examples/isqrt_von_neumann/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="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
   6 <prover id="1" name="Alt-Ergo" version="2.4.3" timelimit="1" steplimit="0" memlimit="1000"/>
   7 <prover id="2" name="Alt-Ergo" version="2.5.2" timelimit="1" steplimit="0" memlimit="1000"/>
   8 <prover id="3" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
   9 <prover id="4" name="Alt-Ergo" version="2.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
  10 <prover id="5" name="Alt-Ergo" version="2.2.0" timelimit="5" steplimit="0" memlimit="1000"/>
  11 <file format="whyml" proved="true">
  12 <path name=".."/><path name="isqrt_von_neumann.mlw"/>
  13 <theory name="VonNeumann16" proved="true">
  14  <goal name="sqr_add2" proved="true">
  15  <proof prover="0" timelimit="1"><result status="valid" time="0.010000" steps="1148"/></proof>
  16  </goal>
  17  <goal name="isqrt16&#39;vc" expl="VC for isqrt16" proved="true">
  18  <transf name="split_goal_right" proved="true" >
  19   <goal name="isqrt16&#39;vc.0" expl="loop invariant init" proved="true">
  20   <proof prover="3"><result status="valid" time="0.010000" steps="4190"/></proof>
  21   </goal>
  22   <goal name="isqrt16&#39;vc.1" expl="loop invariant init" proved="true">
  23   <proof prover="3"><result status="valid" time="0.010000" steps="4238"/></proof>
  24   </goal>
  25   <goal name="isqrt16&#39;vc.2" expl="loop invariant init" proved="true">
  26   <proof prover="3"><result status="valid" time="0.020000" steps="4615"/></proof>
  27   </goal>
  28   <goal name="isqrt16&#39;vc.3" expl="loop invariant init" proved="true">
  29   <proof prover="3"><result status="valid" time="0.020000" steps="4662"/></proof>
  30   </goal>
  31   <goal name="isqrt16&#39;vc.4" expl="loop invariant init" proved="true">
  32   <proof prover="3"><result status="valid" time="0.010000" steps="4280"/></proof>
  33   </goal>
  34   <goal name="isqrt16&#39;vc.5" expl="loop invariant init" proved="true">
  35   <proof prover="3"><result status="valid" time="0.010000" steps="4300"/></proof>
  36   </goal>
  37   <goal name="isqrt16&#39;vc.6" expl="loop invariant init" proved="true">
  38   <proof prover="3"><result status="valid" time="0.010000" steps="4321"/></proof>
  39   </goal>
  40   <goal name="isqrt16&#39;vc.7" expl="loop invariant init" proved="true">
  41   <proof prover="3"><result status="valid" time="0.020000" steps="4785"/></proof>
  42   </goal>
  43   <goal name="isqrt16&#39;vc.8" expl="loop invariant init" proved="true">
  44   <proof prover="3"><result status="valid" time="0.010000" steps="4375"/></proof>
  45   </goal>
  46   <goal name="isqrt16&#39;vc.9" expl="loop invariant init" proved="true">
  47   <proof prover="3"><result status="valid" time="0.010000" steps="5877"/></proof>
  48   </goal>
  49   <goal name="isqrt16&#39;vc.10" expl="assertion" proved="true">
  50   <proof prover="3"><result status="valid" time="0.020000" steps="7552"/></proof>
  51   </goal>
  52   <goal name="isqrt16&#39;vc.11" expl="assertion" proved="true">
  53   <proof prover="3"><result status="valid" time="0.010000" steps="4541"/></proof>
  54   </goal>
  55   <goal name="isqrt16&#39;vc.12" expl="assertion" proved="true">
  56   <proof prover="3"><result status="valid" time="0.010000" steps="4594"/></proof>
  57   </goal>
  58   <goal name="isqrt16&#39;vc.13" expl="assertion" proved="true">
  59   <proof prover="3"><result status="valid" time="0.010000" steps="4697"/></proof>
  60   </goal>
  61   <goal name="isqrt16&#39;vc.14" expl="assertion" proved="true">
  62   <proof prover="3"><result status="valid" time="0.050000" steps="22636"/></proof>
  63   </goal>
  64   <goal name="isqrt16&#39;vc.15" expl="assertion" proved="true">
  65   <proof prover="3"><result status="valid" time="0.080000" steps="26169"/></proof>
  66   </goal>
  67   <goal name="isqrt16&#39;vc.16" expl="assertion" proved="true">
  68   <proof prover="3"><result status="valid" time="0.080000" steps="22542"/></proof>
  69   </goal>
  70   <goal name="isqrt16&#39;vc.17" expl="assertion" proved="true">
  71   <proof prover="3"><result status="valid" time="0.060000" steps="30471"/></proof>
  72   </goal>
  73   <goal name="isqrt16&#39;vc.18" expl="assertion" proved="true">
  74   <proof prover="3"><result status="valid" time="0.060000" steps="23806"/></proof>
  75   </goal>
  76   <goal name="isqrt16&#39;vc.19" expl="loop variant decrease" proved="true">
  77   <proof prover="3"><result status="valid" time="0.080000" steps="33778"/></proof>
  78   </goal>
  79   <goal name="isqrt16&#39;vc.20" expl="loop invariant preservation" proved="true">
  80   <proof prover="3"><result status="valid" time="0.060000" steps="23879"/></proof>
  81   </goal>
  82   <goal name="isqrt16&#39;vc.21" expl="loop invariant preservation" proved="true">
  83   <proof prover="3"><result status="valid" time="0.050000" steps="25288"/></proof>
  84   </goal>
  85   <goal name="isqrt16&#39;vc.22" expl="loop invariant preservation" proved="true">
  86   <proof prover="3"><result status="valid" time="0.190000" steps="62212"/></proof>
  87   </goal>
  88   <goal name="isqrt16&#39;vc.23" expl="loop invariant preservation" proved="true">
  89   <proof prover="3"><result status="valid" time="0.060000" steps="56561"/></proof>
  90   </goal>
  91   <goal name="isqrt16&#39;vc.24" expl="loop invariant preservation" proved="true">
  92   <proof prover="3"><result status="valid" time="0.050000" steps="26144"/></proof>
  93   </goal>
  94   <goal name="isqrt16&#39;vc.25" expl="loop invariant preservation" proved="true">
  95   <proof prover="3"><result status="valid" time="0.010000" steps="5312"/></proof>
  96   </goal>
  97   <goal name="isqrt16&#39;vc.26" expl="loop invariant preservation" proved="true">
  98   <proof prover="3"><result status="valid" time="0.020000" steps="33281"/></proof>
  99   </goal>
 100   <goal name="isqrt16&#39;vc.27" expl="loop invariant preservation" proved="true">
 101   <proof prover="3"><result status="valid" time="0.180000" steps="78568"/></proof>
 102   </goal>
 103   <goal name="isqrt16&#39;vc.28" expl="loop invariant preservation" proved="true">
