why3session.xml 15.1 KB
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
<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="1.4" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Z3" version="4.5.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="5" name="Alt-Ergo" version="2.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<file name="../valuation.mlw" proved="true">
<theory name="Valuation" proved="true">
 <goal name="VC valuation" expl="VC for valuation" proved="true">
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 <transf name="split_goal_right" proved="true" >
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  <goal name="VC valuation.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC valuation.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC valuation.2" expl="variant decrease" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="VC valuation.2.0" expl="variant decrease" proved="true">
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   <transf name="split_vc" proved="true" >
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    <goal name="VC valuation.2.0.0" expl="VC for valuation" proved="true">
    <proof prover="4"><result status="valid" time="0.02"/></proof>
    </goal>
    <goal name="VC valuation.2.0.1" expl="VC for valuation" proved="true">
    <proof prover="1"><result status="valid" time="0.02"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="VC valuation.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="VC valuation.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="VC valuation.5" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC valuation.6" expl="postcondition" proved="true">
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  <transf name="split_vc" proved="true" >
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   <goal name="VC valuation.6.0" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="2.24"/></proof>
   </goal>
   <goal name="VC valuation.6.1" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
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   <proof prover="5"><result status="valid" time="0.01" steps="21"/></proof>
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   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="valuation_mul" proved="true">
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 <transf name="split_vc" proved="true" >
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  <goal name="valuation_mul.0" proved="true">
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  <proof prover="5"><result status="valid" time="0.01" steps="17"/></proof>
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  </goal>
  <goal name="valuation_mul.1" proved="true">
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  <proof prover="5"><result status="valid" time="0.01" steps="37"/></proof>
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  </goal>
  <goal name="valuation_mul.2" proved="true">
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  <proof prover="5"><result status="valid" time="0.00" steps="15"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="power_ge_1" proved="true">
 <proof prover="2"><result status="valid" time="0.05"/></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"/></proof>
   </goal>
   <goal name="power_ge_1.0.1" expl="recursive case" proved="true">
   <proof prover="4"><result status="valid" time="0.04"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="VC valuation_times_pow" expl="VC for valuation_times_pow" proved="true">
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 <transf name="split_vc" proved="true" >
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  <goal name="VC valuation_times_pow.0" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC valuation_times_pow.1" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC valuation_times_pow.2" expl="assertion" proved="true">
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  <transf name="split_vc" proved="true" >
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   <goal name="VC valuation_times_pow.2.0" expl="VC for valuation_times_pow" proved="true">
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   <proof prover="5"><result status="valid" time="0.01" steps="18"/></proof>
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   </goal>
   <goal name="VC valuation_times_pow.2.1" expl="VC for valuation_times_pow" proved="true">
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   <proof prover="5"><result status="valid" time="0.13" steps="47"/></proof>
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   </goal>
   <goal name="VC valuation_times_pow.2.2" expl="VC for valuation_times_pow" proved="true">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC valuation_times_pow.3" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.24"/></proof>
  </goal>
 </transf>
 </goal>
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 <goal name="valuation_split" proved="true">
 <proof prover="4"><result status="timeout" time="1.00"/></proof>
 <proof prover="5"><result status="valid" time="0.48" steps="164"/></proof>
 </goal>
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 <goal name="VC valuation_lower_bound" expl="VC for valuation_lower_bound" proved="true">
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 <transf name="split_vc" proved="true" >
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  <goal name="VC valuation_lower_bound.0" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC valuation_lower_bound.1" expl="assertion" proved="true">
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  <proof prover="5"><result status="valid" time="0.01" steps="17"/></proof>
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  </goal>
  <goal name="VC valuation_lower_bound.2" expl="precondition" proved="true">
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  <proof prover="5"><result status="valid" time="0.02" steps="40"/></proof>
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  </goal>
  <goal name="VC valuation_lower_bound.3" expl="postcondition" proved="true">
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  <proof prover="5"><result status="valid" time="0.06" steps="43"/></proof>
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  </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">
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   <proof prover="5"><result status="valid" time="0.02" steps="25"/></proof>
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   </goal>
   <goal name="valuation_pow.0.1" expl="recursive case" proved="true">
   <proof prover="4"><result status="valid" time="0.90"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="VC valuation_monotonous" expl="VC for valuation_monotonous" proved="true">
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 <transf name="split_vc" proved="true" >
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  <goal name="VC valuation_monotonous.0" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.01"/></proof>
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  </goal>
  <goal name="VC valuation_monotonous.1" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.02"/></proof>
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  </goal>
  <goal name="VC valuation_monotonous.2" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC valuation_monotonous.3" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC valuation_monotonous.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC valuation_monotonous.5" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC valuation_monotonous.6" expl="assertion" proved="true">
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  <transf name="split_vc" proved="true" >
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   <goal name="VC valuation_monotonous.6.0" expl="VC for valuation_monotonous" proved="true">
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   <proof prover="5"><result status="valid" time="0.01" steps="11"/></proof>
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   </goal>
   <goal name="VC valuation_monotonous.6.1" expl="VC for valuation_monotonous" proved="true">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="VC valuation_monotonous.6.2" expl="VC for valuation_monotonous" proved="true">
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   <proof prover="5"><result status="valid" time="0.12" steps="110"/></proof>
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   </goal>
