examples/linear_probing/why3session.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
   2 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
   3 "https://www.why3.org/why3session.dtd">
   4 <why3session shape_version="6">
   5 <prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
   6 <prover id="1" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
   7 <prover id="2" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
   8 <prover id="3" name="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
   9 <prover id="4" name="Z3" version="4.11.2" timelimit="5" steplimit="0" memlimit="1000"/>
  10 <prover id="5" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
  11 <prover id="6" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
  12 <prover id="7" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
  13 <prover id="8" name="Alt-Ergo" version="2.1.0" timelimit="5" steplimit="0" memlimit="1000"/>
  14 <file format="whyml" proved="true">
  15 <path name=".."/><path name="linear_probing.mlw"/>
  16 <theory name="HashedTypeWithDummy" proved="true">
  17  <goal name="neq&#39;vc" expl="VC for neq" proved="true">
  18  <proof prover="1"><result status="valid" time="0.000000" steps="2"/></proof>
  19  </goal>
  20 </theory>
  21 <theory name="LinearProbing" proved="true">
  22  <goal name="bucket&#39;vc" expl="VC for bucket" proved="true">
  23  <proof prover="1"><result status="valid" time="0.010000" steps="48"/></proof>
  24  </goal>
  25  <goal name="NumOfDummy.numof_eq&#39;vc" expl="VC for numof_eq" proved="true">
  26  <proof prover="2"><result status="valid" time="5.000000"/></proof>
  27  </goal>
  28  <goal name="NumOfDummy.dummy_const&#39;vc" expl="VC for dummy_const" proved="true">
  29  <proof prover="1"><result status="valid" time="0.220000" steps="2686"/></proof>
  30  </goal>
  31  <goal name="numof_update&#39;vc" expl="VC for numof_update" proved="true">
  32  <proof prover="8"><result status="valid" time="1.738161" steps="7211"/></proof>
  33  </goal>
  34  <goal name="t&#39;vc" expl="VC for t" proved="true">
  35  <transf name="exists" proved="true" arg1="0">
  36   <goal name="t&#39;vc.0" proved="true">
  37   <transf name="exists" proved="true" arg1="(make 1 dummy)">
  38    <goal name="t&#39;vc.0.0" proved="true">
  39    <transf name="exists" proved="true" arg1="(fun (_:keym1) -&gt; False)">
  40     <goal name="t&#39;vc.0.0.0" proved="true">
  41     <transf name="exists" proved="true" arg1="(fun (_:keym1) -&gt; 0)">
  42      <goal name="t&#39;vc.0.0.0.0" proved="true">
  43      <proof prover="7"><result status="valid" time="0.050000" steps="13643"/></proof>
  44      </goal>
  45     </transf>
  46     </goal>
  47    </transf>
  48    </goal>
  49   </transf>
  50   </goal>
  51  </transf>
  52  </goal>
  53  <goal name="create&#39;vc" expl="VC for create" proved="true">
  54  <proof prover="1"><result status="valid" time="0.020000" steps="106"/></proof>
  55  </goal>
  56  <goal name="clear&#39;vc" expl="VC for clear" proved="true">
  57  <proof prover="1"><result status="valid" time="0.070000" steps="593"/></proof>
  58  </goal>
  59  <goal name="find&#39;vc" expl="VC for find" proved="true">
  60  <transf name="split_goal_right" proved="true" >
  61   <goal name="find&#39;vc.0" expl="precondition" proved="true">
  62   <proof prover="1"><result status="valid" time="0.010000" steps="2"/></proof>
  63   </goal>
  64   <goal name="find&#39;vc.1" expl="index in array bounds" proved="true">
  65   <proof prover="1"><result status="valid" time="0.000000" steps="14"/></proof>
  66   </goal>
  67   <goal name="find&#39;vc.2" expl="index in array bounds" proved="true">
  68   <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
  69   </goal>
  70   <goal name="find&#39;vc.3" expl="variant decrease" proved="true">
  71   <proof prover="4"><result status="valid" time="0.030000" steps="136829"/></proof>
  72   </goal>
  73   <goal name="find&#39;vc.4" expl="precondition" proved="true">
  74   <proof prover="1"><result status="valid" time="0.010000" steps="77"/></proof>
  75   </goal>
  76   <goal name="find&#39;vc.5" expl="precondition" proved="true">
  77   <proof prover="1"><result status="valid" time="0.000000" steps="14"/></proof>
  78   </goal>
  79   <goal name="find&#39;vc.6" expl="precondition" proved="true">
  80   <proof prover="1"><result status="valid" time="0.341811" steps="4906"/></proof>
