why3session.xml 202 KB
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="4">
<prover id="1" name="CVC4" version="1.4" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.5.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="3" name="Eprover" version="1.9.1-001" timelimit="5" steplimit="0" memlimit="2000"/>
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<prover id="4" name="Alt-Ergo" version="2.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<file name="../lineardecision.mlw">
<theory name="LinearEquationsCoeffs" proved="true">
 <goal name="VC czero" expl="VC for czero" proved="true">
 <proof prover="2"><result status="valid" time="0.02"/></proof>
 </goal>
 <goal name="VC cone" expl="VC for cone" proved="true">
 <transf name="split_goal_right" proved="true" >
 </transf>
 </goal>
 <goal name="neg_mul" proved="true">
 <proof prover="3"><result status="valid" time="0.06"/></proof>
 </goal>
</theory>
<theory name="LinearEquationsDecision" proved="true">
 <goal name="VC valid_expr" expl="VC for valid_expr" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC expr_bound" expl="VC for expr_bound" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC valid_eq" expl="VC for valid_eq" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC eq_bound" expl="VC for eq_bound" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC valid_ctx" expl="VC for valid_ctx" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC ctx_bound" expl="VC for ctx_bound" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC expr_bound_w" expl="VC for expr_bound_w" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC expr_bound_w.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC expr_bound_w.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC expr_bound_w.2" expl="precondition" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="12"/></proof>
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  </goal>
  <goal name="VC expr_bound_w.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC expr_bound_w.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC expr_bound_w.5" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="13"/></proof>
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  </goal>
  <goal name="VC expr_bound_w.6" expl="postcondition" proved="true">
62
  <proof prover="4"><result status="valid" time="0.01" steps="34"/></proof>
63 64 65 66
  </goal>
 </transf>
 </goal>
 <goal name="eq_bound_w" proved="true">
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 <proof prover="4"><result status="valid" time="0.00" steps="19"/></proof>
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 </goal>
 <goal name="VC ctx_bound_w" expl="VC for ctx_bound_w" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC ctx_bound_w.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC ctx_bound_w.1" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="12"/></proof>
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  </goal>
  <goal name="VC ctx_bound_w.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC ctx_bound_w.3" expl="postcondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="31"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC apply_r" expl="VC for apply_r" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC apply_r.0" expl="array creation size" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="17"/></proof>
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  </goal>
  <goal name="VC apply_r.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC apply_r.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC apply_r.3" expl="index in array bounds" proved="true">
97
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="22"/></proof>
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  </goal>
  <goal name="VC apply_r.4" expl="index in array bounds" proved="true">
100
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="23"/></proof>
101 102
  </goal>
  <goal name="VC apply_r.5" expl="index in array bounds" proved="true">
103
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="22"/></proof>
104 105
  </goal>
  <goal name="VC apply_r.6" expl="index in array bounds" proved="true">
106
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="22"/></proof>
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  </goal>
  <goal name="VC apply_r.7" expl="exceptional postcondition" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="10"/></proof>
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  </goal>
  <goal name="VC apply_r.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC apply_r.9" expl="postcondition" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="15"/></proof>
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  </goal>
  <goal name="VC apply_r.10" expl="postcondition" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="14"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC apply_l" expl="VC for apply_l" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC apply_l.0" expl="array creation size" proved="true">
125
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="10"/></proof>
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  </goal>
  <goal name="VC apply_l.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC apply_l.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC apply_l.3" expl="index in array bounds" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="22"/></proof>
135 136
  </goal>
  <goal name="VC apply_l.4" expl="index in array bounds" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="23"/></proof>
