examples/stdlib/list/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="4.8.4" timelimit="1" steplimit="0" memlimit="1000"/>
   6 <prover id="1" name="Eprover" version="2.0" timelimit="5" steplimit="0" memlimit="1000"/>
   7 <prover id="2" name="CVC3" version="2.2" timelimit="5" steplimit="0" memlimit="1000"/>
   8 <prover id="3" name="Spass" version="3.9" timelimit="5" steplimit="0" memlimit="1000"/>
   9 <prover id="4" name="CVC5" version="1.1.2" timelimit="5" steplimit="0" memlimit="1000"/>
  10 <prover id="5" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
  11 <prover id="6" name="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
  12 <prover id="7" name="Alt-Ergo" version="2.4.2" timelimit="1" steplimit="0" memlimit="1000"/>
  13 <prover id="8" name="Z3" version="4.13.2" timelimit="5" steplimit="0" memlimit="1000"/>
  14 <prover id="9" name="Alt-Ergo" version="2.6.0" timelimit="5" steplimit="0" memlimit="1000"/>
  15 <file format="whyml" proved="true">
  16 <path name=".."/><path name=".."/><path name=".."/><path name="stdlib"/>
  17 <path name="list.mlw"/>
  18 <theory name="List" proved="true">
  19  <goal name="is_nil&#39;vc" expl="VC for is_nil" proved="true">
  20  <proof prover="0"><result status="valid" time="0.000000" steps="5247"/></proof>
  21  <proof prover="6"><result status="valid" time="0.027129" steps="1888"/></proof>
  22  </goal>
  23 </theory>
  24 <theory name="Length" proved="true">
  25  <goal name="Length_nonnegative" proved="true">
  26  <transf name="induction_ty_lex" proved="true" >
  27   <goal name="Length_nonnegative.0" proved="true">
  28   <proof prover="0"><result status="valid" time="0.000000" steps="6198"/></proof>
  29   <proof prover="6"><result status="valid" time="0.032572" steps="2098"/></proof>
  30   </goal>
  31  </transf>
  32  </goal>
  33  <goal name="Length_nil" proved="true">
  34  <transf name="split_goal_right" proved="true" >
  35   <goal name="Length_nil.0" proved="true">
  36   <proof prover="1"><result status="valid" time="0.010000"/></proof>
  37   <proof prover="4"><result status="valid" time="0.025548" steps="1055"/></proof>
  38   </goal>
  39   <goal name="Length_nil.1" proved="true">
  40   <proof prover="0"><result status="valid" time="0.000000" steps="5054"/></proof>
  41   <proof prover="8"><result status="valid" time="0.004172" steps="5574"/></proof>
  42   </goal>
  43  </transf>
  44  </goal>
  45 </theory>
  46 <theory name="Quant" proved="true">
  47  <goal name="for_all&#39;vc" expl="VC for for_all" proved="true">
  48  <proof prover="5"><result status="valid" time="0.040000" steps="3393"/></proof>
  49  <proof prover="9"><result status="valid" time="0.015683" steps="48"/></proof>
  50  </goal>
  51  <goal name="for_some&#39;vc" expl="VC for for_some" proved="true">
  52  <proof prover="4"><result status="valid" time="0.032673" steps="2032"/></proof>
  53  <proof prover="5"><result status="valid" time="0.020000" steps="4454"/></proof>
  54  </goal>
  55  <goal name="mem&#39;vc" expl="VC for mem" proved="true">
  56  <proof prover="5"><result status="valid" time="0.020000" steps="3745"/></proof>
  57  <proof prover="8"><result status="valid" time="0.003502" steps="10250"/></proof>
  58  </goal>
  59 </theory>
  60 <theory name="Elements" proved="true">
  61  <goal name="elements_mem" proved="true">
  62  <transf name="induction_ty_lex" proved="true" >
  63   <goal name="elements_mem.0" proved="true">
  64   <proof prover="6"><result status="valid" time="0.090000" steps="13026"/></proof>
  65   </goal>
  66  </transf>
  67  </goal>
  68 </theory>
  69 <theory name="NthLength" proved="true">
  70  <goal name="nth_none_1" proved="true">
  71  <transf name="induction_ty_lex" proved="true" >