  81   </goal>
  82   <goal name="find&#39;vc.7" expl="precondition" proved="true">
  83   <proof prover="1"><result status="valid" time="0.050217" steps="460"/></proof>
  84   </goal>
  85   <goal name="find&#39;vc.8" expl="postcondition" proved="true">
  86   <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
  87   </goal>
  88   <goal name="find&#39;vc.9" expl="postcondition" proved="true">
  89   <proof prover="1"><result status="valid" time="0.010000" steps="36"/></proof>
  90   </goal>
  91   <goal name="find&#39;vc.10" expl="postcondition" proved="true">
  92   <proof prover="1"><result status="valid" time="0.010000" steps="50"/></proof>
  93   </goal>
  94   <goal name="find&#39;vc.11" expl="precondition" proved="true">
  95   <proof prover="1"><result status="valid" time="0.010000" steps="0"/></proof>
  96   </goal>
  97   <goal name="find&#39;vc.12" expl="precondition" proved="true">
  98   <proof prover="1"><result status="valid" time="0.010000" steps="3"/></proof>
  99   </goal>
 100   <goal name="find&#39;vc.13" expl="precondition" proved="true">
 101   <proof prover="1"><result status="valid" time="0.010000" steps="21"/></proof>
 102   </goal>
 103   <goal name="find&#39;vc.14" expl="precondition" proved="true">
 104   <proof prover="1"><result status="valid" time="0.010000" steps="72"/></proof>
 105   </goal>
 106   <goal name="find&#39;vc.15" expl="postcondition" proved="true">
 107   <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
 108   </goal>
 109   <goal name="find&#39;vc.16" expl="postcondition" proved="true">
 110   <proof prover="1"><result status="valid" time="0.000000" steps="14"/></proof>
 111   </goal>
 112   <goal name="find&#39;vc.17" expl="postcondition" proved="true">
 113   <proof prover="1"><result status="valid" time="0.010000" steps="30"/></proof>
 114   </goal>
 115  </transf>
 116  </goal>
 117  <goal name="mem&#39;vc" expl="VC for mem" proved="true">
 118  <proof prover="2"><result status="valid" time="2.400000"/></proof>
 119  </goal>
 120  <goal name="resize&#39;vc" expl="VC for resize" proved="true">
 121  <transf name="split_goal_right" proved="true" >
 122   <goal name="resize&#39;vc.0" expl="array creation size" proved="true">
 123   <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
 124   </goal>
 125   <goal name="resize&#39;vc.1" expl="loop invariant init" proved="true">
 126   <proof prover="1"><result status="valid" time="0.010000" steps="500"/></proof>
 127   </goal>
 128   <goal name="resize&#39;vc.2" expl="loop invariant init" proved="true">
 129   <proof prover="1"><result status="valid" time="0.010000" steps="29"/></proof>
 130   </goal>
 131   <goal name="resize&#39;vc.3" expl="loop invariant init" proved="true">
 132   <proof prover="4"><result status="valid" time="0.020000" steps="44327"/></proof>
 133   </goal>
 134   <goal name="resize&#39;vc.4" expl="index in array bounds" proved="true">
 135   <proof prover="1"><result status="valid" time="0.010000" steps="24"/></proof>
 136   </goal>
 137   <goal name="resize&#39;vc.5" expl="precondition" proved="true">
 138   <proof prover="1"><result status="valid" time="0.000000" steps="0"/></proof>
 139   </goal>
 140   <goal name="resize&#39;vc.6" expl="precondition" proved="true">
 141   <proof prover="1"><result status="valid" time="0.030000" steps="175"/></proof>
 142   </goal>
 143   <goal name="resize&#39;vc.7" expl="assertion" proved="true">
 144   <proof prover="2"><result status="valid" time="3.250000"/></proof>
 145   <proof prover="4"><result status="valid" time="0.020000" steps="50964"/></proof>
 146   </goal>
 147   <goal name="resize&#39;vc.8" expl="index in array bounds" proved="true">
 148   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 149   </goal>
 150   <goal name="resize&#39;vc.9" expl="assertion" proved="true">
 151   <proof prover="4"><result status="valid" time="0.040000" steps="291383"/></proof>
 152   </goal>
 153   <goal name="resize&#39;vc.10" expl="loop invariant preservation" proved="true">
 154   <proof prover="4"><result status="valid" time="0.116331" steps="302202"/></proof>
 155   </goal>
 156   <goal name="resize&#39;vc.11" expl="loop invariant preservation" proved="true">
 157   <transf name="split_vc" proved="true" >
 158    <goal name="resize&#39;vc.11.0" expl="loop invariant preservation" proved="true">
