<?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="1" name="Alt-Ergo" version="2.1.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="8" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="Firstorder_formula_spec.mlw"/>
<theory name="Spec" proved="true">
 <goal name="size_positive_lemma_fo_formula&#39;vc" expl="VC for size_positive_lemma_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.077560" steps="1049"/></proof>
 </goal>
 <goal name="renaming_composition_lemma_fo_formula&#39;vc" expl="VC for renaming_composition_lemma_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.083321" steps="1265"/></proof>
 </goal>
 <goal name="renaming_identity_lemma_fo_formula&#39;vc" expl="VC for renaming_identity_lemma_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.059565" steps="903"/></proof>
 </goal>
 <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc" expl="VC for rename_then_subst_composition_lemma_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="23"/></proof>
  </goal>
  <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.070000" steps="23"/></proof>
  </goal>
  <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="70"/></proof>
  </goal>
  <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="47"/></proof>
  </goal>
  <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="70"/></proof>
  </goal>
  <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="21"/></proof>
  </goal>
  <goal name="rename_then_subst_composition_lemma_fo_formula&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="1015"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc" expl="VC for subst_then_rename_composition_lemma_fo_formula" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.200000" steps="38429"/></proof>
  </goal>
  <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.120000" steps="38429"/></proof>
  </goal>
  <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.210000" steps="41790"/></proof>
  </goal>
  <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.240000" steps="43956"/></proof>
  </goal>
  <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.120000" steps="41790"/></proof>
  </goal>
  <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.160000" steps="43956"/></proof>
  </goal>
  <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.120000" steps="36941"/></proof>
  </goal>
  <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7" expl="postcondition" proved="true">
  <transf name="destruct_term_subst" proved="true" arg1="t">
   <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.030000" steps="66"/></proof>
   </goal>
   <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.590000" steps="177088"/></proof>
   <transf name="steps" proved="true" arg1="10">
   </transf>
   </goal>
   <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.2" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.570000" steps="177088"/></proof>
   <transf name="steps" proved="true" arg1="10">
   </transf>
   </goal>
   <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.3" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.820000" steps="185780"/></proof>
   </goal>
   <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.4" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.820000" steps="188947"/></proof>
   </goal>
   <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.5" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.050000" steps="57"/></proof>
   </goal>
   <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.6" expl="postcondition" proved="true">
   <transf name="unfold" proved="true" arg1="subst_fo_formula">
    <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.6.0" expl="postcondition" proved="true">
    <proof prover="1"><result status="valid" time="0.030000" steps="18"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.7" expl="postcondition" proved="true">
   <transf name="unfold" proved="true" arg1="subst_fo_formula">
    <goal name="subst_then_rename_composition_lemma_fo_formula&#39;vc.7.7.0" expl="postcondition" proved="true">
    <proof prover="1"><result status="valid" time="0.030000" steps="18"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="subst_composition_lemma_fo_formula&#39;vc" expl="VC for subst_composition_lemma_fo_formula" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="subst_composition_lemma_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.180000" steps="38722"/></proof>
  </goal>
  <goal name="subst_composition_lemma_fo_formula&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.120000" steps="38722"/></proof>
  </goal>
  <goal name="subst_composition_lemma_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.170000" steps="43091"/></proof>
  </goal>
  <goal name="subst_composition_lemma_fo_formula&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.200000" steps="46283"/></proof>
  </goal>
  <goal name="subst_composition_lemma_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.200000" steps="43091"/></proof>
  </goal>
  <goal name="subst_composition_lemma_fo_formula&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.170000" steps="46283"/></proof>
  </goal>
  <goal name="subst_composition_lemma_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.220000" steps="37234"/></proof>
  </goal>
  <goal name="subst_composition_lemma_fo_formula&#39;vc.7" expl="postcondition" proved="true">
  <transf name="destruct_term_subst" proved="true" arg1="t">
   <goal name="subst_composition_lemma_fo_formula&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.780000" steps="172042"/></proof>
   </goal>
   <goal name="subst_composition_lemma_fo_formula&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.610000" steps="184742"/></proof>
   </goal>
   <goal name="subst_composition_lemma_fo_formula&#39;vc.7.2" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.640000" steps="184742"/></proof>
   </goal>
   <goal name="subst_composition_lemma_fo_formula&#39;vc.7.3" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.790000" steps="189275"/></proof>
   </goal>
   <goal name="subst_composition_lemma_fo_formula&#39;vc.7.4" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.802284" steps="190182"/></proof>
   </goal>
   <goal name="subst_composition_lemma_fo_formula&#39;vc.7.5" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.030000" steps="97"/></proof>
   </goal>
   <goal name="subst_composition_lemma_fo_formula&#39;vc.7.6" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.070000" steps="266"/></proof>
   </goal>
   <goal name="subst_composition_lemma_fo_formula&#39;vc.7.7" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.080000" steps="266"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="subst_identity_lemma_fo_formula&#39;vc" expl="VC for subst_identity_lemma_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_identity_lemma_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="subst_identity_lemma_fo_formula&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="23"/></proof>
  </goal>
  <goal name="subst_identity_lemma_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="subst_identity_lemma_fo_formula&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="58"/></proof>
  </goal>
  <goal name="subst_identity_lemma_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="47"/></proof>
  </goal>
  <goal name="subst_identity_lemma_fo_formula&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="58"/></proof>
  </goal>
  <goal name="subst_identity_lemma_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="21"/></proof>
  </goal>
  <goal name="subst_identity_lemma_fo_formula&#39;vc.7" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="subst_identity_lemma_fo_formula&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.240000" steps="74192"/></proof>
   </goal>
   <goal name="subst_identity_lemma_fo_formula&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.260000" steps="74192"/></proof>
   </goal>
   <goal name="subst_identity_lemma_fo_formula&#39;vc.7.2" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.230000" steps="67937"/></proof>
   </goal>
   <goal name="subst_identity_lemma_fo_formula&#39;vc.7.3" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.210000" steps="67937"/></proof>
   </goal>
   <goal name="subst_identity_lemma_fo_formula&#39;vc.7.4" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.200000" steps="67714"/></proof>
   </goal>
   <goal name="subst_identity_lemma_fo_formula&#39;vc.7.5" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.250000" steps="66094"/></proof>
   </goal>
   <goal name="subst_identity_lemma_fo_formula&#39;vc.7.6" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.240000" steps="66094"/></proof>
   </goal>
   <goal name="subst_identity_lemma_fo_formula&#39;vc.7.7" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.280000" steps="68013"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="renaming_preserve_size_fo_formula&#39;vc" expl="VC for renaming_preserve_size_fo_formula" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="renaming_preserve_size_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.180000" steps="38351"/></proof>
