<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.5.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Eprover" version="1.9.1-001" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="4" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="6" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="7" name="Alt-Ergo" version="2.3.3" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="8" name="CVC4" version="1.7" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="9" name="Alt-Ergo" version="2.4.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="10" name="Eprover" version="2.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="11" name="Spass" version="3.7" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="12" name="Alt-Ergo" version="2.4.1" 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="2760"/></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="11650"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10690"/></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="11690"/></proof>
  </goal>
  <goal name="expr_bound_w&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10720"/></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="12715"/></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="11643"/></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="36481"/></proof>
  </goal>
  <goal name="apply_r&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="37404"/></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="2628"/></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="36484"/></proof>
  </goal>
  <goal name="apply_l&#39;vc.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="37389"/></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="2628"/></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="29220"/></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="2676"/></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="14594"/></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="31238"/></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="32707"/></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="43057"/></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="28778"/></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="35475"/></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="2676"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="29395"/></proof>
  </goal>
  <goal name="infix ==&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3434"/></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="36029"/></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="35269"/></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="36086"/></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="34906"/></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="59602"/></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="43791"/></proof>
  </goal>
  <goal name="opp_expr&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="47582"/></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="36677"/></proof>
   </goal>
   <goal name="opp_expr&#39;vc.12.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="36630"/></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="36136"/></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="3070"/></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="43982"/></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="47994"/></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="3070"/></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="3070"/></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="3086"/></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="38913"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="37533"/></proof>
  </goal>
  <goal name="interp_ctx_impl&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="78695"/></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="35519"/></proof>
  </goal>
  <goal name="interp_ctx_valid&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="38753"/></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="3326"/></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="3326"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="46"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.9" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="49"/></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="61"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3326"/></proof>
  </goal>
  <goal name="mul_expr&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></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="3326"/></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="23721"/></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="86222"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="34336"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.7" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="61"/></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="55"/></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="90005"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="19721"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.11" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="61"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.52" steps="468"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></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="3326"/></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="23748"/></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="86329"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="34321"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.20" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="58"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.18" steps="242"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.22" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="90111"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.23" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="19720"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.24" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="58"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.25" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.36" steps="452"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.26" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.27" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.28" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="35768"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.29" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="34337"/></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="39330"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.33" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="19722"/></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="3326"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.37" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.38" expl="unreachable point" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="35331"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.39" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="85732"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.40" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="89467"/></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="3326"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.44" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="85135"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.45" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="38842"/></proof>
  </goal>
  <goal name="add_expr&#39;vc.46" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></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="45571"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="184389"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="42456"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="40335"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3326"/></proof>
  </goal>
  <goal name="add_eq&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></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="85732"/></proof>
  </goal>
  <goal name="zero_expr&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="89449"/></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="3326"/></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="3326"/></proof>
  </goal>
  <goal name="sub_expr&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3326"/></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="26690"/></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="3326"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></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="3326"/></proof>
  </goal>
  <goal name="same_eq&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3326"/></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="40513"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="47371"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="53250"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3476"/></proof>
  </goal>
  <goal name="norm_context&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3476"/></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="39"/></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="45751"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3476"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="35"/></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="60"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="74"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3476"/></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="35"/></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="60"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="74"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3476"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3476"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="3476"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3476"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="43500"/></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="3476"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="3476"/></proof>
  </goal>
  <goal name="check_combination&#39;vc.22" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3476"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="transpose&#39;vc" expl="VC for transpose" proved="true">
 <proof prover="2"><result status="valid" time="0.18" steps="183219"/></proof>
 </goal>
 <goal name="swap_rows&#39;vc" expl="VC for swap_rows" proved="true">
 <proof prover="2"><result status="valid" time="0.33" steps="459581"/></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="293"/></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="541"/></proof>
 </goal>
