1 tB2Atlor9W4pSnrAz5nHpw 907 0
4 decl uf_1 :: (-> T3 T2 real)
5 decl uf_10 :: (-> T4 T2)
9 decl uf_2 :: (-> T1 T3)
13 #902 := (uf_1 #91 #22)
15 #1084 := (* -1::real #902)
19 #799 := (uf_1 #78 #22)
20 #1267 := (+ #799 #1084)
21 #1272 := (>= #1267 0::real)
22 #1266 := (= #799 #902)
25 #23 := (uf_1 uf_9 #22)
29 #850 := (uf_1 uf_11 #22)
31 decl uf_6 :: (-> T2 T4)
34 #922 := (ite #281 #905 #904)
37 #848 := (uf_1 uf_8 #22)
40 decl uf_5 :: (-> T4 int)
43 #813 := (* -1::int #803)
46 #917 := (<= #916 0::int)
47 #925 := (ite #917 #922 #903)
51 #25 := (uf_1 uf_11 #6)
61 #446 := (ite #20 #444 #445)
62 #120 := (* -1::int #16)
65 #119 := (>= #121 0::int)
66 #448 := (ite #119 #446 #447)
67 #545 := (forall (vars (?x3 T2)) (:pat #541 #542 #543 #544) #448)
68 #451 := (forall (vars (?x3 T2)) #448)
69 #548 := (iff #451 #545)
70 #546 := (iff #448 #448)
72 #549 := [quant-intro #547]: #548
73 #26 := (ite #20 #23 #25)
74 #127 := (ite #119 #26 #19)
76 #369 := (forall (vars (?x3 T2)) #368)
77 #452 := (iff #369 #451)
78 #449 := (iff #368 #448)
79 #450 := [rewrite]: #449
80 #453 := [quant-intro #450]: #452
84 #366 := [nnf-pos #391]: #392
85 decl uf_3 :: (-> T1 T2 real)
88 #135 := (forall (vars (?x3 T2)) #132)
89 #370 := (iff #135 #369)
95 #10 := (forall (vars (?x1 T1) (?x2 T2)) #9)
96 #113 := [asserted]: #10
97 #371 := [rewrite* #113]: #370
99 #27 := (ite #17 #19 #26)
101 #29 := (forall (vars (?x3 T2)) #28)
102 #136 := (iff #29 #135)
103 #133 := (iff #28 #132)
106 #124 := (ite #118 #19 #26)
107 #128 := (= #124 #127)
108 #129 := [rewrite]: #128
110 #122 := (iff #17 #118)
111 #123 := [rewrite]: #122
112 #126 := [monotonicity #123]: #125
113 #131 := [trans #126 #129]: #130
114 #134 := [monotonicity #131]: #133
115 #137 := [quant-intro #134]: #136
116 #114 := [asserted]: #29
117 #138 := [mp #114 #137]: #135
118 #372 := [mp #138 #371]: #369
119 #367 := [mp~ #372 #366]: #369
120 #454 := [mp #367 #453]: #451
121 #550 := [mp #454 #549]: #545
123 #928 := (or #738 #925)
125 #906 := (ite #75 #905 #904)
126 #907 := (+ #803 #120)
127 #908 := (>= #907 0::int)
128 #909 := (ite #908 #906 #903)
129 #929 := (or #738 #909)
130 #931 := (iff #929 #928)
131 #933 := (iff #928 #928)
132 #934 := [rewrite]: #933
133 #926 := (iff #909 #925)
134 #923 := (iff #906 #922)
135 #283 := (iff #75 #281)
136 #284 := [rewrite]: #283
137 #924 := [monotonicity #284]: #923
138 #920 := (iff #908 #917)
139 #910 := (+ #120 #803)
140 #913 := (>= #910 0::int)
141 #918 := (iff #913 #917)
142 #919 := [rewrite]: #918
143 #914 := (iff #908 #913)
144 #911 := (= #907 #910)
145 #912 := [rewrite]: #911
146 #915 := [monotonicity #912]: #914
147 #921 := [trans #915 #919]: #920
148 #927 := [monotonicity #921 #924]: #926
149 #932 := [monotonicity #927]: #931
150 #935 := [trans #932 #934]: #931
151 #930 := [quant-inst]: #929
152 #936 := [mp #930 #935]: #928
153 #1300 := [unit-resolution #936 #550]: #925
155 #1277 := (= #803 #16)
156 #280 := [asserted]: #75
157 #287 := [mp #280 #284]: #281
158 #1276 := [symm #287]: #75
159 #1278 := [monotonicity #1276]: #1277
160 #1301 := [symm #1278]: #989
162 #1303 := (or #1302 #917)
163 #1304 := [th-lemma]: #1303
164 #1305 := [unit-resolution #1304 #1301]: #917
167 #951 := (or #949 #950 #922)
168 #952 := [def-axiom]: #951
169 #1306 := [unit-resolution #952 #1305 #1300]: #922
171 #1307 := (or #937 #905)
173 #939 := (or #937 #938 #905)
174 #940 := [def-axiom]: #939
175 #1308 := [unit-resolution #940 #287]: #1307
176 #1309 := [unit-resolution #1308 #1306]: #905
177 #1356 := (= #799 #23)
183 #815 := (<= #814 0::int)
185 #158 := (* -1::int #41)
186 #1270 := (+ #16 #158)
187 #1265 := (>= #1270 0::int)
191 #286 := (= uf_7 uf_15)
195 #277 := (= uf_15 #72)
196 #278 := (iff #73 #277)
197 #279 := [rewrite]: #278
198 #276 := [asserted]: #73
199 #282 := [mp #276 #279]: #277
200 #1274 := [symm #282]: #73
202 decl uf_17 :: (-> int T4)
205 #1289 := (= #991 #72)
209 #574 := (pattern #56)
212 #575 := (forall (vars (?x7 T4)) (:pat #574) #177)
213 #195 := (forall (vars (?x7 T4)) #177)
214 #578 := (iff #195 #575)
215 #576 := (iff #177 #177)
217 #579 := [quant-intro #577]: #578
218 #405 := (~ #195 #195)
219 #403 := (~ #177 #177)
221 #406 := [nnf-pos #404]: #405
223 #59 := (forall (vars (?x7 T4)) #58)
224 #196 := (iff #59 #195)
225 #193 := (iff #58 #177)
226 #194 := [rewrite]: #193
227 #197 := [quant-intro #194]: #196
228 #155 := [asserted]: #59
229 #200 := [mp #155 #197]: #195
230 #407 := [mp~ #200 #406]: #195
231 #580 := [mp #407 #579]: #575
233 #996 := (or #995 #992)
234 #997 := [quant-inst]: #996
235 #1273 := [unit-resolution #997 #580]: #992
236 #1290 := [symm #1273]: #1289
237 #1293 := (= uf_7 #991)
239 #1287 := (= #993 #991)
240 #1284 := (= #803 #611)
242 #1279 := (= #611 #41)
243 #1280 := [monotonicity #1274]: #1279
244 #1281 := [symm #1280]: #987
245 #1282 := (= #803 #41)
246 #1275 := [hypothesis]: #1269
247 #1283 := [trans #1278 #1275]: #1282
248 #1285 := [trans #1283 #1281]: #1284
249 #1288 := [monotonicity #1285]: #1287
250 #1291 := (= uf_7 #993)
252 #1000 := (or #995 #994)
253 #1001 := [quant-inst]: #1000
254 #1286 := [unit-resolution #1001 #580]: #994
255 #1292 := [trans #287 #1286]: #1291
256 #1294 := [trans #1292 #1288]: #1293
257 #1295 := [trans #1294 #1290]: #729
258 #1296 := [trans #1295 #1274]: #286
260 #76 := (= uf_15 uf_7)
262 #291 := (iff #77 #290)
263 #288 := (iff #76 #286)
264 #289 := [rewrite]: #288
265 #292 := [monotonicity #289]: #291
266 #285 := [asserted]: #77
267 #295 := [mp #285 #292]: #290
268 #1297 := [unit-resolution #295 #1296]: false
269 #1299 := [lemma #1297]: #1298
270 #1342 := (or #1269 #1339)
271 #1271 := (<= #1270 0::int)
272 #621 := (* -1::int #611)
274 #724 := (<= #723 0::int)
278 #771 := (uf_1 #88 #44)
279 #45 := (uf_1 uf_9 #44)
285 #656 := (uf_1 #83 #44)
286 #1239 := (= #656 #771)
288 #1324 := (iff #1252 #796)
289 #1322 := (iff #1239 #772)
290 #1320 := (= #656 #45)
292 #659 := (uf_1 uf_11 #44)
293 #664 := (= #656 #659)
294 #667 := (ite #277 #661 #664)
295 #657 := (uf_1 uf_8 #44)
296 #670 := (= #656 #657)
298 #623 := (<= #622 0::int)
299 #673 := (ite #623 #667 #670)
301 #560 := (pattern #84)
306 #466 := (ite #43 #464 #465)
308 #157 := (>= #159 0::int)
309 #468 := (ite #157 #466 #467)
310 #561 := (forall (vars (?x5 T2)) (:pat #541 #560 #543 #544) #468)
311 #471 := (forall (vars (?x5 T2)) #468)
312 #564 := (iff #471 #561)
313 #562 := (iff #468 #468)
315 #565 := [quant-intro #563]: #564
316 #46 := (ite #43 #45 #25)
317 #165 := (ite #157 #46 #19)
319 #379 := (forall (vars (?x5 T2)) #378)
320 #472 := (iff #379 #471)
321 #469 := (iff #378 #468)
322 #470 := [rewrite]: #469
323 #473 := [quant-intro #470]: #472
324 #359 := (~ #379 #379)
325 #361 := (~ #378 #378)
327 #356 := [nnf-pos #358]: #359
328 #39 := (uf_3 uf_14 #6)
330 #173 := (forall (vars (?x5 T2)) #170)
331 #380 := (iff #173 #379)
332 #381 := [rewrite* #113]: #380
334 #47 := (ite #42 #19 #46)
336 #49 := (forall (vars (?x5 T2)) #48)
337 #174 := (iff #49 #173)
338 #171 := (iff #48 #170)
341 #162 := (ite #156 #19 #46)
342 #166 := (= #162 #165)
343 #167 := [rewrite]: #166
345 #160 := (iff #42 #156)
346 #161 := [rewrite]: #160
347 #164 := [monotonicity #161]: #163
348 #169 := [trans #164 #167]: #168
349 #172 := [monotonicity #169]: #171
350 #175 := [quant-intro #172]: #174
351 #116 := [asserted]: #49
352 #176 := [mp #116 #175]: #173
353 #382 := [mp #176 #381]: #379
354 #357 := [mp~ #382 #356]: #379
355 #474 := [mp #357 #473]: #471
356 #566 := [mp #474 #565]: #561
358 #677 := (or #676 #673)
359 #658 := (= #657 #656)
360 #660 := (= #659 #656)
361 #662 := (ite #73 #661 #660)
362 #612 := (+ #611 #158)
363 #613 := (>= #612 0::int)
364 #663 := (ite #613 #662 #658)
365 #678 := (or #676 #663)
366 #680 := (iff #678 #677)
367 #682 := (iff #677 #677)
368 #683 := [rewrite]: #682
369 #674 := (iff #663 #673)
370 #671 := (iff #658 #670)
371 #672 := [rewrite]: #671
372 #668 := (iff #662 #667)
373 #665 := (iff #660 #664)
374 #666 := [rewrite]: #665
375 #669 := [monotonicity #279 #666]: #668
376 #626 := (iff #613 #623)
377 #615 := (+ #158 #611)
378 #618 := (>= #615 0::int)
379 #624 := (iff #618 #623)
380 #625 := [rewrite]: #624
381 #619 := (iff #613 #618)
382 #616 := (= #612 #615)
383 #617 := [rewrite]: #616
384 #620 := [monotonicity #617]: #619
385 #627 := [trans #620 #625]: #626
386 #675 := [monotonicity #627 #669 #672]: #674
387 #681 := [monotonicity #675]: #680
388 #684 := [trans #681 #683]: #680
389 #679 := [quant-inst]: #678
390 #685 := [mp #679 #684]: #677
391 #1311 := [unit-resolution #685 #566]: #673
393 #1313 := (or #1312 #623)
394 #1314 := [th-lemma]: #1313
395 #1315 := [unit-resolution #1314 #1281]: #623
398 #699 := (or #698 #645 #667)
399 #700 := [def-axiom]: #699
400 #1316 := [unit-resolution #700 #1315 #1311]: #667
402 #1317 := (or #686 #661)
404 #688 := (or #686 #687 #661)
405 #689 := [def-axiom]: #688
406 #1318 := [unit-resolution #689 #282]: #1317
407 #1319 := [unit-resolution #1318 #1316]: #661
