<?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="Alt-Ergo" version="2.2.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="5" name="CVC4" version="1.7" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="7" name="CVC4" version="1.8" alternative="strings" timelimit="5" steplimit="0" memlimit="2000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="stringlemmas.mlw"/>
<theory name="String_lemmas" proved="true">
 <goal name="in_base_concat&#39;vc" expl="VC for in_base_concat" proved="true">
 <proof prover="3"><result status="valid" time="0.06" steps="22701"/></proof>
 </goal>
 <goal name="svalue_le_sub&#39;vc" expl="VC for svalue_le_sub" proved="true">
 <proof prover="3"><result status="valid" time="0.04" steps="19434"/></proof>
 </goal>
 <goal name="svalue_le_sub_tail&#39;vc" expl="VC for svalue_le_sub_tail" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_le_sub_tail&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="18101"/></proof>
  </goal>
  <goal name="svalue_le_sub_tail&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="18070"/></proof>
  </goal>
  <goal name="svalue_le_sub_tail&#39;vc.2" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="svalue_le_sub_tail&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07" steps="18098"/></proof>
  </goal>
  <goal name="svalue_le_sub_tail&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.13"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_le_sub_concat&#39;vc" expl="VC for svalue_le_sub_concat" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_le_sub_concat&#39;vc.0" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.09" steps="18377"/></proof>
  </goal>
  <goal name="svalue_le_sub_concat&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.07" steps="18428"/></proof>
  </goal>
  <goal name="svalue_le_sub_concat&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="18404"/></proof>
  </goal>
  <goal name="svalue_le_sub_concat&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.18" steps="24158"/></proof>
  </goal>
  <goal name="svalue_le_sub_concat&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.05"/></proof>
  </goal>
  <goal name="svalue_le_sub_concat&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.26"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_le_sub_head&#39;vc" expl="VC for svalue_le_sub_head" proved="true">
 <proof prover="3"><result status="valid" time="0.20" steps="24437"/></proof>
 </goal>
 <goal name="svalue_le_sub_frame&#39;vc" expl="VC for svalue_le_sub_frame" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_le_sub_frame&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.07" steps="20339"/></proof>
  </goal>
  <goal name="svalue_le_sub_frame&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.10" steps="24165"/></proof>
  </goal>
  <goal name="svalue_le_sub_frame&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.26" steps="141"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_le_tail&#39;vc" expl="VC for svalue_le_tail" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_le_tail&#39;vc.0" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="19389"/></proof>
  </goal>
  <goal name="svalue_le_tail&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="20252"/></proof>
  </goal>
  <goal name="svalue_le_tail&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="19134"/></proof>
  </goal>
  <goal name="svalue_le_tail&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.17" steps="26103"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_le_concat&#39;vc" expl="VC for svalue_le_concat" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_le_concat&#39;vc.0" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="19510"/></proof>
  </goal>
  <goal name="svalue_le_concat&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="20362"/></proof>
  </goal>
  <goal name="svalue_le_concat&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="19258"/></proof>
  </goal>
  <goal name="svalue_le_concat&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.21" steps="25470"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_sub&#39;vc" expl="VC for svalue_sub" proved="true">
 <proof prover="3"><result status="valid" time="0.06" steps="21114"/></proof>
 </goal>
 <goal name="svalue_sub_tail&#39;vc" expl="VC for svalue_sub_tail" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_sub_tail&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.07"/></proof>
  </goal>
  <goal name="svalue_sub_tail&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.10" steps="19663"/></proof>
  </goal>
  <goal name="svalue_sub_tail&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.20" steps="26368"/></proof>
  </goal>
  <goal name="svalue_sub_tail&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="19691"/></proof>
  </goal>
  <goal name="svalue_sub_tail&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.24"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_sub_concat&#39;vc" expl="VC for svalue_sub_concat" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_sub_concat&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="20006"/></proof>
  </goal>
  <goal name="svalue_sub_concat&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="19990"/></proof>
  </goal>
  <goal name="svalue_sub_concat&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.11" steps="26719"/></proof>
  </goal>
  <goal name="svalue_sub_concat&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.09" steps="20018"/></proof>
  </goal>
  <goal name="svalue_sub_concat&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.34"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_sub_head&#39;vc" expl="VC for svalue_sub_head" proved="true">
