<?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="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"/>
<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="0.06"/></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="0.01" steps="2454"/></proof>
 </goal>
 <goal name="expr_bound&#39;vc" expl="VC for expr_bound" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="2454"/></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="0.02" steps="7800"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="7068"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="12"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="7839"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="7098"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="34"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="eq_bound_w" proved="true">
 <proof prover="4"><result status="valid" time="0.00" 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="0.02" steps="11151"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="12"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10172"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" 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="0.00" steps="13"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="30288"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="31204"/></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="0.00" 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="0.01" 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="0.01" 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="0.01" 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="0.00" steps="6"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2000"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" 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="0.00" 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="0.00" steps="8"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="30295"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="31211"/></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="0.00" 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="0.01" 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="0.01" 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="0.00" 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="0.00" steps="6"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2000"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" 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="0.00" 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="0.02" steps="23321"/></proof>
  </goal>
  <goal name="sprod&#39;vc.1" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" 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="0.00" steps="11"/></proof>
  </goal>
  <goal name="sprod&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="6"/></proof>
  </goal>
  <goal name="sprod&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2048"/></proof>
  </goal>
  <goal name="sprod&#39;vc.5" expl="out of loop bounds" proved="true">
  <proof prover="8" timelimit="1"><result status="valid" time="0.05" steps="11033"/></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="0.02" steps="24605"/></proof>
  </goal>
  <goal name="m_append&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="42"/></proof>
  </goal>
  <goal name="m_append&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="26069"/></proof>
  </goal>
  <goal name="m_append&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" 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="0.00" steps="13"/></proof>
  </goal>
  <goal name="m_append&#39;vc.5" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="36498"/></proof>
  </goal>
  <goal name="m_append&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" 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="0.00" 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="0.00" 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="0.01" 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="0.00" 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="0.01" 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="0.01" 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="0.01" 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="0.01" 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="0.01" 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="0.01" 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="0.01" 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="0.00" steps="31"/></proof>
  </goal>
  <goal name="m_append&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
  <goal name="m_append&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="m_append&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="m_append&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" 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="0.00" 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="0.02" steps="22550"/></proof>
  </goal>
  <goal name="v_append&#39;vc.1" expl="array creation size" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="v_append&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="29244"/></proof>
  </goal>
  <goal name="v_append&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" 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="0.01" 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="0.01" 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="0.00" 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="0.22" 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="0.14" steps="144"/></proof>
  </goal>
  <goal name="v_append&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
  <goal name="v_append&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="17"/></proof>
  </goal>
  <goal name="v_append&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" 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="0.00" 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="0.01" steps="2000"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="23496"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2806"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="30209"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="29559"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.5" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.6" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="17"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="30263"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.8" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="29192"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="max_var&#39;vc" expl="VC for max_var" proved="true">
 <proof prover="4"><result status="valid" time="0.04" 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="0.01" steps="33101"/></proof>
 </goal>
 <goal name="max_var_ctx&#39;vc" expl="VC for max_var_ctx" proved="true">
 <proof prover="4"><result status="valid" time="0.04" 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="0.02" steps="56"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" steps="22"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" steps="25"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.4" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.04" steps="65"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.03" steps="24"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" 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="0.02" steps="31199"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="35578"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.11" expl="assertion" proved="true">
  <proof prover="3" memlimit="1000"><result status="valid" time="0.04"/></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="0.01" steps="9"/></proof>
   </goal>
   <goal name="opp_expr&#39;vc.12.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="31750"/></proof>
   </goal>
   <goal name="opp_expr&#39;vc.12.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="31703"/></proof>
   </goal>
   <goal name="opp_expr&#39;vc.12.3" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.02" 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="0.02" steps="31236"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="opp_expr&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.01" steps="12"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.03" steps="69"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.16" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" 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="0.01" steps="24"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="10"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2454"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="9"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="31199"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="35800"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="25"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="54"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.9" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2510"/></proof>
  </goal>
  <goal name="norm_eq_aux&#39;vc.10" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2454"/></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="0.02" steps="42"/></proof>
  </goal>
  <goal name="norm_eq&#39;vc.1" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></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="0.02" steps="39"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.2.1" expl="VC for norm_eq" proved="true">
   <proof prover="4"><result status="valid" time="0.03" 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="0.16" steps="22461"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.2.3" expl="VC for norm_eq" proved="true">
   <proof prover="4"><result status="valid" time="0.02" 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="0.02" 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="0.02" 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="0.11" steps="20961"/></proof>
   </goal>
   <goal name="norm_eq&#39;vc.3.1" expl="postcondition" proved="true">
   <proof prover="5"><result status="valid" time="0.22"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="norm_eq&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.04" steps="89"/></proof>
  </goal>
  <goal name="norm_eq&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="norm_eq&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2530"/></proof>
  </goal>
  <goal name="norm_eq&#39;vc.7" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </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="0.03" steps="34450"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="33186"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="49454"/></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="0.02" steps="31997"/></proof>
  </goal>
  <goal name="interp_ctx_valid&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="35325"/></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="0.02" steps="140"/></proof>
 </goal>
 <goal name="interp_ctx_wl&#39;vc" expl="VC for interp_ctx_wl" proved="true">
 <proof prover="4"><result status="valid" time="0.02" 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="3"><result status="valid" time="0.12"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="10"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2914"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="18"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="27"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="48"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="51"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="20"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="62"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2914"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></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">
  <proof prover="3"><result status="valid" time="0.22"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="17"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2934"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="add_expr&#39;vc.3.0" expl="postcondition" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="add_expr&#39;vc.3.0.0" expl="postcondition" proved="true">
    <proof prover="3"><result status="valid" time="0.35"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="add_expr&#39;vc.3.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.05"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="add_expr&#39;vc.4" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="add_expr&#39;vc.4.0" expl="postcondition" proved="true">
   <proof prover="0" timelimit="1"><result status="valid" time="0.19" steps="23745"/></proof>
   </goal>
   <goal name="add_expr&#39;vc.4.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.23"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="add_expr&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="52496"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="31139"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.7" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="62"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.8" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="add_expr&#39;vc.8.0" expl="postcondition" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="add_expr&#39;vc.8.0.0" expl="postcondition" proved="true">
    <proof prover="4"><result status="valid" time="0.02" steps="57"/></proof>
    </goal>
    <goal name="add_expr&#39;vc.8.0.1" expl="postcondition" proved="true">
