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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v2//EN" "http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="4">
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 <prover
  id="0"
  name="Alt-Ergo"
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  version="0.95.1"/>
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 <prover
  id="1"
  name="CVC3"
  version="2.4.1"/>
 <prover
  id="2"
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  name="CVC4"
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  version="1.2"/>
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 <prover
  id="3"
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  name="Coq"
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  version="8.4pl2"/>
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 <prover
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  id="4"
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  name="Eprover"
  version="1.6"/>
 <prover
  id="5"
  name="Spass"
  version="3.7"/>
 <prover
  id="6"
  name="Vampire"
  version="0.6"/>
 <prover
  id="7"
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  name="Z3"
  version="3.2"/>
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 <prover
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  id="8"
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  name="Z3"
  version="4.3.1"/>
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 <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="../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="../bellman_ford.mlw"
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    loclnum="30" loccnumb="8" loccnume="29"
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    sum="b53f5921e10c8afb9006fe710f5e239e"
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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="../bellman_ford.mlw"
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    loclnum="36" loccnumb="8" loccnume="24"
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    sum="06e5c788d62947e760a274766425f577"
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    proved="true"
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    expanded="true"
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    shape="amemV1averticesIapathV0V2V1IamemV0averticesF">
    <proof
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     prover="3"
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     timelimit="10"
     memlimit="0"
     edited="bf_Graph_path_in_vertices_2.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.04"/>
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    </proof>
   </goal>
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   <goal
    name="long_path_decomposition_pigeon1"
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    locfile="../bellman_ford.mlw"
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    loclnum="60" loccnumb="8" loccnume="39"
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    sum="f0f7e31c25a12d45a3ad5dc9fe881499"
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    proved="true"
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    expanded="true"
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    shape="amemV2averticesIamemV2aConsV1V0FINainfix =V0aNilIapathasV0V1F">
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    <proof
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     prover="3"
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     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="1.55"/>
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    </proof>
   </goal>
   <goal
    name="long_path_decomposition_pigeon2"
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    locfile="../bellman_ford.mlw"
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    loclnum="65" loccnumb="8" loccnume="39"
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    sum="63a6266f8603de0769159337ca28ae4f"
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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="../bellman_ford.mlw"
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    loclnum="72" loccnumb="8" loccnume="39"
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    sum="80a24999193f86edd4df497d838bd516"
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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
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     prover="3"
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     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="1.80"/>
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    </proof>
   </goal>
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   <goal
    name="long_path_decomposition"
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    locfile="../bellman_ford.mlw"
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    loclnum="80" loccnumb="8" loccnume="31"
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    sum="23fb64f5e5dd1b6dbd03d1f091879b05"
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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
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     prover="3"
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     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="1.47"/>
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    </proof>
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   </goal>
   <goal
    name="simple_path"
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    locfile="../bellman_ford.mlw"
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    loclnum="87" loccnumb="8" loccnume="19"
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    sum="a3c5122f1aaf999a3e09f307916627e4"
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    proved="true"
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    expanded="true"
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    shape="ainfix &lt;alengthV2acardinalaverticesAapathasV2V0EIapathasV1V0F">
    <proof
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     prover="3"
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     timelimit="10"
     memlimit="0"
     edited="bf_Graph_simple_path_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="2.22"/>
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    </proof>