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  </goal>
  <goal name="VC apply_l.5" expl="index in array bounds" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="22"/></proof>
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  </goal>
  <goal name="VC apply_l.6" expl="index in array bounds" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="22"/></proof>
144 145
  </goal>
  <goal name="VC apply_l.7" expl="exceptional postcondition" proved="true">
146
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="10"/></proof>
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  </goal>
  <goal name="VC apply_l.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC apply_l.9" expl="postcondition" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="15"/></proof>
153 154
  </goal>
  <goal name="VC apply_l.10" expl="postcondition" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="14"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC sprod" expl="VC for sprod" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC sprod.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC sprod.1" expl="index in array bounds" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="15"/></proof>
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  </goal>
  <goal name="VC sprod.2" expl="index in array bounds" proved="true">
168
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="15"/></proof>
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  </goal>
  <goal name="VC sprod.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC sprod.4" expl="exceptional postcondition" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="10"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC m_append" expl="VC for m_append" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC m_append.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC m_append.1" expl="precondition" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="59"/></proof>
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  </goal>
  <goal name="VC m_append.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC m_append.3" expl="loop invariant init" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="17"/></proof>
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  </goal>
  <goal name="VC m_append.4" expl="loop invariant init" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="17"/></proof>
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  </goal>
  <goal name="VC m_append.5" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC m_append.6" expl="loop invariant init" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="30"/></proof>
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  </goal>
  <goal name="VC m_append.7" expl="loop invariant init" proved="true">
202
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="27"/></proof>
203 204
  </goal>
  <goal name="VC m_append.8" expl="loop invariant init" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="23"/></proof>
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  </goal>
  <goal name="VC m_append.9" expl="index in array bounds" proved="true">
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  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="28"/></proof>
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  </goal>
  <goal name="VC m_append.10" expl="index in array bounds" proved="true">
211
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="28"/></proof>
212 213
  </goal>
  <goal name="VC m_append.11" expl="loop invariant preservation" proved="true">
214
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="39"/></proof>
215 216
  </goal>
  <goal name="VC m_append.12" expl="loop invariant preservation" proved="true">
217
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="36"/></proof>
218 219
  </goal>
  <goal name="VC m_append.13" expl="loop invariant preservation" proved="true">
220
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="36"/></proof>
221 222
  </goal>
  <goal name="VC m_append.14" expl="index in array bounds" proved="true">
223
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="25"/></proof>
224 225
  </goal>
  <goal name="VC m_append.15" expl="index in array bounds" proved="true">
226
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="26"/></proof>
227 228
  </goal>
  <goal name="VC m_append.16" expl="loop invariant preservation" proved="true">
229
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="94"/></proof>
230 231
  </goal>
  <goal name="VC m_append.17" expl="loop invariant preservation" proved="true">
232
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="33"/></proof>
233 234
  </goal>
  <goal name="VC m_append.18" expl="out of loop bounds" proved="true">
235
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="39"/></proof>
236 237
  </goal>
  <goal name="VC m_append.19" expl="postcondition" proved="true">
238
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="19"/></proof>
239 240
  </goal>
  <goal name="VC m_append.20" expl="postcondition" proved="true">
241
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="20"/></proof>
242 243
  </goal>
  <goal name="VC m_append.21" expl="postcondition" proved="true">
244
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="28"/></proof>
245 246
  </goal>
  <goal name="VC m_append.22" expl="postcondition" proved="true">
247
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="25"/></proof>
248 249
  </goal>
  <goal name="VC m_append.23" expl="out of loop bounds" proved="true">
250
