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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="4">
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 <prover id="0" name="CVC3" version="2.4.1" timelimit="30" memlimit="1000"/>
 <prover id="1" name="Coq" version="8.4pl3" timelimit="5" memlimit="1000"/>
 <prover id="2" name="Z3" version="3.2" timelimit="30" memlimit="1000"/>
 <prover id="3" name="Alt-Ergo" version="0.95.2" timelimit="5"
  memlimit="4000"/>
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 <file name="../euler001.mlw" verified="true"
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  expanded="true">
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  <theory name="DivModHints"
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   verified="true">
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   <goal name="mod_div_unique" sum="c8978bd034ef31685cd436249a7f96b5"
    proved="true"
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    shape="ainfix =V3amodV0V1Aainfix =V2adivV0V1Iainfix &lt;V3V1Aainfix &lt;=c0V3Aainfix =V0ainfix +ainfix *V2V1V3Aainfix &gt;V1c0Aainfix &gt;=V0c0F">
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    <proof prover="1" memlimit="0"
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     edited="euler001_DivModHints_mod_div_unique_1.v">
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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" sum="d95d924371149a44d319c8fd0690ef1e"
    proved="true"
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    shape="ainfix =amodainfix +V0c1V1ainfix +amodV0V1c1INainfix =amodainfix +V0c1V1c0Iainfix &gt;V1c0Aainfix &gt;=V0c0F">
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    <proof prover="1" memlimit="0"
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     edited="euler001_DivModHints_mod_succ_1_1.v">
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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" sum="8a784c6c3642290501cd95c7389f2b8f"
    proved="true"
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    shape="ainfix =amodV0V1ainfix -V1c1Iainfix =amodainfix +V0c1V1c0Iainfix &gt;V1c0Aainfix &gt;=V0c0F">
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    <proof prover="1" memlimit="0"
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     edited="euler001_DivModHints_mod_succ_2_1.v">
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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" sum="08d86a44d1fc01bac0889b3651fa57ac"
    proved="true"
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    shape="ainfix =adivainfix +V0c1V1ainfix +adivV0V1c1Iainfix =amodainfix +V0c1V1c0Iainfix &gt;V1c0Aainfix &gt;=V0c0F">
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    <proof prover="0">
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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" sum="756ceeee8e2c4c56b44f3bab7f7e1389"
    proved="true"
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    shape="ainfix =adivainfix +V0c1V1adivV0V1INainfix =amodainfix +V0c1V1c0Iainfix &gt;V1c0Aainfix &gt;=V0c0F">
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    <proof prover="0">
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     <result status="valid" time="0.10"/>
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    </proof>
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    <proof prover="2">
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     <result status="valid" time="0.91"/>
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    </proof>
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    <proof prover="3" timelimit="30" memlimit="1000">
     <result status="valid" time="2.20"/>
    </proof>
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   </goal>
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   <goal name="mod2_mul2" sum="6a7e8eb3a0d1ff9caa32c2b09886d7d8"
    proved="true"
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    shape="ainfix =amodainfix *c2V0c2c0F">
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    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.01"/>
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    </proof>
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    <proof prover="2" timelimit="5">
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     <result status="valid" time="0.01"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
     <result status="valid" time="0.05"/>
    </proof>
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   </goal>
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   <goal name="mod2_mul2_aux" sum="5891f8c71ddca269bbca79dff5480da7"
    proved="true"
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    shape="ainfix =amodainfix *V1ainfix *c2V0c2c0F">
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    <proof prover="0">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="2">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
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     <result status="valid" time="0.02"/>
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    </proof>
   </goal>
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   <goal name="mod2_mul2_aux2" sum="28e0595d80d6df15bc356a7fc0164c08"
    proved="true"
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    shape="ainfix =amodainfix +ainfix *V1ainfix *c2V0ainfix *V2ainfix *c2V3c2c0F">
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    <proof prover="0" timelimit="35">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="2">
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     <result status="valid" time="0.07"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
     <result status="valid" time="0.03"/>
    </proof>
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   </goal>
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   <goal name="div2_mul2" sum="a00e38beb2042704e875615bafde0761"
    proved="true"
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    shape="ainfix =adivainfix *c2V0c2V0F">
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    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.06"/>
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    </proof>
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    <proof prover="2" timelimit="5">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
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     <result status="valid" time="0.01"/>
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    </proof>
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   </goal>
   <goal name="div2_mul2_aux" sum="90abd643fffae8bdfacfb53d3660d307"
    proved="true"
    shape="ainfix =adivainfix *V1ainfix *c2V0c2ainfix *V1V0F">
    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.08"/>
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    </proof>
