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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="4">
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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="Alt-Ergo"
  version="0.95.2"/>
 <prover
  id="2"
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  name="CVC3"
  version="2.2"/>
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 <prover
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  id="3"
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  name="CVC3"
  version="2.4.1"/>
 <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="Z3"
  version="2.19"/>
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 <prover
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  id="6"
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  name="Z3"
  version="3.2"/>
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 <file
  name="../euler001.mlw"
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  verified="true"
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  expanded="true">
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  <theory
   name="DivModHints"
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   locfile="../euler001.mlw"
   loclnum="8" loccnumb="7" loccnume="18"
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   verified="true"
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   expanded="true">
   <goal
    name="mod_div_unique"
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    locfile="../euler001.mlw"
    loclnum="13" loccnumb="8" loccnume="22"
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    sum="c8978bd034ef31685cd436249a7f96b5"
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    proved="true"
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    expanded="false"
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    shape="ainfix =V3amodV0V1Aainfix =V2adivV0V1Iainfix &lt;V3V1Aainfix &lt;=c0V3Aainfix =V0ainfix +ainfix *V2V1V3Aainfix &gt;V1c0Aainfix &gt;=V0c0F">
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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="euler001_DivModHints_mod_div_unique_1.v"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="1.06"/>
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    </proof>
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   </goal>
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   <goal
    name="mod_succ_1"
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    locfile="../euler001.mlw"
    loclnum="17" loccnumb="8" loccnume="18"
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    sum="d95d924371149a44d319c8fd0690ef1e"
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    proved="true"
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    expanded="false"
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    shape="ainfix =amodainfix +V0c1V1ainfix +amodV0V1c1INainfix =amodainfix +V0c1V1c0Iainfix &gt;V1c0Aainfix &gt;=V0c0F">
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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="euler001_DivModHints_mod_succ_1_1.v"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="1.15"/>
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    </proof>
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   </goal>
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   <goal
    name="mod_succ_2"
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    locfile="../euler001.mlw"
    loclnum="21" loccnumb="8" loccnume="18"
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    sum="8a784c6c3642290501cd95c7389f2b8f"
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    proved="true"
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    expanded="false"
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    shape="ainfix =amodV0V1ainfix -V1c1Iainfix =amodainfix +V0c1V1c0Iainfix &gt;V1c0Aainfix &gt;=V0c0F">
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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="euler001_DivModHints_mod_succ_2_1.v"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="1.14"/>
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    </proof>
   </goal>
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   <goal
    name="div_succ_1"
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    locfile="../euler001.mlw"
    loclnum="25" loccnumb="8" loccnume="18"
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    sum="08d86a44d1fc01bac0889b3651fa57ac"
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    proved="true"
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    expanded="false"
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    shape="ainfix =adivainfix +V0c1V1ainfix +adivV0V1c1Iainfix =amodainfix +V0c1V1c0Iainfix &gt;V1c0Aainfix &gt;=V0c0F">
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    <proof
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     prover="2"
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     timelimit="30"
     memlimit="1000"
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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="3"
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     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.04"/>
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    </proof>
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   </goal>
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   <goal
    name="div_succ_2"
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    locfile="../euler001.mlw"
    loclnum="29" loccnumb="8" loccnume="18"
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    sum="756ceeee8e2c4c56b44f3bab7f7e1389"
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    proved="true"
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    expanded="false"