 159    <proof prover="5" timelimit="1"><result status="valid" time="0.295552" steps="710283"/></proof>
 160    </goal>
 161    <goal name="resize&#39;vc.11.1" expl="loop invariant preservation" proved="true">
 162    <transf name="split_vc" proved="true" >
 163     <goal name="resize&#39;vc.11.1.0" expl="loop invariant preservation" proved="true">
 164     <proof prover="5" memlimit="2000"><result status="valid" time="0.221908" steps="647529"/></proof>
 165     </goal>
 166    </transf>
 167    </goal>
 168   </transf>
 169   </goal>
 170   <goal name="resize&#39;vc.12" expl="loop invariant preservation" proved="true">
 171   <transf name="split_goal_right" proved="true" >
 172    <goal name="resize&#39;vc.12.0" expl="loop invariant preservation" proved="true">
 173    <proof prover="0"><result status="valid" time="0.580000"/></proof>
 174    </goal>
 175    <goal name="resize&#39;vc.12.1" expl="loop invariant preservation" proved="true">
 176    <transf name="remove" proved="true" arg1="real,tuple0,unit,ref,map,list,option,zero,one,(&gt;),(&gt;=),abs,div,mod,const,is_nil,mem,is_none,(!),hash,([]&#39;),([&lt;-]&#39;),next,Assoc,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm,Assoc1,Mul_distr_l,Mul_distr_r,Comm1,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Div_bound,Mod_bound,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_1,Mod_1,Div_inf,Mod_inf,Div_mult,Mod_mult,numof&#39;def,Numof_bounds,Numof_append,Numof_left_no_add,Numof_left_add,Empty,Full,numof_increasing,numof_strictly_increasing,numof_change_any,numof_change_some,numof_change_equiv,is_nil&#39;spec,is_none&#39;spec,neq&#39;spec,hash_nonneg,hash_eq,array&#39;invariant,([&lt;-])&#39;spec,make_spec,bucket&#39;spec,bucket&#39;def,numof_eq,dummy_const">
 177     <goal name="resize&#39;vc.12.1.0" expl="loop invariant preservation" proved="true">
 178     <proof prover="4"><result status="valid" time="0.010000" steps="25131"/></proof>
 179     </goal>
 180    </transf>
 181    </goal>
 182    <goal name="resize&#39;vc.12.2" expl="loop invariant preservation" proved="true">
 183    <transf name="remove" proved="true" arg1="real,tuple0,unit,ref,map,list,option,zero,one,(&gt;),(&gt;=),abs,div,mod,const,is_nil,mem,is_none,(!),hash,([]&#39;),([&lt;-]&#39;),next,Assoc,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm,Assoc1,Mul_distr_l,Mul_distr_r,Comm1,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Abs_le,Abs_pos,Div_mod,Div_bound,Mod_bound,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_1,Mod_1,Div_inf,Mod_inf,Div_mult,Mod_mult,numof&#39;def,Numof_bounds,Numof_append,Numof_left_no_add,Numof_left_add,Empty,Full,numof_increasing,numof_strictly_increasing,numof_change_any,numof_change_some,numof_change_equiv,is_nil&#39;spec,is_none&#39;spec,neq&#39;spec,hash_nonneg,hash_eq,array&#39;invariant,([&lt;-])&#39;spec,make_spec,bucket&#39;spec,bucket&#39;def,numof_eq,dummy_const">
 184     <goal name="resize&#39;vc.12.2.0" expl="loop invariant preservation" proved="true">
 185     <proof prover="4"><result status="valid" time="0.020000" steps="27411"/></proof>
 186     </goal>
 187    </transf>
 188    </goal>
 189    <goal name="resize&#39;vc.12.3" expl="loop invariant preservation" proved="true">
 190    <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),abs,get,set,([]&#39;),([&lt;-]&#39;),const,(!),is_nil,mem,is_none,([]),numof,numofd,next,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,Abs_le,Abs_pos,Div_mod,Div_bound,Mod_bound,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_1,Mod_1,Div_inf,Mod_inf,Div_mult,Mod_mult,numof&#39;def,Numof_bounds,Numof_append,Numof_left_no_add,Numof_left_add,Empty,Full,numof_increasing,numof_strictly_increasing,numof_change_any,numof_change_some,numof_change_equiv,is_nil&#39;spec,is_none&#39;spec,eq&#39;spec,hash_nonneg,hash_eq,array&#39;invariant,([&lt;-])&#39;spec,make_spec,bucket&#39;spec,bucket&#39;def,numof_eq,dummy_const">
 191     <goal name="resize&#39;vc.12.3.0" expl="loop invariant preservation" proved="true">
 192     <proof prover="4" timelimit="1"><result status="valid" time="0.010000" steps="28674"/></proof>
 193     </goal>
 194    </transf>
 195    </goal>
 196    <goal name="resize&#39;vc.12.4" expl="loop invariant preservation" proved="true">