 104   <proof prover="3"><result status="valid" time="0.070000" steps="28432"/></proof>
 105   </goal>
 106   <goal name="isqrt16&#39;vc.29" expl="loop invariant preservation" proved="true">
 107   <proof prover="3"><result status="valid" time="0.040000" steps="35440"/></proof>
 108   </goal>
 109   <goal name="isqrt16&#39;vc.30" expl="loop variant decrease" proved="true">
 110   <proof prover="3"><result status="valid" time="0.070000" steps="32949"/></proof>
 111   </goal>
 112   <goal name="isqrt16&#39;vc.31" expl="loop invariant preservation" proved="true">
 113   <proof prover="3"><result status="valid" time="0.050000" steps="22673"/></proof>
 114   </goal>
 115   <goal name="isqrt16&#39;vc.32" expl="loop invariant preservation" proved="true">
 116   <proof prover="3"><result status="valid" time="0.050000" steps="23915"/></proof>
 117   </goal>
 118   <goal name="isqrt16&#39;vc.33" expl="loop invariant preservation" proved="true">
 119   <proof prover="3"><result status="valid" time="0.080000" steps="58904"/></proof>
 120   </goal>
 121   <goal name="isqrt16&#39;vc.34" expl="loop invariant preservation" proved="true">
 122   <proof prover="3"><result status="valid" time="0.060000" steps="48029"/></proof>
 123   </goal>
 124   <goal name="isqrt16&#39;vc.35" expl="loop invariant preservation" proved="true">
 125   <proof prover="3"><result status="valid" time="0.010000" steps="5382"/></proof>
 126   </goal>
 127   <goal name="isqrt16&#39;vc.36" expl="loop invariant preservation" proved="true">
 128   <proof prover="3"><result status="valid" time="0.010000" steps="5061"/></proof>
 129   </goal>
 130   <goal name="isqrt16&#39;vc.37" expl="loop invariant preservation" proved="true">
 131   <proof prover="3"><result status="valid" time="0.010000" steps="5426"/></proof>
 132   </goal>
 133   <goal name="isqrt16&#39;vc.38" expl="loop invariant preservation" proved="true">
 134   <proof prover="3"><result status="valid" time="0.010000" steps="5447"/></proof>
 135   </goal>
 136   <goal name="isqrt16&#39;vc.39" expl="loop invariant preservation" proved="true">
 137   <proof prover="3"><result status="valid" time="0.060000" steps="24896"/></proof>
 138   </goal>
 139   <goal name="isqrt16&#39;vc.40" expl="loop invariant preservation" proved="true">
 140   <proof prover="3"><result status="valid" time="0.420000" steps="81023"/></proof>
 141   </goal>
 142   <goal name="isqrt16&#39;vc.41" expl="postcondition" proved="true">
 143   <proof prover="3"><result status="valid" time="0.020000" steps="31421"/></proof>
 144   </goal>
 145   <goal name="isqrt16&#39;vc.42" expl="postcondition" proved="true">
 146   <proof prover="3"><result status="valid" time="0.010000" steps="28497"/></proof>
 147   </goal>
 148  </transf>
 149  </goal>
 150 </theory>
 151 <theory name="VonNeumann32" proved="true">
 152  <goal name="sqr_add2" proved="true">
 153  <transf name="unfold" proved="true" arg1="sqr">
 154   <goal name="sqr_add2.0" proved="true">
 155   <proof prover="0" timelimit="20"><result status="valid" time="0.010000" steps="1148"/></proof>
 156   </goal>
 157  </transf>
 158  </goal>
 159  <goal name="isqrt32&#39;vc" expl="VC for isqrt32" proved="true">
 160  <transf name="split_goal_right" proved="true" >
 161   <goal name="isqrt32&#39;vc.0" expl="loop invariant init" proved="true">
 162   <proof prover="3"><result status="valid" time="0.020000" steps="4190"/></proof>
 163   </goal>
 164   <goal name="isqrt32&#39;vc.1" expl="loop invariant init" proved="true">
 165   <proof prover="3"><result status="valid" time="0.010000" steps="4238"/></proof>
 166   </goal>
 167   <goal name="isqrt32&#39;vc.2" expl="loop invariant init" proved="true">
 168   <proof prover="3"><result status="valid" time="0.020000" steps="4615"/></proof>
 169   </goal>
 170   <goal name="isqrt32&#39;vc.3" expl="loop invariant init" proved="true">
 171   <proof prover="3"><result status="valid" time="0.010000" steps="4662"/></proof>
 172   </goal>
 173   <goal name="isqrt32&#39;vc.4" expl="loop invariant init" proved="true">
 174   <proof prover="3"><result status="valid" time="0.010000" steps="4280"/></proof>
 175   </goal>
 176   <goal name="isqrt32&#39;vc.5" expl="loop invariant init" proved="true">
 177   <proof prover="3"><result status="valid" time="0.010000" steps="4300"/></proof>
 178   </goal>
 179   <goal name="isqrt32&#39;vc.6" expl="loop invariant init" proved="true">
 180   <proof prover="3"><result status="valid" time="0.010000" steps="4321"/></proof>
 181   </goal>
 182   <goal name="isqrt32&#39;vc.7" expl="loop invariant init" proved="true">
 183   <proof prover="3"><result status="valid" time="0.020000" steps="4785"/></proof>
 184   </goal>
 185   <goal name="isqrt32&#39;vc.8" expl="loop invariant init" proved="true">
 186   <proof prover="3"><result status="valid" time="0.020000" steps="4375"/></proof>
 187   </goal>
 188   <goal name="isqrt32&#39;vc.9" expl="loop invariant init" proved="true">
 189   <proof prover="3"><result status="valid" time="0.020000" steps="6805"/></proof>
 190   </goal>
 191   <goal name="isqrt32&#39;vc.10" expl="assertion" proved="true">
 192   <proof prover="3"><result status="valid" time="0.020000" steps="9839"/></proof>
 193   </goal>
 194   <goal name="isqrt32&#39;vc.11" expl="assertion" proved="true">
 195   <proof prover="3"><result status="valid" time="0.010000" steps="4541"/></proof>
 196   </goal>
 197   <goal name="isqrt32&#39;vc.12" expl="assertion" proved="true">
 198   <proof prover="3"><result status="valid" time="0.010000" steps="4594"/></proof>
 199   </goal>
 200   <goal name="isqrt32&#39;vc.13" expl="assertion" proved="true">
 201   <proof prover="3"><result status="valid" time="0.010000" steps="4697"/></proof>
 202   </goal>
 203   <goal name="isqrt32&#39;vc.14" expl="assertion" proved="true">
 204   <proof prover="3"><result status="valid" time="0.140000" steps="66538"/></proof>
 205   </goal>
 206   <goal name="isqrt32&#39;vc.15" expl="assertion" proved="true">
 207   <proof prover="3"><result status="valid" time="0.230000" steps="83666"/></proof>
 208   </goal>