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="20"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC v_append" expl="VC for v_append" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC v_append.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC v_append.1" expl="array creation size" proved="true">
260
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="12"/></proof>
261 262 263 264 265
  </goal>
  <goal name="VC v_append.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC v_append.3" expl="loop invariant init" proved="true">
266
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="15"/></proof>
267 268
  </goal>
  <goal name="VC v_append.4" expl="loop invariant init" proved="true">
269
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="17"/></proof>
270 271
  </goal>
  <goal name="VC v_append.5" expl="index in array bounds" proved="true">
272
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="19"/></proof>
273 274
  </goal>
  <goal name="VC v_append.6" expl="index in array bounds" proved="true">
275
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="19"/></proof>
276 277
  </goal>
  <goal name="VC v_append.7" expl="loop invariant preservation" proved="true">
278
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="193"/></proof>
279 280
  </goal>
  <goal name="VC v_append.8" expl="loop invariant preservation" proved="true">
281
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="102"/></proof>
282 283
  </goal>
  <goal name="VC v_append.9" expl="postcondition" proved="true">
284
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="17"/></proof>
285 286
  </goal>
  <goal name="VC v_append.10" expl="postcondition" proved="true">
287
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="21"/></proof>
288 289
  </goal>
  <goal name="VC v_append.11" expl="postcondition" proved="true">
290
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="18"/></proof>
291 292
  </goal>
  <goal name="VC v_append.12" expl="out of loop bounds" proved="true">
293
  <proof prover="4" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="24"/></proof>
294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314
  </goal>
 </transf>
 </goal>
 <goal name="VC infix ==" expl="VC for infix ==" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC infix ==.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC infix ==.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC infix ==.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.3" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.4" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.5" expl="loop invariant preservation" proved="true">
315
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
316 317
  </goal>
  <goal name="VC infix ==.6" expl="loop invariant preservation" proved="true">
318
  <proof prover="4"><result status="valid" time="0.02" steps="21"/></proof>
319 320 321 322 323 324 325 326 327 328
  </goal>
  <goal name="VC infix ==.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.8" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC max_var" expl="VC for max_var" proved="true">
329
 <proof prover="4"><result status="valid" time="0.04" steps="357"/></proof>
330 331 332 333 334
 </goal>
 <goal name="VC max_var_e" expl="VC for max_var_e" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC max_var_ctx" expl="VC for max_var_ctx" proved="true">
335
 <proof prover="4"><result status="valid" time="0.04" steps="259"/></proof>
336 337 338 339 340 341
 </goal>
 <goal name="VC opp_expr" expl="VC for opp_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC opp_expr.0" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC opp_expr.0.0" expl="assertion" proved="true">
342
   <proof prover="4"><result status="valid" time="0.01" steps="11"/></proof>
343 344
   </goal>
   <goal name="VC opp_expr.0.1" expl="assertion" proved="true">
345
   <proof prover="4"><result status="valid" time="0.01" steps="11"/></proof>
346 347 348 349 350 351 352 353 354 355
   </goal>
   <goal name="VC opp_expr.0.2" expl="assertion" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="VC opp_expr.0.2.0" expl="assertion" proved="true">
    <transf name="apply" proved="true" arg1="neg_mul">
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="VC opp_expr.0.3" expl="assertion" proved="true">
356
   <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
357 358 359 360 361 362 363 364 365 366 367 368 369 370 371
   </goal>
  </transf>
  </goal>
  <goal name="VC opp_expr.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC opp_expr.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC opp_expr.3" expl="assertion" proved="true">
  <proof prover="3" memlimit="1000"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC opp_expr.4" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC opp_expr.4.0" expl="assertion" proved="true">
372
   <proof prover="4"><result status="valid" time="0.01" steps="11"/></proof>
373 374 375 376 377 378 379 380
   </goal>
   <goal name="VC opp_expr.4.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="VC opp_expr.4.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="VC opp_expr.4.3" expl="assertion" proved="true">
381
   <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
382 383 384 385 386 387 388 389 390
   </goal>
   <goal name="VC opp_expr.4.4" expl="VC for opp_expr" proved="true">
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC opp_expr.5" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC opp_expr.5.0" expl="postcondition" proved="true">
391
   <proof prover="4"><result status="valid" time="0.01" steps="16"/></proof>