 <goal name="gauss_jordan&#39;vc" expl="VC for gauss_jordan" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="gauss_jordan&#39;vc.0" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.17" steps="179766"/></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="25"/></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="37813"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.8" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="46083"/></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="45227"/></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="45489"/></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="45934"/></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="4540"/></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="48544"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.14" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="48895"/></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="54687"/></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="56053"/></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="56108"/></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="5290"/></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="57237"/></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="3486"/></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="63590"/></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="89468"/></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="709743"/></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="56723"/></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="652024"/></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="3486"/></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="63387"/></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="89053"/></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="59554"/></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="772441"/></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="558668"/></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="3486"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.46" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></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="62207"/></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="31444"/></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="34510"/></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="55692"/></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="64189"/></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="54160"/></proof>
  </goal>
  <goal name="gauss_jordan&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3486"/></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="46881"/></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="54954"/></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="55444"/></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="389607"/></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="52986"/></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="27872"/></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="5186"/></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="0.28" steps="323576"/></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="36491"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="36570"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3620"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.4" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="39958"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.5" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="38291"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.6" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="38506"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="42021"/></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="41680"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.9" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="47653"/></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="48949"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.11" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></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="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.16" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.40" steps="424550"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.17" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="47849"/></proof>
  <proof prover="4"><result status="valid" time="0.02" 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="0.28" steps="424557"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="47849"/></proof>
  <proof prover="4"><result status="valid" time="0.01" 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="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.23" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.24" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.25" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.26" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="52934"/></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="0.03" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.32" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" 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="3486"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.37" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="34"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.38" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" 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="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.44" expl="integer overflow" proved="true">
  <proof prover="1"><result status="valid" time="0.14" steps="33301"/></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="3486"/></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="0.02" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.53" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.02" 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="0.02" steps="3486"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.58" expl="integer overflow" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="32"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.59" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" 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="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.64" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></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="52233"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.70" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.71" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></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="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.76" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.31" steps="441354"/></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="0.40" steps="441360"/></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="3486"/></proof>
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.81" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  <proof prover="4"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.82" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.83" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.84" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="53432"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.85" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4578"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.86" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="48549"/></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="51609"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.89" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="53488"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.90" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="59108"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.91" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="62105"/></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="60967"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.93" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="65076"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.94" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="82704"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.95" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="67208"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="40"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.96" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.97" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></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="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.99" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.100" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.101" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="3486"/></proof>
  </goal>
  <goal name="linear_decision&#39;vc.102" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3486"/></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="192403"/></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="0.18" steps="320969"/></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="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="321923"/></proof>
  </goal>
  <goal name="simp&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.18" steps="326757"/></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="48870"/></proof>
  </goal>
  <goal name="simp&#39;vc.11" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.13" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.18" steps="321951"/></proof>
  </goal>
  <goal name="simp&#39;vc.14" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.18" steps="327001"/></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="49317"/></proof>
  </goal>
  <goal name="simp&#39;vc.17" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></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="4186"/></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="47650"/></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="47551"/></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="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.28" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.29" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></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="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.34" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></proof>
  </goal>
  <goal name="simp&#39;vc.35" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4186"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="simp_eq&#39;vc" expl="VC for simp_eq" proved="true">
 <proof prover="2"><result status="valid" time="0.35" steps="598508"/></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="27476"/></proof>
  </goal>
  <goal name="decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="27482"/></proof>
  </goal>
  <goal name="decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="59677"/></proof>
  </goal>
  <goal name="decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="61233"/></proof>
  </goal>
  <goal name="decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="4740"/></proof>
  </goal>
  <goal name="decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="4740"/></proof>
  </goal>
  <goal name="decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="4290"/></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="5799"/></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="766608"/></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="520"/></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="434"/></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="6193"/></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="10374"/></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="580"/></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="28664"/></proof>
  </goal>
  <goal name="gcd&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="1728"/></proof>
  </goal>
