mirror of
https://github.com/AdaCore/why3.git
synced 2026-02-12 12:34:55 -08:00
731 lines
39 KiB
XML
731 lines
39 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="4.13.2" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="3" name="Alt-Ergo" version="2.6.2" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="4" name="CVC5" version="1.2.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="7" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
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<file format="whyml" proved="true">
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<path name=".."/><path name="linked_list_rev.mlw"/>
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<theory name="InPlaceRev" proved="true">
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<goal name="mem_decomp'vc" expl="VC for mem_decomp" proved="true">
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<proof prover="4"><result status="valid" time="0.069376" steps="5395"/></proof>
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</goal>
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<goal name="list_seg_frame_ext'vc" expl="VC for list_seg_frame_ext" proved="true">
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<proof prover="4"><result status="valid" time="0.084390" steps="5651"/></proof>
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</goal>
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<goal name="list_seg_functional'vc" expl="VC for list_seg_functional" proved="true">
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<proof prover="3"><result status="valid" time="0.071214" steps="315"/></proof>
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</goal>
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<goal name="list_seg_sublistl'vc" expl="VC for list_seg_sublistl" proved="true">
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<proof prover="3"><result status="valid" time="0.040893" steps="218"/></proof>
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</goal>
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<goal name="list_seg_no_repet'vc" expl="VC for list_seg_no_repet" proved="true">
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<proof prover="4"><result status="valid" time="0.062840" steps="7767"/></proof>
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</goal>
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<goal name="list_seg_append'vc" expl="VC for list_seg_append" proved="true">
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<proof prover="3"><result status="valid" time="0.054280" steps="336"/></proof>
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</goal>
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<goal name="app'vc" expl="VC for app" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="app'vc.0" expl="postcondition" proved="true">
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<proof prover="0"><result status="valid" time="0.014539" steps="24602"/></proof>
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</goal>
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<goal name="app'vc.1" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.007031" steps="2428"/></proof>
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</goal>
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<goal name="app'vc.2" expl="loop invariant init" proved="true">
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<proof prover="3"><result status="valid" time="0.022336" steps="14"/></proof>
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</goal>
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<goal name="app'vc.3" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.010166" steps="2220"/></proof>
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</goal>
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<goal name="app'vc.4" expl="loop invariant init" proved="true">
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<proof prover="3"><result status="valid" time="0.027593" steps="16"/></proof>
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</goal>
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<goal name="app'vc.5" expl="loop invariant init" proved="true">
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<proof prover="4"><result status="valid" time="0.047173" steps="4643"/></proof>
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</goal>
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<goal name="app'vc.6" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.034465" steps="22"/></proof>
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</goal>
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<goal name="app'vc.7" expl="unreachable point" proved="true">
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<proof prover="3"><result status="valid" time="0.043675" steps="85"/></proof>
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</goal>
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<goal name="app'vc.8" expl="assertion" proved="true">
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<proof prover="0"><result status="valid" time="0.012902" steps="29525"/></proof>
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</goal>
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<goal name="app'vc.9" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.029045" steps="32"/></proof>
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</goal>
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<goal name="app'vc.10" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.033174" steps="3879"/></proof>
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</goal>
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<goal name="app'vc.11" expl="loop variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.042604" steps="155"/></proof>
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</goal>
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<goal name="app'vc.12" expl="loop invariant preservation" proved="true">
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<proof prover="3"><result status="valid" time="0.029221" steps="36"/></proof>
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</goal>
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<goal name="app'vc.13" expl="loop invariant preservation" proved="true">
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<proof prover="3"><result status="valid" time="0.081578" steps="566"/></proof>
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</goal>
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<goal name="app'vc.14" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.071176" steps="5130"/></proof>
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</goal>
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<goal name="app'vc.15" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.061133" steps="6091"/></proof>
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</goal>
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<goal name="app'vc.16" expl="loop invariant preservation" proved="true">
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<proof prover="3"><result status="valid" time="0.071294" steps="619"/></proof>
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</goal>
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<goal name="app'vc.17" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.034384" steps="26"/></proof>