   </goal>
   <goal
    name="key_lemma_1"
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    locfile="../bellman_ford.mlw"
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    loclnum="108" loccnumb="8" loccnume="19"
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    sum="70b203d2fb9a7d1caed9a15d173c6ee9"
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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
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     prover="3"
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     timelimit="10"
     memlimit="0"
     edited="bf_Graph_key_lemma_1_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="2.93"/>
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    </proof>
   </goal>
  </theory>
  <theory
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   name="BellmanFord"
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   locfile="../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="../bellman_ford.mlw"
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    loclnum="172" loccnumb="8" loccnume="19"
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    sum="05949fab40d8974a00cc9811526df03d"
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    proved="true"
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    expanded="true"
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    shape="Nanegative_cycleV1FIainv2V0aedgesIainv1V0acardinalaverticesaemptyF">
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    <proof
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     prover="3"
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     timelimit="5"
     memlimit="4000"
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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="20.05"/>
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    </proof>
   </goal>
   <goal
    name="WP_parameter relax"
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    locfile="../bellman_ford.mlw"
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    loclnum="176" loccnumb="6" loccnume="11"
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    expl="VC for relax"
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    sum="429ad2b1a6b64cc935964dc39f6b7db4"
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    proved="true"
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    expanded="true"
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    shape="iainv1V0V3aaddaTuple2V1V2V4ainv1V5V3aaddaTuple2V1V2V4Iainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V6aweightV1V2aFiniteVagetV0V1FCfaInfiniteCtaInfiniteainfix &lt;ainfix +V7aweightV1V2V8aFiniteVagetV0V2aFiniteVagetV0V1Iainv1V0V3V4ANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix &lt;=c1V3F">
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    <label
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     name="expl:VC for relax"/>
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    <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="../bellman_ford.mlw"
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      loclnum="176" loccnumb="6" loccnume="11"
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      expl="1. postcondition"
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      sum="3936e30a84a4e73b0f20e80f686c871c"
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      proved="true"
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      expanded="true"
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      shape="postconditionainv1V5V3aaddaTuple2V1V2V4Iainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V6aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V7aweightV1V2V8aFiniteVagetV0V2aFiniteVagetV0V1Iainv1V0V3V4ANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix &lt;=c1V3F">
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      <label
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       name="expl:VC for relax"/>
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      <transf
       name="inline_goal"
       proved="true"
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       expanded="true">
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       <goal
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        name="WP_parameter relax.1.1"
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        locfile="../bellman_ford.mlw"
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        loclnum="176" loccnumb="6" loccnume="11"
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        expl="1. postcondition"
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        sum="107eb16554294cea19ea5d4426377898"
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        proved="true"
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        expanded="true"
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        shape="postconditionCainfix &gt;=ainfix +apath_weightV9V8aweightV8V6V7IamemaTuple2V8V6aaddaTuple2V1V2V4Iainfix &lt;alengthV9V3IapathasV9V8FAainfix &gt;=apath_weightV10V6V7Iainfix &lt;alengthV10V3IapathasV10V6FAainfix =apath_weightV11V6V7AapathasV11V6EaFiniteVainfix &gt;=alengthV13V3IapathasV13V12FIamemaTuple2V12V6aaddaTuple2V1V2V4FAainfix &gt;=alengthV14V3IapathasV14V6FaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V15aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V16aweightV1V2V17aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV21V20aweightV20V18V19IamemaTuple2V20V18V4Iainfix &lt;alengthV21V3IapathasV21V20FAainfix &gt;=apath_weightV22V18V19Iainfix &lt;alengthV22V3IapathasV22V18FAainfix =apath_weightV23V18V19AapathasV23V18EaFiniteVainfix &gt;=alengthV25V3IapathasV25V24FIamemaTuple2V24V18V4FAainfix &gt;=alengthV26V3IapathasV26V18FaInfiniteamixfix []V0V18IamemV18averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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        <label
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         name="expl:VC for relax"/>
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        <transf
         name="split_goal"
         proved="true"
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         expanded="true">
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         <goal
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          name="WP_parameter relax.1.1.1"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="1. postcondition"
