mirror of
https://github.com/AdaCore/why3.git
synced 2026-02-12 12:34:55 -08:00
622 lines
33 KiB
XML
622 lines
33 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="Alt-Ergo" version="2.2.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="1" name="Alt-Ergo" version="2.6.0" timelimit="11" steplimit="0" memlimit="1000"/>
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<prover id="3" name="CVC3" version="2.4.1" timelimit="11" steplimit="0" memlimit="1000"/>
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<prover id="4" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="5" name="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="1000"/>
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<file format="whyml" proved="true">
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<path name=".."/><path name="mergesort_array.mlw"/>
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<theory name="Merge" proved="true">
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<goal name="merge'vc" expl="VC for merge" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="merge'vc.0" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="4"/></proof>
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</goal>
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<goal name="merge'vc.1" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="4"/></proof>
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</goal>
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<goal name="merge'vc.2" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="31"/></proof>
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</goal>
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<goal name="merge'vc.3" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="25"/></proof>
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</goal>
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<goal name="merge'vc.4" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="27"/></proof>
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</goal>
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<goal name="merge'vc.5" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="80"/></proof>
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</goal>
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<goal name="merge'vc.6" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
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</goal>
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<goal name="merge'vc.7" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="54"/></proof>
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</goal>
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<goal name="merge'vc.8" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="54"/></proof>
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</goal>
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<goal name="merge'vc.9" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="52"/></proof>
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</goal>
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<goal name="merge'vc.10" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="53"/></proof>
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</goal>
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<goal name="merge'vc.11" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="57"/></proof>
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</goal>
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<goal name="merge'vc.12" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
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</goal>
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<goal name="merge'vc.13" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.050000"/></proof>
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</goal>
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<goal name="merge'vc.14" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.050000"/></proof>
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</goal>
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<goal name="merge'vc.15" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.060000"/></proof>
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</goal>
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<goal name="merge'vc.16" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="1.322321" steps="9379"/></proof>
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</goal>
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<goal name="merge'vc.17" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="143"/></proof>
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</goal>
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<goal name="merge'vc.18" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="52"/></proof>
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</goal>
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<goal name="merge'vc.19" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="55"/></proof>
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</goal>
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<goal name="merge'vc.20" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="56"/></proof>
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</goal>
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<goal name="merge'vc.21" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
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</goal>
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<goal name="merge'vc.22" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.050000"/></proof>
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</goal>
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<goal name="merge'vc.23" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.070000"/></proof>
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</goal>
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<goal name="merge'vc.24" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.060000"/></proof>
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</goal>
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<goal name="merge'vc.25" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="1.635245" steps="2035"/></proof>
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<proof prover="1" timelimit="5"><result status="timeout" time="5.000000" steps="42460"/></proof>
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</goal>
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<goal name="merge'vc.26" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="235"/></proof>
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</goal>
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<goal name="merge'vc.27" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
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</goal>
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<goal name="merge'vc.28" expl="postcondition" proved="true">
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<transf name="inline_goal" proved="true" >
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<goal name="merge'vc.28.0" expl="postcondition" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="merge'vc.28.0.0" expl="VC for merge" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
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</goal>
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<goal name="merge'vc.28.0.1" expl="VC for merge" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="45"/></proof>
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</goal>
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<goal name="merge'vc.28.0.2" expl="VC for merge" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="68"/></proof>
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</goal>
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<goal name="merge'vc.28.0.3" expl="VC for merge" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="62"/></proof>
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</goal>
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<goal name="merge'vc.28.0.4" expl="VC for merge" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="48"/></proof>
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</goal>
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<goal name="merge'vc.28.0.5" expl="VC for merge" proved="true">
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<proof prover="4" timelimit="11"><result status="valid" time="0.350000"/></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="merge'vc.29" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="54"/></proof>
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</goal>
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<goal name="merge'vc.30" expl="out of loop bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="7"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="merge_using'vc" expl="VC for merge_using" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="merge_using'vc.0" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="20"/></proof>
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</goal>
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<goal name="merge_using'vc.1" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="22"/></proof>
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</goal>
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<goal name="merge_using'vc.2" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="63"/></proof>
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</goal>
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<goal name="merge_using'vc.3" expl="postcondition" proved="true">
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<proof prover="4" timelimit="11"><result status="valid" time="0.040000"/></proof>
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</goal>
