<?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="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="9" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="10" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="Firstorder_tableau_impl.mlw"/>
<theory name="Logic" proved="true">
 <goal name="nlsize_positive_lemma_tableau&#39;vc" expl="VC for nlsize_positive_lemma_tableau" proved="true">
 <proof prover="1"><result status="valid" time="0.13" steps="205"/></proof>
 </goal>
 <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc" expl="VC for nlmodel_subst_commutation_lemma_tableau" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="28"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="16"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="17"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="18"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.4" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="19"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="16"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.6" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="16"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="16"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.8" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="16"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.9" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.05" steps="17"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="17"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="17"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.12" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="17"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_tableau&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="95"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="nlmodel_rename_commutation_lemma_tableau&#39;vc" expl="VC for nlmodel_rename_commutation_lemma_tableau" proved="true">
 <proof prover="1"><result status="valid" time="0.07" steps="28"/></proof>
 </goal>
 <goal name="bound_depth_of_symbol_in_tableau_nonnegative&#39;vc" expl="VC for bound_depth_of_symbol_in_tableau_nonnegative" proved="true">
 <proof prover="1"><result status="valid" time="0.15" steps="179"/></proof>
 </goal>
 <goal name="bound_depth_of_fo_term_in_tableau_nonnegative&#39;vc" expl="VC for bound_depth_of_fo_term_in_tableau_nonnegative" proved="true">
 <proof prover="1"><result status="valid" time="0.18" steps="159"/></proof>
 </goal>
 <goal name="model_equal_tableau&#39;vc" expl="VC for model_equal_tableau" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="model_equal_tableau&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="36"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.25" steps="663"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="13"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.21" steps="477"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.4" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="14"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="33"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.12" steps="614"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="14"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.12" steps="405"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="15"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.10" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="49"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.11" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="711"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.12" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="15"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.13" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.13" steps="595"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.14" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="16"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.15" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="45"/></proof>
  </goal>
  <goal name="model_equal_tableau&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="35"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Impl" proved="true">
 <goal name="bind_var_symbol_in_tableau&#39;vc" expl="VC for bind_var_symbol_in_tableau" proved="true">
 <proof prover="1" timelimit="1"><result status="valid" time="0.66" steps="1946"/></proof>
 </goal>
 <goal name="bind_var_fo_term_in_tableau&#39;vc" expl="VC for bind_var_fo_term_in_tableau" proved="true">
 <proof prover="1" timelimit="1"><result status="valid" time="0.48" steps="1603"/></proof>
 </goal>
 <goal name="unbind_var_symbol_in_tableau&#39;vc" expl="VC for unbind_var_symbol_in_tableau" proved="true">
 <proof prover="9"><result status="valid" time="2.28"/></proof>
 </goal>
 <goal name="unbind_var_fo_term_in_tableau&#39;vc" expl="VC for unbind_var_fo_term_in_tableau" proved="true">
 <proof prover="9"><result status="valid" time="2.32"/></proof>
 </goal>
 <goal name="subst_base_symbol_in_tableau&#39;vc" expl="VC for subst_base_symbol_in_tableau" proved="true">
 <proof prover="1" timelimit="1"><result status="valid" time="0.32" steps="974"/></proof>
 </goal>
 <goal name="subst_base_fo_term_in_tableau&#39;vc" expl="VC for subst_base_fo_term_in_tableau" proved="true">
 <proof prover="1" timelimit="1"><result status="valid" time="0.26" steps="809"/></proof>
 </goal>
 <goal name="construct_tableau&#39;vc" expl="VC for construct_tableau" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="construct_tableau&#39;vc.0" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="12"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="12"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="33"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="42"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.4" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.11" steps="55"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="41"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="41"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="45"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="45"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.9" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="94"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="94"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="142"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.12" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.14" steps="142"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.13" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="93"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.14" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="93"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="249"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.16" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="249"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.17" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="23"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.18" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.16" steps="97301"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.19" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="24"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.20" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.18" steps="97301"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.21" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.22" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.23" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.24" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.25" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="25"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.26" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="24"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.27" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.28" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="24"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.29" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.17" steps="97301"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.30" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.31" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.32" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.33" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.34" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="25"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.35" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="24"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.36" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.37" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="24"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.38" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.17" steps="97301"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.39" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.40" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.41" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.42" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="9"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.43" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="25"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.44" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.22" steps="1175"/></proof>
  </goal>
