examples/fibonacci/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="Alt-Ergo" version="2.4.0" timelimit="5" steplimit="0" memlimit="1000"/>
   6 <prover id="1" name="Z3" version="4.8.10" timelimit="1" steplimit="0" memlimit="1000"/>
   7 <prover id="2" name="Z3" version="4.12.2" timelimit="5" steplimit="0" memlimit="1000"/>
   8 <prover id="3" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
   9 <prover id="4" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
  10 <prover id="5" name="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="1000"/>
  11 <prover id="6" name="Alt-Ergo" version="2.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
  12 <prover id="7" name="Z3" version="4.7.1" timelimit="1" steplimit="0" memlimit="1000"/>
  13 <file format="whyml" proved="true">
  14 <path name=".."/><path name="fibonacci.mlw"/>
  15 <theory name="FibonacciTest" proved="true">
  16  <goal name="isfib_2_1" proved="true">
  17  <proof prover="4" timelimit="5"><result status="valid" time="0.000000" steps="679"/></proof>
  18  <proof prover="7" timelimit="5"><result status="valid" time="0.010000" steps="907"/></proof>
  19  </goal>
  20  <goal name="isfib_6_8" proved="true">
  21  <proof prover="4" timelimit="5"><result status="valid" time="0.000000" steps="1039"/></proof>
  22  <proof prover="7" timelimit="5"><result status="valid" time="0.010000" steps="1445"/></proof>
  23  </goal>
  24  <goal name="not_isfib_2_2" proved="true">
  25  <proof prover="3"><result status="valid" time="0.000000" steps="5"/></proof>
  26  <proof prover="4" timelimit="5"><result status="valid" time="0.000000" steps="376"/></proof>
  27  <proof prover="7" timelimit="5"><result status="valid" time="0.010000" steps="251"/></proof>
  28  </goal>
  29 </theory>
  30 <theory name="FibonacciLinear" proved="true">
  31  <goal name="fib&#39;vc" expl="VC for fib" proved="true">
  32  <proof prover="7"><result status="valid" time="0.020000" steps="3418"/></proof>
  33  </goal>
  34 </theory>
  35 <theory name="FibonacciTailRecList" proved="true">
  36  <goal name="sum_fib&#39;vc" expl="VC for sum_fib" proved="true">
  37  <transf name="split_vc" proved="true" >
  38   <goal name="sum_fib&#39;vc.0" expl="precondition" proved="true">
  39   <proof prover="0"><result status="valid" time="0.016279" steps="200"/></proof>
  40   </goal>
  41   <goal name="sum_fib&#39;vc.1" expl="precondition" proved="true">
  42   <proof prover="0"><result status="valid" time="0.020231" steps="159"/></proof>
  43   </goal>
  44  </transf>
  45  </goal>
  46  <goal name="sum_pow&#39;vc" expl="VC for sum_pow" proved="true">
  47  <transf name="split_all_full" proved="true" >
  48   <goal name="sum_pow&#39;vc.0" expl="assertion" proved="true">
  49   <proof prover="6"><result status="valid" time="0.000000" steps="5"/></proof>
  50   </goal>
  51   <goal name="sum_pow&#39;vc.1" expl="assertion" proved="true">
  52   <proof prover="6"><result status="valid" time="0.010000" steps="8"/></proof>
  53   </goal>
  54   <goal name="sum_pow&#39;vc.2" expl="precondition" proved="true">
  55   <proof prover="6"><result status="valid" time="0.010000" steps="19"/></proof>
  56   </goal>
  57   <goal name="sum_pow&#39;vc.3" expl="postcondition" proved="true">
  58   <proof prover="2"><result status="valid" time="0.020000" steps="936"/></proof>
  59   </goal>
  60   <goal name="sum_pow&#39;vc.4" expl="postcondition" proved="true">
  61   <proof prover="6"><result status="valid" time="0.010000" steps="20"/></proof>
  62   </goal>
  63  </transf>
  64  </goal>
  65  <goal name="pow_pos" proved="true">
