<?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="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="Eprover" version="2.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="koda_ruskey.mlw"/>
<theory name="KodaRuskey_Spec" proved="true">
 <goal name="eq_color&#39;vc" expl="VC for eq_color" proved="true">
 <proof prover="3"><result status="valid" time="0.00" steps="6"/></proof>
 <proof prover="6"><result status="valid" time="0.03" steps="3585"/></proof>
 </goal>
 <goal name="size_forest_nonneg" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="size_forest_nonneg.0" proved="true">
  <proof prover="3"><result status="valid" time="0.00" steps="12"/></proof>
  <proof prover="6"><result status="valid" time="0.03" steps="4372"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="count_forest_nonneg" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="count_forest_nonneg.0" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="16"/></proof>
  <proof prover="6"><result status="valid" time="0.05" steps="7096"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Lemmas" proved="true">
 <goal name="mem_app" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="mem_app.0" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="75"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="10644"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="size_stack_nonneg" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="size_stack_nonneg.0" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="32"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="9459"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="white_forest_equiv" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="white_forest_equiv.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="141"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="8923"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="any_forest_frame" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="any_forest_frame.0" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="179"/></proof>
  <proof prover="6"><result status="valid" time="0.11" steps="16375"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="any_stack_frame" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="any_stack_frame.0" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="any_stack_frame.0.0" proved="true">
   <proof prover="3"><result status="valid" time="0.00" steps="20"/></proof>
   <proof prover="6"><result status="valid" time="0.05" steps="8460"/></proof>
   </goal>
   <goal name="any_stack_frame.0.1" proved="true">
   <transf name="compute_in_goal" proved="true" >
    <goal name="any_stack_frame.0.1.0" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="any_stack_frame.0.1.0.0" proved="true">
     <proof prover="3"><result status="valid" time="0.02" steps="153"/></proof>
     <proof prover="6"><result status="valid" time="0.07" steps="10409"/></proof>
     </goal>
     <goal name="any_stack_frame.0.1.0.1" proved="true">
     <proof prover="2"><result status="valid" time="0.08"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="inverse_frame" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="inverse_frame.0" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="234"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="inverse_frame2" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="inverse_frame2.0" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="256"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="inverse_any&#39;vc" expl="VC for inverse_any" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="inverse_any&#39;vc.0" expl="VC for inverse_any" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="72"/></proof>
  <proof prover="6"><result status="valid" time="0.05" steps="9957"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="inverse_final" proved="true">
 <proof prover="3"><result status="valid" time="0.15" steps="837"/></proof>
 </goal>
 <goal name="inverse_white" proved="true">
 <proof prover="3"><result status="valid" time="0.01" steps="73"/></proof>
 <proof prover="6"><result status="valid" time="0.06" steps="9819"/></proof>
 </goal>
 <goal name="white_final_exclusive&#39;vc" expl="VC for white_final_exclusive" proved="true">
 <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
 <proof prover="6"><result status="valid" time="0.06" steps="8845"/></proof>
 </goal>
 <goal name="final_unique" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="final_unique.0" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="258"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="10937"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="inverse_inverse&#39;vc" expl="VC for inverse_inverse" proved="true">
 <proof prover="3"><result status="valid" time="0.32" steps="1153"/></proof>
 <proof prover="6"><result status="valid" time="0.42" steps="46964"/></proof>
 </goal>
 <goal name="sub_not_nil" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_not_nil.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="20"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="10074"/></proof>
  </goal>
  <goal name="sub_not_nil.1" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="22"/></proof>
