mirror of
https://github.com/AdaCore/why3.git
synced 2026-02-12 12:34:55 -08:00
287 lines
16 KiB
XML
287 lines
16 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="4.8.10" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="2" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="3" name="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="4" name="Eprover" version="2.0" timelimit="15" steplimit="0" memlimit="1000"/>
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<prover id="5" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="6" name="Z3" version="4.12.2" timelimit="1" steplimit="0" memlimit="1000"/>
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<file format="whyml" proved="true">
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<path name=".."/><path name="space_saving.mlw"/>
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<theory name="Top" proved="true">
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<goal name="s'vc" expl="VC for s" proved="true">
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<proof prover="2"><result status="valid" time="0.025721" steps="3344"/></proof>
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</goal>
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<goal name="space_saving_2'vc" expl="VC for space_saving_2" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="space_saving_2'vc.0" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="1297"/></proof>
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</goal>
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<goal name="space_saving_2'vc.1" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="23353"/></proof>
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</goal>
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<goal name="space_saving_2'vc.2" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="2912"/></proof>
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</goal>
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<goal name="space_saving_2'vc.3" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="1578"/></proof>
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</goal>
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<goal name="space_saving_2'vc.4" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="1580"/></proof>
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</goal>
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<goal name="space_saving_2'vc.5" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="1592"/></proof>
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</goal>
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<goal name="space_saving_2'vc.6" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="23245"/></proof>
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</goal>
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<goal name="space_saving_2'vc.7" expl="thm" proved="true">
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<proof prover="0"><result status="valid" time="0.120000" steps="24027"/></proof>
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</goal>
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<goal name="space_saving_2'vc.8" expl="thm" proved="true">
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<proof prover="0"><result status="valid" time="0.040000" steps="30225"/></proof>
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</goal>
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<goal name="space_saving_2'vc.9" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="1810"/></proof>
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</goal>
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<goal name="space_saving_2'vc.10" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="24543"/></proof>
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</goal>
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<goal name="space_saving_2'vc.11" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.050000" steps="28305"/></proof>
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</goal>
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<goal name="space_saving_2'vc.12" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.050000" steps="31844"/></proof>
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</goal>
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<goal name="space_saving_2'vc.13" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="28928"/></proof>
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</goal>
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<goal name="space_saving_2'vc.14" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="13078"/></proof>
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</goal>
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<goal name="space_saving_2'vc.15" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.040000" steps="31320"/></proof>
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</goal>
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<goal name="space_saving_2'vc.16" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="42266"/></proof>
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</goal>
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<goal name="space_saving_2'vc.17" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="24675"/></proof>
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</goal>
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<goal name="space_saving_2'vc.18" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.040000" steps="27700"/></proof>
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</goal>
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<goal name="space_saving_2'vc.19" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.050000" steps="30337"/></proof>
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</goal>
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<goal name="space_saving_2'vc.20" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="13070"/></proof>
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</goal>
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<goal name="space_saving_2'vc.21" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="29086"/></proof>
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</goal>
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<goal name="space_saving_2'vc.22" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="7197"/></proof>
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</goal>
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<goal name="space_saving_2'vc.23" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="41745"/></proof>
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</goal>
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<goal name="space_saving_2'vc.24" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="23835"/></proof>
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</goal>
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<goal name="space_saving_2'vc.25" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.050000" steps="30279"/></proof>
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</goal>
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<goal name="space_saving_2'vc.26" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.060000" steps="30545"/></proof>
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</goal>
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<goal name="space_saving_2'vc.27" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="27254"/></proof>
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</goal>
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<goal name="space_saving_2'vc.28" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="13286"/></proof>
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</goal>
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<goal name="space_saving_2'vc.29" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="7332"/></proof>
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</goal>
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<goal name="space_saving_2'vc.30" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.100000" steps="48058"/></proof>
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</goal>
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<goal name="space_saving_2'vc.31" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="23883"/></proof>
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</goal>
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<goal name="space_saving_2'vc.32" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.040000" steps="28264"/></proof>
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</goal>
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<goal name="space_saving_2'vc.33" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.050000" steps="31719"/></proof>
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</goal>
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<goal name="space_saving_2'vc.34" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="13222"/></proof>
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</goal>
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<goal name="space_saving_2'vc.35" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.040000" steps="27325"/></proof>
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</goal>
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<goal name="space_saving_2'vc.36" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="7343"/></proof>
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</goal>
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<goal name="space_saving_2'vc.37" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.080000" steps="41422"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="minimum'vc" expl="VC for minimum" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="34580"/></proof>
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</goal>
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<goal name="increment'vc" expl="VC for increment" proved="true">
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<proof prover="2" timelimit="1"><result status="valid" time="0.729202" steps="97586"/></proof>
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</goal>