    <proof prover="4"><result status="valid" time="0.01" steps="21"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="add_expr&#39;vc.8.1" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="20"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="add_expr&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="56157"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="17878"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.11" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="62"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.83" steps="500"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2934"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2934"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="19"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.16" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2934"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.17" expl="postcondition" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="add_expr&#39;vc.17.0" expl="postcondition" proved="true">
   <transf name="revert" proved="true" arg1="H">
    <goal name="add_expr&#39;vc.17.0.0" expl="postcondition" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="add_expr&#39;vc.17.0.0.0" expl="postcondition" proved="true">
     <proof prover="0" timelimit="1"><result status="valid" time="0.14" steps="23775"/></proof>
     </goal>
     <goal name="add_expr&#39;vc.17.0.0.1" expl="postcondition" proved="true">
     <proof prover="3"><result status="valid" time="0.37"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="add_expr&#39;vc.18" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="52595"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="31124"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.20" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="59"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.18" steps="244"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.22" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="56255"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.23" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="17877"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.24" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="59"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.36" steps="455"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.26" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2934"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.27" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2934"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.28" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="32524"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.29" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="31140"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.30" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="19"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.32" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="36086"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.33" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="17879"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.34" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.35" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.36" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2934"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.37" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2934"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.38" expl="unreachable point" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="32087"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.39" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="51816"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.40" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="55429"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="13"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.42" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.44" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="51409"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.45" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="35433"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.46" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="mul_eq&#39;vc" expl="VC for mul_eq" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="29"/></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="0.03" steps="42019"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="93686"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="38826"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="36926"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2914"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></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="0.03" steps="51816"/></proof>
  </goal>
  <goal name="zero_expr&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="55410"/></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="4"><result status="valid" time="0.02" steps="26"/></proof>
   </goal>
   <goal name="zero_expr&#39;vc.2.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.23"/></proof>
   </goal>
   <goal name="zero_expr&#39;vc.2.2" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="31"/></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="0"><result status="valid" time="0.06" steps="22426"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="zero_expr&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></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="0.04"/></proof>
   </goal>
   <goal name="sub_expr&#39;vc.0.1" expl="VC for sub_expr" proved="true">
   <proof prover="0"><result status="valid" time="0.05" steps="24704"/></proof>
   </goal>
   <goal name="sub_expr&#39;vc.0.2" expl="VC for sub_expr" proved="true">
   <proof prover="4"><result status="valid" time="0.01" 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="0.01" steps="34"/></proof>
   </goal>
   <goal name="sub_expr&#39;vc.0.4" expl="VC for sub_expr" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sub_expr&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="sub_expr&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></proof>
  </goal>
  <goal name="sub_expr&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2914"/></proof>
  </goal>
  <goal name="sub_expr&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" 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="0"><result status="valid" time="0.09" steps="26802"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.4" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
  <goal name="same_eq&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2914"/></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="0.04" steps="37132"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="43797"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="49305"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3064"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="print_lc&#39;vc" expl="VC for print_lc" proved="true">
 <proof prover="4"><result status="valid" time="0.01" steps="41"/></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="0.04" steps="42297"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="15"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="61"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="76"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></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="0.03" steps="15"/></proof>
   </goal>
   <goal name="check_combination&#39;vc.7.1" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="30"/></proof>
   </goal>
   <goal name="check_combination&#39;vc.7.2" expl="VC for check_combination" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="45"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="check_combination&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.9" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.10" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="61"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="76"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3064"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="3064"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="40004"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.17" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="8"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="1.30"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="19206"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.20" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="3064"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="3064"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.22" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="transpose&#39;vc" expl="VC for transpose" proved="true">
 <proof prover="2"><result status="valid" time="0.06" steps="103701"/></proof>
 </goal>
 <goal name="swap_rows&#39;vc" expl="VC for swap_rows" proved="true">
 <proof prover="2"><result status="valid" time="0.14" steps="243487"/></proof>
 </goal>
 <goal name="mul_row&#39;vc" expl="VC for mul_row" proved="true">
 <proof prover="4"><result status="valid" time="0.12" steps="311"/></proof>
 </goal>
 <goal name="addmul_row&#39;vc" expl="VC for addmul_row" proved="true">
 <proof prover="4"><result status="valid" time="0.14" steps="555"/></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="0.05" steps="100275"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.02" steps="17"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="49"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="26"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.7" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="34029"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.8" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="42715"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="41912"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="42174"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.11" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="42639"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.12" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="4136"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.13" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="45236"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.14" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="45586"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.15" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.16" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="51406"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.17" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="52772"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.18" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="31"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.19" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="31"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="52823"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="31"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.21" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="4886"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.22" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="57"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.23" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="53957"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.24" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="46"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.25" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="67"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.26" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3122"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="9"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.27" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" steps="16"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.28" expl="assertion" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="gauss_jordan&#39;vc.28.0" expl="assertion" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="gauss_jordan&#39;vc.28.0.0" expl="assertion" proved="true">
    <proof prover="0"><result status="valid" time="0.23" steps="32258"/></proof>
    </goal>
    <goal name="gauss_jordan&#39;vc.28.0.1" expl="VC for gauss_jordan" proved="true">
    <proof prover="2"><result status="valid" time="0.04" steps="59528"/></proof>
    </goal>
    <goal name="gauss_jordan&#39;vc.28.0.2" expl="VC for gauss_jordan" proved="true">
    <proof prover="2"><result status="valid" time="0.14" steps="85360"/></proof>
    </goal>
    <goal name="gauss_jordan&#39;vc.28.0.3" expl="VC for gauss_jordan" proved="true">
    <transf name="revert" proved="true" arg1="H">
     <goal name="gauss_jordan&#39;vc.28.0.3.0" expl="VC for gauss_jordan" proved="true">
     <transf name="split_vc" proved="true" >
      <goal name="gauss_jordan&#39;vc.28.0.3.0.0" expl="VC for gauss_jordan" proved="true">
      <proof prover="4"><result status="valid" time="0.14" steps="440"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="gauss_jordan&#39;vc.28.0.4" expl="VC for gauss_jordan" proved="true">