  <proof prover="6"><result status="valid" time="0.04" steps="9546"/></proof>
  </goal>
  <goal name="sub_not_nil.2" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="65"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="12979"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_empty" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_empty.0" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="22"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="11075"/></proof>
  </goal>
  <goal name="sub_empty.1" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="11733"/></proof>
  </goal>
  <goal name="sub_empty.2" proved="true">
  <proof prover="6"><result status="valid" time="0.15" steps="21414"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_mem" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_mem.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="42"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="11101"/></proof>
  </goal>
  <goal name="sub_mem.1" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="26"/></proof>
  <proof prover="6"><result status="valid" time="0.05" steps="9413"/></proof>
  </goal>
  <goal name="sub_mem.2" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="106"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="13966"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_weaken1" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_weaken1.0" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="135"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="12667"/></proof>
  </goal>
  <goal name="sub_weaken1.1" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="11545"/></proof>
  </goal>
  <goal name="sub_weaken1.2" proved="true">
  <proof prover="6"><result status="valid" time="0.16" steps="23806"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_weaken2" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_weaken2.0" proved="true">
  <proof prover="6"><result status="valid" time="0.10" steps="15651"/></proof>
  </goal>
  <goal name="sub_weaken2.1" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="11944"/></proof>
  </goal>
  <goal name="sub_weaken2.2" proved="true">
  <proof prover="6"><result status="valid" time="0.27" steps="36365"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="not_mem_st" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="not_mem_st.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="42"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="11407"/></proof>
  </goal>
  <goal name="not_mem_st.1" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="26"/></proof>
  <proof prover="6"><result status="valid" time="0.05" steps="9784"/></proof>
  </goal>
  <goal name="not_mem_st.2" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="105"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="14278"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_frame" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_frame.0" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="22"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="10813"/></proof>
  </goal>
  <goal name="sub_frame.1" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="138"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="11577"/></proof>
  </goal>
  <goal name="sub_frame.2" proved="true">
  <proof prover="6"><result status="valid" time="0.13" steps="19854"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_no_rep" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_no_rep.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="11815"/></proof>
  </goal>
  <goal name="sub_no_rep.1" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="11057"/></proof>
  </goal>
  <goal name="sub_no_rep.2" proved="true">
  <proof prover="6"><result status="valid" time="0.11" steps="18203"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_no_rep2" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_no_rep2.0" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="55"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="12040"/></proof>
  </goal>
  <goal name="sub_no_rep2.1" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="11146"/></proof>
  </goal>
  <goal name="sub_no_rep2.2" proved="true">
  <proof prover="6" timelimit="15"><result status="valid" time="13.14" steps="1080618"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="white_valid" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="white_valid.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="72"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="10913"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="final_valid" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="final_valid.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="70"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="11099"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valid_coloring_frame" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="valid_coloring_frame.0" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="339"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="15556"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="valid_coloring_set" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="valid_coloring_set.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="59"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="11720"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="head_and_tail" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="head_and_tail.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="88"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="15443"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_valid_coloring_f1" proved="true">
