<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Z3" version="4.12.2" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.4.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.7" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="power.mlw"/>
<theory name="FastExponentiation" proved="true">
 <goal name="Power_even" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="Power_even.0" proved="true">
  <proof prover="0"><result status="valid" time="0.030570" steps="10534"/></proof>
  </goal>
  <goal name="Power_even.1" proved="true">
  <proof prover="2"><result status="valid" time="0.139590" steps="1918"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="fast_exp&#39;vc" expl="VC for fast_exp" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="fast_exp&#39;vc.0" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="2910"/></proof>
  </goal>
  <goal name="fast_exp&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="3878"/></proof>
  </goal>
  <goal name="fast_exp&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.040000" steps="3836"/></proof>
  </goal>
  <goal name="fast_exp&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="2910"/></proof>
  </goal>
  <goal name="fast_exp&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="1492"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="fast_exp_2&#39;vc" expl="VC for fast_exp_2" proved="true">
 <proof prover="2"><result status="valid" time="0.715955" steps="10302"/></proof>
 </goal>
 <goal name="fast_exp_imperative&#39;vc" expl="VC for fast_exp_imperative" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="fast_exp_imperative&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="0"><result status="valid" time="0.013857" steps="1184"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="2931"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="3003"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="3088"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.4" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="5302"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.5" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="5175"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.022984" steps="13084"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.641666" steps="5777"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.8" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000" steps="3060"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.9" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="5251"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.10" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.030000" steps="5121"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.025509" steps="13020"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.325613" steps="3470"/></proof>
  </goal>
  <goal name="fast_exp_imperative&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="104"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