  <goal name="construct_tableau&#39;vc.45" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.20" steps="210"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="destruct_tableau&#39;vc" expl="VC for destruct_tableau" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="destruct_tableau&#39;vc.0" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="23"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.1" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="26"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="20"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.3" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="24"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.4" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="22"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="23"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.6" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="24"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.12" steps="166"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.8" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="28"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.9" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="171"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="29"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.13" steps="249"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.12" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="31"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.13" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="196"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.14" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="32"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="190"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.16" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="34"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.17" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="191"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.18" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="35"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.19" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="22"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.20" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="35"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.21" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="23"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.22" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="36"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.23" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="88"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.24" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="23"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.25" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="34"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.26" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="24"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.27" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="35"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.28" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="103"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.29" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="24"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.30" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="35"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.31" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="25"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.32" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.19" steps="36"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.33" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="97"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.34" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="35"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.35" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="35"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.36" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="36"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.37" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="36"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.38" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="37"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.39" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="37"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.40" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="145"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.41" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.14" steps="145"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.42" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="149"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.43" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.14" steps="149"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.44" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.16" steps="149"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.45" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="149"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.46" expl="postcondition" proved="true">
  <proof prover="1" timelimit="1"><result status="valid" time="0.45" steps="2099"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.47" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="264"/></proof>
  </goal>
  <goal name="destruct_tableau&#39;vc.48" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="510"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="nlsubst_symbol_in_tableau&#39;vc" expl="VC for nlsubst_symbol_in_tableau" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="nlsubst_symbol_in_tableau&#39;vc.0" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="14"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="26"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="15"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="27"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.4" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="14"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="29"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.6" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="15"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="16"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="17"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.9" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_symbol_in_tableau&#39;vc.9.0" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.86" steps="226770"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_tableau&#39;vc.9.1" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.19" steps="287"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_tableau&#39;vc.9.2" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.08" steps="62"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_tableau&#39;vc.9.3" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.35" steps="207914"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_tableau&#39;vc.9.4" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.82" steps="224530"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_tableau&#39;vc.9.5" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.83" steps="229343"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.10" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_symbol_in_tableau&#39;vc.10.0" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.12" steps="100"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_tableau&#39;vc.10.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.39"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_tableau&#39;vc.10.2" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.16" steps="94"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.08" steps="104"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_tableau&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.40" steps="223202"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="nlsubst_fo_term_in_tableau&#39;vc" expl="VC for nlsubst_fo_term_in_tableau" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.0" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="14"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="28"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.15" steps="15"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="29"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.4" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="14"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="31"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.18" steps="33"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.17" steps="17"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.06" steps="18"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.09" steps="19"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.10" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.07" steps="20"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.11" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.11.0" expl="assertion" proved="true">
   <proof prover="10"><result status="valid" time="0.50"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.11.1" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.07" steps="65"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.11.2" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.08" steps="99"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.11.3" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.86" steps="225070"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.11.4" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.10" steps="25"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.11.5" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.15" steps="152"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.12" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.12.0" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.09" steps="98"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.12.1" expl="assertion" proved="true">
   <proof prover="1" timelimit="20"><result status="valid" time="0.11" steps="214"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.12.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.41"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.12.3" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.06" steps="25"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_tableau&#39;vc.12.4" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.13" steps="93"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.12" steps="105"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_tableau&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.40" steps="222625"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
