<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<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_symbol_spec.mlw"/>
<theory name="Spec" proved="true">
 <goal name="size_positive_lemma_symbol&#39;vc" expl="VC for size_positive_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.01"/></proof>
 <proof prover="1"><result status="valid" time="0.02"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="5"/></proof>
 </goal>
 <goal name="renaming_composition_lemma_symbol&#39;vc" expl="VC for renaming_composition_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.04"/></proof>
 <proof prover="1"><result status="valid" time="0.07"/></proof>
 <proof prover="2"><result status="valid" time="0.01" steps="10"/></proof>
 </goal>
 <goal name="renaming_identity_lemma_symbol&#39;vc" expl="VC for renaming_identity_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.02"/></proof>
 <proof prover="1"><result status="valid" time="0.03"/></proof>
 <proof prover="2"><result status="valid" time="0.01" steps="9"/></proof>
 </goal>
 <goal name="associativity_subst_rename_rename_lemma_symbol&#39;vc" expl="VC for associativity_subst_rename_rename_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="22"/></proof>
 </goal>
 <goal name="associativity_rename_subst_rename_lemma_symbol&#39;vc" expl="VC for associativity_rename_subst_rename_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="21"/></proof>
 </goal>
 <goal name="right_rename_subst_by_identity_lemma_symbol&#39;vc" expl="VC for right_rename_subst_by_identity_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.38"/></proof>
 <proof prover="1"><result status="valid" time="0.06"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="35"/></proof>
 </goal>
 <goal name="olifts_composition_lemma_rename_subst_symbol&#39;vc" expl="VC for olifts_composition_lemma_rename_subst_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.14" steps="379"/></proof>
 </goal>
 <goal name="olifts_composition_lemma_subst_rename_symbol&#39;vc" expl="VC for olifts_composition_lemma_subst_rename_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.14" steps="228"/></proof>
 </goal>
 <goal name="rename_then_subst_composition_lemma_symbol&#39;vc" expl="VC for rename_then_subst_composition_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.10"/></proof>
 <proof prover="1"><result status="valid" time="0.08"/></proof>
 <proof prover="2"><result status="valid" time="0.01" steps="10"/></proof>
 </goal>
 <goal name="subst_then_rename_composition_lemma_symbol&#39;vc" expl="VC for subst_then_rename_composition_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.10"/></proof>
 <proof prover="1"><result status="valid" time="0.09"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="10"/></proof>
 </goal>
 <goal name="associativity_rename_subst_subst_lemma_symbol&#39;vc" expl="VC for associativity_rename_subst_subst_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="21"/></proof>
 </goal>
 <goal name="associativity_subst_rename_subst_lemma_symbol&#39;vc" expl="VC for associativity_subst_rename_subst_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="22"/></proof>
 </goal>
 <goal name="associativity_subst_subst_rename_lemma_symbol&#39;vc" expl="VC for associativity_subst_subst_rename_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="22"/></proof>
 </goal>
 <goal name="olifts_composition_lemma_subst_subst_symbol&#39;vc" expl="VC for olifts_composition_lemma_subst_subst_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.12" steps="401"/></proof>
 </goal>
 <goal name="subst_composition_lemma_symbol&#39;vc" expl="VC for subst_composition_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.18"/></proof>
 <proof prover="1"><result status="valid" time="0.09"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="10"/></proof>
 </goal>
 <goal name="associativity_subst_subst_subst_lemma_symbol&#39;vc" expl="VC for associativity_subst_subst_subst_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.02" steps="22"/></proof>
 </goal>
 <goal name="olifts_identity_symbol&#39;vc" expl="VC for olifts_identity_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.28" steps="553"/></proof>
 </goal>
 <goal name="left_rename_subst_identity_lemma_symbol&#39;vc" expl="VC for left_rename_subst_identity_lemma_symbol" proved="true">
 <proof prover="2"><result status="valid" time="0.03" steps="43"/></proof>
 </goal>
 <goal name="subst_identity_lemma_symbol&#39;vc" expl="VC for subst_identity_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.06"/></proof>
