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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session SYSTEM "/home/andrei/prj/why-git/share/why3session.dtd">
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<why3session
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 name="examples/programs/bellman_ford/why3session.xml" shape_version="2">
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 <prover
  id="0"
  name="Alt-Ergo"
  version="0.94"/>
 <prover
  id="1"
  name="CVC3"
  version="2.4.1"/>
 <prover
  id="2"
  name="Coq"
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  version="8.3pl4"/>
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 <prover
  id="3"
  name="Z3"
  version="3.2"/>
 <file
  name="../bellman_ford.mlw"
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  verified="true"
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  expanded="true">
  <theory
   name="Graph"
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   locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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   loclnum="7" loccnumb="7" loccnume="12"
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   verified="true"
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   expanded="true">
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   <goal
    name="vertices_cardinal_pos"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="30" loccnumb="8" loccnume="29"
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    sum="db43f37df5d05a6ae609d7c6068de11d"
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    proved="true"
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    expanded="true"
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    shape="ainfix &gt;acardinalaverticesc0">
    <proof
     prover="0"
     timelimit="10"
     memlimit="0"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.01"/>
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    </proof>
   </goal>
   <goal
    name="path_in_vertices"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="36" loccnumb="8" loccnume="24"
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    sum="12c1fb1d3c97737552bcc8f184602a39"
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    proved="true"
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    expanded="true"
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    shape="amemV1averticesIapathV0V2V1IamemV0averticesF">
    <proof
     prover="2"
     timelimit="10"
     memlimit="0"
     edited="bf_Graph_path_in_vertices_2.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.51"/>
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    </proof>
   </goal>
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   <goal
    name="long_path_decomposition_pigeon1"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="60" loccnumb="8" loccnume="39"
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    sum="3edb2ab0e22060f43004f6452759b727"
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    proved="true"
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    expanded="true"
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    shape="amemV2averticesIamemV2aConsV1V0FIainfix =V0aNilNIapathasV0V1F">
    <proof
     prover="2"
     timelimit="8"
     memlimit="1000"
     edited="bellman_ford_Graph_long_path_decomposition_pigeon1_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.32"/>
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    </proof>
   </goal>
   <goal
    name="long_path_decomposition_pigeon2"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="65" loccnumb="8" loccnume="39"
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    sum="8612670dfa4c5f457fc2a2310ffec83b"
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    proved="true"
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    expanded="true"
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    shape="ainfix =aConsV1V0ainfix ++V3aConsV2ainfix ++V4aConsV2V5EIainfix &gt;alengthaConsV1V0acardinalaverticesIamemV6averticesIamemV6aConsV1V0FF">
    <proof
     prover="0"
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.06"/>
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    </proof>
   </goal>
   <goal
    name="long_path_decomposition_pigeon3"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="72" loccnumb="8" loccnume="39"
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    sum="c087abee97d651a72bc4b7ff8b78719f"
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    proved="true"
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    expanded="true"
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    shape="ainfix =V0ainfix ++V3aConsV2ainfix ++V4aConsV2V5EOainfix =V0ainfix ++V6aConsV1V7EIainfix =aConsV1V0ainfix ++V9aConsV8ainfix ++V10aConsV8V11EF">
    <proof
     prover="2"
     timelimit="7"
     memlimit="1000"
     edited="bellman_ford_Graph_long_path_decomposition_pigeon3_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="2.03"/>
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    </proof>
   </goal>
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   <goal
    name="long_path_decomposition"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="80" loccnumb="8" loccnume="31"
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    sum="b4288a9d762c0655618d52d960edda9b"
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    proved="true"
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    expanded="true"
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    shape="ainfix =V0ainfix ++V3aConsV2ainfix ++V4aConsV2V5EOainfix =V0ainfix ++V6aConsV1V7EIainfix &gt;=alengthV0acardinalaverticesIapathasV0V1F">
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    <proof
     prover="2"
     timelimit="5"
     memlimit="1000"
     edited="bellman_ford_Graph_long_path_decomposition_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="0.95"/>
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    </proof>
