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why3/examples/numeric/sum/why3session.xml
Matteo Manighetti 7ae65be566 Upgrade sessions to use Alt-Ergo 2.6.0
2025-01-14 19:48:35 +01:00

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<?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="0" name="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="1" name="CVC5" version="1.1.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="5" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="Z3" version="4.13.2" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="sum.mlw"/>
<theory name="SumSingle" proved="true">
<goal name="sum_of_fun_le_sum_of_abs_fun&#39;vc" expl="VC for sum_of_fun_le_sum_of_abs_fun" proved="true">
<proof prover="0"><result status="valid" time="1.177361" steps="101707"/></proof>
</goal>
<goal name="usum&#39;vc" expl="VC for usum" proved="true">
<transf name="split_vc" proved="true" >
<goal name="usum&#39;vc.0" expl="loop invariant init" proved="true">
<proof prover="2"><result status="valid" time="0.034162" steps="458"/></proof>
</goal>
<goal name="usum&#39;vc.1" expl="loop invariant preservation" proved="true">
<transf name="inline_trivial" proved="true" >
<goal name="usum&#39;vc.1.0" expl="loop invariant preservation" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (uadd s1 (f @ i)) - (sum (real_fun f) 0 i + to_real (f @ i)))
&lt;= (((((eps * from_int i) + 0.0) + eps)
* (sum (abs_real_fun f) 0 i + abs (to_real (f @ i))))
+ ((((1.0 + eps) + 0.0) * 0.0)
+ (((1.0 + eps) + (eps * from_int i)) * 0.0)))">
<goal name="usum&#39;vc.1.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="uadd_single_error_propagation" arg2="with" arg3="s1,(f @ i)">
<goal name="usum&#39;vc.1.0.0.0" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.008940" steps="10380"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.1" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.007478" steps="10404"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.2" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.100965" steps="827"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.3" expl="apply premises" proved="true">
<proof prover="5"><result status="valid" time="0.067664" steps="17765"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.4" expl="apply premises" proved="true">
<proof prover="5"><result status="valid" time="0.069090" steps="17744"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.5" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.043754" steps="10091"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.6" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.008951" steps="10358"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.7" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.028957" steps="91"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.8" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.003570" steps="10354"/></proof>
</goal>
</transf>
</goal>
<goal name="usum&#39;vc.1.0.1" expl="loop invariant preservation" proved="true">
<proof prover="2"><result status="valid" time="0.220338" steps="1568"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="usum&#39;vc.2" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.053225" steps="127"/></proof>
</goal>
<goal name="usum&#39;vc.3" expl="VC for usum" proved="true">
<proof prover="2"><result status="valid" time="0.062505" steps="86"/></proof>
<transf name="split_vc" proved="true" >
<goal name="usum&#39;vc.3.0" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.048376" steps="86"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="usum_rec&#39;vc" expl="VC for usum_rec" proved="true">
<transf name="split_vc" proved="true" >
<goal name="usum_rec&#39;vc.0" expl="variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.051186" steps="88"/></proof>
</goal>
<goal name="usum_rec&#39;vc.1" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.051579" steps="88"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2" expl="postcondition" proved="true">
<transf name="split_vc" proved="true" >
<goal name="usum_rec&#39;vc.2.0" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.031844" steps="457"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1" expl="postcondition" proved="true">
<transf name="inline_trivial" proved="true" >
<goal name="usum_rec&#39;vc.2.1.0" expl="postcondition" proved="true">
<transf name="assert" proved="true" arg1="abs
(to_real (uadd o (f @ (n -&#39; 1)))
- (sum (real_fun f) 0 (n -&#39; 1) + to_real (f @ (n -&#39; 1))))
&lt;= (((((eps * from_int (n -&#39; 1)) + 0.0) + eps)
* (sum (abs_real_fun f) 0 (n -&#39; 1) + abs (to_real (f @ (n -&#39; 1)))))
+ ((((1.0 + eps) + 0.0) * 0.0)
+ (((1.0 + eps) + (eps * from_int (n -&#39; 1))) * 0.0)))">
<goal name="usum_rec&#39;vc.2.1.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="uadd_single_error_propagation" arg2="with" arg3="o,(f @ (n -&#39; 1))">
<goal name="usum_rec&#39;vc.2.1.0.0.0" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.008611" steps="10405"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.1" expl="apply premises" proved="true">
<proof prover="5"><result status="valid" time="0.068672" steps="17819"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.2" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.071513" steps="475"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.3" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.008893" steps="10397"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.4" expl="apply premises" proved="true">