  72   <goal name="nth_none_1.0" proved="true">
  73   <proof prover="6"><result status="valid" time="0.040000" steps="4983"/></proof>
  74   </goal>
  75  </transf>
  76  </goal>
  77  <goal name="nth_none_2" proved="true">
  78  <transf name="induction_ty_lex" proved="true" >
  79   <goal name="nth_none_2.0" proved="true">
  80   <proof prover="8"><result status="valid" time="0.009367" steps="10101"/></proof>
  81   </goal>
  82  </transf>
  83  </goal>
  84  <goal name="nth_none_3" proved="true">
  85  <transf name="induction_ty_lex" proved="true" >
  86   <goal name="nth_none_3.0" proved="true">
  87   <proof prover="8"><result status="valid" time="0.007798" steps="11021"/></proof>
  88   </goal>
  89  </transf>
  90  </goal>
  91 </theory>
  92 <theory name="NthHdTl" proved="true">
  93  <goal name="Nth_tl" proved="true">
  94  <proof prover="7"><result status="valid" time="0.000000" steps="35"/></proof>
  95  <proof prover="9"><result status="valid" time="0.032111" steps="40"/></proof>
  96  </goal>
  97  <goal name="Nth0_head" proved="true">
  98  <proof prover="1"><result status="valid" time="0.010000"/></proof>
  99  <proof prover="9"><result status="valid" time="0.027840" steps="31"/></proof>
 100  </goal>
 101 </theory>
 102 <theory name="Append" proved="true">
 103  <goal name="Append_assoc" proved="true">
 104  <transf name="induction_ty_lex" proved="true" >
 105   <goal name="Append_assoc.0" proved="true">
 106   <transf name="split_goal_right" proved="true" >
 107    <goal name="Append_assoc.0.0" proved="true">
 108    <proof prover="0"><result status="valid" time="0.000000" steps="5536"/></proof>
 109    <proof prover="4"><result status="valid" time="0.032183" steps="1024"/></proof>
 110    </goal>
 111    <goal name="Append_assoc.0.1" proved="true">
 112    <proof prover="8"><result status="valid" time="0.008830" steps="6046"/></proof>
 113    </goal>
 114   </transf>
 115   </goal>
 116  </transf>
 117  </goal>
 118  <goal name="Append_l_nil" proved="true">
 119  <transf name="induction_ty_lex" proved="true" >
 120   <goal name="Append_l_nil.0" proved="true">
 121   <proof prover="0"><result status="valid" time="0.000000" steps="7048"/></proof>
 122   <proof prover="4"><result status="valid" time="0.029013" steps="1217"/></proof>
 123   </goal>
 124  </transf>
 125  </goal>
 126  <goal name="Append_length" proved="true">
 127  <transf name="induction_ty_lex" proved="true" >
 128   <goal name="Append_length.0" proved="true">
 129   <proof prover="0"><result status="valid" time="0.543827" steps="2199640"/></proof>
 130   <proof prover="6"><result status="valid" time="0.048354" steps="3986"/></proof>
 131   </goal>
 132  </transf>
 133  </goal>
 134  <goal name="mem_append" proved="true">
 135  <transf name="induction_ty_lex" proved="true" >
 136   <goal name="mem_append.0" proved="true">
 137   <proof prover="4"><result status="valid" time="0.040773" steps="3196"/></proof>
 138   </goal>
 139  </transf>
 140  </goal>
 141  <goal name="mem_decomp" proved="true">
 142  <transf name="induction_ty_lex" proved="true" >
 143   <goal name="mem_decomp.0" proved="true">
 144   <transf name="split_goal_right" proved="true" >
 145    <goal name="mem_decomp.0.0" proved="true">
 146    <proof prover="0"><result status="valid" time="0.000000" steps="10451"/></proof>
 147    <proof prover="6"><result status="valid" time="0.033713" steps="3407"/></proof>
 148    </goal>
 149    <goal name="mem_decomp.0.1" proved="true">
 150    <proof prover="3"><result status="valid" time="0.610000"/></proof>
 151    <proof prover="9"><result status="valid" time="0.048216" steps="255"/></proof>
 152    </goal>
 153   </transf>
 154   </goal>
 155  </transf>
 156  </goal>
 157 </theory>