  <goal name="gcd&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="1728"/></proof>
  </goal>
  <goal name="gcd&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="28834"/></proof>
  </goal>
  <goal name="gcd&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="28834"/></proof>
  </goal>
  <goal name="gcd&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="30009"/></proof>
  </goal>
  <goal name="gcd&#39;vc.6" expl="loop variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="32015"/></proof>
  </goal>
  <goal name="gcd&#39;vc.7" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="31429"/></proof>
  </goal>
  <goal name="gcd&#39;vc.8" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="30712"/></proof>
  </goal>
  <goal name="gcd&#39;vc.9" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="30784"/></proof>
  </goal>
  <goal name="gcd&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="29720"/></proof>
  </goal>
  <goal name="gcd&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="28860"/></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="28919"/></proof>
  </goal>
  <goal name="simp&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="28507"/></proof>
  </goal>
  <goal name="simp&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="28507"/></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="28794"/></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="5083"/></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="11"><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="11"><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="11"><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="1728"/></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="31601"/></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="31557"/></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="31741"/></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="1804"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1798"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1798"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1802"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1802"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1800"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.00" steps="1804"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3891"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3891"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1800"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1798"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1796"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1796"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.04" steps="29520"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="29457"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="29395"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1794"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1804"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="1808"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="1808"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="29717"/></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="1822"/></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="1850"/></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="1850"/></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="1850"/></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="1850"/></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="15117"/></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="32"/></proof>
 </goal>
 <goal name="imul&#39;vc" expl="VC for imul" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="32"/></proof>
 </goal>
 <goal name="iopp&#39;vc" expl="VC for iopp" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="32"/></proof>
 </goal>
 <goal name="iinv&#39;vc" expl="VC for iinv" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="32"/></proof>
 </goal>
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="44"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="38"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="38"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="42"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="42"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="40"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="44"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="132"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="132"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="40"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="38"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="36"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="36"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="658"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="622"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="585"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="34"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="44"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="48"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="48"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="593"/></proof>
 </goal>
 <goal name="C.one_def" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="709"/></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="80"/></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="80"/></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="80"/></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="80"/></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="80"/></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="7990"/></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="45802"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="45804"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="160909"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.12" steps="162620"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="8224"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="8224"/></proof>
  </goal>
  <goal name="int_decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="7470"/></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="110419"/></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="148032"/></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="20484"/></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="45478"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.04" steps="411"/></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="45679"/></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="2770"/></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="45496"/></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="45691"/></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="2770"/></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="2770"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.10" steps="21841"/></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="2770"/></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="45476"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.04" steps="402"/></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="45494"/></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="45689"/></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="2770"/></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="2770"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.09" steps="21998"/></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="21473"/></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="45707"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.36" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.04" steps="391"/></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="2770"/></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="45725"/></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="45960"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.44" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.12" steps="28181"/></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="2770"/></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="46098"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="137"/></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="2770"/></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="45899"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.56" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.05" steps="518"/></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="46113"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.58" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.11" steps="28571"/></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="2770"/></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="2770"/></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="45589"/></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="45797"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.65" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.08" steps="20363"/></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="2770"/></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="45610"/></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="45812"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.71" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.12" steps="28022"/></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="2770"/></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="2770"/></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="45226"/></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="47105"/></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="2770"/></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="47194"/></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="2770"/></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="2770"/></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="45251"/></proof>
  </goal>
  <goal name="add_sub_exp&#39;vc.85" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.09" steps="19648"/></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="47050"/></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="2770"/></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="2770"/></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="2770"/></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="2770"/></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="2770"/></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="45197"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="45226"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="45136"/></proof>
  </goal>
  <goal name="zero_exp&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="45251"/></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="2770"/></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="45353"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="2770"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="2770"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="43589"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="45353"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2770"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2770"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="46653"/></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="2770"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="45353"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2770"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="2770"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="95"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.15" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="2770"/></proof>