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   </goal>
   <goal
    name="simple_path"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="87" loccnumb="8" loccnume="19"
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    sum="0afec8d07a229181e66ab00359aedc8c"
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    proved="true"
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    expanded="true"
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    shape="ainfix &lt;alengthV2acardinalaverticesAapathasV2V0EIapathasV1V0F">
    <proof
     prover="2"
     timelimit="10"
     memlimit="0"
     edited="bf_Graph_simple_path_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.48"/>
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    </proof>
   </goal>
   <goal
    name="key_lemma_1"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="108" loccnumb="8" loccnume="19"
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    sum="289818214cd3187dfac6a5450e21a92d"
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    proved="true"
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    expanded="true"
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    shape="anegative_cycleV2EIainfix &lt;apath_weightV3V0V1AapathasV3V0EIainfix &gt;=apath_weightV4V0V1Iainfix &lt;alengthV4acardinalaverticesIapathasV4V0FF">
    <proof
     prover="2"
     timelimit="10"
     memlimit="0"
     edited="bf_Graph_key_lemma_1_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="3.19"/>
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    </proof>
   </goal>
  </theory>
  <theory
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   name="BellmanFord"
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   locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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   loclnum="120" loccnumb="7" loccnume="18"
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   verified="true"
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   expanded="true">
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   <goal
    name="key_lemma_2"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="172" loccnumb="8" loccnume="19"
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    sum="18ace61e702a241b52207ae412a37346"
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    proved="true"
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    expanded="true"
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    shape="anegative_cycleV1NFIainv2V0aedgesIainv1V0acardinalaverticesaemptyF">
    <proof
     prover="2"
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     timelimit="60"
     memlimit="1000"
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     edited="bf_WP_BellmanFord_key_lemma_2_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="21.18"/>
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    </proof>
   </goal>
   <goal
    name="WP_parameter relax"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="176" loccnumb="6" loccnume="11"
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    expl="parameter relax"
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    sum="be6a123356b66119ab61e6bc12723911"
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    proved="true"
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    expanded="true"
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    shape="iCagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V5aweightV0V1V6ainv1V7V2aaddaTuple2V0V1V3Iainfix =V7asetV4V1CagetV4V0aInfiniteaInfiniteaFiniteVaFiniteainfix +V8aweightV0V1Fainv1V4V2aaddaTuple2V0V1V3Iainv1V4V2V3AamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix &lt;=c1V2FF">
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    <label
     name="expl:parameter relax"/>
    <transf
     name="split_goal"
     proved="true"
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     expanded="true">
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     <goal
      name="WP_parameter relax.1"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="176" loccnumb="6" loccnume="11"
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      expl="postcondition"
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      sum="41be2336f5574c85c3532db650de0f2b"
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      proved="true"
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      expanded="true"
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      shape="ainv1V5V2aaddaTuple2V0V1V3Iainfix =V5asetV4V1CagetV4V0aInfiniteaInfiniteaFiniteVaFiniteainfix +V6aweightV0V1FICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V7aweightV0V1V8Iainv1V4V2V3AamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix &lt;=c1V2FF">
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      <label
       name="expl:parameter relax"/>
      <transf
       name="inline_goal"
       proved="true"
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       expanded="true">
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       <goal
        name="WP_parameter relax.1.1"
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        locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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        loclnum="176" loccnumb="6" loccnume="11"
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        expl="postcondition"
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        sum="21e00c28ac76e7aeab141d9d4fde6444"
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        proved="true"
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        expanded="true"