408 #1321 := [symm #1319]: #1320
409 #1323 := [monotonicity #1321]: #1322
410 #1325 := [monotonicity #1323]: #1324
411 #1145 := (* -1::real #771)
412 #1240 := (+ #656 #1145)
413 #1241 := (<= #1240 0::real)
415 #1243 := [hypothesis]: #1241
418 #1040 := (uf_1 uf_18 #44)
419 #1043 := (* -1::real #1040)
420 #1156 := (+ #771 #1043)
421 #1157 := (>= #1156 0::real)
423 #708 := (uf_1 #91 #44)
424 #1168 := (+ #708 #1043)
425 #1169 := (<= #1168 0::real)
426 #1174 := (or #1157 #1169)
429 #552 := (pattern #89)
430 #81 := (uf_1 uf_18 #6)
431 #594 := (pattern #81)
432 #324 := (* -1::real #92)
434 #323 := (>= #325 0::real)
435 #317 := (* -1::real #89)
437 #319 := (<= #318 0::real)
438 #436 := (or #319 #323)
440 #601 := (forall (vars (?x11 T2)) (:pat #594 #552 #542) #437)
441 #440 := (forall (vars (?x11 T2)) #437)
442 #604 := (iff #440 #601)
443 #602 := (iff #437 #437)
445 #605 := [quant-intro #603]: #604
448 #329 := (and #320 #326)
449 #332 := (forall (vars (?x11 T2)) #329)
450 #441 := (iff #332 #440)
451 #438 := (iff #329 #437)
452 #439 := [rewrite]: #438
453 #442 := [quant-intro #439]: #441
454 #425 := (~ #332 #332)
455 #423 := (~ #329 #329)
457 #426 := [nnf-pos #424]: #425
458 #306 := (* -1::real #84)
460 #305 := (>= #307 0::real)
462 #301 := (* -1::real #81)
465 #300 := (>= #302 0::real)
467 #311 := (and #298 #308)
468 #314 := (forall (vars (?x10 T2)) #311)
469 #335 := (and #314 #332)
473 #95 := (forall (vars (?x11 T2)) #94)
477 #87 := (forall (vars (?x10 T2)) #86)
479 #336 := (iff #96 #335)
480 #333 := (iff #95 #332)
481 #330 := (iff #94 #329)
482 #327 := (iff #93 #326)
483 #328 := [rewrite]: #327
484 #321 := (iff #90 #320)
485 #322 := [rewrite]: #321
486 #331 := [monotonicity #322 #328]: #330
487 #334 := [quant-intro #331]: #333
488 #315 := (iff #87 #314)
489 #312 := (iff #86 #311)
490 #309 := (iff #85 #308)
491 #310 := [rewrite]: #309
492 #303 := (iff #82 #298)
493 #304 := [rewrite]: #303
494 #313 := [monotonicity #304 #310]: #312
495 #316 := [quant-intro #313]: #315
496 #337 := [monotonicity #316 #334]: #336
497 #293 := [asserted]: #96
498 #338 := [mp #293 #337]: #335
499 #340 := [and-elim #338]: #332
500 #427 := [mp~ #340 #426]: #332
501 #443 := [mp #427 #442]: #440
502 #606 := [mp #443 #605]: #601
504 #1180 := (or #1124 #1177)
505 #1142 := (* -1::real #708)
506 #1143 := (+ #1040 #1142)
507 #1144 := (>= #1143 0::real)
508 #1146 := (+ #1040 #1145)
509 #1147 := (<= #1146 0::real)
510 #1148 := (or #1147 #1144)
512 #1181 := (or #1124 #1149)
513 #1183 := (iff #1181 #1180)
514 #1185 := (iff #1180 #1180)
515 #1186 := [rewrite]: #1185
516 #1178 := (iff #1149 #1177)
517 #1175 := (iff #1148 #1174)
518 #1172 := (iff #1144 #1169)
519 #1162 := (+ #1142 #1040)
520 #1165 := (>= #1162 0::real)
521 #1170 := (iff #1165 #1169)
522 #1171 := [rewrite]: #1170
523 #1166 := (iff #1144 #1165)
524 #1163 := (= #1143 #1162)
525 #1164 := [rewrite]: #1163
526 #1167 := [monotonicity #1164]: #1166
527 #1173 := [trans #1167 #1171]: #1172
528 #1160 := (iff #1147 #1157)
529 #1150 := (+ #1145 #1040)
530 #1153 := (<= #1150 0::real)
531 #1158 := (iff #1153 #1157)
532 #1159 := [rewrite]: #1158
533 #1154 := (iff #1147 #1153)
534 #1151 := (= #1146 #1150)
535 #1152 := [rewrite]: #1151
536 #1155 := [monotonicity #1152]: #1154
537 #1161 := [trans #1155 #1159]: #1160
538 #1176 := [monotonicity #1161 #1173]: #1175
539 #1179 := [monotonicity #1176]: #1178
540 #1184 := [monotonicity #1179]: #1183
541 #1187 := [trans #1184 #1186]: #1183
542 #1182 := [quant-inst]: #1181
543 #1188 := [mp #1182 #1187]: #1180
544 #1244 := [unit-resolution #1188 #606]: #1177
545 #1190 := (or #1174 #1189)
546 #1191 := [def-axiom]: #1190
547 #1245 := [unit-resolution #1191 #1244]: #1189
548 #1054 := (+ #656 #1043)
549 #1055 := (<= #1054 0::real)
551 #607 := (uf_1 #78 #44)
552 #1044 := (+ #607 #1043)
553 #1045 := (>= #1044 0::real)
554 #1060 := (or #1045 #1055)
556 #567 := (pattern #79)
557 #428 := (or #300 #305)
559 #595 := (forall (vars (?x10 T2)) (:pat #567 #594 #560) #429)
560 #432 := (forall (vars (?x10 T2)) #429)
561 #598 := (iff #432 #595)
562 #596 := (iff #429 #429)
564 #599 := [quant-intro #597]: #598
565 #433 := (iff #314 #432)
566 #430 := (iff #311 #429)
567 #431 := [rewrite]: #430
568 #434 := [quant-intro #431]: #433
569 #420 := (~ #314 #314)
570 #418 := (~ #311 #311)
572 #421 := [nnf-pos #419]: #420
573 #339 := [and-elim #338]: #314
574 #422 := [mp~ #339 #421]: #314
575 #435 := [mp #422 #434]: #432
576 #600 := [mp #435 #599]: #595
578 #1067 := (or #1066 #1063)
579 #1039 := (* -1::real #656)
580 #1041 := (+ #1040 #1039)
581 #1042 := (>= #1041 0::real)
582 #1046 := (or #1045 #1042)
584 #1068 := (or #1066 #1047)
585 #1070 := (iff #1068 #1067)
586 #1072 := (iff #1067 #1067)
587 #1073 := [rewrite]: #1072
588 #1064 := (iff #1047 #1063)
589 #1061 := (iff #1046 #1060)
590 #1058 := (iff #1042 #1055)
591 #1048 := (+ #1039 #1040)
592 #1051 := (>= #1048 0::real)
593 #1056 := (iff #1051 #1055)
594 #1057 := [rewrite]: #1056
595 #1052 := (iff #1042 #1051)
596 #1049 := (= #1041 #1048)
597 #1050 := [rewrite]: #1049
598 #1053 := [monotonicity #1050]: #1052
599 #1059 := [trans #1053 #1057]: #1058
600 #1062 := [monotonicity #1059]: #1061
601 #1065 := [monotonicity #1062]: #1064
602 #1071 := [monotonicity #1065]: #1070
603 #1074 := [trans #1071 #1073]: #1070
604 #1069 := [quant-inst]: #1068
605 #1075 := [mp #1069 #1074]: #1067
606 #1246 := [unit-resolution #1075 #600]: #1063
607 #1080 := (or #1060 #1079)
608 #1081 := [def-axiom]: #1080
609 #1247 := [unit-resolution #1081 #1246]: #1079
610 #1248 := [th-lemma #1247 #1245 #1243]: false
611 #1250 := [lemma #1248]: #1249
612 #1253 := (or #1252 #1241)
613 #1254 := [th-lemma]: #1253
614 #1310 := [unit-resolution #1254 #1250]: #1252
615 #1326 := [mp #1310 #1325]: #796
616 #1328 := (or #724 #772)
619 #609 := (uf_1 uf_13 #44)
620 #773 := (= #609 #771)
621 #775 := (ite #724 #773 #772)
622 #32 := (uf_1 uf_9 #6)
623 #553 := (pattern #32)
624 #34 := (uf_1 uf_13 #6)
625 #551 := (pattern #34)
628 #457 := (ite #119 #455 #456)
629 #554 := (forall (vars (?x4 T2)) (:pat #541 #551 #552 #553) #457)
630 #460 := (forall (vars (?x4 T2)) #457)
631 #557 := (iff #460 #554)
632 #555 := (iff #457 #457)
634 #558 := [quant-intro #556]: #557
635 #143 := (ite #119 #34 #32)
637 #374 := (forall (vars (?x4 T2)) #373)
638 #461 := (iff #374 #460)
639 #458 := (iff #373 #457)
640 #459 := [rewrite]: #458
641 #462 := [quant-intro #459]: #461
642 #362 := (~ #374 #374)
643 #364 := (~ #373 #373)
645 #363 := [nnf-pos #365]: #362
646 #31 := (uf_3 uf_12 #6)
648 #151 := (forall (vars (?x4 T2)) #148)
649 #375 := (iff #151 #374)
650 #376 := [rewrite* #113]: #375
651 #35 := (ite #17 #32 #34)
653 #37 := (forall (vars (?x4 T2)) #36)
654 #152 := (iff #37 #151)
655 #149 := (iff #36 #148)
657 #140 := (ite #118 #32 #34)
658 #144 := (= #140 #143)
659 #145 := [rewrite]: #144
661 #142 := [monotonicity #123]: #141
662 #147 := [trans #142 #145]: #146
663 #150 := [monotonicity #147]: #149
664 #153 := [quant-intro #150]: #152
665 #115 := [asserted]: #37
666 #154 := [mp #115 #153]: #151
667 #377 := [mp #154 #376]: #374
668 #360 := [mp~ #377 #363]: #374
669 #463 := [mp #360 #462]: #460
670 #559 := [mp #463 #558]: #554
672 #779 := (or #778 #775)
673 #714 := (+ #611 #120)
674 #715 := (>= #714 0::int)
675 #774 := (ite #715 #773 #772)
676 #780 := (or #778 #774)
677 #782 := (iff #780 #779)
678 #784 := (iff #779 #779)
679 #785 := [rewrite]: #784
680 #776 := (iff #774 #775)
681 #727 := (iff #715 #724)
682 #717 := (+ #120 #611)
683 #720 := (>= #717 0::int)
684 #725 := (iff #720 #724)
685 #726 := [rewrite]: #725
686 #721 := (iff #715 #720)
687 #718 := (= #714 #717)
688 #719 := [rewrite]: #718
689 #722 := [monotonicity #719]: #721
690 #728 := [trans #722 #726]: #727
691 #777 := [monotonicity #728]: #776
692 #783 := [monotonicity #777]: #782
693 #786 := [trans #783 #785]: #782
694 #781 := [quant-inst]: #780
695 #787 := [mp #781 #786]: #779
696 #1327 := [unit-resolution #787 #559]: #775
698 #791 := (or #788 #724 #772)
699 #792 := [def-axiom]: #791
700 #1329 := [unit-resolution #792 #1327]: #1328
701 #1330 := [unit-resolution #1329 #1326]: #724
702 #988 := (>= #622 0::int)
703 #1331 := (or #1312 #988)
704 #1332 := [th-lemma]: #1331
705 #1333 := [unit-resolution #1332 #1281]: #988
708 #1335 := (or #1271 #1334 #761)
709 #1336 := [th-lemma]: #1335
710 #1337 := [unit-resolution #1336 #1333 #1330]: #1271
712 #1340 := (or #1269 #1338 #1339)
713 #1341 := [th-lemma]: #1340
714 #1343 := [unit-resolution #1341 #1337]: #1342
715 #1344 := [unit-resolution #1343 #1299]: #1339
716 #990 := (>= #916 0::int)
717 #1345 := (or #1302 #990)
718 #1346 := [th-lemma]: #1345
719 #1347 := [unit-resolution #1346 #1301]: #990
721 #1349 := (or #836 #1348 #1265)
722 #1350 := [th-lemma]: #1349
723 #1351 := [unit-resolution #1350 #1347 #1344]: #836
724 #1353 := (or #815 #800)
725 #801 := (uf_1 uf_13 #22)
726 #820 := (= #799 #801)
