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

396 lines
20 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="Z3" version="4.8.10" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="7" name="Z3" version="4.7.1" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="8" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="fibonacci.mlw"/>
<theory name="FibonacciTest" proved="true">
<goal name="isfib_2_1" proved="true">
<proof prover="4" timelimit="5"><result status="valid" time="0.000000" steps="679"/></proof>
<proof prover="7" timelimit="5"><result status="valid" time="0.010000" steps="907"/></proof>
</goal>
<goal name="isfib_6_8" proved="true">
<proof prover="4" timelimit="5"><result status="valid" time="0.000000" steps="1039"/></proof>
<proof prover="7" timelimit="5"><result status="valid" time="0.010000" steps="1445"/></proof>
</goal>
<goal name="not_isfib_2_2" proved="true">
<proof prover="4" timelimit="5"><result status="valid" time="0.000000" steps="376"/></proof>
<proof prover="7" timelimit="5"><result status="valid" time="0.010000" steps="251"/></proof>
<proof prover="8"><result status="valid" time="0.000000" steps="12"/></proof>
</goal>
</theory>
<theory name="FibonacciLinear" proved="true">
<goal name="fib&#39;vc" expl="VC for fib" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="3418"/></proof>
</goal>
</theory>
<theory name="FibonacciTailRecList" proved="true">
<goal name="sum_fib&#39;vc" expl="VC for sum_fib" proved="true">
<transf name="split_vc" proved="true" >
<goal name="sum_fib&#39;vc.0" expl="precondition" proved="true">
<proof prover="8"><result status="valid" time="0.016279" steps="204"/></proof>
</goal>
<goal name="sum_fib&#39;vc.1" expl="precondition" proved="true">
<proof prover="8"><result status="valid" time="0.020231" steps="164"/></proof>
</goal>
</transf>
</goal>
<goal name="sum_pow&#39;vc" expl="VC for sum_pow" proved="true">
<transf name="split_all_full" proved="true" >
<goal name="sum_pow&#39;vc.0" expl="assertion" proved="true">
<proof prover="8" timelimit="1"><result status="valid" time="0.000000" steps="10"/></proof>
</goal>
<goal name="sum_pow&#39;vc.1" expl="assertion" proved="true">
<proof prover="8" timelimit="1"><result status="valid" time="0.010000" steps="16"/></proof>
</goal>
<goal name="sum_pow&#39;vc.2" expl="precondition" proved="true">
<proof prover="8" timelimit="1"><result status="valid" time="0.010000" steps="29"/></proof>
</goal>
<goal name="sum_pow&#39;vc.3" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.020000" steps="936"/></proof>
</goal>
<goal name="sum_pow&#39;vc.4" expl="postcondition" proved="true">
<proof prover="8" timelimit="1"><result status="valid" time="0.010000" steps="27"/></proof>
</goal>
</transf>
</goal>
<goal name="pow_pos" proved="true">
<transf name="split_vc" proved="true" >
<goal name="pow_pos.0" proved="true">
<transf name="induction" proved="true" arg1="x">
<goal name="pow_pos.0.0" expl="base case" proved="true">
<proof prover="2"><result status="valid" time="0.020000" steps="4398"/></proof>
</goal>
<goal name="pow_pos.0.1" expl="recursive case" proved="true">
<proof prover="2"><result status="valid" time="0.020000" steps="4499"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="sum_fib_acc&#39;vc" expl="VC for sum_fib_acc" proved="true">
<transf name="split_vc" proved="true" >
<goal name="sum_fib_acc&#39;vc.0" expl="assertion" proved="true">
<proof prover="8"><result status="valid" time="0.026073" steps="218"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.1" expl="variant decrease" proved="true">
<transf name="split_vc" proved="true" >
<goal name="sum_fib_acc&#39;vc.1.0" expl="variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.020000" steps="11503"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.1.1" expl="variant decrease" proved="true">
<proof prover="8"><result status="valid" time="0.030000" steps="108"/></proof>
</goal>
</transf>
</goal>
<goal name="sum_fib_acc&#39;vc.2" expl="precondition" proved="true">
<transf name="assert" proved="true" arg1="(mem n l)">
<goal name="sum_fib_acc&#39;vc.2.0" expl="asserted formula" proved="true">
<proof prover="8" timelimit="1"><result status="valid" time="0.010000" steps="11"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.2.1" expl="precondition" proved="true">
<proof prover="8" timelimit="1"><result status="valid" time="0.010000" steps="12"/></proof>
</goal>
</transf>
</goal>
<goal name="sum_fib_acc&#39;vc.3" expl="assertion" proved="true">
<transf name="assert" proved="true" arg1="(u = x1 - 2 \/ mem u x)">
<goal name="sum_fib_acc&#39;vc.3.0" expl="asserted formula" proved="true">
<proof prover="8" timelimit="1"><result status="valid" time="0.010000" steps="12"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.3.1" expl="assertion" proved="true">
<transf name="destruct" proved="true" arg1="h">
<goal name="sum_fib_acc&#39;vc.3.1.0" expl="assertion" proved="true">
<proof prover="2"><result status="valid" time="0.020000" steps="9396"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.3.1.1" expl="assertion" proved="true">
<transf name="assert" proved="true" arg1="(mem u l)">
<goal name="sum_fib_acc&#39;vc.3.1.1.0" expl="asserted formula" proved="true">
<proof prover="5"><result status="valid" time="0.030000" steps="2316"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.3.1.1.1" expl="assertion" proved="true">
<proof prover="2"><result status="valid" time="0.020000" steps="9644"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="sum_fib_acc&#39;vc.4" expl="assertion" proved="true">
<proof prover="5"><result status="valid" time="0.030000" steps="2529"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.5" expl="variant decrease" proved="true">
<transf name="split_vc" proved="true" >