 209   <goal name="isqrt32&#39;vc.16" expl="assertion" proved="true">
 210   <proof prover="3"><result status="valid" time="0.180000" steps="69854"/></proof>
 211   </goal>
 212   <goal name="isqrt32&#39;vc.17" expl="assertion" proved="true">
 213   <proof prover="3"><result status="valid" time="0.190000" steps="96537"/></proof>
 214   </goal>
 215   <goal name="isqrt32&#39;vc.18" expl="assertion" proved="true">
 216   <proof prover="3"><result status="valid" time="0.210000" steps="71402"/></proof>
 217   </goal>
 218   <goal name="isqrt32&#39;vc.19" expl="loop variant decrease" proved="true">
 219   <proof prover="3"><result status="valid" time="0.383333" steps="104484"/></proof>
 220   </goal>
 221   <goal name="isqrt32&#39;vc.20" expl="loop invariant preservation" proved="true">
 222   <proof prover="3"><result status="valid" time="0.130000" steps="67895"/></proof>
 223   </goal>
 224   <goal name="isqrt32&#39;vc.21" expl="loop invariant preservation" proved="true">
 225   <proof prover="3"><result status="valid" time="0.140000" steps="70374"/></proof>
 226   </goal>
 227   <goal name="isqrt32&#39;vc.22" expl="loop invariant preservation" proved="true">
 228   <proof prover="3"><result status="valid" time="0.614570" steps="201479"/></proof>
 229   </goal>
 230   <goal name="isqrt32&#39;vc.23" expl="loop invariant preservation" proved="true">
 231   <proof prover="3"><result status="valid" time="0.500000" steps="175624"/></proof>
 232   </goal>
 233   <goal name="isqrt32&#39;vc.24" expl="loop invariant preservation" proved="true">
 234   <proof prover="3"><result status="valid" time="0.130000" steps="71789"/></proof>
 235   </goal>
 236   <goal name="isqrt32&#39;vc.25" expl="loop invariant preservation" proved="true">
 237   <proof prover="3"><result status="valid" time="0.010000" steps="5312"/></proof>
 238   </goal>
 239   <goal name="isqrt32&#39;vc.26" expl="loop invariant preservation" proved="true">
 240   <proof prover="3"><result status="valid" time="0.290051" steps="88525"/></proof>
 241   </goal>
 242   <goal name="isqrt32&#39;vc.27" expl="loop invariant preservation" proved="true">
 243   <transf name="introduce_premises" proved="true" >
 244    <goal name="isqrt32&#39;vc.27.0" expl="loop invariant preservation" proved="true">
 245    <transf name="replace" proved="true" arg1="res_g" arg2="(add res_g1 bits_g1)">
 246     <goal name="isqrt32&#39;vc.27.0.0" expl="loop invariant preservation" proved="true">
 247     <transf name="rewrite" proved="true" arg1="sqr_add2">
 248      <goal name="isqrt32&#39;vc.27.0.0.0" expl="loop invariant preservation" proved="true">
 249      <proof prover="3"><result status="valid" time="0.770000" steps="141299"/></proof>
 250      </goal>
 251     </transf>
 252     </goal>
 253     <goal name="isqrt32&#39;vc.27.0.1" expl="equality hypothesis" proved="true">
 254     <proof prover="3"><result status="valid" time="0.010000" steps="4892"/></proof>
 255     </goal>
 256    </transf>
 257    </goal>
 258   </transf>
 259   </goal>
 260   <goal name="isqrt32&#39;vc.28" expl="loop invariant preservation" proved="true">
 261   <proof prover="3"><result status="valid" time="0.130000" steps="75788"/></proof>
 262   </goal>
 263   <goal name="isqrt32&#39;vc.29" expl="loop invariant preservation" proved="true">
 264   <proof prover="3"><result status="valid" time="0.190000" steps="89649"/></proof>
 265   </goal>
 266   <goal name="isqrt32&#39;vc.30" expl="loop variant decrease" proved="true">
 267   <proof prover="3"><result status="valid" time="0.230000" steps="106161"/></proof>
 268   </goal>
 269   <goal name="isqrt32&#39;vc.31" expl="loop invariant preservation" proved="true">
 270   <proof prover="3"><result status="valid" time="0.110000" steps="66330"/></proof>
 271   </goal>
 272   <goal name="isqrt32&#39;vc.32" expl="loop invariant preservation" proved="true">
 273   <proof prover="3"><result status="valid" time="0.140000" steps="68118"/></proof>
 274   </goal>
 275   <goal name="isqrt32&#39;vc.33" expl="loop invariant preservation" proved="true">
 276   <proof prover="3"><result status="valid" time="0.730000" steps="194358"/></proof>
 277   </goal>
 278   <goal name="isqrt32&#39;vc.34" expl="loop invariant preservation" proved="true">
 279   <proof prover="3"><result status="valid" time="0.300000" steps="147049"/></proof>
 280   </goal>
 281   <goal name="isqrt32&#39;vc.35" expl="loop invariant preservation" proved="true">
 282   <proof prover="3"><result status="valid" time="0.020000" steps="5382"/></proof>
 283   </goal>
 284   <goal name="isqrt32&#39;vc.36" expl="loop invariant preservation" proved="true">
 285   <proof prover="3"><result status="valid" time="0.000000" steps="5061"/></proof>
 286   </goal>
 287   <goal name="isqrt32&#39;vc.37" expl="loop invariant preservation" proved="true">
 288   <proof prover="3"><result status="valid" time="0.010000" steps="5426"/></proof>
 289   </goal>
 290   <goal name="isqrt32&#39;vc.38" expl="loop invariant preservation" proved="true">
 291   <proof prover="3"><result status="valid" time="0.010000" steps="5447"/></proof>
 292   </goal>
 293   <goal name="isqrt32&#39;vc.39" expl="loop invariant preservation" proved="true">
 294   <proof prover="3"><result status="valid" time="0.120000" steps="69677"/></proof>
 295   </goal>
 296   <goal name="isqrt32&#39;vc.40" expl="loop invariant preservation" proved="true">
 297   <proof prover="3" timelimit="120"><result status="valid" time="86.220000" steps="485446"/></proof>
 298   </goal>
 299   <goal name="isqrt32&#39;vc.41" expl="postcondition" proved="true">
 300   <proof prover="3"><result status="valid" time="0.160000" steps="102287"/></proof>
 301   </goal>
 302   <goal name="isqrt32&#39;vc.42" expl="postcondition" proved="true">
 303   <proof prover="3"><result status="valid" time="0.150000" steps="86161"/></proof>
 304   </goal>
 305  </transf>
 306  </goal>
 307 </theory>
 308 <theory name="VonNeumann64" proved="true">
 309  <goal name="sqr_add2" proved="true">
 310  <transf name="unfold" proved="true" arg1="sqr">
 311   <goal name="sqr_add2.0" proved="true">
 312   <proof prover="0" timelimit="1"><result status="valid" time="0.010000" steps="1148"/></proof>