727 #823 := (ite #815 #820 #800)
730 #477 := (ite #157 #475 #476)
731 #568 := (forall (vars (?x6 T2)) (:pat #541 #551 #567 #553) #477)
732 #480 := (forall (vars (?x6 T2)) #477)
733 #571 := (iff #480 #568)
734 #569 := (iff #477 #477)
736 #572 := [quant-intro #570]: #571
737 #181 := (ite #157 #34 #32)
739 #384 := (forall (vars (?x6 T2)) #383)
740 #481 := (iff #384 #480)
741 #478 := (iff #383 #477)
742 #479 := [rewrite]: #478
743 #482 := [quant-intro #479]: #481
744 #352 := (~ #384 #384)
745 #354 := (~ #383 #383)
747 #353 := [nnf-pos #355]: #352
748 #51 := (uf_3 uf_16 #6)
750 #189 := (forall (vars (?x6 T2)) #186)
751 #385 := (iff #189 #384)
752 #386 := [rewrite* #113]: #385
753 #52 := (ite #42 #32 #34)
755 #54 := (forall (vars (?x6 T2)) #53)
756 #190 := (iff #54 #189)
757 #187 := (iff #53 #186)
759 #178 := (ite #156 #32 #34)
760 #182 := (= #178 #181)
761 #183 := [rewrite]: #182
763 #180 := [monotonicity #161]: #179
764 #185 := [trans #180 #183]: #184
765 #188 := [monotonicity #185]: #187
766 #191 := [quant-intro #188]: #190
767 #139 := [asserted]: #54
768 #192 := [mp #139 #191]: #189
769 #387 := [mp #192 #386]: #384
770 #402 := [mp~ #387 #353]: #384
771 #483 := [mp #402 #482]: #480
772 #573 := [mp #483 #572]: #568
774 #826 := (or #634 #823)
775 #802 := (= #801 #799)
776 #804 := (+ #803 #158)
777 #805 := (>= #804 0::int)
778 #806 := (ite #805 #802 #800)
779 #827 := (or #634 #806)
780 #829 := (iff #827 #826)
781 #831 := (iff #826 #826)
782 #832 := [rewrite]: #831
783 #824 := (iff #806 #823)
784 #821 := (iff #802 #820)
785 #822 := [rewrite]: #821
786 #818 := (iff #805 #815)
787 #807 := (+ #158 #803)
788 #810 := (>= #807 0::int)
789 #816 := (iff #810 #815)
790 #817 := [rewrite]: #816
791 #811 := (iff #805 #810)
792 #808 := (= #804 #807)
793 #809 := [rewrite]: #808
794 #812 := [monotonicity #809]: #811
795 #819 := [trans #812 #817]: #818
796 #825 := [monotonicity #819 #822]: #824
797 #830 := [monotonicity #825]: #829
798 #833 := [trans #830 #832]: #829
799 #828 := [quant-inst]: #827
800 #834 := [mp #828 #833]: #826
801 #1352 := [unit-resolution #834 #573]: #823
803 #839 := (or #835 #815 #800)
804 #840 := [def-axiom]: #839
805 #1354 := [unit-resolution #840 #1352]: #1353
806 #1355 := [unit-resolution #1354 #1351]: #800
807 #1357 := [symm #1355]: #1356
808 #1358 := [trans #1357 #1309]: #1266
810 #1360 := (or #1359 #1272)
811 #1361 := [th-lemma]: #1360
812 #1362 := [unit-resolution #1361 #1358]: #1272
813 #1085 := (uf_1 uf_18 #22)
814 #1099 := (* -1::real #1085)
815 #1112 := (+ #902 #1099)
816 #1113 := (<= #1112 0::real)
818 #960 := (uf_1 #88 #22)
819 #1100 := (+ #960 #1099)
820 #1101 := (>= #1100 0::real)
821 #1118 := (or #1101 #1113)
823 #1125 := (or #1124 #1121)
824 #1086 := (+ #1085 #1084)
825 #1087 := (>= #1086 0::real)
826 #1088 := (* -1::real #960)
827 #1089 := (+ #1085 #1088)
828 #1090 := (<= #1089 0::real)
829 #1091 := (or #1090 #1087)
831 #1126 := (or #1124 #1092)
832 #1128 := (iff #1126 #1125)
833 #1130 := (iff #1125 #1125)
834 #1131 := [rewrite]: #1130
835 #1122 := (iff #1092 #1121)
836 #1119 := (iff #1091 #1118)
837 #1116 := (iff #1087 #1113)
838 #1106 := (+ #1084 #1085)
839 #1109 := (>= #1106 0::real)
840 #1114 := (iff #1109 #1113)
841 #1115 := [rewrite]: #1114
842 #1110 := (iff #1087 #1109)
843 #1107 := (= #1086 #1106)
844 #1108 := [rewrite]: #1107
845 #1111 := [monotonicity #1108]: #1110
846 #1117 := [trans #1111 #1115]: #1116
847 #1104 := (iff #1090 #1101)
848 #1093 := (+ #1088 #1085)
849 #1096 := (<= #1093 0::real)
850 #1102 := (iff #1096 #1101)
851 #1103 := [rewrite]: #1102
852 #1097 := (iff #1090 #1096)
853 #1094 := (= #1089 #1093)
854 #1095 := [rewrite]: #1094
855 #1098 := [monotonicity #1095]: #1097
856 #1105 := [trans #1098 #1103]: #1104
857 #1120 := [monotonicity #1105 #1117]: #1119
858 #1123 := [monotonicity #1120]: #1122
859 #1129 := [monotonicity #1123]: #1128
860 #1132 := [trans #1129 #1131]: #1128
861 #1127 := [quant-inst]: #1126
862 #1133 := [mp #1127 #1132]: #1125
863 #1363 := [unit-resolution #1133 #606]: #1121
864 #1138 := (or #1118 #1137)
865 #1139 := [def-axiom]: #1138
866 #1364 := [unit-resolution #1139 #1363]: #1137
867 #1200 := (+ #799 #1099)
868 #1201 := (>= #1200 0::real)
870 #847 := (uf_1 #83 #22)
871 #1210 := (+ #847 #1099)
872 #1211 := (<= #1210 0::real)
873 #1216 := (or #1201 #1211)
875 #1222 := (or #1066 #1219)
876 #1197 := (* -1::real #847)
877 #1198 := (+ #1085 #1197)
878 #1199 := (>= #1198 0::real)
879 #1202 := (or #1201 #1199)
881 #1223 := (or #1066 #1203)
882 #1225 := (iff #1223 #1222)
883 #1227 := (iff #1222 #1222)
884 #1228 := [rewrite]: #1227
885 #1220 := (iff #1203 #1219)
886 #1217 := (iff #1202 #1216)
887 #1214 := (iff #1199 #1211)
888 #1204 := (+ #1197 #1085)
889 #1207 := (>= #1204 0::real)
890 #1212 := (iff #1207 #1211)
891 #1213 := [rewrite]: #1212
892 #1208 := (iff #1199 #1207)
893 #1205 := (= #1198 #1204)
894 #1206 := [rewrite]: #1205
895 #1209 := [monotonicity #1206]: #1208
896 #1215 := [trans #1209 #1213]: #1214
897 #1218 := [monotonicity #1215]: #1217
898 #1221 := [monotonicity #1218]: #1220
899 #1226 := [monotonicity #1221]: #1225
900 #1229 := [trans #1226 #1228]: #1225
901 #1224 := [quant-inst]: #1223
902 #1230 := [mp #1224 #1229]: #1222
903 #1365 := [unit-resolution #1230 #600]: #1219
904 #1232 := (or #1216 #1231)
905 #1233 := [def-axiom]: #1232
906 #1366 := [unit-resolution #1233 #1365]: #1231
907 [th-lemma #1366 #1364 #1362]: false
909 NQHwTeL311Tq3wf2s5BReA 419 0
912 decl uf_4 :: (-> T2 T3 real)
913 decl uf_6 :: (-> T1 T3)
919 #26 := (uf_4 uf_5 #25)
922 #28 := (uf_4 uf_7 #25)
928 #43 := (uf_4 uf_9 #42)
929 #41 := (= uf_3 uf_10)
930 #44 := (ite #41 #43 #28)
932 decl uf_2 :: (-> T1 int)
935 #229 := (* -1::int #39)
938 #228 := (>= #230 0::int)
939 #236 := (ite #228 #44 #26)
941 #244 := (* -1::real #236)
943 #643 := (<= #642 0::real)
946 decl uf_1 :: (-> int T1)
948 #660 := (= #593 uf_10)
949 #594 := (= uf_10 #593)
955 #547 := (forall (vars (?x1 T1)) (:pat #546) #93)
956 #96 := (forall (vars (?x1 T1)) #93)
957 #550 := (iff #96 #547)
958 #548 := (iff #93 #93)
960 #551 := [quant-intro #549]: #550
964 #449 := [nnf-pos #451]: #448
966 #8 := (forall (vars (?x1 T1)) #7)
969 #95 := [rewrite]: #94
970 #98 := [quant-intro #95]: #97
971 #92 := [asserted]: #8
972 #101 := [mp #92 #98]: #96
973 #446 := [mp~ #101 #449]: #96
974 #552 := [mp #446 #551]: #547
976 #600 := (or #595 #594)
977 #601 := [quant-inst]: #600
978 #654 := [unit-resolution #601 #552]: #594
979 #680 := [symm #654]: #660
980 #681 := (= uf_3 #593)
982 #658 := (= #591 #593)
983 #656 := (= #593 #591)
986 #290 := (<= #230 0::int)
988 #388 := (iff #70 #290)
989 #389 := [rewrite]: #388
990 #341 := [asserted]: #70
991 #390 := [mp #341 #389]: #290
992 #646 := [hypothesis]: #228
993 #648 := [th-lemma #646 #390]: #647
994 #653 := [symm #648]: #652
995 #657 := [monotonicity #653]: #656
996 #659 := [symm #657]: #658
997 #592 := (= uf_3 #591)
998 #596 := (or #595 #592)
999 #597 := [quant-inst]: #596
1000 #655 := [unit-resolution #597 #552]: #592
1001 #682 := [trans #655 #659]: #681
1002 #683 := [trans #682 #680]: #41
1006 #59 := (uf_4 uf_11 #42)
1007 #278 := (ite #41 #26 #59)
1008 #459 := (* -1::real #278)
1009 #637 := (+ #26 #459)
1010 #639 := (>= #637 0::real)
1011 #585 := (= #26 #278)
1012 #661 := [hypothesis]: #41
1013 #587 := (or #570 #585)
1014 #588 := [def-axiom]: #587
1015 #662 := [unit-resolution #588 #661]: #585
1017 #664 := (or #663 #639)
1018 #665 := [th-lemma]: #664
1019 #666 := [unit-resolution #665 #662]: #639
1022 #56 := (uf_4 uf_8 #42)
1023 #357 := (* -1::real #56)
1024 #358 := (+ #43 #357)
1025 #356 := (>= #358 0::real)
1027 #374 := (* -1::real #59)
1028 #375 := (+ #56 #374)
1029 #373 := (>= #375 0::real)
1031 #381 := (and #355 #376)
1033 #67 := (ite #64 #43 #59)
1035 #53 := (uf_4 uf_5 #42)
1036 #65 := (ite #64 #53 #43)
1038 #69 := (and #66 #68)
1039 #382 := (iff #69 #381)
1040 #379 := (iff #68 #376)
1042 #377 := (iff #370 #376)
1043 #378 := [rewrite]: #377
1044 #371 := (iff #68 #370)
1046 #363 := (ite false #43 #59)
1047 #366 := (= #363 #59)
1048 #367 := [rewrite]: #366
1049 #364 := (= #67 #363)
1050 #343 := (iff #64 false)
1051 #344 := [rewrite]: #343
1052 #365 := [monotonicity #344]: #364
1053 #369 := [trans #365 #367]: #368
1054 #372 := [monotonicity #369]: #371
1055 #380 := [trans #372 #378]: #379
1056 #361 := (iff #66 #355)
1058 #359 := (iff #352 #355)
1059 #360 := [rewrite]: #359
1060 #353 := (iff #66 #352)
1062 #345 := (ite false #53 #43)
1063 #348 := (= #345 #43)
1064 #349 := [rewrite]: #348
1065 #346 := (= #65 #345)
1066 #347 := [monotonicity #344]: #346
1067 #351 := [trans #347 #349]: #350
1068 #354 := [monotonicity #351]: #353
1069 #362 := [trans #354 #360]: #361
1070 #383 := [monotonicity #362 #380]: #382
1071 #340 := [asserted]: #69
1072 #384 := [mp #340 #383]: #381
1073 #385 := [and-elim #384]: #355
1074 #394 := (* -1::real #53)
1075 #395 := (+ #43 #394)
1076 #393 := (>= #395 0::real)