 <proof prover="3"><result status="valid" time="0.20" steps="26446"/></proof>
 </goal>
 <goal name="svalue_sub_frame&#39;vc" expl="VC for svalue_sub_frame" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_sub_frame&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.12" steps="22042"/></proof>
  </goal>
  <goal name="svalue_sub_frame&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.12" steps="107"/></proof>
  </goal>
  <goal name="svalue_sub_frame&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.19" steps="141"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_le_sub_lower_bound&#39;vc" expl="VC for svalue_le_sub_lower_bound" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_le_sub_lower_bound&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.09" steps="22160"/></proof>
  </goal>
  <goal name="svalue_le_sub_lower_bound&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="20546"/></proof>
  </goal>
  <goal name="svalue_le_sub_lower_bound&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="136"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_sub_lower_bound&#39;vc" expl="VC for svalue_sub_lower_bound" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_sub_lower_bound&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="22257"/></proof>
  </goal>
  <goal name="svalue_sub_lower_bound&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="31"/></proof>
  </goal>
  <goal name="svalue_sub_lower_bound&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.16" steps="137"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_le_sub_upper_bound&#39;vc" expl="VC for svalue_le_sub_upper_bound" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_le_sub_upper_bound&#39;vc.0" expl="precondition" proved="true">
  <proof prover="1" memlimit="2000"><result status="valid" time="0.02" steps="72001"/></proof>
  </goal>
  <goal name="svalue_le_sub_upper_bound&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3" timelimit="5" memlimit="2000"><result status="valid" time="0.12" steps="21578"/></proof>
  </goal>
  <goal name="svalue_le_sub_upper_bound&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="20838"/></proof>
  </goal>
  <goal name="svalue_le_sub_upper_bound&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.09" steps="20924"/></proof>
  </goal>
  <goal name="svalue_le_sub_upper_bound&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="20901"/></proof>
  </goal>
  <goal name="svalue_le_sub_upper_bound&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="22636"/></proof>
  </goal>
  <goal name="svalue_le_sub_upper_bound&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.23" steps="31406"/></proof>
  </goal>
  <goal name="svalue_le_sub_upper_bound&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1" memlimit="2000"><result status="valid" time="0.06" steps="82506"/></proof>
  </goal>
  <goal name="svalue_le_sub_upper_bound&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.23" steps="52894"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="svalue_sub_upper_bound&#39;vc" expl="VC for svalue_sub_upper_bound" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="svalue_sub_upper_bound&#39;vc.0" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.12" steps="22654"/></proof>
  </goal>
  <goal name="svalue_sub_upper_bound&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.10" steps="21786"/></proof>
  </goal>
  <goal name="svalue_sub_upper_bound&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="21046"/></proof>
  </goal>
  <goal name="svalue_sub_upper_bound&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="21136"/></proof>
  </goal>
  <goal name="svalue_sub_upper_bound&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.09" steps="21109"/></proof>
  </goal>
  <goal name="svalue_sub_upper_bound&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.17" steps="22850"/></proof>
  </goal>
  <goal name="svalue_sub_upper_bound&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.24" steps="31726"/></proof>
  </goal>
  <goal name="svalue_sub_upper_bound&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1" timelimit="1"><result status="valid" time="0.02" steps="83331"/></proof>
  </goal>
  <goal name="svalue_sub_upper_bound&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.18" steps="56098"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Conversions" proved="true">
 <goal name="lowconcat" proved="true">
 <proof prover="7"><result status="valid" time="0.08" steps="18542"/></proof>
 </goal>
 <goal name="upconcat" proved="true">
 <proof prover="7"><result status="valid" time="0.09" steps="18561"/></proof>
 </goal>
 <goal name="digitsublow" proved="true">
 <proof prover="7"><result status="valid" time="0.10" steps="18582"/></proof>
 </goal>
 <goal name="digitsubup" proved="true">
 <proof prover="7"><result status="valid" time="0.10" steps="18603"/></proof>
 </goal>
 <goal name="lowsub" proved="true">
 <proof prover="7"><result status="valid" time="0.10" steps="18624"/></proof>
 </goal>
 <goal name="upsub" proved="true">
 <proof prover="7"><result status="valid" time="0.10" steps="18645"/></proof>
 </goal>
 <goal name="lowupconcat" proved="true">
 <proof prover="7"><result status="valid" time="0.10" steps="18664"/></proof>
 </goal>
 <goal name="digitsublowup" proved="true">
 <proof prover="2"><result status="valid" time="0.11" steps="337"/></proof>
 </goal>
 <goal name="upsublowup" proved="true">
 <proof prover="7"><result status="valid" time="0.10" steps="18706"/></proof>
 </goal>
 <goal name="lowsublowup" proved="true">
 <proof prover="7"><result status="valid" time="0.08" steps="18728"/></proof>