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</goal>
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<goal name="app'vc.18" expl="assertion" proved="true">
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<proof prover="4"><result status="valid" time="0.077164" steps="7415"/></proof>
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</goal>
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<goal name="app'vc.19" expl="assertion" proved="true">
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<proof prover="4"><result status="valid" time="0.048458" steps="5517"/></proof>
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</goal>
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<goal name="app'vc.20" expl="assertion" proved="true">
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<proof prover="0"><result status="valid" time="0.015102" steps="27985"/></proof>
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</goal>
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<goal name="app'vc.21" expl="postcondition" proved="true">
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<proof prover="4"><result status="valid" time="0.060074" steps="8013"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="in_place_reverse'vc" expl="VC for in_place_reverse" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="in_place_reverse'vc.0" expl="loop invariant init" proved="true">
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<proof prover="3"><result status="valid" time="0.029338" steps="4"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.1" expl="loop invariant init" proved="true">
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<proof prover="3"><result status="valid" time="0.035348" steps="6"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.2" expl="loop invariant init" proved="true">
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<proof prover="3"><result status="valid" time="0.028139" steps="23"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.3" expl="loop invariant init" proved="true">
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<proof prover="0"><result status="valid" time="0.018380" steps="22631"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.4" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.028524" steps="2954"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.5" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.060067" steps="173"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.6" expl="unreachable point" proved="true">
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<proof prover="3"><result status="valid" time="0.052432" steps="86"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.7" expl="loop variant decrease" proved="true">
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<proof prover="0"><result status="valid" time="0.005049" steps="7748"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.8" expl="loop invariant preservation" proved="true">
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<proof prover="3"><result status="valid" time="0.050370" steps="198"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.9" expl="loop invariant preservation" proved="true">
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<proof prover="4"><result status="valid" time="0.056187" steps="5587"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.10" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.013843" steps="31931"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.11" expl="loop invariant preservation" proved="true">
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<proof prover="0"><result status="valid" time="0.018766" steps="28074"/></proof>
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</goal>
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<goal name="in_place_reverse'vc.12" expl="postcondition" proved="true">
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<proof prover="0"><result status="valid" time="0.008660" steps="27740"/></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="InPlaceRevSeq" proved="true">
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<goal name="non_empty_seq" proved="true">
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<proof prover="7"><result status="valid" time="0.061680" steps="9528"/></proof>
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</goal>
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<goal name="mem_decomp'vc" expl="VC for mem_decomp" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="mem_decomp'vc.0" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.027917" steps="14"/></proof>
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</goal>
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<goal name="mem_decomp'vc.1" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.042809" steps="18"/></proof>
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</goal>
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<goal name="mem_decomp'vc.2" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.040544" steps="27"/></proof>
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</goal>
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<goal name="mem_decomp'vc.3" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.037869" steps="13"/></proof>
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</goal>
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<goal name="mem_decomp'vc.4" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.036961" steps="3930"/></proof>
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</goal>
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<goal name="mem_decomp'vc.5" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.126800" steps="980"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="list_seg_frame_ext" proved="true">
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<proof prover="3"><result status="valid" time="0.059531" steps="131"/></proof>
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</goal>
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<goal name="list_seg_functional'vc" expl="VC for list_seg_functional" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="list_seg_functional'vc.0" expl="assertion" proved="true">
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<proof prover="4"><result status="valid" time="0.041451" steps="4629"/></proof>
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</goal>
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<goal name="list_seg_functional'vc.1" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.026770" steps="4095"/></proof>
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</goal>
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<goal name="list_seg_functional'vc.2" expl="precondition" proved="true">
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<proof prover="7"><result status="valid" time="0.038986" steps="8556"/></proof>
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</goal>
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<goal name="list_seg_functional'vc.3" expl="variant decrease" proved="true">
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<proof prover="7"><result status="valid" time="0.077978" steps="11779"/></proof>
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</goal>
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<goal name="list_seg_functional'vc.4" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.098846" steps="481"/></proof>