 197    <transf name="remove" proved="true" arg1="zero,one,(-),(&gt;),(&lt;=),(&gt;=),abs,get,set,([]&#39;),([&lt;-]&#39;),const,(!),is_nil,mem,is_none,neq,dummym,between,numof,numofd,next,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,Abs_le,Abs_pos,Div_bound,Mod_bound,Div_sign_pos,Div_sign_neg,Mod_sign_pos,Mod_sign_neg,Rounds_toward_zero,Div_1,Mod_1,Div_inf,Mod_inf,Div_mult,Mod_mult,numof&#39;def,Numof_bounds,Numof_append,Numof_left_no_add,Numof_left_add,Empty,Full,numof_increasing,numof_strictly_increasing,numof_change_any,numof_change_some,numof_change_equiv,is_nil&#39;spec,is_none&#39;spec,neq&#39;spec,array&#39;invariant,([&lt;-])&#39;spec,make_spec,bucket&#39;spec,numof_eq,dummy_const">
 198     <goal name="resize&#39;vc.12.4.0" expl="loop invariant preservation" proved="true">
 199     <proof prover="0" timelimit="1"><result status="valid" time="0.130000"/></proof>
 200     </goal>
 201    </transf>
 202    </goal>
 203    <goal name="resize&#39;vc.12.5" expl="loop invariant preservation" proved="true">
 204    <proof prover="0"><result status="valid" time="0.160000"/></proof>
 205    </goal>
 206   </transf>
 207   </goal>
 208   <goal name="resize&#39;vc.13" expl="loop invariant preservation" proved="true">
 209   <proof prover="1"><result status="valid" time="0.020000" steps="134"/></proof>
 210   </goal>
 211   <goal name="resize&#39;vc.14" expl="loop invariant preservation" proved="true">
 212   <proof prover="4"><result status="valid" time="0.020000" steps="42156"/></proof>
 213   </goal>
 214   <goal name="resize&#39;vc.15" expl="loop invariant preservation" proved="true">
 215   <proof prover="4"><result status="valid" time="0.030000" steps="69420"/></proof>
 216   </goal>
 217   <goal name="resize&#39;vc.16" expl="type invariant" proved="true">
 218   <proof prover="7"><result status="valid" time="0.040000" steps="14742"/></proof>
 219   </goal>
 220   <goal name="resize&#39;vc.17" expl="type invariant" proved="true">
 221   <proof prover="7"><result status="valid" time="0.060000" steps="15009"/></proof>
 222   </goal>
 223   <goal name="resize&#39;vc.18" expl="type invariant" proved="true">
 224   <transf name="split_goal_right" proved="true" >
 225    <goal name="resize&#39;vc.18.0" expl="type invariant" proved="true">
 226    <proof prover="0"><result status="valid" time="0.060000"/></proof>
 227    </goal>
 228   </transf>
 229   </goal>
 230   <goal name="resize&#39;vc.19" expl="postcondition" proved="true">
 231   <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
 232   </goal>
 233   <goal name="resize&#39;vc.20" expl="out of loop bounds" proved="true">
 234   <proof prover="1"><result status="valid" time="0.010000" steps="22"/></proof>
 235   </goal>
 236  </transf>
 237  </goal>
 238  <goal name="add&#39;vc" expl="VC for add" proved="true">
 239  <transf name="split_goal_right" proved="true" >
 240   <goal name="add&#39;vc.0" expl="postcondition" proved="true">
 241   <proof prover="1"><result status="valid" time="0.010000" steps="29"/></proof>
 242   </goal>
 243   <goal name="add&#39;vc.1" expl="postcondition" proved="true">
 244   <proof prover="1"><result status="valid" time="0.010000" steps="8"/></proof>
 245   </goal>
 246   <goal name="add&#39;vc.2" expl="precondition" proved="true">
 247   <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
 248   </goal>
 249   <goal name="add&#39;vc.3" expl="precondition" proved="true">
 250   <proof prover="1"><result status="valid" time="0.010000" steps="30"/></proof>
 251   </goal>
 252   <goal name="add&#39;vc.4" expl="index in array bounds" proved="true">
 253   <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
 254   </goal>
 255   <goal name="add&#39;vc.5" expl="index in array bounds" proved="true">
 256   <proof prover="1"><result status="valid" time="0.010000" steps="14"/></proof>
 257   </goal>
 258   <goal name="add&#39;vc.6" expl="assertion" proved="true">
 259   <proof prover="4"><result status="valid" time="0.050000" steps="184975"/></proof>
 260   </goal>
 261   <goal name="add&#39;vc.7" expl="type invariant" proved="true">
 262   <proof prover="7"><result status="valid" time="0.060000" steps="15424"/></proof>
 263   </goal>
 264   <goal name="add&#39;vc.8" expl="type invariant" proved="true">
 265   <proof prover="4" timelimit="1"><result status="valid" time="0.537232" steps="1275466"/></proof>
 266   </goal>
 267   <goal name="add&#39;vc.9" expl="type invariant" proved="true">
 268   <transf name="split_goal_right" proved="true" >
 269    <goal name="add&#39;vc.9.0" expl="type invariant" proved="true">
