<?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="2.4.1" timelimit="120" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.2.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="verifythis_2019_ghc_sort.mlw"/>
<theory name="Top" proved="true">
 <goal name="StrictIncr.Transitive.Trans" proved="true">
 <proof prover="3"><result status="valid" time="0.01" steps="4"/></proof>
 </goal>
 <goal name="RevSorted.Transitive.Trans" proved="true">
 <proof prover="3"><result status="valid" time="0.01" steps="6"/></proof>
 </goal>
 <goal name="eqb&#39;vc" expl="VC for eqb" proved="true">
 <proof prover="3"><result status="valid" time="0.03" steps="180"/></proof>
 </goal>
 <goal name="list_seq&#39;vc" expl="VC for list_seq" proved="true">
 <proof prover="3"><result status="valid" time="0.02" steps="8"/></proof>
 </goal>
 <goal name="nil&#39;vc" expl="VC for nil" proved="true">
 <proof prover="3"><result status="valid" time="0.02" steps="8"/></proof>
 </goal>
 <goal name="extend&#39;vc" expl="VC for extend" proved="true">
 <proof prover="3"><result status="valid" time="0.06" steps="221"/></proof>
 </goal>
 <goal name="cutpoints&#39;vc" expl="VC for cutpoints" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="cutpoints&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="14"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="15"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="66"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="156"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="69"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="83"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.6" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="99"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.7" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="101"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.8" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="30"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.9" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="30"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="30"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.11" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="32"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.12" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="38"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="38"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.14" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="56"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="56"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.12" steps="323"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.17" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="158"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.18" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.88" steps="128255"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.19" expl="loop variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="44"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.20" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="44"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.21" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="44"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="169"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.43" steps="76347"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.40" steps="2043"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="0.09" steps="350"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.26" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="3.24" steps="9223"/></proof>
  <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),get,set,([]&#39;),([&lt;-]&#39;),andb,orb,notb,xorb,implb,is_nil,mem,is_none,nth,hd,tl,(++),reverse,rev_append,num_occ,permut,fold_right,([]&#39;&#39;),singleton,cons,snoc,(++&#39;),of_list,point_wise,([]),sorted2,ge,sorted1,sorted,compat,eqb,n,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans2,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,occ_empty,occ_right_no_add,occ_right_add,occ_left_no_add,occ_left_add,occ_bounds,occ_append,occ_neq,occ_exists,occ_pos,occ_eq,occ_exchange,is_nil&#39;spec,Length_nonnegative,Length_nil,is_none&#39;spec,Nth_tl,Nth0_head,Append_assoc,Append_l_nil,Append_length,mem_append,mem_decomp,reverse_append,reverse_cons,cons_reverse,reverse_reverse,reverse_mem,rev_append_append_l,rev_append_length,rev_append_def,rev_append_append_r,Num_Occ_NonNeg,Mem_Num_Occ,Append_Num_Occ,reverse_num_occ,Permut_refl,Permut_sym,Permut_trans,Permut_cons,Permut_swap,Permut_cons_append,Permut_assoc,Permut_append,Permut_append_swap,Permut_mem,Permut_length,fold_right_append,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,associative,left_neutral,right_neutral,cons_def,snoc_def,double_sub_sequence,cons_back,snoc_back,cat_back,cons_dec,snoc_dec,cat_dec,empty_dec,singleton_dec,to_list_empty,to_list_cons,to_list_length,to_list_nth,to_list_def_cons,elts_seq_of_list,is_of_list,of_list_app,of_list_app_length,of_list_snoc,convolution_to_of_list,array&#39;invariant,([&lt;-])&#39;spec,make_spec,Trans1,sorted_mem2,sorted_append2,Trans,sorted_mem1,sorted_append1,sorted_mem,sorted_append,rev_append_sorted_incr,rev_append_sorted_decr,eqb&#39;spec,nil&#39;def,Requires,Ensures1,LoopInvariant13,H11,LoopInvariant12,LoopInvariant10,LoopInvariant9,LoopInvariant7,H9,H8,H7,H6,H5,H4,H2,LoopInvariant5,LoopInvariant4,LoopInvariant3,LoopInvariant">