 313   </goal>
 314  </transf>
 315  </goal>
 316  <goal name="isqrt64&#39;vc" expl="VC for isqrt64" proved="true">
 317  <transf name="split_goal_right" proved="true" >
 318   <goal name="isqrt64&#39;vc.0" expl="loop invariant init" proved="true">
 319   <proof prover="3"><result status="valid" time="0.010000" steps="4190"/></proof>
 320   </goal>
 321   <goal name="isqrt64&#39;vc.1" expl="loop invariant init" proved="true">
 322   <proof prover="3"><result status="valid" time="0.010000" steps="4238"/></proof>
 323   </goal>
 324   <goal name="isqrt64&#39;vc.2" expl="loop invariant init" proved="true">
 325   <proof prover="3"><result status="valid" time="0.010000" steps="4615"/></proof>
 326   </goal>
 327   <goal name="isqrt64&#39;vc.3" expl="loop invariant init" proved="true">
 328   <proof prover="3"><result status="valid" time="0.010000" steps="4662"/></proof>
 329   </goal>
 330   <goal name="isqrt64&#39;vc.4" expl="loop invariant init" proved="true">
 331   <proof prover="3"><result status="valid" time="0.010000" steps="4280"/></proof>
 332   </goal>
 333   <goal name="isqrt64&#39;vc.5" expl="loop invariant init" proved="true">
 334   <proof prover="3"><result status="valid" time="0.010000" steps="4300"/></proof>
 335   </goal>
 336   <goal name="isqrt64&#39;vc.6" expl="loop invariant init" proved="true">
 337   <proof prover="3"><result status="valid" time="0.010000" steps="4321"/></proof>
 338   </goal>
 339   <goal name="isqrt64&#39;vc.7" expl="loop invariant init" proved="true">
 340   <proof prover="3"><result status="valid" time="0.010000" steps="4785"/></proof>
 341   </goal>
 342   <goal name="isqrt64&#39;vc.8" expl="loop invariant init" proved="true">
 343   <proof prover="3"><result status="valid" time="0.010000" steps="4375"/></proof>
 344   </goal>
 345   <goal name="isqrt64&#39;vc.9" expl="loop invariant init" proved="true">
 346   <proof prover="3"><result status="valid" time="0.020000" steps="8661"/></proof>
 347   </goal>
 348   <goal name="isqrt64&#39;vc.10" expl="assertion" proved="true">
 349   <proof prover="3"><result status="valid" time="0.050000" steps="14525"/></proof>
 350   </goal>
 351   <goal name="isqrt64&#39;vc.11" expl="assertion" proved="true">
 352   <proof prover="3"><result status="valid" time="0.010000" steps="4541"/></proof>
 353   </goal>
 354   <goal name="isqrt64&#39;vc.12" expl="assertion" proved="true">
 355   <proof prover="3"><result status="valid" time="0.010000" steps="4594"/></proof>
 356   </goal>
 357   <goal name="isqrt64&#39;vc.13" expl="assertion" proved="true">
 358   <proof prover="3"><result status="valid" time="0.010000" steps="4697"/></proof>
 359   </goal>
 360   <goal name="isqrt64&#39;vc.14" expl="assertion" proved="true">
 361   <proof prover="3"><result status="valid" time="0.740000" steps="235879"/></proof>
 362   </goal>
 363   <goal name="isqrt64&#39;vc.15" expl="assertion" proved="true">
 364   <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="1.309545" steps="303408"/></proof>
 365   </goal>
 366   <goal name="isqrt64&#39;vc.16" expl="assertion" proved="true">
 367   <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="1.685720" steps="270174"/></proof>
 368   </goal>
 369   <goal name="isqrt64&#39;vc.17" expl="assertion" proved="true">
 370   <proof prover="3" timelimit="5"><result status="valid" time="1.264693" steps="358773"/></proof>
 371   </goal>
 372   <goal name="isqrt64&#39;vc.18" expl="assertion" proved="true">
 373   <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="2.351444" steps="278519"/></proof>
 374   </goal>
 375   <goal name="isqrt64&#39;vc.19" expl="loop variant decrease" proved="true">
 376   <proof prover="3" timelimit="5"><result status="valid" time="1.920000" steps="376838"/></proof>
 377   </goal>
 378   <goal name="isqrt64&#39;vc.20" expl="loop invariant preservation" proved="true">
 379   <proof prover="3"><result status="valid" time="0.500000" steps="235802"/></proof>
 380   </goal>
 381   <goal name="isqrt64&#39;vc.21" expl="loop invariant preservation" proved="true">
 382   <proof prover="3"><result status="valid" time="0.480000" steps="240482"/></proof>
 383   </goal>
 384   <goal name="isqrt64&#39;vc.22" expl="loop invariant preservation" proved="true">
 385   <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="2.827910" steps="729017"/></proof>
 386   </goal>
 387   <goal name="isqrt64&#39;vc.23" expl="loop invariant preservation" proved="true">
 388   <proof prover="3" timelimit="60"><result status="valid" time="2.356394" steps="622368"/></proof>
 389   </goal>
 390   <goal name="isqrt64&#39;vc.24" expl="loop invariant preservation" proved="true">
 391   <proof prover="3"><result status="valid" time="0.490000" steps="242932"/></proof>
 392   </goal>
 393   <goal name="isqrt64&#39;vc.25" expl="loop invariant preservation" proved="true">
 394   <proof prover="3"><result status="valid" time="0.010000" steps="5312"/></proof>
 395   </goal>
 396   <goal name="isqrt64&#39;vc.26" expl="loop invariant preservation" proved="true">
 397   <proof prover="3"><result status="valid" time="0.913049" steps="285206"/></proof>
 398   </goal>
 399   <goal name="isqrt64&#39;vc.27" expl="loop invariant preservation" proved="true">
 400   <transf name="introduce_premises" proved="true" >
 401    <goal name="isqrt64&#39;vc.27.0" expl="loop invariant preservation" proved="true">
 402    <transf name="replace" proved="true" arg1="res_g" arg2="(add res_g1 bits_g1)">
 403     <goal name="isqrt64&#39;vc.27.0.0" expl="loop invariant preservation" proved="true">
 404     <transf name="rewrite" proved="true" arg1="sqr_add2">
 405      <goal name="isqrt64&#39;vc.27.0.0.0" expl="loop invariant preservation" proved="true">
 406      <proof prover="3" timelimit="30"><result status="valid" time="7.788297" steps="550475"/></proof>
 407      </goal>
 408     </transf>
 409     </goal>
 410     <goal name="isqrt64&#39;vc.27.0.1" expl="equality hypothesis" proved="true">
 411     <proof prover="3"><result status="valid" time="0.010000" steps="4892"/></proof>
 412     </goal>
 413    </transf>
 414    </goal>
 415   </transf>
