.02"/>
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        </proof>
       </goal>
       <goal
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        name="WP_parameter move_value_alpha_beta.2.3"
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        locfile="../alphaBeta.mlw"
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        loclnum="109" loccnumb="10" loccnume="31"
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        expl="3. postcondition"
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        sum="8375fb15569dcaa7d79665539ccccad9"
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        proved="true"
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        expanded="false"
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        shape="ainfix &lt;=aprefix -V5V0Iainfix &lt;=V6aprefix -V1NIainfix &lt;V6aprefix -V0Aainfix &lt;aprefix -V1V6NLaminmaxado_moveV2V4ainfix -V3c1Iiainfix &lt;aminmaxado_moveV2V4ainfix -V3c1aprefix -V0Aainfix &lt;aprefix -V1aminmaxado_moveV2V4ainfix -V3c1ainfix =V5aminmaxado_moveV2V4ainfix -V3c1iainfix &lt;=aminmaxado_moveV2V4ainfix -V3c1aprefix -V1ainfix &lt;=V5aprefix -V1ainfix &gt;=V5aprefix -V0FIainfix &gt;=ainfix -V3c1c0Iainfix &gt;=V3c1F">
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        <label
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         name="expl:VC for move_value_alpha_beta"/>
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        <proof
         prover="0"
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
      </transf>
     </goal>
    </transf>
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   </goal>
   <goal
    name="WP_parameter negabeta"
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    locfile="../alphaBeta.mlw"
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    loclnum="121" loccnumb="7" loccnume="15"
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    expl="VC for negabeta"
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    sum="ff6c1977755082f26b247e1c0923a90b"
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    proved="false"
    expanded="true"
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    shape="iainfix =V3c0iainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3ainfix =aposition_valueV2aminmaxV2V3iainfix &lt;=aminmaxV2V3V0ainfix &lt;=aposition_valueV2V0ainfix &gt;=aposition_valueV2V1Calegal_movesV2aNiliainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3ainfix =aposition_valueV2aminmaxV2V3iainfix &lt;=aminmaxV2V3V0ainfix &lt;=aposition_valueV2V0ainfix &gt;=aposition_valueV2V1aConsVViainfix &gt;=V6V1iainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3ainfix =V6aminmaxV2V3iainfix &lt;=aminmaxV2V3V0ainfix &lt;=V6V0ainfix &gt;=V6V1iainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3ainfix =V7aminmaxV2V3iainfix &lt;=aminmaxV2V3V0ainfix &lt;=V7V0ainfix &gt;=V7V1Iiais_emptyV8ainfix =V7V6iainfix &lt;V9V1Aainfix &lt;amaxV6V0V9ainfix =V7V9iainfix &lt;=V9amaxV6V0ainfix &lt;=V7amaxV6V0ainfix &gt;=V7V1LaminaTuple2V2V3V8LaelementsV5FAainfix &gt;=V3c1Iiainfix &lt;V10aprefix -V0Aainfix &lt;aprefix -V1V10ainfix =V6aprefix -V10iainfix &lt;=V10aprefix -V1ainfix &gt;=V6V1ainfix &lt;=V6V0Laminmaxado_moveV2V4ainfix -V3c1FAainfix &gt;=V3c1Iainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
361
    <label
362
     name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
363 364 365 366 367 368
    <transf
     name="split_goal_wp"
     proved="false"
     expanded="true">
     <goal
      name="WP_parameter negabeta.1"
MARCHE Claude's avatar
MARCHE Claude committed
369
      locfile="../alphaBeta.mlw"
370
      loclnum="121" loccnumb="7" loccnume="15"
371
      expl="1. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
372
      sum="489e7cf3b79dacf889b72955ef519dc9"
MARCHE Claude's avatar
MARCHE Claude committed
373
      proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
374
      expanded="false"
375
      shape="iainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3ainfix =aposition_valueV2aminmaxV2V3iainfix &lt;=aminmaxV2V3V0ainfix &lt;=aposition_valueV2V0ainfix &gt;=aposition_valueV2V1Iainfix =V3c0Iainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
376
      <label
377
       name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
378 379 380 381 382 383
      <proof
       prover="1"
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
384
       <result status="valid" time="0.01"/>
MARCHE Claude's avatar
MARCHE Claude committed
385 386 387 388
      </proof>
      <transf
       name="split_goal_wp"
       proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
389
       expanded="false">