   <goal name="cutpoints&#39;vc.26.0" expl="loop invariant preservation" proved="true">
   <proof prover="2"><result status="valid" time="0.52" steps="958"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="cutpoints&#39;vc.27" expl="loop invariant preservation" proved="true">
  <proof prover="3"><result status="valid" time="1.24" steps="2663"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.28" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.50" steps="1744"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.29" expl="assertion" proved="true">
  <proof prover="4"><result status="valid" time="0.73" steps="106166"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.30" expl="postcondition" proved="true">
  <proof prover="4"><result status="valid" time="0.37" steps="63267"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.31" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="40"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.32" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="124"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.33" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07" steps="303"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.34" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="19.96" steps="182927"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.35" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.78" steps="1584"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.36" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="34"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.37" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="39"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.38" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="35"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.39" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="35"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.40" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="103"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.41" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="40"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.42" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="253"/></proof>
  </goal>
  <goal name="cutpoints&#39;vc.43" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="45"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="reverse_sorted_incr" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="reverse_sorted_incr.0" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="12"/></proof>
  </goal>
  <goal name="reverse_sorted_incr.1" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="12"/></proof>
  </goal>
  <goal name="reverse_sorted_incr.2" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="43"/></proof>
  </goal>
  <goal name="reverse_sorted_incr.3" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="81"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="lt_le_sorted&#39;vc" expl="VC for lt_le_sorted" proved="true">
 <proof prover="3"><result status="valid" time="0.06" steps="369"/></proof>
 </goal>
 <goal name="order&#39;vc" expl="VC for order" proved="true">
 <proof prover="3"><result status="valid" time="0.20" steps="1418"/></proof>
 </goal>
 <goal name="list_from&#39;vc" expl="VC for list_from" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="list_from&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="list_from&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="list_from&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="27"/></proof>
  </goal>
  <goal name="list_from&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="82"/></proof>
  </goal>
  <goal name="list_from&#39;vc.4" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="list_from&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.78" steps="2952"/></proof>
  </goal>
  <goal name="list_from&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="219"/></proof>
  </goal>
  <goal name="list_from&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.18" steps="780"/></proof>
  </goal>
  <goal name="list_from&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.43" steps="1588"/></proof>
  </goal>
  <goal name="list_from&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="230"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="occ_slice&#39;vc" expl="VC for occ_slice" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="occ_slice&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="occ_slice&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="occ_slice&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="70"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sorted_lists&#39;vc" expl="VC for sorted_lists" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="sorted_lists&#39;vc.0" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="1.42" steps="3823"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.1" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.17"/></proof>
