<?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="3" name="Alt-Ergo" version="2.1.0" 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="0.010000"/></proof>
 <proof prover="1"><result status="valid" time="0.020000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="8"/></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="0.040000"/></proof>
 <proof prover="1"><result status="valid" time="0.070000"/></proof>
 <proof prover="3"><result status="valid" time="0.010000" steps="27"/></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="0.020000"/></proof>
 <proof prover="1"><result status="valid" time="0.030000"/></proof>
 <proof prover="3"><result status="valid" time="0.010000" steps="25"/></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="3"><result status="valid" time="0.020000" steps="67"/></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="3"><result status="valid" time="0.020000" steps="65"/></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="0.380000"/></proof>
 <proof prover="1"><result status="valid" time="0.060000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="94"/></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="3"><result status="valid" time="0.140000" steps="848"/></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="3"><result status="valid" time="0.140000" steps="896"/></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="0.100000"/></proof>
 <proof prover="1"><result status="valid" time="0.080000"/></proof>
 <proof prover="3"><result status="valid" time="0.010000" steps="27"/></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="0.100000"/></proof>
 <proof prover="1"><result status="valid" time="0.090000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="27"/></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="3"><result status="valid" time="0.020000" steps="65"/></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="3"><result status="valid" time="0.020000" steps="67"/></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="3"><result status="valid" time="0.020000" steps="67"/></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="3"><result status="valid" time="0.120000" steps="758"/></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="0.180000"/></proof>
 <proof prover="1"><result status="valid" time="0.090000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="27"/></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="3"><result status="valid" time="0.020000" steps="67"/></proof>
 </goal>
 <goal name="olifts_identity_symbol&#39;vc" expl="VC for olifts_identity_symbol" proved="true">
 <proof prover="3"><result status="valid" time="4.380000" steps="3490"/></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="3"><result status="valid" time="0.030000" steps="117"/></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="0.060000"/></proof>
 <proof prover="1"><result status="valid" time="0.040000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="8"/></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="2.230000"/></proof>
 <proof prover="1"><result status="valid" time="0.560000"/></proof>
 <proof prover="3"><result status="valid" time="0.030000" steps="87"/></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="0.630000"/></proof>
 <proof prover="1"><result status="valid" time="0.140000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="87"/></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="0.060000"/></proof>
 <proof prover="1"><result status="valid" time="0.040000"/></proof>
 <proof prover="3"><result status="valid" time="0.010000" steps="29"/></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="0.040000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="60"/></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="0.060000"/></proof>
 <proof prover="1"><result status="valid" time="0.070000"/></proof>
 <proof prover="3"><result status="valid" time="0.010000" steps="50"/></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="0.030000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="37"/></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="0.070000"/></proof>
 <proof prover="3"><result status="valid" time="0.010000" steps="58"/></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="0.070000"/></proof>
  <proof prover="1"><result status="valid" time="0.060000"/></proof>
  <proof prover="3"><result status="valid" time="0.020000" steps="10"/></proof>
  </goal>
  <goal name="subst_free_var_inversion_symbol_symbol&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.060000"/></proof>
  <proof prover="3"><result status="valid" time="0.020000" steps="6"/></proof>
  </goal>
  <goal name="subst_free_var_inversion_symbol_symbol&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.060000"/></proof>
  <proof prover="7"><result status="valid" time="0.020000"/></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="0.060000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="39"/></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="0.050000"/></proof>
 <proof prover="1"><result status="valid" time="0.050000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="82"/></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="0.110000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="133"/></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="0.040000"/></proof>
 <proof prover="1"><result status="valid" time="0.070000"/></proof>
 <proof prover="3"><result status="valid" time="0.020000" steps="33"/></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="0.150000"/></proof>
 <proof prover="3"><result status="valid" time="0.030000" steps="383"/></proof>
 </goal>
</theory>
</file>
</why3session>