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        shape="Camixfix []V5V6aFiniteVainfix &gt;=ainfix +apath_weightV9V8aweightV8V6V7IamemaTuple2V8V6aaddaTuple2V0V1V3Iainfix &lt;alengthV9V2IapathasV9V8FAainfix &gt;=apath_weightV10V6V7Iainfix &lt;alengthV10V2IapathasV10V6FAainfix =apath_weightV11V6V7AapathasV11V6EaInfiniteainfix &gt;=alengthV13V2IapathasV13V12FIamemaTuple2V12V6aaddaTuple2V0V1V3FAainfix &gt;=alengthV14V2IapathasV14V6FIamemV6averticesFIainfix =V5asetV4V1CagetV4V0aInfiniteaInfiniteaFiniteVaFiniteainfix +V15aweightV0V1FICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V16aweightV0V1V17ICamixfix []V4V18aFiniteVainfix &gt;=ainfix +apath_weightV21V20aweightV20V18V19IamemaTuple2V20V18V3Iainfix &lt;alengthV21V2IapathasV21V20FAainfix &gt;=apath_weightV22V18V19Iainfix &lt;alengthV22V2IapathasV22V18FAainfix =apath_weightV23V18V19AapathasV23V18EaInfiniteainfix &gt;=alengthV25V2IapathasV25V24FIamemaTuple2V24V18V3FAainfix &gt;=alengthV26V2IapathasV26V18FIamemV18averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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        <label
         name="expl:parameter relax"/>
        <transf
         name="split_goal"
         proved="true"
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         expanded="true">
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         <goal
          name="WP_parameter relax.1.1.1"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="0f69e692283a18448423df01b6bc47b6"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V5V6aFiniteVainfix =apath_weightV8V6V7AapathasV8V6EaInfinitetIamemV6averticesFIainfix =V5asetV4V1CagetV4V0aInfiniteaInfiniteaFiniteVaFiniteainfix +V9aweightV0V1FICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V10aweightV0V1V11ICamixfix []V4V12aFiniteVainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V3Iainfix &lt;alengthV15V2IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V2IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaInfiniteainfix &gt;=alengthV19V2IapathasV19V18FIamemaTuple2V18V12V3FAainfix &gt;=alengthV20V2IapathasV20V12FIamemV12averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="2"
           timelimit="10"
           memlimit="0"
           edited="bf_WP_BellmanFord_WP_parameter_relax_7.v"
           obsolete="false"
           archived="false">
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           <result status="valid" time="1.70"/>
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          </proof>
         </goal>
         <goal
          name="WP_parameter relax.1.1.2"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="2a4b27ec16f341b3678adf7a66fc297d"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V5V6aFiniteVainfix &gt;=apath_weightV8V6V7Iainfix &lt;alengthV8V2IapathasV8V6FaInfinitetIamemV6averticesFIainfix =V5asetV4V1CagetV4V0aInfiniteaInfiniteaFiniteVaFiniteainfix +V9aweightV0V1FICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V10aweightV0V1V11ICamixfix []V4V12aFiniteVainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V3Iainfix &lt;alengthV15V2IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V2IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaInfiniteainfix &gt;=alengthV19V2IapathasV19V18FIamemaTuple2V18V12V3FAainfix &gt;=alengthV20V2IapathasV20V12FIamemV12averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.22"/>
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          </proof>
          <proof
           prover="3"
           timelimit="28"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="1.12"/>
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          </proof>
         </goal>
         <goal
          name="WP_parameter relax.1.1.3"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="5e6c8219dc633a507f8e13ef35b4a9ab"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V5V6aFiniteVainfix &gt;=ainfix +apath_weightV9V8aweightV8V6V7IamemaTuple2V8V6aaddaTuple2V0V1V3Iainfix &lt;alengthV9V2IapathasV9V8FaInfinitetIamemV6averticesFIainfix =V5asetV4V1CagetV4V0aInfiniteaInfiniteaFiniteVaFiniteainfix +V10aweightV0V1FICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V11aweightV0V1V12ICamixfix []V4V13aFiniteVainfix &gt;=ainfix +apath_weightV16V15aweightV15V13V14IamemaTuple2V15V13V3Iainfix &lt;alengthV16V2IapathasV16V15FAainfix &gt;=apath_weightV17V13V14Iainfix &lt;alengthV17V2IapathasV17V13FAainfix =apath_weightV18V13V14AapathasV18V13EaInfiniteainfix &gt;=alengthV20V2IapathasV20V19FIamemaTuple2V19V13V3FAainfix &gt;=alengthV21V2IapathasV21V13FIamemV13averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.71"/>
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          </proof>
         </goal>
         <goal
          name="WP_parameter relax.1.1.4"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="b66a8805f816b5f99b8a00823b9f8903"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V5V6aFiniteVtaInfiniteainfix &gt;=alengthV8V2IapathasV8V6FIamemV6averticesFIainfix =V5asetV4V1CagetV4V0aInfiniteaInfiniteaFiniteVaFiniteainfix +V9aweightV0V1FICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V10aweightV0V1V11ICamixfix []V4V12aFiniteVainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V3Iainfix &lt;alengthV15V2IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V2IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaInfiniteainfix &gt;=alengthV19V2IapathasV19V18FIamemaTuple2V18V12V3FAainfix &gt;=alengthV20V2IapathasV20V12FIamemV12averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="0"
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           timelimit="18"
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           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="6.89"/>
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          </proof>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.30"/>
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          </proof>
          <proof
           prover="3"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.85"/>
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          </proof>
         </goal>
         <goal