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    <proof prover="2" timelimit="5">
     <result status="valid" time="0.01"/>
    </proof>
    <proof prover="3" memlimit="1000">
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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 name="div2_add" sum="b6447f23fa84106b51aa77241ab4a279" proved="true"
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    shape="ainfix =adivainfix +V0V1c2ainfix +adivV0c2adivV1c2Iainfix =amodV1c2c0Aainfix =amodV0c2c0F">
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    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.04"/>
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    </proof>
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    <proof prover="2" timelimit="5">
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     <result status="valid" time="0.02"/>
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    </proof>
   </goal>
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   <goal name="div2_sub" sum="bb961a59aa9ee387b950adadc6b077a2" proved="true"
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    shape="ainfix =adivainfix -V0V1c2ainfix -adivV0c2adivV1c2Iainfix =amodV1c2c0Aainfix =amodV0c2c0F">
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    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.04"/>
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    </proof>
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    <proof prover="2" timelimit="5">
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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>
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  <theory name="TriangularNumbers"
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   verified="true">
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   <goal name="tr_mod_2" sum="d009c147b8522b08838943e94f78084a" proved="true"
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    shape="ainfix =amodainfix *V0ainfix +V0c1c2c0Iainfix &gt;=V0c0F">
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    <proof prover="1"
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     edited="euler001_TriangularNumbers_tr_mod_2_1.v">
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     <result status="valid" time="1.07"/>
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    </proof>
   </goal>
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   <goal name="tr_repr" sum="15106465998005ae09e22a161a94977f" proved="true"
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    shape="ainfix =ainfix *V0ainfix +V0c1ainfix *c2atrV0Iainfix &gt;=V0c0F">
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    <proof prover="2" timelimit="5">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
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     <result status="valid" time="0.01"/>
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    </proof>
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   </goal>
   <goal name="tr_succ" sum="865890a0046e16348f8303cedc34b23a" proved="true"
    shape="ainfix =atrainfix +V0c1ainfix +ainfix +atrV0V0c1Iainfix &gt;=V0c0F">
    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="2" timelimit="5">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
     <result status="valid" time="0.01"/>
    </proof>
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   </goal>
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  </theory>
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  <theory name="SumMultiple"
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   verified="true">
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   <goal name="mod_15" sum="9075c2011b00058de37e2e7059292121" proved="true"
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    shape="ainfix =amodV0c5c0Aainfix =amodV0c3c0qainfix =amodV0c15c0F">
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    <proof prover="0">
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     <result status="valid" time="0.13"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
     <result status="valid" time="0.81"/>
    </proof>
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   </goal>
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   <goal name="Closed_formula_0" sum="b361b70e5cbf8e2d76b2f7bbfe86e77f"
    proved="true"
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    shape="apc0">
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    <proof prover="0">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="2">
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     <result status="valid" time="0.14"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
     <result status="valid" time="0.22"/>
    </proof>
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   </goal>
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   <goal name="Closed_formula_n" sum="254d76f488e003c91c7d833011727243"
    proved="true"
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    shape="apV0INainfix =amodV0c5c0ANainfix =amodV0c3c0Iapainfix -V0c1Iainfix &gt;V0c0F">
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    <proof prover="0" timelimit="10">
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     <result status="valid" time="1.62"/>
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    </proof>
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    <proof prover="3" timelimit="10" memlimit="1000">
     <result status="valid" time="4.68"/>
    </proof>
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   </goal>
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   <goal name="Closed_formula_n_3" sum="9d5a1f4453fe6480edad3308f0404bf5"
    proved="true"
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    shape="apV0INainfix =amodV0c5c0Aainfix =amodV0c3c0Iapainfix -V0c1Iainfix &gt;V0c0F">
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    <proof prover="0" timelimit="10">
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     <result status="valid" time="2.94"/>
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    </proof>
   </goal>
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   <goal name="Closed_formula_n_5" sum="bbce645fb3c88869122baf2e097bcf2d"
    proved="true"
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    shape="apV0Iainfix =amodV0c5c0ANainfix =amodV0c3c0Iapainfix -V0c1Iainfix &gt;V0c0F">
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    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.37"/>
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    </proof>
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   </goal>
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   <goal name="Closed_formula_n_15" sum="48c2a423ea6e87929cb5ee5dc9f1a039"
    proved="true"
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    shape="apV0Iainfix =amodV0c5c0Aainfix =amodV0c3c0Iapainfix -V0c1Iainfix &gt;V0c0F">