 <proof prover="1"><result status="valid" time="0.04"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="5"/></proof>
 </goal>
 <goal name="left_subst_subst_identity_lemma_symbol&#39;vc" expl="VC for left_subst_subst_identity_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="2.23"/></proof>
 <proof prover="1"><result status="valid" time="0.56"/></proof>
 <proof prover="2"><result status="valid" time="0.03" steps="31"/></proof>
 </goal>
 <goal name="right_subst_subst_by_identity_lemma_symbol&#39;vc" expl="VC for right_subst_subst_by_identity_lemma_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.63"/></proof>
 <proof prover="1"><result status="valid" time="0.14"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="31"/></proof>
 </goal>
 <goal name="renaming_preserve_size_symbol&#39;vc" expl="VC for renaming_preserve_size_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.06"/></proof>
 <proof prover="1"><result status="valid" time="0.04"/></proof>
 <proof prover="2"><result status="valid" time="0.01" steps="5"/></proof>
 </goal>
 <goal name="rename_free_var_constructive_inversion_symbol_symbol&#39;vc" expl="VC for rename_free_var_constructive_inversion_symbol_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.04"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="36"/></proof>
 </goal>
 <goal name="rename_free_var_inversion_symbol_symbol&#39;vc" expl="VC for rename_free_var_inversion_symbol_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.06"/></proof>
 <proof prover="1"><result status="valid" time="0.07"/></proof>
 <proof prover="2"><result status="valid" time="0.01" steps="10"/></proof>
 </goal>
 <goal name="rename_free_var_propagation_symbol_symbol&#39;vc" expl="VC for rename_free_var_propagation_symbol_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.03"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="15"/></proof>
 </goal>
 <goal name="subst_free_var_constructive_inversion_symbol_symbol&#39;vc" expl="VC for subst_free_var_constructive_inversion_symbol_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.07"/></proof>
 <proof prover="2"><result status="valid" time="0.01" steps="23"/></proof>
 </goal>
 <goal name="subst_free_var_inversion_symbol_symbol&#39;vc" expl="VC for subst_free_var_inversion_symbol_symbol" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="subst_free_var_inversion_symbol_symbol&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.07"/></proof>
  <proof prover="1"><result status="valid" time="0.06"/></proof>
  <proof prover="2"><result status="valid" time="0.02" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_inversion_symbol_symbol&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.06"/></proof>
  <proof prover="2"><result status="valid" time="0.02" steps="4"/></proof>
  </goal>
  <goal name="subst_free_var_inversion_symbol_symbol&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.06"/></proof>
  <proof prover="7"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="subst_free_var_propagation_symbol_symbol_symbol&#39;vc" expl="VC for subst_free_var_propagation_symbol_symbol_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.06"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="16"/></proof>
 </goal>
 <goal name="free_var_equivalence_of_subst_symbol&#39;vc" expl="VC for free_var_equivalence_of_subst_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.05"/></proof>
 <proof prover="1"><result status="valid" time="0.05"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="24"/></proof>
 </goal>
 <goal name="free_var_equivalence_of_rename_symbol&#39;vc" expl="VC for free_var_equivalence_of_rename_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.11"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="116"/></proof>
 </goal>
 <goal name="free_var_derive_equivalence_of_subst_symbol&#39;vc" expl="VC for free_var_derive_equivalence_of_subst_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.04"/></proof>
 <proof prover="1"><result status="valid" time="0.07"/></proof>
 <proof prover="2"><result status="valid" time="0.02" steps="7"/></proof>
 </goal>
 <goal name="free_var_derive_equivalence_of_rename_symbol&#39;vc" expl="VC for free_var_derive_equivalence_of_rename_symbol" proved="true">
 <proof prover="0"><result status="valid" time="0.15"/></proof>
 <proof prover="2"><result status="valid" time="0.03" steps="125"/></proof>
 </goal>
</theory>
</file>
</why3session>