MARCHE Claude's avatar
MARCHE Claude committed
390
       <goal
391
        name="WP_parameter negabeta.1.1"
MARCHE Claude's avatar
MARCHE Claude committed
392
        locfile="../alphaBeta.mlw"
393
        loclnum="121" loccnumb="7" loccnume="15"
394
        expl="1. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
395
        sum="465d551152bfe083b4fee0dc11e95459"
MARCHE Claude's avatar
MARCHE Claude committed
396
        proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
397
        expanded="false"
398
        shape="ainfix =aposition_valueV2aminmaxV2V3Iainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3Iainfix =V3c0Iainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
399
        <label
400
         name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
401
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
402
         prover="7"
MARCHE Claude's avatar
MARCHE Claude committed
403 404 405 406
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
407
         <result status="valid" time="0.01"/>
MARCHE Claude's avatar
MARCHE Claude committed
408 409
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
410
         prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
411 412 413 414
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
415
         <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
416 417 418
        </proof>
       </goal>
       <goal
419
        name="WP_parameter negabeta.1.2"
MARCHE Claude's avatar
MARCHE Claude committed
420
        locfile="../alphaBeta.mlw"
421
        loclnum="121" loccnumb="7" loccnume="15"
422
        expl="2. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
423
        sum="1a4f137de291c168e659e30634529c12"
MARCHE Claude's avatar
MARCHE Claude committed
424
        proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
425
        expanded="false"
426
        shape="ainfix &lt;=aposition_valueV2V0Iainfix &lt;=aminmaxV2V3V0Iainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3NIainfix =V3c0Iainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
427
        <label
428
         name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
429
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
430
         prover="7"
MARCHE Claude's avatar
MARCHE Claude committed
431 432 433 434
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
435
         <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
436 437
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
438
         prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
439 440 441 442 443 444 445 446
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
       <goal
447
        name="WP_parameter negabeta.1.3"
MARCHE Claude's avatar
MARCHE Claude committed
448
        locfile="../alphaBeta.mlw"
449
        loclnum="121" loccnumb="7" loccnume="15"
450
        expl="3. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
451
        sum="cccb5a149375a7097ef1ba22c3735228"
MARCHE Claude's avatar
MARCHE Claude committed
452
        proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
453
        expanded="false"
454
        shape="ainfix &gt;=aposition_valueV2V1Iainfix &lt;=aminmaxV2V3V0NIainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3NIainfix =V3c0Iainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
455
        <label
456
         name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
457
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
458
         prover="7"
MARCHE Claude's avatar
MARCHE Claude committed
459 460 461 462
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
463
         <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
464 465
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
466
         prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
467 468 469 470 471 472 473 474 475 476 477
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter negabeta.2"
MARCHE Claude's avatar
MARCHE Claude committed
478
      locfile="../alphaBeta.mlw"
479
      loclnum="121" loccnumb="7" loccnume="15"
480
      expl="2. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
481
      sum="da287b2b7c6c3f3b5b73c7588c08aec6"
482
      proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
483
      expanded="false"
484
      shape="Calegal_movesV2aNiliainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3ainfix =aposition_valueV2aminmaxV2V3iainfix &lt;=aminmaxV2V3V0ainfix &lt;=aposition_valueV2V0ainfix &gt;=aposition_valueV2V1aConsVVtIainfix =V3c0NIainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
485
      <label
486
       name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
487 488
      <transf