  66  <transf name="split_vc" proved="true" >
  67   <goal name="pow_pos.0" proved="true">
  68   <transf name="induction" proved="true" arg1="x">
  69    <goal name="pow_pos.0.0" expl="base case" proved="true">
  70    <proof prover="2"><result status="valid" time="0.020000" steps="4398"/></proof>
  71    </goal>
  72    <goal name="pow_pos.0.1" expl="recursive case" proved="true">
  73    <proof prover="2"><result status="valid" time="0.020000" steps="4499"/></proof>
  74    </goal>
  75   </transf>
  76   </goal>
  77  </transf>
  78  </goal>
  79  <goal name="sum_fib_acc&#39;vc" expl="VC for sum_fib_acc" proved="true">
  80  <transf name="split_vc" proved="true" >
  81   <goal name="sum_fib_acc&#39;vc.0" expl="assertion" proved="true">
  82   <proof prover="0"><result status="valid" time="0.026073" steps="213"/></proof>
  83   </goal>
  84   <goal name="sum_fib_acc&#39;vc.1" expl="variant decrease" proved="true">
  85   <transf name="split_vc" proved="true" >
  86    <goal name="sum_fib_acc&#39;vc.1.0" expl="variant decrease" proved="true">
  87    <proof prover="2"><result status="valid" time="0.020000" steps="11503"/></proof>
  88    </goal>
  89    <goal name="sum_fib_acc&#39;vc.1.1" expl="variant decrease" proved="true">
  90    <proof prover="0"><result status="valid" time="0.030000" steps="103"/></proof>
  91    </goal>
  92   </transf>
  93   </goal>
  94   <goal name="sum_fib_acc&#39;vc.2" expl="precondition" proved="true">
  95   <transf name="assert" proved="true" arg1="(mem n l)">
  96    <goal name="sum_fib_acc&#39;vc.2.0" expl="asserted formula" proved="true">
  97    <proof prover="6"><result status="valid" time="0.010000" steps="10"/></proof>
  98    </goal>
  99    <goal name="sum_fib_acc&#39;vc.2.1" expl="precondition" proved="true">
 100    <proof prover="6"><result status="valid" time="0.010000" steps="12"/></proof>
 101    </goal>
 102   </transf>
 103   </goal>
 104   <goal name="sum_fib_acc&#39;vc.3" expl="assertion" proved="true">
 105   <transf name="assert" proved="true" arg1="(u = x1 - 2 \/ mem u x)">
 106    <goal name="sum_fib_acc&#39;vc.3.0" expl="asserted formula" proved="true">
 107    <proof prover="6"><result status="valid" time="0.010000" steps="12"/></proof>
 108    </goal>
 109    <goal name="sum_fib_acc&#39;vc.3.1" expl="assertion" proved="true">
 110    <transf name="destruct" proved="true" arg1="h">
 111     <goal name="sum_fib_acc&#39;vc.3.1.0" expl="assertion" proved="true">
 112     <proof prover="2"><result status="valid" time="0.020000" steps="9396"/></proof>
 113     </goal>
 114     <goal name="sum_fib_acc&#39;vc.3.1.1" expl="assertion" proved="true">
 115     <transf name="assert" proved="true" arg1="(mem u l)">
 116      <goal name="sum_fib_acc&#39;vc.3.1.1.0" expl="asserted formula" proved="true">
 117      <proof prover="5"><result status="valid" time="0.030000" steps="2316"/></proof>
 118      </goal>
 119      <goal name="sum_fib_acc&#39;vc.3.1.1.1" expl="assertion" proved="true">
 120      <proof prover="2"><result status="valid" time="0.020000" steps="9644"/></proof>
 121      </goal>
 122     </transf>
 123     </goal>
 124    </transf>
 125    </goal>
 126   </transf>
 127   </goal>
 128   <goal name="sum_fib_acc&#39;vc.4" expl="assertion" proved="true">
 129   <proof prover="5"><result status="valid" time="0.030000" steps="2529"/></proof>
 130   </goal>
 131   <goal name="sum_fib_acc&#39;vc.5" expl="variant decrease" proved="true">
 132   <transf name="split_vc" proved="true" >
 133    <goal name="sum_fib_acc&#39;vc.5.0" expl="variant decrease" proved="true">