  </goal>
  <goal name="renaming_preserve_size_fo_formula&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.150000" steps="38351"/></proof>
  </goal>
  <goal name="renaming_preserve_size_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.140000" steps="39631"/></proof>
  </goal>
  <goal name="renaming_preserve_size_fo_formula&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.210000" steps="37343"/></proof>
  </goal>
  <goal name="renaming_preserve_size_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.150000" steps="39631"/></proof>
  </goal>
  <goal name="renaming_preserve_size_fo_formula&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.170000" steps="37343"/></proof>
  </goal>
  <goal name="renaming_preserve_size_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.140000" steps="36863"/></proof>
  </goal>
  <goal name="renaming_preserve_size_fo_formula&#39;vc.7" expl="postcondition" proved="true">
  <transf name="destruct_term_subst" proved="true" arg1="t">
   <goal name="renaming_preserve_size_fo_formula&#39;vc.7.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.030000" steps="49"/></proof>
   </goal>
   <goal name="renaming_preserve_size_fo_formula&#39;vc.7.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.270000" steps="76819"/></proof>
   </goal>
   <goal name="renaming_preserve_size_fo_formula&#39;vc.7.2" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.280000" steps="76819"/></proof>
   </goal>
   <goal name="renaming_preserve_size_fo_formula&#39;vc.7.3" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.370000" steps="80159"/></proof>
   </goal>
   <goal name="renaming_preserve_size_fo_formula&#39;vc.7.4" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.290000" steps="82239"/></proof>
   </goal>
   <goal name="renaming_preserve_size_fo_formula&#39;vc.7.5" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.390000" steps="82239"/></proof>
   </goal>
   <goal name="renaming_preserve_size_fo_formula&#39;vc.7.6" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.030000" steps="12"/></proof>
   </goal>
   <goal name="renaming_preserve_size_fo_formula&#39;vc.7.7" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.040000" steps="12"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="rename_free_var_constructive_inversion_symbol_fo_formula&#39;vc" expl="VC for rename_free_var_constructive_inversion_symbol_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.108433" steps="1514"/></proof>
 </goal>
 <goal name="rename_free_var_inversion_symbol_fo_formula&#39;vc" expl="VC for rename_free_var_inversion_symbol_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.100000" steps="41"/></proof>
 </goal>
 <goal name="rename_free_var_constructive_inversion_fo_term_fo_formula&#39;vc" expl="VC for rename_free_var_constructive_inversion_fo_term_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.125861" steps="1807"/></proof>
 </goal>
 <goal name="rename_free_var_inversion_fo_term_fo_formula&#39;vc" expl="VC for rename_free_var_inversion_fo_term_fo_formula" proved="true">
 <proof prover="3"><result status="valid" time="0.200000" steps="62974"/></proof>
 </goal>
 <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc" expl="VC for rename_free_var_propagation_symbol_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="50"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="50"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="21"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_symbol_fo_formula&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="615"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc" expl="VC for rename_free_var_propagation_fo_term_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="47"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="50"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="47"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="50"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="21"/></proof>
  </goal>
  <goal name="rename_free_var_propagation_fo_term_fo_formula&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="840"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc" expl="VC for subst_free_var_constructive_inversion_symbol_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="40"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.070000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="295"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.4" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.060000" steps="469"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="639"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.6" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.7" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="12"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="40"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.10" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="295"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.12" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.040000" steps="469"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.13" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="639"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.14" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.15" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="12"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.16" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="78"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.17" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.18" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="276"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.19" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.20" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="245"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.21" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.22" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="89"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.23" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.24" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="316"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.25" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.26" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.130000" steps="285"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.27" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.28" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="55"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.29" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="78"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.30" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.31" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="277"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.32" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.33" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="246"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.34" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.35" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="89"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.36" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.070000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.37" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="317"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.38" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.39" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.140000" steps="286"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.40" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.41" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="55"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.42" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="33"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.43" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.070000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.44" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="216"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.45" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.46" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="185"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.47" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.48" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="12"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.49" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="29"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.50" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="29"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.51" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.52" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="18"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.53" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="22"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.54" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.55" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="317"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.56" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.57" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="283"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.58" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.59" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="55"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_symbol_fo_formula&#39;vc.60" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="1.986944" steps="16984"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_free_var_inversion_symbol_fo_formula&#39;vc" expl="VC for subst_free_var_inversion_symbol_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.120000" steps="111"/></proof>