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</goal>
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<goal name="list_seg_functional'vc.5" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.180638" steps="996"/></proof>
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</goal>
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<goal name="list_seg_functional'vc.6" expl="postcondition" proved="true">
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<proof prover="0"><result status="valid" time="0.023096" steps="50992"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="list_seg_tail'vc" expl="VC for list_seg_tail" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="list_seg_tail'vc.0" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.025359" steps="3745"/></proof>
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</goal>
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<goal name="list_seg_tail'vc.1" expl="variant decrease" proved="true">
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<proof prover="4"><result status="valid" time="0.047171" steps="5646"/></proof>
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</goal>
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<goal name="list_seg_tail'vc.2" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.071326" steps="244"/></proof>
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</goal>
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<goal name="list_seg_tail'vc.3" expl="precondition" proved="true">
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<proof prover="0"><result status="valid" time="0.026152" steps="36907"/></proof>
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</goal>
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<goal name="list_seg_tail'vc.4" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.141191" steps="1046"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="list_seg_append'vc" expl="VC for list_seg_append" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="list_seg_append'vc.0" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.050809" steps="3818"/></proof>
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</goal>
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<goal name="list_seg_append'vc.1" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.050582" steps="39"/></proof>
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</goal>
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<goal name="list_seg_append'vc.2" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.041572" steps="4674"/></proof>
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</goal>
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<goal name="list_seg_append'vc.3" expl="precondition" proved="true">
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<proof prover="7"><result status="valid" time="0.045030" steps="7989"/></proof>
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</goal>
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<goal name="list_seg_append'vc.4" expl="postcondition" proved="true">
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<proof prover="0"><result status="valid" time="0.859410" steps="2145151"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="seq_tail_append" proved="true">
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<proof prover="3"><result status="valid" time="0.042436" steps="173"/></proof>
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</goal>
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<goal name="list_seg_prefix'vc" expl="VC for list_seg_prefix" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="list_seg_prefix'vc.0" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.026466" steps="4493"/></proof>
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</goal>
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<goal name="list_seg_prefix'vc.1" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.044147" steps="16"/></proof>
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</goal>
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<goal name="list_seg_prefix'vc.2" expl="precondition" proved="true">
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<proof prover="4"><result status="valid" time="0.034853" steps="4512"/></proof>
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</goal>
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<goal name="list_seg_prefix'vc.3" expl="variant decrease" proved="true">
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<proof prover="4"><result status="valid" time="0.061296" steps="8625"/></proof>
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</goal>
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<goal name="list_seg_prefix'vc.4" expl="precondition" proved="true">
|
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<proof prover="3"><result status="valid" time="0.037299" steps="86"/></proof>
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</goal>
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<goal name="list_seg_prefix'vc.5" expl="postcondition" proved="true">
|
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<proof prover="0"><result status="valid" time="0.204323" steps="556691"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="list_seg_sublistl'vc" expl="VC for list_seg_sublistl" proved="true">
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<transf name="split_vc" proved="true" >
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<goal name="list_seg_sublistl'vc.0" expl="assertion" proved="true">
|
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<proof prover="4"><result status="valid" time="0.031875" steps="3621"/></proof>
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</goal>
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<goal name="list_seg_sublistl'vc.1" expl="precondition" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.049324" steps="8507"/></proof>
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</goal>
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<goal name="list_seg_sublistl'vc.2" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.027033" steps="6"/></proof>
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</goal>
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|
<goal name="list_seg_sublistl'vc.3" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.023848" steps="4132"/></proof>
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</goal>
|
|
<goal name="list_seg_sublistl'vc.4" expl="variant decrease" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.040849" steps="56915"/></proof>
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|
</goal>
|
|
<goal name="list_seg_sublistl'vc.5" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.067542" steps="119"/></proof>
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</goal>
|
|
<goal name="list_seg_sublistl'vc.6" expl="postcondition" proved="true">
|
|
<transf name="destruct" proved="true" arg1="H">
|
|
<goal name="list_seg_sublistl'vc.6.0" expl="postcondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.027425" steps="4129"/></proof>
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|
</goal>
|
|
<goal name="list_seg_sublistl'vc.6.1" expl="postcondition" proved="true">
|
|
<transf name="assert" proved="true" arg1="(l1 = empty)">
|
|
<goal name="list_seg_sublistl'vc.6.1.0" expl="asserted formula" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.059797" steps="9708"/></proof>