    <proof prover="0"><result status="valid" time="0.16" steps="35506"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="gauss_jordan&#39;vc.29" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="41"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.30" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.50" steps="706391"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.31" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="53"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.32" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="0.21" steps="39181"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.33" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="38"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.34" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="53443"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.35" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.45" steps="649599"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="44"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.36" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="46"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.37" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3122"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="9"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.38" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" steps="16"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.39" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="gauss_jordan&#39;vc.39.0" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.13" steps="31997"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.39.1" expl="VC for gauss_jordan" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="59325"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.39.2" expl="VC for gauss_jordan" proved="true">
   <proof prover="2"><result status="valid" time="0.13" steps="84945"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.39.3" expl="VC for gauss_jordan" proved="true">
   <proof prover="4"><result status="valid" time="0.13" steps="431"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.39.4" expl="VC for gauss_jordan" proved="true">
   <proof prover="0"><result status="valid" time="0.16" steps="35110"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="gauss_jordan&#39;vc.40" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="56267"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="39"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.41" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.60" steps="769114"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.42" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="51"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.43" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.41" steps="555358"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.44" expl="out of loop bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.45" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3122"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.46" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3122"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="9"/></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="0.03" steps="58145"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.47.1" expl="VC for gauss_jordan" proved="true">
   <proof prover="1"><result status="valid" time="0.12" steps="29202"/></proof>
   </goal>
   <goal name="gauss_jordan&#39;vc.47.2" expl="VC for gauss_jordan" proved="true">
   <proof prover="1"><result status="valid" time="0.14" steps="32268"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="gauss_jordan&#39;vc.48" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="25"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.49" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="52414"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.50" expl="loop invariant preservation" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="gauss_jordan&#39;vc.50.0" expl="loop invariant preservation" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="60105"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="gauss_jordan&#39;vc.51" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="50904"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3122"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.53" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="43593"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.54" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="51648"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.55" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="28"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.56" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="52138"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.57" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.25" steps="386282"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="37"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.58" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="49698"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.59" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="26022"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.60" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4864"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="to_list&#39;vc" expl="VC for to_list" proved="true">
 <proof prover="2"><result status="valid" time="0.09" steps="169038"/></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="0.02" steps="33042"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="33121"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3198"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.4" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="36360"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.5" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="34788"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.6" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="35002"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="38165"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="74"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.8" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="37809"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.9" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="43781"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.10" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="45059"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.11" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.12" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="159"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.02" 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="0.02" steps="182"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.15" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.16" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.12" steps="219376"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.17" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="44041"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="29"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.18" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="70"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.19" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.12" steps="219383"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="44041"/></proof>
  <proof prover="4"><result status="valid" time="0.02" steps="29"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.21" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="70"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.22" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.23" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.24" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.25" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.26" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="49039"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.27" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.03" 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="0.03" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.29" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="33"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.30" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="84"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.31" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.32" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.33" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="82"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.34" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="39"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.35" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.36" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.37" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.38" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.39" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="82"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.40" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="39"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.41" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.42" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.44" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.14" steps="30778"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.45" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.46" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="78"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.47" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="37"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.48" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.49" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.50" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.51" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="80"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.52" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.53" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.54" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="78"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.55" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="37"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.56" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.57" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.58" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.59" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.60" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="78"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.61" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="37"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.62" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.63" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3064"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.64" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.65" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.66" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="31"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.67" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="77"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.68" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.69" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="48365"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.70" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.71" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.72" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.02" 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="0.03" 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="0.03" steps="205"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.75" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.76" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.12" steps="225558"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.77" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="64"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.78" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.12" steps="225564"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.79" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="64"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.80" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.81" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.82" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.83" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.84" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="49038"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.85" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4114"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.86" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="44677"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.87" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="82"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.88" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="47767"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.89" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="49614"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.90" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="55212"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.91" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="58199"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="91"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.92" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="57086"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.93" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="61189"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.94" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="75455"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.95" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="63561"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="41"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.96" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3078"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.97" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.98" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.99" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.100" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.101" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3064"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.102" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3064"/></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="0.17" steps="111371"/></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="0.03" steps="10"/></proof>