 416   </goal>
 417   <goal name="isqrt64&#39;vc.28" expl="loop invariant preservation" proved="true">
 418   <proof prover="3"><result status="valid" time="0.510000" steps="250647"/></proof>
 419   </goal>
 420   <goal name="isqrt64&#39;vc.29" expl="loop invariant preservation" proved="true">
 421   <proof prover="3"><result status="valid" time="0.675419" steps="279666"/></proof>
 422   </goal>
 423   <goal name="isqrt64&#39;vc.30" expl="loop variant decrease" proved="true">
 424   <proof prover="3" timelimit="5"><result status="valid" time="1.528492" steps="396093"/></proof>
 425   </goal>
 426   <goal name="isqrt64&#39;vc.31" expl="loop invariant preservation" proved="true">
 427   <proof prover="3"><result status="valid" time="0.450000" steps="234667"/></proof>
 428   </goal>
 429   <goal name="isqrt64&#39;vc.32" expl="loop invariant preservation" proved="true">
 430   <proof prover="3"><result status="valid" time="0.510000" steps="236390"/></proof>
 431   </goal>
 432   <goal name="isqrt64&#39;vc.33" expl="loop invariant preservation" proved="true">
 433   <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="2.870000" steps="711100"/></proof>
 434   </goal>
 435   <goal name="isqrt64&#39;vc.34" expl="loop invariant preservation" proved="true">
 436   <proof prover="3"><result status="valid" time="1.495005" steps="524978"/></proof>
 437   </goal>
 438   <goal name="isqrt64&#39;vc.35" expl="loop invariant preservation" proved="true">
 439   <proof prover="3"><result status="valid" time="0.010000" steps="5382"/></proof>
 440   </goal>
 441   <goal name="isqrt64&#39;vc.36" expl="loop invariant preservation" proved="true">
 442   <proof prover="3"><result status="valid" time="0.010000" steps="5061"/></proof>
 443   </goal>
 444   <goal name="isqrt64&#39;vc.37" expl="loop invariant preservation" proved="true">
 445   <proof prover="3"><result status="valid" time="0.010000" steps="5426"/></proof>
 446   </goal>
 447   <goal name="isqrt64&#39;vc.38" expl="loop invariant preservation" proved="true">
 448   <proof prover="3"><result status="valid" time="0.010000" steps="5447"/></proof>
 449   </goal>
 450   <goal name="isqrt64&#39;vc.39" expl="loop invariant preservation" proved="true">
 451   <proof prover="3"><result status="valid" time="0.550131" steps="239204"/></proof>
 452   </goal>
 453   <goal name="isqrt64&#39;vc.40" expl="loop invariant preservation" proved="true">
 454   <transf name="introduce_premises" proved="true" >
 455    <goal name="isqrt64&#39;vc.40.0" expl="loop invariant preservation" proved="true">
 456    <transf name="unfold" proved="true" arg1="ule">
 457     <goal name="isqrt64&#39;vc.40.0.0" expl="VC for isqrt64" proved="true">
 458     <transf name="rewrite" proved="true" arg1="sqr_add2">
 459      <goal name="isqrt64&#39;vc.40.0.0.0" expl="VC for isqrt64" proved="true">
 460      <transf name="assert" proved="true" arg1="(x = add (sqr res_g) num)">
 461       <goal name="isqrt64&#39;vc.40.0.0.0.0" expl="asserted formula" proved="true">
 462       <proof prover="3" timelimit="5"><result status="valid" time="0.580000" steps="285552"/></proof>
 463       </goal>
 464       <goal name="isqrt64&#39;vc.40.0.0.0.1" expl="VC for isqrt64" proved="true">
 465       <transf name="unfold" proved="true" arg1="sqr">
 466        <goal name="isqrt64&#39;vc.40.0.0.0.1.0" expl="VC for isqrt64" proved="true">
 467        <transf name="rewrite" proved="true" arg1="h">
 468         <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0" expl="VC for isqrt64" proved="true">
 469         <transf name="assert" proved="true" arg1="(ule num (pred (mul bits_g1 (add (mul (2:t) res_g) bits_g1))))">
 470          <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.0" expl="asserted formula" proved="true">
 471          <transf name="assert" proved="true" arg1="(ult num b)">
 472           <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.0.0" expl="asserted formula" proved="true">
 473           <proof prover="0"><result status="valid" time="0.010000" steps="1264"/></proof>
 474           </goal>
 475           <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.0.1" expl="asserted formula" proved="true">
 476           <transf name="assert" proved="true" arg1="(forall a b. mul a b = mul b a)">
 477            <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.0.1.0" expl="asserted formula" proved="true">
 478            <proof prover="3"><result status="valid" time="0.010000" steps="4846"/></proof>
 479            </goal>
 480            <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.0.1.1" expl="asserted formula" proved="true">
 481            <proof prover="4"><result status="valid" time="0.140000" steps="142"/></proof>
 482            </goal>
 483           </transf>
 484           </goal>
 485          </transf>
 486          </goal>
 487          <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1" expl="VC for isqrt64" proved="true">
 488          <transf name="replace" proved="true" arg1="(pow2 m)" arg2="bits_g1">
 489           <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0" expl="VC for isqrt64" proved="true">
 490           <transf name="assert" proved="true" arg1="(ule (add res_g (pow2 m1)) (0x100000000:t))">
 491            <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.0" expl="asserted formula" proved="true">
 492            <proof prover="0"><result status="valid" time="0.010000" steps="1856"/></proof>
 493            </goal>
 494            <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1" expl="VC for isqrt64" proved="true">
 495            <transf name="assert" proved="true" arg1="(ule (add res_g bits_g1) (0x100000000:t))">
 496             <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.0" expl="asserted formula" proved="true">
 497             <proof prover="3" timelimit="5"><result status="valid" time="0.700000" steps="404857"/></proof>
 498             </goal>
 499             <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1" expl="VC for isqrt64" proved="true">
 500             <transf name="unfold" proved="true" arg1="pred">
