<?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="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.5.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Eprover" version="1.9.1-001" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="4" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="6" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="7" name="Alt-Ergo" version="2.3.3" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="8" name="CVC4" version="1.7" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="9" name="Alt-Ergo" version="2.4.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="10" name="Eprover" version="2.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="11" name="CVC4" version="1.8" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="12" name="Alt-Ergo" version="2.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="13" name="Spass" version="3.9" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="14" name="Alt-Ergo" version="2.4.2" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="lineardecision.mlw"/>
<theory name="LinearEquationsCoeffs" proved="true">
 <goal name="neg_mul" proved="true">
 <proof prover="3"><result status="valid" time="0.060000"/></proof>
 </goal>
</theory>
<theory name="LinearEquationsDecision" proved="true">
 <goal name="valid_expr&#39;vc" expl="VC for valid_expr" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2191"/></proof>
 </goal>
 <goal name="expr_bound&#39;vc" expl="VC for expr_bound" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2191"/></proof>
 </goal>
 <goal name="expr_bound_w&#39;vc" expl="VC for expr_bound_w" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="expr_bound_w&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="6702"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="5845"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="6741"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="5874"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="13"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="eq_bound_w" proved="true">
 <proof prover="4"><result status="valid" time="0.000000" steps="19"/></proof>
 </goal>
 <goal name="ctx_bound_w&#39;vc" expl="VC for ctx_bound_w" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="ctx_bound_w&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10528"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="8740"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="31"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="apply_r&#39;vc" expl="VC for apply_r" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="apply_r&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="13"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="28135"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="29331"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="19"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2018"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="11"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.10" expl="out of loop bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="10"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="apply_l&#39;vc" expl="VC for apply_l" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="apply_l&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="28142"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="29338"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="19"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2018"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="11"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.10" expl="out of loop bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="10"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sprod&#39;vc" expl="VC for sprod" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="sprod&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="21937"/></proof>
  </goal>
  <goal name="sprod&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="11"/></proof>
  </goal>
  <goal name="sprod&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="11"/></proof>
  </goal>
  <goal name="sprod&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="sprod&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2018"/></proof>
  </goal>
  <goal name="sprod&#39;vc.5" expl="out of loop bounds" proved="true">
  <proof prover="8" timelimit="1"><result status="valid" time="0.050000" steps="10888"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="m_append&#39;vc" expl="VC for m_append" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="m_append&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="23628"/></proof>
  </goal>
  <goal name="m_append&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="42"/></proof>
  </goal>
  <goal name="m_append&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="25242"/></proof>
  </goal>
  <goal name="m_append&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="13"/></proof>
  </goal>
  <goal name="m_append&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="13"/></proof>
  </goal>
  <goal name="m_append&#39;vc.5" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="34635"/></proof>
  </goal>
  <goal name="m_append&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="m_append&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="23"/></proof>
  </goal>
  <goal name="m_append&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="19"/></proof>
  </goal>
  <goal name="m_append&#39;vc.9" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="m_append&#39;vc.10" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="24"/></proof>
  </goal>
  <goal name="m_append&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="35"/></proof>
  </goal>
  <goal name="m_append&#39;vc.12" expl="loop invariant preservation" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="m_append&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="m_append&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="21"/></proof>
  </goal>
  <goal name="m_append&#39;vc.15" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="m_append&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="76"/></proof>
  </goal>
  <goal name="m_append&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
  <goal name="m_append&#39;vc.18" expl="out of loop bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="31"/></proof>
  </goal>
  <goal name="m_append&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="15"/></proof>
  </goal>
  <goal name="m_append&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="16"/></proof>
  </goal>
  <goal name="m_append&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="m_append&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="21"/></proof>
  </goal>
  <goal name="m_append&#39;vc.23" expl="out of loop bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="16"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="v_append&#39;vc" expl="VC for v_append" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="v_append&#39;vc.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="21573"/></proof>
  </goal>
  <goal name="v_append&#39;vc.1" expl="array creation size" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="9"/></proof>
  </goal>
  <goal name="v_append&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="27239"/></proof>
  </goal>
  <goal name="v_append&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="11"/></proof>
  </goal>
  <goal name="v_append&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="13"/></proof>
  </goal>
  <goal name="v_append&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="15"/></proof>
  </goal>
  <goal name="v_append&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="15"/></proof>
  </goal>
  <goal name="v_append&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.220000" steps="396"/></proof>
  </goal>
  <goal name="v_append&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.140000" steps="144"/></proof>
  </goal>
  <goal name="v_append&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="13"/></proof>
  </goal>
  <goal name="v_append&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="17"/></proof>
  </goal>
  <goal name="v_append&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="14"/></proof>
  </goal>
  <goal name="v_append&#39;vc.12" expl="out of loop bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="18"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="infix ==&#39;vc" expl="VC for infix ==" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="infix ==&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2018"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="22017"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2706"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="27837"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="26901"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="13"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="16"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="27912"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.8" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="26532"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="max_var&#39;vc" expl="VC for max_var" proved="true">
 <proof prover="4"><result status="valid" time="0.040000" steps="271"/></proof>
 </goal>
 <goal name="max_var_e&#39;vc" expl="VC for max_var_e" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="31080"/></proof>
 </goal>
 <goal name="max_var_ctx&#39;vc" expl="VC for max_var_ctx" proved="true">
 <proof prover="4"><result status="valid" time="0.040000" steps="203"/></proof>
 </goal>
 <goal name="opp_expr&#39;vc" expl="VC for opp_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="opp_expr&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.010000" steps="56"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="22"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="25"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="7"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.4" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="24"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="65"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="24"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="27"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.8" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
  <goal name="opp_expr&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="29379"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="33629"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.11" expl="assertion" proved="true">
  <proof prover="3" memlimit="1000"><result status="valid" time="0.040000"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.12" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="opp_expr&#39;vc.12.0" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.010000" steps="9"/></proof>
   </goal>
   <goal name="opp_expr&#39;vc.12.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.020000" steps="30569"/></proof>
   </goal>
   <goal name="opp_expr&#39;vc.12.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.020000" steps="30523"/></proof>
   </goal>
   <goal name="opp_expr&#39;vc.12.3" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="9"/></proof>
   </goal>
   <goal name="opp_expr&#39;vc.12.4" expl="VC for opp_expr" proved="true">
   <proof prover="2"><result status="valid" time="0.020000" steps="30048"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="opp_expr&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="12"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="24"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="69"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.16" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="12"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.17" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="norm_eq_aux&#39;vc" expl="VC for norm_eq_aux" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="norm_eq_aux&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="10"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2478"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="9"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="11"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="29379"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="33851"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="25"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="54"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.9" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2478"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.10" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2478"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="norm_eq&#39;vc" expl="VC for norm_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="norm_eq&#39;vc.0" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="42"/></proof>
  </goal>
  <goal name="norm_eq&#39;vc.1" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.030000"/></proof>
  </goal>
  <goal name="norm_eq&#39;vc.2" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="norm_eq&#39;vc.2.0" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="55"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.2.1" expl="VC for norm_eq" proved="true">
   <proof prover="4"><result status="valid" time="0.030000" steps="32"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.2.2" expl="VC for norm_eq" proved="true">
   <proof prover="0"><result status="valid" time="0.040000" steps="22664"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.2.3" expl="VC for norm_eq" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="38"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.2.4" expl="VC for norm_eq" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="19"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.2.5" expl="VC for norm_eq" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="14"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="norm_eq&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="norm_eq&#39;vc.3.0" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.110000" steps="21162"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.3.1" expl="postcondition" proved="true">
   <proof prover="5"><result status="valid" time="0.220000"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="norm_eq&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="89"/></proof>
  </goal>
  <goal name="norm_eq&#39;vc.5" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
  <goal name="norm_eq&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2534"/></proof>
  </goal>
  <goal name="norm_eq&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="7"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="interp_ctx_impl&#39;vc" expl="VC for interp_ctx_impl" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="interp_ctx_impl&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="32906"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="31734"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="45472"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="interp_ctx_valid&#39;vc" expl="VC for interp_ctx_valid" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="interp_ctx_valid&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="30565"/></proof>
  </goal>
  <goal name="interp_ctx_valid&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="33846"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="interp_ctx_wr&#39;vc" expl="VC for interp_ctx_wr" proved="true">
 <proof prover="4"><result status="valid" time="0.020000" steps="139"/></proof>
 </goal>
 <goal name="interp_ctx_wl&#39;vc" expl="VC for interp_ctx_wl" proved="true">
 <proof prover="4"><result status="valid" time="0.020000" steps="115"/></proof>
 </goal>
 <goal name="mul_expr&#39;vc" expl="VC for mul_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="mul_expr&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="14"><result status="valid" time="0.020000" steps="672"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="10"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="16"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="11"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2918"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="18"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="46"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="49"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.050000" steps="22193"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="61"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2918"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="add_expr&#39;vc" expl="VC for add_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="add_expr&#39;vc.0" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="add_expr&#39;vc.0.0" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.230000"/></proof>