 </goal>
 <goal name="digits&#39;vc" expl="VC for digits" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="digits&#39;vc.0" expl="assertion" proved="true">
  <proof prover="7"><result status="valid" time="0.08" steps="18751"/></proof>
  </goal>
  <goal name="digits&#39;vc.1" expl="assertion" proved="true">
  <transf name="rewrite" proved="true" arg1="Assert">
   <goal name="digits&#39;vc.1.0" expl="assertion" proved="true">
   <transf name="rewrite" proved="true" arg1="substring_get">
    <goal name="digits&#39;vc.1.0.0" expl="assertion" proved="true">
    <proof prover="2"><result status="valid" time="0.04" steps="55"/></proof>
    <proof prover="5"><result status="valid" time="0.12" steps="18594"/></proof>
    </goal>
    <goal name="digits&#39;vc.1.0.1" expl="rewrite premises" proved="true">
    <proof prover="5"><result status="valid" time="0.23" steps="59946"/></proof>
    </goal>
    <goal name="digits&#39;vc.1.0.2" expl="rewrite premises" proved="true">
    <proof prover="2"><result status="valid" time="0.03" steps="55"/></proof>
    <proof prover="5"><result status="valid" time="0.11" steps="18573"/></proof>
    </goal>
    <goal name="digits&#39;vc.1.0.3" expl="rewrite premises" proved="true">
    <proof prover="5"><result status="valid" time="0.35" steps="59862"/></proof>
    </goal>
    <goal name="digits&#39;vc.1.0.4" expl="rewrite premises" proved="true">
    <proof prover="5"><result status="valid" time="0.12" steps="18589"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="digits&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.02" steps="59"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="lower&#39;vc" expl="VC for lower" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="lower&#39;vc.0" expl="assertion" proved="true">
  <proof prover="7"><result status="valid" time="0.10" steps="18791"/></proof>
  </goal>
  <goal name="lower&#39;vc.1" expl="assertion" proved="true">
  <transf name="rewrite" proved="true" arg1="Assert">
   <goal name="lower&#39;vc.1.0" expl="assertion" proved="true">
   <transf name="rewrite" proved="true" arg1="substring_get">
    <goal name="lower&#39;vc.1.0.0" expl="assertion" proved="true">
    <proof prover="5"><result status="valid" time="0.10" steps="18626"/></proof>
    </goal>
    <goal name="lower&#39;vc.1.0.1" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.10" steps="18820"/></proof>
    </goal>
    <goal name="lower&#39;vc.1.0.2" expl="rewrite premises" proved="true">
    <proof prover="5"><result status="valid" time="0.08" steps="18605"/></proof>
    </goal>
    <goal name="lower&#39;vc.1.0.3" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.09" steps="18813"/></proof>
    </goal>
    <goal name="lower&#39;vc.1.0.4" expl="rewrite premises" proved="true">
    <proof prover="2"><result status="valid" time="0.02" steps="57"/></proof>
    <proof prover="5"><result status="valid" time="0.10" steps="18621"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="lower&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.02" steps="61"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="upper&#39;vc" expl="VC for upper" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="upper&#39;vc.0" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="upper&#39;vc.0.0" expl="assertion" proved="true">
   <proof prover="7"><result status="valid" time="0.08" steps="18830"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="upper&#39;vc.1" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="upper&#39;vc.1.0" expl="assertion" proved="true">
   <transf name="rewrite" proved="true" arg1="Assert">
    <goal name="upper&#39;vc.1.0.0" expl="assertion" proved="true">
    <transf name="rewrite" proved="true" arg1="substring_get">
     <goal name="upper&#39;vc.1.0.0.0" expl="assertion" proved="true">
     <proof prover="2"><result status="valid" time="0.03" steps="59"/></proof>
     <proof prover="5"><result status="valid" time="0.09" steps="18627"/></proof>
     </goal>
     <goal name="upper&#39;vc.1.0.0.1" expl="rewrite premises" proved="true">
     <proof prover="7"><result status="valid" time="0.08" steps="18859"/></proof>
     </goal>
     <goal name="upper&#39;vc.1.0.0.2" expl="rewrite premises" proved="true">
     <proof prover="2"><result status="valid" time="0.02" steps="59"/></proof>
     <proof prover="5"><result status="valid" time="0.10" steps="18636"/></proof>
     </goal>
     <goal name="upper&#39;vc.1.0.0.3" expl="rewrite premises" proved="true">
     <proof prover="7"><result status="valid" time="0.10" steps="18852"/></proof>
     </goal>
     <goal name="upper&#39;vc.1.0.0.4" expl="rewrite premises" proved="true">
     <proof prover="5"><result status="valid" time="0.08" steps="18652"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="upper&#39;vc.1.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="59"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="upper&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="64"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="diglow" proved="true">
 <proof prover="5"><result status="valid" time="0.09" steps="18789"/></proof>
 </goal>
 <goal name="digup" proved="true">
 <proof prover="5"><result status="valid" time="0.09" steps="18822"/></proof>
 </goal>
 <goal name="lowup" proved="true">
 <proof prover="5"><result status="valid" time="0.09" steps="18863"/></proof>
 </goal>
 <goal name="tnt_low&#39;vc" expl="VC for tnt_low" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="tnt_low&#39;vc.0" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_low&#39;vc.0.0" expl="assertion" proved="true">
   <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.15" steps="552"/></proof>