 270    <transf name="unfold" proved="true" arg1="valid">
 271     <goal name="add&#39;vc.9.0.0" expl="VC for add" proved="true">
 272     <transf name="split_goal_right" proved="true" >
 273      <goal name="add&#39;vc.9.0.0.0" expl="VC for add" proved="true">
 274      <proof prover="7"><result status="valid" time="0.080000" steps="20014"/></proof>
 275      </goal>
 276      <goal name="add&#39;vc.9.0.0.1" expl="VC for add" proved="true">
 277      <transf name="inline_all" proved="true" >
 278       <goal name="add&#39;vc.9.0.0.1.0" expl="VC for add" proved="true">
 279       <proof prover="7"><result status="valid" time="0.160000" steps="34590"/></proof>
 280       </goal>
 281      </transf>
 282      </goal>
 283      <goal name="add&#39;vc.9.0.0.2" expl="VC for add" proved="true">
 284      <transf name="introduce_premises" proved="true" >
 285       <goal name="add&#39;vc.9.0.0.2.0" expl="VC for add" proved="true">
 286       <transf name="subst_all" proved="true" >
 287        <goal name="add&#39;vc.9.0.0.2.0.0" expl="VC for add" proved="true">
 288        <transf name="case" proved="true" arg1="(i=i1)">
 289         <goal name="add&#39;vc.9.0.0.2.0.0.0" expl="true case" proved="true">
 290         <proof prover="1" timelimit="1"><result status="valid" time="0.030000" steps="81"/></proof>
 291         </goal>
 292         <goal name="add&#39;vc.9.0.0.2.0.0.1" expl="false case" proved="true">
 293         <transf name="inline_all" proved="true" >
 294          <goal name="add&#39;vc.9.0.0.2.0.0.1.0" expl="false case" proved="true">
 295          <proof prover="7"><result status="valid" time="0.130000" steps="35402"/></proof>
 296          </goal>
 297         </transf>
 298         </goal>
 299        </transf>
 300        </goal>
 301       </transf>
 302       </goal>
 303      </transf>
 304      </goal>
 305      <goal name="add&#39;vc.9.0.0.3" expl="VC for add" proved="true">
 306      <transf name="split_all_full" proved="true" >
 307       <goal name="add&#39;vc.9.0.0.3.0" expl="VC for add" proved="true">
 308       <proof prover="4" timelimit="1"><result status="valid" time="0.381460" steps="824794"/></proof>
 309       </goal>
 310      </transf>
 311      </goal>
 312      <goal name="add&#39;vc.9.0.0.4" expl="VC for add" proved="true">
 313      <transf name="split_all_full" proved="true" >
 314       <goal name="add&#39;vc.9.0.0.4.0" expl="VC for add" proved="true">
 315       <proof prover="4" timelimit="1"><result status="valid" time="0.430000" steps="911071"/></proof>
 316       </goal>
 317      </transf>
 318      </goal>
 319      <goal name="add&#39;vc.9.0.0.5" expl="VC for add" proved="true">
 320      <transf name="inline_all" proved="true" >
 321       <goal name="add&#39;vc.9.0.0.5.0" expl="VC for add" proved="true">
 322       <proof prover="3"><result status="valid" time="0.268669" steps="32245"/></proof>
 323       </goal>
 324      </transf>
 325      </goal>
 326      <goal name="add&#39;vc.9.0.0.6" expl="VC for add" proved="true">
 327      <transf name="inline_all" proved="true" >
 328       <goal name="add&#39;vc.9.0.0.6.0" expl="VC for add" proved="true">
 329       <proof prover="4" timelimit="10" memlimit="4000"><result status="valid" time="0.142569" steps="406956"/></proof>
 330       </goal>
 331      </transf>
 332      </goal>
 333      <goal name="add&#39;vc.9.0.0.7" expl="VC for add" proved="true">
 334      <proof prover="7"><result status="valid" time="0.200000" steps="43593"/></proof>
 335      </goal>
 336     </transf>
 337     </goal>
 338    </transf>
 339    </goal>
 340   </transf>
 341   </goal>
 342   <goal name="add&#39;vc.10" expl="postcondition" proved="true">
 343   <proof prover="1"><result status="valid" time="0.010000" steps="34"/></proof>
 344   </goal>
 345   <goal name="add&#39;vc.11" expl="type invariant" proved="true">
 346   <proof prover="7"><result status="valid" time="0.050000" steps="13886"/></proof>
 347   </goal>
 348   <goal name="add&#39;vc.12" expl="type invariant" proved="true">
 349   <proof prover="7"><result status="valid" time="0.060000" steps="14204"/></proof>
 350   </goal>
 351   <goal name="add&#39;vc.13" expl="type invariant" proved="true">
 352   <proof prover="7"><result status="valid" time="0.110000" steps="22603"/></proof>
 353   </goal>
 354   <goal name="add&#39;vc.14" expl="postcondition" proved="true">
