why3session.xml 13.8 KB
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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"
  version="0.94"/>
 <prover
  id="1"
  name="Alt-Ergo"
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  version="0.95"/>
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 <prover
  id="2"
  name="CVC3"
  version="2.2"/>
 <prover
  id="3"
  name="CVC3"
  version="2.4.1"/>
 <prover
  id="4"
  name="Z3"
  version="2.19"/>
 <prover
  id="5"
  name="Z3"
  version="3.2"/>
 <file
  name="../triangle_inequality.why"
  verified="true"
  expanded="true">
  <theory
   name="CauchySchwarzInequality"
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   locfile="../triangle_inequality.why"
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   loclnum="16" loccnumb="7" loccnume="30"
   verified="true"
   expanded="true">
   <goal
    name="norm2_pos"
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    locfile="../triangle_inequality.why"
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    loclnum="30" loccnumb="8" loccnume="17"
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    sum="76cb925d3fd001024ee55e3bd1635962"
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    proved="true"
    expanded="false"
    shape="ainfix &gt;=anorm2V0V1c0.0F">
    <proof
     prover="4"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.02"/>
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    </proof>
    <proof
     prover="5"
     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
    name="p_expr"
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    locfile="../triangle_inequality.why"
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    loclnum="43" loccnumb="8" loccnume="14"
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    sum="42b2c0ff1ca0582f8cf5fd1cd988d1f8"
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    proved="true"
    expanded="false"
    shape="ainfix =apV0V1V2V3V4anorm2ainfix +V0ainfix *V4V2ainfix +V1ainfix *V4V3F">
    <proof
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     prover="2"
     timelimit="30"
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     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"
     timelimit="3"
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     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.00"/>
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    </proof>
    <proof
     prover="5"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="p_pos"
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    locfile="../triangle_inequality.why"
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    loclnum="47" loccnumb="8" loccnume="13"
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    sum="1363c1076109399bb5a7b0bdbad42ba9"
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    proved="true"
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    expanded="true"
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    shape="ainfix &gt;=apV0V1V2V3V4c0.0F">
    <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="0.01"/>
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    </proof>
   </goal>
   <goal
    name="mul_div_simpl"
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    locfile="../triangle_inequality.why"
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    loclnum="50" loccnumb="8" loccnume="21"
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    sum="e714c31ede6847ce2b47da9a53d97eb8"
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    proved="true"
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    expanded="true"
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    shape="ainfix =ainfix *ainfix /V0V1V1V0Iainfix =V1c0.0NF">
    <proof
     prover="4"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.02"/>
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    </proof>
    <proof
     prover="5"
     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
    name="p_val_part"
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    locfile="../triangle_inequality.why"
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    loclnum="53" loccnumb="8" loccnume="18"
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    sum="708a8affda43419fe72638239e14ff90"
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    proved="true"
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    expanded="true"
    shape="ainfix =apV0V1V2V3aprefix -ainfix /adotV0V1V2V3anorm2V2V3ainfix -anorm2V0V1ainfix /asqradotV0V1V2V3anorm2V2V3Iainfix &gt;anorm2V2V3c0.0F">
    <proof
     prover="0"
     timelimit="5"
     memlimit="4000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.98"/>
    </proof>
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    <proof
     prover="1"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.72"/>
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    </proof>
   </goal>
   <goal
    name="p_val_part_pos"
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    locfile="../triangle_inequality.why"
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    loclnum="59" loccnumb="8" loccnume="22"
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    sum="902cc117d299a2301fdfce3240def934"
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    proved="true"
    expanded="false"
    shape="ainfix &gt;=ainfix -anorm2V0V1ainfix /asqradotV0V1V2V3anorm2V2V3c0.0Iainfix &gt;anorm2V2V3c0.0F">
    <proof
     prover="0"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.05"/>
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    </proof>
    <proof
     prover="1"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.06"/>
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    </proof>
   </goal>
   <goal
    name="p_val_part_pos_aux"
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    locfile="../triangle_inequality.why"
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    loclnum="64" loccnumb="8" loccnume="26"
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    sum="9bce2e4aa7069267c00b2837ee577532"
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    proved="true"
    expanded="false"
    shape="ainfix &gt;=ainfix *anorm2V2V3apV0V1V2V3ainfix /aprefix -adotV0V1V2V3anorm2V2V3c0.0Iainfix &gt;anorm2V2V3c0.0F">
    <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>
    <proof
     prover="1"
     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
    name="CauchySchwarz_aux_non_null"
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    locfile="../triangle_inequality.why"
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    loclnum="69" loccnumb="8" loccnume="34"
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    sum="3bad2dbfcdca2527d6a6f5c32c775c7a"
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    proved="true"
    expanded="false"
    shape="ainfix &lt;=asqradotV0V1V2V3ainfix *anorm2V0V1anorm2V2V3Iainfix &gt;anorm2V2V3c0.0F">
    <proof
     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="1.39"/>
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    </proof>
    <proof
     prover="1"
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.80"/>
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    </proof>
   </goal>
   <goal
    name="norm_null"
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    locfile="../triangle_inequality.why"
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    loclnum="74" loccnumb="8" loccnume="17"
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    sum="6dc7c1095220ea980dbca0d8aa628587"
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    proved="true"
    expanded="false"
    shape="ainfix =V1c0.0Oainfix =V0c0.0Iainfix =anorm2V0V1c0.0F">
    <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>
    <proof