 </goal>
 <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc" expl="VC for subst_free_var_constructive_inversion_fo_term_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="43"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.2" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="183"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="90"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.4" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="255"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.5" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="12"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="43"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.7" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.8" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="183"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.140000" steps="90"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="255"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.11" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="12"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.12" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="78"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.13" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.14" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="18"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="22"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.16" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="89"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.17" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.18" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="20"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.19" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="24"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.20" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="55"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.21" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="78"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.22" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.23" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="18"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.24" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="22"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.25" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="89"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.26" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.27" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="20"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.28" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.500000"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.29" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.130000" steps="55"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.30" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="33"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.31" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.32" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="18"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.33" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="22"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.34" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="12"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.35" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="29"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.36" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="29"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.37" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.38" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="18"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.39" expl="assertion" proved="true">
  <proof prover="8"><result status="valid" time="0.540000"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.40" expl="unreachable point" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="43"/></proof>
  </goal>
  <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="369"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_free_var_inversion_fo_term_fo_formula&#39;vc" expl="VC for subst_free_var_inversion_fo_term_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.110000" steps="38"/></proof>
 </goal>
 <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc" expl="VC for subst_free_var_propagation_symbol_symbol_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="53"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="47"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.9" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="53"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.12" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.13" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.14" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_symbol_symbol_fo_formula&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.170000" steps="773"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc" expl="VC for subst_free_var_propagation_fo_term_symbol_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="61"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="61"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="52"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.020000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="47"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.9" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="52"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.12" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.13" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.14" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.130000" steps="778"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc" expl="VC for subst_free_var_propagation_fo_term_fo_term_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="67"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="23"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.3" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="67"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="52"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.7" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="47"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.9" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.10" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.120000" steps="52"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.12" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.13" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.14" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.140000" steps="813"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc" expl="VC for free_var_equivalence_of_subst_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.0" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="43"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.4" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="201"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.5" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.6" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="23"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.8" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="43"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="201"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.12" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.13" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="43"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.14" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="45"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.16" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.090000" steps="14"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.17" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="79"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.18" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="59"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.19" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="59"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.20" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.21" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.22" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="47"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.23" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="43"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.24" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="45"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.25" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.26" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.27" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="79"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.28" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="59"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.29" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="59"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.30" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.31" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.32" expl="variant