<goal name="sum_fib_acc&#39;vc.5.0" expl="variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.010000" steps="11510"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.5.1" expl="variant decrease" proved="true">
<proof prover="5"><result status="valid" time="0.050000" steps="3933"/></proof>
</goal>
</transf>
</goal>
<goal name="sum_fib_acc&#39;vc.6" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.030000" steps="10179"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.7" expl="postcondition" proved="true">
<transf name="split_vc" proved="true" >
<goal name="sum_fib_acc&#39;vc.7.0" expl="postcondition" proved="true">
<proof prover="2" timelimit="1"><result status="valid" time="0.010000" steps="27836"/></proof>
</goal>
<goal name="sum_fib_acc&#39;vc.7.1" expl="postcondition" proved="true">
<proof prover="5"><result status="valid" time="0.030000" steps="5678"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="fib&#39;vc" expl="VC for fib" proved="true">
<proof prover="5"><result status="valid" time="0.040000" steps="3821"/></proof>
</goal>
</theory>
<theory name="FibRecGhost" proved="true">
<goal name="fib_aux&#39;vc" expl="VC for fib_aux" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="2439"/></proof>
</goal>
<goal name="fib&#39;vc" expl="VC for fib" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="9"/></proof>
</goal>
<goal name="test42&#39;vc" expl="VC for test42" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="0"/></proof>
</goal>
</theory>
<theory name="FibRecNoGhost" proved="true">
<goal name="fib_aux&#39;vc" expl="VC for fib_aux" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="9992"/></proof>
</goal>
<goal name="fib&#39;vc" expl="VC for fib" proved="true">
<proof prover="7"><result status="valid" time="0.190000" steps="220087"/></proof>
</goal>
</theory>
<theory name="SmallestFibAbove" proved="true">
<goal name="smallest_fib_above&#39;vc" expl="VC for smallest_fib_above" proved="true">
<proof prover="4"><result status="valid" time="0.040000" steps="5188"/></proof>
</goal>
</theory>
<theory name="Zeckendorf" proved="true">
<goal name="fib_nonneg&#39;vc" expl="VC for fib_nonneg" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="109"/></proof>
</goal>
<goal name="fib_increasing&#39;vc" expl="VC for fib_increasing" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="2380"/></proof>
</goal>
<goal name="greatest_fib&#39;vc" expl="VC for greatest_fib" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="16394"/></proof>
</goal>
<goal name="zeckendorf&#39;vc" expl="VC for zeckendorf" proved="true">
<proof prover="4"><result status="valid" time="0.230000" steps="28799"/></proof>
</goal>
<goal name="zeckendorf_fast&#39;vc" expl="VC for zeckendorf_fast" proved="true">
<proof prover="4"><result status="valid" time="0.660000" steps="63532"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc" expl="VC for zeckendorf_unique" proved="true">
<transf name="split_goal_right" proved="true" >
<goal name="zeckendorf_unique&#39;vc.0" expl="unreachable point" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="6853"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.1" expl="precondition" proved="true">
<proof prover="4"><result status="valid" time="0.010000" steps="4765"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.2" expl="variant decrease" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="8564"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.3" expl="precondition" proved="true">
<proof prover="4"><result status="valid" time="0.020000" steps="4904"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.4" expl="precondition" proved="true">
<proof prover="4"><result status="valid" time="0.020000" steps="4961"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.5" expl="precondition" proved="true">
<proof prover="4"><result status="valid" time="0.030000" steps="11653"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.6" expl="postcondition" proved="true">
<proof prover="4"><result status="valid" time="0.060000" steps="13970"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.7" expl="postcondition" proved="true">
<proof prover="4"><result status="valid" time="0.060000" steps="7547"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.8" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.000000" steps="2290"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.9" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="7385"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.10" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="7592"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.11" expl="unreachable point" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="10395"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.12" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="2290"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.13" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="7385"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.14" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="7592"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.15" expl="unreachable point" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="10395"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.16" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="2269"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.17" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="7510"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.18" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="7604"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.19" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="8122"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.20" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.010000" steps="9074"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.21" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="9288"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.22" expl="variant decrease" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="15182"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.23" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="8900"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.24" expl="precondition" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="26995"/></proof>