   </goal>
   <goal name="add_expr&#39;vc.0.1" expl="postcondition" proved="true">
   <proof prover="0" timelimit="1"><result status="valid" time="0.030000" steps="20405"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="add_expr&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="17"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="add_expr&#39;vc.3.0" expl="postcondition" proved="true">
   <proof prover="14" timelimit="10" memlimit="4000"><result status="valid" time="5.520490" steps="47018"/></proof>
   </goal>
   <goal name="add_expr&#39;vc.3.1" expl="postcondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="add_expr&#39;vc.3.1.0" expl="postcondition" proved="true">
    <proof prover="14" timelimit="10" memlimit="4000"><result status="valid" time="5.610515" steps="48012"/></proof>
    </goal>
    <goal name="add_expr&#39;vc.3.1.1" expl="postcondition" proved="true">
    <proof prover="11"><result status="valid" time="0.040000" steps="20275"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="add_expr&#39;vc.4" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="add_expr&#39;vc.4.0" expl="postcondition" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="add_expr&#39;vc.4.0.0" expl="postcondition" proved="true">
    <proof prover="14"><result status="valid" time="0.303639" steps="6599"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="add_expr&#39;vc.4.1" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.030000" steps="97"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="add_expr&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="49260"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="29796"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.7" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="61"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.220000" steps="253"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="52775"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="17466"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.11" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="61"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.070000" steps="23754"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="19"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.16" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.17" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="add_expr&#39;vc.17.0" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="1.076467"/></proof>
   </goal>
   <goal name="add_expr&#39;vc.17.1" expl="postcondition" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="add_expr&#39;vc.17.1.0" expl="postcondition" proved="true">
    <proof prover="3"><result status="valid" time="0.154757"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="add_expr&#39;vc.18" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="49360"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="29781"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.20" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="58"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.171929" steps="242"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.22" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="52874"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.23" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="17465"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.24" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="58"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.361462" steps="452"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.26" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.27" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.28" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="31191"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.29" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="29797"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.30" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="19"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.32" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="34633"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.33" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="17467"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.34" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.35" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.030000"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.36" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.37" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.38" expl="unreachable point" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="30754"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.39" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="48580"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.40" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="52036"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.050000" steps="21369"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.42" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.44" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="48183"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.45" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="9"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.46" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="mul_eq&#39;vc" expl="VC for mul_eq" proved="true">
 <proof prover="4"><result status="valid" time="0.010000" steps="24"/></proof>
 </goal>
 <goal name="add_eq&#39;vc" expl="VC for add_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="add_eq&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="40420"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="86429"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="37115"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="35474"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2918"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="zero_expr&#39;vc" expl="VC for zero_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="zero_expr&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="48580"/></proof>
  </goal>
  <goal name="zero_expr&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="52018"/></proof>
  </goal>
  <goal name="zero_expr&#39;vc.2" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="zero_expr&#39;vc.2.0" expl="postcondition" proved="true">
   <proof prover="11"><result status="valid" time="0.050000" steps="21104"/></proof>
   </goal>
   <goal name="zero_expr&#39;vc.2.1" expl="postcondition" proved="true">
   <proof prover="14"><result status="valid" time="0.030000" steps="1145"/></proof>
   </goal>
   <goal name="zero_expr&#39;vc.2.2" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.060000" steps="22667"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="zero_expr&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="zero_expr&#39;vc.3.0" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.020000"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="zero_expr&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_expr&#39;vc" expl="VC for sub_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="sub_expr&#39;vc.0" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="sub_expr&#39;vc.0.0" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.040000"/></proof>
   </goal>
   <goal name="sub_expr&#39;vc.0.1" expl="VC for sub_expr" proved="true">
   <proof prover="11"><result status="valid" time="0.050000" steps="23501"/></proof>
   </goal>
   <goal name="sub_expr&#39;vc.0.2" expl="VC for sub_expr" proved="true">
   <proof prover="4"><result status="valid" time="0.010000" steps="8"/></proof>
   </goal>
   <goal name="sub_expr&#39;vc.0.3" expl="VC for sub_expr" proved="true">
   <proof prover="4"><result status="valid" time="0.010000" steps="34"/></proof>
   </goal>
   <goal name="sub_expr&#39;vc.0.4" expl="VC for sub_expr" proved="true">
   <proof prover="0"><result status="valid" time="0.050000" steps="22253"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sub_expr&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="7"/></proof>
  </goal>
  <goal name="sub_expr&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2918"/></proof>
  </goal>
  <goal name="sub_expr&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="sub_expr&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="12"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="same_eq&#39;vc" expl="VC for same_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="same_eq&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="74"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.090000" steps="18772"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.5" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
  <goal name="same_eq&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2918"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="norm_context&#39;vc" expl="VC for norm_context" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="norm_context&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="35673"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="42194"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="47506"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3068"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="print_lc&#39;vc" expl="VC for print_lc" proved="true">
 <proof prover="4"><result status="valid" time="0.010000" steps="17"/></proof>
 </goal>
 <goal name="check_combination&#39;vc" expl="VC for check_combination" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="check_combination&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="40795"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="35"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="15"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="60"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="7"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.7" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="check_combination&#39;vc.7.0" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.030000" steps="15"/></proof>
   </goal>
   <goal name="check_combination&#39;vc.7.1" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="26"/></proof>
   </goal>
   <goal name="check_combination&#39;vc.7.2" expl="VC for check_combination" proved="true">
   <proof prover="4"><result status="valid" time="0.030000" steps="35"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="check_combination&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="35"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="3068"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.10" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="60"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="7"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3068"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="3068"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.16" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="10"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.17" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="8"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="14"><result status="valid" time="0.020000" steps="141"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.020000" steps="19519"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.20" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="3068"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.020000"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.22" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="transpose&#39;vc" expl="VC for transpose" proved="true">
 <proof prover="2"><result status="valid" time="0.060000" steps="97753"/></proof>
 </goal>
 <goal name="swap_rows&#39;vc" expl="VC for swap_rows" proved="true">
 <proof prover="2"><result status="valid" time="0.140000" steps="225052"/></proof>
 </goal>
 <goal name="mul_row&#39;vc" expl="VC for mul_row" proved="true">
 <proof prover="4"><result status="valid" time="0.120000" steps="293"/></proof>
 </goal>
 <goal name="addmul_row&#39;vc" expl="VC for addmul_row" proved="true">
 <proof prover="4"><result status="valid" time="0.140000" steps="541"/></proof>
 </goal>
 <goal name="gauss_jordan&#39;vc" expl="VC for gauss_jordan" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="gauss_jordan&#39;vc.0" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="93830"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.020000" steps="17"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="20"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="18"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="20"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="49"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="25"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.7" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="32700"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="9"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.8" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="39700"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="38942"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="39204"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.11" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="39667"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="15"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.12" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="4024"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.13" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="42630"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.14" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="21"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.15" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="41395"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="23"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.16" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="48814"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.17" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="50377"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.18" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="30"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="50043"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.20" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="30"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.21" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="32"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.22" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="55"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.23" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="51269"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.24" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.220000" steps="323021"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="45"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.25" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="65"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.26" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3072"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.27" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="14"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.28" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="gauss_jordan&#39;vc.28.0" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.130000" steps="32145"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.28.1" expl="VC for gauss_jordan" proved="true">
   <proof prover="2"><result status="valid" time="0.030000" steps="55778"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.28.2" expl="VC for gauss_jordan" proved="true">
   <proof prover="2"><result status="valid" time="0.130000" steps="75499"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.28.3" expl="VC for gauss_jordan" proved="true">
   <proof prover="4"><result status="valid" time="0.130000" steps="439"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.28.4" expl="VC for gauss_jordan" proved="true">
   <proof prover="0"><result status="valid" time="0.160000" steps="34878"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="gauss_jordan&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.30" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.290000" steps="355596"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.31" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="4910"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.32" expl="loop invariant preservation" proved="true">