       name="split_goal_wp"
489
       proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
490
       expanded="false">
MARCHE Claude's avatar
MARCHE Claude committed
491
       <goal
492
        name="WP_parameter negabeta.2.1"
MARCHE Claude's avatar
MARCHE Claude committed
493
        locfile="../alphaBeta.mlw"
494
        loclnum="121" loccnumb="7" loccnume="15"
495
        expl="1. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
496
        sum="2d95f57ac8728f253948d1306cc076a2"
497
        proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
498
        expanded="false"
499
        shape="Calegal_movesV2aNilainfix =aposition_valueV2aminmaxV2V3Iainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3aConsVVtIainfix =V3c0NIainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
500
        <label
501
         name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
502 503 504 505 506 507
        <proof
         prover="1"
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
508
         <result status="valid" time="0.01"/>
MARCHE Claude's avatar
MARCHE Claude committed
509 510
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
511
         prover="7"
MARCHE Claude's avatar
MARCHE Claude committed
512 513 514 515
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
516
         <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
517 518
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
519
         prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
520 521 522 523
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
524
         <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
525 526 527
        </proof>
       </goal>
       <goal
528
        name="WP_parameter negabeta.2.2"
MARCHE Claude's avatar
MARCHE Claude committed
529
        locfile="../alphaBeta.mlw"
530
        loclnum="121" loccnumb="7" loccnume="15"
531
        expl="2. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
532
        sum="c2f4b25fea42605fc28196e65f9ebe76"
533
        proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
534
        expanded="false"
535
        shape="Calegal_movesV2aNilainfix &lt;=aposition_valueV2V0Iainfix &lt;=aminmaxV2V3V0Iainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3NaConsVVtIainfix =V3c0NIainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
536
        <label
537
         name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
538 539 540 541 542 543
        <proof
         prover="1"
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
544
         <result status="valid" time="0.01"/>
MARCHE Claude's avatar
MARCHE Claude committed
545 546
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
547
         prover="7"
MARCHE Claude's avatar
MARCHE Claude committed
548 549 550 551
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
552
         <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
553 554
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
555
         prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
556 557 558 559
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
560
         <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
561 562 563
        </proof>
       </goal>
       <goal
564
        name="WP_parameter negabeta.2.3"
MARCHE Claude's avatar
MARCHE Claude committed
565
        locfile="../alphaBeta.mlw"
566
        loclnum="121" loccnumb="7" loccnume="15"
567
        expl="3. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
568
        sum="a099e861a7b3c5ed07db90da336b1b54"
569
        proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
570
        expanded="false"
571
        shape="Calegal_movesV2aNilainfix &gt;=aposition_valueV2V1Iainfix &lt;=aminmaxV2V3V0NIainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3NaConsVVtIainfix =V3c0NIainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
572
        <label
573
         name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
574 575 576 577 578 579
        <proof
         prover="1"
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
580
         <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
581 582
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
583
         prover="7"
MARCHE Claude's avatar
MARCHE Claude committed
584 585 586 587
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
588
         <result status="valid" time="0.03"/>
MARCHE Claude's avatar
MARCHE Claude committed
589 590
        </proof>
        <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
591
         prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
592 593 594 595
         timelimit="3"
         memlimit="1000"
         obsolete="false"
