<?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="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.4.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="7" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="Firstorder_formula_list_impl.mlw"/>
<theory name="Logic" proved="true">
 <goal name="nlsize_positive_lemma_fo_formula_list&#39;vc" expl="VC for nlsize_positive_lemma_fo_formula_list" proved="true">
 <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="483"/></proof>
 </goal>
 <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc" expl="VC for nlmodel_subst_commutation_lemma_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="53"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.029197" steps="57"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="62"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="67"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="426"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="11"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.6" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.130000" steps="11"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.7" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="11"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.8" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="11"/></proof>
  </goal>
  <goal name="nlmodel_subst_commutation_lemma_fo_formula_list&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="684"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="nlmodel_rename_commutation_lemma_fo_formula_list&#39;vc" expl="VC for nlmodel_rename_commutation_lemma_fo_formula_list" proved="true">
 <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="70"/></proof>
 </goal>
 <goal name="bound_depth_of_symbol_in_fo_formula_list_nonnegative&#39;vc" expl="VC for bound_depth_of_symbol_in_fo_formula_list_nonnegative" proved="true">
 <proof prover="2"><result status="valid" time="0.130000" steps="255"/></proof>
 </goal>
 <goal name="bound_depth_of_fo_term_in_fo_formula_list_nonnegative&#39;vc" expl="VC for bound_depth_of_fo_term_in_fo_formula_list_nonnegative" proved="true">
 <proof prover="2" timelimit="1"><result status="valid" time="0.140000" steps="300"/></proof>
 </goal>
 <goal name="model_equal_fo_formula_list&#39;vc" expl="VC for model_equal_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="model_equal_fo_formula_list&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.035647" steps="196"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.025147" steps="14"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.100000" steps="231"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.021891" steps="15"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.027086" steps="32"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.035905" steps="183"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.038403" steps="221"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.024680" steps="17"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.034008" steps="217"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.022659" steps="17"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.024128" steps="41"/></proof>
  </goal>
  <goal name="model_equal_fo_formula_list&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.032411" steps="131"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Impl" proved="true">
 <goal name="bind_var_symbol_in_fo_formula_list&#39;vc" expl="VC for bind_var_symbol_in_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.024061" steps="37"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.026096" steps="77"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.024692" steps="41"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.026008" steps="18"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.4" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="18"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="18"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.030023" steps="200"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="41"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="88"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="71"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="153"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="2026"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="1023"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.308711" steps="2751"/></proof>
  </goal>
  <goal name="bind_var_symbol_in_fo_formula_list&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="1580"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc" expl="VC for bind_var_fo_term_in_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="36"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="76"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="41"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="18"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.4" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="18"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="18"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.140000" steps="169"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.024442" steps="41"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.022914" steps="90"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.026854" steps="70"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="156"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="1397"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="722"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="1770"/></proof>
  </goal>
  <goal name="bind_var_fo_term_in_fo_formula_list&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="1090"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc" expl="VC for unbind_var_symbol_in_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="40"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="89"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.024361" steps="51"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.021496" steps="24"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.4" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="24"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.026301" steps="24"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.130000" steps="232"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="24"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="47"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030588" steps="105"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.019398" steps="24"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.11" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.023421" steps="24"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.12" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="36"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.13" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="71"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.14" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.070000" steps="164"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.15" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.020476" steps="36"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.027292" steps="36"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.17" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="2204"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.170000" steps="2486"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.291406" steps="2620"/></proof>
  </goal>
  <goal name="unbind_var_symbol_in_fo_formula_list&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="1819"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc" expl="VC for unbind_var_fo_term_in_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="42"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="84"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="53"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="26"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.4" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="26"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="26"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="195"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="26"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.140000" steps="50"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="104"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="26"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.11" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="26"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.12" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="26"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.13" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.024861" steps="38"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.14" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.140000" steps="72"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.15" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="166"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.025179" steps="38"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.17" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="38"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.18" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="38"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.19" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="1593"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.20" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="1836"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.21" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.254870" steps="2255"/></proof>
  </goal>
  <goal name="unbind_var_fo_term_in_fo_formula_list&#39;vc.22" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="1260"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_base_symbol_in_fo_formula_list&#39;vc" expl="VC for subst_base_symbol_in_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.024459" steps="35"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.030493" steps="84"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="42"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="20"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.4" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="20"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.021630" steps="20"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.026304" steps="217"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="43"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.026427" steps="22"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="22"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.090000" steps="64"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.11" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="30"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.12" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.028992" steps="30"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="2028"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.277687" steps="2649"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.306767" steps="3011"/></proof>
  </goal>
  <goal name="subst_base_symbol_in_fo_formula_list&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.205807" steps="1723"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc" expl="VC for subst_base_fo_term_in_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.033368" steps="38"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.031855" steps="78"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="43"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="22"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.4" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.024894" steps="22"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.028881" steps="22"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.028537" steps="174"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.026439" steps="45"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.023779" steps="24"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="24"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.025285" steps="24"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.11" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.028424" steps="66"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.12" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.017849" steps="32"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.13" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="32"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.14" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="32"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="1798"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.170000" steps="1817"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.17" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.160000" steps="1997"/></proof>
  </goal>