 <proof prover="3"><result status="valid" time="0.04" steps="140"/></proof>
 <proof prover="6"><result status="valid" time="0.07" steps="12078"/></proof>
 </goal>
 <goal name="sub_valid_coloring" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_valid_coloring.0" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="171"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="14663"/></proof>
  </goal>
  <goal name="sub_valid_coloring.1" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="sub_valid_coloring.1.0" proved="true">
   <transf name="compute_in_goal" proved="true" >
    <goal name="sub_valid_coloring.1.0.0" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="sub_valid_coloring.1.0.0.0" proved="true">
     <proof prover="3"><result status="valid" time="0.16" steps="366"/></proof>
     <proof prover="6"><result status="valid" time="0.16" steps="26730"/></proof>
     </goal>
     <goal name="sub_valid_coloring.1.0.0.1" proved="true">
     <proof prover="2"><result status="valid" time="2.29"/></proof>
     </goal>
     <goal name="sub_valid_coloring.1.0.0.2" proved="true">
     <proof prover="2"><result status="valid" time="1.76"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="sub_valid_coloring.2" proved="true">
  <proof prover="3"><result status="valid" time="0.32" steps="885"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sub_Cons_N" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="sub_Cons_N.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="13249"/></proof>
  </goal>
  <goal name="sub_Cons_N.1" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="13806"/></proof>
  </goal>
  <goal name="sub_Cons_N.2" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="259"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="14999"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="white_white" proved="true">
 <proof prover="3"><result status="valid" time="0.02" steps="47"/></proof>
 <proof prover="6"><result status="valid" time="0.07" steps="11531"/></proof>
 </goal>
 <goal name="sub_valid_coloring_white&#39;vc" expl="VC for sub_valid_coloring_white" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="sub_valid_coloring_white&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="85"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="12231"/></proof>
  </goal>
  <goal name="sub_valid_coloring_white&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="22"/></proof>
  <proof prover="6"><result status="valid" time="0.05" steps="10939"/></proof>
  </goal>
  <goal name="sub_valid_coloring_white&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="11852"/></proof>
  </goal>
  <goal name="sub_valid_coloring_white&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.04" steps="10496"/></proof>
  </goal>
  <goal name="sub_valid_coloring_white&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="85"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="13021"/></proof>
  </goal>
  <goal name="sub_valid_coloring_white&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="11952"/></proof>
  </goal>
  <goal name="sub_valid_coloring_white&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="11974"/></proof>
  </goal>
  <goal name="sub_valid_coloring_white&#39;vc.7" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="24"/></proof>
  <proof prover="6"><result status="valid" time="0.04" steps="11455"/></proof>
  </goal>
  <goal name="sub_valid_coloring_white&#39;vc.8" expl="postcondition" proved="true">
  <transf name="compute_in_goal" proved="true" >
   <goal name="sub_valid_coloring_white&#39;vc.8.0" expl="postcondition" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="sub_valid_coloring_white&#39;vc.8.0.0" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="2.98"/></proof>
    </goal>
    <goal name="sub_valid_coloring_white&#39;vc.8.0.1" expl="postcondition" proved="true">
    <proof prover="3"><result status="valid" time="0.76" steps="2213"/></proof>
    </goal>
    <goal name="sub_valid_coloring_white&#39;vc.8.0.2" expl="postcondition" proved="true">
    <proof prover="2"><result status="valid" time="2.60"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="count_stack_nonneg" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="count_stack_nonneg.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="39"/></proof>
  <proof prover="6"><result status="valid" time="0.09" steps="18653"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="stored_trans1&#39;vc" expl="VC for stored_trans1" proved="true">
 <proof prover="3"><result status="valid" time="0.42" steps="426"/></proof>
 </goal>
 <goal name="stored_trans2&#39;vc" expl="VC for stored_trans2" proved="true">
 <proof prover="3"><result status="valid" time="0.40" steps="423"/></proof>
 </goal>
</theory>
<theory name="KodaRuskey" proved="true">