  <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),get,set,([]&#39;),([&lt;-]&#39;),andb,orb,notb,xorb,implb,is_nil,length1,is_none,nth,hd,tl,(++),reverse,rev_append,num_occ,permut,fold_right,([]&#39;&#39;),singleton,cons,snoc,(++&#39;),of_list,point_wise,([]),sorted2,ge,sorted1,sorted,compat,eqb,seq,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans2,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,occ_empty,occ_right_no_add,occ_right_add,occ_left_no_add,occ_left_add,occ_bounds,occ_append,occ_neq,occ_exists,occ_pos,occ_eq,occ_exchange,is_nil&#39;spec,Length_nonnegative,Length_nil,is_none&#39;spec,Nth_tl,Nth0_head,Append_assoc,Append_l_nil,Append_length,mem_append,mem_decomp,reverse_append,reverse_cons,cons_reverse,reverse_reverse,reverse_mem,Reverse_length,rev_append_append_l,rev_append_length,rev_append_def,rev_append_append_r,Num_Occ_NonNeg,Mem_Num_Occ,Append_Num_Occ,reverse_num_occ,Permut_refl,Permut_sym,Permut_trans,Permut_cons,Permut_swap,Permut_cons_append,Permut_assoc,Permut_append,Permut_append_swap,Permut_mem,Permut_length,fold_right_append,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,associative,left_neutral,right_neutral,cons_def,snoc_def,double_sub_sequence,cons_back,snoc_back,cat_back,cons_dec,snoc_dec,cat_dec,empty_dec,singleton_dec,to_list_empty,to_list_cons,to_list_length,to_list_nth,to_list_def_cons,length_of_list,elts_seq_of_list,is_of_list,of_list_app,of_list_app_length,of_list_snoc,convolution_to_of_list,array&#39;invariant,([&lt;-])&#39;spec,make_spec,Trans1,sorted_mem2,sorted_append2,Trans,sorted_mem1,sorted_append1,sorted_mem,sorted_append,rev_append_sorted_incr,rev_append_sorted_decr,eqb&#39;spec,list_seq&#39;invariant,nil&#39;def,reverse_sorted_incr,lt_le_sorted,order&#39;spec,order&#39;def,occ_slice,Requires3,Requires2,Requires,Assert">
   <goal name="sorted_lists&#39;vc.1.0" expl="precondition" proved="true">
   <proof prover="1" timelimit="1"><result status="valid" time="0.02"/></proof>
   <proof prover="3"><result status="valid" time="0.02" steps="178"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sorted_lists&#39;vc.2" expl="precondition" proved="true">
  <proof prover="1"><result status="valid" time="0.16"/></proof>
  <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),get,set,([]&#39;),([&lt;-]&#39;),andb,orb,notb,xorb,implb,is_nil,length1,mem,is_none,nth,tl,(++),reverse,rev_append,permut,fold_right,([]&#39;&#39;),singleton,cons,snoc,(++&#39;),of_list,point_wise,([]),sorted2,ge,sorted1,sorted,compat,eqb,seq,Assoc1,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm1,Assoc,Mul_distr_l,Mul_distr_r,Comm,Unitary,NonTrivialRing,Refl,Trans2,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,occ_empty,occ_right_no_add,occ_right_add,occ_left_no_add,occ_left_add,occ_bounds,occ_append,occ_neq,occ_exists,occ_pos,occ_eq,is_nil&#39;spec,Length_nonnegative,Length_nil,is_none&#39;spec,Nth_tl,Nth0_head,Append_assoc,Append_l_nil,Append_length,mem_append,mem_decomp,reverse_append,reverse_cons,cons_reverse,reverse_reverse,reverse_mem,Reverse_length,rev_append_append_l,rev_append_length,rev_append_def,rev_append_append_r,Append_Num_Occ,reverse_num_occ,Permut_refl,Permut_sym,Permut_trans,Permut_cons,Permut_swap,Permut_cons_append,Permut_assoc,Permut_append,Permut_append_swap,Permut_mem,Permut_length,fold_right_append,length_nonnegative,(==)&#39;spec,create&#39;spec,empty&#39;def,set&#39;spec,set&#39;def,([&lt;-])&#39;def,singleton&#39;spec,cons&#39;spec,snoc&#39;spec,([..])&#39;spec,([..])&#39;def,([_..])&#39;def,([.._])&#39;def,(++)&#39;spec,associative,left_neutral,right_neutral,cons_def,snoc_def,double_sub_sequence,cons_back,snoc_back,cat_back,cons_dec,snoc_dec,cat_dec,empty_dec,singleton_dec,to_list_empty,to_list_cons,to_list_length,to_list_nth,to_list_def_cons,length_of_list,elts_seq_of_list,is_of_list,of_list_app,of_list_app_length,of_list_snoc,convolution_to_of_list,array&#39;invariant,([&lt;-])&#39;spec,make_spec,Trans1,sorted_mem2,sorted_append2,Trans,sorted_mem1,sorted_append1,sorted_mem,sorted_append,rev_append_sorted_incr,rev_append_sorted_decr,eqb&#39;spec,list_seq&#39;invariant,nil&#39;def,reverse_sorted_incr,lt_le_sorted,order&#39;spec,order&#39;def,occ_slice,Requires4,Requires3,Requires1,Assert,Requires">
   <goal name="sorted_lists&#39;vc.2.0" expl="precondition" proved="true">
   <proof prover="1" timelimit="1"><result status="valid" time="0.07"/></proof>
   <proof prover="3"><result status="valid" time="0.03" steps="247"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sorted_lists&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="247"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="100"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="1.33" steps="2303"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.6" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="30"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="188"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.8" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="128"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.9" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="158"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.10" expl="precondition" proved="true">
  <proof prover="4"><result status="valid" time="1.41" steps="213560"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.11" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.51" steps="897"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.12" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="28"/></proof>
  </goal>
  <goal name="sorted_lists&#39;vc.13" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="sorted_lists&#39;vc.13.0" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
   </goal>
   <goal name="sorted_lists&#39;vc.13.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
   </goal>
   <goal name="sorted_lists&#39;vc.13.2" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.03" steps="54"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="sorted_lists&#39;vc.14" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="sorted_lists&#39;vc.14.0" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.03" steps="20"/></proof>