         archived="false">
596
         <result status="valid" time="0.03"/>
MARCHE Claude's avatar
MARCHE Claude committed
597 598 599 600 601 602
        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter negabeta.3"
MARCHE Claude's avatar
MARCHE Claude committed
603
      locfile="../alphaBeta.mlw"
604
      loclnum="121" loccnumb="7" loccnume="15"
605
      expl="3. precondition"
MARCHE Claude's avatar
MARCHE Claude committed
606
      sum="cedb45baa8d038288ccd7521e119ddda"
MARCHE Claude's avatar
MARCHE Claude committed
607
      proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
608
      expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
609 610
      shape="Calegal_movesV2aNiltaConsVVainfix &gt;=V3c1Iainfix =V3c0NIainfix &gt;=V3c0F">
      <label
611
       name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
612 613 614 615 616 617
      <proof
       prover="1"
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
618
       <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
619 620
      </proof>
      <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
621
       prover="7"
MARCHE Claude's avatar
MARCHE Claude committed
622 623 624 625
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
626
       <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
627 628
      </proof>
      <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
629
       prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
630 631 632 633
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
634
       <result status="valid" time="0.03"/>
MARCHE Claude's avatar
MARCHE Claude committed
635 636 637 638
      </proof>
     </goal>
     <goal
      name="WP_parameter negabeta.4"
MARCHE Claude's avatar
MARCHE Claude committed
639
      locfile="../alphaBeta.mlw"
640
      loclnum="121" loccnumb="7" loccnume="15"
641
      expl="4. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
642
      sum="1e253830c031164ea76fdf61b7900f7c"
MARCHE Claude's avatar
MARCHE Claude committed
643 644
      proved="false"
      expanded="true"
645
      shape="Calegal_movesV2aNiltaConsVViainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3ainfix =V6aminmaxV2V3iainfix &lt;=aminmaxV2V3V0ainfix &lt;=V6V0ainfix &gt;=V6V1Iainfix &gt;=V6V1Iiainfix &lt;V7aprefix -V0Aainfix &lt;aprefix -V1V7ainfix =V6aprefix -V7iainfix &lt;=V7aprefix -V1ainfix &gt;=V6V1ainfix &lt;=V6V0Laminmaxado_moveV2V4ainfix -V3c1FIainfix &gt;=V3c1Iainfix =V3c0NIainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
646
      <label
647
       name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
648 649 650
     </goal>
     <goal
      name="WP_parameter negabeta.5"
MARCHE Claude's avatar
MARCHE Claude committed
651
      locfile="../alphaBeta.mlw"
652
      loclnum="121" loccnumb="7" loccnume="15"
653
      expl="5. precondition"
MARCHE Claude's avatar
MARCHE Claude committed
654
      sum="563184465ddec553604aa3248df427b9"
MARCHE Claude's avatar
MARCHE Claude committed
655
      proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
656
      expanded="false"
657
      shape="Calegal_movesV2aNiltaConsVVainfix &gt;=V3c1Iainfix &gt;=V6V1NIiainfix &lt;V7aprefix -V0Aainfix &lt;aprefix -V1V7ainfix =V6aprefix -V7iainfix &lt;=V7aprefix -V1ainfix &gt;=V6V1ainfix &lt;=V6V0Laminmaxado_moveV2V4ainfix -V3c1FIainfix &gt;=V3c1Iainfix =V3c0NIainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
658
      <label
659
       name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
660 661 662 663 664 665
      <proof
       prover="1"
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
666
       <result status="valid" time="0.01"/>
MARCHE Claude's avatar
MARCHE Claude committed
667 668
      </proof>
      <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
669
       prover="7"
MARCHE Claude's avatar
MARCHE Claude committed
670 671 672 673
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
674
       <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
675 676
      </proof>
      <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
677
       prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
678 679 680 681
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
682
       <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
683 684 685 686
      </proof>
     </goal>
     <goal
      name="WP_parameter negabeta.6"
MARCHE Claude's avatar
MARCHE Claude committed
687
      locfile="../alphaBeta.mlw"
688
      loclnum="121" loccnumb="7" loccnume="15"
689
      expl="6. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
690
      sum="900c7b124ed942878c44afd849dadcf0"
MARCHE Claude's avatar
MARCHE Claude committed
691 692