 <goal name="enum&#39;vc" expl="VC for enum" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="enum&#39;vc.0" expl="unreachable point" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="26"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="22675"/></proof>
  </goal>
  <goal name="enum&#39;vc.1" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="32"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="22770"/></proof>
  </goal>
  <goal name="enum&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="14"/></proof>
  <proof prover="6"><result status="valid" time="0.06" steps="20370"/></proof>
  </goal>
  <goal name="enum&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="131"/></proof>
  <proof prover="6"><result status="valid" time="0.14" steps="30207"/></proof>
  </goal>
  <goal name="enum&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="32"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="27164"/></proof>
  </goal>
  <goal name="enum&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="208"/></proof>
  </goal>
  <goal name="enum&#39;vc.6" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="162"/></proof>
  <proof prover="6"><result status="valid" time="0.11" steps="25811"/></proof>
  </goal>
  <goal name="enum&#39;vc.7" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="34"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="22834"/></proof>
  </goal>
  <goal name="enum&#39;vc.8" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="34"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="22847"/></proof>
  </goal>
  <goal name="enum&#39;vc.9" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="36"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="23861"/></proof>
  </goal>
  <goal name="enum&#39;vc.10" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="38"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="23818"/></proof>
  </goal>
  <goal name="enum&#39;vc.11" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="40"/></proof>
  <proof prover="6"><result status="valid" time="0.11" steps="23866"/></proof>
  </goal>
  <goal name="enum&#39;vc.12" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="40"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="22973"/></proof>
  </goal>
  <goal name="enum&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="46"/></proof>
  <proof prover="6"><result status="valid" time="0.12" steps="26399"/></proof>
  </goal>
  <goal name="enum&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="111"/></proof>
  <proof prover="6"><result status="valid" time="0.12" steps="26652"/></proof>
  </goal>
  <goal name="enum&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="44"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="22945"/></proof>
  </goal>
  <goal name="enum&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.80" steps="1710"/></proof>
  </goal>
  <goal name="enum&#39;vc.17" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.42" steps="688"/></proof>
  <proof prover="6"><result status="valid" time="0.20" steps="39967"/></proof>
  </goal>
  <goal name="enum&#39;vc.18" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.40" steps="681"/></proof>
  <proof prover="6"><result status="valid" time="0.22" steps="39849"/></proof>
  </goal>
  <goal name="enum&#39;vc.19" expl="index in array bounds" proved="true">
  <proof prover="5"><result status="valid" time="0.48"/></proof>
  </goal>
  <goal name="enum&#39;vc.20" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="165"/></proof>
  <proof prover="6"><result status="valid" time="0.15" steps="30761"/></proof>
  </goal>
  <goal name="enum&#39;vc.21" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="22908"/></proof>
  </goal>
  <goal name="enum&#39;vc.22" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="22925"/></proof>
  </goal>
  <goal name="enum&#39;vc.23" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="38"/></proof>
  <proof prover="6"><result status="valid" time="0.11" steps="23912"/></proof>
  </goal>
  <goal name="enum&#39;vc.24" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="14"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="20370"/></proof>
  </goal>
  <goal name="enum&#39;vc.25" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="213"/></proof>
  <proof prover="6"><result status="valid" time="0.13" steps="26276"/></proof>
  </goal>
  <goal name="enum&#39;vc.26" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="23022"/></proof>
  </goal>
  <goal name="enum&#39;vc.27" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.44" steps="572"/></proof>
  <proof prover="6"><result status="valid" time="0.26" steps="46527"/></proof>
  </goal>
  <goal name="enum&#39;vc.28" expl="index in array bounds" proved="true">
  <proof prover="5"><result status="valid" time="0.50"/></proof>
  </goal>
  <goal name="enum&#39;vc.29" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.46" steps="635"/></proof>
  <proof prover="6"><result status="valid" time="0.36" steps="61132"/></proof>
  </goal>
  <goal name="enum&#39;vc.30" expl="assertion" proved="true">
  <proof prover="5"><result status="valid" time="0.18"/></proof>
  <proof prover="6"><result status="valid" time="0.58" steps="78042"/></proof>