          name="WP_parameter relax.1.1.5"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="7ace30d2507f4097b50af8741284dfa4"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V5V6aFiniteVtaInfiniteainfix &gt;=alengthV9V2IapathasV9V8FIamemaTuple2V8V6aaddaTuple2V0V1V3FIamemV6averticesFIainfix =V5asetV4V1CagetV4V0aInfiniteaInfiniteaFiniteVaFiniteainfix +V10aweightV0V1FICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V11aweightV0V1V12ICamixfix []V4V13aFiniteVainfix &gt;=ainfix +apath_weightV16V15aweightV15V13V14IamemaTuple2V15V13V3Iainfix &lt;alengthV16V2IapathasV16V15FAainfix &gt;=apath_weightV17V13V14Iainfix &lt;alengthV17V2IapathasV17V13FAainfix =apath_weightV18V13V14AapathasV18V13EaInfiniteainfix &gt;=alengthV20V2IapathasV20V19FIamemaTuple2V19V13V3FAainfix &gt;=alengthV21V2IapathasV21V13FIamemV13averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.75"/>
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          </proof>
         </goal>
        </transf>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter relax.2"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="176" loccnumb="6" loccnume="11"
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      expl="postcondition"
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      sum="7f1b47c4e83c7ad7a6e975c6ffe94ea0"
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      proved="true"
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      expanded="true"
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      shape="ainv1V4V2aaddaTuple2V0V1V3ICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V5aweightV0V1V6NIainv1V4V2V3AamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix &lt;=c1V2FF">
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      <label
       name="expl:parameter relax"/>
      <transf
       name="inline_goal"
       proved="true"
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       expanded="true">
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       <goal
        name="WP_parameter relax.2.1"
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        locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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        loclnum="176" loccnumb="6" loccnume="11"
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        expl="postcondition"
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        sum="1e4cdb1b5558b5c1138c9e279b881924"
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        proved="true"
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        expanded="true"
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        shape="Camixfix []V4V5aFiniteVainfix &gt;=ainfix +apath_weightV8V7aweightV7V5V6IamemaTuple2V7V5aaddaTuple2V0V1V3Iainfix &lt;alengthV8V2IapathasV8V7FAainfix &gt;=apath_weightV9V5V6Iainfix &lt;alengthV9V2IapathasV9V5FAainfix =apath_weightV10V5V6AapathasV10V5EaInfiniteainfix &gt;=alengthV12V2IapathasV12V11FIamemaTuple2V11V5aaddaTuple2V0V1V3FAainfix &gt;=alengthV13V2IapathasV13V5FIamemV5averticesFICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V14aweightV0V1V15NICamixfix []V4V16aFiniteVainfix &gt;=ainfix +apath_weightV19V18aweightV18V16V17IamemaTuple2V18V16V3Iainfix &lt;alengthV19V2IapathasV19V18FAainfix &gt;=apath_weightV20V16V17Iainfix &lt;alengthV20V2IapathasV20V16FAainfix =apath_weightV21V16V17AapathasV21V16EaInfiniteainfix &gt;=alengthV23V2IapathasV23V22FIamemaTuple2V22V16V3FAainfix &gt;=alengthV24V2IapathasV24V16FIamemV16averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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        <label
         name="expl:parameter relax"/>
        <transf
         name="split_goal"
         proved="true"
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         expanded="true">
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         <goal
          name="WP_parameter relax.2.1.1"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="fa4245d89ae475b44dba18154cff6dfa"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V4V5aFiniteVainfix =apath_weightV7V5V6AapathasV7V5EaInfinitetIamemV5averticesFICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V8aweightV0V1V9NICamixfix []V4V10aFiniteVainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V3Iainfix &lt;alengthV13V2IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V2IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaInfiniteainfix &gt;=alengthV17V2IapathasV17V16FIamemaTuple2V16V10V3FAainfix &gt;=alengthV18V2IapathasV18V10FIamemV10averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="0"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.51"/>
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          </proof>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.12"/>
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          </proof>
          <proof
           prover="3"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.08"/>
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          </proof>
         </goal>
         <goal
          name="WP_parameter relax.2.1.2"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="cef21940b1429cda4dc2b6774e7fc49c"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V4V5aFiniteVainfix &gt;=apath_weightV7V5V6Iainfix &lt;alengthV7V2IapathasV7V5FaInfinitetIamemV5averticesFICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V8aweightV0V1V9NICamixfix []V4V10aFiniteVainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V3Iainfix &lt;alengthV13V2IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V2IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaInfiniteainfix &gt;=alengthV17V2IapathasV17V16FIamemaTuple2V16V10V3FAainfix &gt;=alengthV18V2IapathasV18V10FIamemV10averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="0"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="3.07"/>
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          </proof>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.28"/>
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          </proof>
          <proof
           prover="3"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.14"/>
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          </proof>