  <proof prover="11"><result status="valid" time="0.184423" steps="37678"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.33" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="37"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.34" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="50633"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.35" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="42"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.36" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="44"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.37" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3072"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.38" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3072"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="8"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.39" expl="assertion" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="gauss_jordan&#39;vc.39.0" expl="assertion" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="gauss_jordan&#39;vc.39.0.0" expl="assertion" proved="true">
    <proof prover="0"><result status="valid" time="0.063160" steps="31888"/></proof>
    </goal>
    <goal name="gauss_jordan&#39;vc.39.0.1" expl="VC for gauss_jordan" proved="true">
    <proof prover="2"><result status="valid" time="0.040000" steps="55594"/></proof>
    </goal>
    <goal name="gauss_jordan&#39;vc.39.0.2" expl="VC for gauss_jordan" proved="true">
    <proof prover="2"><result status="valid" time="0.022408" steps="74997"/></proof>
    </goal>
    <goal name="gauss_jordan&#39;vc.39.0.3" expl="VC for gauss_jordan" proved="true">
    <transf name="revert" proved="true" arg1="H">
     <goal name="gauss_jordan&#39;vc.39.0.3.0" expl="VC for gauss_jordan" proved="true">
     <transf name="split_vc" proved="true" >
      <goal name="gauss_jordan&#39;vc.39.0.3.0.0" expl="VC for gauss_jordan" proved="true">
      <proof prover="4"><result status="valid" time="0.140000" steps="429"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="gauss_jordan&#39;vc.39.0.4" expl="VC for gauss_jordan" proved="true">
    <proof prover="0"><result status="valid" time="0.160000" steps="34488"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="gauss_jordan&#39;vc.40" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="53466"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="37"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.41" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.256592" steps="355198"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.42" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.079189" steps="36415"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.43" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="5.152922" steps="8617"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.44" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="34"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.45" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3072"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.46" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="14"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.47" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="gauss_jordan&#39;vc.47.0" expl="VC for gauss_jordan" proved="true">
   <proof prover="2"><result status="valid" time="0.030000" steps="54435"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.47.1" expl="VC for gauss_jordan" proved="true">
   <proof prover="1"><result status="valid" time="0.120000" steps="27486"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.47.2" expl="VC for gauss_jordan" proved="true">
   <proof prover="1"><result status="valid" time="0.140000" steps="30097"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="gauss_jordan&#39;vc.48" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="24"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.49" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="49940"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.50" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="4736"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.51" expl="loop invariant preservation" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="gauss_jordan&#39;vc.51.0" expl="loop invariant preservation" proved="true">
   <proof prover="2"><result status="valid" time="0.020000" steps="54242"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="gauss_jordan&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3068"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.53" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="40622"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.54" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="47995"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.55" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.56" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="48616"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.57" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="188875"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.58" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="45538"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.59" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="24603"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="21"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.60" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="4690"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="to_list&#39;vc" expl="VC for to_list" proved="true">
 <proof prover="2"><result status="valid" time="0.090000" steps="156136"/></proof>
 </goal>
 <goal name="linear_decision&#39;vc" expl="VC for linear_decision" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="linear_decision&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="31698"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="31777"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3202"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.4" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="37"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.5" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="33421"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.6" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="33633"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="37008"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="74"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.8" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="36583"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.9" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="41379"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.10" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="42868"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.11" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.12" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.249612" steps="523950"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="182"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="182"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.15" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3068"/></proof>
  <proof prover="4"><result status="valid" time="0.010000" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.16" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="201909"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.17" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="41512"/></proof>
  <proof prover="4"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.18" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="70"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.19" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="201916"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="41512"/></proof>
  <proof prover="4"><result status="valid" time="0.020000" steps="29"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.21" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="70"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.22" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.23" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.24" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  <proof prover="4"><result status="valid" time="0.020000" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.25" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  <proof prover="4"><result status="valid" time="0.010000" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.26" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="47114"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.27" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.28" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.29" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="33"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.30" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="84"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.31" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.32" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.33" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="82"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.34" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="39"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.35" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="36"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.36" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.37" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.38" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.39" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="82"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.40" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="39"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.41" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="36"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.42" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  <proof prover="4"><result status="valid" time="0.010000" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.44" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.45" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.46" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="78"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.47" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="37"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.48" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.49" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.50" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.51" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="80"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.52" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.53" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.54" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="78"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.55" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="37"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.56" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.57" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.58" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.140000" steps="29759"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.59" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.60" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="78"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.61" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="37"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.62" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.63" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.64" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.65" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.66" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.67" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="77"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.68" expl="precondition" proved="true">
  <proof prover="11"><result status="valid" time="0.060000" steps="28604"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.69" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="46608"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.70" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.71" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.72" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="147"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.73" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="205"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.74" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="205"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.75" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.76" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="207224"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.77" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="64"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.78" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="207231"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.79" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="64"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.80" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  <proof prover="4"><result status="valid" time="0.010000" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.81" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  <proof prover="4"><result status="valid" time="0.020000" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.82" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.83" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.84" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="46663"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.85" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="24"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.86" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="42403"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.87" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="82"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.88" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="45127"/></proof>
  <proof prover="4"><result status="valid" time="0.010000" steps="27"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.89" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="47226"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.90" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="52837"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.91" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="56021"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.92" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="54708"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.93" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="59280"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.94" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="72277"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.95" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="61251"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="40"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.96" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.97" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="3068"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.010000" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.98" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.99" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.100" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.101" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="3068"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.102" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valid_expr&#39;&#39;vc" expl="VC for valid_expr&#39;" proved="true">
 <proof prover="2"><result status="valid" time="0.040000" steps="103625"/></proof>
 </goal>
 <goal name="simp&#39;vc" expl="VC for simp" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="simp&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="10"/></proof>
  </goal>
  <goal name="simp&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="30"/></proof>
  </goal>
  <goal name="simp&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.050000" steps="24123"/></proof>
  </goal>
  <goal name="simp&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="12"/></proof>
  </goal>
  <goal name="simp&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="94753"/></proof>
  </goal>
  <goal name="simp&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="116"/></proof>
  </goal>
  <goal name="simp&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="19"/></proof>
  </goal>