 134    <proof prover="2"><result status="valid" time="0.010000" steps="11510"/></proof>
 135    </goal>
 136    <goal name="sum_fib_acc&#39;vc.5.1" expl="variant decrease" proved="true">
 137    <proof prover="5"><result status="valid" time="0.050000" steps="3933"/></proof>
 138    </goal>
 139   </transf>
 140   </goal>
 141   <goal name="sum_fib_acc&#39;vc.6" expl="precondition" proved="true">
 142   <proof prover="2"><result status="valid" time="0.030000" steps="10179"/></proof>
 143   </goal>
 144   <goal name="sum_fib_acc&#39;vc.7" expl="postcondition" proved="true">
 145   <transf name="split_vc" proved="true" >
 146    <goal name="sum_fib_acc&#39;vc.7.0" expl="postcondition" proved="true">
 147    <proof prover="2" timelimit="1"><result status="valid" time="0.010000" steps="27836"/></proof>
 148    </goal>
 149    <goal name="sum_fib_acc&#39;vc.7.1" expl="postcondition" proved="true">
 150    <proof prover="5"><result status="valid" time="0.030000" steps="5678"/></proof>
 151    </goal>
 152   </transf>
 153   </goal>
 154  </transf>
 155  </goal>
 156  <goal name="fib&#39;vc" expl="VC for fib" proved="true">
 157  <proof prover="5"><result status="valid" time="0.040000" steps="3821"/></proof>
 158  </goal>
 159 </theory>
 160 <theory name="FibRecGhost" proved="true">
 161  <goal name="fib_aux&#39;vc" expl="VC for fib_aux" proved="true">
 162  <proof prover="7"><result status="valid" time="0.010000" steps="2439"/></proof>
 163  </goal>
 164  <goal name="fib&#39;vc" expl="VC for fib" proved="true">
 165  <proof prover="3"><result status="valid" time="0.000000" steps="4"/></proof>
 166  </goal>
 167  <goal name="test42&#39;vc" expl="VC for test42" proved="true">
 168  <proof prover="3"><result status="valid" time="0.000000" steps="3"/></proof>
 169  </goal>
 170 </theory>
 171 <theory name="FibRecNoGhost" proved="true">
 172  <goal name="fib_aux&#39;vc" expl="VC for fib_aux" proved="true">
 173  <proof prover="7"><result status="valid" time="0.020000" steps="9992"/></proof>
 174  </goal>
 175  <goal name="fib&#39;vc" expl="VC for fib" proved="true">
 176  <proof prover="7"><result status="valid" time="0.190000" steps="220087"/></proof>
 177  </goal>
 178 </theory>
 179 <theory name="SmallestFibAbove" proved="true">
 180  <goal name="smallest_fib_above&#39;vc" expl="VC for smallest_fib_above" proved="true">
 181  <proof prover="4"><result status="valid" time="0.040000" steps="5188"/></proof>
 182  </goal>
 183 </theory>
 184 <theory name="Zeckendorf" proved="true">
 185  <goal name="fib_nonneg&#39;vc" expl="VC for fib_nonneg" proved="true">
 186  <proof prover="3"><result status="valid" time="0.000000" steps="17"/></proof>
 187  </goal>
 188  <goal name="fib_increasing&#39;vc" expl="VC for fib_increasing" proved="true">
 189  <proof prover="7"><result status="valid" time="0.010000" steps="2380"/></proof>
 190  </goal>
 191  <goal name="greatest_fib&#39;vc" expl="VC for greatest_fib" proved="true">
 192  <proof prover="7"><result status="valid" time="0.020000" steps="16394"/></proof>
 193  </goal>
 194  <goal name="zeckendorf&#39;vc" expl="VC for zeckendorf" proved="true">
 195  <proof prover="4"><result status="valid" time="0.230000" steps="28799"/></proof>
 196  </goal>
 197  <goal name="zeckendorf_fast&#39;vc" expl="VC for zeckendorf_fast" proved="true">
 198  <proof prover="4"><result status="valid" time="0.660000" steps="63532"/></proof>
 199  </goal>
 200  <goal name="zeckendorf_unique&#39;vc" expl="VC for zeckendorf_unique" proved="true">
 201  <transf name="split_goal_right" proved="true" >
 202   <goal name="zeckendorf_unique&#39;vc.0" expl="unreachable point" proved="true">