 355   <proof prover="1"><result status="valid" time="0.010000" steps="28"/></proof>
 356   </goal>
 357  </transf>
 358  </goal>
 359  <goal name="copy&#39;vc" expl="VC for copy" proved="true">
 360  <proof prover="2"><result status="valid" time="2.780000"/></proof>
 361  </goal>
 362  <goal name="find_dummy&#39;vc" expl="VC for find_dummy" proved="true">
 363  <proof prover="1"><result status="valid" time="0.290685" steps="2559"/></proof>
 364  </goal>
 365  <goal name="delete&#39;vc" expl="VC for delete" proved="true">
 366  <transf name="split_goal_right" proved="true" >
 367   <goal name="delete&#39;vc.0" expl="index in array bounds" proved="true">
 368   <proof prover="1"><result status="valid" time="0.010000" steps="74"/></proof>
 369   </goal>
 370   <goal name="delete&#39;vc.1" expl="precondition" proved="true">
 371   <proof prover="1"><result status="valid" time="0.010000" steps="13"/></proof>
 372   </goal>
 373   <goal name="delete&#39;vc.2" expl="variant decrease" proved="true">
 374   <proof prover="1"><result status="valid" time="0.032436" steps="187"/></proof>
 375   </goal>
 376   <goal name="delete&#39;vc.3" expl="precondition" proved="true">
 377   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 378   </goal>
 379   <goal name="delete&#39;vc.4" expl="precondition" proved="true">
 380   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 381   </goal>
 382   <goal name="delete&#39;vc.5" expl="precondition" proved="true">
 383   <proof prover="1"><result status="valid" time="0.020000" steps="100"/></proof>
 384   </goal>
 385   <goal name="delete&#39;vc.6" expl="precondition" proved="true">
 386   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 387   </goal>
 388   <goal name="delete&#39;vc.7" expl="precondition" proved="true">
 389   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 390   </goal>
 391   <goal name="delete&#39;vc.8" expl="precondition" proved="true">
 392   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 393   </goal>
 394   <goal name="delete&#39;vc.9" expl="precondition" proved="true">
 395   <proof prover="1"><result status="valid" time="0.030000" steps="128"/></proof>
 396   </goal>
 397   <goal name="delete&#39;vc.10" expl="precondition" proved="true">
 398   <proof prover="1"><result status="valid" time="0.100000" steps="316"/></proof>
 399   </goal>
 400   <goal name="delete&#39;vc.11" expl="precondition" proved="true">
 401   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 402   </goal>
 403   <goal name="delete&#39;vc.12" expl="precondition" proved="true">
 404   <proof prover="1"><result status="valid" time="0.010000" steps="61"/></proof>
 405   </goal>
 406   <goal name="delete&#39;vc.13" expl="precondition" proved="true">
 407   <proof prover="1"><result status="valid" time="0.440626" steps="7145"/></proof>
 408   </goal>
 409   <goal name="delete&#39;vc.14" expl="postcondition" proved="true">
 410   <proof prover="1"><result status="valid" time="0.010000" steps="42"/></proof>
 411   </goal>
 412   <goal name="delete&#39;vc.15" expl="postcondition" proved="true">
 413   <proof prover="1"><result status="valid" time="0.010000" steps="42"/></proof>
 414   </goal>
 415   <goal name="delete&#39;vc.16" expl="precondition" proved="true">
 416   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 417   </goal>
 418   <goal name="delete&#39;vc.17" expl="precondition" proved="true">
 419   <proof prover="1"><result status="valid" time="0.010000" steps="58"/></proof>
 420   </goal>
 421   <goal name="delete&#39;vc.18" expl="index in array bounds" proved="true">
 422   <proof prover="1"><result status="valid" time="0.010000" steps="40"/></proof>
 423   </goal>
 424   <goal name="delete&#39;vc.19" expl="precondition" proved="true">
 425   <proof prover="1"><result status="valid" time="0.010000" steps="50"/></proof>
 426   </goal>
 427   <goal name="delete&#39;vc.20" expl="precondition" proved="true">
 428   <proof prover="1"><result status="valid" time="0.020000" steps="217"/></proof>
 429   </goal>
 430   <goal name="delete&#39;vc.21" expl="precondition" proved="true">
 431   <proof prover="1"><result status="valid" time="0.020000" steps="107"/></proof>
 432   </goal>
 433   <goal name="delete&#39;vc.22" expl="precondition" proved="true">
 434   <proof prover="1"><result status="valid" time="0.010000" steps="54"/></proof>
 435   </goal>