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    shape="ainfix =adivainfix +V0c1V1adivV0V1INainfix =amodainfix +V0c1V1c0Iainfix &gt;V1c0Aainfix &gt;=V0c0F">
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    <proof
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     prover="0"
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     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="2.20"/>
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    </proof>
    <proof
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     prover="2"
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     timelimit="30"
     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="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.10"/>
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    </proof>
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    <proof
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     prover="5"
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     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.14"/>
    </proof>
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    <proof
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     prover="6"
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     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.91"/>
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    </proof>
   </goal>
   <goal
    name="mod2_mul2"
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    locfile="../euler001.mlw"
    loclnum="33" loccnumb="8" loccnume="17"
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    sum="6a7e8eb3a0d1ff9caa32c2b09886d7d8"
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    proved="true"
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    expanded="false"
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    shape="ainfix =amodainfix *c2V0c2c0F">
    <proof
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     prover="0"
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     timelimit="5"
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     memlimit="1000"
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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="2"
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     timelimit="5"
     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="5"
     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="5"
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     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.02"/>
    </proof>
    <proof
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     prover="6"
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     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.01"/>
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    </proof>
   </goal>
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   <goal
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    name="mod2_mul2_aux"
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    locfile="../euler001.mlw"
    loclnum="36" loccnumb="8" loccnume="21"
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    sum="5891f8c71ddca269bbca79dff5480da7"
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    proved="true"
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    expanded="false"
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    shape="ainfix =amodainfix *V1ainfix *c2V0c2c0F">
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    <proof
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     prover="0"
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     timelimit="5"
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     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="30"
     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="30"
     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="5"
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     timelimit="30"
     memlimit="1000"
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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="6"
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     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.02"/>
    </proof>
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   </goal>
   <goal
    name="mod2_mul2_aux2"
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    locfile="../euler001.mlw"
    loclnum="39" loccnumb="8" loccnume="22"
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    sum="28e0595d80d6df15bc356a7fc0164c08"
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    proved="true"
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    expanded="false"
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    shape="ainfix =amodainfix +ainfix *V1ainfix *c2V0ainfix *V2ainfix *c2V3c2c0F">
    <proof
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     prover="0"
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     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.03"/>
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    </proof>
    <proof
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     prover="2"
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     timelimit="30"
     memlimit="1000"
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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="3"
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     timelimit="35"
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     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="5"
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     timelimit="30"
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     memlimit="1000"
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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="6"
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     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.07"/>