392 393 394 395
   </goal>
   <goal name="VC opp_expr.5.1" expl="postcondition" proved="true">
   <transf name="compute_in_goal" proved="true" >
    <goal name="VC opp_expr.5.1.0" expl="postcondition" proved="true">
396
    <proof prover="4"><result status="valid" time="0.04" steps="27"/></proof>
397 398 399 400
    </goal>
   </transf>
   </goal>
   <goal name="VC opp_expr.5.2" expl="postcondition" proved="true">
401
   <proof prover="4"><result status="valid" time="0.02" steps="12"/></proof>
402 403 404 405
   </goal>
  </transf>
  </goal>
  <goal name="VC opp_expr.6" expl="postcondition" proved="true">
406
  <proof prover="4"><result status="valid" time="0.02" steps="163"/></proof>
407 408
  </goal>
  <goal name="VC opp_expr.7" expl="postcondition" proved="true">
409
  <proof prover="4"><result status="valid" time="0.02" steps="147"/></proof>
410 411 412 413 414 415
  </goal>
 </transf>
 </goal>
 <goal name="VC norm_eq_aux" expl="VC for norm_eq_aux" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC norm_eq_aux.0" expl="postcondition" proved="true">
416
  <proof prover="4"><result status="valid" time="0.01" steps="26"/></proof>
417 418
  </goal>
  <goal name="VC norm_eq_aux.1" expl="postcondition" proved="true">
419
  <proof prover="4"><result status="valid" time="0.01" steps="12"/></proof>
420 421 422 423 424
  </goal>
  <goal name="VC norm_eq_aux.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC norm_eq_aux.3" expl="postcondition" proved="true">
425
  <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
426 427
  </goal>
  <goal name="VC norm_eq_aux.4" expl="postcondition" proved="true">
428
  <proof prover="4"><result status="valid" time="0.02" steps="13"/></proof>
429 430 431 432 433 434 435 436
  </goal>
  <goal name="VC norm_eq_aux.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC norm_eq_aux.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC norm_eq_aux.7" expl="postcondition" proved="true">
437
  <proof prover="4"><result status="valid" time="0.02" steps="27"/></proof>
438 439
  </goal>
  <goal name="VC norm_eq_aux.8" expl="postcondition" proved="true">
440
  <proof prover="4"><result status="valid" time="0.02" steps="74"/></proof>
441 442 443 444 445 446 447 448 449 450 451 452
  </goal>
  <goal name="VC norm_eq_aux.9" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC norm_eq_aux.10" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC norm_eq" expl="VC for norm_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC norm_eq.0" expl="assertion" proved="true">
453
  <proof prover="4"><result status="valid" time="0.02" steps="56"/></proof>
454 455 456 457 458 459 460
  </goal>
  <goal name="VC norm_eq.1" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC norm_eq.2" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC norm_eq.2.0" expl="assertion" proved="true">
461
   <proof prover="4"><result status="valid" time="0.02" steps="47"/></proof>
462 463
   </goal>
   <goal name="VC norm_eq.2.1" expl="VC for norm_eq" proved="true">
464
   <proof prover="4"><result status="valid" time="0.03" steps="40"/></proof>
465 466 467 468 469
   </goal>
   <goal name="VC norm_eq.2.2" expl="VC for norm_eq" proved="true">
   <proof prover="1"><result status="valid" time="0.05"/></proof>
   </goal>
   <goal name="VC norm_eq.2.3" expl="VC for norm_eq" proved="true">
470
   <proof prover="4"><result status="valid" time="0.02" steps="46"/></proof>
471 472
   </goal>
   <goal name="VC norm_eq.2.4" expl="VC for norm_eq" proved="true">
473
   <proof prover="4"><result status="valid" time="0.02" steps="21"/></proof>
474 475
   </goal>
   <goal name="VC norm_eq.2.5" expl="VC for norm_eq" proved="true">
476
   <proof prover="4"><result status="valid" time="0.02" steps="16"/></proof>
477 478 479 480 481 482
   </goal>
  </transf>
  </goal>
  <goal name="VC norm_eq.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC norm_eq.3.0" expl="postcondition" proved="true">
483
   <proof prover="4"><result status="valid" time="0.02" steps="13"/></proof>
484 485 486 487 488 489 490
   </goal>
   <goal name="VC norm_eq.3.1" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.60"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC norm_eq.4" expl="postcondition" proved="true">
491
  <proof prover="4"><result status="valid" time="0.02" steps="41"/></proof>
492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521
  </goal>
  <goal name="VC norm_eq.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC interp_ctx_impl" expl="VC for interp_ctx_impl" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC interp_ctx_impl.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC interp_ctx_impl.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC interp_ctx_impl.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC interp_ctx_valid" expl="VC for interp_ctx_valid" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC interp_ctx_valid.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC interp_ctx_valid.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC interp_ctx_wr" expl="VC for interp_ctx_wr" proved="true">
522
 <proof prover="4"><result status="valid" time="0.02" steps="172"/></proof>
523 524
 </goal>
 <goal name="VC interp_ctx_wl" expl="VC for interp_ctx_wl" proved="true">
525
 <proof prover="4"><result status="valid" time="0.02" steps="141"/></proof>
526 527 528 529 530 531 532
 </goal>
 <goal name="VC mul_expr" expl="VC for mul_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC mul_expr.0" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.12"/></proof>
  </goal>