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          sum="8a38391a2b8023c4cb8a3d9b7c83ae11"
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          proved="true"
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          expanded="true"
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          shape="postconditionCainfix =apath_weightV8V6V7AapathasV8V6EaFiniteVtaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V9aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V10aweightV1V2V11aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V4Iainfix &lt;alengthV15V3IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V3IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaFiniteVainfix &gt;=alengthV19V3IapathasV19V18FIamemaTuple2V18V12V4FAainfix &gt;=alengthV20V3IapathasV20V12FaInfiniteamixfix []V0V12IamemV12averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <proof
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           prover="3"
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           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="1.63"/>
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          </proof>
         </goal>
         <goal
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          name="WP_parameter relax.1.1.2"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="2. postcondition"
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          sum="0fe723bc01e593ca850d11ca9fe43fb0"
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          proved="true"
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          expanded="true"
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          shape="postconditionCainfix &gt;=apath_weightV8V6V7Iainfix &lt;alengthV8V3IapathasV8V6FaFiniteVtaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V9aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V10aweightV1V2V11aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V4Iainfix &lt;alengthV15V3IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V3IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaFiniteVainfix &gt;=alengthV19V3IapathasV19V18FIamemaTuple2V18V12V4FAainfix &gt;=alengthV20V3IapathasV20V12FaInfiniteamixfix []V0V12IamemV12averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <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>
         </goal>
         <goal
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          name="WP_parameter relax.1.1.3"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="3. postcondition"
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          sum="162785f88876ebf8ebdfd0e586704f37"
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          proved="true"
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          expanded="true"
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          shape="postconditionCainfix &gt;=ainfix +apath_weightV9V8aweightV8V6V7IamemaTuple2V8V6aaddaTuple2V1V2V4Iainfix &lt;alengthV9V3IapathasV9V8FaFiniteVtaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V10aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V11aweightV1V2V12aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV16V15aweightV15V13V14IamemaTuple2V15V13V4Iainfix &lt;alengthV16V3IapathasV16V15FAainfix &gt;=apath_weightV17V13V14Iainfix &lt;alengthV17V3IapathasV17V13FAainfix =apath_weightV18V13V14AapathasV18V13EaFiniteVainfix &gt;=alengthV20V3IapathasV20V19FIamemaTuple2V19V13V4FAainfix &gt;=alengthV21V3IapathasV21V13FaInfiniteamixfix []V0V13IamemV13averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.62"/>
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          </proof>
         </goal>
         <goal
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          name="WP_parameter relax.1.1.4"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="4. postcondition"
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          sum="f616484826d28906296c5064806b66a2"
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          proved="true"
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          expanded="true"
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          shape="postconditionCtaFiniteVainfix &gt;=alengthV8V3IapathasV8V6FaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V9aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V10aweightV1V2V11aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V4Iainfix &lt;alengthV15V3IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V3IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaFiniteVainfix &gt;=alengthV19V3IapathasV19V18FIamemaTuple2V18V12V4FAainfix &gt;=alengthV20V3IapathasV20V12FaInfiniteamixfix []V0V12IamemV12averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <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="0.89"/>
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          </proof>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.25"/>
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          </proof>
         </goal>
         <goal
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          name="WP_parameter relax.1.1.5"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="5. postcondition"
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          sum="8b5a1456f3d4ead3619b3f038a083b4c"
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          proved="true"
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          expanded="true"
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          shape="postconditionCtaFiniteVainfix &gt;=alengthV9V3IapathasV9V8FIamemaTuple2V8V6aaddaTuple2V1V2V4FaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V10aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V11aweightV1V2V12aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV16V15aweightV15V13V14IamemaTuple2V15V13V4Iainfix &lt;alengthV16V3IapathasV16V15FAainfix &gt;=apath_weightV17V13V14Iainfix &lt;alengthV17V3IapathasV17V13FAainfix =apath_weightV18V13V14AapathasV18V13EaFiniteVainfix &gt;=alengthV20V3IapathasV20V19FIamemaTuple2V19V13V4FAainfix &gt;=alengthV21V3IapathasV21V13FaInfiniteamixfix []V0V13IamemV13averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.45"/>
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          </proof>
         </goal>
        </transf>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter relax.2"