   </goal>
   <goal name="tnt_low&#39;vc.0.1" expl="assertion" proved="true">
   <proof prover="5" timelimit="1" memlimit="1000"><result status="valid" time="0.06" steps="18885"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="tnt_low&#39;vc.1" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_low&#39;vc.1.0" expl="assertion" proved="true">
   <proof prover="5"><result status="valid" time="0.14" steps="20896"/></proof>
   </goal>
   <goal name="tnt_low&#39;vc.1.1" expl="assertion" proved="true">
   <transf name="rewrite" proved="true" arg1="substring_get">
    <goal name="tnt_low&#39;vc.1.1.0" expl="assertion" proved="true">
    <proof prover="2"><result status="valid" time="0.02" steps="74"/></proof>
    </goal>
    <goal name="tnt_low&#39;vc.1.1.1" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.11" steps="19211"/></proof>
    </goal>
    <goal name="tnt_low&#39;vc.1.1.2" expl="rewrite premises" proved="true">
    <proof prover="2"><result status="valid" time="0.03" steps="74"/></proof>
    </goal>
    <goal name="tnt_low&#39;vc.1.1.3" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.11" steps="19204"/></proof>
    </goal>
    <goal name="tnt_low&#39;vc.1.1.4" expl="rewrite premises" proved="true">
    <proof prover="2"><result status="valid" time="0.03" steps="74"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="tnt_low&#39;vc.1.2" expl="VC for tnt_low" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="79"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="tnt_low&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.08" steps="275"/></proof>
  </goal>
  <goal name="tnt_low&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.10" steps="274"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="tnt_up&#39;vc" expl="VC for tnt_up" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="tnt_up&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.16" steps="572"/></proof>
  </goal>
  <goal name="tnt_up&#39;vc.1" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_up&#39;vc.1.0" expl="assertion" proved="true">
   <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.04" steps="74"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.1.1" expl="assertion" proved="true">
   <transf name="rewrite" proved="true" arg1="substring_get">
    <goal name="tnt_up&#39;vc.1.1.0" expl="assertion" proved="true">
    <proof prover="5"><result status="valid" time="0.11" steps="19374"/></proof>
    </goal>
    <goal name="tnt_up&#39;vc.1.1.1" expl="rewrite premises" proved="true">
    <proof prover="5"><result status="valid" time="0.59" steps="85430"/></proof>
    </goal>
    <goal name="tnt_up&#39;vc.1.1.2" expl="rewrite premises" proved="true">
    <proof prover="5"><result status="valid" time="0.09" steps="19346"/></proof>
    </goal>
    <goal name="tnt_up&#39;vc.1.1.3" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.11" steps="19716"/></proof>
    </goal>
    <goal name="tnt_up&#39;vc.1.1.4" expl="rewrite premises" proved="true">
    <proof prover="1" timelimit="1"><result status="valid" time="0.02" steps="19105"/></proof>
    <proof prover="2"><result status="valid" time="0.03" steps="74"/></proof>
    <proof prover="5" timelimit="1" memlimit="1000"><result status="valid" time="0.11" steps="19369"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="tnt_up&#39;vc.1.2" expl="VC for tnt_up" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="79"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="tnt_up&#39;vc.2" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_up&#39;vc.2.0" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="76"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.2.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="78"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.2.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="76"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.2.3" expl="VC for tnt_up" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="80"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.2.4" expl="VC for tnt_up" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="81"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.2.5" expl="VC for tnt_up" proved="true">
   <proof prover="2"><result status="valid" time="0.04" steps="84"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.2.6" expl="VC for tnt_up" proved="true">
   <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.07" steps="82"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.2.7" expl="VC for tnt_up" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="85"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="tnt_up&#39;vc.3" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_up&#39;vc.3.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="272"/></proof>
   </goal>
   <goal name="tnt_up&#39;vc.3.1" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.04" steps="78"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="tnt_both&#39;vc" expl="VC for tnt_both" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="tnt_both&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.16" steps="555"/></proof>
  </goal>
  <goal name="tnt_both&#39;vc.1" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_both&#39;vc.1.0" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="81"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.1.1" expl="assertion" proved="true">
   <transf name="rewrite" proved="true" arg1="substring_get">
    <goal name="tnt_both&#39;vc.1.1.0" expl="assertion" proved="true">
    <proof prover="2"><result status="valid" time="0.02" steps="81"/></proof>
    </goal>
