Files
why3/examples/random_access_list/why3session.xml
2025-01-14 19:48:35 +01:00

314 lines
15 KiB
XML

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"https://www.why3.org/why3session.dtd">
<why3session shape_version="6">
<prover id="1" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="random_access_list.mlw"/>
<theory name="RandomAccessList" proved="true">
<goal name="length_flatten&#39;vc" expl="VC for length_flatten" proved="true">
<transf name="split_vc" proved="true" >
<goal name="length_flatten&#39;vc.0" expl="variant decrease" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="39"/></proof>
</goal>
<goal name="length_flatten&#39;vc.1" expl="postcondition" proved="true">
<transf name="unfold" proved="true" arg1="flatten">
<goal name="length_flatten&#39;vc.1.0" expl="postcondition" proved="true">
<proof prover="5"><result status="valid" time="0.010000" steps="14430"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="size&#39;vc" expl="VC for size" proved="true">
<proof prover="1"><result status="valid" time="0.020000" steps="152"/></proof>
</goal>
<goal name="cons&#39;vc" expl="VC for cons" proved="true">
<proof prover="1"><result status="valid" time="0.030000" steps="182"/></proof>
</goal>
<goal name="nth_flatten&#39;vc" expl="VC for nth_flatten" proved="true">
<transf name="split_vc" proved="true" >
<goal name="nth_flatten&#39;vc.0" expl="variant decrease" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="41"/></proof>
</goal>
<goal name="nth_flatten&#39;vc.1" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="15"/></proof>
</goal>
<goal name="nth_flatten&#39;vc.2" expl="postcondition" proved="true">
<transf name="destruct_term_subst" proved="true" arg1="l">
<goal name="nth_flatten&#39;vc.2.0" expl="postcondition" proved="true">
<transf name="case" proved="true" arg1="(i = 0)">
<goal name="nth_flatten&#39;vc.2.0.0" expl="true case (postcondition)" proved="true">
<transf name="subst" proved="true" arg1="i">
<goal name="nth_flatten&#39;vc.2.0.0.0" expl="true case (postcondition)" proved="true">
<transf name="destruct_term_subst" proved="true" arg1="x1">
<goal name="nth_flatten&#39;vc.2.0.0.0.0" expl="true case (postcondition)" proved="true">
<transf name="compute_in_goal" proved="true" >
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="nth_flatten&#39;vc.2.0.1" expl="false case (postcondition)" proved="true">
<transf name="replace" proved="true" arg1="(nth i (Cons x1 x))" arg2="(nth (i - 1) x)">
<goal name="nth_flatten&#39;vc.2.0.1.0" expl="false case (postcondition)" proved="true">
<transf name="destruct_term_subst" proved="true" arg1="x1">
<goal name="nth_flatten&#39;vc.2.0.1.0.0" expl="false case (postcondition)" proved="true">
<transf name="replace" proved="true" arg1="(2 * i)" arg2="((2 * (i - 1) + 1) + 1)">
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0" expl="false case (postcondition)" proved="true">
<transf name="destruct_term_subst" proved="true" arg1="(nth (i - 1) x)">
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0" expl="false case (postcondition)" proved="true">
<transf name="destruct_term_subst" proved="true" arg1="x">
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0" expl="false case (postcondition)" proved="true">
<transf name="replace" proved="true" arg1="(nth (i - 1) x2)" arg2="(Some (x1, x))">
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.0" expl="false case (postcondition)" proved="true">
<transf name="assert" proved="true" arg1="(match Some (x1, x) with None -&gt; false | Some (x0, x11) -&gt; Some x0 = nth (2 * (i - 1)) (flatten x2) /\ Some x11 = nth ((2 * (i - 1)) + 1) (flatten x2) end)">
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.0.0" expl="asserted formula" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="64"/></proof>
</goal>
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.0.1" expl="false case (postcondition)" proved="true">
<transf name="unfold" proved="true" arg1="flatten">
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.0.1.0" expl="false case (postcondition)" proved="true">
<proof prover="1"><result status="valid" time="0.020000" steps="152"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0.0.0.1" expl="equality hypothesis" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="10"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="nth_flatten&#39;vc.2.0.1.0.0.0.1" expl="false case (postcondition)" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