  </goal>
  <goal name="simp&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="100816"/></proof>
  </goal>
  <goal name="simp&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="30"/></proof>
  </goal>
  <goal name="simp&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="12"/></proof>
  </goal>
  <goal name="simp&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
  <goal name="simp&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
  <goal name="simp&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
  <goal name="simp&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="101610"/></proof>
  </goal>
  <goal name="simp&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="106355"/></proof>
  </goal>
  <goal name="simp&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="19"/></proof>
  </goal>
  <goal name="simp&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="42162"/></proof>
  </goal>
  <goal name="simp&#39;vc.11" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3498"/></proof>
  </goal>
  <goal name="simp&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
  <goal name="simp&#39;vc.13" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="101673"/></proof>
  </goal>
  <goal name="simp&#39;vc.14" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="107032"/></proof>
  </goal>
  <goal name="simp&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="simp&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="42609"/></proof>
  </goal>
  <goal name="simp&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3498"/></proof>
  </goal>
  <goal name="simp&#39;vc.18" expl="exceptional postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.02" steps="14"/></proof>
  </goal>
  <goal name="simp&#39;vc.19" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
  <goal name="simp&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="35"/></proof>
  </goal>
  <goal name="simp&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="41166"/></proof>
  </goal>
  <goal name="simp&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="10"/></proof>
  </goal>
  <goal name="simp&#39;vc.23" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="41076"/></proof>
  </goal>
  <goal name="simp&#39;vc.24" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="110"/></proof>
  </goal>
  <goal name="simp&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="14"/></proof>
  </goal>
  <goal name="simp&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="26"/></proof>
  </goal>
  <goal name="simp&#39;vc.27" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3498"/></proof>
  </goal>
  <goal name="simp&#39;vc.28" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
  <goal name="simp&#39;vc.29" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
  <goal name="simp&#39;vc.30" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="110"/></proof>
  </goal>
  <goal name="simp&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="14"/></proof>
  </goal>
  <goal name="simp&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="26"/></proof>
  </goal>
  <goal name="simp&#39;vc.33" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3498"/></proof>
  </goal>
  <goal name="simp&#39;vc.34" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
  <goal name="simp&#39;vc.35" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3434"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="simp_eq&#39;vc" expl="VC for simp_eq" proved="true">
 <proof prover="2"><result status="valid" time="0.14" steps="243352"/></proof>
 </goal>
 <goal name="simp_ctx&#39;vc" expl="VC for simp_ctx" proved="true">
 <proof prover="4"><result status="valid" time="0.15" steps="844"/></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="0.03" steps="25282"/></proof>
  </goal>
  <goal name="decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="25288"/></proof>
  </goal>
  <goal name="decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="55390"/></proof>
  </goal>
  <goal name="decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="56906"/></proof>
  </goal>
  <goal name="decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="4318"/></proof>
  </goal>
  <goal name="decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="4318"/></proof>
  </goal>
  <goal name="decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3736"/></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="0.03" steps="3587"/></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="0.25" steps="735972"/></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="0.08" steps="5259"/></proof>
     </goal>
     <goal name="cross_d&#39;vc.0.1.0.1" expl="apply premises" proved="true">
     <proof prover="2"><result status="valid" time="0.01" steps="476"/></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="0.00" steps="390"/></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="0.02" steps="5621"/></proof>
  </goal>
  <goal name="cross_ind&#39;vc.1" expl="assertion" proved="true">
  <proof prover="3" timelimit="10"><result status="valid" time="0.01"/></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="2.28"/></proof>
   </goal>
   <goal name="cross_ind&#39;vc.2.1" expl="VC for cross_ind" proved="true">
   <proof prover="4"><result status="valid" time="0.00" 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="2.46"/></proof>
   </goal>
   <goal name="cross_ind&#39;vc.2.3" expl="VC for cross_ind" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="9802"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="cross_ind&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="536"/></proof>
  </goal>
  <goal name="cross_ind&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="cross" proved="true">
 <proof prover="4"><result status="valid" time="0.00" steps="14"/></proof>
 </goal>
 <goal name="gcd&#39;vc" expl="VC for gcd" proved="true">
 <proof prover="0"><result status="valid" time="0.11" steps="31096"/></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="0.02" steps="28563"/></proof>
  </goal>
  <goal name="gcd&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="1724"/></proof>
  </goal>
  <goal name="gcd&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="1724"/></proof>
  </goal>
  <goal name="gcd&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="28734"/></proof>
  </goal>
  <goal name="gcd&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="28734"/></proof>
  </goal>
  <goal name="gcd&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="29908"/></proof>
  </goal>
  <goal name="gcd&#39;vc.6" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="31914"/></proof>
  </goal>
  <goal name="gcd&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="31328"/></proof>
  </goal>
  <goal name="gcd&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="30611"/></proof>
  </goal>
  <goal name="gcd&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="30683"/></proof>
  </goal>
  <goal name="gcd&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="29619"/></proof>
  </goal>
  <goal name="gcd&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="28760"/></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="0.03" steps="28191"/></proof>
  </goal>
  <goal name="simp&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="27790"/></proof>
  </goal>
  <goal name="simp&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="27790"/></proof>
  </goal>
  <goal name="simp&#39;vc.3" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.06" steps="16825"/></proof>
  </goal>
  <goal name="simp&#39;vc.4" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="10"/></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="0.02" steps="28070"/></proof>
   </goal>
   <goal name="simp&#39;vc.5.1" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.02" steps="198"/></proof>
   </goal>
   <goal name="simp&#39;vc.5.2" expl="postcondition" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.13" steps="5085"/></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="0.01"/></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="1.34"/></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="0.46"/></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="0.01" 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="0.02"/></proof>
   </goal>
   <goal name="radd&#39;vc.1.3" expl="VC for radd" proved="true">
   <proof prover="10"><result status="valid" time="0.76"/></proof>
   </goal>
   <goal name="radd&#39;vc.1.4" expl="VC for radd" proved="true">
   <proof prover="12"><result status="valid" time="0.77" steps="4862"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="radd&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="13"><result status="valid" time="0.02"/></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="0.22"/></proof>
  </goal>
  <goal name="rmul&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="1676"/></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="0.00" 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="0.02" steps="29976"/></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="0.01" steps="30827"/></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="0.20"/></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="0.02" steps="30116"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="LinearDecisionRational" proved="true">
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1752"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1746"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1746"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1750"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1750"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1748"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.00" steps="1752"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3760"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3760"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1748"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1746"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1744"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1744"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.04" steps="28798"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="28735"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="28673"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1742"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1752"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1756"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1756"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="28987"/></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="0.02"/></proof>
   </goal>
   <goal name="one_def.0.1" expl="equality hypothesis" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="1770"/></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="0.03" steps="1798"/></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="0.01" steps="1798"/></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="0.01" steps="1798"/></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="0.01" steps="1798"/></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="0.02" steps="14762"/></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="0.01" steps="18"/></proof>
 </goal>
 <goal name="imul&#39;vc" expl="VC for imul" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="18"/></proof>
 </goal>
 <goal name="iopp&#39;vc" expl="VC for iopp" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="18"/></proof>
 </goal>
 <goal name="iinv&#39;vc" expl="VC for iinv" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="18"/></proof>
 </goal>
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="24"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="24"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="28"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="28"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="26"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="89"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="89"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="26"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="24"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="22"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="22"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="500"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="464"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="427"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="20"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="30"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="34"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="34"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="52"/></proof>
 </goal>
 <goal name="C.one_def" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="70"/></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="0.02" 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="0.02" 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="0.03" 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="0.01" 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="0.01" steps="86"/></proof>
 </goal>
 <goal name="m_y&#39;vc" expl="VC for m_y" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="6200"/></proof>
 </goal>
 <goal name="m&#39;vc" expl="VC for m" proved="true">