<proof prover="5"><result status="valid" time="0.089177" steps="18200"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.5" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.010460" steps="10377"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.6" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.030007" steps="92"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.7" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.028360" steps="92"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.8" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.044777" steps="10088"/></proof>
</goal>
</transf>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.1" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.241551" steps="1619"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="example1&#39;vc" expl="VC for example1" proved="true">
<transf name="split_vc" proved="true" >
<goal name="example1&#39;vc.0" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.051935" steps="85"/></proof>
</goal>
<goal name="example1&#39;vc.1" expl="postcondition" proved="true">
<transf name="inline_trivial" proved="true" >
<goal name="example1&#39;vc.1.0" expl="postcondition" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real result - sum exact_f 0 n)
&lt;= (sum f&#39; 0 n * (f_rel_err + ((eps * from_int n) * (1.0 + f_rel_err))))">
<goal name="example1&#39;vc.1.0.0" expl="asserted formula" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real result - sum exact_f 0 n)
&lt;= (((f_rel_err + ((eps * from_int n) * (1.0 + f_rel_err))) * sum f&#39; 0 n)
+ (((0.0 * from_int n) * (1.0 + (eps * from_int n))) + 0.0))">
<goal name="example1&#39;vc.1.0.0.0" expl="asserted formula" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real result - sum exact_f 0 n)
&lt;= (((f_rel_err + ((eps * from_int n) * (1.0 + f_rel_err))) * sum f&#39; 0 n)
+ (((0.0 * from_int n) * (1.0 + (eps * from_int n))) + 0.0))">
<goal name="example1&#39;vc.1.0.0.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="sum_single_error_propagation" arg2="with" arg3="f, abs_real_fun f">
<goal name="example1&#39;vc.1.0.0.0.0.0" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.061286" steps="662"/></proof>
</goal>
<goal name="example1&#39;vc.1.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.092140" steps="736"/></proof>
</goal>
<goal name="example1&#39;vc.1.0.0.0.0.2" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.068011" steps="95"/></proof>
</goal>
<goal name="example1&#39;vc.1.0.0.0.0.3" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.064263" steps="273"/></proof>
</goal>
<goal name="example1&#39;vc.1.0.0.0.0.4" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.043990" steps="88"/></proof>
</goal>
</transf>
</goal>
<goal name="example1&#39;vc.1.0.0.0.1" expl="asserted formula" proved="true">
<proof prover="2"><result status="valid" time="0.031842" steps="100"/></proof>
</goal>
</transf>
</goal>
<goal name="example1&#39;vc.1.0.0.1" expl="asserted formula" proved="true">
<proof prover="2"><result status="valid" time="0.044346" steps="100"/></proof>
</goal>
</transf>
</goal>
<goal name="example1&#39;vc.1.0.1" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.040926" steps="100"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
</theory>
<theory name="SumDouble" proved="true">
<goal name="sum_of_fun_le_sum_of_abs_fun&#39;vc" expl="VC for sum_of_fun_le_sum_of_abs_fun" proved="true">
<proof prover="2"><result status="valid" time="0.840504" steps="15772"/></proof>
</goal>
<goal name="usum&#39;vc" expl="VC for usum" proved="true">
<transf name="split_vc" proved="true" >
<goal name="usum&#39;vc.0" expl="loop invariant init" proved="true">
<proof prover="2"><result status="valid" time="0.044292" steps="458"/></proof>
</goal>
<goal name="usum&#39;vc.1" expl="loop invariant preservation" proved="true">
<transf name="inline_trivial" proved="true" >
<goal name="usum&#39;vc.1.0" expl="loop invariant preservation" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real (uadd s1 (f @ i)) - (sum (real_fun f) 0 i + to_real (f @ i)))
&lt;= (((((eps * from_int i) + 0.0) + eps)
* (sum (abs_real_fun f) 0 i + abs (to_real (f @ i))))
+ ((((1.0 + eps) + 0.0) * 0.0)
+ (((1.0 + eps) + (eps * from_int i)) * 0.0)))">
<goal name="usum&#39;vc.1.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="uadd_double_error_propagation" arg2="with" arg3="s1,(f @ i)">
<goal name="usum&#39;vc.1.0.0.0" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.023670" steps="99"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.1" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.007352" steps="10412"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.2" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.129491" steps="26896"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.3" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.052268" steps="10091"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.4" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.036775" steps="79910"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.5" expl="apply premises" proved="true">
<proof prover="5"><result status="valid" time="0.073414" steps="17742"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.6" expl="apply premises" proved="true">
<proof prover="5"><result status="valid" time="0.072468" steps="17742"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.7" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.045388" steps="10091"/></proof>
</goal>
<goal name="usum&#39;vc.1.0.0.8" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.024249" steps="91"/></proof>
</goal>
</transf>
</goal>
<goal name="usum&#39;vc.1.0.1" expl="loop invariant preservation" proved="true">
<proof prover="2"><result status="valid" time="0.214830" steps="1568"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="usum&#39;vc.2" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.080165" steps="127"/></proof>
