<?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="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="vstte12_combinators.mlw"/>
<theory name="Combinators" proved="true">
 <goal name="eq&#39;vc" expl="VC for eq" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="51"/></proof>
 </goal>
 <goal name="subst_c&#39;vc" expl="VC for subst_c" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="78"/></proof>
 </goal>
 <goal name="subst_c_commute" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="subst_c_commute.0" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="46"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="reduction&#39;vc" expl="VC for reduction" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="reduction&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
  <goal name="reduction&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
  <goal name="reduction&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.00" steps="15"/></proof>
  </goal>
  <goal name="reduction&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
  <goal name="reduction&#39;vc.4" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="reduction&#39;vc.5" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="19"/></proof>
  </goal>
  <goal name="reduction&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.23" steps="732"/></proof>
  </goal>
  <goal name="reduction&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="reduction&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.22" steps="724"/></proof>
  </goal>
  <goal name="reduction&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="reduction&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.15" steps="674"/></proof>
  </goal>
  <goal name="reduction&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="89"/></proof>
  </goal>
  <goal name="reduction&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.90"/></proof>
  </goal>
  <goal name="reduction&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="73"/></proof>
  </goal>
  <goal name="reduction&#39;vc.14" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="21"/></proof>
  </goal>
  <goal name="reduction&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.20"/></proof>
  </goal>
  <goal name="reduction&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="reduction&#39;vc.17" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="267"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="test_SKK&#39;vc" expl="VC for test_SKK" proved="true">
 <proof prover="0"><result status="valid" time="0.00" steps="12"/></proof>
 </goal>
 <goal name="reduce_step&#39;vc" expl="VC for reduce_step" proved="true">
 <proof prover="0"><result status="valid" time="0.08" steps="742"/></proof>
 </goal>
 <goal name="value_in_context&#39;vc" expl="VC for value_in_context" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="value_in_context&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="2" timelimit="5"><result status="valid" time="0.02" steps="6128"/></proof>
  </goal>
  <goal name="value_in_context&#39;vc.1" expl="precondition" proved="true">
  <transf name="destruct_term_subst" proved="true" arg1="(subst x1 t)">
   <goal name="value_in_context&#39;vc.1.0" expl="precondition" proved="true">
   <transf name="destruct_term_subst" proved="true" arg1="x2">
    <goal name="value_in_context&#39;vc.1.0.0" expl="precondition" proved="true">
    <proof prover="3"><result status="valid" time="0.04" steps="6186"/></proof>
    </goal>
    <goal name="value_in_context&#39;vc.1.0.1" expl="precondition" proved="true">
    <proof prover="3"><result status="valid" time="0.03" steps="6084"/></proof>
    </goal>
    <goal name="value_in_context&#39;vc.1.0.2" expl="precondition" proved="true">
    <proof prover="3"><result status="valid" time="0.04" steps="6094"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="value_in_context&#39;vc.1.1" expl="precondition" proved="true">
   <proof prover="3"><result status="valid" time="0.02" steps="5640"/></proof>
   </goal>
   <goal name="value_in_context&#39;vc.1.2" expl="precondition" proved="true">
   <proof prover="3"><result status="valid" time="0.03" steps="5654"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="value_in_context&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="2" timelimit="5"><result status="valid" time="0.03" steps="6088"/></proof>
  </goal>
  <goal name="value_in_context&#39;vc.3" expl="precondition" proved="true">
  <transf name="destruct_term_subst" proved="true" arg1="(subst x t)">
   <goal name="value_in_context&#39;vc.3.0" expl="precondition" proved="true">
   <transf name="destruct_term_subst" proved="true" arg1="x3">
    <goal name="value_in_context&#39;vc.3.0.0" expl="precondition" proved="true">
    <transf name="destruct_term_subst" proved="true" arg1="x4">
     <goal name="value_in_context&#39;vc.3.0.0.0" expl="precondition" proved="true">
     <proof prover="3"><result status="valid" time="0.04" steps="6307"/></proof>
     </goal>
     <goal name="value_in_context&#39;vc.3.0.0.1" expl="precondition" proved="true">
     <proof prover="3"><result status="valid" time="0.04" steps="6199"/></proof>
     </goal>
     <goal name="value_in_context&#39;vc.3.0.0.2" expl="precondition" proved="true">
     <proof prover="3"><result status="valid" time="0.03" steps="6207"/></proof>
     </goal>
    </transf>
    </goal>
    <goal name="value_in_context&#39;vc.3.0.1" expl="precondition" proved="true">
    <proof prover="3"><result status="valid" time="0.03" steps="6062"/></proof>
    </goal>
    <goal name="value_in_context&#39;vc.3.0.2" expl="precondition" proved="true">
    <proof prover="3"><result status="valid" time="0.03" steps="6062"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="value_in_context&#39;vc.3.1" expl="precondition" proved="true">
   <proof prover="3"><result status="valid" time="0.02" steps="5640"/></proof>
   </goal>
   <goal name="value_in_context&#39;vc.3.2" expl="precondition" proved="true">
   <proof prover="3"><result status="valid" time="0.03" steps="5654"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="value_in_context&#39;vc.4" expl="postcondition" proved="true">
  <transf name="destruct_term_subst" proved="true" arg1="c">
   <goal name="value_in_context&#39;vc.4.0" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="5017"/></proof>
   </goal>
   <goal name="value_in_context&#39;vc.4.1" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.01" steps="5017"/></proof>
   </goal>
   <goal name="value_in_context&#39;vc.4.2" expl="postcondition" proved="true">
   <proof prover="2"><result status="valid" time="0.02" steps="5607"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="irreducible_is_value&#39;vc" expl="VC for irreducible_is_value" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="719"/></proof>
 </goal>
 <goal name="reduction2&#39;vc" expl="VC for reduction2" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="reduction2&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="58"/></proof>
  </goal>
  <goal name="reduction2&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="40"/></proof>
  </goal>
  <goal name="reduction2&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="76"/></proof>
  </goal>
  <goal name="reduction2&#39;vc.3" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="85"/></proof>
  </goal>
  <goal name="reduction2&#39;vc.4" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.20" steps="915"/></proof>
  </goal>
  <goal name="reduction2&#39;vc.5" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="156"/></proof>
  </goal>
  <goal name="reduction2&#39;vc.6" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="23"/></proof>
  </goal>
  <goal name="reduction2&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.11" steps="670"/></proof>
  </goal>
  <goal name="reduction2&#39;vc.8" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="reduction2&#39;vc.8.0" expl="postcondition" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="20"/></proof>
   </goal>
   <goal name="reduction2&#39;vc.8.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.42"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="ks&#39;vc" expl="VC for ks" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="33"/></proof>
 </goal>
 <goal name="reduction3&#39;vc" expl="VC for reduction3" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="reduction3&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.1" expl="precondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="74"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="26"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.3" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.4" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.07" steps="603"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.5" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="149"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.6" expl="unreachable point" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="27"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.38"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.11" steps="612"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.06" steps="344"/></proof>
  </goal>
  <goal name="reduction3&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.03"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="ks_even_odd&#39;vc" expl="VC for ks_even_odd" proved="true">
 <proof prover="0"><result status="valid" time="0.09" steps="258"/></proof>
 </goal>
</theory>
</file>
</why3session>