 <proof prover="4"><result status="valid" time="0.10" steps="106"/></proof>
 </goal>
 <goal name="m_cprod&#39;vc" expl="VC for m_cprod" proved="true">
 <proof prover="4"><result status="valid" time="0.16" steps="173"/></proof>
 </goal>
 <goal name="m_expr&#39;vc" expl="VC for m_expr" proved="true">
 <proof prover="4"><result status="valid" time="0.54" steps="2134"/></proof>
 </goal>
 <goal name="m_eq&#39;vc" expl="VC for m_eq" proved="true">
 <proof prover="4"><result status="valid" time="0.04" steps="137"/></proof>
 </goal>
 <goal name="m_ctx&#39;vc" expl="VC for m_ctx" proved="true">
 <proof prover="4"><result status="valid" time="0.14" 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="0.02" steps="44996"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="44998"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="158777"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.12" steps="160408"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="8074"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="8074"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="6236"/></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="0.05" steps="107071"/></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="0.16" steps="127806"/></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="0.05" 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="0.04" steps="35"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.09" steps="18853"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="23"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="41654"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.04" steps="410"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="43573"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="61"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.8" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="41672"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="420"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.11" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="43585"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="119"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.10" steps="19280"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="53"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="39"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.19" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="41652"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.04" steps="403"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.21" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="64"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="61"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.23" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.24" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.25" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="41670"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="423"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.27" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="43583"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.28" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="119"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.29" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.30" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.09" steps="19437"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="55"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.33" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.09" steps="19843"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.34" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="18"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.35" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="41883"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.36" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.04" steps="394"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.37" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="73"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="67"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.39" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.40" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.41" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="41901"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.42" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="477"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.43" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="43853"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.44" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.12" steps="20817"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.45" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="2618"/></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="0.01" steps="30"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.48" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="98"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.49" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="80"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.50" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.21" steps="2002"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.51" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="43992"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="136"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.53" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.54" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.55" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="42075"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.56" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.05" steps="521"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.57" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="44007"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.58" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.11" steps="21197"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.59" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.60" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.61" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.62" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="41765"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.63" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="334"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.64" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="43690"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.65" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.08" steps="19274"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.66" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.67" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.68" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="41786"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.69" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="338"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.70" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="43705"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.71" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.12" steps="20650"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.72" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="6"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.73" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.74" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.75" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="41401"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.76" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="37"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.77" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="44999"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.78" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="19"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.79" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.80" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="45088"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.81" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="16"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.82" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.83" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.84" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="41419"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.85" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.09" steps="18551"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.86" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="44944"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.87" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="19"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.88" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.89" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="72"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.90" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="16"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.91" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2618"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.92" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="2514"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.93" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="13"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.94" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="2514"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="add_exp&#39;vc" expl="VC for add_exp" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="2618"/></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="0.02" steps="6"/></proof>
  </goal>
  <goal name="add_exp&#39;vc.1" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></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="0.05" steps="41379"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="41401"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="43030"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="41419"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="55"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="46"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="59"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></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="0.02" steps="9"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="43247"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="2618"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2618"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="41494"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="43247"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2618"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2618"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="42854"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="80"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.10" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="43247"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2618"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="2618"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="96"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.15" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2618"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.16" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="2618"/></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="0.02" steps="46726"/></proof>
  </goal>
  <goal name="madd&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="47633"/></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="0.05"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.1" expl="assertion" proved="true">
   <proof prover="13"><result status="valid" time="0.05"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.2" expl="assertion" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.05" steps="14826"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.3" expl="assertion" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.02" steps="165"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.4" expl="VC for madd" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.07" steps="16698"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="madd&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="6"/></proof>
  </goal>
  <goal name="madd&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="2618"/></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="0.07"/></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="0.04"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.1" expl="VC for mmul" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.03" steps="164"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.2" expl="VC for mmul" proved="true">
   <proof prover="13"><result status="valid" time="0.05"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.3" expl="VC for mmul" proved="true">
   <proof prover="13"><result status="valid" time="0.04"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.4" expl="VC for mmul" proved="true">
   <proof prover="9" timelimit="1"><result status="valid" time="0.02" 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="0.04" steps="533"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.6" expl="VC for mmul" proved="true">
   <proof prover="8" timelimit="1"><result status="valid" time="0.06" steps="16705"/></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="0.03" steps="6"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="mmul&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2514"/></proof>
  </goal>
