<?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="Eprover" version="1.9.1-001" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="2" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Z3" version="4.5.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="valuation.mlw"/>
<theory name="Valuation" proved="true">
 <goal name="valuation&#39;vc" expl="VC for valuation" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="valuation&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="12444"/></proof>
  </goal>
  <goal name="valuation&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="12477"/></proof>
  </goal>
  <goal name="valuation&#39;vc.2" expl="variant decrease" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="valuation&#39;vc.2.0" expl="variant decrease" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="valuation&#39;vc.2.0.0" expl="variant decrease" proved="true">
    <proof prover="4"><result status="valid" time="0.02" steps="16173"/></proof>
    </goal>
    <goal name="valuation&#39;vc.2.0.1" expl="variant decrease" proved="true">
    <proof prover="1"><result status="valid" time="0.02"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="valuation&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="12354"/></proof>
  </goal>
  <goal name="valuation&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.00" steps="14611"/></proof>
  </goal>
  <goal name="valuation&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="12798"/></proof>
  </goal>
  <goal name="valuation&#39;vc.6" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="valuation&#39;vc.6.0" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="3.38"/></proof>
   </goal>
   <goal name="valuation&#39;vc.6.1" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="20018"/></proof>
   <proof prover="5"><result status="valid" time="0.01" steps="23"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_mul" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="valuation_mul.0" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="valuation_mul.1" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="36"/></proof>
  </goal>
  <goal name="valuation_mul.2" proved="true">
  <proof prover="5"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="power_ge_1" proved="true">
 <proof prover="2" timelimit="5"><result status="valid" time="0.05" steps="13680"/></proof>
 <transf name="introduce_premises" proved="true" >
  <goal name="power_ge_1.0" proved="true">
  <transf name="induction" proved="true" arg1="e">
   <goal name="power_ge_1.0.0" expl="base case" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="14224"/></proof>
   </goal>
   <goal name="power_ge_1.0.1" expl="recursive case" proved="true">
   <proof prover="4"><result status="valid" time="0.04" steps="17361"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_times_pow&#39;vc" expl="VC for valuation_times_pow" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="valuation_times_pow&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="1714"/></proof>
  </goal>
  <goal name="valuation_times_pow&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="16104"/></proof>
  </goal>
  <goal name="valuation_times_pow&#39;vc.2" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="valuation_times_pow&#39;vc.2.0" expl="assertion" proved="true">
   <proof prover="5"><result status="valid" time="0.01" steps="18"/></proof>
   </goal>
   <goal name="valuation_times_pow&#39;vc.2.1" expl="assertion" proved="true">
   <proof prover="5"><result status="valid" time="0.13" steps="47"/></proof>
   </goal>
   <goal name="valuation_times_pow&#39;vc.2.2" expl="VC for valuation_times_pow" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="22203"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_times_pow&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.24"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_split" proved="true">
 <proof prover="5"><result status="valid" time="0.48" steps="126"/></proof>
 </goal>
 <goal name="valuation_lower_bound&#39;vc" expl="VC for valuation_lower_bound" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="valuation_lower_bound&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="16017"/></proof>
  </goal>
  <goal name="valuation_lower_bound&#39;vc.1" expl="assertion" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="17"/></proof>
  </goal>
  <goal name="valuation_lower_bound&#39;vc.2" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.02" steps="41"/></proof>
  </goal>
  <goal name="valuation_lower_bound&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="5"><result status="valid" time="0.06" steps="43"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_pow" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="valuation_pow.0" proved="true">
  <transf name="induction" proved="true" arg1="k">
   <goal name="valuation_pow.0.0" expl="base case" proved="true">
   <proof prover="5"><result status="valid" time="0.02" steps="25"/></proof>
   </goal>
   <goal name="valuation_pow.0.1" expl="recursive case" proved="true">
   <proof prover="4"><result status="valid" time="0.93" steps="927349"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_monotonous&#39;vc" expl="VC for valuation_monotonous" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="valuation_monotonous&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="14225"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="14267"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.10" steps="27875"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="17203"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4" timelimit="1"><result status="valid" time="0.02" steps="16353"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="17618"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.6" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="valuation_monotonous&#39;vc.6.0" expl="VC for valuation_monotonous" proved="true">
   <proof prover="5" timelimit="1"><result status="valid" time="0.01" steps="12"/></proof>
   </goal>
   <goal name="valuation_monotonous&#39;vc.6.1" expl="VC for valuation_monotonous" proved="true">
   <proof prover="2"><result status="valid" time="0.04" steps="14882"/></proof>
   </goal>
   <goal name="valuation_monotonous&#39;vc.6.2" expl="VC for valuation_monotonous" proved="true">
   <proof prover="5" timelimit="1"><result status="valid" time="0.10" steps="112"/></proof>
   </goal>
