<?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="2" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
<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"/>
<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="0.010000" steps="8"/></proof>
  </goal>
  <goal name="t&#39;vc.1" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.000000" steps="0"/></proof>
  </goal>
  <goal name="t&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.100000" steps="737"/></proof>
  </goal>
  <goal name="t&#39;vc.3" expl="loop variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="121"/></proof>
  </goal>
  <goal name="t&#39;vc.4" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" 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="0.010000" steps="63"/></proof>
 </goal>
 <goal name="no_duplicate" proved="true">
 <proof prover="2"><result status="valid" time="0.020000" steps="11143"/></proof>
 <proof prover="8"><result status="valid" time="0.010000"/></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="0.862784" steps="4221"/></proof>
  </goal>
  <goal name="t3&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="87"/></proof>
  </goal>
  <goal name="t3&#39;vc.2" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="t3&#39;vc.3" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="26"/></proof>
  </goal>
  <goal name="t3&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="22"/></proof>
  </goal>
  <goal name="t3&#39;vc.5" expl="loop invariant init" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="24"/></proof>
  </goal>
  <goal name="t3&#39;vc.6" expl="precondition" proved="true">
  <proof prover="9"><result status="valid" time="0.010000" steps="32"/></proof>
  </goal>
  <goal name="t3&#39;vc.7" expl="variant decrease" proved="true">
  <proof prover="9"><result status="valid" time="0.100000" steps="522"/></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="0.010000" steps="42"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.1" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.100000" steps="460"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.2" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="42"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.3" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="163"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.4" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.040000" steps="163"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.5" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.517001" steps="2224"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.6" expl="precondition" proved="true">
   <proof prover="0"><result status="valid" time="0.675719" steps="978"/></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="0.000000" steps="22"/></proof>
    <proof prover="9"><result status="valid" time="0.010000" steps="38"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="t3&#39;vc.8.7" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="0.560000" steps="2044"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.8" expl="precondition" proved="true">
   <proof prover="0"><result status="valid" time="1.170000" steps="943"/></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="0.000000" steps="21"/></proof>
    <proof prover="9"><result status="valid" time="0.010000" steps="38"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="t3&#39;vc.8.9" expl="precondition" proved="true">
   <proof prover="9"><result status="valid" time="1.020000" steps="2934"/></proof>
   </goal>
   <goal name="t3&#39;vc.8.10" expl="precondition" proved="true">
   <proof prover="0"><result status="valid" time="0.540000" steps="654"/></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="0.000000" steps="21"/></proof>
    <proof prover="9"><result status="valid" time="0.010000" steps="38"/></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="0.240000" steps="1006"/></proof>
     </goal>
     <goal name="t3&#39;vc.8.11.0.1" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.210000" steps="673"/></proof>
     </goal>
     <goal name="t3&#39;vc.8.11.0.2" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.720000" steps="2478"/></proof>
     </goal>
     <goal name="t3&#39;vc.8.11.0.3" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.720478" steps="2359"/></proof>
     </goal>
     <goal name="t3&#39;vc.8.11.0.4" expl="precondition" proved="true">
     <proof prover="9"><result status="valid" time="0.550000" steps="2358"/></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="0.030000" steps="67"/></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="0.020000" steps="58"/></proof>
   </goal>
   <goal name="t3&#39;vc.10.1" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.020000" steps="58"/></proof>
   </goal>
   <goal name="t3&#39;vc.10.2" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="58"/></proof>
   </goal>
   <goal name="t3&#39;vc.10.3" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="72"/></proof>
   </goal>
   <goal name="t3&#39;vc.10.4" expl="loop invariant preservation" proved="true">
   <proof prover="0"><result status="valid" time="1.450000" steps="2170"/></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="0.010000" steps="44"/></proof>
    <proof prover="9"><result status="valid" time="0.050000" steps="83"/></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="12.180000"/></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="0.060000" steps="277"/></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="0.020000" steps="76"/></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="0.060000" steps="280"/></proof>
      </goal>
      <goal name="t3&#39;vc.10.6.1.1.1" expl="apply premises" proved="true">
      <proof prover="9"><result status="valid" time="0.020000" steps="76"/></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="1.880000" steps="2836"/></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="0.100000" steps="216"/></proof>
   <proof prover="9"><result status="valid" time="0.140000" steps="396"/></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="0.020000" steps="83"/></proof>
   </goal>
   <goal name="t3&#39;vc.12.1" expl="loop invariant preservation" proved="true">
   <proof prover="9"><result status="valid" time="0.030000" steps="85"/></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="3.170000" steps="17135"/></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="0.290000" steps="1637"/></proof>
  </goal>
  <goal name="t3&#39;vc.14" expl="loop invariant preservation" proved="true">
  <proof prover="9"><result status="valid" time="0.170000" steps="667"/></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="0.000000" steps="32"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.1" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="32"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.2" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="32"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.3" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="32"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.4" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="1.452455" steps="5106"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.5" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.310000" steps="1674"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.6" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.070000" steps="469"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.7" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="32"/></proof>
   </goal>
   <goal name="t3&#39;vc.15.8" expl="postcondition" proved="true">
   <proof prover="9"><result status="valid" time="0.010000" steps="32"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="t3&#39;vc.16" expl="postcondition" proved="true">
  <proof prover="9"><result status="valid" time="0.050000" steps="184"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="queens3&#39;vc" expl="VC for queens3" proved="true">
 <proof prover="9"><result status="valid" time="0.100000" steps="758"/></proof>
 </goal>
</theory>
</file>
</why3session>