  <goal name="mmul&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="3" timelimit="10"><result status="valid" time="0.07"/></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="0.03" 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="0.08" steps="495"/></proof>
 </goal>
 <goal name="meq&#39;vc" expl="VC for meq" proved="true">
 <proof prover="9" timelimit="1"><result status="valid" time="0.93" steps="26768"/></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="0.13" steps="51027"/></proof>
  </goal>
  <goal name="minv&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="51914"/></proof>
  </goal>
  <goal name="minv&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3052"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="LinearDecisionRationalMP" proved="true">
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3064"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3058"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3058"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3062"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3062"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3060"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="6785"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="6785"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3060"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3058"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3056"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3056"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.10" steps="49444"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.10" steps="49381"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.09" steps="49319"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3054"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3064"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3068"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3068"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="52152"/></proof>
 </goal>
 <goal name="C.one_def" proved="true">
 <proof prover="4"><result status="valid" time="0.04" 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="0.02" steps="3126"/></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="0.02" steps="3126"/></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="0.01" steps="3126"/></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="0.01" steps="3126"/></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="0.01" steps="3126"/></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="0.01" steps="3156"/></proof>
 </goal>
 <goal name="mpmul&#39;vc" expl="VC for mpmul" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3156"/></proof>
 </goal>
 <goal name="mpopp&#39;vc" expl="VC for mpopp" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3156"/></proof>
 </goal>
 <goal name="mpeq&#39;vc" expl="VC for mpeq" proved="true">
 <proof prover="2"><result status="valid" time="0.06" steps="3190"/></proof>
 </goal>
 <goal name="mpinv&#39;vc" expl="VC for mpinv" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3190"/></proof>
 </goal>
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3202"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3196"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3196"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3200"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3200"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3198"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3202"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="7138"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="7138"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3198"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3196"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3194"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3194"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.11" steps="51460"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.11" steps="51369"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.09" steps="51324"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3192"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3202"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3206"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3204"/></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="0.04" 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="0.02" steps="3236"/></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="0.02" steps="3236"/></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="0.02" steps="3236"/></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="0.02" steps="3236"/></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="0.02" steps="3236"/></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="4"><result status="valid" time="0.10" steps="65"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="m&#39;vc.0.1" expl="postcondition" proved="true">
   <proof prover="12" timelimit="5"><result status="valid" time="0.08" steps="460"/></proof>
   </goal>
   <goal name="m&#39;vc.0.2" expl="postcondition" proved="true">
   <proof prover="12" timelimit="5"><result status="valid" time="0.12" steps="1033"/></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="0.01" steps="7648"/></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="0.06" 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="0.19" steps="1094"/></proof>
 </goal>
 <goal name="m_eq&#39;vc" expl="VC for m_eq" proved="true">
 <proof prover="0"><result status="valid" time="0.29" steps="60221"/></proof>
 </goal>
 <goal name="m_ctx&#39;vc" expl="VC for m_ctx" proved="true">
 <proof prover="4"><result status="valid" time="0.11" steps="655"/></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="0.03" steps="55006"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="55008"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.17" steps="194514"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="197647"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="9978"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="9978"/></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="0.10" steps="168"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="169"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="168"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="169"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="168"/></proof>
  </goal>
  <goal name="expr_bound&#39;&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.10" 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="2"><result status="valid" time="1.08" steps="1302808"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="19"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="43"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="1.06" steps="1302211"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="20"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="44"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="1.09" steps="1302819"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.7" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="19"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.8" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.11" 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="0.07" steps="182"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.10" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="20"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.11" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" 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="0.07" steps="379"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.13" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="19"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.14" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" 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="0.07" steps="176"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.16" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="19"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.17" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.05" steps="59"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.06" steps="357"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="eq_bound_w&#39;" proved="true">
 <proof prover="4"><result status="valid" time="0.09" 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="0.08" steps="53"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="44"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="165587"/></proof>
  </goal>
  <goal name="ctx_bound_w&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.06" 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="0.10" steps="179"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="164961"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.07" steps="381"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="44"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="1.18" steps="1307085"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.13" steps="164962"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="181"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="165171"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="1.09" steps="1307118"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.9" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.15" steps="42"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="174"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.11" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="42"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="144"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" 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="0.14" steps="167035"/></proof>
  </goal>
  <goal name="max_var_e&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.13" steps="167447"/></proof>
  </goal>
  <goal name="max_var_e&#39;&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="182322"/></proof>
  </goal>
  <goal name="max_var_e&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" 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="0.16" steps="190674"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="43"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.18" steps="171302"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="1.40" steps="1336084"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" 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="0.22" steps="191969"/></proof>
  </goal>
  <goal name="interp_ctx_valid&#39;&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.14" steps="183684"/></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="0.12" steps="50"/></proof>
  </goal>
  <goal name="interp_ctx_wr&#39;&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.07" 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="0.25" steps="192493"/></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="0.10" steps="490"/></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="0.16" steps="190997"/></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="0.23" steps="201362"/></proof>
  </goal>
  <goal name="holds_interp_ctx&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="55"/></proof>
  </goal>
  <goal name="holds_interp_ctx&#39;&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="140"/></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="0.13" steps="204676"/></proof>
  </goal>
  <goal name="interp_holds&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.06" steps="147"/></proof>
  </goal>
  <goal name="interp_holds&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="46"/></proof>
  </goal>
  <goal name="interp_holds&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="76"/></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="0.07" steps="71"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="22"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.09" steps="202411"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.05" steps="66"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="179336"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="179387"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" 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="0.02" steps="176750"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="176772"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="10288"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="176818"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10290"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="10296"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="182841"/></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="0.19" steps="203238"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.22" steps="183579"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="188533"/></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="0.06" 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="0.06" steps="53"/></proof>
  </goal>
  <goal name="impl_wl&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.05" steps="62"/></proof>
  </goal>
  <goal name="impl_wl&#39;&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="135"/></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="0.16" steps="196919"/></proof>
  </goal>
  <goal name="impl_self&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.14" steps="176917"/></proof>
  </goal>
  <goal name="impl_self&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" 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="4"><result status="valid" time="0.04" steps="19"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.04" steps="21"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.2" expl="array creation size" proved="true">