     prover="1"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.06"/>
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    </proof>
   </goal>
   <goal
    name="CauchySchwarz_aux_null"
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    locfile="../triangle_inequality.why"
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    loclnum="78" loccnumb="8" loccnume="30"
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    sum="5b8ea3e101c1379e7ad441c17ed8d18a"
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    proved="true"
    expanded="false"
    shape="ainfix &lt;=asqradotV0V1V2V3ainfix *anorm2V0V1anorm2V2V3Iainfix =anorm2V2V3c0.0F">
    <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="0.06"/>
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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="0.06"/>
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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
     prover="3"
     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">
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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="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.28"/>
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    </proof>
   </goal>
   <goal
    name="CauchySchwarz_aux"
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    locfile="../triangle_inequality.why"
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    loclnum="83" loccnumb="8" loccnume="25"
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    sum="f98aebd8656d073c9b0672c270bea7ac"
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    proved="true"
    expanded="false"
    shape="ainfix &lt;=asqradotV0V1V2V3ainfix *anorm2V0V1anorm2V2V3F">
    <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="0.00"/>
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    </proof>
    <proof
     prover="3"
     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="0.16"/>
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    </proof>
   </goal>
   <goal
    name="norm_pos"
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    locfile="../triangle_inequality.why"
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    loclnum="91" loccnumb="8" loccnume="16"
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    sum="5ac098a76c92a77b81414fda62d58628"
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    proved="true"
    expanded="false"
    shape="ainfix &gt;=anormV0V1c0.0F">
    <proof
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     prover="0"
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     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
407
     <result status="valid" time="0.01"/>
408 409
    </proof>
    <proof
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     prover="1"
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     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
415
     <result status="valid" time="0.02"/>
416 417
    </proof>
    <proof
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     prover="2"
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     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
423
     <result status="valid" time="0.01"/>
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    </proof>
    <proof
     prover="3"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
431
     <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">
439
     <result status="valid" time="0.02"/>
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    </proof>
    <proof
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     prover="5"
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     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
447
     <result status="valid" time="0.02"/>
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    </proof>
   </goal>
   <goal
    name="sqr_le_sqrt"
452
    locfile="../triangle_inequality.why"
453
    loclnum="95" loccnumb="8" loccnume="19"
454
    sum="c115b360b8b52f71b86301cc73f27275"
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    proved="true"
    expanded="false"
    shape="ainfix &lt;=V0asqrtV1Iainfix &lt;=asqrV0V1Aainfix &lt;=c0.0asqrV0Aainfix &lt;=c0.0V0F">
    <proof
     prover="0"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.03"/>
    </proof>
    <proof
     prover="1"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
472
     <result status="valid" time="0.03"/>
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    </proof>
   </goal>
   <goal
    name="CauchySchwarz"
477
    locfile="../triangle_inequality.why"
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    loclnum="99" loccnumb="8" loccnume="21"
479
    sum="0e271f0352943fccc6eff4dbe26df0ac"
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    proved="true"
    expanded="false"
    shape="ainfix &lt;=adotV0V1V2V3ainfix *anormV0V1anormV2V3F">
    <proof
     prover="0"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.20"/>
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    </proof>
    <proof
     prover="1"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.19"/>
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    </proof>
   </goal>
  </theory>
  <theory
   name="TriangleInequality"
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   locfile="../triangle_inequality.why"
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   loclnum="106" loccnumb="7" loccnume="25"
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   verified="true"
   expanded="true">
   <goal
    name="triangle_aux"
509
    locfile="../triangle_inequality.why"
510
    loclnum="118" loccnumb="8" loccnume="20"
511
    sum="42170f0ebaf7243bb1407f07705781ed"
512 513 514 515 516 517 518 519 520
    proved="true"
    expanded="false"
    shape="ainfix &lt;=anorm2ainfix +V0V2ainfix +V1V3asqrainfix +anormV0V1anormV2V3F">
    <proof
     prover="4"
     timelimit="30"
     memlimit="1000"
     obsolete="false"
     archived="false">
521
     <result status="valid" time="0.01"/>
522 523 524 525
    </proof>
   </goal>
   <goal
    name="sqr_sqrt_le"
526
    locfile="../triangle_inequality.why"
527
    loclnum="123" loccnumb="8" loccnume="19"
528
    sum="7e3031e53ff2f0f33205257de5642a86"
529 530 531 532
    proved="true"
    expanded="false"
    shape="ainfix &lt;=asqrtV0V1Iainfix &lt;=V0asqrV1Aainfix &lt;=c0.0V0Aainfix &lt;=c0.0V1F">
    <proof
533
     prover="0"
534 535 536 537
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
538
     <result status="valid" time="0.03"/>
539 540
    </proof>
    <proof
541
     prover="1"
542 543 544 545
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
546
     <result status="valid" time="0.02"/>
547 548
    </proof>
    <proof
549
     prover="2"
550 551 552 553
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
554
     <result status="valid" time="0.01"/>
555 556
    </proof>
    <proof
557
     prover="3"
558 559 560 561
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
562
     <result status="valid" time="0.01"/>
563 564 565 566
    </proof>
   </goal>
   <goal
    name="triangle"
567
    locfile="../triangle_inequality.why"
568
    loclnum="126" loccnumb="8" loccnume="16"
569
    sum="e59da4de6697d01b11dc130a93604b8e"
570 571 572 573 574 575 576 577 578
    proved="true"
    expanded="false"
    shape="ainfix &lt;=anormainfix +V0V2ainfix +V1V3ainfix +anormV0V1anormV2V3F">
    <proof
     prover="0"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
579
     <result status="valid" time="0.10"/>
580 581 582 583 584 585 586
    </proof>
    <proof
     prover="1"
     timelimit="3"
     memlimit="1000"
     obsolete="false"
     archived="false">
587
     <result status="valid" time="0.09"/>
588 589 590 591 592
    </proof>
   </goal>
  </theory>
 </file>
</why3session>