decrease" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="21"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.33" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="39"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.34" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="41"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.35" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="12"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.36" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.060000" steps="43"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.37" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.38" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="14"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.39" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.110000" steps="53"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.40" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.080000" steps="59"/></proof>
  </goal>
  <goal name="free_var_equivalence_of_subst_fo_formula&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.100000" steps="292"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="free_var_equivalence_of_rename_fo_formula&#39;vc" expl="VC for free_var_equivalence_of_rename_fo_formula" proved="true">
 <proof prover="1"><result status="valid" time="0.050000" steps="94"/></proof>
 </goal>
 <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.090000" steps="25"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.090000" steps="58"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="134"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3.0" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="61"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3.1" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="14"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3.2" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="61"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3.3" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.050000" steps="246"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3.4" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="18"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3.5" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.060000" steps="246"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3.6" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.070000" steps="23"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.3.7" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="2"><result status="valid" time="1.240000"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="25"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.5" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.100000" steps="58"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.6" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.140000" steps="134"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7.0" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="61"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7.1" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="14"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7.2" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="61"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7.3" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.070000" steps="246"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7.4" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="18"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7.5" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.070000" steps="246"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7.6" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="23"/></proof>
   </goal>
   <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.7.7" expl="VC for free_var_derive_equivalence_of_subst_fo_formula" proved="true">
   <proof prover="2"><result status="valid" time="1.270000"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="55"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.9" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.060000" steps="54"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.10" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="264"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.11" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="272"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.12" expl="variant decrease" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="55"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.13" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="54"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.14" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.050000" steps="268"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.060000" steps="275"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.16" expl="variant decrease" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="55"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.17" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.070000" steps="54"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.18" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.040000" steps="265"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.19" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="274"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.20" expl="variant decrease" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="55"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.21" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.110000" steps="54"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.22" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.060000" steps="269"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.23" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="276"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.24" expl="variant decrease" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.060000" steps="23"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.25" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.090000" steps="46"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.26" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.040000" steps="126"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.27" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.140000" steps="139"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.28" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.140000" steps="53"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.29" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.110000" steps="346"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.30" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.100000" steps="50"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.31" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.060000" steps="245"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.32" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.030000" steps="255"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.33" expl="postcondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.090000" steps="217"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula&#39;vc.34" expl="postcondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.070000" steps="248"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="free_var_derive_equivalence_of_rename_fo_formula&#39;vc" expl="VC for free_var_derive_equivalence_of_rename_fo_formula" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="free_var_derive_equivalence_of_rename_fo_formula&#39;vc.0" expl="precondition" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.050000" steps="10"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_rename_fo_formula&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.100000" steps="35"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_rename_fo_formula&#39;vc.2" expl="assertion" proved="true">
  <proof prover="1" timelimit="5"><result status="valid" time="0.080000" steps="59"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_rename_fo_formula&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.580000"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_rename_fo_formula&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="8"><result status="valid" time="0.530000"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