</goal>
<goal name="zeckendorf_unique&#39;vc.25" expl="postcondition" proved="true">
<proof prover="7"><result status="valid" time="0.020000" steps="26536"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="Mat22" proved="true">
<goal name="Assoc" proved="true">
<proof prover="8"><result status="valid" time="0.030000" steps="346"/></proof>
</goal>
<goal name="Unit_def_l" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="14"/></proof>
</goal>
<goal name="Unit_def_r" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="13"/></proof>
</goal>
</theory>
<theory name="FibonacciLogarithmic" proved="true">
<goal name="logfib&#39;vc" expl="VC for logfib" proved="true">
<transf name="split_goal_right" proved="true" >
<goal name="logfib&#39;vc.0" expl="assertion" proved="true">
<proof prover="8"><result status="valid" time="0.010000" steps="10"/></proof>
</goal>
<goal name="logfib&#39;vc.1" expl="precondition" proved="true">
<proof prover="8"><result status="valid" time="0.010000" steps="3"/></proof>
</goal>
<goal name="logfib&#39;vc.2" expl="variant decrease" proved="true">
<proof prover="8"><result status="valid" time="0.010000" steps="31"/></proof>
</goal>
<goal name="logfib&#39;vc.3" expl="precondition" proved="true">
<proof prover="8"><result status="valid" time="0.010000" steps="0"/></proof>
</goal>
<goal name="logfib&#39;vc.4" expl="precondition" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="10"/></proof>
</goal>
<goal name="logfib&#39;vc.5" expl="assertion" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="10"/></proof>
</goal>
<goal name="logfib&#39;vc.6" expl="assertion" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="11"/></proof>
</goal>
<goal name="logfib&#39;vc.7" expl="postcondition" proved="true">
<proof prover="3"><result status="valid" time="0.195871" steps="93"/></proof>
<proof prover="8"><result status="timeout" time="5.000000" steps="2438"/></proof>
</goal>
</transf>
</goal>
<goal name="fib_m&#39;vc" expl="VC for fib_m" proved="true">
<proof prover="8" timelimit="1"><result status="valid" time="0.100000" steps="804"/></proof>
</goal>
<goal name="fibo&#39;vc" expl="VC for fibo" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="60"/></proof>
</goal>
<goal name="test0&#39;vc" expl="VC for test0" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="5"/></proof>
</goal>
<goal name="test1&#39;vc" expl="VC for test1" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="5"/></proof>
</goal>
<goal name="test7&#39;vc" expl="VC for test7" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="5"/></proof>
</goal>
<goal name="test42&#39;vc" expl="VC for test42" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="5"/></proof>
</goal>
<goal name="test2014&#39;vc" expl="VC for test2014" proved="true">
<proof prover="8"><result status="valid" time="0.000000" steps="5"/></proof>
</goal>
</theory>
<theory name="FibSquare" proved="true">
<goal name="fib_12" proved="true">
<proof prover="1"><result status="valid" time="0.033991" steps="3319"/></proof>
</goal>
<goal name="fib_13" proved="true">
<proof prover="1"><result status="valid" time="0.022074" steps="3176"/></proof>
</goal>
<goal name="fib_14" proved="true">
<proof prover="1"><result status="valid" time="0.024020" steps="1932"/></proof>
</goal>
<goal name="fib_bigger_than_square&#39;vc" expl="VC for fib_bigger_than_square" proved="true">
<transf name="split_vc" proved="true" >
<goal name="fib_bigger_than_square&#39;vc.0" expl="loop invariant init" proved="true">
<proof prover="1"><result status="valid" time="0.022034" steps="232"/></proof>
</goal>
<goal name="fib_bigger_than_square&#39;vc.1" expl="loop invariant init" proved="true">
<proof prover="1"><result status="valid" time="0.019268" steps="265"/></proof>
</goal>
<goal name="fib_bigger_than_square&#39;vc.2" expl="assertion" proved="true">
<transf name="split_vc" proved="true" >
<goal name="fib_bigger_than_square&#39;vc.2.0" expl="assertion" proved="true">
<proof prover="1"><result status="valid" time="0.026418" steps="2884"/></proof>
</goal>
<goal name="fib_bigger_than_square&#39;vc.2.1" expl="assertion" proved="true">
<proof prover="1"><result status="valid" time="0.024580" steps="2400"/></proof>
</goal>
<goal name="fib_bigger_than_square&#39;vc.2.2" expl="assertion" proved="true">
<proof prover="1"><result status="valid" time="0.068004" steps="297395"/></proof>
</goal>
</transf>
</goal>
<goal name="fib_bigger_than_square&#39;vc.3" expl="loop invariant preservation" proved="true">
<proof prover="1"><result status="valid" time="0.018691" steps="283"/></proof>
</goal>
<goal name="fib_bigger_than_square&#39;vc.4" expl="loop invariant preservation" proved="true">
<proof prover="1"><result status="valid" time="0.022627" steps="3124"/></proof>
</goal>
<goal name="fib_bigger_than_square&#39;vc.5" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.018833" steps="218"/></proof>
</goal>
<goal name="fib_bigger_than_square&#39;vc.6" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.022600" steps="1609"/></proof>
</goal>
</transf>
</goal>
<goal name="fib_square" proved="true">
<proof prover="1"><result status="valid" time="0.035983" steps="29834"/></proof>
</goal>
</theory>
</file>
</why3session>