  <goal name="simp&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="64"/></proof>
  </goal>
  <goal name="simp&#39;vc.11" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.13" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="110"/></proof>
  </goal>
  <goal name="simp&#39;vc.14" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="99524"/></proof>
  </goal>
  <goal name="simp&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="20"/></proof>
  </goal>
  <goal name="simp&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="41133"/></proof>
  </goal>
  <goal name="simp&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.18" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.19" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="35"/></proof>
  </goal>
  <goal name="simp&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="28"/></proof>
  </goal>
  <goal name="simp&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="10"/></proof>
  </goal>
  <goal name="simp&#39;vc.23" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="39625"/></proof>
  </goal>
  <goal name="simp&#39;vc.24" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.050000" steps="24832"/></proof>
  </goal>
  <goal name="simp&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="14"/></proof>
  </goal>
  <goal name="simp&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.050000" steps="24899"/></proof>
  </goal>
  <goal name="simp&#39;vc.27" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="14"/></proof>
  </goal>
  <goal name="simp&#39;vc.28" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.29" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.30" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.050000" steps="24840"/></proof>
  </goal>
  <goal name="simp&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="14"/></proof>
  </goal>
  <goal name="simp&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.040000" steps="24899"/></proof>
  </goal>
  <goal name="simp&#39;vc.33" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.34" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
  <goal name="simp&#39;vc.35" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3068"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="simp_eq&#39;vc" expl="VC for simp_eq" proved="true">
 <proof prover="2"><result status="valid" time="0.140000" steps="224015"/></proof>
 </goal>
 <goal name="simp_ctx&#39;vc" expl="VC for simp_ctx" proved="true">
 <proof prover="4"><result status="valid" time="0.150000" steps="824"/></proof>
 </goal>
 <goal name="decision&#39;vc" expl="VC for decision" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="decision&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="24827"/></proof>
  </goal>
  <goal name="decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="24833"/></proof>
  </goal>
  <goal name="decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="53729"/></proof>
  </goal>
  <goal name="decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="55186"/></proof>
  </goal>
  <goal name="decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="4312"/></proof>
  </goal>
  <goal name="decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="4312"/></proof>
  </goal>
  <goal name="decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="3740"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="RationalCoeffs" proved="true">
 <goal name="prod_compat_eq&#39;vc" expl="VC for prod_compat_eq" proved="true">
 <proof prover="2"><result status="valid" time="0.030000" steps="374"/></proof>
 </goal>
 <goal name="cross_d&#39;vc" expl="VC for cross_d" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="cross_d&#39;vc.0" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="cross_d&#39;vc.0.0" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.250000" steps="721717"/></proof>
   </goal>
   <goal name="cross_d&#39;vc.0.1" expl="VC for cross_d" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="cross_d&#39;vc.0.1.0" expl="VC for cross_d" proved="true">
    <transf name="apply" proved="true" arg1="prod_compat_eq" arg2="with" arg3="d">
     <goal name="cross_d&#39;vc.0.1.0.0" expl="apply premises" proved="true">
     <proof prover="0"><result status="valid" time="0.080000" steps="4905"/></proof>
     </goal>
     <goal name="cross_d&#39;vc.0.1.0.1" expl="apply premises" proved="true">
     <proof prover="2"><result status="valid" time="0.010000" steps="420"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="cross_d&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="52"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="cross_ind&#39;vc" expl="VC for cross_ind" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="cross_ind&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="4652"/></proof>
  </goal>
  <goal name="cross_ind&#39;vc.1" expl="assertion" proved="true">
  <proof prover="3" timelimit="10"><result status="valid" time="0.010000"/></proof>
  </goal>
  <goal name="cross_ind&#39;vc.2" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="cross_ind&#39;vc.2.0" expl="VC for cross_ind" proved="true">
   <proof prover="3" timelimit="10"><result status="valid" time="2.280000"/></proof>
   </goal>
   <goal name="cross_ind&#39;vc.2.1" expl="VC for cross_ind" proved="true">
   <proof prover="4"><result status="valid" time="0.000000" steps="8"/></proof>
   </goal>
   <goal name="cross_ind&#39;vc.2.2" expl="VC for cross_ind" proved="true">
   <proof prover="3" timelimit="10"><result status="valid" time="2.460000"/></proof>
   </goal>
   <goal name="cross_ind&#39;vc.2.3" expl="VC for cross_ind" proved="true">
   <proof prover="2"><result status="valid" time="0.010000" steps="8794"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="cross_ind&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="480"/></proof>
  </goal>
  <goal name="cross_ind&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="13"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="cross" proved="true">
 <proof prover="4"><result status="valid" time="0.000000" steps="14"/></proof>
 </goal>
 <goal name="gcd&#39;vc" expl="VC for gcd" proved="true">
 <proof prover="0"><result status="valid" time="0.110000" steps="30771"/></proof>
 <transf name="split_goal_right" proved="true" >
  <goal name="gcd&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="26181"/></proof>
  </goal>
  <goal name="gcd&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="1620"/></proof>
  </goal>
  <goal name="gcd&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="1620"/></proof>
  </goal>
  <goal name="gcd&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="26358"/></proof>
  </goal>
  <goal name="gcd&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="26358"/></proof>
  </goal>
  <goal name="gcd&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="27505"/></proof>
  </goal>
  <goal name="gcd&#39;vc.6" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="29481"/></proof>
  </goal>
  <goal name="gcd&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="28906"/></proof>
  </goal>
  <goal name="gcd&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="28182"/></proof>
  </goal>
  <goal name="gcd&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="28251"/></proof>
  </goal>
  <goal name="gcd&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="27223"/></proof>
  </goal>
  <goal name="gcd&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="26382"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="simp&#39;vc" expl="VC for simp" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="simp&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="26432"/></proof>
  </goal>
  <goal name="simp&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="26043"/></proof>
  </goal>
  <goal name="simp&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="26043"/></proof>
  </goal>
  <goal name="simp&#39;vc.3" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.060000" steps="16512"/></proof>
  </goal>
  <goal name="simp&#39;vc.4" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.000000" steps="8"/></proof>
  </goal>
  <goal name="simp&#39;vc.5" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="simp&#39;vc.5.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.020000" steps="26300"/></proof>
   </goal>
   <goal name="simp&#39;vc.5.1" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="199"/></proof>
   </goal>
   <goal name="simp&#39;vc.5.2" expl="postcondition" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.130000" steps="5080"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="radd&#39;vc" expl="VC for radd" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="radd&#39;vc.0" expl="exceptional postcondition" proved="true">
  <proof prover="13"><result status="valid" time="0.010000"/></proof>
  </goal>
  <goal name="radd&#39;vc.1" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="radd&#39;vc.1.0" expl="assertion" proved="true">
   <proof prover="10" timelimit="5" memlimit="2000"><result status="valid" time="1.340000"/></proof>
   </goal>
   <goal name="radd&#39;vc.1.1" expl="VC for radd" proved="true">
   <transf name="unfold" proved="true" arg1="b">
    <goal name="radd&#39;vc.1.1.0" expl="VC for radd" proved="true">
    <transf name="unfold" proved="true" arg1="rinterp">
     <goal name="radd&#39;vc.1.1.0.0" expl="VC for radd" proved="true">
     <transf name="compute_in_goal" proved="true" >
      <goal name="radd&#39;vc.1.1.0.0.0" expl="VC for radd" proved="true">
      <transf name="replace" proved="true" arg1="(from_int a1 * from_int b1)" arg2="(from_int b1 * from_int a1)">
       <goal name="radd&#39;vc.1.1.0.0.0.0" expl="VC for radd" proved="true">
       <proof prover="10" timelimit="4"><result status="valid" time="0.460000"/></proof>
       </goal>
       <goal name="radd&#39;vc.1.1.0.0.0.1" expl="equality hypothesis" proved="true">
       <proof prover="12" timelimit="5"><result status="valid" time="0.010000" steps="17"/></proof>
       </goal>
      </transf>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="radd&#39;vc.1.2" expl="VC for radd" proved="true">
   <proof prover="13"><result status="valid" time="0.020000"/></proof>
   </goal>
   <goal name="radd&#39;vc.1.3" expl="VC for radd" proved="true">
   <proof prover="10"><result status="valid" time="0.760000"/></proof>
   </goal>
   <goal name="radd&#39;vc.1.4" expl="VC for radd" proved="true">
   <proof prover="12"><result status="valid" time="0.770000" steps="4862"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="radd&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="13"><result status="valid" time="0.020000"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="rmul&#39;vc" expl="VC for rmul" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="rmul&#39;vc.0" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
  <goal name="rmul&#39;vc.1" expl="assertion" proved="true">
  <proof prover="10"><result status="valid" time="0.220000"/></proof>
  </goal>
  <goal name="rmul&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="1620"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="ropp&#39;vc" expl="VC for ropp" proved="true">
 <transf name="compute_in_goal" proved="true" >
  <goal name="ropp&#39;vc.0" expl="VC for ropp" proved="true">
  <proof prover="4"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="req&#39;vc" expl="VC for req" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="req&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="28167"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="rinv&#39;vc" expl="VC for rinv" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="rinv&#39;vc.0" expl="exceptional postcondition" proved="true">
  <transf name="compute_in_goal" proved="true" >
  </transf>
  </goal>
  <goal name="rinv&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="29012"/></proof>
  </goal>
  <goal name="rinv&#39;vc.2" expl="postcondition" proved="true">
  <transf name="compute_in_goal" proved="true" >
   <goal name="rinv&#39;vc.2.0" expl="postcondition" proved="true">
   <proof prover="3" timelimit="10"><result status="valid" time="0.200000"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="is_zero&#39;vc" expl="VC for is_zero" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="is_zero&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="28140"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="LinearDecisionRational" proved="true">
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="1696"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1690"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="1690"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="1694"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="1694"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1692"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.000000" steps="1696"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3625"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3625"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1692"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="1690"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1688"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1688"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.040000" steps="27010"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="26946"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="26889"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1686"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1696"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="1700"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1700"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.030000" steps="27188"/></proof>
 </goal>
 <goal name="C.one_def" proved="true">
 <transf name="compute_in_goal" proved="true" >
  <goal name="one_def.0" proved="true">
  <transf name="replace" proved="true" arg1="one" arg2="1.0">
   <goal name="one_def.0.0" proved="true">
   <proof prover="3"><result status="valid" time="0.020000"/></proof>
   </goal>
   <goal name="one_def.0.1" expl="equality hypothesis" proved="true">
   <proof prover="2"><result status="valid" time="0.030000" steps="1714"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="C.add&#39;refn&#39;vc" expl="VC for add&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.030000" steps="1742"/></proof>
 </goal>
 <goal name="C.mul&#39;refn&#39;vc" expl="VC for mul&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1742"/></proof>
 </goal>
 <goal name="C.opp&#39;refn&#39;vc" expl="VC for opp&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1742"/></proof>
 </goal>
 <goal name="C.eq&#39;refn&#39;vc" expl="VC for eq&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="1742"/></proof>
 </goal>
 <goal name="C.inv&#39;refn&#39;vc" expl="VC for inv&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="13359"/></proof>
 </goal>
</theory>
<theory name="LinearDecisionInt" proved="true">
 <goal name="iadd&#39;vc" expl="VC for iadd" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2"/></proof>
 </goal>
 <goal name="imul&#39;vc" expl="VC for imul" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2"/></proof>
 </goal>
 <goal name="iopp&#39;vc" expl="VC for iopp" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2"/></proof>
 </goal>
 <goal name="iinv&#39;vc" expl="VC for iinv" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2"/></proof>
 </goal>
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="14"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="8"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="8"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="12"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="12"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="10"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="30"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="89"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="89"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="26"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="24"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="6"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="6"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="355"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="330"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="235"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="4"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="14"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="34"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="18"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.030000" steps="36"/></proof>
 </goal>
 <goal name="C.one_def" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="54"/></proof>
 </goal>