 501              <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0" expl="VC for isqrt64" proved="true">
 502              <transf name="unfold" proved="true" arg1="pred" arg2="in" arg3="h2">
 503               <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0" expl="VC for isqrt64" proved="true">
 504               <transf name="assert" proved="true" arg1="(forall a b c. t&#39;int b + t&#39;int c &lt; two_power_size -&gt; ule a b -&gt; ule (add a c) (add b c))">
 505                <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.0" expl="asserted formula" proved="true">
 506                <proof prover="5"><result status="valid" time="0.160856" steps="620"/></proof>
 507                </goal>
 508                <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1" expl="VC for isqrt64" proved="true">
 509                <transf name="case" proved="true" arg1="(add (sqr res_g) (mul bits_g1 (add (mul (2:t) res_g) bits_g1)) = (0:t))">
 510                 <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.0" expl="true case" proved="true">
 511                 <transf name="unfold" proved="true" arg1="sqr" arg2="in" arg3="h">
 512                  <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.0.0" expl="true case" proved="true">
 513                  <proof prover="3" timelimit="5"><result status="valid" time="3.277349" steps="508151"/></proof>
 514                  </goal>
 515                 </transf>
 516                 </goal>
 517                 <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1" expl="false case" proved="true">
 518                 <transf name="case" proved="true" arg1="(res_g = (0:t))">
 519                  <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.0" expl="false case (true case)" proved="true">
 520                  <proof prover="3" timelimit="5"><result status="valid" time="3.607718" steps="592821"/></proof>
 521                  </goal>
 522                  <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1" expl="false case" proved="true">
 523                  <transf name="rewrite" proved="true" arg1="to_uint_sub_bounded">
 524                   <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0" expl="false case" proved="true">
 525                   <transf name="rewrite" proved="true" arg1="to_uint_add_bounded">
 526                    <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0" expl="false case" proved="true">
 527                    <transf name="rewrite" proved="true" arg1="to_uint_add_bounded">
 528                     <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0" expl="false case" proved="true">
 529                     <transf name="unfold" proved="true" arg1="sqr">
 530                      <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0.0" expl="false case" proved="true">
 531                      <transf name="assert" proved="true" arg1="(forall a b c. b &lt;= c -&gt; a + b &lt;= a + c)">
 532                       <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0.0.0" expl="asserted formula" proved="true">
 533                       <proof prover="0"><result status="valid" time="0.010000" steps="1460"/></proof>
 534                       </goal>
 535                       <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0.0.1" expl="false case" proved="true">
 536                       <transf name="unfold" proved="true" arg1="ule" arg2="in" arg3="h6">
 537                        <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0.0.1.0" expl="false case" proved="true">
 538                        <transf name="rewrite" proved="true" arg1="to_uint_sub_bounded" arg2="in" arg3="h6">
 539                         <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0.0.1.0.0" expl="false case" proved="true">
 540                         <proof prover="0"><result status="valid" time="0.010000" steps="1513"/></proof>
 541                         </goal>
 542                         <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0.0.1.0.1" expl="rewrite premises" proved="true">
 543                         <transf name="assert" proved="true" arg1="(0 &lt;= t&#39;int b - t&#39;int (1:t))">
 544                          <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0.0.1.0.1.0" expl="asserted formula" proved="true">
 545                          <proof prover="5"><result status="valid" time="0.095791" steps="219"/></proof>
 546                          </goal>
 547                          <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.0.0.1.0.1.1" expl="rewrite premises" proved="true">
 548                          <proof prover="0" timelimit="1"><result status="valid" time="0.491190" steps="1599592"/></proof>
 549                          </goal>
 550                         </transf>
 551                         </goal>
 552                        </transf>
 553                        </goal>
 554                       </transf>
 555                       </goal>
 556                      </transf>
 557                      </goal>
 558                     </transf>
 559                     </goal>
 560                     <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1" expl="rewrite premises" proved="true">
 561                     <transf name="rewrite" proved="true" arg1="to_uint_mul_bounded">
 562                      <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0" expl="rewrite premises" proved="true">
 563                      <transf name="rewrite" proved="true" arg1="to_uint_mul_bounded">
 564                       <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0" expl="rewrite premises" proved="true">
 565                       <transf name="rewrite" proved="true" arg1="to_uint_add_bounded">
 566                        <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0" expl="rewrite premises" proved="true">
 567                        <transf name="rewrite" proved="true" arg1="to_uint_mul_bounded">
 568                         <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0" expl="rewrite premises" proved="true">