   <goal name="VC valuation_monotonous.6.3" expl="VC for valuation_monotonous" proved="true">
   <proof prover="4"><result status="valid" time="0.01"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC valuation_monotonous.7" expl="postcondition" proved="true">
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  <proof prover="5"><result status="valid" time="0.01" steps="24"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="valuation_nondiv" proved="true">
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 <proof prover="5"><result status="valid" time="0.13" steps="98"/></proof>
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 </goal>
 <goal name="valuation_zero_prod" proved="true">
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 <proof prover="5"><result status="valid" time="0.29" steps="84"/></proof>
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 </goal>
 <goal name="VC valuation_times_nondiv" expl="VC for valuation_times_nondiv" proved="true">
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 <transf name="split_vc" proved="true" >
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  <goal name="VC valuation_times_nondiv.0" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.03"/></proof>
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  </goal>
  <goal name="VC valuation_times_nondiv.1" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.02"/></proof>
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  </goal>
  <goal name="VC valuation_times_nondiv.2" expl="variant decrease" proved="true">
  <proof prover="4"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC valuation_times_nondiv.3" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC valuation_times_nondiv.4" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC valuation_times_nondiv.5" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC valuation_times_nondiv.6" expl="assertion" proved="true">
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  <transf name="split_vc" proved="true" >
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   <goal name="VC valuation_times_nondiv.6.0" expl="VC for valuation_times_nondiv" proved="true">
   <proof prover="0"><result status="valid" time="0.08"/></proof>
   </goal>
   <goal name="VC valuation_times_nondiv.6.1" expl="VC for valuation_times_nondiv" proved="true">
   <transf name="apply" proved="true" arg1="valuation_mul">
    <goal name="VC valuation_times_nondiv.6.1.0" proved="true">
    <proof prover="4"><result status="valid" time="0.01"/></proof>
    </goal>
    <goal name="VC valuation_times_nondiv.6.1.1" proved="true">
    <proof prover="4"><result status="valid" time="0.02"/></proof>
    </goal>
    <goal name="VC valuation_times_nondiv.6.1.2" proved="true">
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    <proof prover="5"><result status="valid" time="0.02" steps="35"/></proof>
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    </goal>
   </transf>
   </goal>
   <goal name="VC valuation_times_nondiv.6.2" expl="VC for valuation_times_nondiv" proved="true">
   <proof prover="4"><result status="valid" time="0.01"/></proof>
   </goal>
   <goal name="VC valuation_times_nondiv.6.3" expl="VC for valuation_times_nondiv" proved="true">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC valuation_times_nondiv.7" expl="postcondition" proved="true">
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  <proof prover="5"><result status="valid" time="0.02" steps="28"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="valuation_prod" proved="true">
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 <transf name="split_vc" proved="true" >
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  <goal name="valuation_prod.0" proved="true">
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  <proof prover="5"><result status="valid" time="0.04" steps="37"/></proof>
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  </goal>
  <goal name="valuation_prod.1" proved="true">
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  <proof prover="5"><result status="valid" time="0.04" steps="40"/></proof>
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  </goal>
  <goal name="valuation_prod.2" proved="true">
  <proof prover="4"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="valuation_prod.3" proved="true">
  <proof prover="4"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="valuation_prod.4" proved="true">
  <transf name="apply" proved="true" arg1="valuation_zero_prod">
   <goal name="valuation_prod.4.0" proved="true">
   <proof prover="4"><result status="valid" time="0.04"/></proof>
   </goal>
   <goal name="valuation_prod.4.1" proved="true">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="valuation_prod.4.2" proved="true">
   <proof prover="4"><result status="valid" time="0.01"/></proof>
   </goal>
   <goal name="valuation_prod.4.3" proved="true">
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   <proof prover="5"><result status="valid" time="0.02" steps="22"/></proof>
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   </goal>
   <goal name="valuation_prod.4.4" proved="true">
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   <proof prover="5"><result status="valid" time="0.02" steps="22"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.5" proved="true">
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  <proof prover="5"><result status="valid" time="0.02" steps="12"/></proof>
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  </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"/></proof>
   </goal>
   <goal name="valuation_prod.6.1" proved="true">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="valuation_prod.6.2" proved="true">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.7" proved="true">
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  <proof prover="5"><result status="valid" time="0.04" steps="35"/></proof>
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  </goal>
  <goal name="valuation_prod.8" proved="true">
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  <proof prover="5"><result status="valid" time="0.04" steps="36"/></proof>
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  </goal>
  <goal name="valuation_prod.9" proved="true">
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  <proof prover="5"><result status="valid" time="0.01" steps="16"/></proof>
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  </goal>
  <goal name="valuation_prod.10" proved="true">
  <proof prover="4"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="valuation_prod.11" proved="true">
  <transf name="apply" proved="true" arg1="valuation_times_nondiv">
   <goal name="valuation_prod.11.0" proved="true">
   <proof prover="4"><result status="valid" time="0.01"/></proof>
   </goal>
   <goal name="valuation_prod.11.1" proved="true">
   <proof prover="4"><result status="valid" time="0.00"/></proof>
   </goal>
   <goal name="valuation_prod.11.2" proved="true">
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   <transf name="split_vc" proved="true" >
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    <goal name="valuation_prod.11.2.0" proved="true">
    <proof prover="4"><result status="valid" time="0.03"/></proof>
    </goal>
    <goal name="valuation_prod.11.2.1" proved="true">
    <proof prover="4"><result status="valid" time="0.02"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="valuation_prod.12" proved="true">
  <proof prover="4"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="valuation_prod.13" proved="true">
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  <proof prover="5"><result status="valid" time="0.01" steps="20"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="valuation_mod" proved="true">
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 <proof prover="5"><result status="valid" time="0.01" steps="20"/></proof>
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 </goal>
 <goal name="valuation_decomp" proved="true">
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 <transf name="split_vc" proved="true" >
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  <goal name="valuation_decomp.0" proved="true">
  <proof prover="4"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="valuation_decomp.1" proved="true">
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  <proof prover="5"><result status="valid" time="0.01" steps="16"/></proof>
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  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>