<?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="Alt-Ergo" version="2.4.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.4.1" 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="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="6" name="Alt-Ergo" version="2.3.3" 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="0.020000" steps="16797"/></proof>
  </goal>
  <goal name="valuation&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="16830"/></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="0.020000" steps="17757"/></proof>
    </goal>
    <goal name="valuation&#39;vc.2.0.1" expl="variant decrease" proved="true">
    <proof prover="1"><result status="valid" time="0.020000"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="valuation&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.000000" steps="16718"/></proof>
  </goal>
  <goal name="valuation&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.000000" steps="24323"/></proof>
  </goal>
  <goal name="valuation&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="17249"/></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="1.970000"/></proof>
   </goal>
   <goal name="valuation&#39;vc.6.1" expl="postcondition" proved="true">
   <proof prover="6"><result status="valid" time="0.010000" steps="70"/></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="6"><result status="valid" time="0.010000" steps="12"/></proof>
  </goal>
  <goal name="valuation_mul.1" proved="true">
  <proof prover="6"><result status="valid" time="0.010000" steps="63"/></proof>
  </goal>
  <goal name="valuation_mul.2" proved="true">
  <proof prover="6"><result status="valid" time="0.000000" steps="16"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="power_ge_1" proved="true">
 <proof prover="5" timelimit="5"><result status="valid" time="0.050000" steps="12597"/></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="0.030000" steps="17762"/></proof>
   </goal>
   <goal name="power_ge_1.0.1" expl="recursive case" proved="true">
   <proof prover="4"><result status="valid" time="0.040000" steps="21087"/></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="0.010000" steps="3560"/></proof>
  </goal>
  <goal name="valuation_times_pow&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="20753"/></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="6"><result status="valid" time="0.010000" steps="18"/></proof>
   </goal>
   <goal name="valuation_times_pow&#39;vc.2.1" expl="assertion" proved="true">
   <proof prover="6"><result status="valid" time="0.011208" steps="18"/></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="0.020000" steps="26230"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_times_pow&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.240000"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_split" proved="true">
 <proof prover="6"><result status="valid" time="0.549507" steps="395"/></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="0.030000" steps="12048"/></proof>
  </goal>
  <goal name="valuation_lower_bound&#39;vc.1" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.010000" steps="80"/></proof>
  </goal>
  <goal name="valuation_lower_bound&#39;vc.2" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="18"/></proof>
  </goal>
  <goal name="valuation_lower_bound&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.060000" steps="20"/></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="6"><result status="valid" time="0.020000" steps="56"/></proof>
   </goal>
   <goal name="valuation_pow.0.1" expl="recursive case" proved="true">
   <proof prover="4"><result status="valid" time="1.174098" steps="930285"/></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="5"><result status="valid" time="0.040000" steps="10099"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.1" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.040000" steps="10132"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.2" expl="assertion" proved="true">
  <proof prover="5"><result status="valid" time="0.100000" steps="19364"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="5"><result status="valid" time="0.163150" steps="18074"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4" timelimit="1"><result status="valid" time="0.020000" steps="26648"/></proof>
  </goal>
  <goal name="valuation_monotonous&#39;vc.5" expl="assertion" proved="true">
  <proof prover="5"><result status="valid" time="0.166407" steps="18419"/></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="6" timelimit="1"><result status="valid" time="0.010000" steps="14"/></proof>
   </goal>
   <goal name="valuation_monotonous&#39;vc.6.1" expl="VC for valuation_monotonous" proved="true">
   <proof prover="6" timelimit="1"><result status="valid" time="0.100000" steps="14"/></proof>
   </goal>
   <goal name="valuation_monotonous&#39;vc.6.2" expl="VC for valuation_monotonous" proved="true">
   <proof prover="2"><result status="valid" time="0.017339" steps="543"/></proof>
   </goal>
   <goal name="valuation_monotonous&#39;vc.6.3" expl="VC for valuation_monotonous" proved="true">