  <goal name="VC mul_expr.1" expl="postcondition" proved="true">
533
  <proof prover="4"><result status="valid" time="0.02" steps="12"/></proof>
534 535
  </goal>
  <goal name="VC mul_expr.2" expl="postcondition" proved="true">
536
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
537 538
  </goal>
  <goal name="VC mul_expr.3" expl="postcondition" proved="true">
539
  <proof prover="4"><result status="valid" time="0.02" steps="13"/></proof>
540 541 542 543 544
  </goal>
  <goal name="VC mul_expr.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC mul_expr.5" expl="postcondition" proved="true">
545
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
546 547
  </goal>
  <goal name="VC mul_expr.6" expl="postcondition" proved="true">
548
  <proof prover="4"><result status="valid" time="0.01" steps="35"/></proof>
549 550 551 552 553
  </goal>
  <goal name="VC mul_expr.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC mul_expr.8" expl="variant decrease" proved="true">
554
  <proof prover="4"><result status="valid" time="0.02" steps="60"/></proof>
555 556
  </goal>
  <goal name="VC mul_expr.9" expl="variant decrease" proved="true">
557
  <proof prover="4"><result status="valid" time="0.01" steps="63"/></proof>
558 559
  </goal>
  <goal name="VC mul_expr.10" expl="postcondition" proved="true">
560
  <proof prover="4"><result status="valid" time="0.03" steps="22"/></proof>
561 562
  </goal>
  <goal name="VC mul_expr.11" expl="postcondition" proved="true">
563
  <proof prover="4"><result status="valid" time="0.02" steps="81"/></proof>
564 565 566 567 568 569 570 571 572 573 574 575 576 577 578
  </goal>
  <goal name="VC mul_expr.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC mul_expr.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC add_expr" expl="VC for add_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC add_expr.0" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.29"/></proof>
  </goal>
  <goal name="VC add_expr.1" expl="postcondition" proved="true">
579
  <proof prover="4"><result status="valid" time="0.03" steps="19"/></proof>
580 581 582 583 584 585 586 587 588
  </goal>
  <goal name="VC add_expr.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC add_expr.3.0" expl="postcondition" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="VC add_expr.3.0.0" expl="postcondition" proved="true">
589
    <proof prover="3"><result status="valid" time="0.46"/></proof>
590 591 592 593 594 595 596 597 598 599 600
    </goal>
   </transf>
   </goal>
   <goal name="VC add_expr.3.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.05"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC add_expr.4" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="VC add_expr.4.0" expl="postcondition" proved="true">
601
   <proof prover="3"><result status="valid" time="0.54"/></proof>
602 603
   </goal>
   <goal name="VC add_expr.4.1" expl="postcondition" proved="true">
604
   <proof prover="3" memlimit="1000"><result status="valid" time="0.29"/></proof>
605 606 607 608 609 610 611 612 613 614
   </goal>
  </transf>
  </goal>
  <goal name="VC add_expr.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.7" expl="assertion" proved="true">
615
  <proof prover="4"><result status="valid" time="0.02" steps="69"/></proof>
616 617
  </goal>
  <goal name="VC add_expr.8" expl="postcondition" proved="true">
618 619 620 621 622 623 624 625 626 627 628 629 630 631 632
  <transf name="split_goal_right" proved="true" >
   <goal name="VC add_expr.8.0" expl="postcondition" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="VC add_expr.8.0.0" expl="postcondition" proved="true">
    <proof prover="4"><result status="valid" time="0.02" steps="64"/></proof>
    </goal>
    <goal name="VC add_expr.8.0.1" expl="postcondition" proved="true">
    <proof prover="4"><result status="valid" time="0.01" steps="23"/></proof>
    </goal>
   </transf>
   </goal>
   <goal name="VC add_expr.8.1" expl="postcondition" proved="true">
   <proof prover="4"><result status="valid" time="0.03" steps="22"/></proof>
   </goal>
  </transf>
633 634 635 636 637 638 639 640
  </goal>
  <goal name="VC add_expr.9" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.11" expl="assertion" proved="true">
641
  <proof prover="4"><result status="valid" time="0.02" steps="69"/></proof>
642 643
  </goal>
  <goal name="VC add_expr.12" expl="postcondition" proved="true">
644
  <proof prover="4"><result status="valid" time="1.11" steps="541"/></proof>
645 646 647 648 649 650 651 652
  </goal>
  <goal name="VC add_expr.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.15" expl="postcondition" proved="true">
653
  <proof prover="4"><result status="valid" time="0.02" steps="21"/></proof>
654 655 656 657 658 659 660 661 662 663 664
  </goal>
  <goal name="VC add_expr.16" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.17" expl="postcondition" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="VC add_expr.17.0" expl="postcondition" proved="true">
   <transf name="revert" proved="true" arg1="H">
    <goal name="VC add_expr.17.0.0" expl="postcondition" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="VC add_expr.17.0.0.0" expl="postcondition" proved="true">
665
     <proof prover="3"><result status="valid" time="0.52"/></proof>
666 667
     </goal>
     <goal name="VC add_expr.17.0.0.1" expl="postcondition" proved="true">
668
     <proof prover="3"><result status="valid" time="0.27"/></proof>
669 670 671 672 673 674 675 676 677 678 679 680 681 682