   </goal>
   <goal name="sorted_lists&#39;vc.14.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.05" steps="151"/></proof>
   </goal>
   <goal name="sorted_lists&#39;vc.14.2" expl="postcondition" proved="true">
   <transf name="assert" proved="true" arg1="(occ x (elts s) (get1 (seq1 cutp) 0) (get1 (seq1 cutp) (length2 (seq1 cutp) - 1)) = occ x (elts s) (get1 (seq1 cutp) 0) (get1 (seq1 lseq) (length2 (seq1 lseq) - 1)) + occ x (elts s) (get1 (seq1 lseq) (length2 (seq1 lseq) - 1)) (get1 (seq1 cutp) (length2 (seq1 cutp) - 1)))">
    <goal name="sorted_lists&#39;vc.14.2.0" expl="asserted formula" proved="true">
    <proof prover="3"><result status="valid" time="0.18" steps="424"/></proof>
    </goal>
    <goal name="sorted_lists&#39;vc.14.2.1" expl="postcondition" proved="true">
    <proof prover="0" timelimit="1"><result status="valid" time="0.69" steps="4751"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="merge&#39;vc" expl="VC for merge" proved="true">
 <transf name="split_all_full" proved="true" >
  <goal name="merge&#39;vc.0" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.49" steps="2814"/></proof>
  </goal>
  <goal name="merge&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="56"/></proof>
  </goal>
  <goal name="merge&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="merge&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="merge&#39;vc.4" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.15" steps="388"/></proof>
  </goal>
  <goal name="merge&#39;vc.5" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="56"/></proof>
  </goal>
  <goal name="merge&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="22"/></proof>
  </goal>
  <goal name="merge&#39;vc.7" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="merge&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
  </goal>
  <goal name="merge&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="25"/></proof>
  </goal>
  <goal name="merge&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="merge&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="87"/></proof>
  </goal>
  <goal name="merge&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="merge&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="83"/></proof>
  </goal>
  <goal name="merge&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.08" steps="298"/></proof>
  </goal>
  <goal name="merge&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="158"/></proof>
  </goal>
  <goal name="merge&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.10" steps="380"/></proof>
  </goal>
  <goal name="merge&#39;vc.17" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.17" steps="420"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="merge_pair&#39;vc" expl="VC for merge_pair" proved="true">
 <transf name="split_all_full" proved="true" >
  <goal name="merge_pair&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="19"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="192"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="91"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.05" steps="190"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="16"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.5" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="23"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="21"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="18"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="25"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="23"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.12" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="39"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.13" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="84"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.14" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="44"/></proof>
  </goal>
  <goal name="merge_pair&#39;vc.15" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.68" steps="1808"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="mergerec&#39;vc" expl="VC for mergerec" proved="true">
 <proof prover="3"><result status="valid" time="0.16" steps="985"/></proof>
 </goal>
 <goal name="find&#39;vc" expl="VC for find" proved="true">
 <proof prover="3"><result status="valid" time="0.10" steps="214"/></proof>
 </goal>
 <goal name="same_occs_same_lengths&#39;vc" expl="VC for same_occs_same_lengths" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="same_occs_same_lengths&#39;vc.0" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.11" steps="328"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.1" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="same_occs_same_lengths&#39;vc.1.0" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.04" steps="61"/></proof>
   </goal>
   <goal name="same_occs_same_lengths&#39;vc.1.1" expl="VC for same_occs_same_lengths" proved="true">
   <proof prover="3"><result status="valid" time="0.04" steps="61"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="63"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="28"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="30"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.7" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="same_occs_same_lengths&#39;vc.7.0" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.23" steps="656"/></proof>
   </goal>