      proved="false"
      expanded="true"
693
      shape="Calegal_movesV2aNiltaConsVViainfix &lt;aminmaxV2V3V1Aainfix &lt;V0aminmaxV2V3ainfix =V7aminmaxV2V3iainfix &lt;=aminmaxV2V3V0ainfix &lt;=V7V0ainfix &gt;=V7V1Iiais_emptyV8ainfix =V7V6iainfix &lt;V9V1Aainfix &lt;amaxV6V0V9ainfix =V7V9iainfix &lt;=V9amaxV6V0ainfix &lt;=V7amaxV6V0ainfix &gt;=V7V1LaminaTuple2V2V3V8LaelementsV5FIainfix &gt;=V3c1Iainfix &gt;=V6V1NIiainfix &lt;V10aprefix -V0Aainfix &lt;aprefix -V1V10ainfix =V6aprefix -V10iainfix &lt;=V10aprefix -V1ainfix &gt;=V6V1ainfix &lt;=V6V0Laminmaxado_moveV2V4ainfix -V3c1FIainfix &gt;=V3c1Iainfix =V3c0NIainfix &gt;=V3c0F">
MARCHE Claude's avatar
MARCHE Claude committed
694
      <label
695
       name="expl:VC for negabeta"/>
MARCHE Claude's avatar
MARCHE Claude committed
696 697
     </goal>
    </transf>
MARCHE Claude's avatar
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698 699 700
   </goal>
   <goal
    name="WP_parameter negabeta_rec"
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701
    locfile="../alphaBeta.mlw"
702
    loclnum="139" loccnumb="7" loccnume="19"
703
    expl="VC for negabeta_rec"
MARCHE Claude's avatar
MARCHE Claude committed
704
    sum="0c0b2dedce3f81e08a8ab69099ccd44d"
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MARCHE Claude committed
705
    proved="false"
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    expanded="true"
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    shape="CV5aNiliainfix &lt;V7V1Aainfix &lt;V0V7ainfix =V4V7iainfix &lt;=V7V0ainfix &lt;=V4V0ainfix &gt;=V4V1LaminaTuple2V2V3V6Iais_emptyV6NLaelementsV5aConsVViainfix &gt;=amaxV10V4V1iais_emptyV11ainfix =amaxV10V4V4iainfix &lt;V12V1Aainfix &lt;V0V12ainfix =amaxV10V4V12iainfix &lt;=V12V0ainfix &lt;=amaxV10V4V0ainfix &gt;=amaxV10V4V1LaminaTuple2V2V3V11LaelementsV5iais_emptyV14ainfix =V13V4iainfix &lt;V15V1Aainfix &lt;V0V15ainfix =V13V15iainfix &lt;=V15V0ainfix &lt;=V13V0ainfix &gt;=V13V1LaminaTuple2V2V3V14LaelementsV5Iiais_emptyV16ainfix =V13amaxV10V4iainfix &lt;V17V1Aainfix &lt;amaxamaxV10V4V0V17ainfix =V13V17iainfix &lt;=V17amaxamaxV10V4V0ainfix &lt;=V13amaxamaxV10V4V0ainfix &gt;=V13V1LaminaTuple2V2V3V16LaelementsV9FAainfix &gt;=V3c1Iiainfix &lt;V18aprefix -V0Aainfix &lt;aprefix -V1V18ainfix =V10aprefix -V18iainfix &lt;=V18aprefix -V1ainfix &gt;=V10V1ainfix &lt;=V10V0Laminmaxado_moveV2V8ainfix -V3c1FAainfix &gt;=V3c1Iainfix &gt;=V3c1F">
MARCHE Claude's avatar
MARCHE Claude committed
708
    <label
709
     name="expl:VC for negabeta_rec"/>
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710 711 712 713 714 715
    <transf
     name="split_goal_wp"
     proved="false"
     expanded="true">
     <goal
      name="WP_parameter negabeta_rec.1"
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MARCHE Claude committed
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      locfile="../alphaBeta.mlw"
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      loclnum="139" loccnumb="7" loccnume="19"
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      expl="1. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
719
      sum="3588b2a391a2c2a894f03d0e0094ab00"
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MARCHE Claude committed
720
      proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
721
      expanded="false"
722
      shape="CV5aNiliainfix &lt;V7V1Aainfix &lt;V0V7ainfix =V4V7iainfix &lt;=V7V0ainfix &lt;=V4V0ainfix &gt;=V4V1LaminaTuple2V2V3V6Iais_emptyV6NLaelementsV5aConsVVtIainfix &gt;=V3c1F">
MARCHE Claude's avatar
MARCHE Claude committed
723
      <label
724
       name="expl:VC for negabeta_rec"/>
MARCHE Claude's avatar
MARCHE Claude committed
725
      <proof
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       prover="8"
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727 728 729 730
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
731
       <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
732 733 734 735
      </proof>
     </goal>
     <goal
      name="WP_parameter negabeta_rec.2"
MARCHE Claude's avatar
MARCHE Claude committed
736
      locfile="../alphaBeta.mlw"
737
      loclnum="139" loccnumb="7" loccnume="19"
738
      expl="2. precondition"
MARCHE Claude's avatar
MARCHE Claude committed
739
      sum="2340cb631a5af087712eb69afbc6a0ba"
MARCHE Claude's avatar
MARCHE Claude committed
740
      proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
741
      expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
742 743
      shape="CV5aNiltaConsVVainfix &gt;=V3c1Iainfix &gt;=V3c1F">
      <label
744
       name="expl:VC for negabeta_rec"/>
MARCHE Claude's avatar
MARCHE Claude committed
745
      <proof