  <proof prover="4"><result status="valid" time="0.14" steps="26"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="211"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.15" steps="222"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="7"><result status="valid" time="0.10" steps="456"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="8" timelimit="1"><result status="valid" time="0.96" steps="295793"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.22" steps="871"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.23" steps="1713"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.9" expl="assertion" proved="true">
  <proof prover="7"><result status="valid" time="0.10" steps="414"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.10" expl="index in array bounds" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.11" steps="243"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.13" steps="531"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.19" steps="1389"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.13" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.31" steps="73275"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="245"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="1.37" steps="2770"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.14" steps="165"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.17" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.33" steps="73271"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.18" expl="index in array bounds" proved="true">
  <proof prover="8"><result status="valid" time="0.32" steps="76735"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.28" steps="1699"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.04" steps="238"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="191970"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.22" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="70"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.23" expl="precondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="prop_ctx&#39;vc.23.0" expl="precondition" proved="true">
   <proof prover="2"><result status="valid" time="0.08" steps="191987"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="prop_ctx&#39;vc.24" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="60"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.25" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.05" steps="102"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.26" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="198124"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.27" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="198959"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.28" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="203118"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.29" expl="array creation size" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="27"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="36"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10712"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10712"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.33" expl="variant decrease" proved="true">
  <proof prover="4" memlimit="2000"><result status="valid" time="0.10" steps="83"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.34" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="195835"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.35" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="196547"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.36" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="46"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.37" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.27" steps="74656"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="214442"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.39" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.40" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.09" steps="10712"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="104054"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.42" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.43" steps="471"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.43" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.44" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10712"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.45" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10712"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.46" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.72" steps="124009"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.47" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="36"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.48" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.14" steps="195646"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.49" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.30" steps="74610"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.50" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="39"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.51" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.11" steps="271341"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="108548"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.53" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.28" steps="75375"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.54" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="45"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.55" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10712"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.56" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="10712"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.57" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.78" steps="124166"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.58" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="36"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.59" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="195645"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.60" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.31" steps="74622"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.61" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="107153"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.62" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="1.53" steps="1059"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.63" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="42"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.64" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.28" steps="75383"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.65" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="prop_ctx&#39;vc.65.0" expl="postcondition" proved="true">
   <transf name="unfold" proved="true" arg1="numof">
    <goal name="prop_ctx&#39;vc.65.0.0" expl="postcondition" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="prop_ctx&#39;vc.65.0.0.0" expl="postcondition" proved="true">
     <proof prover="0" timelimit="15" memlimit="2000"><result status="valid" time="0.31" steps="75791"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="prop_ctx&#39;vc.66" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="10712"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.67" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.68" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.13" steps="253"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.69" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="195094"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.70" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="195636"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.71" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.13" steps="39"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.72" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.30" steps="74208"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.73" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="41"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.74" expl="exceptional postcondition" proved="true">
  <proof prover="7"><result status="valid" time="0.08" steps="32"/></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="0.04" 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="0.07" 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="0.07" 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="0.14" steps="752"/></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="2.34" steps="16250"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.5" expl="VC for prop_ctx" proved="true">
   <proof prover="12"><result status="valid" time="0.14" 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="0.43" steps="94282"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.7" expl="VC for prop_ctx" proved="true">
   <proof prover="8"><result status="valid" time="1.14" steps="202936"/></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="0.42" steps="94185"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.9" expl="VC for prop_ctx" proved="true">
   <proof prover="12"><result status="valid" time="0.05" steps="82"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="prop_ctx&#39;vc.76" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.14" steps="201383"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.77" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="195160"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.78" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.08" steps="283"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.79" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="96"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.80" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="195842"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.81" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.09" steps="196364"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.82" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="211240"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.83" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="prop_ctx&#39;vc.83.0" expl="postcondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="prop_ctx&#39;vc.83.0.0" expl="postcondition" proved="true">
    <transf name="split_all_full" proved="true" >
     <goal name="prop_ctx&#39;vc.83.0.0.0" expl="postcondition" proved="true">
     <transf name="split_vc" proved="true" >
      <goal name="prop_ctx&#39;vc.83.0.0.0.0" expl="postcondition" proved="true">
      <proof prover="8" memlimit="2000"><result status="valid" time="3.40" steps="522208"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="prop_ctx&#39;vc.84" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.24" steps="1213"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.85" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.24" steps="1386"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.86" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.87" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.88" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.08" 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="0.09" steps="33"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.90" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="34"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.91" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="11158"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.92" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="100979"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.93" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.94" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="34"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.95" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.96" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.30" steps="72668"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.97" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.98" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.15" steps="195"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.99" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="195"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.100" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.30" steps="72411"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.101" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.102" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.103" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="195"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.104" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="195"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.105" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.30" steps="72419"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.106" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.107" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.108" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="191"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.109" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="76"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.110" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.111" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.112" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.113" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="97"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.114" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="96"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.115" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.116" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="213287"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.117" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.13" steps="200053"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.118" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="158"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.119" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.32" steps="72240"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.120" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="10674"/></proof>