    <goal name="tnt_both&#39;vc.1.1.1" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.10" steps="19999"/></proof>
    </goal>
    <goal name="tnt_both&#39;vc.1.1.2" expl="rewrite premises" proved="true">
    <proof prover="2"><result status="valid" time="0.03" steps="81"/></proof>
    </goal>
    <goal name="tnt_both&#39;vc.1.1.3" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.10" steps="19992"/></proof>
    </goal>
    <goal name="tnt_both&#39;vc.1.1.4" expl="rewrite premises" proved="true">
    <proof prover="2"><result status="valid" time="0.02" steps="81"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="tnt_both&#39;vc.1.2" expl="VC for tnt_both" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="86"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="tnt_both&#39;vc.2" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_both&#39;vc.2.0" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="83"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.2.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.04" steps="85"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.2.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="83"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.2.3" expl="VC for tnt_both" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="87"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.2.4" expl="VC for tnt_both" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="88"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.2.5" expl="VC for tnt_both" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="91"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.2.6" expl="VC for tnt_both" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="89"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.2.7" expl="VC for tnt_both" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="92"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="tnt_both&#39;vc.3" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_both&#39;vc.3.0" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="83"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.3.1" expl="assertion" proved="true">
   <transf name="rewrite" proved="true" arg1="substring_get">
    <goal name="tnt_both&#39;vc.3.1.0" expl="assertion" proved="true">
    <proof prover="2"><result status="valid" time="0.03" steps="83"/></proof>
    </goal>
    <goal name="tnt_both&#39;vc.3.1.1" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.10" steps="20025"/></proof>
    </goal>
    <goal name="tnt_both&#39;vc.3.1.2" expl="rewrite premises" proved="true">
    <proof prover="2"><result status="valid" time="0.03" steps="83"/></proof>
    </goal>
    <goal name="tnt_both&#39;vc.3.1.3" expl="rewrite premises" proved="true">
    <proof prover="7"><result status="valid" time="0.09" steps="20018"/></proof>
    </goal>
    <goal name="tnt_both&#39;vc.3.1.4" expl="rewrite premises" proved="true">
    <proof prover="2"><result status="valid" time="0.03" steps="83"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="tnt_both&#39;vc.3.2" expl="VC for tnt_both" proved="true">
   <proof prover="2"><result status="valid" time="0.04" steps="88"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="tnt_both&#39;vc.4" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.09" steps="284"/></proof>
  </goal>
  <goal name="tnt_both&#39;vc.5" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt_both&#39;vc.5.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.04" steps="272"/></proof>
   </goal>
   <goal name="tnt_both&#39;vc.5.1" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="77"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="tnt&#39;vc" expl="VC for tnt" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="tnt&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="80"/></proof>
  </goal>
  <goal name="tnt&#39;vc.1" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="tnt&#39;vc.1.0" expl="precondition" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="78"/></proof>
   </goal>
   <goal name="tnt&#39;vc.1.1" expl="precondition" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="86"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="tnt&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="85"/></proof>
  </goal>
  <goal name="tnt&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="438"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="String_value" proved="true">
 <goal name="abs_value_sub_text&#39;vc" expl="VC for abs_value_sub_text" proved="true">
 <proof prover="5"><result status="valid" time="0.19" steps="26968"/></proof>
 </goal>
 <goal name="text_conversion&#39;vc" expl="VC for text_conversion" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="text_conversion&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.07" steps="68"/></proof>
  </goal>
  <goal name="text_conversion&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.12" steps="265"/></proof>
  </goal>
  <goal name="text_conversion&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.11"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="abs_value_sub_text_frame&#39;vc" expl="VC for abs_value_sub_text_frame" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="abs_value_sub_text_frame&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.02" steps="66"/></proof>
  </goal>
  <goal name="abs_value_sub_text_frame&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.04" steps="72"/></proof>
  </goal>
  <goal name="abs_value_sub_text_frame&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="2" timelimit="5" memlimit="2000"><result status="valid" time="0.24" steps="337"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
