mirror of
https://github.com/AdaCore/why3.git
synced 2026-02-12 12:34:55 -08:00
266 lines
14 KiB
XML
266 lines
14 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
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"https://www.why3.org/why3session.dtd">
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<why3session shape_version="6">
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<prover id="0" name="Z3" version="4.11.2" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="1" name="Alt-Ergo" version="2.5.4" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="2" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="3" name="Alt-Ergo" version="2.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<file format="whyml" proved="true">
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<path name=".."/><path name="dijkstra.mlw"/>
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<theory name="DijkstraShortestPath" proved="true">
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<goal name="relax'vc" expl="VC for relax" proved="true">
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<proof prover="2"><result status="valid" time="0.050000" steps="13283"/></proof>
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</goal>
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<goal name="Length_nonneg" proved="true">
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<transf name="induction_pr" proved="true" >
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<goal name="Length_nonneg.0" proved="true">
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<proof prover="2"><result status="valid" time="0.020000" steps="5021"/></proof>
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</goal>
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<goal name="Length_nonneg.1" proved="true">
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<proof prover="2"><result status="valid" time="0.030000" steps="9672"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="Path_inversion" proved="true">
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<proof prover="2"><result status="valid" time="0.040000" steps="8860"/></proof>
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</goal>
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<goal name="Path_shortest_path" proved="true">
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<transf name="introduce_premises" proved="true" >
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<goal name="Path_shortest_path.0" proved="true">
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<transf name="induction" proved="true" arg1="d">
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<goal name="Path_shortest_path.0.0" expl="base case" proved="true">
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<proof prover="2"><result status="valid" time="0.020000" steps="7054"/></proof>
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</goal>
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<goal name="Path_shortest_path.0.1" expl="recursive case" proved="true">
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<proof prover="2"><result status="valid" time="0.060000" steps="14531"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="Main_lemma" proved="true">
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<proof prover="2"><result status="valid" time="0.140000" steps="21428"/></proof>
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</goal>
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<goal name="Completeness_lemma" proved="true">
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<transf name="induction_pr" proved="true" >
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<goal name="Completeness_lemma.0" proved="true">
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<proof prover="2"><result status="valid" time="0.020000" steps="9206"/></proof>
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</goal>
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<goal name="Completeness_lemma.1" proved="true">
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<proof prover="2"><result status="valid" time="0.030000" steps="10220"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="inside_or_exit" proved="true">
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<transf name="induction_pr" proved="true" >
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<goal name="inside_or_exit.0" proved="true">
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<proof prover="2"><result status="valid" time="0.030000" steps="9643"/></proof>
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</goal>
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<goal name="inside_or_exit.1" proved="true">
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<proof prover="2"><result status="valid" time="0.140000" steps="38312"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc" expl="VC for shortest_path_code" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="shortest_path_code'vc.0" expl="loop invariant init" proved="true">
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<transf name="unfold" proved="true" arg1="inv">
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<goal name="shortest_path_code'vc.0.0" expl="VC for shortest_path_code" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="shortest_path_code'vc.0.0.0" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.060000" steps="12056"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.0.0.1" expl="VC for shortest_path_code" proved="true">
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<proof prover="3"><result status="valid" time="0.010000" steps="41"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.0.0.2" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.050000" steps="12640"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.0.0.3" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.060000" steps="12763"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.0.0.4" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.050000" steps="11291"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.0.0.5" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.030000" steps="11409"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.0.0.6" expl="VC for shortest_path_code" proved="true">
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<proof prover="3"><result status="valid" time="0.080000" steps="70"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.1" expl="loop invariant init" proved="true">
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<proof prover="2"><result status="valid" time="0.050000" steps="13257"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.2" expl="loop invariant init" proved="true">
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<proof prover="2"><result status="valid" time="0.100000" steps="14705"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.3" expl="precondition" proved="true">
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<proof prover="2"><result status="valid" time="0.030000" steps="11645"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.4" expl="assertion" proved="true">
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<proof prover="2"><result status="valid" time="0.080000" steps="17638"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.5" expl="loop invariant init" proved="true">
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<proof prover="2"><result status="valid" time="0.050000" steps="13605"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.6" expl="loop invariant init" proved="true">
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<transf name="unfold" proved="true" arg1="inv">
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<goal name="shortest_path_code'vc.6.0" expl="VC for shortest_path_code" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="shortest_path_code'vc.6.0.0" expl="VC for shortest_path_code" proved="true">
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<proof prover="3"><result status="valid" time="0.020000" steps="180"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.6.0.1" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.040000" steps="13736"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.6.0.2" expl="VC for shortest_path_code" proved="true">
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<transf name="unfold" proved="true" arg1="subset">
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<goal name="shortest_path_code'vc.6.0.2.0" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.180000" steps="17044"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.6.0.3" expl="VC for shortest_path_code" proved="true">