</goal>
</transf>
</goal>
<goal name="nth_flatten&#39;vc.2.0.1.0.0.1" expl="equality hypothesis" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="7"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="nth_flatten&#39;vc.2.0.1.1" expl="equality hypothesis" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="16"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="nth_flatten&#39;vc.2.1" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="7"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="lookup&#39;vc" expl="VC for lookup" proved="true">
<proof prover="1"><result status="valid" time="0.036179" steps="583"/></proof>
</goal>
<goal name="tail&#39;vc" expl="VC for tail" proved="true">
<proof prover="2"><result status="valid" time="0.200000" steps="35079"/></proof>
</goal>
<goal name="update&#39;vc" expl="VC for update" proved="true">
<transf name="split_goal_right" proved="true" >
<goal name="update&#39;vc.0" expl="unreachable point" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="7"/></proof>
</goal>
<goal name="update&#39;vc.1" expl="variant decrease" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
</goal>
<goal name="update&#39;vc.2" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.040000" steps="66"/></proof>
</goal>
<goal name="update&#39;vc.3" expl="unreachable point" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="31"/></proof>
</goal>
<goal name="update&#39;vc.4" expl="unreachable point" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="35"/></proof>
</goal>
<goal name="update&#39;vc.5" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="8"/></proof>
</goal>
<goal name="update&#39;vc.6" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.040000" steps="77"/></proof>
</goal>
<goal name="update&#39;vc.7" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
</goal>
<goal name="update&#39;vc.8" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="16"/></proof>
</goal>
<goal name="update&#39;vc.9" expl="variant decrease" proved="true">
<proof prover="1"><result status="valid" time="0.060000" steps="218"/></proof>
</goal>
<goal name="update&#39;vc.10" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="115"/></proof>
</goal>
<goal name="update&#39;vc.11" expl="assertion" proved="true">
<transf name="split_goal_right" proved="true" >
<goal name="update&#39;vc.11.0" expl="assertion" proved="true">
<proof prover="1"><result status="valid" time="0.080000" steps="155"/></proof>
</goal>
<goal name="update&#39;vc.11.1" expl="assertion" proved="true">
<proof prover="1"><result status="valid" time="0.120000" steps="469"/></proof>
</goal>
<goal name="update&#39;vc.11.2" expl="assertion" proved="true">
<proof prover="1" timelimit="1"><result status="valid" time="0.093943" steps="937"/></proof>
</goal>
</transf>
</goal>
<goal name="update&#39;vc.12" expl="postcondition" proved="true">
<proof prover="1" timelimit="1"><result status="valid" time="0.140000" steps="675"/></proof>
</goal>
<goal name="update&#39;vc.13" expl="postcondition" proved="true">
<proof prover="1" timelimit="1"><result status="valid" time="0.050000" steps="360"/></proof>
</goal>
<goal name="update&#39;vc.14" expl="postcondition" proved="true">
<proof prover="1" timelimit="1"><result status="valid" time="0.070000" steps="355"/></proof>
</goal>
<goal name="update&#39;vc.15" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.060000" steps="532"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="RAL" proved="true">
<goal name="t&#39;vc" expl="VC for t" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
</goal>
<goal name="empty&#39;vc" expl="VC for empty" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="12"/></proof>
</goal>
<goal name="size&#39;vc" expl="VC for size" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
</goal>
<goal name="cons&#39;vc" expl="VC for cons" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="21"/></proof>
</goal>
<goal name="lookup&#39;vc" expl="VC for lookup" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="9"/></proof>
</goal>
</theory>
<theory name="RandomAccessListWithSeq" proved="true">
<goal name="cons_flatten" proved="true">