  <proof prover="4"><result status="valid" time="0.10" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.121" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="74"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.122" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="74"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.123" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.06" steps="129"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.124" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="167"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.125" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.126" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.127" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="34"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.128" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.17" steps="214170"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.129" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="104430"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.130" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.14" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.131" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="256"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.132" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.24" steps="66943"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.133" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="69"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.134" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="37"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.135" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.12" steps="1314"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.136" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="38"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.137" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.31" steps="73525"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.138" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.139" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.14" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.140" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="256"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.141" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.20" steps="64449"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.142" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.13" steps="69"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.143" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="37"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.144" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.13" steps="1355"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.145" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="38"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.146" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="194"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.147" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.148" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.149" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="1.43" steps="1650377"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.150" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.22" steps="64457"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.151" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.11" steps="69"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.152" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="273"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.153" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.22" steps="67021"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.154" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.14" steps="71"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.155" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="39"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.156" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.30" steps="77404"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.157" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="40"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.158" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="205"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.159" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.160" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.161" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="1.44" steps="1650390"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.162" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.22" steps="64457"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.163" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="69"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.164" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="273"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.165" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.25" steps="67021"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.166" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="71"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.167" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.22" steps="67695"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.168" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="147"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.169" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.22" steps="207847"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.170" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="205"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.171" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.172" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.173" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.174" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="210572"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.175" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="205832"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.176" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.28" steps="72527"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.177" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.178" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="197166"/></proof>
  <proof prover="4"><result status="valid" time="0.14" steps="34"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.179" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.23" steps="197329"/></proof>
  <proof prover="4"><result status="valid" time="0.09" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.180" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="205235"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.181" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.14" steps="205407"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.182" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="206894"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.183" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="274"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.184" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.25" steps="207485"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.185" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="213479"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.186" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.187" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.10" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.188" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.20" steps="196048"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.189" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.09" steps="36"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.190" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.12" steps="37"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.191" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05" steps="38"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.192" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.24" steps="227011"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.193" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="74"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.194" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="200753"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.195" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.17" steps="238097"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.196" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.21" steps="67817"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.197" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.28" steps="73271"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.198" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.21" steps="209002"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.199" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.24" steps="68550"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.200" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.36" steps="79255"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.201" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.31" steps="75102"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.202" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.14" steps="212282"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.203" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.32" steps="75334"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.204" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.205" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10674"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.206" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="204572"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.207" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="192066"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.208" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="74"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.209" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.210" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.14" steps="35"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.211" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="106173"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.212" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.06" steps="53"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.213" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.13" steps="136"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.214" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.07" steps="17"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.215" expl="exceptional postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.15" 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="0.08" 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="0.06" steps="181332"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="181359"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="97858"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="97877"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.22" steps="193155"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.26" steps="204723"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10478"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="10478"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10478"/></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="0.08" steps="516"/></proof>
   </goal>
   <goal name="g.0.1" proved="true">
   <proof prover="4"><result status="valid" time="0.04" steps="42"/></proof>
   </goal>
   <goal name="g.0.2" proved="true">
   <proof prover="2"><result status="valid" time="0.24" steps="192323"/></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="0.07" steps="491"/></proof>
   </goal>
   <goal name="g&#39;.0.1" proved="true">
   <proof prover="2"><result status="valid" time="0.16" steps="188851"/></proof>
   </goal>
   <goal name="g&#39;.0.2" proved="true">
   <proof prover="4"><result status="valid" time="0.08" steps="44"/></proof>
   </goal>
   <goal name="g&#39;.0.3" proved="true">
   <proof prover="2"><result status="valid" time="0.15" steps="192437"/></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="0.08" steps="47"/></proof>
    </goal>
    <goal name="g&#39;.0.0.1" proved="true">
    <proof prover="2"><result status="valid" time="0.15" steps="192115"/></proof>
    </goal>
    <goal name="g&#39;.0.0.2" proved="true">
    <proof prover="2"><result status="valid" time="0.15" steps="192114"/></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="0.04" 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="0.05" steps="49"/></proof>
     </goal>
     <goal name="g&#39;&#39;.0.1.0.1" proved="true">
     <proof prover="2"><result status="valid" time="0.25" steps="193373"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="g&#39;&#39;.0.1.1" expl="equality hypothesis" proved="true">
    <proof prover="2"><result status="valid" time="0.02" steps="10506"/></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="0.02" steps="80"/></proof>
 </goal>
</theory>
</file>
</why3session>