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|
</goal>
|
|
<goal name="list_seg_sublistl'vc.6.1.1" expl="postcondition" proved="true">
|
|
<transf name="assert" proved="true" arg1="(forall l:seq 'a. empty ++ l = l)">
|
|
<goal name="list_seg_sublistl'vc.6.1.1.0" expl="asserted formula" proved="true">
|
|
<transf name="assert" proved="true" arg1="(forall l:seq 'a. empty ++ l == l)">
|
|
<goal name="list_seg_sublistl'vc.6.1.1.0.0" expl="asserted formula" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.065919" steps="197"/></proof>
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|
</goal>
|
|
<goal name="list_seg_sublistl'vc.6.1.1.0.1" expl="asserted formula" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.030656" steps="4963"/></proof>
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</goal>
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|
</transf>
|
|
</goal>
|
|
<goal name="list_seg_sublistl'vc.6.1.1.1" expl="postcondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.049638" steps="5199"/></proof>
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|
</goal>
|
|
</transf>
|
|
</goal>
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|
</transf>
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|
</goal>
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|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="get_tail" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.022061" steps="48440"/></proof>
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|
</goal>
|
|
<goal name="tail_suffix" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.044640" steps="145"/></proof>
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|
</goal>
|
|
<goal name="list_seg_no_repet'vc" expl="VC for list_seg_no_repet" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="list_seg_no_repet'vc.0" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.032396" steps="4306"/></proof>
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</goal>
|
|
<goal name="list_seg_no_repet'vc.1" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.026986" steps="6"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.2" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.207020" steps="15853"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.3" expl="precondition" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.060730" steps="9950"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.4" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.034360" steps="71"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.5" expl="assertion" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.054838" steps="147"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.6" expl="assertion" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.007871" steps="3926"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.7" expl="variant decrease" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.066046" steps="7058"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.8" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.026997" steps="15"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.9" expl="assertion" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.509003" steps="51720"/></proof>
|
|
</goal>
|
|
<goal name="list_seg_no_repet'vc.10" expl="postcondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.050764" steps="100027"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="app'vc" expl="VC for app" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="app'vc.0" expl="postcondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.030679" steps="58308"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.1" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.030509" steps="3625"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.2" expl="loop invariant init" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.032103" steps="12"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.3" expl="loop invariant init" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.037811" steps="40"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.4" expl="loop invariant init" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.009212" steps="2787"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.5" expl="loop invariant init" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.047030" steps="5447"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.6" expl="loop invariant init" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.016151" steps="43572"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.7" expl="precondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.005794" steps="3410"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.8" expl="assertion" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.028025" steps="50722"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.9" expl="assertion" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.020929" steps="56174"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.10" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.032718" steps="4984"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.11" expl="precondition" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.044785" steps="11106"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.12" expl="loop variant decrease" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.073523" steps="10940"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.13" expl="loop invariant preservation" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.046514" steps="11202"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.14" expl="loop invariant preservation" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.328743" steps="2969"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.15" expl="loop invariant preservation" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.057694" steps="62"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.16" expl="loop invariant preservation" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.086896" steps="14055"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.17" expl="loop invariant preservation" proved="true">
|
|
<transf name="remove" proved="true" arg1="zero,one,(-),(>),(<=),(>=),get1,set1,([]'),([<-]'),(!),([]),singleton,cons,snoc,(++),reverse,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,length_nonnegative,create'spec,empty'def,set'spec,set'def,([<-])'def,singleton'spec,cons'spec,snoc'spec,([..])'def,([.._])'def,mem_append,mem_tail,eq_loc'spec,non_empty_seq,list_seg_frame_ext,list_seg_functional,list_seg_tail,list_seg_append,seq_tail_append,list_seg_prefix,list_seg_sublistl,get_tail,tail_suffix,Requires2,Requires1,Requires,Ensures11,H1,Ensures10,LoopInvariant8,LoopInvariant7,Ensures9,H,Assert,Ensures8,Ensures7,Ensures6,Ensures5,Ensures4,Ensures3,LoopInvariant3,LoopInvariant2,LoopInvariant1">
|
|
<goal name="app'vc.17.0" expl="loop invariant preservation" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.074011" steps="477"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="app'vc.18" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.041598" steps="26"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.19" expl="assertion" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.126484" steps="14474"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.20" expl="assertion" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.063971" steps="7392"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.21" expl="assertion" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.075932" steps="138426"/></proof>