  </goal>
  <goal name="same_exp&#39;vc.16" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="2770"/></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="47817"/></proof>
  </goal>
  <goal name="madd&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="48813"/></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="11"><result status="valid" time="0.05"/></proof>
   </goal>
   <goal name="madd&#39;vc.2.1" expl="assertion" proved="true">
   <proof prover="11"><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="15531"/></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="166"/></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="17128"/></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="2770"/></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="11"><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="165"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.2" expl="VC for mmul" proved="true">
   <proof prover="11"><result status="valid" time="0.05"/></proof>
   </goal>
   <goal name="mmul&#39;vc.1.3" expl="VC for mmul" proved="true">
   <proof prover="11"><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="17135"/></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="2770"/></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="24910"/></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="51876"/></proof>
  </goal>
  <goal name="minv&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="52763"/></proof>
  </goal>
  <goal name="minv&#39;vc.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="3124"/></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="3136"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3130"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3130"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3134"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3134"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3132"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3136"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="6961"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="6961"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3132"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3130"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3128"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3128"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.10" steps="50287"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.10" steps="50224"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.09" steps="50162"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3126"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3136"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3140"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3140"/></proof>
 </goal>
 <goal name="C.zero_def" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="53164"/></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="3198"/></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="3198"/></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="3198"/></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="3198"/></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="3198"/></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="3262"/></proof>
 </goal>
 <goal name="mpmul&#39;vc" expl="VC for mpmul" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3262"/></proof>
 </goal>
 <goal name="mpopp&#39;vc" expl="VC for mpopp" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3262"/></proof>
 </goal>
 <goal name="mpeq&#39;vc" expl="VC for mpeq" proved="true">
 <proof prover="2"><result status="valid" time="0.06" steps="3262"/></proof>
 </goal>
 <goal name="mpinv&#39;vc" expl="VC for mpinv" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3262"/></proof>
 </goal>
 <goal name="C.A.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3274"/></proof>
 </goal>
 <goal name="C.A.Unit_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3268"/></proof>
 </goal>
 <goal name="C.A.Unit_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3268"/></proof>
 </goal>
 <goal name="C.A.Inv_def_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3272"/></proof>
 </goal>
 <goal name="C.A.Inv_def_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3272"/></proof>
 </goal>
 <goal name="C.A.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3270"/></proof>
 </goal>
 <goal name="C.A.MulAssoc.Assoc" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3274"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_l" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="7314"/></proof>
 </goal>
 <goal name="C.A.Mul_distr_r" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="7314"/></proof>
 </goal>
 <goal name="C.A.MulComm.Comm" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3270"/></proof>
 </goal>
 <goal name="C.A.Unitary" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3268"/></proof>
 </goal>
 <goal name="C.A.NonTrivialRing" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3266"/></proof>
 </goal>
 <goal name="C.A.Refl" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3266"/></proof>
 </goal>
 <goal name="C.A.Trans" proved="true">
 <proof prover="2"><result status="valid" time="0.11" steps="52303"/></proof>
 </goal>
 <goal name="C.A.Antisymm" proved="true">
 <proof prover="2"><result status="valid" time="0.11" steps="52212"/></proof>
 </goal>
 <goal name="C.A.Total" proved="true">
 <proof prover="2"><result status="valid" time="0.09" steps="52167"/></proof>
 </goal>
 <goal name="C.A.ZeroLessOne" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3264"/></proof>
 </goal>
 <goal name="C.A.CompatOrderAdd" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="3274"/></proof>
 </goal>
 <goal name="C.A.CompatOrderMult" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3278"/></proof>
 </goal>
 <goal name="C.sub_def" proved="true">
 <proof prover="2"><result status="valid" time="0.01" steps="3276"/></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="3308"/></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="3308"/></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="3308"/></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="3308"/></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="3308"/></proof>
 </goal>
 <goal name="m&#39;vc" expl="VC for m" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="m&#39;vc.0" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="m&#39;vc.0.0" expl="postcondition" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="m&#39;vc.0.0.0" expl="postcondition" proved="true">
    <transf name="compute_in_goal" proved="true" >
     <goal name="m&#39;vc.0.0.0.0" expl="postcondition" proved="true">
     <proof prover="4"><result status="valid" time="0.08" steps="65"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="m&#39;vc.1" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="m&#39;vc.1.0" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.06" steps="514"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="m&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.08" steps="104"/></proof>
  </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="9630"/></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="56004"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="56006"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.17" steps="196901"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="200194"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10152"/></proof>
  </goal>
  <goal name="mp_decision&#39;vc.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10152"/></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="2.78" steps="2816548"/></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="2.82" steps="2819288"/></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="2.92" steps="2816566"/></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="381"/></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="361"/></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="167580"/></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="222"/></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="166980"/></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="386"/></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="3.20" steps="2820085"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.13" steps="166981"/></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="167190"/></proof>
  </goal>
  <goal name="max_var&#39;&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="2.87" steps="2817054"/></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="169054"/></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="169466"/></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="187010"/></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="195496"/></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="173321"/></proof>
  </goal>
  <goal name="max_var_ctx&#39;&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="2.58" steps="2869124"/></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="196791"/></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="185871"/></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="301"/></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="197314"/></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="193647"/></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="207067"/></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="59"/></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="210566"/></proof>
  </goal>
  <goal name="interp_holds&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.06" steps="149"/></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="207273"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.3" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.05" steps="67"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="181329"/></proof>
  </goal>
  <goal name="impl_holds&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="181380"/></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="178743"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="178765"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="10462"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="178811"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10464"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="10470"/></proof>
  </goal>
  <goal name="ctx_impl&#39;&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="185020"/></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="207987"/></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="185598"/></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="190712"/></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="63"/></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="201742"/></proof>
  </goal>