1077 #54 := (uf_4 uf_7 #42)
1078 #402 := (* -1::real #54)
1079 #403 := (+ #53 #402)
1080 #401 := (>= #403 0::real)
1081 #397 := (+ #43 #374)
1082 #398 := (<= #397 0::real)
1083 #412 := (and #393 #398 #401)
1086 #74 := (and #72 #73)
1088 #75 := (and #71 #74)
1089 #415 := (iff #75 #412)
1090 #406 := (and #393 #398)
1091 #409 := (and #401 #406)
1092 #413 := (iff #409 #412)
1093 #414 := [rewrite]: #413
1094 #410 := (iff #75 #409)
1095 #407 := (iff #74 #406)
1096 #399 := (iff #73 #398)
1097 #400 := [rewrite]: #399
1098 #392 := (iff #72 #393)
1099 #396 := [rewrite]: #392
1100 #408 := [monotonicity #396 #400]: #407
1101 #404 := (iff #71 #401)
1102 #405 := [rewrite]: #404
1103 #411 := [monotonicity #405 #408]: #410
1104 #416 := [trans #411 #414]: #415
1105 #342 := [asserted]: #75
1106 #417 := [mp #342 #416]: #412
1107 #418 := [and-elim #417]: #393
1108 #650 := (+ #26 #394)
1109 #651 := (<= #650 0::real)
1114 #668 := [monotonicity #661]: #667
1115 #670 := [symm #668]: #669
1116 #672 := [monotonicity #670]: #671
1117 #673 := [symm #672]: #649
1119 #675 := (or #674 #651)
1120 #676 := [th-lemma]: #675
1121 #677 := [unit-resolution #676 #673]: #651
1122 #462 := (+ #56 #459)
1123 #465 := (>= #462 0::real)
1125 #316 := (ite #290 #278 #43)
1126 #326 := (* -1::real #316)
1127 #327 := (+ #56 #326)
1128 #325 := (>= #327 0::real)
1130 #439 := (iff #324 #438)
1131 #466 := (iff #325 #465)
1132 #463 := (= #327 #462)
1133 #460 := (= #326 #459)
1134 #457 := (= #316 #278)
1136 #452 := (ite true #278 #43)
1137 #455 := (= #452 #278)
1138 #456 := [rewrite]: #455
1139 #453 := (= #316 #452)
1140 #444 := (iff #290 true)
1141 #445 := [iff-true #390]: #444
1142 #454 := [monotonicity #445]: #453
1143 #458 := [trans #454 #456]: #457
1144 #461 := [monotonicity #458]: #460
1145 #464 := [monotonicity #461]: #463
1146 #467 := [monotonicity #464]: #466
1147 #468 := [monotonicity #467]: #439
1148 #297 := (ite #290 #54 #53)
1149 #305 := (* -1::real #297)
1150 #306 := (+ #56 #305)
1151 #307 := (<= #306 0::real)
1153 #332 := (and #308 #324)
1154 #58 := (= uf_10 uf_3)
1155 #60 := (ite #58 #26 #59)
1157 #61 := (ite #52 #43 #60)
1159 #55 := (ite #52 #53 #54)
1161 #63 := (and #57 #62)
1162 #335 := (iff #63 #332)
1163 #281 := (ite #52 #43 #278)
1164 #284 := (< #56 #281)
1165 #287 := (and #57 #284)
1166 #333 := (iff #287 #332)
1167 #330 := (iff #284 #324)
1168 #321 := (< #56 #316)
1169 #328 := (iff #321 #324)
1170 #329 := [rewrite]: #328
1171 #322 := (iff #284 #321)
1172 #319 := (= #281 #316)
1174 #313 := (ite #291 #43 #278)
1175 #317 := (= #313 #316)
1176 #318 := [rewrite]: #317
1177 #314 := (= #281 #313)
1178 #292 := (iff #52 #291)
1179 #293 := [rewrite]: #292
1180 #315 := [monotonicity #293]: #314
1181 #320 := [trans #315 #318]: #319
1182 #323 := [monotonicity #320]: #322
1183 #331 := [trans #323 #329]: #330
1184 #311 := (iff #57 #308)
1185 #302 := (< #297 #56)
1186 #309 := (iff #302 #308)
1187 #310 := [rewrite]: #309
1188 #303 := (iff #57 #302)
1189 #300 := (= #55 #297)
1190 #294 := (ite #291 #53 #54)
1191 #298 := (= #294 #297)
1192 #299 := [rewrite]: #298
1193 #295 := (= #55 #294)
1194 #296 := [monotonicity #293]: #295
1195 #301 := [trans #296 #299]: #300
1196 #304 := [monotonicity #301]: #303
1197 #312 := [trans #304 #310]: #311
1198 #334 := [monotonicity #312 #331]: #333
1199 #288 := (iff #63 #287)
1200 #285 := (iff #62 #284)
1201 #282 := (= #61 #281)
1202 #279 := (= #60 #278)
1203 #225 := (iff #58 #41)
1204 #277 := [rewrite]: #225
1205 #280 := [monotonicity #277]: #279
1206 #283 := [monotonicity #280]: #282
1207 #286 := [monotonicity #283]: #285
1208 #289 := [monotonicity #286]: #288
1209 #336 := [trans #289 #334]: #335
1210 #179 := [asserted]: #63
1211 #337 := [mp #179 #336]: #332
1212 #339 := [and-elim #337]: #324
1213 #469 := [mp #339 #468]: #438
1214 #678 := [th-lemma #469 #677 #418 #385 #666]: false
1215 #679 := [lemma #678]: #570
1216 #684 := [unit-resolution #679 #683]: false
1217 #685 := [lemma #684]: #227
1218 #577 := (or #228 #567)
1219 #578 := [def-axiom]: #577
1220 #645 := [unit-resolution #578 #685]: #567
1222 #687 := (or #686 #643)
1223 #688 := [th-lemma]: #687
1224 #689 := [unit-resolution #688 #645]: #643
1225 #31 := (uf_4 uf_8 #25)
1226 #245 := (+ #31 #244)
1227 #246 := (<= #245 0::real)
1229 #34 := (uf_4 uf_9 #25)
1230 #48 := (uf_4 uf_11 #25)
1231 #255 := (ite #228 #48 #34)
1232 #264 := (* -1::real #255)
1233 #265 := (+ #31 #264)
1234 #263 := (>= #265 0::real)
1236 #271 := (and #247 #266)
1238 #49 := (ite #40 #34 #48)
1240 #45 := (ite #40 #26 #44)
1242 #51 := (and #46 #50)
1243 #272 := (iff #51 #271)
1244 #269 := (iff #50 #266)
1245 #260 := (< #31 #255)
1246 #267 := (iff #260 #266)
1247 #268 := [rewrite]: #267
1248 #261 := (iff #50 #260)
1249 #258 := (= #49 #255)
1250 #252 := (ite #227 #34 #48)
1251 #256 := (= #252 #255)
1252 #257 := [rewrite]: #256
1253 #253 := (= #49 #252)
1254 #231 := (iff #40 #227)
1255 #232 := [rewrite]: #231
1256 #254 := [monotonicity #232]: #253
1257 #259 := [trans #254 #257]: #258
1258 #262 := [monotonicity #259]: #261
1259 #270 := [trans #262 #268]: #269
1260 #250 := (iff #46 #247)
1261 #241 := (< #236 #31)
1262 #248 := (iff #241 #247)
1263 #249 := [rewrite]: #248
1264 #242 := (iff #46 #241)
1265 #239 := (= #45 #236)
1266 #233 := (ite #227 #26 #44)
1267 #237 := (= #233 #236)
1268 #238 := [rewrite]: #237
1269 #234 := (= #45 #233)
1270 #235 := [monotonicity #232]: #234
1271 #240 := [trans #235 #238]: #239
1272 #243 := [monotonicity #240]: #242
1273 #251 := [trans #243 #249]: #250
1274 #273 := [monotonicity #251 #270]: #272
1275 #178 := [asserted]: #51
1276 #274 := [mp #178 #273]: #271
1277 #275 := [and-elim #274]: #247
1278 #196 := (* -1::real #31)
1279 #212 := (+ #26 #196)
1280 #213 := (<= #212 0::real)
1282 #197 := (+ #28 #196)
1283 #195 := (>= #197 0::real)
1285 #219 := (and #193 #214)
1287 #35 := (ite #23 #34 #26)
1289 #29 := (ite #23 #26 #28)
1291 #37 := (and #32 #36)
1292 #220 := (iff #37 #219)
1293 #217 := (iff #36 #214)
1295 #215 := (iff #209 #214)
1296 #216 := [rewrite]: #215
1297 #210 := (iff #36 #209)
1299 #202 := (ite false #34 #26)
1300 #205 := (= #202 #26)
1301 #206 := [rewrite]: #205
1302 #203 := (= #35 #202)
1303 #180 := (iff #23 false)
1304 #181 := [rewrite]: #180
1305 #204 := [monotonicity #181]: #203
1306 #208 := [trans #204 #206]: #207
1307 #211 := [monotonicity #208]: #210
1308 #218 := [trans #211 #216]: #217
1309 #200 := (iff #32 #193)
1311 #198 := (iff #189 #193)
1312 #199 := [rewrite]: #198
1313 #190 := (iff #32 #189)
1315 #182 := (ite false #26 #28)
1316 #185 := (= #182 #28)
1317 #186 := [rewrite]: #185
1318 #183 := (= #29 #182)
1319 #184 := [monotonicity #181]: #183
1320 #188 := [trans #184 #186]: #187
1321 #191 := [monotonicity #188]: #190
1322 #201 := [trans #191 #199]: #200
1323 #221 := [monotonicity #201 #218]: #220
1324 #177 := [asserted]: #37
1325 #222 := [mp #177 #221]: #219
1326 #224 := [and-elim #222]: #214
1327 [th-lemma #224 #275 #689]: false
1329 NX/HT1QOfbspC2LtZNKpBA 428 0
1335 #45 := (= uf_3 uf_10)
1336 decl uf_1 :: (-> int T1)
1337 decl uf_2 :: (-> T1 int)
1340 #686 := (= #588 uf_10)
1341 #589 := (= uf_10 #588)
1344 #541 := (pattern #5)
1347 #542 := (forall (vars (?x1 T1)) (:pat #541) #93)
1348 #96 := (forall (vars (?x1 T1)) #93)
1349 #545 := (iff #96 #542)
1350 #543 := (iff #93 #93)
1351 #544 := [refl]: #543
1352 #546 := [quant-intro #544]: #545
1355 #457 := [refl]: #456
1356 #455 := [nnf-pos #457]: #454
1358 #8 := (forall (vars (?x1 T1)) #7)
1361 #95 := [rewrite]: #94
1362 #98 := [quant-intro #95]: #97
1363 #92 := [asserted]: #8
1364 #101 := [mp #92 #98]: #96
1365 #452 := [mp~ #101 #455]: #96
1366 #547 := [mp #452 #546]: #542
1368 #595 := (or #590 #589)
1369 #596 := [quant-inst]: #595
1370 #680 := [unit-resolution #596 #547]: #589
1371 #687 := [symm #680]: #686
1372 #688 := (= uf_3 #588)
1375 #684 := (= #586 #588)
1376 #682 := (= #588 #586)
1381 #230 := (* -1::int #39)
1382 #231 := (+ #22 #230)
1383 #296 := (<= #231 0::int)
1385 #393 := (iff #70 #296)
1386 #394 := [rewrite]: #393
1387 #347 := [asserted]: #70
1388 #395 := [mp #347 #394]: #296
1389 #229 := (>= #231 0::int)
1390 decl uf_4 :: (-> T2 T3 real)
1391 decl uf_6 :: (-> T1 T3)
1395 #28 := (uf_4 uf_7 #25)
1398 #34 := (uf_4 uf_9 #25)
1402 #47 := (uf_4 uf_5 #46)
1403 #48 := (ite #45 #47 #34)
1404 #256 := (ite #229 #48 #28)
1405 #568 := (= #28 #256)
1409 #265 := (* -1::real #256)
1410 #640 := (+ #28 #265)
1411 #642 := (>= #640 0::real)
1413 #643 := [hypothesis]: #642
1416 #31 := (uf_4 uf_8 #25)
1417 #266 := (+ #31 #265)
1418 #264 := (>= #266 0::real)
1420 #26 := (uf_4 uf_5 #25)
1423 #42 := (uf_4 uf_11 #25)
1424 #237 := (ite #229 #42 #26)
1425 #245 := (* -1::real #237)
1426 #246 := (+ #31 #245)
1427 #247 := (<= #246 0::real)
1429 #272 := (and #248 #267)
1431 #49 := (ite #40 #28 #48)
1433 #43 := (ite #40 #26 #42)
1435 #51 := (and #44 #50)
1436 #273 := (iff #51 #272)
1437 #270 := (iff #50 #267)