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    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.30"/>
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    </proof>
   </goal>
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   <goal name="Closed_formula_ind" sum="bc6f923fa3def51a3c94714b12a727f6"
    proved="true"
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    shape="apV0Iainfix &lt;=c0V0F">
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    <proof prover="0" timelimit="5">
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     <result status="valid" time="0.02"/>
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    </proof>
   </goal>
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   <goal name="div_15" sum="283ebcba54397b4303881ba01358bb33" proved="true"
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    shape="ainfix &gt;=adivV0c15c0Iainfix &lt;=c0V0F">
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    <proof prover="0">
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     <result status="valid" time="0.01"/>
    </proof>
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    <proof prover="2">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
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     <result status="valid" time="0.01"/>
    </proof>
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   </goal>
   <goal name="div_5" sum="48a31fcc19b3924661a02fb7894022a0" proved="true"
    shape="ainfix &gt;=adivV0c5c0Iainfix &lt;=c0V0F">
    <proof prover="0">
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     <result status="valid" time="0.01"/>
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    </proof>
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    <proof prover="2">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
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     <result status="valid" time="0.01"/>
    </proof>
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   </goal>
   <goal name="div_3" sum="2aed5f6570effde5cf940925cca959a3" proved="true"
    shape="ainfix &gt;=adivV0c3c0Iainfix &lt;=c0V0F">
    <proof prover="0">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="2">
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     <result status="valid" time="0.02"/>
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    </proof>
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    <proof prover="3" memlimit="1000">
     <result status="valid" time="0.01"/>
    </proof>
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   </goal>
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   <goal name="Closed_Formula" sum="7d0372d71bdf683508f8539086531ccd"
    proved="true"
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    shape="ainfix =asum_multiple_3_5_ltainfix +V0c1aclosed_formulaV0Iainfix &lt;=c0V0F">
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    <proof prover="1" timelimit="30"
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     edited="euler001_SumMultiple_Closed_Formula_1.v">
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     <result status="valid" time="1.14"/>
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    </proof>
   </goal>
  </theory>
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  <theory name="Euler001"
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   verified="true">
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   <goal name="WP_parameter solve" expl="VC for solve"
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    sum="200296912b5b99c365d044e031f76312" proved="true"
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    shape="ainfix =adivainfix -ainfix +ainfix *ainfix *c3V1ainfix +V1c1ainfix *ainfix *c5V2ainfix +V2c1ainfix *ainfix *c15V3ainfix +V3c1c2asum_multiple_3_5_ltV0Ladivainfix -V0c1c15Ladivainfix -V0c1c5Ladivainfix -V0c1c3Iainfix &gt;=V0c1F">
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    <label name="expl:VC for solve"/>
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    <proof prover="0">
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     <result status="valid" time="0.06"/>
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    </proof>
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    <proof prover="2">
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     <result status="valid" time="0.02"/>
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    </proof>
   </goal>
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   <goal name="WP_parameter run" expl="VC for run"
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    sum="284d1b9e6d12920da46e6f6c54a8037f" proved="true"
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    shape="ainfix &gt;=c1000c1">
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    <label name="expl:VC for run"/>
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    <proof prover="3" memlimit="1000">
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     <result status="valid" time="0.01"/>
    </proof>
   </goal>
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   <goal name="WP_parameter bench" expl="VC for bench"
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    sum="5dada1ffeee7c305d1541d7f4093abcd" proved="true"
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    shape="t">
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    <label name="expl:VC for bench"/>
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    <proof prover="3">
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     <result status="valid" time="0.01"/>
    </proof>
   </goal>
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   <goal name="WP_parameter go" expl="VC for go"
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    sum="0ac8af78cda25414bc3f614bbe49b1cf" proved="true"
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    shape="ainfix =V12ainfix +V0c1Iainfix =V15aConsareverseV11V3Aainfix =V12ainfix +V0c1Aainfix =V14aNilAainfix =V13c0FIainfix =V11aConsaPrCharamk charc32V9Aainfix =V10ainfix +V8c1FAainfix &lt;=c32c255Aainfix &lt;=c0c32Iainfix =V9aConsaPrCharamk charc58V7Aainfix =V8ainfix +V6c1FAainfix &lt;=c58c255Aainfix &lt;=c0c58Iainfix =V7aConsaPrCharamk charc79V5Aainfix =V6ainfix +V4c1FAainfix &lt;=c79c255Aainfix &lt;=c0c79Iainfix =V5aConsaPrCharamk charc71V2Aainfix =V4ainfix +V1c1FAainfix &lt;=c71c255Aainfix &lt;=c0c71F">
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    <label name="expl:VC for go"/>
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    <proof prover="3" memlimit="1000">
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     <result status="valid" time="0.02"/>
    </proof>
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   </goal>
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  </theory>
 </file>
</why3session>