         </goal>
         <goal
          name="WP_parameter relax.2.1.3"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="1ad66e833337e3e7d6eba84fef97d617"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V4V5aFiniteVainfix &gt;=ainfix +apath_weightV8V7aweightV7V5V6IamemaTuple2V7V5aaddaTuple2V0V1V3Iainfix &lt;alengthV8V2IapathasV8V7FaInfinitetIamemV5averticesFICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V9aweightV0V1V10NICamixfix []V4V11aFiniteVainfix &gt;=ainfix +apath_weightV14V13aweightV13V11V12IamemaTuple2V13V11V3Iainfix &lt;alengthV14V2IapathasV14V13FAainfix &gt;=apath_weightV15V11V12Iainfix &lt;alengthV15V2IapathasV15V11FAainfix =apath_weightV16V11V12AapathasV16V11EaInfiniteainfix &gt;=alengthV18V2IapathasV18V17FIamemaTuple2V17V11V3FAainfix &gt;=alengthV19V2IapathasV19V11FIamemV11averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.44"/>
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          </proof>
          <proof
           prover="3"
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           timelimit="40"
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           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.47"/>
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          </proof>
         </goal>
         <goal
          name="WP_parameter relax.2.1.4"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="058d544a605900dc72cfbfd6f79adf9c"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V4V5aFiniteVtaInfiniteainfix &gt;=alengthV7V2IapathasV7V5FIamemV5averticesFICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V8aweightV0V1V9NICamixfix []V4V10aFiniteVainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V3Iainfix &lt;alengthV13V2IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V2IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaInfiniteainfix &gt;=alengthV17V2IapathasV17V16FIamemaTuple2V16V10V3FAainfix &gt;=alengthV18V2IapathasV18V10FIamemV10averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="0"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="4.51"/>
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          </proof>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.08"/>
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          </proof>
          <proof
           prover="3"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.18"/>
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          </proof>
         </goal>
         <goal
          name="WP_parameter relax.2.1.5"
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          locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="postcondition"
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          sum="dc47029f01e46c0c5c54693221cbe0ef"
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          proved="true"
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          expanded="true"
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          shape="Camixfix []V4V5aFiniteVtaInfiniteainfix &gt;=alengthV8V2IapathasV8V7FIamemaTuple2V7V5aaddaTuple2V0V1V3FIamemV5averticesFICagetV4V0aInfinitefaFiniteVCagetV4V1aInfinitetaFiniteVainfix &lt;ainfix +V9aweightV0V1V10NICamixfix []V4V11aFiniteVainfix &gt;=ainfix +apath_weightV14V13aweightV13V11V12IamemaTuple2V13V11V3Iainfix &lt;alengthV14V2IapathasV14V13FAainfix &gt;=apath_weightV15V11V12Iainfix &lt;alengthV15V2IapathasV15V11FAainfix =apath_weightV16V11V12AapathasV16V11EaInfiniteainfix &gt;=alengthV18V2IapathasV18V17FIamemaTuple2V17V11V3FAainfix &gt;=alengthV19V2IapathasV19V11FIamemV11averticesFAamemaTuple2V0V1V3NAamemaTuple2V0V1aedgesAainfix =c1V2Oainfix &lt;c1V2FF">
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          <label
           name="expl:parameter relax"/>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.13"/>
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          </proof>
          <proof
           prover="3"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.28"/>
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          </proof>
         </goal>
        </transf>
       </goal>
      </transf>
     </goal>
    </transf>
   </goal>
   <goal
    name="WP_parameter bellman_ford"
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    locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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    loclnum="186" loccnumb="6" loccnume="18"
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    expl="parameter bellman_ford"
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    sum="206724dfbeec66a265fb81fdd6512567"
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    proved="true"
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    expanded="true"
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    shape="iainfix =V3aTrueNiCagetV0V5aInfinitefaFiniteVCagetV0V6aInfinitetaFiniteVainfix &lt;ainfix +V8aweightV5V6V9anegative_cycleV10Eainfix &lt;acardinalV4acardinalV2Aainfix &lt;=c0acardinalV2Aainv2V0adiffaedgesV4AasubsetV4aedgesIainfix =V4aremoveV7V2AamemV7V2LaTuple2V5V6FFAais_emptyV2NCagetV0V11aFiniteVainfix &gt;=apath_weightV13V11V12IapathasV13V11FAainfix =apath_weightV14V11V12AapathasV14V11EaInfiniteapathasV15V11NFIamemV11averticesFAainv2V0aedgesIais_emptyV2qainfix =V3aTrueFIainv2V0adiffaedgesV2AasubsetV2aedgesFAainv2V0adiffaedgesV1AasubsetV1aedgesIainfix =V1aedgesFAainv1V0acardinalaverticesaemptyIainv1V0ainfix +ainfix -acardinalaverticesc1c1aemptyAiainfix =V20aTrueNainfix &lt;acardinalV21acardinalV18Aainfix &lt;=c0acardinalV18Aainv1V25V16adiffaedgesV21AasubsetV21aedgesIainv1V25V16aaddaTuple2V22V23adiffaedgesV18FAainv1V19V16adiffaedgesV18AamemaTuple2V22V23adiffaedgesV18NAamemaTuple2V22V23aedgesAainfix &lt;=c1V16Iainfix =V21aremoveV24V18AamemV24V18LaTuple2V22V23FFAais_emptyV18Nainv1V19ainfix +V16c1aemptyAainv1V19V16aedgesIais_emptyV18qainfix =V20aTrueFIainv1V19V16adiffaedgesV18AasubsetV18aedgesFAainv1V0V16adiffaedgesV17AasubsetV17aedgesIainfix =V17aedgesFIainv1V0V16aemptyIainfix &lt;=V16ainfix -acardinalaverticesc1Aainfix &lt;=c1V16FFAainv1ainitialize_single_sourceasc1aemptyIainfix &lt;=c1ainfix -acardinalaverticesc1Aiainfix =V28aTrueNiCagetainitialize_single_sourceasV30aInfinitefaFiniteVCagetainitialize_single_sourceasV31aInfinitetaFiniteVainfix &lt;ainfix +V33aweightV30V31V34anegative_cycleV35Eainfix &lt;acardinalV29acardinalV27Aainfix &lt;=c0acardinalV27Aainv2ainitialize_single_sourceasadiffaedgesV29AasubsetV29aedgesIainfix =V29aremoveV32V27AamemV32V27LaTuple2V30V31FFAais_emptyV27NCagetainitialize_single_sourceasV36aFiniteVainfix &gt;=apath_weightV38V36V37IapathasV38V36FAainfix =apath_weightV39V36V37AapathasV39V36EaInfiniteapathasV40V36NFIamemV36averticesFAainv2ainitialize_single_sourceasaedgesIais_emptyV27qainfix =V28aTrueFIainv2ainitialize_single_sourceasadiffaedgesV27AasubsetV27aedgesFAainv2ainitialize_single_sourceasadiffaedgesV26AasubsetV26aedgesIainfix =V26aedgesFAainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
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    <label
     name="expl:parameter bellman_ford"/>
    <transf
     name="split_goal"
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     proved="true"
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     expanded="true">
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     <goal
      name="WP_parameter bellman_ford.1"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="assertion"
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      sum="8b4401a193292be324d0dbf8a9e50442"
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      proved="true"
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      expanded="true"
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      shape="ainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
      <label
       name="expl:parameter bellman_ford"/>
      <proof
       prover="1"
       timelimit="15"
       memlimit="0"
       obsolete="false"
       archived="false">
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       <result status="valid" time="1.94"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter bellman_ford.2"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="loop invariant init"
612
      sum="6175d1ec70026cdd7a6c77d442ab5f3d"
613
      proved="true"
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      expanded="true"
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      shape="ainv2ainitialize_single_sourceasadiffaedgesV0AasubsetV0aedgesIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
      <label
       name="expl:parameter bellman_ford"/>
      <proof
       prover="0"
       timelimit="10"
       memlimit="0"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.09"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter bellman_ford.3"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="precondition"
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      sum="ef1e9f9b117e7a270c0360594f659264"
633
      proved="true"
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      expanded="true"
635 636 637 638 639 640 641 642 643
      shape="ais_emptyV1NIainfix =V2aTrueNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
      <label
       name="expl:parameter bellman_ford"/>
      <proof
       prover="0"
       timelimit="10"
       memlimit="0"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter bellman_ford.4"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="exceptional postcondition"
652
      sum="51186535507486c6665f334f0598ff98"
653
      proved="true"
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      expanded="true"
655
      shape="anegative_cycleV7EICagetainitialize_single_sourceasV4aInfinitefaFiniteVCagetainitialize_single_sourceasV5aInfinitetaFiniteVainfix &lt;ainfix +V8aweightV4V5V9Iainfix =V3aremoveV6V1AamemV6V1LaTuple2V4V5FFIais_emptyV1NIainfix =V2aTrueNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
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      <label
       name="expl:parameter bellman_ford"/>
      <proof
       prover="2"
       timelimit="10"
       memlimit="0"
       edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_20.v"
       obsolete="false"
       archived="false">
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       <result status="valid" time="1.96"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter bellman_ford.5"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="loop invariant preservation"
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      sum="91e19a84692d7be76ca91a537314908d"
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      proved="true"
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      expanded="true"
676
      shape="ainv2ainitialize_single_sourceasadiffaedgesV3AasubsetV3aedgesICagetainitialize_single_sourceasV4aInfinitefaFiniteVCagetainitialize_single_sourceasV5aInfinitetaFiniteVainfix &lt;ainfix +V7aweightV4V5V8NIainfix =V3aremoveV6V1AamemV6V1LaTuple2V4V5FFIais_emptyV1NIainfix =V2aTrueNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
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      <label
       name="expl:parameter bellman_ford"/>
      <transf
       name="split_goal"
       proved="true"
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       expanded="true">
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       <goal
        name="WP_parameter bellman_ford.5.1"
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        locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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        loclnum="186" loccnumb="6" loccnume="18"
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        expl="parameter bellman_ford"
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        sum="0cd55616814591c847091f75ac8c70a2"
689
        proved="true"
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        expanded="true"
691