1438 #261 := (< #31 #256)
1439 #268 := (iff #261 #267)
1440 #269 := [rewrite]: #268
1441 #262 := (iff #50 #261)
1442 #259 := (= #49 #256)
1444 #253 := (ite #228 #28 #48)
1445 #257 := (= #253 #256)
1446 #258 := [rewrite]: #257
1447 #254 := (= #49 #253)
1448 #232 := (iff #40 #228)
1449 #233 := [rewrite]: #232
1450 #255 := [monotonicity #233]: #254
1451 #260 := [trans #255 #258]: #259
1452 #263 := [monotonicity #260]: #262
1453 #271 := [trans #263 #269]: #270
1454 #251 := (iff #44 #248)
1455 #242 := (< #237 #31)
1456 #249 := (iff #242 #248)
1457 #250 := [rewrite]: #249
1458 #243 := (iff #44 #242)
1459 #240 := (= #43 #237)
1460 #234 := (ite #228 #26 #42)
1461 #238 := (= #234 #237)
1462 #239 := [rewrite]: #238
1463 #235 := (= #43 #234)
1464 #236 := [monotonicity #233]: #235
1465 #241 := [trans #236 #239]: #240
1466 #244 := [monotonicity #241]: #243
1467 #252 := [trans #244 #250]: #251
1468 #274 := [monotonicity #252 #271]: #273
1469 #178 := [asserted]: #51
1470 #275 := [mp #178 #274]: #272
1471 #277 := [and-elim #275]: #267
1472 #196 := (* -1::real #31)
1473 #197 := (+ #28 #196)
1474 #195 := (>= #197 0::real)
1476 #213 := (* -1::real #34)
1477 #214 := (+ #31 #213)
1478 #212 := (>= #214 0::real)
1480 #220 := (and #193 #215)
1482 #35 := (ite #23 #28 #34)
1484 #29 := (ite #23 #26 #28)
1486 #37 := (and #32 #36)
1487 #221 := (iff #37 #220)
1488 #218 := (iff #36 #215)
1490 #216 := (iff #209 #215)
1491 #217 := [rewrite]: #216
1492 #210 := (iff #36 #209)
1494 #202 := (ite false #28 #34)
1495 #205 := (= #202 #34)
1496 #206 := [rewrite]: #205
1497 #203 := (= #35 #202)
1498 #180 := (iff #23 false)
1499 #181 := [rewrite]: #180
1500 #204 := [monotonicity #181]: #203
1501 #208 := [trans #204 #206]: #207
1502 #211 := [monotonicity #208]: #210
1503 #219 := [trans #211 #217]: #218
1504 #200 := (iff #32 #193)
1506 #198 := (iff #189 #193)
1507 #199 := [rewrite]: #198
1508 #190 := (iff #32 #189)
1510 #182 := (ite false #26 #28)
1511 #185 := (= #182 #28)
1512 #186 := [rewrite]: #185
1513 #183 := (= #29 #182)
1514 #184 := [monotonicity #181]: #183
1515 #188 := [trans #184 #186]: #187
1516 #191 := [monotonicity #188]: #190
1517 #201 := [trans #191 #199]: #200
1518 #222 := [monotonicity #201 #219]: #221
1519 #177 := [asserted]: #37
1520 #223 := [mp #177 #222]: #220
1521 #224 := [and-elim #223]: #193
1522 #644 := [th-lemma #224 #277 #643]: false
1523 #646 := [lemma #644]: #645
1524 #647 := [hypothesis]: #568
1525 #649 := (or #648 #642)
1526 #650 := [th-lemma]: #649
1527 #651 := [unit-resolution #650 #647 #646]: false
1528 #652 := [lemma #651]: #648
1529 #578 := (or #229 #568)
1530 #579 := [def-axiom]: #578
1531 #675 := [unit-resolution #579 #652]: #229
1532 #677 := [th-lemma #675 #395]: #676
1533 #679 := [symm #677]: #678
1534 #683 := [monotonicity #679]: #682
1535 #685 := [symm #683]: #684
1536 #587 := (= uf_3 #586)
1537 #591 := (or #590 #587)
1538 #592 := [quant-inst]: #591
1539 #681 := [unit-resolution #592 #547]: #587
1540 #689 := [trans #681 #685]: #688
1541 #690 := [trans #689 #687]: #45
1543 #54 := (uf_4 uf_11 #46)
1544 #279 := (ite #45 #28 #54)
1545 #465 := (* -1::real #279)
1546 #632 := (+ #28 #465)
1547 #633 := (<= #632 0::real)
1548 #580 := (= #28 #279)
1549 #656 := [hypothesis]: #45
1550 #582 := (or #571 #580)
1551 #583 := [def-axiom]: #582
1552 #657 := [unit-resolution #583 #656]: #580
1554 #659 := (or #658 #633)
1555 #660 := [th-lemma]: #659
1556 #661 := [unit-resolution #660 #657]: #633
1557 #57 := (uf_4 uf_8 #46)
1558 #363 := (* -1::real #57)
1559 #379 := (+ #47 #363)
1560 #380 := (<= #379 0::real)
1562 #364 := (+ #54 #363)
1563 #362 := (>= #364 0::real)
1565 #386 := (and #361 #381)
1566 #59 := (uf_4 uf_7 #46)
1568 #67 := (ite #64 #59 #47)
1570 #65 := (ite #64 #47 #54)
1572 #69 := (and #66 #68)
1573 #387 := (iff #69 #386)
1574 #384 := (iff #68 #381)
1576 #382 := (iff #376 #381)
1577 #383 := [rewrite]: #382
1578 #377 := (iff #68 #376)
1580 #369 := (ite false #59 #47)
1581 #372 := (= #369 #47)
1582 #373 := [rewrite]: #372
1583 #370 := (= #67 #369)
1584 #349 := (iff #64 false)
1585 #350 := [rewrite]: #349
1586 #371 := [monotonicity #350]: #370
1587 #375 := [trans #371 #373]: #374
1588 #378 := [monotonicity #375]: #377
1589 #385 := [trans #378 #383]: #384
1590 #367 := (iff #66 #361)
1592 #365 := (iff #358 #361)
1593 #366 := [rewrite]: #365
1594 #359 := (iff #66 #358)
1596 #351 := (ite false #47 #54)
1597 #354 := (= #351 #54)
1598 #355 := [rewrite]: #354
1599 #352 := (= #65 #351)
1600 #353 := [monotonicity #350]: #352
1601 #357 := [trans #353 #355]: #356
1602 #360 := [monotonicity #357]: #359
1603 #368 := [trans #360 #366]: #367
1604 #388 := [monotonicity #368 #385]: #387
1605 #346 := [asserted]: #69
1606 #389 := [mp #346 #388]: #386
1607 #391 := [and-elim #389]: #381
1608 #397 := (* -1::real #59)
1609 #398 := (+ #47 #397)
1610 #399 := (<= #398 0::real)
1611 #409 := (* -1::real #54)
1612 #410 := (+ #47 #409)
1613 #408 := (>= #410 0::real)
1614 #60 := (uf_4 uf_9 #46)
1615 #402 := (* -1::real #60)
1616 #403 := (+ #59 #402)
1617 #404 := (<= #403 0::real)
1618 #418 := (and #399 #404 #408)
1621 #74 := (and #72 #73)
1623 #75 := (and #71 #74)
1624 #421 := (iff #75 #418)
1625 #412 := (and #399 #404)
1626 #415 := (and #408 #412)
1627 #419 := (iff #415 #418)
1628 #420 := [rewrite]: #419
1629 #416 := (iff #75 #415)
1630 #413 := (iff #74 #412)
1631 #405 := (iff #73 #404)
1632 #406 := [rewrite]: #405
1633 #400 := (iff #72 #399)
1634 #401 := [rewrite]: #400
1635 #414 := [monotonicity #401 #406]: #413
1636 #407 := (iff #71 #408)
1637 #411 := [rewrite]: #407
1638 #417 := [monotonicity #411 #414]: #416
1639 #422 := [trans #417 #420]: #421
1640 #348 := [asserted]: #75
1641 #423 := [mp #348 #422]: #418
1642 #424 := [and-elim #423]: #399
1643 #637 := (+ #28 #397)
1644 #639 := (>= #637 0::real)
1649 #663 := [monotonicity #656]: #662
1650 #665 := [symm #663]: #664
1651 #667 := [monotonicity #665]: #666
1652 #668 := [symm #667]: #636
1654 #670 := (or #669 #639)
1655 #671 := [th-lemma]: #670
1656 #672 := [unit-resolution #671 #668]: #639
1657 #468 := (+ #57 #465)
1658 #471 := (<= #468 0::real)
1660 #322 := (ite #296 #279 #47)
1661 #330 := (* -1::real #322)
1662 #331 := (+ #57 #330)
1663 #332 := (<= #331 0::real)
1665 #445 := (iff #333 #444)
1666 #472 := (iff #332 #471)
1667 #469 := (= #331 #468)
1668 #466 := (= #330 #465)
1669 #463 := (= #322 #279)
1671 #458 := (ite true #279 #47)
1672 #461 := (= #458 #279)
1673 #462 := [rewrite]: #461
1674 #459 := (= #322 #458)
1675 #450 := (iff #296 true)
1676 #451 := [iff-true #395]: #450
1677 #460 := [monotonicity #451]: #459
1678 #464 := [trans #460 #462]: #463
1679 #467 := [monotonicity #464]: #466
1680 #470 := [monotonicity #467]: #469
1681 #473 := [monotonicity #470]: #472
1682 #474 := [monotonicity #473]: #445
1683 #303 := (ite #296 #60 #59)
1684 #313 := (* -1::real #303)
1685 #314 := (+ #57 #313)
1686 #312 := (>= #314 0::real)
1688 #338 := (and #311 #333)
1690 #61 := (ite #52 #59 #60)
1692 #53 := (= uf_10 uf_3)
1693 #55 := (ite #53 #28 #54)
1694 #56 := (ite #52 #47 #55)
1696 #63 := (and #58 #62)
1697 #341 := (iff #63 #338)
1698 #282 := (ite #52 #47 #279)
1699 #285 := (< #282 #57)
1700 #291 := (and #62 #285)
1701 #339 := (iff #291 #338)
1702 #336 := (iff #285 #333)
1703 #327 := (< #322 #57)
1704 #334 := (iff #327 #333)
1705 #335 := [rewrite]: #334
1706 #328 := (iff #285 #327)
1707 #325 := (= #282 #322)
1709 #319 := (ite #297 #47 #279)
1710 #323 := (= #319 #322)
1711 #324 := [rewrite]: #323
1712 #320 := (= #282 #319)
1713 #298 := (iff #52 #297)
1714 #299 := [rewrite]: #298
1715 #321 := [monotonicity #299]: #320
1716 #326 := [trans #321 #324]: #325
1717 #329 := [monotonicity #326]: #328
1718 #337 := [trans #329 #335]: #336
1719 #317 := (iff #62 #311)
1720 #308 := (< #57 #303)
1721 #315 := (iff #308 #311)
1722 #316 := [rewrite]: #315
1723 #309 := (iff #62 #308)
1724 #306 := (= #61 #303)
1725 #300 := (ite #297 #59 #60)
1726 #304 := (= #300 #303)
1727 #305 := [rewrite]: #304
1728 #301 := (= #61 #300)
1729 #302 := [monotonicity #299]: #301
1730 #307 := [trans #302 #305]: #306
1731 #310 := [monotonicity #307]: #309
1732 #318 := [trans #310 #316]: #317
1733 #340 := [monotonicity #318 #337]: #339
1734 #294 := (iff #63 #291)
1735 #288 := (and #285 #62)
1736 #292 := (iff #288 #291)
1737 #293 := [rewrite]: #292
1738 #289 := (iff #63 #288)
1739 #286 := (iff #58 #285)
1740 #283 := (= #56 #282)
1741 #280 := (= #55 #279)
1742 #226 := (iff #53 #45)
1743 #278 := [rewrite]: #226
1744 #281 := [monotonicity #278]: #280
1745 #284 := [monotonicity #281]: #283
1746 #287 := [monotonicity #284]: #286
1747 #290 := [monotonicity #287]: #289
1748 #295 := [trans #290 #293]: #294
1749 #342 := [trans #295 #340]: #341
1750 #179 := [asserted]: #63
1751 #343 := [mp #179 #342]: #338
1752 #345 := [and-elim #343]: #333
1753 #475 := [mp #345 #474]: #444
1754 #673 := [th-lemma #475 #672 #424 #391 #661]: false
1755 #674 := [lemma #673]: #571