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<goal name="merge_using'vc.4" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="43"/></proof>
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</goal>
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<goal name="merge_using'vc.5" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
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</goal>
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<goal name="merge_using'vc.6" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="22"/></proof>
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</goal>
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<goal name="merge_using'vc.7" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="10"/></proof>
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</goal>
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<goal name="merge_using'vc.8" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="30"/></proof>
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</goal>
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<goal name="merge_using'vc.9" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="85"/></proof>
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</goal>
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<goal name="merge_using'vc.10" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="91"/></proof>
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</goal>
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<goal name="merge_using'vc.11" expl="assertion" proved="true">
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<transf name="inline_goal" proved="true" >
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<goal name="merge_using'vc.11.0" expl="assertion" proved="true">
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<proof prover="4" timelimit="11"><result status="valid" time="0.650000"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="merge_using'vc.12" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="32"/></proof>
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</goal>
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<goal name="merge_using'vc.13" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="44"/></proof>
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</goal>
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<goal name="merge_using'vc.14" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="50"/></proof>
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</goal>
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<goal name="merge_using'vc.15" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="18"/></proof>
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</goal>
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<goal name="merge_using'vc.16" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="31"/></proof>
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</goal>
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<goal name="merge_using'vc.17" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="0"/></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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<theory name="TopDownMergesort" proved="true">
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<goal name="mergesort_rec'vc" expl="VC for mergesort_rec" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="mergesort_rec'vc.0" expl="postcondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="16"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.1" expl="postcondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="33"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.2" expl="check division by zero" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="10"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.3" expl="assertion" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="49"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.4" expl="variant decrease" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.000000" steps="14"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.5" expl="precondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.000000" steps="14"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.6" expl="assertion" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="27"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.7" expl="variant decrease" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="86"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.8" expl="precondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="24"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.9" expl="assertion" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="38"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.10" expl="precondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="34"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.11" expl="precondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.040347" steps="250"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.12" expl="precondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="39"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.13" expl="postcondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.010000" steps="40"/></proof>
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</goal>
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<goal name="mergesort_rec'vc.14" expl="postcondition" proved="true">
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<proof prover="1" timelimit="5"><result status="valid" time="0.140000" steps="307"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="mergesort'vc" expl="VC for mergesort" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="55"/></proof>
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</goal>
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</theory>
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<theory name="BottomUpMergesort" proved="true">
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<goal name="bottom_up_mergesort'vc" expl="VC for bottom_up_mergesort" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="bottom_up_mergesort'vc.0" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="2"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.1" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="15"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.2" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.3" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.000000" steps="10"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.4" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.5" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.6" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="30"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.7" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.8" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.020000" steps="56"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.9" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="2.934901" steps="55029"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.10" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.030000" steps="124"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.11" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="71"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.12" expl="precondition" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.13" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.232022" steps="3161"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.14" expl="assertion" proved="true">
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<transf name="inline_goal" proved="true" >
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<goal name="bottom_up_mergesort'vc.14.0" expl="assertion" proved="true">
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<proof prover="4" timelimit="11"><result status="valid" time="0.490000"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="bottom_up_mergesort'vc.15" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="47"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.16" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.010000" steps="47"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.17" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="4.388111" steps="95048"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.18" expl="assertion" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="bottom_up_mergesort'vc.18.0" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.040000"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.18.1" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.060000"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.18.2" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.030000" steps="412"/></proof>
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</goal>
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<goal name="bottom_up_mergesort'vc.18.3" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.572022" steps="16337"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.18.4" expl="assertion" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="69"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.18.5" expl="assertion" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="69"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.19" expl="loop variant decrease" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="47"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.20" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="47"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.21" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="302"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.22" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.030000" steps="110"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.23" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="438"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.24" expl="assertion" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.321274" steps="7336"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.25" expl="loop variant decrease" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.26" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.27" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="58"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.28" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="118"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.29" expl="assertion" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="49"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.30" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="77"/></proof>