|
|
</goal>
|
|
<goal name="app'vc.22" expl="postcondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.124831" steps="245249"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc" expl="VC for in_place_reverse" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="in_place_reverse'vc.0" expl="loop invariant init" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.025444" steps="3152"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.1" expl="loop invariant init" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.061387" steps="3770"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.2" expl="loop invariant init" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.014903" steps="32787"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.3" expl="loop invariant init" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.065521" steps="6867"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.4" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.028038" steps="14"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.5" expl="precondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.007133" steps="5081"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.6" expl="assertion" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.034851" steps="50576"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.7" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.052801" steps="35"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.8" expl="loop variant decrease" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.084944" steps="9407"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.9" expl="loop invariant preservation" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.128843" steps="17500"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.10" expl="loop invariant preservation" proved="true">
|
|
<proof prover="3"><result status="valid" time="3.905371" steps="27546"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.11" expl="loop invariant preservation" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.550000" steps="76920"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.12" expl="loop invariant preservation" proved="true">
|
|
<transf name="assert" proved="true" arg1="(length pM1 > 0)">
|
|
<goal name="in_place_reverse'vc.12.0" expl="asserted formula" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.055326" steps="57"/></proof>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.12.1" expl="loop invariant preservation" proved="true">
|
|
<transf name="remove" proved="true" arg1="LoopInvariant,LoopInvariant1,LoopInvariant2,LoopInvariant4,LoopInvariant5,LoopInvariant6,Ensures2,Ensures3,Ensures4,Ensures5,Ensures6,Ensures7,Ensures8">
|
|
<goal name="in_place_reverse'vc.12.1.0" expl="loop invariant preservation" proved="true">
|
|
<transf name="remove" proved="true" arg1="zero,one,(-),(>),(<=),(>=),get1,set1,([]'),([<-]'),(!),([]),singleton,cons,snoc,(++),mem,disjoint,no_repet,list_seg,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,length_nonnegative,empty'def,set'spec,set'def,([<-])'def,singleton'spec,snoc'spec,([..])'def,([.._])'def,mem_append,mem_tail,eq_loc'spec,non_empty_seq,list_seg_frame_ext,list_seg_functional,list_seg_tail,list_seg_append,seq_tail_append,list_seg_prefix,list_seg_sublistl,get_tail,tail_suffix,list_seg_no_repet,Requires,H,Assert">
|
|
<goal name="in_place_reverse'vc.12.1.0.0" expl="loop invariant preservation" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.080109" steps="291"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="in_place_reverse'vc.13" expl="postcondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.074000" steps="297"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</theory>
|
|
<theory name="YetAnotherInPlaceRev" proved="true">
|
|
<goal name="cdr'vc" expl="VC for cdr" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.033250" steps="8"/></proof>
|
|
</goal>
|
|
<goal name="set_cdr'vc" expl="VC for set_cdr" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.031385" steps="14"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc" expl="VC for list_reversal" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.026951" steps="45555"/></proof>
|
|
</goal>
|
|
<goal name="is_list'vc" expl="VC for is_list" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.038059" steps="14"/></proof>
|
|
</goal>
|
|
<goal name="cells_of_list'vc" expl="VC for cells_of_list" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="cells_of_list'vc.0" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.025364" steps="660"/></proof>
|
|
</goal>
|
|
<goal name="cells_of_list'vc.1" expl="variant decrease" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.001968" steps="175"/></proof>
|
|
</goal>
|
|
<goal name="cells_of_list'vc.2" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.021894" steps="6"/></proof>
|
|
</goal>
|
|
<goal name="cells_of_list'vc.3" expl="precondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.016204" steps="19960"/></proof>
|
|
</goal>
|
|
<goal name="cells_of_list'vc.4" expl="postcondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.260398" steps="2678"/></proof>
|
|
</goal>
|
|
<goal name="cells_of_list'vc.5" expl="postcondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.104372" steps="577"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="list_of_cells'vc" expl="VC for list_of_cells" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="list_of_cells'vc.0" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.062153" steps="2429"/></proof>
|
|
</goal>
|
|
<goal name="list_of_cells'vc.1" expl="variant decrease" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.039468" steps="1904"/></proof>
|
|
</goal>
|
|
<goal name="list_of_cells'vc.2" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.024735" steps="8"/></proof>
|
|
</goal>
|
|
<goal name="list_of_cells'vc.3" expl="precondition" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.080234" steps="11767"/></proof>
|
|
</goal>
|
|
<goal name="list_of_cells'vc.4" expl="precondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.010083" steps="10242"/></proof>
|
|
</goal>
|
|
<goal name="list_of_cells'vc.5" expl="postcondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.210748" steps="20953"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="list_reversal_final'vc" expl="VC for list_reversal_final" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.355770" steps="50031"/></proof>
|
|
</goal>
|
|
</theory>
|
|
<theory name="Termination" proved="true">
|
|
<goal name="cdr'vc" expl="VC for cdr" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.043607" steps="1034"/></proof>
|
|
</goal>
|
|
<goal name="set_cdr'vc" expl="VC for set_cdr" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.029232" steps="1598"/></proof>
|
|
</goal>
|
|
<goal name="set_idx'vc" expl="VC for set_idx" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="set_idx'vc.0" expl="assertion" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="set_idx'vc.0.0" expl="assertion" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.025584" steps="43"/></proof>
|
|
</goal>
|
|
<goal name="set_idx'vc.0.1" expl="VC for set_idx" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.186811" steps="1108"/></proof>
|
|
</goal>
|
|