1756 [unit-resolution #674 #690]: false
1758 IL2powemHjRpCJYwmXFxyw 211 0
1761 decl uf_11 :: (-> T5 T6 real)
1766 #31 := (uf_11 uf_16 uf_15)
1767 decl uf_12 :: (-> T7 T8 T5)
1770 decl uf_13 :: (-> T1 T7)
1774 #27 := (uf_12 #25 uf_14)
1775 #29 := (uf_11 #27 uf_15)
1777 #84 := (* -1::real #29)
1779 #74 := (* -1::real #31)
1781 #112 := (>= #75 0::real)
1782 #119 := (ite #112 #75 #85)
1783 #127 := (* -1::real #119)
1786 #38 := (uf_11 uf_17 uf_15)
1788 #103 := (* -1/3::real #38)
1789 #128 := (+ #103 #127)
1791 #101 := (* 1/3::real #31)
1792 #129 := (+ #101 #128)
1793 #130 := (<= #129 0::real)
1797 #41 := (/ #39 3::real)
1800 #34 := (< #32 0::real)
1801 #36 := (ite #34 #35 #32)
1803 #136 := (iff #42 #131)
1804 #104 := (+ #101 #103)
1805 #78 := (< #75 0::real)
1806 #90 := (ite #78 #85 #75)
1807 #109 := (< #90 #104)
1808 #134 := (iff #109 #131)
1809 #124 := (< #119 #104)
1810 #132 := (iff #124 #131)
1811 #133 := [rewrite]: #132
1812 #125 := (iff #109 #124)
1813 #122 := (= #90 #119)
1815 #116 := (ite #113 #85 #75)
1816 #120 := (= #116 #119)
1817 #121 := [rewrite]: #120
1818 #117 := (= #90 #116)
1819 #114 := (iff #78 #113)
1820 #115 := [rewrite]: #114
1821 #118 := [monotonicity #115]: #117
1822 #123 := [trans #118 #121]: #122
1823 #126 := [monotonicity #123]: #125
1824 #135 := [trans #126 #133]: #134
1825 #110 := (iff #42 #109)
1826 #107 := (= #41 #104)
1827 #93 := (* -1::real #38)
1829 #97 := (/ #94 3::real)
1830 #105 := (= #97 #104)
1831 #106 := [rewrite]: #105
1834 #96 := [rewrite]: #95
1835 #99 := [monotonicity #96]: #98
1836 #108 := [trans #99 #106]: #107
1839 #77 := [rewrite]: #76
1843 #87 := [rewrite]: #86
1845 #83 := [monotonicity #77]: #82
1846 #89 := [trans #83 #87]: #88
1847 #79 := (iff #34 #78)
1848 #80 := [monotonicity #77]: #79
1849 #92 := [monotonicity #80 #89 #77]: #91
1850 #111 := [monotonicity #92 #108]: #110
1851 #137 := [trans #111 #135]: #136
1852 #72 := [asserted]: #42
1853 #138 := [mp #72 #137]: #131
1857 #44 := (uf_12 #43 uf_14)
1858 #45 := (uf_11 #44 uf_15)
1859 #149 := (* -1::real #45)
1860 #150 := (+ #38 #149)
1862 #161 := (<= #150 0::real)
1863 #168 := (ite #161 #140 #150)
1864 #176 := (* -1::real #168)
1865 #177 := (+ #103 #176)
1866 #178 := (+ #101 #177)
1867 #179 := (<= #178 0::real)
1871 #47 := (< #46 0::real)
1872 #49 := (ite #47 #48 #46)
1874 #185 := (iff #50 #180)
1875 #143 := (< #140 0::real)
1876 #155 := (ite #143 #150 #140)
1877 #158 := (< #155 #104)
1878 #183 := (iff #158 #180)
1879 #173 := (< #168 #104)
1880 #181 := (iff #173 #180)
1881 #182 := [rewrite]: #181
1882 #174 := (iff #158 #173)
1883 #171 := (= #155 #168)
1885 #165 := (ite #162 #150 #140)
1886 #169 := (= #165 #168)
1887 #170 := [rewrite]: #169
1888 #166 := (= #155 #165)
1889 #163 := (iff #143 #162)
1890 #164 := [rewrite]: #163
1891 #167 := [monotonicity #164]: #166
1892 #172 := [trans #167 #170]: #171
1893 #175 := [monotonicity #172]: #174
1894 #184 := [trans #175 #182]: #183
1895 #159 := (iff #50 #158)
1896 #156 := (= #49 #155)
1897 #141 := (= #46 #140)
1898 #142 := [rewrite]: #141
1899 #153 := (= #48 #150)
1901 #151 := (= #146 #150)
1902 #152 := [rewrite]: #151
1903 #147 := (= #48 #146)
1904 #148 := [monotonicity #142]: #147
1905 #154 := [trans #148 #152]: #153
1906 #144 := (iff #47 #143)
1907 #145 := [monotonicity #142]: #144
1908 #157 := [monotonicity #145 #154 #142]: #156
1909 #160 := [monotonicity #157 #108]: #159
1910 #186 := [trans #160 #184]: #185
1911 #139 := [asserted]: #50
1912 #187 := [mp #139 #186]: #180
1913 #299 := (+ #140 #176)
1914 #300 := (<= #299 0::real)
1915 #290 := (= #140 #168)
1916 #329 := [hypothesis]: #162
1917 #191 := (+ #29 #149)
1918 #192 := (<= #191 0::real)
1920 #193 := (iff #51 #192)
1921 #194 := [rewrite]: #193
1922 #188 := [asserted]: #51
1923 #195 := [mp #188 #194]: #192
1924 #298 := (+ #75 #127)
1925 #301 := (<= #298 0::real)
1926 #284 := (= #75 #119)
1927 #302 := [hypothesis]: #113
1928 #296 := (+ #85 #127)
1929 #297 := (<= #296 0::real)
1930 #285 := (= #85 #119)
1931 #288 := (or #112 #285)
1932 #289 := [def-axiom]: #288
1933 #303 := [unit-resolution #289 #302]: #285
1935 #305 := (or #304 #297)
1936 #306 := [th-lemma]: #305
1937 #307 := [unit-resolution #306 #303]: #297
1940 #311 := (or #310 #112)
1941 #308 := [hypothesis]: #300
1942 #309 := [th-lemma #308 #307 #138 #302 #187 #195]: false
1943 #312 := [lemma #309]: #311
1944 #322 := [unit-resolution #312 #302]: #310
1945 #316 := (or #315 #300)
1946 #313 := [hypothesis]: #310
1947 #314 := [hypothesis]: #290
1948 #317 := [th-lemma]: #316
1949 #318 := [unit-resolution #317 #314 #313]: false
1950 #319 := [lemma #318]: #316
1951 #323 := [unit-resolution #319 #322]: #315
1952 #292 := (or #162 #290)
1953 #293 := [def-axiom]: #292
1954 #324 := [unit-resolution #293 #323]: #162
1955 #325 := [th-lemma #324 #307 #138 #302 #195]: false
1956 #326 := [lemma #325]: #112
1957 #286 := (or #113 #284)
1958 #287 := [def-axiom]: #286
1959 #330 := [unit-resolution #287 #326]: #284
1961 #332 := (or #331 #301)
1962 #333 := [th-lemma]: #332
1963 #334 := [unit-resolution #333 #330]: #301
1964 #335 := [th-lemma #326 #334 #195 #329 #138]: false
1965 #336 := [lemma #335]: #161
1966 #327 := [unit-resolution #293 #336]: #290
1967 #328 := [unit-resolution #319 #327]: #300
1968 [th-lemma #326 #334 #195 #328 #187 #138]: false
1970 GX51o3DUO/UBS3eNP2P9kA 285 0
1976 #116 := (* -1::real uf_4)
1979 #117 := (+ uf_3 #116)
1980 #128 := (<= #117 0::real)
1983 #221 := (* 2/3::real uf_3)
1984 #222 := (+ #221 #116)
1988 #68 := (* 1/3::real uf_2)
1989 #233 := (+ #68 #222)
1990 #243 := (<= #233 0::real)
1992 #287 := [hypothesis]: #268
1993 #41 := (* -1::real uf_2)
1997 #79 := (>= #42 0::real)
1999 #297 := (or #80 #243)
2000 #158 := (+ uf_1 #116)
2001 #159 := (<= #158 0::real)
2002 #22 := (<= uf_1 uf_4)
2003 #160 := (iff #22 #159)
2004 #161 := [rewrite]: #160
2005 #155 := [asserted]: #22
2006 #162 := [mp #155 #161]: #159
2007 #200 := (* 1/3::real uf_3)
2009 #199 := (* -4/3::real uf_2)
2010 #201 := (+ #199 #200)
2011 #202 := (+ uf_1 #201)
2012 #203 := (>= #202 0::real)
2014 #292 := [hypothesis]: #79
2015 #293 := (or #80 #258)
2017 #70 := (* -1/3::real uf_3)
2019 #187 := (* -2/3::real uf_2)
2020 #188 := (+ #187 #70)
2021 #189 := (+ uf_1 #188)
2022 #204 := (<= #189 0::real)
2023 #205 := (ite #79 #203 #204)
2025 #51 := (* -1::real uf_1)
2027 #86 := (ite #79 #42 #52)
2028 #94 := (* -1::real #86)
2031 #97 := (<= #96 0::real)
2033 #211 := (iff #98 #210)
2034 #208 := (iff #97 #205)
2036 #183 := (* 4/3::real uf_2)
2037 #184 := (+ #183 #70)
2038 #185 := (+ #51 #184)
2039 #190 := (ite #79 #185 #189)
2040 #195 := (<= #190 0::real)
2041 #206 := (iff #195 #205)
2042 #207 := [rewrite]: #206
2043 #196 := (iff #97 #195)
2044 #193 := (= #96 #190)
2046 #173 := (+ uf_1 #172)
2047 #170 := (+ uf_2 #70)
2048 #171 := (+ #51 #170)
2049 #174 := (ite #79 #171 #173)
2050 #179 := (+ #68 #174)
2051 #191 := (= #179 #190)
2052 #192 := [rewrite]: #191
2053 #180 := (= #96 #179)
2054 #177 := (= #95 #174)
2055 #164 := (ite #79 #52 #42)
2056 #167 := (+ #70 #164)
2057 #175 := (= #167 #174)
2058 #176 := [rewrite]: #175
2059 #168 := (= #95 #167)
2060 #156 := (= #94 #164)
2061 #165 := [rewrite]: #156
2062 #169 := [monotonicity #165]: #168
2063 #178 := [trans #169 #176]: #177
2064 #181 := [monotonicity #178]: #180
2065 #194 := [trans #181 #192]: #193
2066 #197 := [monotonicity #194]: #196
2067 #209 := [trans #197 #207]: #208
2068 #212 := [monotonicity #209]: #211
2070 #12 := (- uf_2 uf_3)
2071 #14 := (/ #12 3::real)
2074 #8 := (< #6 0::real)
2075 #10 := (ite #8 #9 #6)
2077 #103 := (iff #15 #98)
2079 #45 := (< #42 0::real)
2080 #57 := (ite #45 #52 #42)
2082 #101 := (iff #76 #98)
2084 #99 := (iff #91 #98)
2085 #100 := [rewrite]: #99
2086 #92 := (iff #76 #91)
2088 #83 := (ite #80 #52 #42)
2090 #88 := [rewrite]: #87
2092 #81 := (iff #45 #80)
2093 #82 := [rewrite]: #81
2094 #85 := [monotonicity #82]: #84
2095 #90 := [trans #85 #88]: #89
2096 #93 := [monotonicity #90]: #92
2097 #102 := [trans #93 #100]: #101
2098 #77 := (iff #15 #76)
2100 #60 := (* -1::real uf_3)
2102 #64 := (/ #61 3::real)
2104 #73 := [rewrite]: #72
2107 #63 := [rewrite]: #62
2108 #66 := [monotonicity #63]: #65
2109 #75 := [trans #66 #73]: #74
2112 #44 := [rewrite]: #43
2116 #54 := [rewrite]: #53
2118 #50 := [monotonicity #44]: #49
2119 #56 := [trans #50 #54]: #55
2121 #47 := [monotonicity #44]: #46
2122 #59 := [monotonicity #47 #56 #44]: #58
2123 #78 := [monotonicity #59 #75]: #77
2124 #104 := [trans #78 #102]: #103
2125 #39 := [asserted]: #15
2126 #105 := [mp #39 #104]: #98
2127 #213 := [mp #105 #212]: #210
2128 #259 := (or #205 #80 #258)
2129 #260 := [def-axiom]: #259
2130 #294 := [unit-resolution #260 #213]: #293
2131 #295 := [unit-resolution #294 #292]: #258
2132 #296 := [th-lemma #287 #292 #295 #162]: false
2133 #298 := [lemma #296]: #297
2134 #299 := [unit-resolution #298 #287]: #80
2136 #281 := (or #79 #261)
2137 #262 := (or #205 #79 #261)