</goal>
<goal name="usum&#39;vc.3" expl="VC for usum" proved="true">
<proof prover="2"><result status="valid" time="0.059429" steps="86"/></proof>
</goal>
</transf>
</goal>
<goal name="usum_rec&#39;vc" expl="VC for usum_rec" proved="true">
<transf name="split_vc" proved="true" >
<goal name="usum_rec&#39;vc.0" expl="variant decrease" proved="true">
<proof prover="2"><result status="valid" time="0.071763" steps="88"/></proof>
</goal>
<goal name="usum_rec&#39;vc.1" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.060039" steps="88"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2" expl="postcondition" proved="true">
<transf name="split_vc" proved="true" >
<goal name="usum_rec&#39;vc.2.0" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.120517" steps="457"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1" expl="postcondition" proved="true">
<transf name="inline_trivial" proved="true" >
<goal name="usum_rec&#39;vc.2.1.0" expl="postcondition" proved="true">
<transf name="assert" proved="true" arg1="abs
(to_real (uadd o (f @ (n -&#39; 1)))
- (sum (real_fun f) 0 (n -&#39; 1) + to_real (f @ (n -&#39; 1))))
&lt;= (((((eps * from_int (n -&#39; 1)) + 0.0) + eps)
* (sum (abs_real_fun f) 0 (n -&#39; 1) + abs (to_real (f @ (n -&#39; 1)))))
+ ((((1.0 + eps) + 0.0) * 0.0)
+ (((1.0 + eps) + (eps * from_int (n -&#39; 1))) * 0.0)))">
<goal name="usum_rec&#39;vc.2.1.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="uadd_double_error_propagation" arg2="with" arg3="o,(f @ (n -&#39; 1))">
<goal name="usum_rec&#39;vc.2.1.0.0.0" expl="apply premises" proved="true">
<proof prover="1"><result status="valid" time="0.054615" steps="11386"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.1" expl="apply premises" proved="true">
<proof prover="5"><result status="valid" time="0.079130" steps="17819"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.2" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.073816" steps="475"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.3" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.032913" steps="101"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.4" expl="apply premises" proved="true">
<proof prover="5"><result status="valid" time="0.091759" steps="18200"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.5" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.037012" steps="92"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.6" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.007651" steps="10385"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.7" expl="apply premises" proved="true">
<proof prover="2" memlimit="1000"><result status="valid" time="0.031995" steps="92"/></proof>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.0.8" expl="apply premises" proved="true">
<proof prover="6"><result status="valid" time="0.007954" steps="10381"/></proof>
</goal>
</transf>
</goal>
<goal name="usum_rec&#39;vc.2.1.0.1" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.223455" steps="1619"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
<goal name="example1&#39;vc" expl="VC for example1" proved="true">
<transf name="split_vc" proved="true" >
<goal name="example1&#39;vc.0" expl="precondition" proved="true">
<proof prover="2"><result status="valid" time="0.057153" steps="85"/></proof>
</goal>
<goal name="example1&#39;vc.1" expl="postcondition" proved="true">
<transf name="inline_trivial" proved="true" >
<goal name="example1&#39;vc.1.0" expl="postcondition" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real result - sum exact_f 0 n)
&lt;= (sum f&#39; 0 n * (f_rel_err + ((eps * from_int n) * (1.0 + f_rel_err))))">
<goal name="example1&#39;vc.1.0.0" expl="asserted formula" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real result - sum exact_f 0 n)
&lt;= (((f_rel_err + ((eps * from_int n) * (1.0 + f_rel_err))) * sum f&#39; 0 n)
+ (((0.0 * from_int n) * (1.0 + (eps * from_int n))) + 0.0))">
<goal name="example1&#39;vc.1.0.0.0" expl="asserted formula" proved="true">
<transf name="assert" proved="true" arg1="abs (to_real result - sum exact_f 0 n)
&lt;= (((f_rel_err + ((eps * from_int n) * (1.0 + f_rel_err))) * sum f&#39; 0 n)
+ (((0.0 * from_int n) * (1.0 + (eps * from_int n))) + 0.0))">
<goal name="example1&#39;vc.1.0.0.0.0" expl="asserted formula" proved="true">
<transf name="apply" proved="true" arg1="sum_double_error_propagation" arg2="with" arg3="f, abs_real_fun f">
<goal name="example1&#39;vc.1.0.0.0.0.0" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.061058" steps="662"/></proof>
</goal>
<goal name="example1&#39;vc.1.0.0.0.0.1" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.089933" steps="736"/></proof>
</goal>
<goal name="example1&#39;vc.1.0.0.0.0.2" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.063734" steps="95"/></proof>
</goal>
<goal name="example1&#39;vc.1.0.0.0.0.3" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.071667" steps="273"/></proof>
</goal>
<goal name="example1&#39;vc.1.0.0.0.0.4" expl="apply premises" proved="true">
<proof prover="2"><result status="valid" time="0.049998" steps="88"/></proof>
</goal>
</transf>
</goal>
<goal name="example1&#39;vc.1.0.0.0.1" expl="asserted formula" proved="true">
<proof prover="2"><result status="valid" time="0.037307" steps="100"/></proof>
</goal>
</transf>
</goal>
<goal name="example1&#39;vc.1.0.0.1" expl="asserted formula" proved="true">
<proof prover="2"><result status="valid" time="0.035820" steps="100"/></proof>
</goal>
</transf>
</goal>
<goal name="example1&#39;vc.1.0.1" expl="postcondition" proved="true">
<proof prover="2"><result status="valid" time="0.037716" steps="100"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>
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