 158 <theory name="NthLengthAppend" proved="true">
 159  <goal name="nth_append_1" proved="true">
 160  <transf name="induction_ty_lex" proved="true" >
 161   <goal name="nth_append_1.0" proved="true">
 162   <proof prover="6"><result status="valid" time="0.070000" steps="8986"/></proof>
 163   </goal>
 164  </transf>
 165  </goal>
 166  <goal name="nth_append_2" proved="true">
 167  <transf name="induction_ty_lex" proved="true" >
 168   <goal name="nth_append_2.0" proved="true">
 169   <proof prover="6"><result status="valid" time="0.150000" steps="19312"/></proof>
 170   </goal>
 171  </transf>
 172  </goal>
 173 </theory>
 174 <theory name="Reverse" proved="true">
 175  <goal name="reverse_append" proved="true">
 176  <transf name="induction_ty_lex" proved="true" >
 177   <goal name="reverse_append.0" proved="true">
 178   <proof prover="0"><result status="valid" time="0.090000" steps="125921"/></proof>
 179   <proof prover="9"><result status="valid" time="0.098232" steps="872"/></proof>
 180   </goal>
 181  </transf>
 182  </goal>
 183  <goal name="reverse_cons" proved="true">
 184  <proof prover="0"><result status="valid" time="0.010000" steps="13224"/></proof>
 185  <proof prover="4"><result status="valid" time="0.043542" steps="3083"/></proof>
 186  </goal>
 187  <goal name="cons_reverse" proved="true">
 188  <transf name="induction_ty_lex" proved="true" >
 189   <goal name="cons_reverse.0" proved="true">
 190   <proof prover="0"><result status="valid" time="0.010000" steps="26142"/></proof>
 191   <proof prover="6"><result status="valid" time="0.069426" steps="7841"/></proof>
 192   </goal>
 193  </transf>
 194  </goal>
 195  <goal name="reverse_reverse" proved="true">
 196  <transf name="induction_ty_lex" proved="true" >
 197   <goal name="reverse_reverse.0" proved="true">
 198   <proof prover="0"><result status="valid" time="0.010000" steps="15285"/></proof>
 199   <proof prover="8"><result status="valid" time="0.015806" steps="16305"/></proof>
 200   </goal>
 201  </transf>
 202  </goal>
 203  <goal name="reverse_mem" proved="true">
 204  <transf name="induction_ty_lex" proved="true" >
 205   <goal name="reverse_mem.0" proved="true">
 206   <proof prover="4"><result status="valid" time="0.064063" steps="6924"/></proof>
 207   </goal>
 208  </transf>
 209  </goal>
 210  <goal name="Reverse_length" proved="true">
 211  <transf name="induction_ty_lex" proved="true" >
 212   <goal name="Reverse_length.0" proved="true">
 213   <proof prover="4"><result status="valid" time="0.110530" steps="11682"/></proof>
 214   </goal>
 215  </transf>
 216  </goal>
 217 </theory>
 218 <theory name="RevAppend" proved="true">
 219  <goal name="rev_append_append_l" proved="true">
 220  <transf name="induction_ty_lex" proved="true" >
 221   <goal name="rev_append_append_l.0" proved="true">
 222   <proof prover="4"><result status="valid" time="0.059347" steps="5669"/></proof>
 223   </goal>
 224  </transf>
 225  </goal>
 226  <goal name="rev_append_length" proved="true">
 227  <transf name="induction_ty_lex" proved="true" >
 228   <goal name="rev_append_length.0" proved="true">
 229   <proof prover="0"><result status="valid" time="0.010000" steps="122154"/></proof>
 230   <proof prover="4"><result status="valid" time="0.069418" steps="5687"/></proof>
 231   </goal>
 232  </transf>
 233  </goal>
 234  <goal name="rev_append_def" proved="true">
 235  <transf name="induction_ty_lex" proved="true" >
 236   <goal name="rev_append_def.0" proved="true">
 237   <proof prover="0"><result status="valid" time="0.467655" steps="547574"/></proof>
 238   <proof prover="4"><result status="valid" time="0.050254" steps="5029"/></proof>
 239   </goal>
 240  </transf>
 241  </goal>