2138 #263 := [def-axiom]: #262
2139 #282 := [unit-resolution #263 #213]: #281
2140 #300 := [unit-resolution #282 #299]: #261
2141 #290 := (or #79 #204 #243)
2142 #276 := [hypothesis]: #261
2143 #288 := [hypothesis]: #80
2144 #289 := [th-lemma #288 #276 #162 #287]: false
2145 #291 := [lemma #289]: #290
2146 #301 := [unit-resolution #291 #300 #299 #287]: false
2147 #302 := [lemma #301]: #243
2148 #303 := (or #129 #268)
2149 #223 := (* -4/3::real uf_3)
2150 #224 := (+ #223 uf_4)
2151 #234 := (+ #68 #224)
2152 #244 := (<= #234 0::real)
2153 #245 := (ite #128 #243 #244)
2155 #107 := (+ #60 uf_4)
2156 #135 := (ite #128 #107 #117)
2157 #143 := (* -1::real #135)
2158 #144 := (+ #70 #143)
2159 #145 := (+ #68 #144)
2160 #146 := (<= #145 0::real)
2162 #251 := (iff #147 #250)
2163 #248 := (iff #146 #245)
2164 #235 := (ite #128 #233 #234)
2165 #240 := (<= #235 0::real)
2166 #246 := (iff #240 #245)
2167 #247 := [rewrite]: #246
2168 #241 := (iff #146 #240)
2169 #238 := (= #145 #235)
2170 #225 := (ite #128 #222 #224)
2171 #230 := (+ #68 #225)
2172 #236 := (= #230 #235)
2173 #237 := [rewrite]: #236
2174 #231 := (= #145 #230)
2175 #228 := (= #144 #225)
2176 #214 := (ite #128 #117 #107)
2177 #217 := (+ #70 #214)
2178 #226 := (= #217 #225)
2179 #227 := [rewrite]: #226
2180 #218 := (= #144 #217)
2181 #215 := (= #143 #214)
2182 #216 := [rewrite]: #215
2183 #219 := [monotonicity #216]: #218
2184 #229 := [trans #219 #227]: #228
2185 #232 := [monotonicity #229]: #231
2186 #239 := [trans #232 #237]: #238
2187 #242 := [monotonicity #239]: #241
2188 #249 := [trans #242 #247]: #248
2189 #252 := [monotonicity #249]: #251
2190 #17 := (- uf_4 uf_3)
2192 #18 := (< #17 0::real)
2193 #20 := (ite #18 #19 #17)
2195 #152 := (iff #21 #147)
2196 #110 := (< #107 0::real)
2197 #122 := (ite #110 #117 #107)
2198 #125 := (< #122 #71)
2199 #150 := (iff #125 #147)
2200 #140 := (< #135 #71)
2201 #148 := (iff #140 #147)
2202 #149 := [rewrite]: #148
2203 #141 := (iff #125 #140)
2204 #138 := (= #122 #135)
2205 #132 := (ite #129 #117 #107)
2206 #136 := (= #132 #135)
2207 #137 := [rewrite]: #136
2208 #133 := (= #122 #132)
2209 #130 := (iff #110 #129)
2210 #131 := [rewrite]: #130
2211 #134 := [monotonicity #131]: #133
2212 #139 := [trans #134 #137]: #138
2213 #142 := [monotonicity #139]: #141
2214 #151 := [trans #142 #149]: #150
2215 #126 := (iff #21 #125)
2216 #123 := (= #20 #122)
2217 #108 := (= #17 #107)
2218 #109 := [rewrite]: #108
2219 #120 := (= #19 #117)
2221 #118 := (= #113 #117)
2222 #119 := [rewrite]: #118
2223 #114 := (= #19 #113)
2224 #115 := [monotonicity #109]: #114
2225 #121 := [trans #115 #119]: #120
2226 #111 := (iff #18 #110)
2227 #112 := [monotonicity #109]: #111
2228 #124 := [monotonicity #112 #121 #109]: #123
2229 #127 := [monotonicity #124 #75]: #126
2230 #153 := [trans #127 #151]: #152
2231 #106 := [asserted]: #21
2232 #154 := [mp #106 #153]: #147
2233 #253 := [mp #154 #252]: #250
2234 #269 := (or #245 #129 #268)
2235 #270 := [def-axiom]: #269
2236 #304 := [unit-resolution #270 #253]: #303
2237 #305 := [unit-resolution #304 #302]: #129
2239 #306 := (or #128 #271)
2240 #272 := (or #245 #128 #271)
2241 #273 := [def-axiom]: #272
2242 #307 := [unit-resolution #273 #253]: #306
2243 #308 := [unit-resolution #307 #305]: #271
2244 #285 := (or #128 #244)
2245 #274 := [hypothesis]: #271
2246 #275 := [hypothesis]: #129
2247 #278 := (or #204 #128 #244)
2248 #277 := [th-lemma #276 #275 #274 #162]: false
2249 #279 := [lemma #277]: #278
2250 #280 := [unit-resolution #279 #275 #274]: #204
2251 #283 := [unit-resolution #282 #280]: #79
2252 #284 := [th-lemma #275 #274 #283 #162]: false
2253 #286 := [lemma #284]: #285
2254 [unit-resolution #286 #308 #305]: false
2256 cebG074uorSr8ODzgTmcKg 97 0
2259 decl uf_1 :: (-> T2 T1 real)
2264 #20 := (uf_1 uf_2 uf_5)
2266 #53 := (* -1::real #20)
2269 #19 := (uf_1 uf_3 uf_5)
2271 #63 := (<= #54 0::real)
2273 #22 := (< 0::real #21)
2275 #74 := (iff #23 #63)
2276 #57 := (< 0::real #54)
2278 #72 := (iff #60 #63)
2281 #70 := (iff #67 #63)
2282 #71 := [rewrite]: #70
2283 #68 := (iff #60 #67)
2284 #65 := (iff #57 #64)
2285 #66 := [rewrite]: #65
2286 #69 := [monotonicity #66]: #68
2287 #73 := [trans #69 #71]: #72
2288 #61 := (iff #23 #60)
2289 #58 := (iff #22 #57)
2291 #56 := [rewrite]: #55
2292 #59 := [monotonicity #56]: #58
2293 #62 := [monotonicity #59]: #61
2294 #75 := [trans #62 #73]: #74
2295 #41 := [asserted]: #23
2296 #76 := [mp #41 #75]: #63
2298 #8 := (uf_1 uf_3 #5)
2299 #141 := (pattern #8)
2300 #6 := (uf_1 uf_2 #5)
2301 #140 := (pattern #6)
2302 #45 := (* -1::real #8)
2304 #44 := (>= #46 0::real)
2306 #142 := (forall (vars (?x1 T1)) (:pat #140 #141) #43)
2307 #49 := (forall (vars (?x1 T1)) #43)
2308 #145 := (iff #49 #142)
2309 #143 := (iff #43 #43)
2310 #144 := [refl]: #143
2311 #146 := [quant-intro #144]: #145
2315 #81 := [nnf-pos #83]: #80
2317 #10 := (forall (vars (?x1 T1)) #9)
2318 #50 := (iff #10 #49)
2320 #48 := [rewrite]: #47
2321 #51 := [quant-intro #48]: #50
2322 #39 := [asserted]: #10
2323 #52 := [mp #39 #51]: #49
2324 #79 := [mp~ #52 #81]: #49
2325 #147 := [mp #79 #146]: #142
2327 #165 := (or #164 #64)
2328 #148 := (* -1::real #19)
2329 #149 := (+ #20 #148)
2330 #150 := (>= #149 0::real)
2332 #166 := (or #164 #151)
2333 #168 := (iff #166 #165)
2334 #170 := (iff #165 #165)
2335 #171 := [rewrite]: #170
2336 #162 := (iff #151 #64)
2337 #160 := (iff #150 #63)
2338 #152 := (+ #148 #20)
2339 #155 := (>= #152 0::real)
2340 #158 := (iff #155 #63)
2341 #159 := [rewrite]: #158
2342 #156 := (iff #150 #155)
2343 #153 := (= #149 #152)
2344 #154 := [rewrite]: #153
2345 #157 := [monotonicity #154]: #156
2346 #161 := [trans #157 #159]: #160
2347 #163 := [monotonicity #161]: #162
2348 #169 := [monotonicity #163]: #168
2349 #172 := [trans #169 #171]: #168
2350 #167 := [quant-inst]: #166
2351 #173 := [mp #167 #172]: #165
2352 [unit-resolution #173 #147 #76]: false
2354 DKRtrJ2XceCkITuNwNViRw 57 0
2357 decl uf_1 :: (-> T2 real)
2358 decl uf_2 :: (-> T1 T1 T2)
2359 decl uf_12 :: (-> T4 T1)
2365 #38 := (uf_12 uf_10)
2366 #40 := (uf_2 #38 #39)
2368 #264 := (>= #41 0::real)
2370 #43 := (= #41 0::real)
2372 #131 := [asserted]: #44
2373 #272 := (or #43 #266)
2374 #42 := (<= #41 0::real)
2375 #130 := [asserted]: #42
2377 #270 := (or #43 #265 #266)
2378 #271 := [th-lemma]: #270
2379 #273 := [unit-resolution #271 #130]: #272
2380 #274 := [unit-resolution #273 #131]: #266
2384 #241 := (pattern #7)
2386 #65 := (>= #8 0::real)
2387 #242 := (forall (vars (?x1 T1) (?x2 T1)) (:pat #241) #65)
2388 #66 := (forall (vars (?x1 T1) (?x2 T1)) #65)
2389 #245 := (iff #66 #242)
2390 #243 := (iff #65 #65)
2391 #244 := [refl]: #243
2392 #246 := [quant-intro #244]: #245
2395 #152 := [refl]: #151
2396 #150 := [nnf-pos #152]: #149
2397 #9 := (<= 0::real #8)
2398 #10 := (forall (vars (?x1 T1) (?x2 T1)) #9)
2399 #67 := (iff #10 #66)
2401 #64 := [rewrite]: #63
2402 #68 := [quant-intro #64]: #67
2403 #60 := [asserted]: #10
2404 #69 := [mp #60 #68]: #66
2405 #147 := [mp~ #69 #150]: #66
2406 #247 := [mp #147 #246]: #242
2408 #268 := (or #267 #264)
2409 #269 := [quant-inst]: #268
2410 [unit-resolution #269 #247 #274]: false
2412 97KJAJfUio+nGchEHWvgAw 91 0
2415 decl uf_1 :: (-> T1 T2 real)
2420 #8 := (uf_1 uf_4 uf_3)
2422 #36 := (* -1::real #8)
2425 #6 := (uf_1 uf_2 uf_3)
2427 #130 := (>= #37 0::real)
2433 #56 := (iff #16 #55)
2434 #53 := (iff #15 #43)
2435 #54 := [rewrite]: #53
2436 #57 := [monotonicity #54]: #56
2437 #34 := [asserted]: #16
2438 #60 := [mp #34 #57]: #55
2439 #158 := (or #43 #155)
2440 #39 := (<= #37 0::real)
2443 #41 := [rewrite]: #40
2444 #32 := [asserted]: #9
2445 #42 := [mp #32 #41]: #39
2447 #156 := (or #43 #154 #155)
2448 #157 := [th-lemma]: #156
2449 #159 := [unit-resolution #157 #42]: #158
2450 #160 := [unit-resolution #159 #60]: #155
2452 #12 := (uf_1 uf_2 #10)
2453 #123 := (pattern #12)
2454 #11 := (uf_1 uf_4 #10)
2455 #122 := (pattern #11)
2456 #44 := (* -1::real #12)
2458 #46 := (<= #45 0::real)
2459 #124 := (forall (vars (?x1 T2)) (:pat #122 #123) #46)
2460 #49 := (forall (vars (?x1 T2)) #46)
2461 #127 := (iff #49 #124)
2462 #125 := (iff #46 #46)
2463 #126 := [refl]: #125
2464 #128 := [quant-intro #126]: #127
2468 #63 := [nnf-pos #65]: #62
2470 #14 := (forall (vars (?x1 T2)) #13)
2471 #50 := (iff #14 #49)
2472 #47 := (iff #13 #46)
2473 #48 := [rewrite]: #47
2474 #51 := [quant-intro #48]: #50
2475 #33 := [asserted]: #14
2476 #52 := [mp #33 #51]: #49
2477 #61 := [mp~ #52 #63]: #49
2478 #129 := [mp #61 #128]: #124
2480 #145 := (or #144 #130)
2481 #131 := (* -1::real #6)
2483 #133 := (<= #132 0::real)
2484 #146 := (or #144 #133)
2485 #148 := (iff #146 #145)
2486 #150 := (iff #145 #145)
2487 #151 := [rewrite]: #150
2488 #142 := (iff #133 #130)
2490 #137 := (<= #134 0::real)
2491 #140 := (iff #137 #130)
2492 #141 := [rewrite]: #140
2493 #138 := (iff #133 #137)
2494 #135 := (= #132 #134)
2495 #136 := [rewrite]: #135
