mirror of
https://github.com/AdaCore/why3.git
synced 2026-02-12 12:34:55 -08:00
412 lines
22 KiB
XML
412 lines
22 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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"http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="6">
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<prover id="0" name="Z3" version="4.8.6" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="1" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="2" name="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="4" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="5" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<file format="whyml" proved="true">
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<path name=".."/><path name="maximum_subarray.mlw"/>
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<theory name="Algo1" proved="true">
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<goal name="maximum_subarray'vc" expl="VC for maximum_subarray" proved="true">
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<proof prover="5"><result status="valid" time="0.26" steps="501"/></proof>
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</goal>
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</theory>
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<theory name="Algo2" proved="true">
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<goal name="maximum_subarray'vc" expl="VC for maximum_subarray" proved="true">
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<proof prover="5"><result status="valid" time="0.25" steps="461"/></proof>
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</goal>
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</theory>
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<theory name="Algo3" proved="true">
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<goal name="maximum_subarray_rec'vc" expl="VC for maximum_subarray_rec" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="maximum_subarray_rec'vc.0" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="12"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.1" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="14"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.2" expl="precondition" proved="true">
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<proof prover="5"><result status="valid" time="0.02" steps="5"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.3" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="16"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.4" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="13"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.5" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="11"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.6" expl="index in array bounds" proved="true">
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<proof prover="5"><result status="valid" time="0.02" steps="27"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.7" expl="assertion" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="21"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.8" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="19"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.9" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="26"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.10" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="22"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.11" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="17"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.12" expl="loop invariant preservation" proved="true">
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<transf name="inline_all" proved="true" >
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<goal name="maximum_subarray_rec'vc.12.0" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.05" steps="13008"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="maximum_subarray_rec'vc.13" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="17"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.14" expl="assertion" proved="true">
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<proof prover="5"><result status="valid" time="0.02" steps="17"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.15" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="14"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.16" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.02" steps="22"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.17" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="16"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.18" expl="index in array bounds" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="20"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.19" expl="assertion" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="29"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.20" expl="assertion" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="38"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.21" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="26"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.22" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.07" steps="178618"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.23" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="29"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.24" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="24"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.25" expl="loop invariant preservation" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="maximum_subarray_rec'vc.25.0" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.04" steps="92118"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="maximum_subarray_rec'vc.26" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="24"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.27" expl="variant decrease" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="34"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.28" expl="precondition" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="18"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.29" expl="variant decrease" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="26"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.30" expl="precondition" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="35"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.31" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="35"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.32" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="45"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.33" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="31"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.34" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="42"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.35" expl="variant decrease" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="23"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.36" expl="precondition" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="32"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.37" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="32"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.38" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="42"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.39" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="28"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.40" expl="postcondition" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="36"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.41" expl="out of loop bounds" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="26"/></proof>
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</goal>
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<goal name="maximum_subarray_rec'vc.42" expl="out of loop bounds" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="28"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="maximum_subarray'vc" expl="VC for maximum_subarray" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="13"/></proof>
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</goal>
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</theory>
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<theory name="Algo4" proved="true">
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<goal name="maximum_subarray'vc" expl="VC for maximum_subarray" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="maximum_subarray'vc.0" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="11"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.1" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="18"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.2" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="12"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.3" expl="loop invariant init" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="15"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.4" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="30"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.5" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.10" steps="101"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.6" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.05" steps="103017"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.7" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="50"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.8" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="59"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.9" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="38"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.10" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.04" steps="89981"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.11" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.10" steps="97"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.12" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.03" steps="54023"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.13" expl="index in array bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="30"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.14" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.02" steps="58"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.15" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.03" steps="63143"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.16" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.01" steps="48"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.17" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.01" steps="56"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.18" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="36"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.19" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.03" steps="51893"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.20" expl="loop invariant preservation" proved="true">