   <proof prover="5"><result status="valid" time="0.040000" steps="14355"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_monotonous&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="6" timelimit="1"><result status="valid" time="0.010000" steps="41"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_nondiv" proved="true">
 <proof prover="6"><result status="valid" time="0.013325" steps="78"/></proof>
 </goal>
 <goal name="valuation_zero_prod" proved="true">
 <proof prover="6"><result status="valid" time="0.022977" 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="0.020000" steps="12902"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="12929"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.110000" steps="1942"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.040000" steps="35576"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="11916"/></proof>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.010000" steps="3998"/></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="0.080000"/></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="6"><result status="valid" time="0.020000" steps="82"/></proof>
    </goal>
    <goal name="valuation_times_nondiv&#39;vc.6.1.1" expl="apply premises" proved="true">
    <proof prover="4"><result status="valid" time="0.020000" steps="20519"/></proof>
    </goal>
    <goal name="valuation_times_nondiv&#39;vc.6.1.2" expl="apply premises" proved="true">
    <proof prover="4"><result status="valid" time="0.010000" steps="3940"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="valuation_times_nondiv&#39;vc.6.2" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.010000" steps="3946"/></proof>
   </goal>
   <goal name="valuation_times_nondiv&#39;vc.6.3" expl="assertion" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="23496"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_times_nondiv&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="67"/></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="6"><result status="valid" time="0.040000" steps="195"/></proof>
  </goal>
  <goal name="valuation_prod.1" proved="true">
  <proof prover="6"><result status="valid" time="4.458047" steps="593"/></proof>
  </goal>
  <goal name="valuation_prod.2" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="50816"/></proof>
  </goal>
  <goal name="valuation_prod.3" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="53855"/></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="6"><result status="valid" time="0.020000" steps="89"/></proof>
   </goal>
   <goal name="valuation_prod.4.1" expl="apply premises" proved="true">
   <proof prover="6"><result status="valid" time="0.020000" steps="89"/></proof>
   </goal>
   <goal name="valuation_prod.4.2" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.010000" steps="12185"/></proof>
   </goal>
   <goal name="valuation_prod.4.3" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="4040"/></proof>
   </goal>
   <goal name="valuation_prod.4.4" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.040000" steps="4040"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.5" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="22"/></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="0.020000" steps="4042"/></proof>
   </goal>
   <goal name="valuation_prod.6.1" expl="rewrite premises" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="25790"/></proof>
   </goal>
   <goal name="valuation_prod.6.2" expl="rewrite premises" proved="true">
   <proof prover="4"><result status="valid" time="0.020000" steps="25794"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.7" proved="true">
  <proof prover="6"><result status="valid" time="0.156057" steps="152"/></proof>
  </goal>
  <goal name="valuation_prod.8" proved="true">
  <proof prover="6"><result status="valid" time="0.162178" steps="161"/></proof>
  </goal>
  <goal name="valuation_prod.9" proved="true">
  <proof prover="6"><result status="valid" time="0.010000" steps="29"/></proof>
  </goal>
  <goal name="valuation_prod.10" proved="true">
  <proof prover="4"><result status="valid" time="0.030000" steps="31437"/></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="0.030000" steps="27906"/></proof>
    </goal>
    <goal name="valuation_prod.11.0.1" expl="apply premises" proved="true">
    <proof prover="4"><result status="valid" time="0.020000" steps="4066"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="valuation_prod.11.1" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.000000" steps="12374"/></proof>
   </goal>
   <goal name="valuation_prod.11.2" expl="apply premises" proved="true">
   <proof prover="4"><result status="valid" time="0.010000" steps="4068"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.12" proved="true">
  <proof prover="4"><result status="valid" time="0.020000" steps="29569"/></proof>
  </goal>
  <goal name="valuation_prod.13" proved="true">
  <proof prover="6"><result status="valid" time="0.010000" steps="48"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_mod" proved="true">
 <proof prover="6"><result status="valid" time="0.010000" steps="58"/></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="0.020000" steps="20513"/></proof>
  </goal>
  <goal name="valuation_decomp.1" proved="true">
  <proof prover="6"><result status="valid" time="0.010000" steps="83"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