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<goal name="find'vc" expl="VC for find" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="28979"/></proof>
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</goal>
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<goal name="minimum_k'vc" expl="VC for minimum_k" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="111309"/></proof>
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</goal>
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<goal name="space_saving_k'vc" expl="VC for space_saving_k" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="space_saving_k'vc.0" expl="array creation size" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="29041"/></proof>
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</goal>
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<goal name="space_saving_k'vc.1" expl="array creation size" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="34200"/></proof>
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</goal>
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<goal name="space_saving_k'vc.2" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="72221"/></proof>
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</goal>
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<goal name="space_saving_k'vc.3" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="49051"/></proof>
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</goal>
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<goal name="space_saving_k'vc.4" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="47738"/></proof>
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</goal>
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<goal name="space_saving_k'vc.5" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="49375"/></proof>
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</goal>
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<goal name="space_saving_k'vc.6" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="51739"/></proof>
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</goal>
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<goal name="space_saving_k'vc.7" expl="thm" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="51529"/></proof>
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</goal>
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<goal name="space_saving_k'vc.8" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="49548"/></proof>
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</goal>
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<goal name="space_saving_k'vc.9" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="5422"/></proof>
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</goal>
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<goal name="space_saving_k'vc.10" expl="thm" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="space_saving_k'vc.10.0" expl="thm" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="52820"/></proof>
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</goal>
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<goal name="space_saving_k'vc.10.1" expl="VC for space_saving_k" proved="true">
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<transf name="case" proved="true" arg1="(occurs v e)">
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<goal name="space_saving_k'vc.10.1.0" expl="true case" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="3687"/></proof>
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</goal>
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<goal name="space_saving_k'vc.10.1.1" expl="false case" proved="true">
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<transf name="assert" proved="true" arg1="(occ v s 0 n <= c[minimum c])">
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<goal name="space_saving_k'vc.10.1.1.0" expl="asserted formula" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="51172"/></proof>
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</goal>
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<goal name="space_saving_k'vc.10.1.1.1" expl="false case" proved="true">
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<transf name="assert" proved="true" arg1="(k * occ v s 0 n <= n)">
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<goal name="space_saving_k'vc.10.1.1.1.0" expl="asserted formula" proved="true">
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<proof prover="4"><result status="valid" time="1.542753"/></proof>
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</goal>
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<goal name="space_saving_k'vc.10.1.1.1.1" expl="false case" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="3703"/></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="space_saving_k'vc.11" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="3675"/></proof>
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</goal>
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<goal name="space_saving_k'vc.12" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="17818"/></proof>
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</goal>
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<goal name="space_saving_k'vc.13" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="56052"/></proof>
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</goal>
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<goal name="space_saving_k'vc.14" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="14599"/></proof>
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</goal>
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<goal name="space_saving_k'vc.15" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="56180"/></proof>
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</goal>
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<goal name="space_saving_k'vc.16" expl="loop invariant preservation" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="space_saving_k'vc.16.0" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="58740"/></proof>
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</goal>
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<goal name="space_saving_k'vc.16.1" expl="loop invariant preservation" proved="true">
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<proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="2.988107" steps="271127"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="space_saving_k'vc.17" expl="loop invariant preservation" proved="true">
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<proof prover="3" timelimit="1"><result status="valid" time="0.140000" steps="15708"/></proof>
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</goal>
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<goal name="space_saving_k'vc.18" expl="loop invariant preservation" proved="true">
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<proof prover="5" timelimit="1"><result status="valid" time="0.050000" steps="468"/></proof>
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</goal>
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<goal name="space_saving_k'vc.19" expl="loop invariant preservation" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="space_saving_k'vc.19.0" expl="loop invariant preservation" proved="true">
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<proof prover="2"><result status="valid" time="0.122653" steps="31267"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="space_saving_k'vc.20" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="52392"/></proof>
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</goal>
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<goal name="space_saving_k'vc.21" expl="index in array bounds" proved="true">
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<proof prover="0"><result status="valid" time="0.030000" steps="53479"/></proof>
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</goal>
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<goal name="space_saving_k'vc.22" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.020000" steps="55928"/></proof>
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</goal>
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<goal name="space_saving_k'vc.23" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="15304"/></proof>
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</goal>
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<goal name="space_saving_k'vc.24" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.010000" steps="56421"/></proof>
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</goal>
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<goal name="space_saving_k'vc.25" expl="loop invariant preservation" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="space_saving_k'vc.25.0" expl="loop invariant preservation" proved="true">
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<proof prover="2" timelimit="1"><result status="valid" time="0.080000" steps="15554"/></proof>
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</goal>
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<goal name="space_saving_k'vc.25.1" expl="loop invariant preservation" proved="true">
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<proof prover="6"><result status="valid" time="0.406278" steps="769842"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="space_saving_k'vc.26" expl="loop invariant preservation" proved="true">
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<proof prover="3"><result status="valid" time="0.150000" steps="26706"/></proof>
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</goal>
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<goal name="space_saving_k'vc.27" expl="loop invariant preservation" proved="true">
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<proof prover="5"><result status="valid" time="0.417346" steps="5173"/></proof>
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</goal>
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<goal name="space_saving_k'vc.28" expl="loop invariant preservation" proved="true">
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<proof prover="2"><result status="valid" time="3.079743" steps="292152"/></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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