 <goal name="C.add&#39;refn&#39;vc" expl="VC for add&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="86"/></proof>
 </goal>
 <goal name="C.mul&#39;refn&#39;vc" expl="VC for mul&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="86"/></proof>
 </goal>
 <goal name="C.opp&#39;refn&#39;vc" expl="VC for opp&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.030000" steps="86"/></proof>
 </goal>
 <goal name="C.eq&#39;refn&#39;vc" expl="VC for eq&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="86"/></proof>
 </goal>
 <goal name="C.inv&#39;refn&#39;vc" expl="VC for inv&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="86"/></proof>
 </goal>
 <goal name="m_y&#39;vc" expl="VC for m_y" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="6230"/></proof>
 </goal>
 <goal name="m&#39;vc" expl="VC for m" proved="true">
 <proof prover="4"><result status="valid" time="0.100000" steps="106"/></proof>
 </goal>
 <goal name="m_cprod&#39;vc" expl="VC for m_cprod" proved="true">
 <proof prover="4"><result status="valid" time="0.160000" steps="173"/></proof>
 </goal>
 <goal name="m_expr&#39;vc" expl="VC for m_expr" proved="true">
 <proof prover="4"><result status="valid" time="0.540000" steps="2134"/></proof>
 </goal>
 <goal name="m_eq&#39;vc" expl="VC for m_eq" proved="true">
 <proof prover="4"><result status="valid" time="0.040000" steps="140"/></proof>
 </goal>
 <goal name="m_ctx&#39;vc" expl="VC for m_ctx" proved="true">
 <proof prover="4"><result status="valid" time="0.140000" steps="497"/></proof>
 </goal>
 <goal name="int_decision&#39;vc" expl="VC for int_decision" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="int_decision&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="44668"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="44676"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="157201"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="158735"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.100000" steps="8092"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="8092"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="6274"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Test" proved="true">
 <goal name="g" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="g.0" proved="true">
  <transf name="reflection_f" proved="true" arg1="decision">
   <goal name="g.0.0" expl="reification check" proved="true">
   <proof prover="2"><result status="valid" time="0.050000" steps="90905"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="TestInt" proved="true">
 <goal name="g" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="g.0" proved="true">
  <transf name="reflection_f" proved="true" arg1="int_decision">
   <goal name="g.0.0" expl="reification check" proved="true">
   <proof prover="2"><result status="valid" time="0.039686" steps="111786"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="MP64Coeffs" proved="true">
 <goal name="qinterp_def" proved="true">
 <transf name="compute_in_goal" proved="true" >
 </transf>
 </goal>
 <goal name="opp_exp&#39;vc" expl="VC for opp_exp" proved="true">
 <proof prover="4"><result status="valid" time="0.050000" steps="182"/></proof>
 </goal>
 <goal name="add_sub_exp&#39;vc" expl="VC for add_sub_exp" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="add_sub_exp&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="35"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.090000" steps="16532"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="22"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="40458"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="410"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="42495"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="61"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.8" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="40476"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="419"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.11" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="42507"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="119"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.100000" steps="16942"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="53"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="39"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.19" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="40456"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="403"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.21" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="64"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="61"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.23" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.24" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.25" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="40474"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="422"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.27" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="42505"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.28" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="119"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.29" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.30" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.090000" steps="17099"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="55"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.33" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.090000" steps="17526"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.34" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="18"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.35" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="40687"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.36" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.040000" steps="394"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.37" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="73"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="67"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.39" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.40" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.000000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.41" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="40705"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.42" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="476"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.43" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="42775"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.44" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.120000" steps="18442"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.45" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.46" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
  <goal name="add_sub_exp&#39;vc.47" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.48" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="98"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.49" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="80"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.50" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.210000" steps="2001"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.51" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="42914"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="136"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.53" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.54" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.55" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="40879"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.56" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="522"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.57" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="42929"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.58" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.110000" steps="18822"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.59" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.60" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.61" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.62" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="40569"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.63" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="333"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.64" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="42612"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.65" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.080000" steps="16970"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.66" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.67" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.68" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="40590"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.69" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="337"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.70" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.000000" steps="42627"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.71" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.120000" steps="18275"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.72" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.73" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.74" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.75" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="40205"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.76" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="36"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.77" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="43921"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.78" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="18"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.79" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.80" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="44010"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.81" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="16"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.82" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.83" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.84" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="40230"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.85" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.090000" steps="16221"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.86" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="43866"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.87" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="18"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.88" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.89" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="72"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.90" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="16"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.91" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.92" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="2220"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.93" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="13"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.94" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="2220"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="add_exp&#39;vc" expl="VC for add_exp" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2220"/></proof>
 <transf name="split_goal_right" proved="true" >
  <goal name="add_exp&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="6"/></proof>
  </goal>
  <goal name="add_exp&#39;vc.1" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="zero_exp&#39;vc" expl="VC for zero_exp" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="zero_exp&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="40176"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="40205"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="41952"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="40230"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="55"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="46"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="59"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2438"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="same_exp&#39;vc" expl="VC for same_exp" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="same_exp&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="9"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="42169"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="2220"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="40421"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="42169"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2220"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2220"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="41637"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="80"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.10" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2220"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="42169"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2220"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="2220"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="96"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.15" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2220"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.16" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="2220"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="madd&#39;vc" expl="VC for madd" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="madd&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="45648"/></proof>
  </goal>
  <goal name="madd&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="46555"/></proof>
  </goal>
  <goal name="madd&#39;vc.2" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="madd&#39;vc.2.0" expl="assertion" proved="true">
   <proof prover="13"><result status="valid" time="0.050000"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.1" expl="assertion" proved="true">
   <proof prover="13"><result status="valid" time="0.050000"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.2" expl="assertion" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.050000" steps="13048"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.3" expl="assertion" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.020000" steps="163"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.4" expl="VC for madd" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.070000" steps="14668"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="madd&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="6"/></proof>
  </goal>
  <goal name="madd&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="2438"/></proof>
  </goal>
  <goal name="madd&#39;vc.5" expl="exceptional postcondition" proved="true">
  <transf name="compute_in_goal" proved="true" >
  </transf>
  </goal>
  <goal name="madd&#39;vc.6" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="mmul&#39;vc" expl="VC for mmul" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="mmul&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="10"><result status="valid" time="0.070000"/></proof>
  </goal>
  <goal name="mmul&#39;vc.1" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="mmul&#39;vc.1.0" expl="assertion" proved="true">
   <proof prover="13"><result status="valid" time="0.040000"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.1" expl="VC for mmul" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.030000" steps="162"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.2" expl="VC for mmul" proved="true">
   <proof prover="13"><result status="valid" time="0.050000"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.3" expl="VC for mmul" proved="true">
   <proof prover="13"><result status="valid" time="0.040000"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.4" expl="VC for mmul" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.020000" steps="27"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.5" expl="VC for mmul" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.040000" steps="531"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.6" expl="VC for mmul" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.060000" steps="14718"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mmul&#39;vc.2" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="mmul&#39;vc.2.0" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.030000" steps="6"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mmul&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="2438"/></proof>