<transf name="split_vc" proved="true" >
<goal name="cons_flatten.0" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="5"/></proof>
</goal>
<goal name="cons_flatten.1" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="17"/></proof>
</goal>
<goal name="cons_flatten.2" proved="true">
<proof prover="1"><result status="valid" time="0.060000" steps="262"/></proof>
</goal>
<goal name="cons_flatten.3" proved="true">
<proof prover="1"><result status="valid" time="0.217679" steps="1464"/></proof>
</goal>
<goal name="cons_flatten.4" proved="true">
<proof prover="1"><result status="valid" time="0.020000" steps="115"/></proof>
</goal>
<goal name="cons_flatten.5" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="3"/></proof>
</goal>
</transf>
</goal>
<goal name="size&#39;vc" expl="VC for size" proved="true">
<proof prover="1"><result status="valid" time="0.030000" steps="174"/></proof>
</goal>
<goal name="cons&#39;vc" expl="VC for cons" proved="true">
<proof prover="1"><result status="valid" time="0.050000" steps="334"/></proof>
</goal>
<goal name="lookup&#39;vc" expl="VC for lookup" proved="true">
<transf name="split_vc" proved="true" >
<goal name="lookup&#39;vc.0" expl="unreachable point" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="17"/></proof>
</goal>
<goal name="lookup&#39;vc.1" expl="variant decrease" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
</goal>
<goal name="lookup&#39;vc.2" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="45"/></proof>
</goal>
<goal name="lookup&#39;vc.3" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.000000" steps="6"/></proof>
</goal>
<goal name="lookup&#39;vc.4" expl="variant decrease" proved="true">
<proof prover="1"><result status="valid" time="0.040000" steps="130"/></proof>
</goal>
<goal name="lookup&#39;vc.5" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.030000" steps="74"/></proof>
</goal>
<goal name="lookup&#39;vc.6" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
</goal>
<goal name="lookup&#39;vc.7" expl="postcondition" proved="true">
<transf name="split_vc" proved="true" >
<goal name="lookup&#39;vc.7.0" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="70"/></proof>
</goal>
<goal name="lookup&#39;vc.7.1" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="142"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="tail&#39;vc" expl="VC for tail" proved="true">
<proof prover="1"><result status="valid" time="0.110000" steps="774"/></proof>
</goal>
<goal name="aux&#39;vc" expl="VC for aux" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="0"/></proof>
</goal>
<goal name="fupdate&#39;vc" expl="VC for fupdate" proved="true">
<transf name="split_vc" proved="true" >
<goal name="fupdate&#39;vc.0" expl="unreachable point" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="17"/></proof>
</goal>
<goal name="fupdate&#39;vc.1" expl="variant decrease" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
</goal>
<goal name="fupdate&#39;vc.2" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="45"/></proof>
</goal>
<goal name="fupdate&#39;vc.3" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
</goal>
<goal name="fupdate&#39;vc.4" expl="variant decrease" proved="true">
<proof prover="1"><result status="valid" time="0.040000" steps="130"/></proof>
</goal>
<goal name="fupdate&#39;vc.5" expl="precondition" proved="true">
<proof prover="1"><result status="valid" time="0.030000" steps="74"/></proof>
</goal>
<goal name="fupdate&#39;vc.6" expl="assertion" proved="true">
<proof prover="1"><result status="valid" time="0.150019" steps="742"/></proof>
</goal>
<goal name="fupdate&#39;vc.7" expl="postcondition" proved="true">
<transf name="split_vc" proved="true" >
<goal name="fupdate&#39;vc.7.0" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.030000" steps="456"/></proof>
</goal>
<goal name="fupdate&#39;vc.7.1" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.030000" steps="263"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="f&#39;vc" expl="VC for f" proved="true">
<proof prover="1" timelimit="1"><result status="valid" time="0.010000" steps="0"/></proof>
</goal>
<goal name="update&#39;vc" expl="VC for update" proved="true">
<proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
</goal>
</theory>
</file>
</why3session>