 569                         <transf name="assert" proved="true" arg1="(forall a b. a * a + b * ((2 * a) + b) = (a + b) * (a + b))">
 570                          <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.0" expl="asserted formula" proved="true">
 571                          <proof prover="0"><result status="valid" time="0.010000" steps="5332"/></proof>
 572                          </goal>
 573                          <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.1" expl="rewrite premises" proved="true">
 574                          <transf name="replace" proved="true" arg1="(t&#39;int (2:t))" arg2="2">
 575                           <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.1.0" expl="rewrite premises" proved="true">
 576                           <transf name="rewrite" proved="true" arg1="h">
 577                            <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.1.0.0" expl="rewrite premises" proved="true">
 578                            <transf name="replace" proved="true" arg1="two_power_size" arg2="(0x100000000 * 0x100000000)">
 579                             <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.1.0.0.0" expl="rewrite premises" proved="true">
 580                             <transf name="rewrite" proved="true" arg1="&lt;-" arg2="to_uint_add_bounded">
 581                              <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.1.0.0.0.0" expl="rewrite premises" proved="true">
 582                              <proof prover="1"><result status="valid" time="0.325152" steps="3492"/></proof>
 583                              </goal>
 584                              <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.1.0.0.0.1" expl="rewrite premises" proved="true">
 585                              <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="3.140000" steps="598362"/></proof>
 586                              </goal>
 587                             </transf>
 588                             </goal>
 589                             <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.1.0.0.1" expl="equality hypothesis" proved="true">
 590                             <proof prover="3" timelimit="5"><result status="valid" time="0.010000" steps="5118"/></proof>
 591                             </goal>
 592                            </transf>
 593                            </goal>
 594                           </transf>
 595                           </goal>
 596                           <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.0.1.1" expl="equality hypothesis" proved="true">
 597                           <proof prover="3"><result status="valid" time="0.010000" steps="5881"/></proof>
 598                           </goal>
 599                          </transf>
 600                          </goal>
 601                         </transf>
 602                         </goal>
 603                         <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.0.1" expl="rewrite premises" proved="true">
 604                         <proof prover="5" timelimit="1"><result status="valid" time="0.020000" steps="219"/></proof>
 605                         </goal>
 606                        </transf>
 607                        </goal>
 608                        <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.0.1" expl="rewrite premises" proved="true">
 609                        <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="2.890000" steps="598149"/></proof>
 610                        </goal>
 611                       </transf>
 612                       </goal>
 613                       <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1" expl="rewrite premises" proved="true">
 614                       <transf name="rewrite" proved="true" arg1="to_uint_add_bounded">
 615                        <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0" expl="rewrite premises" proved="true">
 616                        <transf name="rewrite" proved="true" arg1="to_uint_mul_bounded">
 617                         <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0" expl="rewrite premises" proved="true">
 618                         <transf name="assert" proved="true" arg1="(forall a b. a * ((2 * b) + a) = (a + b) * (a + b) - b * b)">
 619                          <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.0" expl="asserted formula" proved="true">
 620                          <proof prover="5"><result status="valid" time="0.020000" steps="215"/></proof>
 621                          </goal>
 622                          <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1" expl="rewrite premises" proved="true">
 623                          <transf name="replace" proved="true" arg1="(t&#39;int (2:t))" arg2="2">
 624                           <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0" expl="rewrite premises" proved="true">
 625                           <transf name="rewrite" proved="true" arg1="h">
 626                            <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0" expl="rewrite premises" proved="true">
 627                            <transf name="assert" proved="true" arg1="(((t&#39;int bits_g1 + t&#39;int res_g) * (t&#39;int bits_g1 + t&#39;int res_g)) &lt;= two_power_size)">
 628                             <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.0" expl="asserted formula" proved="true">
 629                             <transf name="replace" proved="true" arg1="two_power_size" arg2="(0x100000000 * 0x100000000)">
 630                              <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.0.0" expl="asserted formula" proved="true">
 631                              <transf name="rewrite" proved="true" arg1="&lt;-" arg2="to_uint_add_bounded">
 632                               <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.0.0.0" expl="asserted formula" proved="true">
 633                               <transf name="assert" proved="true" arg1="(forall a b. add a b = add b a)">
 634                                <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.0.0.0.0" expl="asserted formula" proved="true">