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    </proof>
   </goal>
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   <goal
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    name="div2_mul2"
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    locfile="../euler001.mlw"
    loclnum="42" loccnumb="8" loccnume="17"
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    sum="a00e38beb2042704e875615bafde0761"
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    proved="true"
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    expanded="false"
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    shape="ainfix =adivainfix *c2V0c2V0F">
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    <proof
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     prover="0"
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     timelimit="5"
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     memlimit="1000"
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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="2"
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     timelimit="5"
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     memlimit="1000"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.05"/>
    </proof>
    <proof
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     prover="3"
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     timelimit="5"
     memlimit="1000"
     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="5"
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     timelimit="5"
     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="6"
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     timelimit="5"
     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="div2_mul2_aux"
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    locfile="../euler001.mlw"
    loclnum="45" loccnumb="8" loccnume="21"
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    sum="90abd643fffae8bdfacfb53d3660d307"
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    proved="true"
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    expanded="false"
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    shape="ainfix =adivainfix *V1ainfix *c2V0c2ainfix *V1V0F">
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    <proof
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     prover="0"
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     timelimit="5"
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     memlimit="1000"
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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="2"
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     timelimit="5"
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     memlimit="1000"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.07"/>
    </proof>
    <proof
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     prover="3"
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     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.08"/>
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    </proof>
    <proof
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     prover="5"
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     timelimit="5"
     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="6"
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     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.01"/>
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    </proof>
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   </goal>
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   <goal
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    name="div2_add"
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    locfile="../euler001.mlw"
    loclnum="48" loccnumb="8" loccnume="16"
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    sum="b6447f23fa84106b51aa77241ab4a279"
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    proved="true"
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    expanded="false"
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    shape="ainfix =adivainfix +V0V1c2ainfix +adivV0c2adivV1c2Iainfix =amodV1c2c0Aainfix =amodV0c2c0F">
MARCHE Claude's avatar
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    <proof
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     prover="2"
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     timelimit="5"
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     memlimit="1000"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.04"/>
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    </proof>
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    <proof
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     prover="3"
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     timelimit="5"
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MARCHE Claude committed
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     memlimit="1000"
     obsolete="false"
     archived="false">
437
     <result status="valid" time="0.04"/>
MARCHE Claude's avatar
MARCHE Claude committed
438 439
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
440
     prover="5"
MARCHE Claude's avatar
MARCHE Claude committed
441 442 443 444
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
445
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
446 447
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
448
     prover="6"
MARCHE Claude's avatar
MARCHE Claude committed
449 450
     timelimit="5"
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
451 452
     obsolete="false"
     archived="false">
453
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
454 455 456 457
    </proof>
   </goal>
   <goal
    name="div2_sub"
458 459
    locfile="../euler001.mlw"
    loclnum="52" loccnumb="8" loccnume="16"
Andrei Paskevich's avatar