 436   <goal name="delete&#39;vc.23" expl="precondition" proved="true">
 437   <proof prover="1"><result status="valid" time="0.010000" steps="83"/></proof>
 438   </goal>
 439   <goal name="delete&#39;vc.24" expl="index in array bounds" proved="true">
 440   <proof prover="1"><result status="valid" time="0.048788" steps="216"/></proof>
 441   </goal>
 442   <goal name="delete&#39;vc.25" expl="precondition" proved="true">
 443   <proof prover="1"><result status="valid" time="0.080000" steps="288"/></proof>
 444   </goal>
 445   <goal name="delete&#39;vc.26" expl="precondition" proved="true">
 446   <proof prover="1"><result status="valid" time="0.020000" steps="436"/></proof>
 447   </goal>
 448   <goal name="delete&#39;vc.27" expl="precondition" proved="true">
 449   <proof prover="1"><result status="valid" time="0.120000" steps="1113"/></proof>
 450   </goal>
 451   <goal name="delete&#39;vc.28" expl="variant decrease" proved="true">
 452   <proof prover="1"><result status="valid" time="0.075802" steps="688"/></proof>
 453   </goal>
 454   <goal name="delete&#39;vc.29" expl="precondition" proved="true">
 455   <proof prover="1"><result status="valid" time="0.010000" steps="54"/></proof>
 456   </goal>
 457   <goal name="delete&#39;vc.30" expl="precondition" proved="true">
 458   <proof prover="1"><result status="valid" time="0.080000" steps="335"/></proof>
 459   </goal>
 460   <goal name="delete&#39;vc.31" expl="precondition" proved="true">
 461   <proof prover="1"><result status="valid" time="0.080000" steps="0"/></proof>
 462   </goal>
 463   <goal name="delete&#39;vc.32" expl="precondition" proved="true">
 464   <proof prover="1"><result status="valid" time="0.010000" steps="118"/></proof>
 465   </goal>
 466   <goal name="delete&#39;vc.33" expl="precondition" proved="true">
 467   <proof prover="1"><result status="valid" time="0.020000" steps="109"/></proof>
 468   </goal>
 469   <goal name="delete&#39;vc.34" expl="precondition" proved="true">
 470   <proof prover="1"><result status="valid" time="0.020000" steps="141"/></proof>
 471   </goal>
 472   <goal name="delete&#39;vc.35" expl="precondition" proved="true">
 473   <proof prover="1"><result status="valid" time="0.020000" steps="119"/></proof>
 474   </goal>
 475   <goal name="delete&#39;vc.36" expl="precondition" proved="true">
 476   <proof prover="4"><result status="valid" time="0.688933" steps="1787479"/></proof>
 477   </goal>
 478   <goal name="delete&#39;vc.37" expl="precondition" proved="true">
 479   <proof prover="1"><result status="valid" time="0.010000" steps="54"/></proof>
 480   </goal>
 481   <goal name="delete&#39;vc.38" expl="precondition" proved="true">
 482   <transf name="split_goal_right" proved="true" >
 483    <goal name="delete&#39;vc.38.0" expl="precondition" proved="true">
 484    <proof prover="0"><result status="valid" time="0.610000"/></proof>
 485    </goal>
 486    <goal name="delete&#39;vc.38.1" expl="precondition" proved="true">
 487    <proof prover="0"><result status="valid" time="1.130000"/></proof>
 488    </goal>
 489   </transf>
 490   </goal>
 491   <goal name="delete&#39;vc.39" expl="precondition" proved="true">
 492   <proof prover="7"><result status="valid" time="0.150000" steps="35225"/></proof>
 493   </goal>
 494   <goal name="delete&#39;vc.40" expl="postcondition" proved="true">
 495   <proof prover="1"><result status="valid" time="0.010000" steps="68"/></proof>
 496   </goal>
 497   <goal name="delete&#39;vc.41" expl="postcondition" proved="true">
 498   <proof prover="1"><result status="valid" time="0.020000" steps="68"/></proof>
 499   </goal>
 500   <goal name="delete&#39;vc.42" expl="postcondition" proved="true">
 501   <proof prover="1"><result status="valid" time="0.010000" steps="0"/></proof>
 502   </goal>
 503   <goal name="delete&#39;vc.43" expl="postcondition" proved="true">
 504   <proof prover="2"><result status="valid" time="0.130000"/></proof>
 505   <proof prover="4"><result status="valid" time="0.040000" steps="76150"/></proof>
 506   </goal>
 507  </transf>
 508  </goal>
 509  <goal name="remove&#39;vc" expl="VC for remove" proved="true">
 510  <transf name="split_goal_right" proved="true" >
 511   <goal name="remove&#39;vc.0" expl="precondition" proved="true">
 512   <proof prover="1"><result status="valid" time="0.010000" steps="0"/></proof>
 513   </goal>
 514   <goal name="remove&#39;vc.1" expl="precondition" proved="true">