  <goal name="subst_base_fo_term_in_fo_formula_list&#39;vc.18" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.170000" steps="1187"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="construct_fo_formula_list&#39;vc" expl="VC for construct_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="construct_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="25"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.016961" steps="25"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="53"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.3" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="73"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.023515" steps="23"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="25"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.6" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="175"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.7" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.150000" steps="174"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.8" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.130000" steps="159"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.9" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.060000" steps="156"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.10" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="42"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.11" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.080000" steps="51"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.12" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.028894" steps="47"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.13" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.022032" steps="9"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.14" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.022692" steps="49"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.15" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.260000" steps="85956"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.022745" steps="16"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.17" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="9"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.18" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="16"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.120000" steps="9"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.20" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="50"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.21" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="26"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.22" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.080000" steps="9"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.23" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.022695" steps="26"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.24" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.130000" steps="85956"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.25" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="16"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.26" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.017018" steps="9"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.27" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="16"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.28" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="9"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.29" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.029952" steps="50"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.741080" steps="7759"/></proof>
  </goal>
  <goal name="construct_fo_formula_list&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="495"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="destruct_fo_formula_list&#39;vc" expl="VC for destruct_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="destruct_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.033867" steps="71"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.1" expl="unreachable point" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.140000" steps="38"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.031500" steps="45"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.3" expl="unreachable point" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="51"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.4" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="50"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.140000" steps="52"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.6" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.100000" steps="125"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.7" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="301"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.8" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.080000" steps="141"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.9" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.042503" steps="361"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.10" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.034044" steps="72"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.11" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="373"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.12" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="73"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.13" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="377"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.14" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.025035" steps="26"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.15" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="69"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.026012" steps="28"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.17" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="71"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.18" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.140000" steps="76"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.19" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="28"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="72"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.21" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="30"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.22" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="74"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.23" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="78"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.24" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="84"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.25" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="84"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.26" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.030433" steps="90"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.27" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.028593" steps="91"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.28" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.130000" steps="1156"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.29" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.180000" steps="1163"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.30" expl="assertion" proved="true">
  <proof prover="2"><result status="valid" time="0.090000" steps="1137"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.31" expl="assertion" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.090000" steps="1132"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.844051" steps="9408"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.33" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.170000" steps="1855"/></proof>
  </goal>
  <goal name="destruct_fo_formula_list&#39;vc.34" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.668134" steps="7439"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc" expl="VC for nlsubst_symbol_in_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.033830" steps="32"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="25"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.150000" steps="47"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.060000" steps="35"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.040000" steps="40"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.022964" steps="24"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.027985" steps="35"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.050000" steps="36"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.024125" steps="43"/></proof>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.9" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.9.0" expl="assertion" proved="true">
   <proof prover="2" timelimit="1"><result status="valid" time="0.140000" steps="257"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.9.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.067261" steps="785"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.9.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.060000" steps="264"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.9.3" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.420000" steps="171758"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.9.4" expl="assertion" proved="true">
   <proof prover="1"><result status="valid" time="0.760000" steps="186378"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.9.5" expl="assertion" proved="true">
   <proof prover="2" timelimit="1"><result status="valid" time="0.311609" steps="3568"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.10" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.10.0" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.080000" steps="223"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.10.1" expl="assertion" proved="true">
   <proof prover="5" timelimit="30"><result status="valid" time="0.340000"/></proof>
   </goal>
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.10.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.150000" steps="217"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.11" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.11.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.516764" steps="6078"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_symbol_in_fo_formula_list&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.370000" steps="187076"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc" expl="VC for nlsubst_fo_term_in_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.0" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="32"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.1" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="26"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="49"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.3" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.100000" steps="39"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.140000" steps="41"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.5" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.5.0" expl="VC for nlsubst_fo_term_in_fo_formula_list" proved="true">
   <proof prover="6"><result status="valid" time="0.350000"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.5.1" expl="VC for nlsubst_fo_term_in_fo_formula_list" proved="true">
   <proof prover="2"><result status="valid" time="0.060000" steps="20"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="26"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="39"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.8" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.130000" steps="40"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.9" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.120000" steps="47"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.10" expl="precondition" proved="true">
  <proof prover="2" timelimit="1"><result status="valid" time="0.110000" steps="50"/></proof>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.11" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.11.0" expl="assertion" proved="true">
   <proof prover="7"><result status="valid" time="0.380000"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.11.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.045304" steps="268"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.11.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.080000" steps="258"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.11.3" expl="assertion" proved="true">
   <proof prover="2" timelimit="1"><result status="valid" time="0.170000" steps="512"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.11.4" expl="assertion" proved="true">
   <proof prover="6"><result status="valid" time="0.410000"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.11.5" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.120000" steps="970"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.12" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.12.0" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.031858" steps="267"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.12.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.170000" steps="580"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.12.2" expl="assertion" proved="true">
   <proof prover="5"><result status="valid" time="0.440000"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.12.3" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.026160" steps="52"/></proof>
   </goal>
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.12.4" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.070000" steps="223"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.13" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.13.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.350308" steps="3989"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="nlsubst_fo_term_in_fo_formula_list&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.350000" steps="186499"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