Andrei Paskevich committed
460
    sum="bb961a59aa9ee387b950adadc6b077a2"
MARCHE Claude's avatar
MARCHE Claude committed
461
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
462
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
463 464
    shape="ainfix =adivainfix -V0V1c2ainfix -adivV0c2adivV1c2Iainfix =amodV1c2c0Aainfix =amodV0c2c0F">
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
465
     prover="2"
MARCHE Claude's avatar
MARCHE Claude committed
466 467 468 469
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
470
     <result status="valid" time="0.04"/>
MARCHE Claude's avatar
MARCHE Claude committed
471 472
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
473
     prover="3"
MARCHE Claude's avatar
MARCHE Claude committed
474
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
475
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
476 477
     obsolete="false"
     archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
478
     <result status="valid" time="0.04"/>
MARCHE Claude's avatar
MARCHE Claude committed
479 480
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
481
     prover="5"
MARCHE Claude's avatar
MARCHE Claude committed
482 483 484 485
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
486
     <result status="valid" time="0.06"/>
MARCHE Claude's avatar
MARCHE Claude committed
487 488
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
489
     prover="6"
MARCHE Claude's avatar
MARCHE Claude committed
490 491 492 493
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
494
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
495
    </proof>
496
   </goal>
MARCHE Claude's avatar
MARCHE Claude committed
497 498 499
  </theory>
  <theory
   name="TriangularNumbers"
500 501
   locfile="../euler001.mlw"
   loclnum="58" loccnumb="7" loccnume="24"
MARCHE Claude's avatar
MARCHE Claude committed
502 503
   verified="true"
   expanded="true">
504
   <goal
MARCHE Claude's avatar
MARCHE Claude committed
505
    name="tr_mod_2"
506 507
    locfile="../euler001.mlw"
    loclnum="65" loccnumb="8" loccnume="16"
Andrei Paskevich's avatar
Andrei Paskevich committed
508
    sum="d009c147b8522b08838943e94f78084a"
MARCHE Claude's avatar
MARCHE Claude committed
509
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
510
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
511
    shape="ainfix =amodainfix *V0ainfix +V0c1c2c0Iainfix &gt;=V0c0F">
MARCHE Claude's avatar
MARCHE Claude committed
512
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
513
     prover="4"
MARCHE Claude's avatar
MARCHE Claude committed
514
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
515 516 517 518
     memlimit="1000"
     edited="euler001_TriangularNumbers_tr_mod_2_1.v"
     obsolete="false"
     archived="false">
519
     <result status="valid" time="1.07"/>
MARCHE Claude's avatar
MARCHE Claude committed
520 521 522 523
    </proof>
   </goal>
   <goal
    name="tr_repr"
524 525
    locfile="../euler001.mlw"
    loclnum="70" loccnumb="8" loccnume="15"
Andrei Paskevich's avatar
Andrei Paskevich committed
526
    sum="15106465998005ae09e22a161a94977f"
MARCHE Claude's avatar
MARCHE Claude committed
527
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
528
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
529 530 531 532 533 534 535
    shape="ainfix =ainfix *V0ainfix +V0c1ainfix *c2atrV0Iainfix &gt;=V0c0F">
    <proof
     prover="0"
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
536 537 538
     <result status="valid" time="0.01"/>
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
539
     prover="6"
MARCHE Claude's avatar
MARCHE Claude committed
540 541 542 543
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
544
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
545 546 547 548
    </proof>
   </goal>
   <goal
    name="tr_succ"
549 550
    locfile="../euler001.mlw"
    loclnum="73" loccnumb="8" loccnume="15"
Andrei Paskevich's avatar
Andrei Paskevich committed
551
    sum="865890a0046e16348f8303cedc34b23a"
MARCHE Claude's avatar
MARCHE Claude committed
552
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
553
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
554 555
    shape="ainfix =atrainfix +V0c1ainfix +ainfix +atrV0V0c1Iainfix &gt;=V0c0F">
    <proof
556
     prover="0"
MARCHE Claude's avatar
MARCHE Claude committed
557 558
     timelimit="5"
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
559 560
     obsolete="false"
     archived="false">
561
     <result status="valid" time="0.01"/>
MARCHE Claude's avatar
MARCHE Claude committed
562
    </proof>
563
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
564
     prover="2"
565
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
566
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
567 568
     obsolete="false"
     archived="false">
569
     <result status="valid" time="0.02"/>
570 571
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
572
     prover="3"
573
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
574
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
575 576
     obsolete="false"
     archived="false">
577
     <result status="valid" time="0.02"/>
578 579
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
580
     prover="5"
581
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
582
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
583 584
     obsolete="false"
     archived="false">
585
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
586 587
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
588
     prover="6"
MARCHE Claude's avatar
MARCHE Claude committed
589 590 591 592
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
593
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
594 595
    </proof>
   </goal>
MARCHE Claude's avatar
MARCHE Claude committed
596 597 598
  </theory>
  <theory
   name="SumMultiple"
599 600
   locfile="../euler001.mlw"