 242  <goal name="rev_append_append_r" proved="true">
 243  <proof prover="0"><result status="valid" time="0.010000" steps="27074"/></proof>
 244  <proof prover="8"><result status="valid" time="0.016168" steps="29527"/></proof>
 245  </goal>
 246 </theory>
 247 <theory name="Sorted" proved="true">
 248  <goal name="sorted_mem" proved="true">
 249  <transf name="split_goal_right" proved="true" >
 250   <goal name="sorted_mem.0" proved="true">
 251   <proof prover="6"><result status="valid" time="0.060000" steps="7488"/></proof>
 252   </goal>
 253   <goal name="sorted_mem.1" proved="true">
 254   <transf name="induction_pr" proved="true" >
 255    <goal name="sorted_mem.1.0" proved="true">
 256    <proof prover="0"><result status="valid" time="0.000000" steps="6419"/></proof>
 257    <proof prover="4"><result status="valid" time="0.024481" steps="862"/></proof>
 258    </goal>
 259    <goal name="sorted_mem.1.1" proved="true">
 260    <proof prover="0"><result status="valid" time="0.000000" steps="6813"/></proof>
 261    <proof prover="8"><result status="valid" time="0.012435" steps="6842"/></proof>
 262    </goal>
 263    <goal name="sorted_mem.1.2" proved="true">
 264    <proof prover="0"><result status="valid" time="1.023832" steps="4256466"/></proof>
 265    <proof prover="9"><result status="valid" time="0.026964" steps="73"/></proof>
 266    </goal>
 267   </transf>
 268   </goal>
 269   <goal name="sorted_mem.2" proved="true">
 270   <proof prover="0"><result status="valid" time="0.010000" steps="7015"/></proof>
 271   <proof prover="8"><result status="valid" time="0.012060" steps="4591"/></proof>
 272   </goal>
 273  </transf>
 274  </goal>
 275  <goal name="sorted_append" proved="true">
 276  <transf name="induction_ty_lex" proved="true" >
 277   <goal name="sorted_append.0" proved="true">
 278   <transf name="split_goal_right" proved="true" >
 279    <goal name="sorted_append.0.0" proved="true">
 280    <proof prover="0"><result status="valid" time="0.010000" steps="13792"/></proof>
 281    <proof prover="6"><result status="valid" time="0.039904" steps="4224"/></proof>
 282    </goal>
 283    <goal name="sorted_append.0.1" proved="true">
 284    <proof prover="0"><result status="valid" time="0.000000" steps="13371"/></proof>
 285    <proof prover="9"><result status="valid" time="0.025228" steps="4"/></proof>
 286    </goal>
 287    <goal name="sorted_append.0.2" proved="true">
 288    <proof prover="0"><result status="valid" time="0.000000" steps="13733"/></proof>
 289    <proof prover="9"><result status="valid" time="0.020688" steps="8"/></proof>
 290    </goal>
 291    <goal name="sorted_append.0.3" proved="true">
 292    <proof prover="0"><result status="valid" time="0.000000" steps="13817"/></proof>
 293    <proof prover="4"><result status="valid" time="0.032890" steps="2795"/></proof>
 294    </goal>
 295    <goal name="sorted_append.0.4" proved="true">
 296    <proof prover="6"><result status="valid" time="0.070000" steps="9703"/></proof>
 297    </goal>
 298    <goal name="sorted_append.0.5" proved="true">
 299    <proof prover="4"><result status="valid" time="0.065769" steps="5746"/></proof>
 300    </goal>
 301    <goal name="sorted_append.0.6" proved="true">
 302    <proof prover="6"><result status="valid" time="0.050000" steps="5935"/></proof>
 303    </goal>
 304    <goal name="sorted_append.0.7" proved="true">
 305    <proof prover="6"><result status="valid" time="0.100000" steps="12706"/></proof>
 306    </goal>
 307   </transf>
 308   </goal>
 309  </transf>
 310  </goal>
 311 </theory>
 312 <theory name="SortedInt" proved="true">
 313  <goal name="Transitive.Trans" proved="true">
 314  <proof prover="0"><result status="valid" time="0.000000" steps="456"/></proof>