  <goal name="impl_self&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.14" steps="178936"/></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="0.18" 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="1.20" steps="178877"/></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="1717"/></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="1390"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.13" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.31" steps="75582"/></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="75578"/></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="79794"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.28" steps="1695"/></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="194899"/></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="194902"/></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="201071"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.27" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="202092"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.28" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="206574"/></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="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10886"/></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="197828"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.35" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="198552"/></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="75820"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="216461"/></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="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="105356"/></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="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.45" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.46" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.72" steps="131498"/></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="197639"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.49" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.30" steps="75774"/></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="279126"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="109850"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.53" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.28" steps="76539"/></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="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.56" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.57" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.78" steps="131634"/></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="197638"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.60" expl="variant decrease" proved="true">
  <proof prover="8"><result status="valid" time="0.31" steps="75786"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.61" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="108455"/></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="76547"/></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="10886"/></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="197087"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.70" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="197629"/></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="75372"/></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="207"/></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="231"/></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="749"/></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="1.90" steps="16251"/></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="737"/></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="97912"/></proof>
   </goal>
   <goal name="prop_ctx&#39;vc.75.7" expl="VC for prop_ctx" proved="true">
   <proof prover="8"><result status="valid" time="1.09" steps="213236"/></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="97813"/></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="203403"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.77" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="197153"/></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="197835"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.81" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.09" steps="198357"/></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="213257"/></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="3.99" steps="574051"/></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="1208"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.85" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.24" steps="1391"/></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="10886"/></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="11420"/></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="103069"/></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="74260"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.97" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10886"/></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="74003"/></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="74011"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.106" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.107" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10886"/></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="10886"/></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="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.116" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="217266"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.117" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.13" steps="203393"/></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="73832"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.120" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="10886"/></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="10886"/></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="218149"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.129" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="106529"/></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="68276"/></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="1313"/></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="75117"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.138" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10886"/></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="65782"/></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="1354"/></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="10886"/></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="5.72" steps="3465368"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.150" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.22" steps="65790"/></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="68354"/></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="79756"/></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="10886"/></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="6.00" steps="3465395"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.162" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.22" steps="65790"/></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="68354"/></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="69028"/></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="211204"/></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="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.172" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10886"/></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="214096"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.175" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="209189"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.176" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.28" steps="74119"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.177" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.178" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="200523"/></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="200686"/></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="208592"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.181" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.14" steps="208764"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.182" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="210251"/></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="210842"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.185" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.15" steps="217022"/></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="199388"/></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="230867"/></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="204110"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.195" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.17" steps="244633"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.196" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.21" steps="69150"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.197" expl="precondition" proved="true">
  <proof prover="8"><result status="valid" time="0.28" steps="74863"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.198" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.21" steps="212359"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.199" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.24" steps="69883"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.200" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.36" steps="81740"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.201" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.31" steps="76694"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.202" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.27" steps="215639"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.203" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.32" steps="76926"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.204" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.205" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01" steps="10886"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.206" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="208420"/></proof>
  </goal>
  <goal name="prop_ctx&#39;vc.207" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="195391"/></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="108272"/></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="187673"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.08" steps="187700"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="101376"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.07" steps="101395"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.22" steps="199534"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.26" steps="211716"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="10886"/></proof>
  </goal>
  <goal name="prop_mp_decision&#39;vc.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="10886"/></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="10886"/></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="198705"/></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="195211"/></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="198819"/></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="198497"/></proof>
    </goal>
    <goal name="g&#39;.0.0.2" proved="true">
    <proof prover="2"><result status="valid" time="0.15" steps="198496"/></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="199755"/></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="10914"/></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>