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      locfile="../bellman_ford.mlw"
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      loclnum="176" loccnumb="6" loccnume="11"
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      expl="2. postcondition"
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      sum="517e2497aee242d2213d819d12592a43"
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      proved="true"
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      expanded="true"
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      shape="postconditionainv1V0V3aaddaTuple2V1V2V4INCfaInfiniteCtaInfiniteainfix &lt;ainfix +V5aweightV1V2V6aFiniteVagetV0V2aFiniteVagetV0V1Iainv1V0V3V4ANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix &lt;=c1V3F">
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      <label
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       name="expl:VC for relax"/>
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      <transf
       name="inline_goal"
       proved="true"
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       expanded="true">
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       <goal
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        name="WP_parameter relax.2.1"
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        locfile="../bellman_ford.mlw"
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        loclnum="176" loccnumb="6" loccnume="11"
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        expl="1. postcondition"
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        sum="df31f990bb179991336aff0e72def585"
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        proved="true"
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        expanded="true"
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        shape="postconditionCainfix &gt;=ainfix +apath_weightV8V7aweightV7V5V6IamemaTuple2V7V5aaddaTuple2V1V2V4Iainfix &lt;alengthV8V3IapathasV8V7FAainfix &gt;=apath_weightV9V5V6Iainfix &lt;alengthV9V3IapathasV9V5FAainfix =apath_weightV10V5V6AapathasV10V5EaFiniteVainfix &gt;=alengthV12V3IapathasV12V11FIamemaTuple2V11V5aaddaTuple2V1V2V4FAainfix &gt;=alengthV13V3IapathasV13V5FaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V14aweightV1V2V15aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV19V18aweightV18V16V17IamemaTuple2V18V16V4Iainfix &lt;alengthV19V3IapathasV19V18FAainfix &gt;=apath_weightV20V16V17Iainfix &lt;alengthV20V3IapathasV20V16FAainfix =apath_weightV21V16V17AapathasV21V16EaFiniteVainfix &gt;=alengthV23V3IapathasV23V22FIamemaTuple2V22V16V4FAainfix &gt;=alengthV24V3IapathasV24V16FaInfiniteamixfix []V0V16IamemV16averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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        <label
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         name="expl:VC for relax"/>
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        <transf
         name="split_goal"
         proved="true"
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         expanded="true">
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         <goal
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          name="WP_parameter relax.2.1.1"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="1. postcondition"
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          sum="b6ffaebfc230f6cbfa344cf297abfdc3"
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          proved="true"
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          expanded="true"
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          shape="postconditionCainfix =apath_weightV7V5V6AapathasV7V5EaFiniteVtaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV1V2V9aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V4Iainfix &lt;alengthV13V3IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V3IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaFiniteVainfix &gt;=alengthV17V3IapathasV17V16FIamemaTuple2V16V10V4FAainfix &gt;=alengthV18V3IapathasV18V10FaInfiniteamixfix []V0V10IamemV10averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <proof
           prover="0"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.04"/>
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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>
         </goal>
         <goal
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          name="WP_parameter relax.2.1.2"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="2. postcondition"
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          sum="235156fc29b70c946126b6dcf4d49c2d"
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          proved="true"
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          expanded="true"
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          shape="postconditionCainfix &gt;=apath_weightV7V5V6Iainfix &lt;alengthV7V3IapathasV7V5FaFiniteVtaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV1V2V9aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V4Iainfix &lt;alengthV13V3IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V3IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaFiniteVainfix &gt;=alengthV17V3IapathasV17V16FIamemaTuple2V16V10V4FAainfix &gt;=alengthV18V3IapathasV18V10FaInfiniteamixfix []V0V10IamemV10averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <proof
           prover="0"
           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="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.28"/>
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          </proof>
         </goal>
         <goal
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          name="WP_parameter relax.2.1.3"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="3. postcondition"
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          sum="075891715faa47a9404d6004b75498b3"
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          proved="true"
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          expanded="true"