<goal name="set_idx'vc.0.2" expl="VC for set_idx" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.024141" steps="45154"/></proof>
|
|
</goal>
|
|
<goal name="set_idx'vc.0.3" expl="VC for set_idx" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.738491" steps="2155411"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="set_idx'vc.1" expl="postcondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.026919" steps="1748"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="list_reversal'vc" expl="VC for list_reversal" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="list_reversal'vc.0" expl="loop invariant init" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.047437" steps="2927"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.1" expl="loop invariant init" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.028736" steps="2992"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.2" expl="loop invariant init" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.029817" steps="1838"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.3" expl="loop invariant init" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.017088" steps="15115"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.4" expl="loop invariant init" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.029980" steps="46"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.5" expl="loop invariant init" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.008919" steps="14613"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.6" expl="loop invariant init" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.011647" steps="21089"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.7" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.026456" steps="2415"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.8" expl="precondition" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.026056" steps="3983"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.9" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.043664" steps="2412"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.10" expl="precondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.006858" steps="1796"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.11" expl="precondition" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.025477" steps="2427"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.12" expl="precondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.006235" steps="1674"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.13" expl="precondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.001015" steps="1683"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.14" expl="loop variant decrease" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.012805" steps="22300"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.15" expl="loop invariant preservation" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.057839" steps="10010"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.16" expl="loop invariant preservation" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.031270" steps="2967"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.17" expl="loop invariant preservation" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.034736" steps="43546"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.18" expl="loop invariant preservation" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.054839" steps="5046"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.19" expl="loop invariant preservation" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.037124" steps="152"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.20" expl="loop invariant preservation" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.046385" steps="118"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.21" expl="loop invariant preservation" proved="true">
|
|
<transf name="case" proved="true" arg1="(idx l = 0)">
|
|
<goal name="list_reversal'vc.21.0" expl="true case (loop invariant preservation)" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.042334" steps="106"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.21.1" expl="false case (loop invariant preservation)" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.103483" steps="789"/></proof>
|
|
</goal>
|
|
</transf>
|
|
<transf name="case" proved="true" arg1="(idx l = -1)">
|
|
<goal name="list_reversal'vc.21.0" expl="true case (loop invariant preservation)" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.052935" steps="10330"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.21.1" expl="false case (loop invariant preservation)" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.056595" steps="10608"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="list_reversal'vc.22" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.026721" steps="26"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.23" expl="precondition" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.008923" steps="1636"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.24" expl="loop variant decrease" proved="true">
|
|
<transf name="right" proved="true" >
|
|
<goal name="list_reversal'vc.24.0" expl="right case" proved="true">
|
|
<transf name="split_vc" proved="true" >
|
|
<goal name="list_reversal'vc.24.0.0" expl="right case" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.057732" steps="3664"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.24.0.1" expl="right case" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.032267" steps="110"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="list_reversal'vc.25" expl="loop invariant preservation" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.065040" steps="6596"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.26" expl="loop invariant preservation" proved="true">
|
|
<proof prover="4"><result status="valid" time="0.025268" steps="2802"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.27" expl="loop invariant preservation" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.037785" steps="49539"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.28" expl="loop invariant preservation" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.040305" steps="37"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.29" expl="loop invariant preservation" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.009939" steps="22860"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.30" expl="loop invariant preservation" proved="true">
|
|
<proof prover="0"><result status="valid" time="0.017504" steps="19654"/></proof>
|
|
</goal>
|
|
<goal name="list_reversal'vc.31" expl="loop invariant preservation" proved="true">
|
|
<transf name="case" proved="true" arg1="(idx l = 0)">
|
|
<goal name="list_reversal'vc.31.0" expl="true case (loop invariant preservation)" proved="true">
|
|
<transf name="rewrite" proved="true" arg1="h">
|
|
<goal name="list_reversal'vc.31.0.0" expl="true case (loop invariant preservation)" proved="true">
|
|
<transf name="compute_in_goal" proved="true" >
|
|
<goal name="list_reversal'vc.31.0.0.0" expl="true case (loop invariant preservation)" proved="true">
|
|
<proof prover="7"><result status="valid" time="0.032791" steps="5664"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
<goal name="list_reversal'vc.31.1" expl="false case (loop invariant preservation)" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.061225" steps="181"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</theory>
|
|
</file>
|
|
</why3session>
|