MARCHE Claude's avatar
MARCHE Claude committed
746
       prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
747 748 749 750
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
751
       <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
752 753 754 755
      </proof>
     </goal>
     <goal
      name="WP_parameter negabeta_rec.3"
MARCHE Claude's avatar
MARCHE Claude committed
756
      locfile="../alphaBeta.mlw"
757
      loclnum="139" loccnumb="7" loccnume="19"
758
      expl="3. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
759
      sum="d35c091cedb5878157356798f59ed4db"
MARCHE Claude's avatar
MARCHE Claude committed
760 761
      proved="false"
      expanded="true"
762
      shape="CV5aNiltaConsVViais_emptyV9ainfix =amaxV8V4V4iainfix &lt;V10V1Aainfix &lt;V0V10ainfix =amaxV8V4V10iainfix &lt;=V10V0ainfix &lt;=amaxV8V4V0ainfix &gt;=amaxV8V4V1LaminaTuple2V2V3V9LaelementsV5Iainfix &gt;=amaxV8V4V1Iiainfix &lt;V11aprefix -V0Aainfix &lt;aprefix -V1V11ainfix =V8aprefix -V11iainfix &lt;=V11aprefix -V1ainfix &gt;=V8V1ainfix &lt;=V8V0Laminmaxado_moveV2V6ainfix -V3c1FIainfix &gt;=V3c1Iainfix &gt;=V3c1F">
MARCHE Claude's avatar
MARCHE Claude committed
763
      <label
764
       name="expl:VC for negabeta_rec"/>
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MARCHE Claude committed
765 766 767
     </goal>
     <goal
      name="WP_parameter negabeta_rec.4"
MARCHE Claude's avatar
MARCHE Claude committed
768
      locfile="../alphaBeta.mlw"
769
      loclnum="139" loccnumb="7" loccnume="19"
770
      expl="4. precondition"
MARCHE Claude's avatar
MARCHE Claude committed
771
      sum="526d7164221d72a60befa04964995fdb"
MARCHE Claude's avatar
MARCHE Claude committed
772
      proved="true"
Andrei Paskevich's avatar
Andrei Paskevich committed
773
      expanded="false"
774
      shape="CV5aNiltaConsVVainfix &gt;=V3c1Iainfix &gt;=amaxV8V4V1NIiainfix &lt;V9aprefix -V0Aainfix &lt;aprefix -V1V9ainfix =V8aprefix -V9iainfix &lt;=V9aprefix -V1ainfix &gt;=V8V1ainfix &lt;=V8V0Laminmaxado_moveV2V6ainfix -V3c1FIainfix &gt;=V3c1Iainfix &gt;=V3c1F">
MARCHE Claude's avatar
MARCHE Claude committed
775
      <label
776
       name="expl:VC for negabeta_rec"/>
MARCHE Claude's avatar
MARCHE Claude committed
777
      <proof
MARCHE Claude's avatar
MARCHE Claude committed
778
       prover="8"
MARCHE Claude's avatar
MARCHE Claude committed
779 780 781 782
       timelimit="3"
       memlimit="1000"
       obsolete="false"
       archived="false">
783
       <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
784 785 786 787
      </proof>
     </goal>
     <goal
      name="WP_parameter negabeta_rec.5"
MARCHE Claude's avatar
MARCHE Claude committed
788
      locfile="../alphaBeta.mlw"
789
      loclnum="139" loccnumb="7" loccnume="19"
790
      expl="5. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
791
      sum="acc9956fd01105206f0bacf4e92622bb"
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MARCHE Claude committed
792 793
      proved="false"
      expanded="true"
794
      shape="CV5aNiltaConsVViais_emptyV10ainfix =V9V4iainfix &lt;V11V1Aainfix &lt;V0V11ainfix =V9V11iainfix &lt;=V11V0ainfix &lt;=V9V0ainfix &gt;=V9V1LaminaTuple2V2V3V10LaelementsV5Iiais_emptyV12ainfix =V9amaxV8V4iainfix &lt;V13V1Aainfix &lt;amaxamaxV8V4V0V13ainfix =V9V13iainfix &lt;=V13amaxamaxV8V4V0ainfix &lt;=V9amaxamaxV8V4V0ainfix &gt;=V9V1LaminaTuple2V2V3V12LaelementsV7FIainfix &gt;=V3c1Iainfix &gt;=amaxV8V4V1NIiainfix &lt;V14aprefix -V0Aainfix &lt;aprefix -V1V14ainfix =V8aprefix -V14iainfix &lt;=V14aprefix -V1ainfix &gt;=V8V1ainfix &lt;=V8V0Laminmaxado_moveV2V6ainfix -V3c1FIainfix &gt;=V3c1Iainfix &gt;=V3c1F">
MARCHE Claude's avatar
MARCHE Claude committed
795
      <label
796
       name="expl:VC for negabeta_rec"/>
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MARCHE Claude committed
797 798
     </goal>
    </transf>
MARCHE Claude's avatar
MARCHE Claude committed
799 800 801
   </goal>
   <goal
    name="WP_parameter alpha_beta"
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802
    locfile="../alphaBeta.mlw"
803
    loclnum="161" loccnumb="4" loccnume="14"
804
    expl="VC for alpha_beta"
MARCHE Claude's avatar
MARCHE Claude committed
805
    sum="5de2d33dad45be2736115fc2f77016e7"
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806
    proved="true"
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Andrei Paskevich committed
807
    expanded="false"
808
    shape="ainfix =V2aminmaxV0V1Iiainfix &lt;aminmaxV0V1ainfinityAainfix &lt;aprefix -ainfinityaminmaxV0V1ainfix =V2aminmaxV0V1iainfix &lt;=aminmaxV0V1aprefix -ainfinityainfix &lt;=V2aprefix -ainfinityainfix &gt;=V2ainfinityFAainfix &gt;=V1c0Iainfix &gt;=V1c0F">