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<proof prover="3"><result status="valid" time="0.020000" steps="177"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.6.0.4" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.050000" steps="16339"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.6.0.5" expl="VC for shortest_path_code" proved="true">
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<proof prover="3"><result status="valid" time="0.070000" steps="251"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.6.0.6" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.110000" steps="16218"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.7" expl="loop invariant init" proved="true">
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<transf name="unfold" proved="true" arg1="inv_succ2">
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<goal name="shortest_path_code'vc.7.0" expl="VC for shortest_path_code" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="shortest_path_code'vc.7.0.0" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.090000" steps="22810"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.7.0.1" expl="VC for shortest_path_code" proved="true">
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<proof prover="3"><result status="valid" time="0.060000" steps="592"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.8" expl="precondition" proved="true">
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<proof prover="2"><result status="valid" time="0.030000" steps="13259"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.9" expl="assertion" proved="true">
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<transf name="destruct" proved="true" arg1="Ensures">
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<goal name="shortest_path_code'vc.9.0" expl="assertion" proved="true">
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<proof prover="0"><result status="valid" time="0.040000" steps="194242"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.9.1" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.050000" steps="541"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.10" expl="loop variant decrease" proved="true">
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<proof prover="2"><result status="valid" time="0.100000" steps="17886"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.11" expl="loop invariant preservation" proved="true">
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<proof prover="2"><result status="valid" time="0.080000" steps="18125"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.12" expl="loop invariant preservation" proved="true">
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<transf name="unfold" proved="true" arg1="inv">
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<goal name="shortest_path_code'vc.12.0" expl="VC for shortest_path_code" proved="true">
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<transf name="unfold" proved="true" arg1="inv" arg2="in" arg3="LoopInvariant2">
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<goal name="shortest_path_code'vc.12.0.0" expl="VC for shortest_path_code" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="shortest_path_code'vc.12.0.0.0" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.070000" steps="19197"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.12.0.0.1" expl="VC for shortest_path_code" proved="true">
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<transf name="case" proved="true" arg1="(v=src)">
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<goal name="shortest_path_code'vc.12.0.0.1.0" expl="true case" proved="true">
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<proof prover="2"><result status="valid" time="0.240000" steps="33769"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.12.0.0.1.1" expl="false case" proved="true">
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<proof prover="3"><result status="valid" time="0.070000" steps="576"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.12.0.0.2" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.040000" steps="13821"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.12.0.0.3" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.250000" steps="33247"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.12.0.0.4" expl="VC for shortest_path_code" proved="true">
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<proof prover="2"><result status="valid" time="0.050000" steps="15325"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.12.0.0.5" expl="VC for shortest_path_code" proved="true">
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<proof prover="3"><result status="valid" time="0.090000" steps="733"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.12.0.0.6" expl="VC for shortest_path_code" proved="true">
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<transf name="case" proved="true" arg1="(v=v1)">
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<goal name="shortest_path_code'vc.12.0.0.6.0" expl="true case" proved="true">
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<proof prover="1"><result status="valid" time="0.478677" steps="7089"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.12.0.0.6.1" expl="false case" proved="true">
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<proof prover="3"><result status="valid" time="0.137070" steps="2091"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.13" expl="loop invariant preservation" proved="true">
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<transf name="unfold" proved="true" arg1="inv_succ2">
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<goal name="shortest_path_code'vc.13.0" expl="VC for shortest_path_code" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="shortest_path_code'vc.13.0.0" expl="VC for shortest_path_code" proved="true">
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<transf name="split_all_full" proved="true" >
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<goal name="shortest_path_code'vc.13.0.0.0" expl="VC for shortest_path_code" proved="true">
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<proof prover="2" timelimit="10" memlimit="4000"><result status="valid" time="0.200000" steps="39681"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.13.0.1" expl="VC for shortest_path_code" proved="true">
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<proof prover="3" timelimit="5"><result status="valid" time="0.270505" steps="4221"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="shortest_path_code'vc.14" expl="loop variant decrease" proved="true">
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<proof prover="2"><result status="valid" time="0.150000" steps="20060"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.15" expl="loop invariant preservation" proved="true">
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<proof prover="2"><result status="valid" time="0.030000" steps="13257"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.16" expl="loop invariant preservation" proved="true">
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<proof prover="2"><result status="valid" time="0.160000" steps="22426"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.17" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.360000" steps="561164"/></proof>
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<proof prover="3"><result status="valid" time="0.483272" steps="4759"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.18" expl="postcondition" proved="true">
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<proof prover="2"><result status="valid" time="0.060000" steps="14069"/></proof>
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</goal>
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<goal name="shortest_path_code'vc.19" expl="postcondition" proved="true">
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<proof prover="2"><result status="valid" time="0.410000" steps="45046"/></proof>
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</goal>
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</transf>
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</goal>
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</theory>
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</file>
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</why3session>
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