<?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="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="Firstorder_symbol_impl.mlw"/>
<theory name="Logic" proved="true">
 <goal name="nlsize_positive_lemma_symbol&#39;vc" expl="VC for nlsize_positive_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="17"/></proof>
 </goal>
 <goal name="shiftb_compose_lemma_symbol&#39;vc" expl="VC for shiftb_compose_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.08" steps="144"/></proof>
 </goal>
 <goal name="nlmodel_subst_commutation_lemma_symbol&#39;vc" expl="VC for nlmodel_subst_commutation_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="24"/></proof>
 </goal>
 <goal name="nlmodel_rename_commutation_lemma_symbol&#39;vc" expl="VC for nlmodel_rename_commutation_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.04" steps="32"/></proof>
 </goal>
 <goal name="bound_depth_of_symbol_in_symbol_nonnegative&#39;vc" expl="VC for bound_depth_of_symbol_in_symbol_nonnegative" proved="true">
 <proof prover="2"><result status="valid" time="0.04" steps="31"/></proof>
 </goal>
 <goal name="model_equal_symbol&#39;vc" expl="VC for model_equal_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.04" steps="50"/></proof>
 </goal>
</theory>
<theory name="Impl" proved="true">
 <goal name="bind_var_symbol_in_symbol&#39;vc" expl="VC for bind_var_symbol_in_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.10" steps="210"/></proof>
 </goal>
 <goal name="unbind_var_symbol_in_symbol&#39;vc" expl="VC for unbind_var_symbol_in_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.04" steps="189"/></proof>
 </goal>
 <goal name="subst_base_symbol_in_symbol&#39;vc" expl="VC for subst_base_symbol_in_symbol" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_base_symbol_in_symbol&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="9"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_symbol&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="4"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_symbol&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="9"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_symbol&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02" steps="17"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_symbol&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="15"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_symbol&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="71"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="construct_symbol&#39;vc" expl="VC for construct_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.06" steps="183"/></proof>
 </goal>
 <goal name="destruct_symbol&#39;vc" expl="VC for destruct_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.04" steps="84"/></proof>
 </goal>
 <goal name="nlsubst_symbol_in_symbol&#39;vc" expl="VC for nlsubst_symbol_in_symbol" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="nlsubst_symbol_in_symbol&#39;vc.0" expl="precondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="nlsubst_symbol_in_symbol&#39;vc.0.0" expl="precondition" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="nlsubst_symbol_in_symbol&#39;vc.0.0.0" expl="precondition" proved="true">
    <proof prover="2"><result status="valid" time="0.00" steps="11"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="19"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="8"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="22"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04" steps="10"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.5" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="11"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="12"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.7" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_symbol_in_symbol&#39;vc.7.0" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.08" steps="91"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_symbol&#39;vc.7.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.08" steps="231"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_symbol&#39;vc.7.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="54"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_symbol&#39;vc.7.3" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.08"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_symbol&#39;vc.7.4" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.10"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.8" expl="postcondition" proved="true">
  <transf name="inline_goal" proved="true" >
   <goal name="nlsubst_symbol_in_symbol&#39;vc.8.0" expl="postcondition" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="nlsubst_symbol_in_symbol&#39;vc.8.0.0" expl="VC for nlsubst_symbol_in_symbol" proved="true">
    <proof prover="2"><result status="valid" time="0.03" steps="20"/></proof>
    </goal>
    <goal name="nlsubst_symbol_in_symbol&#39;vc.8.0.1" expl="VC for nlsubst_symbol_in_symbol" proved="true">
    <proof prover="2"><result status="valid" time="0.05" steps="72"/></proof>
    </goal>
    <goal name="nlsubst_symbol_in_symbol&#39;vc.8.0.2" expl="VC for nlsubst_symbol_in_symbol" proved="true">
    <proof prover="2"><result status="valid" time="0.11" steps="23"/></proof>
    </goal>
    <goal name="nlsubst_symbol_in_symbol&#39;vc.8.0.3" expl="VC for nlsubst_symbol_in_symbol" proved="true">
    <proof prover="0"><result status="valid" time="0.16" steps="38852"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_symbol_in_symbol&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="14489"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
