<?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="3236"/></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="3128"/></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="4133"/></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="7877"/></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="6693"/></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="7054"/></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="13366"/></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="6509"/></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="8441"/></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="8298"/></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="8125"/></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="7097"/></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="9212"/></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="40094"/></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="7856"/></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="8035"/></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="11236"/></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="9376"/></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="9989"/></proof>
  </goal>
  <goal name="sub_empty.2" proved="true">
  <proof prover="6"><result status="valid" time="0.15" steps="18382"/></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="9400"/></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="7771"/></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="11997"/></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="10833"/></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="9803"/></proof>
  </goal>
  <goal name="sub_weaken1.2" proved="true">
  <proof prover="6"><result status="valid" time="0.16" steps="20232"/></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="15529"/></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="10202"/></proof>
  </goal>
  <goal name="sub_weaken2.2" proved="true">
  <proof prover="6"><result status="valid" time="0.27" steps="31056"/></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="9707"/></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="8142"/></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="12309"/></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="9376"/></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="10156"/></proof>
  </goal>
  <goal name="sub_frame.2" proved="true">
  <proof prover="6"><result status="valid" time="0.13" steps="18417"/></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="10246"/></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="9532"/></proof>
  </goal>
  <goal name="sub_no_rep.2" proved="true">
  <proof prover="6"><result status="valid" time="0.11" steps="16634"/></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="10561"/></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="9711"/></proof>
  </goal>
  <goal name="sub_no_rep2.2" proved="true">
  <proof prover="6" timelimit="15"><result status="valid" time="13.14" steps="1078615"/></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="9996"/></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="10220"/></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="14496"/></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="10909"/></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="14542"/></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="11210"/></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="13814"/></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="25780"/></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="12380"/></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="12939"/></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="14130"/></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="10667"/></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="11356"/></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="10127"/></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="10977"/></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="9801"/></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="12176"/></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="11126"/></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="11148"/></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="10760"/></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="17742"/></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="22320"/></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="22415"/></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="20015"/></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="29630"/></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="26810"/></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="25265"/></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="22479"/></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="22492"/></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="23357"/></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="23314"/></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="23362"/></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="22618"/></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="25853"/></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="26107"/></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="22590"/></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="39263"/></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="39146"/></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="30616"/></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="22818"/></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="22835"/></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="23820"/></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="20280"/></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="26184"/></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="22932"/></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="46121"/></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="60677"/></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="76450"/></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="27835"/></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="24984"/></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="28203"/></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="25028"/></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="25102"/></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="25494"/></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="20280"/></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="28592"/></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="28289"/></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="29947"/></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="26116"/></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="31615"/></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="26681"/></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="46792"/></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="45386"/></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="45659"/></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="28611"/></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="27905"/></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="77339"/></proof>
  </goal>
  <goal name="enum&#39;vc.51" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.58" steps="73293"/></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="23326"/></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="26013"/></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="25864"/></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="26682"/></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="22895"/></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="22912"/></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="26096"/></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="20280"/></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="26870"/></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="23020"/></proof>
  </goal>
  <goal name="enum&#39;vc.62" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.30" steps="50602"/></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="4.10" steps="330140"/></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="35975"/></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="24967"/></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="49401"/></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="80600"/></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="35721"/></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="25316"/></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="25390"/></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="25501"/></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="20280"/></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="41729"/></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="30111"/></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="30582"/></proof>
  </goal>
  <goal name="enum&#39;vc.76" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="1.17" steps="114529"/></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="26537"/></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="43789"/></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="44262"/></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="44651"/></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="28533"/></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="27909"/></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="42851"/></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="79508"/></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="23330"/></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="25873"/></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>