   <goal name="same_occs_same_lengths&#39;vc.7.1" expl="VC for same_occs_same_lengths" proved="true">
   <proof prover="3"><result status="valid" time="0.29" steps="318"/></proof>
   </goal>
   <goal name="same_occs_same_lengths&#39;vc.7.2" expl="VC for same_occs_same_lengths" proved="true">
   <proof prover="3"><result status="valid" time="0.06" steps="143"/></proof>
   </goal>
   <goal name="same_occs_same_lengths&#39;vc.7.3" expl="VC for same_occs_same_lengths" proved="true">
   <proof prover="3"><result status="valid" time="0.09" steps="284"/></proof>
   </goal>
   <goal name="same_occs_same_lengths&#39;vc.7.4" expl="VC for same_occs_same_lengths" proved="true">
   <proof prover="3"><result status="valid" time="0.08" steps="282"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.8" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.9" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="36"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.10" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.09" steps="227"/></proof>
  </goal>
  <goal name="same_occs_same_lengths&#39;vc.11" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="90"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="num_occ_seq_occ&#39;vc" expl="VC for num_occ_seq_occ" proved="true">
 <transf name="split_all_full" proved="true" >
  <goal name="num_occ_seq_occ&#39;vc.0" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.11" steps="429"/></proof>
  </goal>
  <goal name="num_occ_seq_occ&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="168"/></proof>
  </goal>
  <goal name="num_occ_seq_occ&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="77"/></proof>
  </goal>
  <goal name="num_occ_seq_occ&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.40" steps="1093"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sort_to_list&#39;vc" expl="VC for sort_to_list" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="sort_to_list&#39;vc.0" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="14"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="29"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.3" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="24"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.07" steps="185"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="24"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.7" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="104"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="26"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.06" steps="105"/></proof>
  </goal>
  <goal name="sort_to_list&#39;vc.10" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="28"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="copy_list&#39;vc" expl="VC for copy_list" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="copy_list&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="24"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="22"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="66"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.3" expl="index in array bounds" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="65"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.4" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="108"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="24"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.6" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="27"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="91"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.8" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="131"/></proof>
  </goal>
  <goal name="copy_list&#39;vc.9" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.11" steps="379"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="mem_nth_in_bounds&#39;vc" expl="VC for mem_nth_in_bounds" proved="true">
 <proof prover="3"><result status="valid" time="0.04" steps="196"/></proof>
 </goal>
 <goal name="sorted_list_nth&#39;vc" expl="VC for sorted_list_nth" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="sorted_list_nth&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="106"/></proof>
  </goal>
  <goal name="sorted_list_nth&#39;vc.1" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="28"/></proof>
  </goal>
  <goal name="sorted_list_nth&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="30"/></proof>
  </goal>
  <goal name="sorted_list_nth&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.12" steps="536"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="ghc_sort&#39;vc" expl="VC for ghc_sort" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="ghc_sort&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="70"/></proof>
  </goal>
  <goal name="ghc_sort&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="50"/></proof>
  </goal>
  <goal name="ghc_sort&#39;vc.2" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.03" steps="18"/></proof>
  </goal>
  <goal name="ghc_sort&#39;vc.3" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="ghc_sort&#39;vc.4" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="20"/></proof>
  </goal>
  <goal name="ghc_sort&#39;vc.5" expl="precondition" proved="true">
  <proof prover="3"><result status="valid" time="0.02" steps="21"/></proof>
  </goal>
  <goal name="ghc_sort&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.12" steps="377"/></proof>
  </goal>
  <goal name="ghc_sort&#39;vc.7" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="94"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