 515   <proof prover="1"><result status="valid" time="0.010000" steps="18"/></proof>
 516   </goal>
 517   <goal name="remove&#39;vc.2" expl="index in array bounds" proved="true">
 518   <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
 519   </goal>
 520   <goal name="remove&#39;vc.3" expl="index in array bounds" proved="true">
 521   <proof prover="1"><result status="valid" time="0.010000" steps="6"/></proof>
 522   </goal>
 523   <goal name="remove&#39;vc.4" expl="assertion" proved="true">
 524   <proof prover="4"><result status="valid" time="0.050000" steps="195487"/></proof>
 525   </goal>
 526   <goal name="remove&#39;vc.5" expl="precondition" proved="true">
 527   <proof prover="1"><result status="valid" time="0.010000" steps="11"/></proof>
 528   </goal>
 529   <goal name="remove&#39;vc.6" expl="precondition" proved="true">
 530   <proof prover="1"><result status="valid" time="0.010000" steps="148"/></proof>
 531   </goal>
 532   <goal name="remove&#39;vc.7" expl="precondition" proved="true">
 533   <proof prover="1"><result status="valid" time="0.010000" steps="229"/></proof>
 534   </goal>
 535   <goal name="remove&#39;vc.8" expl="precondition" proved="true">
 536   <proof prover="4"><result status="valid" time="0.040000" steps="151079"/></proof>
 537   </goal>
 538   <goal name="remove&#39;vc.9" expl="precondition" proved="true">
 539   <proof prover="1"><result status="valid" time="0.020000" steps="182"/></proof>
 540   </goal>
 541   <goal name="remove&#39;vc.10" expl="precondition" proved="true">
 542   <proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
 543   </goal>
 544   <goal name="remove&#39;vc.11" expl="precondition" proved="true">
 545   <proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
 546   </goal>
 547   <goal name="remove&#39;vc.12" expl="precondition" proved="true">
 548   <proof prover="1"><result status="valid" time="0.010000" steps="0"/></proof>
 549   </goal>
 550   <goal name="remove&#39;vc.13" expl="precondition" proved="true">
 551   <proof prover="1"><result status="valid" time="0.010000" steps="0"/></proof>
 552   </goal>
 553   <goal name="remove&#39;vc.14" expl="precondition" proved="true">
 554   <proof prover="1"><result status="valid" time="0.010000" steps="44"/></proof>
 555   </goal>
 556   <goal name="remove&#39;vc.15" expl="precondition" proved="true">
 557   <proof prover="1"><result status="valid" time="0.010000" steps="26"/></proof>
 558   </goal>
 559   <goal name="remove&#39;vc.16" expl="precondition" proved="true">
 560   <proof prover="1"><result status="valid" time="0.010000" steps="55"/></proof>
 561   </goal>
 562   <goal name="remove&#39;vc.17" expl="precondition" proved="true">
 563   <proof prover="1"><result status="valid" time="0.020000" steps="54"/></proof>
 564   </goal>
 565   <goal name="remove&#39;vc.18" expl="precondition" proved="true">
 566   <proof prover="1"><result status="valid" time="0.020000" steps="271"/></proof>
 567   </goal>
 568   <goal name="remove&#39;vc.19" expl="precondition" proved="true">
 569   <proof prover="7"><result status="valid" time="0.150000" steps="34601"/></proof>
 570   </goal>
 571   <goal name="remove&#39;vc.20" expl="precondition" proved="true">
 572   <proof prover="6"><result status="valid" time="3.319903" steps="2613"/></proof>
 573   </goal>
 574   <goal name="remove&#39;vc.21" expl="type invariant" proved="true">
 575   <proof prover="7"><result status="valid" time="0.560000" steps="89387"/></proof>
 576   </goal>
 577   <goal name="remove&#39;vc.22" expl="type invariant" proved="true">
 578   <proof prover="4" timelimit="1"><result status="valid" time="0.060000" steps="168662"/></proof>
 579   </goal>
 580   <goal name="remove&#39;vc.23" expl="type invariant" proved="true">
 581   <proof prover="4"><result status="valid" time="0.020000" steps="41865"/></proof>
 582   </goal>
 583   <goal name="remove&#39;vc.24" expl="postcondition" proved="true">
 584   <proof prover="1"><result status="valid" time="0.010000" steps="46"/></proof>
 585   </goal>
 586   <goal name="remove&#39;vc.25" expl="postcondition" proved="true">
 587   <proof prover="2"><result status="valid" time="0.160000"/></proof>
 588   <proof prover="4"><result status="valid" time="0.030000" steps="158235"/></proof>
 589   </goal>
 590  </transf>
 591  </goal>
 592 </theory>
 593 </file>
 594 </why3session>