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          shape="postconditionCainfix &gt;=ainfix +apath_weightV8V7aweightV7V5V6IamemaTuple2V7V5aaddaTuple2V1V2V4Iainfix &lt;alengthV8V3IapathasV8V7FaFiniteVtaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V9aweightV1V2V10aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV14V13aweightV13V11V12IamemaTuple2V13V11V4Iainfix &lt;alengthV14V3IapathasV14V13FAainfix &gt;=apath_weightV15V11V12Iainfix &lt;alengthV15V3IapathasV15V11FAainfix =apath_weightV16V11V12AapathasV16V11EaFiniteVainfix &gt;=alengthV18V3IapathasV18V17FIamemaTuple2V17V11V4FAainfix &gt;=alengthV19V3IapathasV19V11FaInfiniteamixfix []V0V11IamemV11averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <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>
         </goal>
         <goal
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          name="WP_parameter relax.2.1.4"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="4. postcondition"
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          sum="dc9b41e6689825672c77c7e826ee5774"
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          proved="true"
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          expanded="true"
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          shape="postconditionCtaFiniteVainfix &gt;=alengthV7V3IapathasV7V5FaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV1V2V9aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V4Iainfix &lt;alengthV13V3IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V3IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaFiniteVainfix &gt;=alengthV17V3IapathasV17V16FIamemaTuple2V16V10V4FAainfix &gt;=alengthV18V3IapathasV18V10FaInfiniteamixfix []V0V10IamemV10averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <proof
           prover="0"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.07"/>
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          </proof>
          <proof
           prover="1"
           timelimit="15"
           memlimit="0"
           obsolete="false"
           archived="false">
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           <result status="valid" time="0.08"/>
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          </proof>
         </goal>
         <goal
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          name="WP_parameter relax.2.1.5"
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          locfile="../bellman_ford.mlw"
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          loclnum="176" loccnumb="6" loccnume="11"
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          expl="5. postcondition"
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          sum="5c79f0cbbb7af85119788c66b2e8fbd8"
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          proved="true"
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          expanded="true"
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          shape="postconditionCtaFiniteVainfix &gt;=alengthV8V3IapathasV8V7FIamemaTuple2V7V5aaddaTuple2V1V2V4FaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V9aweightV1V2V10aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV14V13aweightV13V11V12IamemaTuple2V13V11V4Iainfix &lt;alengthV14V3IapathasV14V13FAainfix &gt;=apath_weightV15V11V12Iainfix &lt;alengthV15V3IapathasV15V11FAainfix =apath_weightV16V11V12AapathasV16V11EaFiniteVainfix &gt;=alengthV18V3IapathasV18V17FIamemaTuple2V17V11V4FAainfix &gt;=alengthV19V3IapathasV19V11FaInfiniteamixfix []V0V11IamemV11averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
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          <label
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           name="expl:VC for relax"/>
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          <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>
         </goal>
        </transf>
       </goal>
      </transf>
     </goal>
    </transf>
   </goal>
   <goal
    name="WP_parameter bellman_ford"
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    locfile="../bellman_ford.mlw"
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    loclnum="186" loccnumb="6" loccnume="18"
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    expl="VC for bellman_ford"
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    sum="1ef9a114b5cec15978d360e0c7e0ca60"
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    proved="true"
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    expanded="true"
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    shape="iCainfix &gt;=apath_weightV7V5V6IapathasV7V5FAainfix =apath_weightV8V5V6AapathasV8V5EaFiniteVNapathasV9V5FaInfiniteagetV1V5IamemV5averticesFAainv2V1aedgesiainfix &lt;acardinalV10acardinalV3Aainfix &lt;=c0acardinalV3Aainv2V1adiffaedgesV10AasubsetV10aedgesanegative_cycleV14ECfaInfiniteCtaInfiniteainfix &lt;ainfix +V15aweightV11V12V16aFiniteVagetV1V12aFiniteVagetV1V11Iainfix =V10aremoveV13V3AamemV13V3LaTuple2V11V12FFANais_emptyV3Nainfix =V4aTrueIais_emptyV3qainfix =V4aTrueFIainv2V1adiffaedgesV3AasubsetV3aedgesFAainv2V1adiffaedgesV2AasubsetV2aedgesIainfix =V2aedgesFAainv1V1acardinalaverticesaemptyIainv1V1ainfix +V0c1aemptyAiainv1V20ainfix +V17c1aemptyAainv1V20V17aedgesainfix &lt;acardinalV23acardinalV19Aainfix &lt;=c0acardinalV19Aainv1V27V17adiffaedgesV23AasubsetV23aedgesIainv1V27V17aaddaTuple2V24V25V22FAainv1V20V17V22ANamemaTuple2V24V25V22AamemaTuple2V24V25aedgesAainfix &lt;=c1V17Iainfix =V23aremoveV26V19AamemV26V19LaTuple2V24V25FFANais_emptyV19LadiffaedgesV19Nainfix =V21aTrueIais_emptyV19qainfix =V21aTrueFIainv1V20V17adiffaedgesV19AasubsetV19aedgesFAainv1V1V17adiffaedgesV18AasubsetV18aedgesIainfix =V18aedgesFIainv1V1V17aemptyIainfix &lt;=V17V0Aainfix &lt;=c1V17FFAainv1ainitialize_single_sourceasc1aemptyIainfix &lt;=c1V0AiCainfix &gt;=apath_weightV33V31V32IapathasV33V31FAainfix =apath_weightV34V31V32AapathasV34V31EaFiniteVNapathasV35V31FaInfiniteagetainitialize_single_sourceasV31IamemV31averticesFAainv2ainitialize_single_sourceasaedgesiainfix &lt;acardinalV36acardinalV29Aainfix &lt;=c0acardinalV29Aainv2ainitialize_single_sourceasadiffaedgesV36AasubsetV36aedgesanegative_cycleV40ECfaInfiniteCtaInfiniteainfix &lt;ainfix +V41aweightV37V38V42aFiniteVagetainitialize_single_sourceasV38aFiniteVagetainitialize_single_sourceasV37Iainfix =V36aremoveV39V29AamemV39V29LaTuple2V37V38FFANais_emptyV29Nainfix =V30aTrueIais_emptyV29qainfix =V30aTrueFIainv2ainitialize_single_sourceasadiffaedgesV29AasubsetV29aedgesFAainv2ainitialize_single_sourceasadiffaedgesV28AasubsetV28aedgesIainfix =V28aedgesFAainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
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    <label
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     name="expl:VC for bellman_ford"/>