  </goal>
  <goal name="mmul&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="3" timelimit="10"><result status="valid" time="0.070000"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="mopp&#39;vc" expl="VC for mopp" proved="true">
 <transf name="compute_in_goal" proved="true" >
  <goal name="mopp&#39;vc.0" expl="VC for mopp" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="10"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="pure_same_exp&#39;vc" expl="VC for pure_same_exp" proved="true">
 <proof prover="4"><result status="valid" time="0.080000" steps="495"/></proof>
 </goal>
 <goal name="meq&#39;vc" expl="VC for meq" proved="true">
 <proof prover="9" timelimit="1"><result status="valid" time="0.930000" steps="26770"/></proof>
 </goal>
 <goal name="minv&#39;vc" expl="VC for minv" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="minv&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.130000" steps="49949"/></proof>
  </goal>
  <goal name="minv&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="50836"/></proof>
  </goal>
  <goal name="minv&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="2984"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="LinearDecisionRationalMP" proved="true">
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2996"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2990"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2990"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2994"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2994"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2992"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2996"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="6602"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="6602"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2992"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2990"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2988"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2988"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.100000" steps="48371"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.100000" steps="48308"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.090000" steps="48246"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2986"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2996"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3000"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3000"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="51074"/></proof>
 </goal>
 <goal name="C.one_def" proved="true">
 <proof prover="4"><result status="valid" time="0.040000" steps="17"/></proof>
 </goal>
 <goal name="C.add&#39;refn&#39;vc" expl="VC for add&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3058"/></proof>
 </goal>
 <goal name="C.mul&#39;refn&#39;vc" expl="VC for mul&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3058"/></proof>
 </goal>
 <goal name="C.opp&#39;refn&#39;vc" expl="VC for opp&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3058"/></proof>
 </goal>
 <goal name="C.eq&#39;refn&#39;vc" expl="VC for eq&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3058"/></proof>
 </goal>
 <goal name="C.inv&#39;refn&#39;vc" expl="VC for inv&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3058"/></proof>
 </goal>
</theory>
<theory name="LinearDecisionIntMP" proved="true">
 <goal name="mpadd&#39;vc" expl="VC for mpadd" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2984"/></proof>
 </goal>
 <goal name="mpmul&#39;vc" expl="VC for mpmul" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="2984"/></proof>
 </goal>
 <goal name="mpopp&#39;vc" expl="VC for mpopp" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2984"/></proof>
 </goal>
 <goal name="mpeq&#39;vc" expl="VC for mpeq" proved="true">
 <proof prover="2"><result status="valid" time="0.060000" steps="2984"/></proof>
 </goal>
 <goal name="mpinv&#39;vc" expl="VC for mpinv" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3122"/></proof>
 </goal>
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3134"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3128"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3128"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3132"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3132"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3130"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3134"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="6953"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="6953"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3130"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3128"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3126"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3126"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.110000" steps="50378"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.110000" steps="50287"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.090000" steps="50242"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3124"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3134"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3138"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="3136"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <transf name="compute_in_goal" proved="true" >
 </transf>
 </goal>
 <goal name="C.one_def" proved="true">
 <proof prover="4"><result status="valid" time="0.040000" steps="11"/></proof>
 </goal>
 <goal name="C.add&#39;refn&#39;vc" expl="VC for add&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3168"/></proof>
 </goal>
 <goal name="C.mul&#39;refn&#39;vc" expl="VC for mul&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3168"/></proof>
 </goal>
 <goal name="C.opp&#39;refn&#39;vc" expl="VC for opp&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3168"/></proof>
 </goal>
 <goal name="C.eq&#39;refn&#39;vc" expl="VC for eq&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3168"/></proof>
 </goal>
 <goal name="C.inv&#39;refn&#39;vc" expl="VC for inv&#39;refn" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="3168"/></proof>
 </goal>
 <goal name="m&#39;vc" expl="VC for m" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="m&#39;vc.0" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="m&#39;vc.0.0" expl="postcondition" proved="true">
   <transf name="compute_in_goal" proved="true" >
    <goal name="m&#39;vc.0.0.0" expl="postcondition" proved="true">
    <proof prover="14"><result status="valid" time="0.030000" steps="280"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="m&#39;vc.0.1" expl="postcondition" proved="true">
   <proof prover="12" timelimit="5"><result status="valid" time="0.080000" steps="460"/></proof>
   </goal>
   <goal name="m&#39;vc.0.2" expl="postcondition" proved="true">
   <proof prover="14"><result status="valid" time="0.040000" steps="1035"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="m_y&#39;vc" expl="VC for m_y" proved="true">
 <proof prover="2"><result status="valid" time="0.010000" steps="7678"/></proof>
 </goal>
 <goal name="m_cprod&#39;vc" expl="VC for m_cprod" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="m_cprod&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="116"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="m_expr&#39;vc" expl="VC for m_expr" proved="true">
 <proof prover="4"><result status="valid" time="0.190000" steps="1094"/></proof>
 </goal>
 <goal name="m_eq&#39;vc" expl="VC for m_eq" proved="true">
 <proof prover="0"><result status="valid" time="0.151684" steps="59968"/></proof>
 </goal>
 <goal name="m_ctx&#39;vc" expl="VC for m_ctx" proved="true">
 <proof prover="4"><result status="valid" time="0.110000" steps="651"/></proof>
 </goal>
 <goal name="mp_decision&#39;vc" expl="VC for mp_decision" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="mp_decision&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="54662"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="54670"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.051753" steps="189841"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="195097"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="9998"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="9998"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="EqPropMP" proved="true">
 <goal name="expr_bound&#39;&#39;vc" expl="VC for expr_bound&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="expr_bound&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="168"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="169"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="168"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="169"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="168"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="168"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="expr_bound_w&#39;&#39;vc" expl="VC for expr_bound_w&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="expr_bound_w&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.252615" steps="63728"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="19"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="43"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.256642" steps="63790"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="20"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="44"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.266463" steps="63740"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.7" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="19"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.8" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.110000" steps="43"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="182"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.10" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="20"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.11" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="44"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.12" expl="variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="380"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.13" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="19"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.14" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="43"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.15" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="176"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.16" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="19"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.17" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="59"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="357"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="eq_bound_w&#39;" proved="true">
 <proof prover="4"><result status="valid" time="0.090000" steps="93"/></proof>
 </goal>
 <goal name="ctx_bound_w&#39;&#39;vc" expl="VC for ctx_bound_w&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="ctx_bound_w&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="53"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="44"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="164094"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="221"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="max_var&#39;&#39;vc" expl="VC for max_var&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="max_var&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="179"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="163169"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="381"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="44"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.261906" steps="64214"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.130000" steps="163170"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="181"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="163379"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.274577" steps="64193"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.9" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.150000" steps="42"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="174"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.11" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="42"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="144"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="376"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="max_var_e&#39;&#39;vc" expl="VC for max_var_e&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="max_var_e&#39;&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.130000" steps="165298"/></proof>
  </goal>
  <goal name="max_var_e&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="165702"/></proof>
  </goal>
  <goal name="max_var_e&#39;&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="179030"/></proof>
  </goal>
  <goal name="max_var_e&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="94"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="max_var_ctx&#39;&#39;vc" expl="VC for max_var_ctx&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="max_var_ctx&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="187105"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.110000" steps="43"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.180000" steps="169509"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.261933" steps="65877"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="152"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="interp_ctx_valid&#39;&#39;vc" expl="VC for interp_ctx_valid&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="interp_ctx_valid&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.220000" steps="188441"/></proof>
  </goal>
  <goal name="interp_ctx_valid&#39;&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="181406"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="interp_ctx_wr&#39;&#39;vc" expl="VC for interp_ctx_wr&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="interp_ctx_wr&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="50"/></proof>
  </goal>
  <goal name="interp_ctx_wr&#39;&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.070000" steps="298"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="interp_ctx_wl&#39;&#39;vc" expl="VC for interp_ctx_wl&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="interp_ctx_wl&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.108468" steps="188965"/></proof>
  </goal>
  <goal name="interp_ctx_wl&#39;&#39;vc.1" expl="postcondition" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="interp_ctx_wl&#39;&#39;vc.1.0" expl="postcondition" proved="true">
   <transf name="compute_in_goal" proved="true" >
    <goal name="interp_ctx_wl&#39;&#39;vc.1.0.0" expl="postcondition" proved="true">
    <proof prover="4"><result status="valid" time="0.100000" steps="486"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="interp_ctx_cons&#39;&#39;vc" expl="VC for interp_ctx_cons&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="interp_ctx_cons&#39;&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="187527"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="holds_interp_ctx&#39;&#39;vc" expl="VC for holds_interp_ctx&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="holds_interp_ctx&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.230000" steps="197426"/></proof>
  </goal>
  <goal name="holds_interp_ctx&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="52"/></proof>
  </goal>
  <goal name="holds_interp_ctx&#39;&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="56"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="interp_holds&#39;&#39;vc" expl="VC for interp_holds&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="interp_holds&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.130000" steps="200341"/></proof>
  </goal>
  <goal name="interp_holds&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.060000" steps="147"/></proof>
  </goal>
  <goal name="interp_holds&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="46"/></proof>
  </goal>
