<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Coq" version="8.11.2" timelimit="0" steplimit="0" memlimit="0"/>
<prover id="8" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="9" name="Alt-Ergo" version="2.3.3" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="10" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="queens.mlw"/>
<theory name="NQueensSetsTermination" proved="true">
 <goal name="t&#39;vc" expl="VC for t" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="t&#39;vc.0" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="8"/></proof>
  </goal>
  <goal name="t&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.00" steps="0"/></proof>
  </goal>
  <goal name="t&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.10" steps="737"/></proof>
  </goal>
  <goal name="t&#39;vc.3" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="121"/></proof>
  </goal>
  <goal name="t&#39;vc.4" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="46"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Solution" proved="true">
 <goal name="partial_solution_eq_prefix" proved="true">
 <proof prover="9"><result status="valid" time="0.01" steps="63"/></proof>
 </goal>
 <goal name="no_duplicate" proved="true">
 <proof prover="8"><result status="valid" time="0.01"/></proof>
 <proof prover="10"><result status="valid" time="0.02"/></proof>
 </goal>
</theory>
<theory name="NQueensSets" proved="true">
 <goal name="t3&#39;vc" expl="VC for t3" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="t3&#39;vc.0" expl="assertion" proved="true">
  <proof prover="9"><result status="valid" time="0.90" steps="4031"/></proof>
  </goal>
  <goal name="t3&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.02" steps="89"/></proof>
  </goal>
  <goal name="t3&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="t3&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="28"/></proof>
  </goal>
  <goal name="t3&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="24"/></proof>
  </goal>
  <goal name="t3&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="26"/></proof>
  </goal>
  <goal name="t3&#39;vc.6" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.01" steps="36"/></proof>
  </goal>
  <goal name="t3&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.10" steps="485"/></proof>
  </goal>
  <goal name="t3&#39;vc.8" expl="precondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="t3&#39;vc.8.0" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="46"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.10" steps="464"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.2" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="46"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.3" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.04" steps="167"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.4" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.04" steps="167"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.5" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.50" steps="1700"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.6" expl="precondition" proved="true">
   <proof prover="0"><result status="valid" time="0.51" steps="980"/></proof>
   <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),get,set,(!),(==),subset,is_empty,singleton,disjoint,eq_sol,partial_solution,solution,lt_sol,sorted,d,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,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,add_def,mem_singleton,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,diff_def,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk&#39;spec,choose&#39;spec,partial_solution_eq_prefix,no_duplicate,H17,H16,H14,H13,H12,H11,Ensures11,Ensures10,Assert,H10,H9,H7,H6,H5,H4,LoopInvariant3,LoopInvariant2,LoopInvariant,H3,Ensures7,Ensures6,Ensures5,Ensures4,Ensures3,Ensures2,Ensures">
    <goal name="t3&#39;vc.8.6.0" expl="precondition" proved="true">
    <proof prover="0"><result status="valid" time="0.00" steps="30"/></proof>
    <proof prover="9"><result status="valid" time="0.01" steps="42"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="t3&#39;vc.8.7" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.56" steps="2100"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.8" expl="precondition" proved="true">
   <proof prover="0"><result status="valid" time="0.88" steps="945"/></proof>
   <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),get,set,(!),(==),subset,is_empty,singleton,disjoint,eq_sol,partial_solution,solution,lt_sol,sorted,d,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,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,mem_singleton,remove_def,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,diff_def,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk&#39;spec,choose&#39;spec,partial_solution_eq_prefix,no_duplicate,H16,H15,H14,H12,H11,H10,Ensures11,Ensures10,Assert,H9,H8,H6,H5,H4,H3,LoopInvariant3,LoopInvariant2,LoopInvariant,H2,Ensures7,Ensures6,Ensures5,Ensures3,Ensures1,Ensures,H1">