  </goal>
  <goal name="enum&#39;vc.31" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.41" steps="774"/></proof>
  <proof prover="6"><result status="valid" time="0.14" steps="27947"/></proof>
  </goal>
  <goal name="enum&#39;vc.32" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="64"/></proof>
  <proof prover="6"><result status="valid" time="0.11" steps="25076"/></proof>
  </goal>
  <goal name="enum&#39;vc.33" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="70"/></proof>
  <proof prover="6"><result status="valid" time="0.13" steps="28315"/></proof>
  </goal>
  <goal name="enum&#39;vc.34" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="40"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="25120"/></proof>
  </goal>
  <goal name="enum&#39;vc.35" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="40"/></proof>
  <proof prover="6"><result status="valid" time="0.09" steps="25194"/></proof>
  </goal>
  <goal name="enum&#39;vc.36" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="70"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="25586"/></proof>
  </goal>
  <goal name="enum&#39;vc.37" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="14"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="20370"/></proof>
  </goal>
  <goal name="enum&#39;vc.38" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.16" steps="226"/></proof>
  <proof prover="6"><result status="valid" time="0.14" steps="28700"/></proof>
  </goal>
  <goal name="enum&#39;vc.39" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="76"/></proof>
  <proof prover="6"><result status="valid" time="0.12" steps="28397"/></proof>
  </goal>
  <goal name="enum&#39;vc.40" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.28" steps="372"/></proof>
  <proof prover="6"><result status="valid" time="0.15" steps="30055"/></proof>
  </goal>
  <goal name="enum&#39;vc.41" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="82"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="26208"/></proof>
  </goal>
  <goal name="enum&#39;vc.42" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="1.08" steps="1322"/></proof>
  <proof prover="6"><result status="valid" time="0.16" steps="31758"/></proof>
  </goal>
  <goal name="enum&#39;vc.43" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="68"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="26773"/></proof>
  </goal>
  <goal name="enum&#39;vc.44" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.62"/></proof>
  </goal>
  <goal name="enum&#39;vc.45" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.76" steps="2092"/></proof>
  <proof prover="6"><result status="valid" time="0.28" steps="47443"/></proof>
  </goal>
  <goal name="enum&#39;vc.46" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.08" steps="1208"/></proof>
  <proof prover="6"><result status="valid" time="0.22" steps="45609"/></proof>
  </goal>
  <goal name="enum&#39;vc.47" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.13" steps="1385"/></proof>
  <proof prover="6"><result status="valid" time="0.22" steps="45882"/></proof>
  </goal>
  <goal name="enum&#39;vc.48" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="68"/></proof>
  <proof prover="6"><result status="valid" time="0.09" steps="28701"/></proof>
  </goal>
  <goal name="enum&#39;vc.49" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="68"/></proof>
  <proof prover="6"><result status="valid" time="0.09" steps="27995"/></proof>
  </goal>
  <goal name="enum&#39;vc.50" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="1.30" steps="1478"/></proof>
  <proof prover="6"><result status="valid" time="0.66" steps="77701"/></proof>
  </goal>
  <goal name="enum&#39;vc.51" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.58" steps="72449"/></proof>
  </goal>
  <goal name="enum&#39;vc.52" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="68"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="23416"/></proof>
  </goal>
  <goal name="enum&#39;vc.53" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="68"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="26103"/></proof>
  </goal>
  <goal name="enum&#39;vc.54" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.10" steps="325"/></proof>
  <proof prover="6"><result status="valid" time="0.12" steps="25977"/></proof>
  </goal>
  <goal name="enum&#39;vc.55" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="44"/></proof>
  <proof prover="6"><result status="valid" time="0.12" steps="26795"/></proof>
  </goal>
  <goal name="enum&#39;vc.56" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="22985"/></proof>
  </goal>
  <goal name="enum&#39;vc.57" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="23002"/></proof>
  </goal>
  <goal name="enum&#39;vc.58" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="40"/></proof>
  <proof prover="6"><result status="valid" time="0.11" steps="26209"/></proof>
  </goal>
  <goal name="enum&#39;vc.59" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="14"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="20370"/></proof>
  </goal>
  <goal name="enum&#39;vc.60" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.17" steps="370"/></proof>