   loclnum="79" loccnumb="7" loccnume="18"
MARCHE Claude's avatar
MARCHE Claude committed
601 602
   verified="true"
   expanded="true">
603
   <goal
MARCHE Claude's avatar
MARCHE Claude committed
604
    name="mod_15"
605 606
    locfile="../euler001.mlw"
    loclnum="111" loccnumb="8" loccnume="14"
Andrei Paskevich's avatar
Andrei Paskevich committed
607
    sum="9075c2011b00058de37e2e7059292121"
MARCHE Claude's avatar
MARCHE Claude committed
608
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
609
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
610
    shape="ainfix =amodV0c5c0Aainfix =amodV0c3c0qainfix =amodV0c15c0F">
611
    <proof
612
     prover="0"
613 614 615 616
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
617
     <result status="valid" time="0.81"/>
618 619
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
620
     prover="2"
MARCHE Claude's avatar
MARCHE Claude committed
621 622 623 624
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
625
     <result status="valid" time="0.11"/>
MARCHE Claude's avatar
MARCHE Claude committed
626 627
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
628
     prover="3"
MARCHE Claude's avatar
MARCHE Claude committed
629 630
     timelimit="30"
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
631 632
     obsolete="false"
     archived="false">
633
     <result status="valid" time="0.13"/>
MARCHE Claude's avatar
MARCHE Claude committed
634 635 636 637
    </proof>
   </goal>
   <goal
    name="Closed_formula_0"
638 639
    locfile="../euler001.mlw"
    loclnum="115" loccnumb="8" loccnume="24"
Andrei Paskevich's avatar
Andrei Paskevich committed
640
    sum="b361b70e5cbf8e2d76b2f7bbfe86e77f"
MARCHE Claude's avatar
MARCHE Claude committed
641
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
642
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
643 644
    shape="apc0">
    <proof
645
     prover="0"
646
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
647
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
648 649
     obsolete="false"
     archived="false">
650
     <result status="valid" time="0.36"/>
651
    </proof>
MARCHE Claude's avatar
MARCHE Claude committed
652
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
653
     prover="2"
MARCHE Claude's avatar
MARCHE Claude committed
654 655 656 657
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
658
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
659 660
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
661
     prover="3"
MARCHE Claude's avatar
MARCHE Claude committed
662 663 664 665
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
666
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
667 668
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
669
     prover="5"
MARCHE Claude's avatar
MARCHE Claude committed
670 671 672 673
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
674 675 676
     <result status="valid" time="0.02"/>
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
677
     prover="6"
678 679 680 681
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
682
     <result status="valid" time="0.14"/>
MARCHE Claude's avatar
MARCHE Claude committed
683 684 685 686
    </proof>
   </goal>
   <goal
    name="Closed_formula_n"
687 688
    locfile="../euler001.mlw"
    loclnum="117" loccnumb="8" loccnume="24"
Andrei Paskevich's avatar
Andrei Paskevich committed
689
    sum="254d76f488e003c91c7d833011727243"
MARCHE Claude's avatar
MARCHE Claude committed
690
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
691
    expanded="false"
692
    shape="apV0INainfix =amodV0c5c0ANainfix =amodV0c3c0Iapainfix -V0c1Iainfix &gt;V0c0F">
693
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
694
     prover="0"
695
     timelimit="10"
MARCHE Claude's avatar
MARCHE Claude committed
696
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
697 698
     obsolete="false"
     archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
699
     <result status="valid" time="4.68"/>
MARCHE Claude's avatar
MARCHE Claude committed
700 701
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
702
     prover="2"
703
     timelimit="10"
704 705 706 707 708 709
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.12"/>
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
710
     prover="3"
711
     timelimit="10"
MARCHE Claude's avatar
MARCHE Claude committed
712 713 714
     memlimit="1000"
     obsolete="false"
     archived="false">
715
     <result status="valid" time="1.62"/>
716 717 718
    </proof>
   </goal>
   <goal
MARCHE Claude's avatar
MARCHE Claude committed
719
    name="Closed_formula_n_3"
720 721
    locfile="../euler001.mlw"
    loclnum="121" loccnumb="8" loccnume="26"
Andrei Paskevich's avatar
Andrei Paskevich committed
722
    sum="9d5a1f4453fe6480edad3308f0404bf5"
MARCHE Claude's avatar
MARCHE Claude committed
723
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
724
    expanded="false"
725
    shape="apV0INainfix =amodV0c5c0Aainfix =amodV0c3c0Iapainfix -V0c1Iainfix &gt;V0c0F">
726
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
727
     prover="2"
MARCHE Claude's avatar
MARCHE Claude committed
728 729 730 731
     timelimit="10"
     memlimit="1000"
     obsolete="false"
     archived="false">
732
     <result status="valid" time="0.44"/>
MARCHE Claude's avatar
MARCHE Claude committed
733 734 735 736
    </proof>
   </goal>
   <goal
    name="Closed_formula_n_5"
737 738
    locfile="../euler001.mlw"
    loclnum="125" loccnumb="8" loccnume="26"
Andrei Paskevich's avatar
Andrei Paskevich committed
739
    sum="bbce645fb3c88869122baf2e097bcf2d"
MARCHE Claude's avatar
MARCHE Claude committed
740
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
741
    expanded="false"
742
    shape="apV0Iainfix =amodV0c5c0ANainfix =amodV0c3c0Iapainfix -V0c1Iainfix &gt;V0c0F">
MARCHE Claude's avatar
MARCHE Claude committed
743