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="VC add_expr.18" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.20" expl="assertion" proved="true">
683
  <proof prover="4"><result status="valid" time="0.02" steps="66"/></proof>
684 685
  </goal>
  <goal name="VC add_expr.21" expl="postcondition" proved="true">
686
  <proof prover="4"><result status="valid" time="0.34" steps="268"/></proof>
687 688 689 690 691 692 693 694
  </goal>
  <goal name="VC add_expr.22" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.23" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.24" expl="assertion" proved="true">
695
  <proof prover="4"><result status="valid" time="0.02" steps="66"/></proof>
696 697
  </goal>
  <goal name="VC add_expr.25" expl="postcondition" proved="true">
698
  <proof prover="4"><result status="valid" time="0.35" steps="496"/></proof>
699 700 701 702 703 704 705 706 707 708 709 710 711 712
  </goal>
  <goal name="VC add_expr.26" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.27" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.28" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.29" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.30" expl="assertion" proved="true">
713
  <proof prover="4"><result status="valid" time="0.01" steps="20"/></proof>
714 715
  </goal>
  <goal name="VC add_expr.31" expl="postcondition" proved="true">
716
  <proof prover="4"><result status="valid" time="0.02" steps="21"/></proof>
717 718 719 720 721 722 723 724
  </goal>
  <goal name="VC add_expr.32" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.33" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.34" expl="assertion" proved="true">
725
  <proof prover="4"><result status="valid" time="0.01" steps="20"/></proof>
726 727
  </goal>
  <goal name="VC add_expr.35" expl="postcondition" proved="true">
728
  <proof prover="4"><result status="valid" time="0.02" steps="22"/></proof>
729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745
  </goal>
  <goal name="VC add_expr.36" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.37" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.38" expl="unreachable point" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.39" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.40" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.41" expl="postcondition" proved="true">
746
  <proof prover="4"><result status="valid" time="0.02" steps="15"/></proof>
747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765
  </goal>
  <goal name="VC add_expr.42" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.44" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.45" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC add_expr.46" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC mul_eq" expl="VC for mul_eq" proved="true">
766
 <proof prover="4"><result status="valid" time="0.01" steps="37"/></proof>
767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
 </goal>
 <goal name="VC add_eq" expl="VC for add_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC add_eq.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC add_eq.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16"/></proof>
  </goal>
  <goal name="VC add_eq.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC add_eq.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_eq.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_eq.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC zero_expr" expl="VC for zero_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC zero_expr.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC zero_expr.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC zero_expr.2" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC zero_expr.2.0" expl="postcondition" proved="true">
801
   <proof prover="4"><result status="valid" time="0.02" steps="34"/></proof>
802 803 804 805 806
   </goal>
   <goal name="VC zero_expr.2.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.40"/></proof>
   </goal>
   <goal name="VC zero_expr.2.2" expl="postcondition" proved="true">
807
   <proof prover="4"><result status="valid" time="0.03" steps="39"/></proof>
808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833
   </goal>
  </transf>
  </goal>
  <goal name="VC zero_expr.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC zero_expr.3.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.06"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC zero_expr.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC sub_expr" expl="VC for sub_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC sub_expr.0" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC sub_expr.0.0" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.04"/></proof>
   </goal>
   <goal name="VC sub_expr.0.1" expl="VC for sub_expr" proved="true">
   <proof prover="1"><result status="valid" time="0.05"/></proof>
   </goal>
   <goal name="VC sub_expr.0.2" expl="VC for sub_expr" proved="true">
834
   <proof prover="4"><result status="valid" time="0.01" steps="10"/></proof>
835 836
   </goal>
   <goal name="VC sub_expr.0.3" expl="VC for sub_expr" proved="true">
837
   <proof prover="4"><result status="valid" time="0.01" steps="42"/></proof>
838 839
   </goal>
   <goal name="VC sub_expr.0.4" expl="VC for sub_expr" proved="true">
840
   <proof prover="4"><result status="valid" time="0.02" steps="13"/></proof>
841 842 843 844
   </goal>
  </transf>
  </goal>
  <goal name="VC sub_expr.1" expl="postcondition" proved="true">
845
  <proof prover="4"><result status="valid" time="0.01" steps="10"/></proof>
846 847 848 849 850 851 852 853 854 855 856 857