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    <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="../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="1. assertion"
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      sum="9380df2341a08ae2153ea1be5444df7a"
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      proved="true"
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      expanded="true"
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      shape="assertionainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
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      <label
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       name="expl:VC for bellman_ford"/>
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      <transf
       name="inline_goal"
       proved="true"
       expanded="true">
       <goal
        name="WP_parameter bellman_ford.1.1"
        locfile="../bellman_ford.mlw"
        loclnum="186" loccnumb="6" loccnume="18"
        expl="1. assertion"
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        sum="7c6b7cc8b2221ca95bc2873101e6810a"
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        proved="true"
        expanded="true"
        shape="assertionCainfix &gt;=ainfix +apath_weightV4V3aweightV3V1V2IamemaTuple2V3V1aemptyIainfix &lt;alengthV4acardinalaverticesIapathasV4V3FAainfix &gt;=apath_weightV5V1V2Iainfix &lt;alengthV5acardinalaverticesIapathasV5V1FAainfix =apath_weightV6V1V2AapathasV6V1EaFiniteVainfix &gt;=alengthV8acardinalaverticesIapathasV8V7FIamemaTuple2V7V1aemptyFAainfix &gt;=alengthV9acardinalaverticesIapathasV9V1FaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
        <label
         name="expl:VC for bellman_ford"/>
        <transf
         name="split_goal_wp"
         proved="true"
         expanded="true">
         <goal
          name="WP_parameter bellman_ford.1.1.1"
          locfile="../bellman_ford.mlw"
          loclnum="186" loccnumb="6" loccnume="18"
          expl="1. assertion"
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          sum="407659f6c3975ebcc19cd8bd868dfea7"
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          proved="true"
          expanded="true"
          shape="assertionCainfix =apath_weightV3V1V2AapathasV3V1EaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
          <label
           name="expl:VC for bellman_ford"/>
          <proof
           prover="4"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.11"/>
          </proof>
          <proof
           prover="5"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
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           <result status="valid" time="3.12"/>
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          </proof>
          <proof
           prover="6"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.16"/>
          </proof>
         </goal>
         <goal
          name="WP_parameter bellman_ford.1.1.2"
          locfile="../bellman_ford.mlw"
          loclnum="186" loccnumb="6" loccnume="18"
          expl="2. assertion"
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          sum="033b77deaf474f328d69d1146c3ff01d"
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          proved="true"
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          expanded="true"
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          shape="assertionCainfix &gt;=apath_weightV3V1V2Iainfix &lt;alengthV3acardinalaverticesIapathasV3V1FaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
          <label
           name="expl:VC for bellman_ford"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.03"/>
          </proof>
         </goal>
         <goal
          name="WP_parameter bellman_ford.1.1.3"
          locfile="../bellman_ford.mlw"
          loclnum="186" loccnumb="6" loccnume="18"
          expl="3. assertion"
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          sum="c778939075c92dbd0c9ff2e0b5dbf423"
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          proved="true"
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          expanded="true"
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          shape="assertionCainfix &gt;=ainfix +apath_weightV4V3aweightV3V1V2IamemaTuple2V3V1aemptyIainfix &lt;alengthV4acardinalaverticesIapathasV4V3FaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
          <label
           name="expl:VC for bellman_ford"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.03"/>
          </proof>
         </goal>
         <goal
          name="WP_parameter bellman_ford.1.1.4"
          locfile="../bellman_ford.mlw"
          loclnum="186" loccnumb="6" loccnume="18"
          expl="4. assertion"
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MARCHE Claude committed
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          sum="4e7dfcd19446e75320a289068a333998"
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          proved="true"
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          expanded="true"
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          shape="assertionCtaFiniteVainfix &gt;=alengthV3acardinalaverticesIapathasV3V1FaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
          <label
           name="expl:VC for bellman_ford"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.03"/>
          </proof>
         </goal>
         <goal
          name="WP_parameter bellman_ford.1.1.5"
          locfile="../bellman_ford.mlw"
          loclnum="186" loccnumb="6" loccnume="18"
          expl="5. assertion"
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MARCHE Claude committed
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          sum="18823ce9161eee58cea4526f3ecb2c6e"
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          proved="true"
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          expanded="true"
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          shape="assertionCtaFiniteVainfix &gt;=alengthV4acardinalaverticesIapathasV4V3FIamemaTuple2V3V1aemptyFaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
          <label
           name="expl:VC for bellman_ford"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.03"/>
          </proof>
         </goal>
        </transf>
       </goal>
      </transf>
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     </goal>