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<proof prover="1"><result status="valid" time="0.01" steps="54"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.21" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.03" steps="46195"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.22" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="22"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.23" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.01" steps="44"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.24" expl="out of loop bounds" proved="true">
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<proof prover="1"><result status="valid" time="0.00" steps="7"/></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="Algo5" proved="true">
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<goal name="maximum_subarray'vc" expl="VC for maximum_subarray" proved="true">
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<proof prover="5"><result status="valid" time="1.40" steps="1524"/></proof>
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</goal>
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</theory>
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<theory name="BoundedIntegers" proved="true">
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<goal name="maximum_subarray'vc" expl="VC for maximum_subarray" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="maximum_subarray'vc.0" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="41"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.1" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="15"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.2" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="12"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.3" expl="loop invariant init" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="13"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.4" expl="index in array bounds" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="17"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.5" expl="integer overflow" proved="true">
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<proof prover="5"><result status="valid" time="0.04" steps="24"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.6" expl="loop variant decrease" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="24"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.7" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.24" steps="686"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.8" expl="loop invariant preservation" proved="true">
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<proof prover="5" timelimit="60"><result status="valid" time="9.95" steps="5297"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.9" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.00" steps="30"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.10" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="37"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.11" expl="integer overflow" proved="true">
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<proof prover="5"><result status="valid" time="0.05" steps="21"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.12" expl="loop variant decrease" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="21"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.13" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="21"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.14" expl="loop invariant preservation" proved="true">
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<proof prover="5" timelimit="120"><result status="valid" time="46.00" steps="29222"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.15" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.05" steps="142"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.16" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.20" steps="42793"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.17" expl="assertion" proved="true">
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<proof prover="2" timelimit="15"><result status="valid" time="0.01" steps="40034"/></proof>
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<proof prover="5" timelimit="15"><result status="valid" time="0.01" steps="19"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.18" expl="index in array bounds" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="18"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.19" expl="integer overflow" proved="true">
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<proof prover="5" timelimit="15"><result status="valid" time="0.05" steps="186"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.20" expl="integer overflow" proved="true">
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<proof prover="5"><result status="valid" time="0.02" steps="24"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.21" expl="loop variant decrease" proved="true">
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<proof prover="5"><result status="valid" time="0.01" steps="24"/></proof>
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</goal>
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<goal name="maximum_subarray'vc.22" expl="loop invariant preservation" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.04" steps="648"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.23" expl="loop invariant preservation" proved="true">
|
|
<transf name="simplify_trivial_quantification" proved="true" >
|
|
<goal name="maximum_subarray'vc.23.0" expl="loop invariant preservation" proved="true">
|
|
<transf name="introduce_premises" proved="true" >
|
|
<goal name="maximum_subarray'vc.23.0.0" expl="loop invariant preservation" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="maximum_subarray'vc.23.0.0.0" expl="loop invariant preservation" proved="true">
|
|
<transf name="case" proved="true" arg1="(h' < i)">
|
|
<goal name="maximum_subarray'vc.23.0.0.0.0" expl="true case (loop invariant preservation)" proved="true">
|
|
<proof prover="4" timelimit="1"><result status="valid" time="0.04" steps="16534"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.23.0.0.0.1" expl="false case (loop invariant preservation)" proved="true">
|
|
<proof prover="2"><result status="valid" time="0.12" steps="86485"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
<transf name="split_all_full" proved="true" >
|
|
<goal name="maximum_subarray'vc.23.0" expl="loop invariant preservation" proved="true">
|
|
<transf name="introduce_premises" proved="true" >
|
|
<goal name="maximum_subarray'vc.23.0.0" expl="loop invariant preservation" proved="true">
|
|
<transf name="inline_goal" proved="true" >
|
|
<goal name="maximum_subarray'vc.23.0.0.0" expl="loop invariant preservation" proved="true">
|
|
<proof prover="4" timelimit="30" memlimit="4000"><result status="valid" time="1.14" steps="109704"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.24" expl="loop invariant preservation" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.06" steps="30"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.25" expl="loop invariant preservation" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.02" steps="36"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.26" expl="integer overflow" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.02" steps="21"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.27" expl="loop variant decrease" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.01" steps="21"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.28" expl="loop invariant preservation" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.05" steps="21"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.29" expl="loop invariant preservation" proved="true">
|
|
<transf name="simplify_trivial_quantification" proved="true" >
|
|
<goal name="maximum_subarray'vc.29.0" expl="loop invariant preservation" proved="true">
|
|
<transf name="introduce_premises" proved="true" >
|
|
<goal name="maximum_subarray'vc.29.0.0" expl="loop invariant preservation" proved="true">
|
|
<transf name="case" proved="true" arg1="(h' < i)">
|
|
<goal name="maximum_subarray'vc.29.0.0.0" expl="true case (loop invariant preservation)" proved="true">
|
|
<proof prover="4" timelimit="1"><result status="valid" time="0.04" steps="16458"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.29.0.0.1" expl="false case (loop invariant preservation)" proved="true">
|
|
<proof prover="2"><result status="valid" time="0.08" steps="81474"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.30" expl="loop invariant preservation" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.03" steps="116"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.31" expl="loop invariant preservation" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.18" steps="36785"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.32" expl="postcondition" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.01" steps="16"/></proof>
|
|
</goal>
|
|
<goal name="maximum_subarray'vc.33" expl="postcondition" proved="true">
|
|
<proof prover="5"><result status="valid" time="0.01" steps="20"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</theory>
|
|
</file>
|
|
</why3session>
|