    <goal name="t3&#39;vc.8.8.0" expl="precondition" proved="true">
    <proof prover="0"><result status="valid" time="0.00" steps="25"/></proof>
    <proof prover="9"><result status="valid" time="0.01" steps="42"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="t3&#39;vc.8.9" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.61" steps="2085"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.10" expl="precondition" proved="true">
   <proof prover="0"><result status="valid" time="0.38" steps="656"/></proof>
   <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),get,set,(!),(==),subset,is_empty,singleton,disjoint,eq_sol,partial_solution,solution,lt_sol,sorted,d,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,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,mem_singleton,remove_def,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,diff_def,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk&#39;spec,choose&#39;spec,partial_solution_eq_prefix,no_duplicate,H16,H15,H14,H13,H11,H10,Ensures11,Ensures10,Assert,H9,H8,H6,H5,H4,H3,LoopInvariant3,LoopInvariant2,LoopInvariant,H2,Ensures6,Ensures4,Ensures3,Ensures2,Ensures1,Ensures,H1">
    <goal name="t3&#39;vc.8.10.0" expl="precondition" proved="true">
    <proof prover="0"><result status="valid" time="0.00" steps="25"/></proof>
    <proof prover="9"><result status="valid" time="0.01" steps="42"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="t3&#39;vc.8.11" expl="precondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="t3&#39;vc.8.11.0" expl="precondition" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="t3&#39;vc.8.11.0.0" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.24" steps="664"/></proof>
     </goal>
     <goal name="t3&#39;vc.8.11.0.1" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.21" steps="663"/></proof>
     </goal>
     <goal name="t3&#39;vc.8.11.0.2" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.56" steps="2480"/></proof>
     </goal>
     <goal name="t3&#39;vc.8.11.0.3" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.54" steps="2363"/></proof>
     </goal>
     <goal name="t3&#39;vc.8.11.0.4" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.55" steps="2362"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="t3&#39;vc.9" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.03" steps="71"/></proof>
  </goal>
  <goal name="t3&#39;vc.10" expl="loop invariant preservation" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="t3&#39;vc.10.0" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.02" steps="62"/></proof>
   </goal>
   <goal name="t3&#39;vc.10.1" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.02" steps="62"/></proof>
   </goal>
   <goal name="t3&#39;vc.10.2" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="62"/></proof>
   </goal>
   <goal name="t3&#39;vc.10.3" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.03" steps="76"/></proof>
   </goal>
   <goal name="t3&#39;vc.10.4" expl="loop invariant preservation" proved="true">
   <proof prover="0"><result status="valid" time="1.20" steps="2165"/></proof>
   <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),get,set,(!),(==),subset,is_empty,singleton,disjoint,eq_sol,partial_solution,solution,lt_sol,sorted,d,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,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,add_def,mem_singleton,remove_def,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,diff_def,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk&#39;spec,choose&#39;spec,no_duplicate,H21,H20,H19,H17,H15,H14,Ensures15,Ensures14,Assert,H13,H12,H10,H8,H7,LoopInvariant3,LoopInvariant1,LoopInvariant,H6,Ensures11,Ensures8,Ensures7,Ensures6,Ensures5,H,Ensures3">
    <goal name="t3&#39;vc.10.4.0" expl="loop invariant preservation" proved="true">
    <proof prover="0"><result status="valid" time="0.01" steps="48"/></proof>
    <proof prover="9"><result status="valid" time="0.05" steps="87"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="t3&#39;vc.10.5" expl="loop invariant preservation" proved="true">
   <transf name="generalize_introduced" proved="true" >
    <goal name="t3&#39;vc.10.5.0" expl="loop invariant preservation" proved="true">
    <proof prover="1"><path name="queens_NQueensSets_VC_t3_2.v"/><result status="valid" time="12.28"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="t3&#39;vc.10.6" expl="loop invariant preservation" proved="true">
   <transf name="case" proved="true" arg1="(i = d)">
    <goal name="t3&#39;vc.10.6.0" expl="true case (loop invariant preservation)" proved="true">
    <proof prover="9"><result status="valid" time="0.06" steps="281"/></proof>
    </goal>