  <goal name="interp_holds&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="74"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="impl_holds&#39;&#39;vc" expl="VC for impl_holds&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="impl_holds&#39;&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="68"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.100000" steps="177574"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.090000" steps="198532"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="66"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="177617"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="23"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="75"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="ctx_impl&#39;&#39;vc" expl="VC for ctx_impl&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="ctx_impl&#39;&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="175031"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="175053"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10332"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="175099"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.100000" steps="10334"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="10340"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="180576"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="interp_ctx_impl&#39;&#39;vc" expl="VC for interp_ctx_impl&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="interp_ctx_impl&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.190000" steps="199305"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.220000" steps="181803"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="186076"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="impl_cons&#39;vc" expl="VC for impl_cons" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="impl_cons&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="21"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="impl_wl&#39;&#39;vc" expl="VC for impl_wl&#39;" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="impl_wl&#39;&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="53"/></proof>
  </goal>
  <goal name="impl_wl&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="62"/></proof>
  </goal>
  <goal name="impl_wl&#39;&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="131"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="impl_self&#39;vc" expl="VC for impl_self" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="impl_self&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="193391"/></proof>
  </goal>
  <goal name="impl_self&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="175428"/></proof>
  </goal>
  <goal name="impl_self&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="141"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="prop_ctx&#39;vc" expl="VC for prop_ctx" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="prop_ctx&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="178209"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.140000" steps="21"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.2" expl="array creation size" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="26"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="8" timelimit="1"><result status="valid" time="0.769270" steps="233918"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.775230" steps="150613"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.150000" steps="211"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="222"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.220000" steps="871"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="14"><result status="valid" time="0.180000" steps="1714"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.9" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.310000" steps="69567"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.10" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.330000" steps="81630"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.270000" steps="531"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.190000" steps="1388"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.13" expl="assertion" proved="true">
  <proof prover="7"><result status="valid" time="0.100000" steps="465"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.460000" steps="83175"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="1.296364" steps="2770"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.040000" steps="165"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.17" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.330000" steps="71221"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.18" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="245"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="1.241579" steps="2770"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="14"><result status="valid" time="0.120000" steps="1163"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.140000" steps="28"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.22" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="70"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.23" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="28"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.24" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="60"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.25" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="67"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.110000" steps="97"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.27" expl="precondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="prop_ctx&#39;vc.27.0" expl="precondition" proved="true">
   <proof prover="2"><result status="valid" time="0.240000" steps="196459"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="prop_ctx&#39;vc.28" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="57"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.29" expl="array creation size" proved="true">
  <proof prover="4"><result status="valid" time="0.140000" steps="27"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.090000" steps="96"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="32"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.33" expl="variant decrease" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.100000" steps="83"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.34" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="40"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.35" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="194699"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.36" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="prop_ctx&#39;vc.36.0" expl="postcondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="prop_ctx&#39;vc.36.0.0" expl="postcondition" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="prop_ctx&#39;vc.36.0.0.0" expl="postcondition" proved="true">
     <transf name="split_vc" proved="true" >
      <goal name="prop_ctx&#39;vc.36.0.0.0.0" expl="postcondition" proved="true">
      <proof prover="8" memlimit="2000"><result status="valid" time="0.221332" steps="79226"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="prop_ctx&#39;vc.36.1" expl="postcondition" proved="true">
   <proof prover="11"><result status="valid" time="0.220000" steps="67638"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="prop_ctx&#39;vc.37" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.198284" steps="72895"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="48"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.39" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.40" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="104306"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.42" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.280000" steps="71966"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.43" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.44" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.45" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="10736"/></proof>
  <proof prover="4"><result status="valid" time="0.100000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.46" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.150000" steps="257"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.47" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="193239"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.48" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="193782"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.49" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.310000" steps="72549"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.50" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="107257"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.51" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="265581"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.110000" steps="42"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.53" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.110000" steps="102"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.54" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="prop_ctx&#39;vc.54.0" expl="postcondition" proved="true">
   <transf name="unfold" proved="true" arg1="numof">
    <goal name="prop_ctx&#39;vc.54.0.0" expl="postcondition" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="prop_ctx&#39;vc.54.0.0.0" expl="postcondition" proved="true">
     <proof prover="0" timelimit="15" memlimit="2000"><result status="valid" time="0.178271" steps="75146"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="prop_ctx&#39;vc.55" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.100000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.56" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.57" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.110000" steps="257"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.58" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="193238"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.59" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="36"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.60" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.300000" steps="72561"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.61" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="39"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.62" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="265580"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.63" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.034374" steps="108650"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.64" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.300000" steps="73334"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.65" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150346" steps="211431"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.66" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.67" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.68" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.638416" steps="120124"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.69" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="36"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.70" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.090000" steps="193772"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.71" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="107239"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.72" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.280000" steps="72159"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.73" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="138"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.74" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.75" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="prop_ctx&#39;vc.75.0" expl="VC for prop_ctx" proved="true">
   <proof prover="12"><result status="valid" time="0.040000" steps="68"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.1" expl="VC for prop_ctx" proved="true">
   <proof prover="12"><result status="valid" time="0.070000" steps="202"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.2" expl="VC for prop_ctx" proved="true">
   <proof prover="12"><result status="valid" time="0.070000" steps="234"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.3" expl="VC for prop_ctx" proved="true">
   <proof prover="12"><result status="valid" time="0.140000" steps="751"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.4" expl="VC for prop_ctx" proved="true">
   <proof prover="12" timelimit="5"><result status="valid" time="2.340000" steps="16255"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.5" expl="VC for prop_ctx" proved="true">
   <proof prover="12"><result status="valid" time="0.140000" steps="741"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.6" expl="VC for prop_ctx" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.430000" steps="92010"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.7" expl="VC for prop_ctx" proved="true">
   <proof prover="8"><result status="valid" time="1.140000" steps="195432"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.8" expl="VC for prop_ctx" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.420000" steps="91913"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.9" expl="VC for prop_ctx" proved="true">
   <proof prover="12"><result status="valid" time="0.050000" steps="82"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="prop_ctx&#39;vc.76" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.110000" steps="36"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.77" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.080000" steps="78"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.78" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.067982" steps="283"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.79" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="96"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.80" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="194256"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.81" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.110000" steps="194778"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.82" expl="index in array bounds" proved="true">
  <proof prover="8"><result status="valid" time="0.320000" steps="67507"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.83" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.320000" steps="449"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.84" expl="postcondition" proved="true">
  <proof prover="14"><result status="valid" time="0.240534" steps="939"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.85" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="116"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.86" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.090000" steps="10774"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.87" expl="exceptional postcondition" proved="true">