   <goal name="valuation_monotonous&#39;vc.6.3" expl="VC for valuation_monotonous" proved="true">
   <proof prover="2"><result status="valid" time="0.04" steps="15337"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_monotonous&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="5" timelimit="1"><result status="valid" time="0.01" steps="25"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_nondiv" proved="true">
 <proof prover="5"><result status="valid" time="0.13" steps="102"/></proof>
 </goal>
 <goal name="valuation_zero_prod" proved="true">
 <proof prover="5"><result status="valid" time="0.29" steps="85"/></proof>
 </goal>
 <goal name="valuation_times_nondiv&#39;vc" expl="VC for valuation_times_nondiv" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="valuation_times_nondiv&#39;vc.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="16684"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="20066"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="39431"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04" steps="24001"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="1894"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="1898"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.6" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="valuation_times_nondiv&#39;vc.6.0" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.08"/></proof>
   </goal>
   <goal name="valuation_times_nondiv&#39;vc.6.1" expl="assertion" proved="true">
   <transf name="apply" proved="true" arg1="valuation_mul">
    <goal name="valuation_times_nondiv&#39;vc.6.1.0" expl="apply premises" proved="true">
    <proof prover="5"><result status="valid" time="0.02" steps="29"/></proof>
    </goal>
    <goal name="valuation_times_nondiv&#39;vc.6.1.1" expl="apply premises" proved="true">
    <proof prover="4"><result status="valid" time="0.02" steps="21033"/></proof>
    </goal>
    <goal name="valuation_times_nondiv&#39;vc.6.1.2" expl="apply premises" proved="true">
    <proof prover="4"><result status="valid" time="0.01" steps="1896"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="valuation_times_nondiv&#39;vc.6.2" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.01" steps="1902"/></proof>
   </goal>
   <goal name="valuation_times_nondiv&#39;vc.6.3" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="21555"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="5"><result status="valid" time="0.02" steps="28"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_prod" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="valuation_prod.0" proved="true">
  <proof prover="5"><result status="valid" time="0.04" steps="37"/></proof>
  </goal>
  <goal name="valuation_prod.1" proved="true">
  <proof prover="5"><result status="valid" time="0.04" steps="40"/></proof>
  </goal>
  <goal name="valuation_prod.2" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="19073"/></proof>
  </goal>
  <goal name="valuation_prod.3" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="19668"/></proof>
  </goal>
  <goal name="valuation_prod.4" proved="true">
  <transf name="apply" proved="true" arg1="valuation_zero_prod">
   <goal name="valuation_prod.4.0" expl="apply premises" proved="true">
   <proof prover="5"><result status="valid" time="0.02" steps="22"/></proof>
   </goal>
   <goal name="valuation_prod.4.1" expl="apply premises" proved="true">
   <proof prover="5"><result status="valid" time="0.02" steps="22"/></proof>
   </goal>
   <goal name="valuation_prod.4.2" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.01" steps="1926"/></proof>
   </goal>
   <goal name="valuation_prod.4.3" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="1928"/></proof>
   </goal>
   <goal name="valuation_prod.4.4" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.04" steps="1928"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.5" proved="true">
  <proof prover="5"><result status="valid" time="0.02" steps="12"/></proof>
  </goal>
  <goal name="valuation_prod.6" proved="true">
  <transf name="rewrite" proved="true" arg1="&lt;-" arg2="Power_sum">
   <goal name="valuation_prod.6.0" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="1930"/></proof>
   </goal>
   <goal name="valuation_prod.6.1" expl="rewrite premises" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="20653"/></proof>
   </goal>
   <goal name="valuation_prod.6.2" expl="rewrite premises" proved="true">
   <proof prover="4"><result status="valid" time="0.02" steps="20657"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.7" proved="true">
  <proof prover="5"><result status="valid" time="0.04" steps="35"/></proof>
  </goal>
  <goal name="valuation_prod.8" proved="true">
  <proof prover="5"><result status="valid" time="0.04" steps="36"/></proof>
  </goal>
  <goal name="valuation_prod.9" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="valuation_prod.10" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="24688"/></proof>
  </goal>
  <goal name="valuation_prod.11" proved="true">
  <transf name="apply" proved="true" arg1="valuation_times_nondiv">
   <goal name="valuation_prod.11.0" expl="apply premises" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="valuation_prod.11.0.0" expl="apply premises" proved="true">
    <proof prover="4"><result status="valid" time="0.03" steps="22451"/></proof>
    </goal>
    <goal name="valuation_prod.11.0.1" expl="apply premises" proved="true">
    <proof prover="4"><result status="valid" time="0.02" steps="1954"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="valuation_prod.11.1" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.00" steps="1954"/></proof>
   </goal>
   <goal name="valuation_prod.11.2" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.01" steps="1956"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.12" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="23518"/></proof>
  </goal>
  <goal name="valuation_prod.13" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="26"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_mod" proved="true">
 <proof prover="5"><result status="valid" time="0.01" steps="21"/></proof>
 </goal>
 <goal name="valuation_decomp" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="valuation_decomp.0" proved="true">
  <proof prover="4"><result status="valid" time="0.02" steps="16431"/></proof>
  </goal>
  <goal name="valuation_decomp.1" proved="true">
  <proof prover="5"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