 315  <proof prover="4"><result status="valid" time="0.023990" steps="224"/></proof>
 316  </goal>
 317 </theory>
 318 <theory name="RevSorted" proved="true">
 319  <goal name="Incr.Transitive.Trans" proved="true">
 320  <proof prover="0"><result status="valid" time="0.000000" steps="26"/></proof>
 321  <proof prover="8"><result status="valid" time="0.004170" steps="55"/></proof>
 322  </goal>
 323  <goal name="Decr.Transitive.Trans" proved="true">
 324  <proof prover="0"><result status="valid" time="0.000000" steps="11093"/></proof>
 325  <proof prover="9"><result status="valid" time="0.027516" steps="10"/></proof>
 326  </goal>
 327  <goal name="rev_append_sorted_incr" proved="true">
 328  <transf name="induction_ty_lex" proved="true" >
 329   <goal name="rev_append_sorted_incr.0" proved="true">
 330   <transf name="split_goal_right" proved="true" >
 331    <goal name="rev_append_sorted_incr.0.0" proved="true">
 332    <proof prover="0"><result status="valid" time="0.010000" steps="23687"/></proof>
 333    <proof prover="6"><result status="valid" time="0.044590" steps="6325"/></proof>
 334    </goal>
 335    <goal name="rev_append_sorted_incr.0.1" proved="true">
 336    <proof prover="0"><result status="valid" time="0.010000" steps="24362"/></proof>
 337    <proof prover="9"><result status="valid" time="0.032790" steps="10"/></proof>
 338    </goal>
 339    <goal name="rev_append_sorted_incr.0.2" proved="true">
 340    <proof prover="4"><result status="valid" time="0.060699" steps="6985"/></proof>
 341    <proof prover="7"><result status="valid" time="0.010000" steps="78"/></proof>
 342    </goal>
 343    <goal name="rev_append_sorted_incr.0.3" proved="true">
 344    <proof prover="0"><result status="valid" time="0.010000" steps="25331"/></proof>
 345    <proof prover="9"><result status="valid" time="0.029288" steps="12"/></proof>
 346    </goal>
 347    <goal name="rev_append_sorted_incr.0.4" proved="true">
 348    <proof prover="5"><result status="valid" time="0.070000" steps="21952"/></proof>
 349    <proof prover="6"><result status="valid" time="0.147218" steps="21122"/></proof>
 350    </goal>
 351    <goal name="rev_append_sorted_incr.0.5" proved="true">
 352    <proof prover="0"><result status="valid" time="0.030000" steps="56802"/></proof>
 353    <proof prover="9"><result status="valid" time="0.041116" steps="64"/></proof>
 354    </goal>
 355    <goal name="rev_append_sorted_incr.0.6" proved="true">
 356    <proof prover="4"><result status="valid" time="0.262353" steps="28420"/></proof>
 357    </goal>
 358    <goal name="rev_append_sorted_incr.0.7" proved="true">
 359    <proof prover="1"><result status="valid" time="1.266128"/></proof>
 360    <proof prover="6"><result status="valid" time="0.194227" steps="27295"/></proof>
 361    </goal>
 362   </transf>
 363   </goal>
 364  </transf>
 365  </goal>
 366  <goal name="rev_append_sorted_decr" proved="true">
 367  <transf name="induction_ty_lex" proved="true" >
 368   <goal name="rev_append_sorted_decr.0" proved="true">
 369   <transf name="split_goal_right" proved="true" >
 370    <goal name="rev_append_sorted_decr.0.0" proved="true">
 371    <proof prover="0"><result status="valid" time="0.010000" steps="24906"/></proof>
 372    <proof prover="9"><result status="valid" time="0.028260" steps="6"/></proof>
 373    </goal>
 374    <goal name="rev_append_sorted_decr.0.1" proved="true">
 375    <proof prover="0"><result status="valid" time="0.010000" steps="25627"/></proof>
 376    <proof prover="4"><result status="valid" time="0.055025" steps="5684"/></proof>
 377    </goal>
 378    <goal name="rev_append_sorted_decr.0.2" proved="true">
 379    <proof prover="0"><result status="valid" time="0.010000" steps="25866"/></proof>