  <proof prover="7"><result status="valid" time="0.080000" steps="32"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.88" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="28"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.89" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="33"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.90" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="190609"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.91" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="11188"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.92" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="38"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.93" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.94" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="190627"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.95" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.96" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.300000" steps="70614"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.97" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.98" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="195"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.99" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.198607" steps="70313"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.100" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.300000" steps="70357"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.101" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.102" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.103" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="195"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.104" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.130000" steps="195"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.105" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="78"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.106" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.107" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.108" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="191"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.109" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.270000" steps="69917"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.110" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.140000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.111" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="211305"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.112" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010122" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.113" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="115"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.114" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="96"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.115" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.116" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.117" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.118" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.168146" steps="1381"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.119" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="90"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.120" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.121" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="74"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.122" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.110000" steps="74"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.123" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="82"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.124" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.181143" steps="70955"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.125" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.126" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.127" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="34"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.128" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.170000" steps="210239"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.129" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.032910" steps="104517"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.130" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.100000" steps="56868"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.131" expl="variant decrease" proved="true">
  <proof prover="11"><result status="valid" time="0.224091" steps="78310"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.132" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.220000" steps="65168"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.133" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="69"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.134" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="37"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.135" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.120000" steps="1314"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.136" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="38"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.137" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="194"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.138" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.139" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.140" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="256"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.141" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.140000" steps="68"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.142" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.105079" steps="195438"/></proof>
  <proof prover="4"><result status="valid" time="0.090000" steps="69"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.143" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.220000" steps="65836"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.144" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.230000" steps="132"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.145" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="38"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.146" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.310000" steps="71475"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.147" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.148" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.149" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="266"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.150" expl="precondition" proved="true">
  <proof prover="11"><result status="valid" time="0.310000" steps="70137"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.151" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="195449"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.152" expl="variant decrease" proved="true">
  <proof prover="7"><result status="valid" time="0.100000" steps="749"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.153" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.250000" steps="65246"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.154" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="71"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.155" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="39"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.156" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.360000" steps="81885"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.157" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.170000" steps="204878"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.158" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.140000" steps="205"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.159" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.160" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.161" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="266"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.162" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.240000" steps="62752"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.163" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="69"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.164" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.060000" steps="273"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.165" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.220000" steps="65246"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.166" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.140000" steps="71"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.167" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="39"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.168" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.130000" steps="555"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.169" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="40"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.170" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="205"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.171" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.010000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.172" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.173" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.174" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.145605" steps="65398"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.175" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.220000" steps="203026"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.176" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.080000" steps="96"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.177" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.178" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.134357" steps="62647"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.179" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.130000" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.180" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.220000" steps="65063"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.181" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.110000" steps="37"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.182" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="204013"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.183" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120342" steps="313"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.184" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.115426" steps="204512"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.185" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="209899"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.186" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.187" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.100000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.188" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.098897" steps="59526"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.189" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="36"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.190" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.100000" steps="199797"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.191" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.023687" steps="60586"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.192" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.140000" steps="61552"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.193" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="118"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.194" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="198185"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.195" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.170000" steps="232387"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.196" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.210000" steps="66028"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.197" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="77"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.198" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.210000" steps="205917"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.199" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.270000" steps="74334"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.200" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.360000" steps="76939"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.201" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="50"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.202" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.050000" steps="45"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.203" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.300000" steps="79821"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.204" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.070000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.205" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.120000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.206" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="201285"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.207" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="32"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.208" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="211024"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.209" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.148125" steps="64955"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.210" expl="precondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.040000" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.211" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.160000" steps="61082"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.212" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.090000" steps="45"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.213" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.130000" steps="136"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.214" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10736"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.215" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.150000" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.216" expl="out of loop bounds" proved="true">
  <proof prover="7"><result status="valid" time="0.080000" steps="73"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="prop_mp_decision&#39;vc" expl="VC for prop_mp_decision" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="prop_mp_decision&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.100000" steps="180470"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="180498"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="98630"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="98650"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.094593" steps="191654"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.107750" steps="202310"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10540"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030000" steps="10540"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020000" steps="10540"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="TestMP" proved="true">
 <goal name="g" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="g.0" proved="true">
  <transf name="reflection_f" proved="true" arg1="mp_decision">
   <goal name="g.0.0" expl="reification check" proved="true">
   <proof prover="9"><result status="valid" time="0.080000" steps="516"/></proof>
   </goal>
   <goal name="g.0.1" proved="true">
   <proof prover="4"><result status="valid" time="0.040000" steps="42"/></proof>
   </goal>
   <goal name="g.0.2" proved="true">
   <proof prover="2"><result status="valid" time="0.092703" steps="190486"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="g&#39;" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="g&#39;.0" proved="true">
  <transf name="reflection_f" proved="true" arg1="prop_mp_decision">
   <goal name="g&#39;.0.0" expl="reification check" proved="true">
   <proof prover="9"><result status="valid" time="0.070000" steps="491"/></proof>
   </goal>
   <goal name="g&#39;.0.1" proved="true">
   <proof prover="2"><result status="valid" time="0.160000" steps="187147"/></proof>
   </goal>
   <goal name="g&#39;.0.2" proved="true">
   <proof prover="4"><result status="valid" time="0.080000" steps="44"/></proof>
   </goal>
   <goal name="g&#39;.0.3" proved="true">
   <proof prover="2"><result status="valid" time="0.150000" steps="190600"/></proof>
   </goal>
  </transf>
  <transf name="subst" proved="true" arg1="j">
   <goal name="g&#39;.0.0" proved="true">
   <transf name="reflection_f" proved="true" arg1="mp_decision">
    <goal name="g&#39;.0.0.0" expl="reification check" proved="true">
    <proof prover="4"><result status="valid" time="0.080000" steps="47"/></proof>
    </goal>
    <goal name="g&#39;.0.0.1" proved="true">
    <proof prover="2"><result status="valid" time="0.150000" steps="190278"/></proof>
    </goal>
    <goal name="g&#39;.0.0.2" proved="true">
    <proof prover="2"><result status="valid" time="0.150000" steps="190277"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="g&#39;&#39;" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="g&#39;&#39;.0" proved="true">
  <transf name="replace" proved="true" arg1="c" arg2="0">
   <goal name="g&#39;&#39;.0.0" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="52"/></proof>
   </goal>
   <goal name="g&#39;&#39;.0.1" expl="equality hypothesis" proved="true">
   <transf name="replace" proved="true" arg1="c" arg2="0" arg3="in" arg4="H2">
    <goal name="g&#39;&#39;.0.1.0" expl="equality hypothesis" proved="true">
    <transf name="reflection_f" proved="true" arg1="mp_decision">
     <goal name="g&#39;&#39;.0.1.0.0" expl="equality hypothesis" proved="true">
     <proof prover="4"><result status="valid" time="0.050000" steps="49"/></proof>
     </goal>
     <goal name="g&#39;&#39;.0.1.0.1" proved="true">
     <proof prover="2"><result status="valid" time="0.107806" steps="191536"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="g&#39;&#39;.0.1.1" expl="equality hypothesis" proved="true">
    <proof prover="2"><result status="valid" time="0.020000" steps="10568"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Fmla" proved="true">
 <goal name="f&#39;vc" expl="VC for f" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="2"/></proof>
 </goal>
</theory>
</file>
</why3session>