 203   <proof prover="7"><result status="valid" time="0.020000" steps="6853"/></proof>
 204   </goal>
 205   <goal name="zeckendorf_unique&#39;vc.1" expl="precondition" proved="true">
 206   <proof prover="4"><result status="valid" time="0.010000" steps="4765"/></proof>
 207   </goal>
 208   <goal name="zeckendorf_unique&#39;vc.2" expl="variant decrease" proved="true">
 209   <proof prover="7"><result status="valid" time="0.020000" steps="8564"/></proof>
 210   </goal>
 211   <goal name="zeckendorf_unique&#39;vc.3" expl="precondition" proved="true">
 212   <proof prover="4"><result status="valid" time="0.020000" steps="4904"/></proof>
 213   </goal>
 214   <goal name="zeckendorf_unique&#39;vc.4" expl="precondition" proved="true">
 215   <proof prover="4"><result status="valid" time="0.020000" steps="4961"/></proof>
 216   </goal>
 217   <goal name="zeckendorf_unique&#39;vc.5" expl="precondition" proved="true">
 218   <proof prover="4"><result status="valid" time="0.030000" steps="11653"/></proof>
 219   </goal>
 220   <goal name="zeckendorf_unique&#39;vc.6" expl="postcondition" proved="true">
 221   <proof prover="4"><result status="valid" time="0.060000" steps="13970"/></proof>
 222   </goal>
 223   <goal name="zeckendorf_unique&#39;vc.7" expl="postcondition" proved="true">
 224   <proof prover="4"><result status="valid" time="0.060000" steps="7547"/></proof>
 225   </goal>
 226   <goal name="zeckendorf_unique&#39;vc.8" expl="precondition" proved="true">
 227   <proof prover="7"><result status="valid" time="0.000000" steps="2290"/></proof>
 228   </goal>
 229   <goal name="zeckendorf_unique&#39;vc.9" expl="precondition" proved="true">
 230   <proof prover="7"><result status="valid" time="0.010000" steps="7385"/></proof>
 231   </goal>
 232   <goal name="zeckendorf_unique&#39;vc.10" expl="precondition" proved="true">
 233   <proof prover="7"><result status="valid" time="0.020000" steps="7592"/></proof>
 234   </goal>
 235   <goal name="zeckendorf_unique&#39;vc.11" expl="unreachable point" proved="true">
 236   <proof prover="7"><result status="valid" time="0.020000" steps="10395"/></proof>
 237   </goal>
 238   <goal name="zeckendorf_unique&#39;vc.12" expl="precondition" proved="true">
 239   <proof prover="7"><result status="valid" time="0.010000" steps="2290"/></proof>
 240   </goal>
 241   <goal name="zeckendorf_unique&#39;vc.13" expl="precondition" proved="true">
 242   <proof prover="7"><result status="valid" time="0.020000" steps="7385"/></proof>
 243   </goal>
 244   <goal name="zeckendorf_unique&#39;vc.14" expl="precondition" proved="true">
 245   <proof prover="7"><result status="valid" time="0.020000" steps="7592"/></proof>
 246   </goal>
 247   <goal name="zeckendorf_unique&#39;vc.15" expl="unreachable point" proved="true">
 248   <proof prover="7"><result status="valid" time="0.010000" steps="10395"/></proof>
 249   </goal>
 250   <goal name="zeckendorf_unique&#39;vc.16" expl="precondition" proved="true">
 251   <proof prover="7"><result status="valid" time="0.010000" steps="2269"/></proof>
 252   </goal>
 253   <goal name="zeckendorf_unique&#39;vc.17" expl="precondition" proved="true">
 254   <proof prover="7"><result status="valid" time="0.010000" steps="7510"/></proof>
 255   </goal>
 256   <goal name="zeckendorf_unique&#39;vc.18" expl="precondition" proved="true">
 257   <proof prover="7"><result status="valid" time="0.010000" steps="7604"/></proof>
 258   </goal>
 259   <goal name="zeckendorf_unique&#39;vc.19" expl="precondition" proved="true">