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
744
     prover="2"
745
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
746 747 748
     memlimit="1000"
     obsolete="false"
     archived="false">
749
     <result status="valid" time="0.22"/>
MARCHE Claude's avatar
MARCHE Claude committed
750 751
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
752
     prover="3"
MARCHE Claude's avatar
MARCHE Claude committed
753 754
     timelimit="5"
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
755 756
     obsolete="false"
     archived="false">
757
     <result status="valid" time="0.37"/>
758
    </proof>
MARCHE Claude's avatar
MARCHE Claude committed
759 760 761
   </goal>
   <goal
    name="Closed_formula_n_15"
762 763
    locfile="../euler001.mlw"
    loclnum="129" loccnumb="8" loccnume="27"
Andrei Paskevich's avatar
Andrei Paskevich committed
764
    sum="48c2a423ea6e87929cb5ee5dc9f1a039"
MARCHE Claude's avatar
MARCHE Claude committed
765
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
766
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
767
    shape="apV0Iainfix =amodV0c5c0Aainfix =amodV0c3c0Iapainfix -V0c1Iainfix &gt;V0c0F">
768
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
769
     prover="2"
770
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
771
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
772 773
     obsolete="false"
     archived="false">
774
     <result status="valid" time="0.19"/>
MARCHE Claude's avatar
MARCHE Claude committed
775
    </proof>
776
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
777
     prover="3"
778
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
779
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
780 781
     obsolete="false"
     archived="false">
782
     <result status="valid" time="0.30"/>
783 784 785
    </proof>
   </goal>
   <goal
MARCHE Claude's avatar
MARCHE Claude committed
786
    name="Closed_formula_ind"
787 788
    locfile="../euler001.mlw"
    loclnum="137" loccnumb="8" loccnume="26"
Andrei Paskevich's avatar
Andrei Paskevich committed
789
    sum="bc6f923fa3def51a3c94714b12a727f6"
MARCHE Claude's avatar
MARCHE Claude committed
790
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
791
    expanded="false"
792
    shape="apV0Iainfix &lt;=c0V0F">
MARCHE Claude's avatar
MARCHE Claude committed
793
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
794
     prover="2"
MARCHE Claude's avatar
MARCHE Claude committed
795
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
796
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
797 798
     obsolete="false"
     archived="false">
799
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
800
    </proof>
801
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
802
     prover="3"
Andrei Paskevich's avatar
Andrei Paskevich committed
803
     timelimit="5"
MARCHE Claude's avatar
MARCHE Claude committed
804
     memlimit="1000"
MARCHE Claude's avatar
MARCHE Claude committed
805 806
     obsolete="false"
     archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
807
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
808 809 810 811
    </proof>
   </goal>
   <goal
    name="div_15"
812 813
    locfile="../euler001.mlw"
    loclnum="148" loccnumb="8" loccnume="14"
Andrei Paskevich's avatar
Andrei Paskevich committed
814
    sum="283ebcba54397b4303881ba01358bb33"
MARCHE Claude's avatar
MARCHE Claude committed
815
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
816
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
817 818
    shape="ainfix &gt;=adivV0c15c0Iainfix &lt;=c0V0F">
    <proof
819
     prover="0"
820 821 822 823 824 825 826
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.01"/>
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
827
     prover="2"
MARCHE Claude's avatar
MARCHE Claude committed
828 829 830 831
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
832
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
833 834
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
835
     prover="3"
MARCHE Claude's avatar
MARCHE Claude committed
836 837 838 839
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
840
     <result status="valid" time="0.01"/>
MARCHE Claude's avatar
MARCHE Claude committed
841 842
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
843
     prover="5"
MARCHE Claude's avatar
MARCHE Claude committed
844 845 846 847
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
848
     <result status="valid" time="0.03"/>
MARCHE Claude's avatar
MARCHE Claude committed
849 850
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
851
     prover="6"
MARCHE Claude's avatar
MARCHE Claude committed
852 853 854 855
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
856
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
857 858 859 860
    </proof>
   </goal>
   <goal
    name="div_5"
861 862
    locfile="../euler001.mlw"
    loclnum="149" loccnumb="8" loccnume="13"
Andrei Paskevich's avatar
Andrei Paskevich committed
863
    sum="48a31fcc19b3924661a02fb7894022a0"
MARCHE Claude's avatar
MARCHE Claude committed
864
    proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
865
    expanded="false"
MARCHE Claude's avatar
MARCHE Claude committed
866 867
    shape="ainfix &gt;=adivV0c5c0Iainfix &lt;=c0V0F">
    <proof
868
     prover="0"
869 870 871 872 873 874 875
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.01"/>
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
876
     prover="2"
MARCHE Claude's avatar
MARCHE Claude committed
877 878 879 880
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
881
     <result status="valid" time="0.02"/>
MARCHE Claude's avatar
MARCHE Claude committed
882 883
    </proof>
    <proof
MARCHE Claude's avatar
MARCHE Claude committed
884
     prover="3"
MARCHE Claude's avatar
MARCHE Claude committed
885 886 887 888
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
<