 380    <proof prover="9"><result status="valid" time="0.038416" steps="67"/></proof>
 381    </goal>
 382    <goal name="rev_append_sorted_decr.0.3" proved="true">
 383    <proof prover="0"><result status="valid" time="0.010000" steps="25980"/></proof>
 384    <proof prover="9"><result status="valid" time="0.033064" steps="12"/></proof>
 385    </goal>
 386    <goal name="rev_append_sorted_decr.0.4" proved="true">
 387    <proof prover="5"><result status="valid" time="0.160399" steps="25025"/></proof>
 388    <proof prover="6"><result status="valid" time="0.149644" steps="22281"/></proof>
 389    </goal>
 390    <goal name="rev_append_sorted_decr.0.5" proved="true">
 391    <proof prover="0"><result status="valid" time="0.030000" steps="57503"/></proof>
 392    <proof prover="9"><result status="valid" time="0.033231" steps="69"/></proof>
 393    </goal>
 394    <goal name="rev_append_sorted_decr.0.6" proved="true">
 395    <proof prover="0"><result status="valid" time="0.090000" steps="119779"/></proof>
 396    <proof prover="6"><result status="valid" time="0.086449" steps="11338"/></proof>
 397    </goal>
 398    <goal name="rev_append_sorted_decr.0.7" proved="true">
 399    <proof prover="5"><result status="valid" time="0.070000" steps="12905"/></proof>
 400    <proof prover="6"><result status="valid" time="0.112972" steps="12702"/></proof>
 401    </goal>
 402   </transf>
 403   </goal>
 404  </transf>
 405  </goal>
 406 </theory>
 407 <theory name="NumOcc" proved="true">
 408  <goal name="Num_Occ_NonNeg" proved="true">
 409  <transf name="induction_ty_lex" proved="true" >
 410   <goal name="Num_Occ_NonNeg.0" proved="true">
 411   <proof prover="0"><result status="valid" time="0.000000" steps="224319"/></proof>
 412   <proof prover="4"><result status="valid" time="0.031939" steps="1495"/></proof>
 413   </goal>
 414  </transf>
 415  </goal>
 416  <goal name="Mem_Num_Occ" proved="true">
 417  <transf name="induction_ty_lex" proved="true" >
 418   <goal name="Mem_Num_Occ.0" proved="true">
 419   <transf name="split_goal_right" proved="true" >
 420    <goal name="Mem_Num_Occ.0.0" proved="true">
 421    <proof prover="0"><result status="valid" time="0.000000" steps="7256"/></proof>
 422    <proof prover="8"><result status="valid" time="0.008619" steps="8353"/></proof>
 423    </goal>
 424    <goal name="Mem_Num_Occ.0.1" proved="true">
 425    <proof prover="0"><result status="valid" time="0.000000" steps="7542"/></proof>
 426    <proof prover="4"><result status="valid" time="0.024433" steps="1448"/></proof>
 427    </goal>
 428    <goal name="Mem_Num_Occ.0.2" proved="true">
 429    <proof prover="0"><result status="valid" time="0.163232" steps="387084"/></proof>
 430    <proof prover="6"><result status="valid" time="0.040861" steps="2954"/></proof>
 431    </goal>
 432    <goal name="Mem_Num_Occ.0.3" proved="true">
 433    <proof prover="0"><result status="valid" time="0.103497" steps="265865"/></proof>
 434    <proof prover="6"><result status="valid" time="0.035197" steps="2917"/></proof>
 435    </goal>
 436   </transf>
 437   </goal>
 438  </transf>
 439  </goal>
 440  <goal name="Append_Num_Occ" proved="true">
 441  <transf name="induction_ty_lex" proved="true" >
 442   <goal name="Append_Num_Occ.0" proved="true">
 443   <proof prover="6"><result status="valid" time="0.050000" steps="7551"/></proof>
 444   </goal>
 445  </transf>
 446  </goal>
 447  <goal name="reverse_num_occ" proved="true">
 448  <transf name="induction_ty_lex" proved="true" >
 449   <goal name="reverse_num_occ.0" proved="true">
 450   <proof prover="9"><result status="valid" time="0.043104" steps="190"/></proof>
 451   </goal>
 452  </transf>
 453  </goal>
 454 </theory>