  </goal>
  <goal name="VC sub_expr.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC sub_expr.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC same_eq" expl="VC for same_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC same_eq.0" expl="postcondition" proved="true">
858
  <proof prover="1"><result status="valid" time="0.17"/></proof>
859 860
  </goal>
  <goal name="VC same_eq.1" expl="postcondition" proved="true">
861
  <proof prover="4"><result status="valid" time="0.01" steps="9"/></proof>
862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900
  </goal>
  <goal name="VC same_eq.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC same_eq.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC same_eq.4" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
  <goal name="VC same_eq.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC same_eq.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC norm_context" expl="VC for norm_context" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC norm_context.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC norm_context.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC norm_context.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC norm_context.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC norm_context.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC print_lc" expl="VC for print_lc" proved="true">
901
 <proof prover="4"><result status="valid" time="0.01" steps="47"/></proof>
902 903 904 905 906 907 908 909 910 911
 </goal>
 <goal name="VC check_combination" expl="VC for check_combination" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC check_combination.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC check_combination.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC check_combination.2" expl="variant decrease" proved="true">
912
  <proof prover="4"><result status="valid" time="0.02" steps="43"/></proof>
913 914
  </goal>
  <goal name="VC check_combination.3" expl="precondition" proved="true">
915
  <proof prover="4"><result status="valid" time="0.02" steps="17"/></proof>
916 917
  </goal>
  <goal name="VC check_combination.4" expl="precondition" proved="true">
918
  <proof prover="4"><result status="valid" time="0.02" steps="68"/></proof>
919 920
  </goal>
  <goal name="VC check_combination.5" expl="postcondition" proved="true">
921
  <proof prover="4"><result status="valid" time="0.02" steps="88"/></proof>
922 923 924 925 926 927 928
  </goal>
  <goal name="VC check_combination.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC check_combination.7" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC check_combination.7.0" expl="assertion" proved="true">
929
   <proof prover="4"><result status="valid" time="0.03" steps="17"/></proof>
930 931
   </goal>
   <goal name="VC check_combination.7.1" expl="assertion" proved="true">
932
   <proof prover="4"><result status="valid" time="0.02" steps="32"/></proof>
933 934
   </goal>
   <goal name="VC check_combination.7.2" expl="VC for check_combination" proved="true">
935
   <proof prover="4"><result status="valid" time="0.03" steps="47"/></proof>
936 937 938 939
   </goal>
  </transf>
  </goal>
  <goal name="VC check_combination.8" expl="variant decrease" proved="true">
940
  <proof prover="4"><result status="valid" time="0.02" steps="43"/></proof>
941 942
  </goal>
  <goal name="VC check_combination.9" expl="precondition" proved="true">
943
  <proof prover="4"><result status="valid" time="0.02" steps="14"/></proof>
944 945
  </goal>
  <goal name="VC check_combination.10" expl="precondition" proved="true">
946
  <proof prover="4"><result status="valid" time="0.02" steps="68"/></proof>
947 948
  </goal>
  <goal name="VC check_combination.11" expl="postcondition" proved="true">
949
  <proof prover="4"><result status="valid" time="0.02" steps="88"/></proof>
950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966
  </goal>
  <goal name="VC check_combination.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC check_combination.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC check_combination.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="VC check_combination.15" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC check_combination.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC check_combination.17" expl="precondition" proved="true">
967
  <proof prover="4"><result status="valid" time="0.02" steps="10"/></proof>
968 969
  </goal>
  <goal name="VC check_combination.18" expl="postcondition" proved="true">
970
  <proof prover="1"><result status="valid" time="1.45"/></proof>
971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992
  </goal>
  <goal name="VC check_combination.19" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC check_combination.20" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="VC check_combination.21" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="VC check_combination.22" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC transpose" expl="VC for transpose" proved="true">
 <proof prover="2"><result status="valid" time="0.18"/></proof>
 </goal>
 <goal name="VC swap_rows" expl="VC for swap_rows" proved="true">
 <proof prover="2"><result status="valid" time="0.26"/></proof>
 </goal>
 <goal name="VC mul_row" expl="VC for mul_row" proved="true">
993
 <proof prover="4"><result status="valid" time="0.12" steps="429"/></proof>
994 995
 </goal>
 <goal name="VC addmul_row" expl="VC for addmul_row" proved="true">
996
 <proof prover="4"><result status="vali