        shape="asubsetV3aedgesICagetainitialize_single_sourceasV4aInfinitefaFiniteVCagetainitialize_single_sourceasV5aInfinitetaFiniteVainfix &lt;ainfix +V7aweightV4V5V8NIainfix =V3aremoveV6V1AamemV6V1LaTuple2V4V5FFIais_emptyV1NIainfix =V2aTrueNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
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        <label
         name="expl:parameter bellman_ford"/>
        <proof
         prover="0"
         timelimit="15"
         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.02"/>
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        </proof>
       </goal>
       <goal
        name="WP_parameter bellman_ford.5.2"
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        locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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        loclnum="186" loccnumb="6" loccnume="18"
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        expl="parameter bellman_ford"
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        sum="b0c6702ef6f4d7ef55cb3fb2d68057a8"
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        proved="true"
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        expanded="true"
711
        shape="ainv2ainitialize_single_sourceasadiffaedgesV3ICagetainitialize_single_sourceasV4aInfinitefaFiniteVCagetainitialize_single_sourceasV5aInfinitetaFiniteVainfix &lt;ainfix +V7aweightV4V5V8NIainfix =V3aremoveV6V1AamemV6V1LaTuple2V4V5FFIais_emptyV1NIainfix =V2aTrueNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
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        <label
         name="expl:parameter bellman_ford"/>
        <proof
         prover="0"
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         timelimit="79"
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         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="30.29"/>
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        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter bellman_ford.6"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="loop variant decrease"
730
      sum="e4abd08ecf1c6260da65b6726e0e69f8"
731
      proved="true"
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Andrei Paskevich committed
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      expanded="true"
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      shape="ainfix &lt;acardinalV3acardinalV1Aainfix &lt;=c0acardinalV1ICagetainitialize_single_sourceasV4aInfinitefaFiniteVCagetainitialize_single_sourceasV5aInfinitetaFiniteVainfix &lt;ainfix +V7aweightV4V5V8NIainfix =V3aremoveV6V1AamemV6V1LaTuple2V4V5FFIais_emptyV1NIainfix =V2aTrueNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
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      <label
       name="expl:parameter bellman_ford"/>
      <proof
       prover="0"
       timelimit="10"
       memlimit="0"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter bellman_ford.7"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="assertion"
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      sum="8555b974216fe0b08013e971ea754001"
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      proved="true"
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      expanded="true"
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      shape="ainv2ainitialize_single_sourceasaedgesIainfix =V2aTrueNNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
      <label
       name="expl:parameter bellman_ford"/>
      <transf
       name="inline_goal"
       proved="true"
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       expanded="true">
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       <goal
        name="WP_parameter bellman_ford.7.1"
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        locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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        loclnum="186" loccnumb="6" loccnume="18"
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        expl="assertion"
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        sum="3b850dacedd2a4478f79b5c9105b3452"
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        proved="true"
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        expanded="true"
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        shape="aleamixfix []ainitialize_single_sourceasV4aaddamixfix []ainitialize_single_sourceasV3aFiniteaweightV3V4IamemaTuple2V3V4aedgesFIainfix =V2aTrueNNIamemV5V1NFqainfix =V2aTrueFIaleamixfix []ainitialize_single_sourceasV7aaddamixfix []ainitialize_single_sourceasV6aFiniteaweightV6V7IamemaTuple2V6V7adiffaedgesV1FAamemV8aedgesIamemV8V1FFIainfix =V0aedgesFICamixfix []ainitialize_single_sourceasV9aFiniteVainfix &gt;=ainfix +apath_weightV12V11aweightV11V9V10IamemaTuple2V11V9aemptyIainfix &lt;alengthV12acardinalaverticesIapathasV12V11FAainfix &gt;=apath_weightV13V9V10Iainfix &lt;alengthV13acardinalaverticesIapathasV13V9FAainfix =apath_weightV14V9V10AapathasV14V9EaInfiniteainfix &gt;=alengthV16acardinalaverticesIapathasV16V15FIamemaTuple2V15V9aemptyFAainfix &gt;=alengthV17acardinalaverticesIapathasV17V9FIamemV9averticesFIainfix &lt;ainfix -acardinalaverticesc1c1">
        <label
         name="expl:parameter bellman_ford"/>
        <proof
         prover="0"
         timelimit="29"
         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="4.24"/>
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        </proof>
        <proof
         prover="1"
         timelimit="5"
         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.45"/>
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        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter bellman_ford.8"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
793
      loclnum="186" loccnumb="6" loccnume="18"
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      expl="postcondition"
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      sum="14230b3ef66fad126fdc86b63c5a01ae"
796
      proved="true"
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      expanded="true"