 455 <theory name="Permut" proved="true">
 456  <goal name="Permut_refl" proved="true">
 457  <proof prover="0"><result status="valid" time="0.010000" steps="12126"/></proof>
 458  <proof prover="4"><result status="valid" time="0.033497" steps="2488"/></proof>
 459  </goal>
 460  <goal name="Permut_sym" proved="true">
 461  <proof prover="0"><result status="valid" time="0.010000" steps="12632"/></proof>
 462  <proof prover="8"><result status="valid" time="0.009796" steps="14693"/></proof>
 463  </goal>
 464  <goal name="Permut_trans" proved="true">
 465  <proof prover="0"><result status="valid" time="0.010000" steps="13498"/></proof>
 466  <proof prover="4"><result status="valid" time="0.043349" steps="3153"/></proof>
 467  </goal>
 468  <goal name="Permut_cons" proved="true">
 469  <proof prover="9"><result status="valid" time="0.039675" steps="93"/></proof>
 470  </goal>
 471  <goal name="Permut_swap" proved="true">
 472  <proof prover="9"><result status="valid" time="0.045781" steps="113"/></proof>
 473  </goal>
 474  <goal name="Permut_cons_append" proved="true">
 475  <proof prover="0"><result status="valid" time="1.711697" steps="2354555"/></proof>
 476  <proof prover="6"><result status="valid" time="0.116500" steps="14165"/></proof>
 477  </goal>
 478  <goal name="Permut_assoc" proved="true">
 479  <proof prover="0"><result status="valid" time="0.010000" steps="19786"/></proof>
 480  <proof prover="6"><result status="valid" time="0.046294" steps="5809"/></proof>
 481  </goal>
 482  <goal name="Permut_append" proved="true">
 483  <proof prover="0"><result status="valid" time="0.509292" steps="701200"/></proof>
 484  <proof prover="6"><result status="valid" time="0.063615" steps="7719"/></proof>
 485  </goal>
 486  <goal name="Permut_append_swap" proved="true">
 487  <proof prover="0"><result status="valid" time="0.010000" steps="26556"/></proof>
 488  <proof prover="4"><result status="valid" time="0.062656" steps="5885"/></proof>
 489  </goal>
 490  <goal name="Permut_mem" proved="true">
 491  <proof prover="0"><result status="valid" time="0.010000" steps="19402"/></proof>
 492  <proof prover="4"><result status="valid" time="0.032281" steps="3923"/></proof>
 493  </goal>
 494  <goal name="Permut_length" proved="true">
 495  <transf name="induction_ty_lex" proved="true" >
 496   <goal name="Permut_length.0" proved="true">
 497   <transf name="split_vc" proved="true" >
 498    <goal name="Permut_length.0.0" proved="true">
 499    <transf name="destruct_term" proved="true" arg1="l2">
 500     <goal name="Permut_length.0.0.0" proved="true">
 501     <proof prover="0"><result status="valid" time="0.020000" steps="53289"/></proof>
 502     <proof prover="6"><result status="valid" time="0.082424" steps="9958"/></proof>
 503     </goal>
 504     <goal name="Permut_length.0.0.1" proved="true">
 505     <proof prover="5" timelimit="1"><result status="valid" time="0.010000" steps="6565"/></proof>
 506     <proof prover="9"><result status="valid" time="0.028770" steps="6"/></proof>
 507     </goal>
 508    </transf>
 509    </goal>
 510    <goal name="Permut_length.0.1" proved="true">
 511    <transf name="unfold" proved="true" arg1="permut" arg2="in" arg3="H">
 512     <goal name="Permut_length.0.1.0" proved="true">
 513     <transf name="assert" proved="true" arg1="(num_occ x1 l1 &gt;= 1)">
 514      <goal name="Permut_length.0.1.0.0" expl="asserted formula" proved="true">
 515      <proof prover="5" timelimit="1"><result status="valid" time="0.020000" steps="8070"/></proof>
 516      <proof prover="6"><result status="valid" time="0.069704" steps="8132"/></proof>
 517      </goal>
 518      <goal name="Permut_length.0.1.0.1" proved="true">
 519      <transf name="assert" proved="true" arg1="(mem x1 l2)">