     <goal
      name="WP_parameter bellman_ford.2"
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      locfile="../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="2. loop invariant init"
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MARCHE Claude committed
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      sum="59d6899678476704fe2a9718033b13ad"
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      proved="true"
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      expanded="true"
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      shape="loop invariant initainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
709
      <label
710
       name="expl:VC for bellman_ford"/>
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      <proof
       prover="0"
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Andrei Paskevich committed
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       timelimit="5"
       memlimit="1000"
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       obsolete="false"
       archived="false">
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Andrei Paskevich committed
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       <result status="valid" time="0.03"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter bellman_ford.3"
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      locfile="../bellman_ford.mlw"
723
      loclnum="186" loccnumb="6" loccnume="18"
724
      expl="3. precondition"
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MARCHE Claude committed
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      sum="f4c30831eb46d01864503d0c71031c1d"
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      proved="true"
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      expanded="true"
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      shape="preconditionNais_emptyV2INainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
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      <label
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       name="expl:VC for bellman_ford"/>
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      <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"
742
      locfile="../bellman_ford.mlw"
743
      loclnum="186" loccnumb="6" loccnume="18"
744
      expl="4. exceptional postcondition"
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MARCHE Claude committed
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      sum="4af87fa6db9bfa92f3289758feef93a4"
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      proved="true"
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      expanded="true"
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      shape="exceptional postconditionanegative_cycleV8EICfaInfiniteCtaInfiniteainfix &lt;ainfix +V9aweightV5V6V10aFiniteVagetainitialize_single_sourceasV6aFiniteVagetainitialize_single_sourceasV5Iainfix =V4aremoveV7V2AamemV7V2LaTuple2V5V6FFINais_emptyV2INainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
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      <label
750
       name="expl:VC for bellman_ford"/>
751
      <proof
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       prover="3"
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Andrei Paskevich committed
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       timelimit="5"
       memlimit="1000"
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       edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_20.v"
       obsolete="false"
       archived="false">
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MARCHE Claude committed
758
       <result status="valid" time="2.12"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter bellman_ford.5"
763
      locfile="../bellman_ford.mlw"
764
      loclnum="186" loccnumb="6" loccnume="18"
765
      expl="5. loop invariant preservation"
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MARCHE Claude committed
766
      sum="be056799ea660063c1d98b9e84fa71aa"
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      proved="true"
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      expanded="true"
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      shape="loop invariant preservationainv2ainitialize_single_sourceasadiffaedgesV4AasubsetV4aedgesINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV5V6V9aFiniteVagetainitialize_single_sourceasV6aFiniteVagetainitialize_single_sourceasV5Iainfix =V4aremoveV7V2AamemV7V2LaTuple2V5V6FFINais_emptyV2INainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
770
      <label
771
       name="expl:VC for bellman_ford"/>
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Andrei Paskevich committed
772 773 774 775 776 777
      <proof
       prover="0"
       timelimit="10"
       memlimit="0"
       obsolete="false"
       archived="false">
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MARCHE Claude committed
778
       <result status="valid" time="3.25"/>
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Andrei Paskevich committed
779
      </proof>
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     </goal>
     <goal
      name="WP_parameter bellman_ford.6"
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      locfile="../bellman_ford.mlw"
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      loclnum="186" loccnumb="6" loccnume="18"
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      expl="6. loop variant decrease"
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MARCHE Claude committed
786
      sum="726bbe5d9c3829c0e877cdf962088371"
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      proved="true"
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      expanded="true"
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      shape="loop variant decreaseainfix &lt;acardinalV4acardinalV2Aainfix &lt;=c0acardinalV2INCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV5V6V9aFiniteVagetainitialize_single_sourceasV6aFiniteVagetainitialize_single_sourceasV5Iainfix =V4aremoveV7V2AamemV7V2LaTuple2V5V6FFINais_emptyV2INainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
790
      <label
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       name="expl:VC for bellman_ford"/>
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      <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"
803