 635                                <proof prover="0"><result status="valid" time="0.010000" steps="1517"/></proof>
 636                                </goal>
 637                                <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.0.0.0.1" expl="asserted formula" proved="true">
 638                                <transf name="rewrite" proved="true" arg1="h1">
 639                                 <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.0.0.0.1.0" expl="asserted formula" proved="true">
 640                                 <proof prover="4"><result status="valid" time="0.020000" steps="135"/></proof>
 641                                 </goal>
 642                                </transf>
 643                                </goal>
 644                               </transf>
 645                               </goal>
 646                               <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.0.0.1" expl="rewrite premises" proved="true">
 647                               <proof prover="3" timelimit="5"><result status="valid" time="3.040000" steps="598376"/></proof>
 648                               </goal>
 649                              </transf>
 650                              </goal>
 651                              <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.0.1" expl="equality hypothesis" proved="true">
 652                              <proof prover="3" timelimit="5"><result status="valid" time="0.010000" steps="5122"/></proof>
 653                              </goal>
 654                             </transf>
 655                             </goal>
 656                             <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.0.0.1" expl="rewrite premises" proved="true">
 657                             <proof prover="5"><result status="valid" time="0.180000" steps="221"/></proof>
 658                             </goal>
 659                            </transf>
 660                            </goal>
 661                           </transf>
 662                           </goal>
 663                           <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.0.1.1" expl="equality hypothesis" proved="true">
 664                           <proof prover="3" timelimit="5"><result status="valid" time="0.010000" steps="5885"/></proof>
 665                           </goal>
 666                          </transf>
 667                          </goal>
 668                         </transf>
 669                         </goal>
 670                         <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.0.1" expl="rewrite premises" proved="true">
 671                         <proof prover="3" timelimit="5"><result status="valid" time="1.721112" steps="562733"/></proof>
 672                         </goal>
 673                        </transf>
 674                        </goal>
 675                        <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.0.1.1" expl="rewrite premises" proved="true">
 676                        <proof prover="3" timelimit="5"><result status="valid" time="2.301000" steps="598149"/></proof>
 677                        </goal>
 678                       </transf>
 679                       </goal>
 680                      </transf>
 681                      </goal>
 682                      <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.0.1.1" expl="rewrite premises" proved="true">
 683                      <proof prover="5"><result status="valid" time="0.130843" steps="219"/></proof>
 684                      </goal>
 685                     </transf>
 686                     </goal>
 687                    </transf>
 688                    </goal>
 689                    <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.0.1" expl="rewrite premises" proved="true">
 690                    <proof prover="5"><result status="valid" time="0.114149" steps="219"/></proof>
 691                    </goal>
 692                   </transf>
 693                   </goal>
 694                   <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.0.1.1.0.0.1.1.1.1" expl="rewrite premises" proved="true">
 695                   <proof prover="2"><result status="valid" time="0.118514" steps="1358"/></proof>
 696                   </goal>
 697                  </transf>
 698                  </goal>
 699                 </transf>
 700                 </goal>
 701                </transf>
 702                </goal>
 703               </transf>
 704               </goal>
 705              </transf>
 706              </goal>
 707             </transf>
 708             </goal>
 709            </transf>
 710            </goal>
 711           </transf>
 712           </goal>
 713           <goal name="isqrt64&#39;vc.40.0.0.0.1.0.0.1.1" expl="equality hypothesis" proved="true">
 714           <proof prover="3"><result status="valid" time="0.010000" steps="4859"/></proof>
 715           </goal>
 716          </transf>
 717          </goal>
 718         </transf>
 719         </goal>
 720        </transf>
 721        </goal>
 722       </transf>
 723       </goal>
 724      </transf>
 725      </goal>
 726     </transf>
 727     </goal>
 728    </transf>
 729    </goal>
 730   </transf>
 731   </goal>
 732   <goal name="isqrt64&#39;vc.41" expl="assertion" proved="true">
 733   <proof prover="3"><result status="valid" time="0.350000" steps="178406"/></proof>
 734   </goal>
 735   <goal name="isqrt64&#39;vc.42" expl="assertion" proved="true">
 736   <proof prover="3"><result status="valid" time="0.000000" steps="4463"/></proof>
 737   </goal>
 738   <goal name="isqrt64&#39;vc.43" expl="postcondition" proved="true">
 739   <proof prover="3"><result status="valid" time="0.050000" steps="25748"/></proof>
 740   </goal>
 741   <goal name="isqrt64&#39;vc.44" expl="postcondition" proved="true">
 742   <proof prover="3"><result status="valid" time="0.010000" steps="4855"/></proof>
 743   </goal>
 744  </transf>
 745  </goal>
 746 </theory>
 747 </file>
 748 </why3session>