 260   <proof prover="7"><result status="valid" time="0.010000" steps="8122"/></proof>
 261   </goal>
 262   <goal name="zeckendorf_unique&#39;vc.20" expl="precondition" proved="true">
 263   <proof prover="7"><result status="valid" time="0.010000" steps="9074"/></proof>
 264   </goal>
 265   <goal name="zeckendorf_unique&#39;vc.21" expl="precondition" proved="true">
 266   <proof prover="7"><result status="valid" time="0.020000" steps="9288"/></proof>
 267   </goal>
 268   <goal name="zeckendorf_unique&#39;vc.22" expl="variant decrease" proved="true">
 269   <proof prover="7"><result status="valid" time="0.020000" steps="15182"/></proof>
 270   </goal>
 271   <goal name="zeckendorf_unique&#39;vc.23" expl="precondition" proved="true">
 272   <proof prover="7"><result status="valid" time="0.020000" steps="8900"/></proof>
 273   </goal>
 274   <goal name="zeckendorf_unique&#39;vc.24" expl="precondition" proved="true">
 275   <proof prover="7"><result status="valid" time="0.020000" steps="26995"/></proof>
 276   </goal>
 277   <goal name="zeckendorf_unique&#39;vc.25" expl="postcondition" proved="true">
 278   <proof prover="7"><result status="valid" time="0.020000" steps="26536"/></proof>
 279   </goal>
 280  </transf>
 281  </goal>
 282 </theory>
 283 <theory name="Mat22" proved="true">
 284  <goal name="Assoc" proved="true">
 285  <proof prover="3"><result status="valid" time="0.030000" steps="2"/></proof>
 286  </goal>
 287  <goal name="Unit_def_l" proved="true">
 288  <proof prover="3"><result status="valid" time="0.000000" steps="2"/></proof>
 289  </goal>
 290  <goal name="Unit_def_r" proved="true">
 291  <proof prover="3"><result status="valid" time="0.000000" steps="2"/></proof>
 292  </goal>
 293 </theory>
 294 <theory name="FibonacciLogarithmic" proved="true">
 295  <goal name="logfib&#39;vc" expl="VC for logfib" proved="true">
 296  <transf name="split_goal_right" proved="true" >
 297   <goal name="logfib&#39;vc.0" expl="assertion" proved="true">
 298   <proof prover="3"><result status="valid" time="0.010000" steps="8"/></proof>
 299   </goal>
 300   <goal name="logfib&#39;vc.1" expl="precondition" proved="true">
 301   <proof prover="3"><result status="valid" time="0.010000" steps="6"/></proof>
 302   </goal>
 303   <goal name="logfib&#39;vc.2" expl="variant decrease" proved="true">
 304   <proof prover="3"><result status="valid" time="0.010000" steps="10"/></proof>
 305   </goal>
 306   <goal name="logfib&#39;vc.3" expl="precondition" proved="true">
 307   <proof prover="3"><result status="valid" time="0.010000" steps="3"/></proof>
 308   </goal>
 309   <goal name="logfib&#39;vc.4" expl="precondition" proved="true">
 310   <proof prover="3"><result status="valid" time="0.000000" steps="7"/></proof>
 311   </goal>
 312   <goal name="logfib&#39;vc.5" expl="assertion" proved="true">
 313   <proof prover="3"><result status="valid" time="0.000000" steps="8"/></proof>
 314   </goal>
 315   <goal name="logfib&#39;vc.6" expl="assertion" proved="true">
 316   <proof prover="3"><result status="valid" time="0.000000" steps="8"/></proof>
 317   </goal>
 318   <goal name="logfib&#39;vc.7" expl="postcondition" proved="true">
 319   <proof prover="3"><result status="valid" time="0.427068" steps="93"/></proof>
 320   </goal>
 321  </transf>
 322  </goal>
 323  <goal name="fib_m&#39;vc" expl="VC for fib_m" proved="true">
 324  <proof prover="6"><result status="valid" time="0.100000" steps="1018"/></proof>
 325  </goal>
 326  <goal name="fibo&#39;vc" expl="VC for fibo" proved="true">
 327  <proof prover="3"><result status="valid" time="0.000000" steps="7"/></proof>
 328  </goal>