      locfile="../bellman_ford.mlw"
804
      loclnum="186" loccnumb="6" loccnume="18"
805
      expl="7. assertion"
MARCHE Claude's avatar
MARCHE Claude committed
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      sum="7ef5502853d707f5071be7e68abbae79"
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      proved="true"
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      expanded="true"
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      shape="assertionainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
810
      <label
811
       name="expl:VC for bellman_ford"/>
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Andrei Paskevich committed
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.06"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter bellman_ford.8"
823
      locfile="../bellman_ford.mlw"
824
      loclnum="186" loccnumb="6" loccnume="18"
825
      expl="8. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
826
      sum="d31ce1ad869813a1876b5b2460bd97f7"
827
      proved="true"
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      expanded="true"
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      shape="postconditionCainfix &gt;=apath_weightV6V4V5IapathasV6V4FAainfix =apath_weightV7V4V5AapathasV7V4EaFiniteVNapathasV8V4FaInfiniteagetainitialize_single_sourceasV4IamemV4averticesFIainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
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      <label
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       name="expl:VC for bellman_ford"/>
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      <transf
       name="split_goal"
       proved="true"
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       expanded="true">
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       <goal
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        name="WP_parameter bellman_ford.8.1"
838
        locfile="../bellman_ford.mlw"
839
        loclnum="186" loccnumb="6" loccnume="18"
840
        expl="1. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
841
        sum="deed884afdc39ec1015b75ac5ac187b3"
842
        proved="true"
843
        expanded="true"
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        shape="postconditionCainfix =apath_weightV6V4V5AapathasV6V4EaFiniteVtaInfiniteagetainitialize_single_sourceasV4IamemV4averticesFIainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
845
        <label
846
         name="expl:VC for bellman_ford"/>
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Andrei Paskevich committed
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        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.06"/>
        </proof>
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        <proof
         prover="1"
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Andrei Paskevich committed
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         timelimit="15"
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         memlimit="0"
         obsolete="false"
         archived="false">
861
         <result status="valid" time="0.07"/>
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Andrei Paskevich committed
862 863
        </proof>
        <proof
864
         prover="8"
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Andrei Paskevich committed
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         timelimit="10"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
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        </proof>
       </goal>
       <goal
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        name="WP_parameter bellman_ford.8.2"
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        locfile="../bellman_ford.mlw"
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        loclnum="186" loccnumb="6" loccnume="18"
876
        expl="2. postcondition"
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MARCHE Claude committed
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        sum="0ce3147f0c096a635e3d73b3fa3ff53e"
878
        proved="true"
879
        expanded="true"
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        shape="postconditionCainfix &gt;=apath_weightV6V4V5IapathasV6V4FaFiniteVtaInfiniteagetainitialize_single_sourceasV4IamemV4averticesFIainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
881
        <label
882
         name="expl:VC for bellman_ford"/>
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        <proof
         prover="1"
         timelimit="30"
         memlimit="0"
         obsolete="false"
         archived="false">
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Andrei Paskevich committed
889
         <result status="valid" time="0.10"/>
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        </proof>
       </goal>
       <goal
893
        name="WP_parameter bellman_ford.8.3"
894
        locfile="../bellman_ford.mlw"
895
        loclnum="186" loccnumb="6" loccnume="18"
896
        expl="3. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
897
        sum="1c4b72888844e21e856e75edfe18f9b7"
898
        proved="true"
899
        expanded="true"
900
        shape="postconditionCtaFiniteVNapathasV6V4FaInfiniteagetainitialize_single_sourceasV4IamemV4averticesFIainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
901
        <label
902
         name="expl:VC for bellman_ford"/>
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        <proof
         prover="0"
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Andrei Paskevich committed
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         timelimit="10"
         memlimit="1000"
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         obsolete="false"
         archived="false">
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MARCHE Claude committed
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         <result status="valid" time="7.09"/>
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        </proof>
        <proof
         prover="1"
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         timelimit="10"
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         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.04"/>
918 919
        </proof>
        <proof
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         prover="8"
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