|
|
</goal>
|
|
<goal name="bottom_up_mergesort'vc.31" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="10"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</theory>
|
|
<theory name="NaturalMergesort" proved="true">
|
|
<goal name="find_run'vc" expl="VC for find_run" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.130000" steps="73"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc" expl="VC for natural_mergesort" proved="true">
|
|
<transf name="split_goal_right" proved="true" >
|
|
<goal name="natural_mergesort'vc.0" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="10"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.1" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.2" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="15"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.3" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.000000" steps="21"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.4" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="12"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.5" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="12"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.6" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.7" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.8" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.000000" steps="38"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.9" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.10" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="79"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.11" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="75"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.12" expl="loop variant decrease" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.13" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="29"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.14" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="84"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.15" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="54"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.16" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="62"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.17" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="56"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.18" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="56"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.19" expl="assertion" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.040000" steps="417"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.20" expl="assertion" proved="true">
|
|
<transf name="inline_goal" proved="true" >
|
|
<goal name="natural_mergesort'vc.20.0" expl="assertion" proved="true">
|
|
<transf name="split_goal_right" proved="true" >
|
|
<goal name="natural_mergesort'vc.20.0.0" expl="VC for natural_mergesort" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="51"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.20.0.1" expl="VC for natural_mergesort" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.211514" steps="31513"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.21" expl="loop variant decrease" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="64"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.22" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="64"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.23" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="138"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.24" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="64"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.25" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="134"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.26" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="136"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.27" expl="loop variant decrease" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="64"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.28" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="64"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.29" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="64"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.30" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="186"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.31" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="64"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.32" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="137"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.33" expl="loop variant decrease" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="46"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.34" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
|
|
</goal>
|
|
<goal name="natural_mergesort'vc.35" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="66"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="naturalrec'vc" expl="VC for naturalrec" proved="true">
|
|
<transf name="split_goal_right" proved="true" >
|
|
<goal name="naturalrec'vc.0" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.000000" steps="2"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.1" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="18"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.2" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="32"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.3" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="0"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.4" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="5"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.5" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="2"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.6" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="5"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.7" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.8" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.9" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="23"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.10" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.11" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="68"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.12" expl="loop invariant init" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.13" expl="variant decrease" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.14" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="48"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.15" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.16" expl="assertion" proved="true">
|
|
<transf name="inline_goal" proved="true" >
|
|
<goal name="naturalrec'vc.16.0" expl="assertion" proved="true">
|
|
<proof prover="4" timelimit="11"><result status="valid" time="0.060000"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="naturalrec'vc.17" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="67"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.18" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="170"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.19" expl="precondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="56"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.20" expl="assertion" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.040000" steps="238"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.21" expl="assertion" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="83"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.22" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="66"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.23" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="66"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.24" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.040000" steps="88"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.25" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="166"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.26" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="83"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.27" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="66"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.28" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.030000" steps="92"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.29" expl="loop invariant preservation" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.020000" steps="169"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.30" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="44"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.31" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.000000" steps="28"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.32" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.33" expl="postcondition" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="54"/></proof>
|
|
</goal>
|
|
<goal name="naturalrec'vc.34" expl="out of loop bounds" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="natural_mergesort2'vc" expl="VC for natural_mergesort2" proved="true">
|
|
<proof prover="1"><result status="valid" time="0.010000" steps="87"/></proof>
|
|
</goal>
|
|
</theory>
|
|
</file>
|
|
</why3session>
|