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      shape="Cagetainitialize_single_sourceasV3aFiniteVainfix &gt;=apath_weightV5V3V4IapathasV5V3FAainfix =apath_weightV6V3V4AapathasV6V3EaInfiniteapathasV7V3NFIamemV3averticesFIainv2ainitialize_single_sourceasaedgesIainfix =V2aTrueNNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
      <label
       name="expl:parameter bellman_ford"/>
      <transf
       name="split_goal"
       proved="true"
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       expanded="true">
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       <goal
        name="WP_parameter bellman_ford.8.1"
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        locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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        loclnum="186" loccnumb="6" loccnume="18"
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        expl="postcondition"
810
        sum="a60905d2b1f26d23beb73071aa906fe5"
811
        proved="true"
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        expanded="true"
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        shape="Cagetainitialize_single_sourceasV3aFiniteVainfix =apath_weightV5V3V4AapathasV5V3EaInfinitetIamemV3averticesFIainv2ainitialize_single_sourceasaedgesIainfix =V2aTrueNNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
        <label
         name="expl:parameter bellman_ford"/>
        <proof
         prover="1"
         timelimit="10"
         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.39"/>
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        </proof>
       </goal>
       <goal
        name="WP_parameter bellman_ford.8.2"
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        locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
828
        loclnum="186" loccnumb="6" loccnume="18"
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        expl="postcondition"
830
        sum="16b813cbf348f16d320e5f0a4730c93b"
831
        proved="true"
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        expanded="true"
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        shape="Cagetainitialize_single_sourceasV3aFiniteVainfix &gt;=apath_weightV5V3V4IapathasV5V3FaInfinitetIamemV3averticesFIainv2ainitialize_single_sourceasaedgesIainfix =V2aTrueNNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
        <label
         name="expl:parameter bellman_ford"/>
        <proof
         prover="1"
         timelimit="30"
         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.10"/>
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        </proof>
       </goal>
       <goal
        name="WP_parameter bellman_ford.8.3"
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        locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
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        loclnum="186" loccnumb="6" loccnume="18"
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        expl="postcondition"
850
        sum="20e7af0f4e201b3b880e17274a6d8545"
851
        proved="true"
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        expanded="true"
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        shape="Cagetainitialize_single_sourceasV3aFiniteVtaInfiniteapathasV5V3NFIamemV3averticesFIainv2ainitialize_single_sourceasaedgesIainfix =V2aTrueNNIais_emptyV1qainfix =V2aTrueFIainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesFIainfix =V0aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1ainfix -acardinalaverticesc1">
        <label
         name="expl:parameter bellman_ford"/>
        <proof
         prover="0"
         timelimit="15"
         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="4.94"/>
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        </proof>
        <proof
         prover="1"
         timelimit="15"
         memlimit="0"
         obsolete="false"
         archived="false">
870
         <result status="valid" time="0.04"/>
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        </proof>
        <proof
         prover="3"
         timelimit="15"
         memlimit="0"
         obsolete="false"
         archived="false">
878
         <result status="valid" time="0.04"/>
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        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter bellman_ford.9"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
886
      loclnum="186" loccnumb="6" loccnume="18"
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      expl="loop invariant init"
888
      sum="8a95033fc1341581e7ad27e27cd02186"
889
      proved="true"
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890
      expanded="true"
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      shape="ainv1ainitialize_single_sourceasc1aemptyIainfix &lt;=c1ainfix -acardinalaverticesc1">
      <label
       name="expl:parameter bellman_ford"/>
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      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="1.97"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter bellman_ford.10"
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      locfile="examples/programs/bellman_ford/../bellman_ford.mlw"
906
      loclnum="186" loccnumb="6" loccnume="18"
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Andrei Paskevich committed
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      expl="loop invariant init"
      sum="8af0b911e540c10e4ea8476b95fbfa25"
909
      proved="true"
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910 911
      expanded="true"
      shape="ainv1V0V1adiffaedgesV2AasubsetV2aedgesIainfix =V2aedgesFIainv1V0V1aemptyIainfix &lt;=V1ainfix -acardinalaverticesc1Aainfix &lt;=c1V1FFIainfix &lt;=c1ainfix -acardinalaverticesc1">
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      <label
       name="expl:parameter bellman_ford"/>
      <transf
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