  <proof prover="6"><result status="valid" time="0.13" steps="26979"/></proof>
  </goal>
  <goal name="enum&#39;vc.61" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="36"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="23110"/></proof>
  </goal>
  <goal name="enum&#39;vc.62" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.30" steps="50986"/></proof>
  </goal>
  <goal name="enum&#39;vc.63" expl="index in array bounds" proved="true">
  <proof prover="5"><result status="valid" time="0.40"/></proof>
  <proof prover="6"><result status="valid" time="3.63" steps="366500"/></proof>
  </goal>
  <goal name="enum&#39;vc.64" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="4.25" steps="2911"/></proof>
  <proof prover="6"><result status="valid" time="0.17" steps="36138"/></proof>
  </goal>
  <goal name="enum&#39;vc.65" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="62"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="25059"/></proof>
  </goal>
  <goal name="enum&#39;vc.66" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="3.83" steps="2517"/></proof>
  <proof prover="6"><result status="valid" time="0.28" steps="49585"/></proof>
  </goal>
  <goal name="enum&#39;vc.67" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="3.60" steps="2060"/></proof>
  <proof prover="6"><result status="valid" time="0.55" steps="80955"/></proof>
  </goal>
  <goal name="enum&#39;vc.68" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.22" steps="267"/></proof>
  <proof prover="6"><result status="valid" time="0.18" steps="35884"/></proof>
  </goal>
  <goal name="enum&#39;vc.69" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="40"/></proof>
  <proof prover="6"><result status="valid" time="0.11" steps="25408"/></proof>
  </goal>
  <goal name="enum&#39;vc.70" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="40"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="25482"/></proof>
  </goal>
  <goal name="enum&#39;vc.71" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="71"/></proof>
  <proof prover="6"><result status="valid" time="0.10" steps="25593"/></proof>
  </goal>
  <goal name="enum&#39;vc.72" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="14"/></proof>
  <proof prover="6"><result status="valid" time="0.07" steps="20370"/></proof>
  </goal>
  <goal name="enum&#39;vc.73" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.68" steps="1651"/></proof>
  <proof prover="6"><result status="valid" time="0.22" steps="41904"/></proof>
  </goal>
  <goal name="enum&#39;vc.74" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.48" steps="711"/></proof>
  <proof prover="6"><result status="valid" time="0.15" steps="30224"/></proof>
  </goal>
  <goal name="enum&#39;vc.75" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.29" steps="296"/></proof>
  <proof prover="6"><result status="valid" time="0.15" steps="30695"/></proof>
  </goal>
  <goal name="enum&#39;vc.76" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="1.17" steps="116744"/></proof>
  </goal>
  <goal name="enum&#39;vc.77" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="66"/></proof>
  <proof prover="6"><result status="valid" time="0.11" steps="26629"/></proof>
  </goal>
  <goal name="enum&#39;vc.78" expl="precondition" proved="true">
  <proof prover="5"><result status="valid" time="0.68"/></proof>
  </goal>
  <goal name="enum&#39;vc.79" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="2.27" steps="1875"/></proof>
  <proof prover="6"><result status="valid" time="0.22" steps="44019"/></proof>
  </goal>
  <goal name="enum&#39;vc.80" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.81" steps="1821"/></proof>
  <proof prover="6"><result status="valid" time="0.21" steps="44498"/></proof>
  </goal>
  <goal name="enum&#39;vc.81" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.80" steps="1810"/></proof>
  <proof prover="6"><result status="valid" time="0.23" steps="44887"/></proof>
  </goal>
  <goal name="enum&#39;vc.82" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="66"/></proof>
  <proof prover="6"><result status="valid" time="0.09" steps="28623"/></proof>
  </goal>
  <goal name="enum&#39;vc.83" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="66"/></proof>
  <proof prover="6"><result status="valid" time="0.09" steps="27999"/></proof>
  </goal>
  <goal name="enum&#39;vc.84" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="1.43" steps="1861"/></proof>
  <proof prover="6"><result status="valid" time="0.22" steps="43085"/></proof>
  </goal>
  <goal name="enum&#39;vc.85" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="4.76" steps="3160"/></proof>
  <proof prover="6"><result status="valid" time="0.63" steps="79898"/></proof>
  </goal>
  <goal name="enum&#39;vc.86" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="66"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="23420"/></proof>
  </goal>
  <goal name="enum&#39;vc.87" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="66"/></proof>
  <proof prover="6"><result status="valid" time="0.08" steps="25963"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="main&#39;vc" expl="VC for main" proved="true">
 <proof prover="3"><result status="valid" time="0.06" steps="281"/></proof>
 </goal>
</theory>
</file>
</why3session>