 520       <goal name="Permut_length.0.1.0.1.0" expl="asserted formula" proved="true">
 521       <proof prover="5" timelimit="1"><result status="valid" time="0.020000" steps="8175"/></proof>
 522       <proof prover="9"><result status="valid" time="0.037488" steps="20"/></proof>
 523       </goal>
 524       <goal name="Permut_length.0.1.0.1.1" proved="true">
 525       <transf name="instantiate" proved="true" arg1="mem_decomp" arg2="x1,l2">
 526        <goal name="Permut_length.0.1.0.1.1.0" proved="true">
 527        <transf name="destruct" proved="true" arg1="Hinst">
 528         <goal name="Permut_length.0.1.0.1.1.0.0" expl="destruct premise" proved="true">
 529         <proof prover="5" timelimit="1"><result status="valid" time="0.010000" steps="7089"/></proof>
 530         <proof prover="9"><result status="valid" time="0.022108" steps="6"/></proof>
 531         </goal>
 532         <goal name="Permut_length.0.1.0.1.1.0.1" proved="true">
 533         <transf name="destruct" proved="true" arg1="Hinst">
 534          <goal name="Permut_length.0.1.0.1.1.0.1.0" proved="true">
 535          <transf name="destruct" proved="true" arg1="Hinst">
 536           <goal name="Permut_length.0.1.0.1.1.0.1.0.0" proved="true">
 537           <transf name="assert" proved="true" arg1="(permut x (l1 ++ l2))">
 538            <goal name="Permut_length.0.1.0.1.1.0.1.0.0.0" expl="asserted formula" proved="true">
 539            <proof prover="2"><result status="valid" time="5.209500"/></proof>
 540            </goal>
 541            <goal name="Permut_length.0.1.0.1.1.0.1.0.0.1" proved="true">
 542            <proof prover="5" timelimit="1"><result status="valid" time="0.040000" steps="9618"/></proof>
 543            <proof prover="9"><result status="valid" time="0.039441" steps="36"/></proof>
 544            </goal>
 545           </transf>
 546           </goal>
 547          </transf>
 548          </goal>
 549         </transf>
 550         </goal>
 551        </transf>
 552        </goal>
 553       </transf>
 554       </goal>
 555      </transf>
 556      </goal>
 557     </transf>
 558     </goal>
 559    </transf>
 560    </goal>
 561   </transf>
 562   </goal>
 563  </transf>
 564  </goal>
 565 </theory>
 566 <theory name="Distinct" proved="true">
 567  <goal name="distinct_append" proved="true">
 568  <transf name="induction_ty_lex" proved="true" >
 569   <goal name="distinct_append.0" proved="true">
 570   <transf name="split_goal_right" proved="true" >
 571    <goal name="distinct_append.0.0" proved="true">
 572    <proof prover="0"><result status="valid" time="0.000000" steps="13870"/></proof>
 573    <proof prover="4"><result status="valid" time="0.035563" steps="2945"/></proof>
 574    </goal>
 575    <goal name="distinct_append.0.1" proved="true">
 576    <proof prover="6"><result status="valid" time="0.110000" steps="15507"/></proof>
 577    </goal>
 578   </transf>
 579   </goal>
 580  </transf>
 581  </goal>
 582 </theory>
 583 <theory name="FoldLeft" proved="true">
 584  <goal name="fold_left_append" proved="true">
 585  <transf name="induction_ty_lex" proved="true" >
 586   <goal name="fold_left_append.0" proved="true">
 587   <proof prover="6"><result status="valid" time="0.060000" steps="7424"/></proof>
 588   </goal>
 589  </transf>
 590  </goal>
 591 </theory>
 592 <theory name="FoldRight" proved="true">
 593  <goal name="fold_right_append" proved="true">
 594  <transf name="induction_ty_lex" proved="true" >
 595   <goal name="fold_right_append.0" proved="true">
 596   <proof prover="6"><result status="valid" time="0.060000" steps="6984"/></proof>
 597   </goal>
 598  </transf>
 599  </goal>
 600 </theory>
 601 </file>
 602 </why3session>