    <goal name="t3&#39;vc.10.6.1" expl="false case (loop invariant preservation)" proved="true">
    <transf name="case" proved="true" arg1="(j = d)">
     <goal name="t3&#39;vc.10.6.1.0" expl="false case (true case. loop invariant preservation)" proved="true">
     <proof prover="9"><result status="valid" time="0.02" steps="80"/></proof>
     </goal>
     <goal name="t3&#39;vc.10.6.1.1" expl="false case (loop invariant preservation)" proved="true">
     <transf name="apply" proved="true" arg1="H9">
      <goal name="t3&#39;vc.10.6.1.1.0" expl="apply premises" proved="true">
      <proof prover="9"><result status="valid" time="0.06" steps="284"/></proof>
      </goal>
      <goal name="t3&#39;vc.10.6.1.1.1" expl="apply premises" proved="true">
      <proof prover="9"><result status="valid" time="0.02" steps="80"/></proof>
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="t3&#39;vc.11" expl="loop invariant preservation" proved="true">
  <proof prover="0"><result status="valid" time="1.56" steps="2838"/></proof>
  <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),get,set,(!),(==),subset,is_empty,singleton,disjoint,partial_solution,solution,lt_sol,sorted,d,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,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,extensionality,subset_refl,subset_trans,is_empty_empty,empty_is_empty,add_def,mem_singleton,add_remove,remove_add,subset_remove,union_def,subset_union_1,subset_union_2,inter_def,subset_inter_1,subset_inter_2,subset_diff,pick_def,disjoint_inter_empty,disjoint_diff_eq,disjoint_diff_s2,filter_def,subset_filter,map_def,mem_map,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,cardinal_subset,subset_eq,cardinal1,cardinal_union,cardinal_inter_disjoint,cardinal_diff,cardinal_filter,cardinal_map,min_elt_def,max_elt_def,interval_def,cardinal_interval,mk&#39;spec,choose&#39;spec,partial_solution_eq_prefix,no_duplicate,H22,H20,H19,H18,H17,H16,Ensures15,Ensures14,H15,H14,H13,H12,H11,H10,H9,LoopInvariant3,LoopInvariant1,H8,Ensures11,Ensures10,Ensures9,Ensures8,Ensures7,Ensures6,Ensures5,Ensures4,H7,H5,Ensures3,Ensures">
   <goal name="t3&#39;vc.11.0" expl="loop invariant preservation" proved="true">
   <proof prover="0"><result status="valid" time="0.10" steps="268"/></proof>
   <proof prover="9"><result status="valid" time="0.14" steps="633"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="t3&#39;vc.12" expl="loop invariant preservation" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="t3&#39;vc.12.0" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.02" steps="87"/></proof>
   </goal>
   <goal name="t3&#39;vc.12.1" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.03" steps="89"/></proof>
   </goal>
   <goal name="t3&#39;vc.12.2" expl="loop invariant preservation" proved="true">
   <transf name="instantiate" proved="true" arg1="LoopInvariant3" arg2="t">
    <goal name="t3&#39;vc.12.2.0" expl="loop invariant preservation" proved="true">
    <transf name="instantiate" proved="true" arg1="H14" arg2="t">
     <goal name="t3&#39;vc.12.2.0.0" expl="loop invariant preservation" proved="true">
     <proof prover="9"><result status="valid" time="1.07" steps="5261"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="t3&#39;vc.13" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.29" steps="1641"/></proof>
  </goal>
  <goal name="t3&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.17" steps="671"/></proof>
  </goal>
  <goal name="t3&#39;vc.15" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="t3&#39;vc.15.0" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.00" steps="36"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.1" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="36"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.2" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="36"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.3" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="36"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.4" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="1.22" steps="5108"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.5" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.31" steps="1684"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.6" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.07" steps="473"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.7" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="36"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.8" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.01" steps="36"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="t3&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.05" steps="185"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="queens3&#39;vc" expl="VC for queens3" proved="true">
 <proof prover="9"><result status="valid" time="0.10" steps="758"/></proof>
 </goal>
</theory>
</file>
</why3session>