 329  <goal name="test0&#39;vc" expl="VC for test0" proved="true">
 330  <proof prover="3"><result status="valid" time="0.000000" steps="3"/></proof>
 331  </goal>
 332  <goal name="test1&#39;vc" expl="VC for test1" proved="true">
 333  <proof prover="3"><result status="valid" time="0.000000" steps="3"/></proof>
 334  </goal>
 335  <goal name="test7&#39;vc" expl="VC for test7" proved="true">
 336  <proof prover="3"><result status="valid" time="0.000000" steps="3"/></proof>
 337  </goal>
 338  <goal name="test42&#39;vc" expl="VC for test42" proved="true">
 339  <proof prover="3"><result status="valid" time="0.000000" steps="3"/></proof>
 340  </goal>
 341  <goal name="test2014&#39;vc" expl="VC for test2014" proved="true">
 342  <proof prover="3"><result status="valid" time="0.000000" steps="3"/></proof>
 343  </goal>
 344 </theory>
 345 <theory name="FibSquare" proved="true">
 346  <goal name="fib_12" proved="true">
 347  <proof prover="1"><result status="valid" time="0.033991" steps="3319"/></proof>
 348  </goal>
 349  <goal name="fib_13" proved="true">
 350  <proof prover="1"><result status="valid" time="0.022074" steps="3176"/></proof>
 351  </goal>
 352  <goal name="fib_14" proved="true">
 353  <proof prover="1"><result status="valid" time="0.024020" steps="1932"/></proof>
 354  </goal>
 355  <goal name="fib_bigger_than_square&#39;vc" expl="VC for fib_bigger_than_square" proved="true">
 356  <transf name="split_vc" proved="true" >
 357   <goal name="fib_bigger_than_square&#39;vc.0" expl="loop invariant init" proved="true">
 358   <proof prover="1"><result status="valid" time="0.022034" steps="232"/></proof>
 359   </goal>
 360   <goal name="fib_bigger_than_square&#39;vc.1" expl="loop invariant init" proved="true">
 361   <proof prover="1"><result status="valid" time="0.019268" steps="265"/></proof>
 362   </goal>
 363   <goal name="fib_bigger_than_square&#39;vc.2" expl="assertion" proved="true">
 364   <transf name="split_vc" proved="true" >
 365    <goal name="fib_bigger_than_square&#39;vc.2.0" expl="assertion" proved="true">
 366    <proof prover="1"><result status="valid" time="0.026418" steps="2884"/></proof>
 367    </goal>
 368    <goal name="fib_bigger_than_square&#39;vc.2.1" expl="assertion" proved="true">
 369    <proof prover="1"><result status="valid" time="0.024580" steps="2400"/></proof>
 370    </goal>
 371    <goal name="fib_bigger_than_square&#39;vc.2.2" expl="assertion" proved="true">
 372    <proof prover="1"><result status="valid" time="0.068004" steps="297395"/></proof>
 373    </goal>
 374   </transf>
 375   </goal>
 376   <goal name="fib_bigger_than_square&#39;vc.3" expl="loop invariant preservation" proved="true">
 377   <proof prover="1"><result status="valid" time="0.018691" steps="283"/></proof>
 378   </goal>
 379   <goal name="fib_bigger_than_square&#39;vc.4" expl="loop invariant preservation" proved="true">
 380   <proof prover="1"><result status="valid" time="0.022627" steps="3124"/></proof>
 381   </goal>
 382   <goal name="fib_bigger_than_square&#39;vc.5" expl="postcondition" proved="true">
 383   <proof prover="1"><result status="valid" time="0.018833" steps="218"/></proof>
 384   </goal>
 385   <goal name="fib_bigger_than_square&#39;vc.6" expl="postcondition" proved="true">
 386   <proof prover="1"><result status="valid" time="0.022600" steps="1609"/></proof>
 387   </goal>
 388  </transf>
 389  </goal>
 390  <goal name="fib_square" proved="true">
 391  <proof prover="1"><result status="valid" time="0.035983" steps="29834"/></proof>
 392  </goal>
 393 </theory>
 394 </file>
 395 </why3session>