<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="Firstorder_formula_list_spec.mlw"/>
<theory name="Spec" proved="true">
 <goal name="size_positive_lemma_fo_formula_list&#39;vc" expl="VC for size_positive_lemma_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.10" steps="92"/></proof>
 </goal>
 <goal name="renaming_composition_lemma_fo_formula_list&#39;vc" expl="VC for renaming_composition_lemma_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.07" steps="98"/></proof>
 </goal>
 <goal name="renaming_identity_lemma_fo_formula_list&#39;vc" expl="VC for renaming_identity_lemma_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.07" steps="114"/></proof>
 </goal>
 <goal name="rename_then_subst_composition_lemma_fo_formula_list&#39;vc" expl="VC for rename_then_subst_composition_lemma_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.07" steps="269"/></proof>
 </goal>
 <goal name="subst_then_rename_composition_lemma_fo_formula_list&#39;vc" expl="VC for subst_then_rename_composition_lemma_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.12" steps="271"/></proof>
 </goal>
 <goal name="subst_composition_lemma_fo_formula_list&#39;vc" expl="VC for subst_composition_lemma_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_composition_lemma_fo_formula_list&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.06" steps="35"/></proof>
  </goal>
  <goal name="subst_composition_lemma_fo_formula_list&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.06" steps="66"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_identity_lemma_fo_formula_list&#39;vc" expl="VC for subst_identity_lemma_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.11" steps="119"/></proof>
 </goal>
 <goal name="renaming_preserve_size_fo_formula_list&#39;vc" expl="VC for renaming_preserve_size_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.07" steps="87"/></proof>
 </goal>
 <goal name="rename_free_var_constructive_inversion_symbol_fo_formula_list&#39;vc" expl="VC for rename_free_var_constructive_inversion_symbol_fo_formula_list" proved="true">
 <proof prover="0"><result status="valid" time="0.12" steps="205"/></proof>
 </goal>
 <goal name="rename_free_var_inversion_symbol_fo_formula_list&#39;vc" expl="VC for rename_free_var_inversion_symbol_fo_formula_list" proved="true">
 <proof prover="0"><result status="valid" time="0.08" steps="10"/></proof>
 </goal>
 <goal name="rename_free_var_constructive_inversion_fo_term_fo_formula_list&#39;vc" expl="VC for rename_free_var_constructive_inversion_fo_term_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.09" steps="205"/></proof>
 </goal>
 <goal name="rename_free_var_inversion_fo_term_fo_formula_list&#39;vc" expl="VC for rename_free_var_inversion_fo_term_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.06" steps="10"/></proof>
 </goal>
 <goal name="rename_free_var_propagation_symbol_fo_formula_list&#39;vc" expl="VC for rename_free_var_propagation_symbol_fo_formula_list" proved="true">
 <proof prover="0"><result status="valid" time="0.14" steps="213"/></proof>
 </goal>
 <goal name="rename_free_var_propagation_fo_term_fo_formula_list&#39;vc" expl="VC for rename_free_var_propagation_fo_term_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.11" steps="213"/></proof>
 </goal>
 <goal name="subst_free_var_constructive_inversion_symbol_fo_formula_list&#39;vc" expl="VC for subst_free_var_constructive_inversion_symbol_fo_formula_list" proved="true">
 <proof prover="0"><result status="valid" time="0.34" steps="1894"/></proof>
 </goal>
 <goal name="subst_free_var_inversion_symbol_fo_formula_list&#39;vc" expl="VC for subst_free_var_inversion_symbol_fo_formula_list" proved="true">
 <proof prover="0"><result status="valid" time="0.09" steps="26"/></proof>
 </goal>
 <goal name="subst_free_var_constructive_inversion_fo_term_fo_formula_list&#39;vc" expl="VC for subst_free_var_constructive_inversion_fo_term_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.14" steps="645"/></proof>
 </goal>
 <goal name="subst_free_var_inversion_fo_term_fo_formula_list&#39;vc" expl="VC for subst_free_var_inversion_fo_term_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.07" steps="10"/></proof>
 </goal>
 <goal name="subst_free_var_propagation_symbol_symbol_fo_formula_list&#39;vc" expl="VC for subst_free_var_propagation_symbol_symbol_fo_formula_list" proved="true">
 <proof prover="0"><result status="valid" time="0.26" steps="796"/></proof>
 </goal>
 <goal name="subst_free_var_propagation_fo_term_symbol_fo_formula_list&#39;vc" expl="VC for subst_free_var_propagation_fo_term_symbol_fo_formula_list" proved="true">
 <proof prover="0"><result status="valid" time="0.10" steps="578"/></proof>
 </goal>
 <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula_list&#39;vc" expl="VC for subst_free_var_propagation_fo_term_fo_term_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula_list&#39;vc.0" expl="assertion" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.04" steps="8"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula_list&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.05" steps="21"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.05" steps="8"/></proof>
  </goal>
  <goal name="subst_free_var_propagation_fo_term_fo_term_fo_formula_list&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="0" timelimit="1"><result status="valid" time="0.05" steps="268"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="free_var_equivalence_of_subst_fo_formula_list&#39;vc" expl="VC for free_var_equivalence_of_subst_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.11" steps="656"/></proof>
 </goal>
 <goal name="free_var_equivalence_of_rename_fo_formula_list&#39;vc" expl="VC for free_var_equivalence_of_rename_fo_formula_list" proved="true">
 <proof prover="0" timelimit="1"><result status="valid" time="0.08" steps="116"/></proof>
 </goal>
 <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc" expl="VC for free_var_derive_equivalence_of_subst_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.0" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.10" steps="75"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.08" steps="108"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.06" steps="118"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.08" steps="23"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.07" steps="58"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.5" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="107"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.6" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="117"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.09" steps="39"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_subst_fo_formula_list&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.10" steps="39"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="free_var_derive_equivalence_of_rename_fo_formula_list&#39;vc" expl="VC for free_var_derive_equivalence_of_rename_fo_formula_list" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="free_var_derive_equivalence_of_rename_fo_formula_list&#39;vc.0" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.08" steps="6"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_rename_fo_formula_list&#39;vc.1" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.09" steps="22"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_rename_fo_formula_list&#39;vc.2" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.10" steps="31"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_rename_fo_formula_list&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.74"/></proof>
  </goal>
  <goal name="free_var_derive_equivalence_of_rename_fo_formula_list&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.74"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