2496 #139 := [monotonicity #136]: #138
2497 #143 := [trans #139 #141]: #142
2498 #149 := [monotonicity #143]: #148
2499 #152 := [trans #149 #151]: #148
2500 #147 := [quant-inst]: #146
2501 #153 := [mp #147 #152]: #145
2502 [unit-resolution #153 #129 #160]: false
2504 flJYbeWfe+t2l/zsRqdujA 149 0
2507 decl uf_1 :: (-> T1 T2 real)
2512 #8 := (uf_1 uf_4 uf_3)
2514 #156 := (* -1::real #8)
2517 #6 := (uf_1 uf_2 uf_3)
2519 #205 := (>= #203 0::real)
2521 #40 := [asserted]: #9
2523 #209 := (or #208 #205)
2524 #210 := [th-lemma]: #209
2525 #211 := [unit-resolution #210 #40]: #205
2528 #22 := (uf_1 uf_5 uf_3)
2529 #160 := (* -1::real #22)
2531 #207 := (>= #161 0::real)
2537 #217 := (iff #70 #216)
2538 #214 := (iff #62 #206)
2539 #212 := (iff #206 #62)
2540 #213 := [monotonicity #40]: #212
2541 #215 := [symm #213]: #214
2542 #218 := [monotonicity #215]: #217
2545 #71 := (iff #24 #70)
2546 #68 := (iff #23 #62)
2547 #69 := [rewrite]: #68
2548 #72 := [monotonicity #69]: #71
2549 #43 := [asserted]: #24
2550 #75 := [mp #43 #72]: #70
2551 #219 := [mp #75 #218]: #216
2552 #225 := (or #206 #222)
2553 #162 := (<= #161 0::real)
2555 #173 := (>= #172 0::real)
2558 #181 := (or #163 #178)
2561 #15 := (uf_1 uf_4 #10)
2562 #149 := (pattern #15)
2563 #13 := (uf_1 uf_5 #10)
2564 #148 := (pattern #13)
2565 #11 := (uf_1 uf_2 #10)
2566 #147 := (pattern #11)
2567 #50 := (* -1::real #15)
2569 #52 := (<= #51 0::real)
2571 #45 := (* -1::real #13)
2573 #47 := (<= #46 0::real)
2577 #150 := (forall (vars (?x1 T2)) (:pat #147 #148 #149) #83)
2578 #86 := (forall (vars (?x1 T2)) #83)
2579 #153 := (iff #86 #150)
2580 #151 := (iff #83 #83)
2581 #152 := [refl]: #151
2582 #154 := [quant-intro #152]: #153
2583 #55 := (and #47 #52)
2584 #58 := (forall (vars (?x1 T2)) #55)
2585 #87 := (iff #58 #86)
2586 #84 := (iff #55 #83)
2587 #85 := [rewrite]: #84
2588 #88 := [quant-intro #85]: #87
2592 #80 := [nnf-pos #82]: #79
2595 #17 := (and #14 #16)
2596 #18 := (forall (vars (?x1 T2)) #17)
2597 #59 := (iff #18 #58)
2598 #56 := (iff #17 #55)
2599 #53 := (iff #16 #52)
2600 #54 := [rewrite]: #53
2601 #48 := (iff #14 #47)
2602 #49 := [rewrite]: #48
2603 #57 := [monotonicity #49 #54]: #56
2604 #60 := [quant-intro #57]: #59
2605 #41 := [asserted]: #18
2606 #61 := [mp #41 #60]: #58
2607 #77 := [mp~ #61 #80]: #58
2608 #89 := [mp #77 #88]: #86
2609 #155 := [mp #89 #154]: #150
2611 #188 := (or #187 #184)
2612 #157 := (+ #22 #156)
2613 #158 := (<= #157 0::real)
2615 #164 := (or #163 #159)
2617 #189 := (or #187 #165)
2618 #191 := (iff #189 #188)
2619 #193 := (iff #188 #188)
2620 #194 := [rewrite]: #193
2621 #185 := (iff #165 #184)
2622 #182 := (iff #164 #181)
2623 #179 := (iff #159 #178)
2624 #176 := (iff #158 #173)
2625 #166 := (+ #156 #22)
2626 #169 := (<= #166 0::real)
2627 #174 := (iff #169 #173)
2628 #175 := [rewrite]: #174
2629 #170 := (iff #158 #169)
2630 #167 := (= #157 #166)
2631 #168 := [rewrite]: #167
2632 #171 := [monotonicity #168]: #170
2633 #177 := [trans #171 #175]: #176
2634 #180 := [monotonicity #177]: #179
2635 #183 := [monotonicity #180]: #182
2636 #186 := [monotonicity #183]: #185
2637 #192 := [monotonicity #186]: #191
2638 #195 := [trans #192 #194]: #191
2639 #190 := [quant-inst]: #189
2640 #196 := [mp #190 #195]: #188
2641 #220 := [unit-resolution #196 #155]: #184
2642 #197 := (or #181 #162)
2643 #198 := [def-axiom]: #197
2644 #221 := [unit-resolution #198 #220]: #162
2645 #223 := (or #206 #163 #222)
2646 #224 := [th-lemma]: #223
2647 #226 := [unit-resolution #224 #221]: #225
2648 #227 := [unit-resolution #226 #219]: #222
2649 #199 := (or #181 #173)
2650 #200 := [def-axiom]: #199
2651 #228 := [unit-resolution #200 #220]: #173
2652 [th-lemma #228 #227 #211]: false
2654 rbrrQuQfaijtLkQizgEXnQ 222 0
2657 decl uf_2 :: (-> T2 T1 real)
2662 #20 := (uf_2 uf_3 uf_5)
2665 #18 := (uf_2 uf_6 uf_5)
2667 #73 := (* -1::real #18)
2671 #78 := (* -1::real #20)
2673 #144 := (+ uf_1 #79)
2674 #145 := (<= #144 0::real)
2675 #148 := (ite #145 uf_1 #106)
2676 #279 := (* -1::real #148)
2677 #280 := (+ uf_1 #279)
2678 #281 := (<= #280 0::real)
2681 #151 := (* 1/2::real #148)
2682 #248 := (<= #151 0::real)
2683 #162 := (= #151 0::real)
2686 #28 := (<= uf_1 #27)
2687 #29 := (ite #28 uf_1 #27)
2688 #30 := (/ #29 2::real)
2693 #165 := (iff #34 #162)
2694 #109 := (<= uf_1 #106)
2695 #112 := (ite #109 uf_1 #106)
2696 #118 := (* 1/2::real #112)
2697 #123 := (+ #18 #118)
2698 #129 := (= #18 #123)
2699 #163 := (iff #129 #162)
2700 #154 := (+ #18 #151)
2701 #157 := (= #18 #154)
2702 #160 := (iff #157 #162)
2703 #161 := [rewrite]: #160
2704 #158 := (iff #129 #157)
2705 #155 := (= #123 #154)
2706 #152 := (= #118 #151)
2707 #149 := (= #112 #148)
2708 #146 := (iff #109 #145)
2709 #147 := [rewrite]: #146
2710 #150 := [monotonicity #147]: #149
2711 #153 := [monotonicity #150]: #152
2712 #156 := [monotonicity #153]: #155
2713 #159 := [monotonicity #156]: #158
2714 #164 := [trans #159 #161]: #163
2715 #142 := (iff #34 #129)
2718 #140 := (iff #137 #129)
2719 #141 := [rewrite]: #140
2720 #138 := (iff #34 #137)
2721 #135 := (iff #33 #134)
2722 #132 := (iff #32 #129)
2723 #126 := (= #123 #18)
2724 #130 := (iff #126 #129)
2725 #131 := [rewrite]: #130
2726 #127 := (iff #32 #126)
2727 #124 := (= #31 #123)
2728 #121 := (= #30 #118)
2729 #115 := (/ #112 2::real)
2730 #119 := (= #115 #118)
2731 #120 := [rewrite]: #119
2732 #116 := (= #30 #115)
2733 #113 := (= #29 #112)
2734 #107 := (= #27 #106)
2735 #108 := [rewrite]: #107
2736 #110 := (iff #28 #109)
2737 #111 := [monotonicity #108]: #110
2738 #114 := [monotonicity #111 #108]: #113
2739 #117 := [monotonicity #114]: #116
2740 #122 := [trans #117 #120]: #121
2741 #125 := [monotonicity #122]: #124
2742 #128 := [monotonicity #125]: #127
2743 #133 := [trans #128 #131]: #132
2744 #136 := [monotonicity #133]: #135
2745 #139 := [monotonicity #136]: #138
2746 #143 := [trans #139 #141]: #142
2747 #166 := [trans #143 #164]: #165
2748 #105 := [asserted]: #34
2749 #167 := [mp #105 #166]: #162
2751 #284 := (or #283 #248)
2752 #285 := [th-lemma]: #284
2753 #286 := [unit-resolution #285 #167]: #248
2754 #287 := [hypothesis]: #281
2755 #53 := (<= uf_1 0::real)
2757 #6 := (< 0::real uf_1)
2759 #56 := [rewrite]: #55
2760 #50 := [asserted]: #6
2761 #57 := [mp #50 #56]: #54
2762 #288 := [th-lemma #57 #287 #286]: false
2763 #290 := [lemma #288]: #289
2764 #241 := (= uf_1 #148)
2765 #242 := (= #106 #148)
2767 #282 := (+ #106 #279)
2768 #291 := (<= #282 0::real)
2772 #16 := (uf_2 uf_4 uf_5)
2774 #261 := (>= #260 0::real)
2777 #11 := (uf_2 uf_4 #8)
2778 #234 := (pattern #11)
2779 #9 := (uf_2 uf_3 #8)
2780 #233 := (pattern #9)
2781 #60 := (* -1::real #11)
2783 #62 := (<= #61 0::real)
2785 #235 := (forall (vars (?x1 T1)) (:pat #233 #234) #179)
2786 #178 := (forall (vars (?x1 T1)) #179)
2787 #238 := (iff #178 #235)
2788 #236 := (iff #179 #179)
2789 #237 := [refl]: #236
2790 #239 := [quant-intro #237]: #238
2791 #65 := (exists (vars (?x1 T1)) #62)
2793 #175 := (~ #68 #178)
2794 #180 := (~ #179 #179)
2795 #177 := [refl]: #180
2796 #176 := [nnf-neg #177]: #175
2798 #13 := (exists (vars (?x1 T1)) #12)
2800 #69 := (iff #14 #68)
2801 #66 := (iff #13 #65)
2802 #63 := (iff #12 #62)
2803 #64 := [rewrite]: #63
2804 #67 := [quant-intro #64]: #66
2805 #70 := [monotonicity #67]: #69
2806 #51 := [asserted]: #14
2807 #71 := [mp #51 #70]: #68
2808 #173 := [mp~ #71 #176]: #178
2809 #240 := [mp #173 #239]: #235
2811 #270 := (or #269 #266)
2812 #250 := (* -1::real #16)
2813 #251 := (+ #20 #250)
2814 #252 := (<= #251 0::real)
2816 #271 := (or #269 #253)
2817 #273 := (iff #271 #270)
2818 #275 := (iff #270 #270)
2819 #276 := [rewrite]: #275
2820 #267 := (iff #253 #266)
2821 #264 := (iff #252 #261)
2822 #254 := (+ #250 #20)
2823 #257 := (<= #254 0::real)
2824 #262 := (iff #257 #261)
2825 #263 := [rewrite]: #262
2826 #258 := (iff #252 #257)
2827 #255 := (= #251 #254)
2828 #256 := [rewrite]: #255
2829 #259 := [monotonicity #256]: #258
2830 #265 := [trans #259 #263]: #264
2831 #268 := [monotonicity #265]: #267
2832 #274 := [monotonicity #268]: #273
2833 #277 := [trans #274 #276]: #273
2834 #272 := [quant-inst]: #271
2835 #278 := [mp #272 #277]: #270
2836 #293 := [unit-resolution #278 #240]: #266
2837 #90 := (* 1/2::real #20)
2839 #89 := (* 1/2::real #16)
2840 #103 := (+ #89 #102)
2841 #100 := (>= #103 0::real)
2843 #25 := (/ #23 2::real)
2845 #98 := (iff #26 #100)
2848 #97 := (iff #94 #100)
2849 #99 := [rewrite]: #97
2850 #95 := (iff #26 #94)
2852 #93 := [rewrite]: #92
2853 #96 := [monotonicity #93]: #95
2854 #101 := [trans #96 #99]: #98
2855 #58 := [asserted]: #26
2856 #104 := [mp #58 #101]: #100
2857 #294 := [hypothesis]: #291
2858 #295 := [th-lemma #294 #104 #293 #286]: false
2859 #297 := [lemma #295]: #296
2860 #298 := [hypothesis]: #242
2861 #300 := (or #299 #291)
2862 #301 := [th-lemma]: #300
2863 #302 := [unit-resolution #301 #298 #297]: false
2864 #303 := [lemma #302]: #299
2865 #246 := (or #145 #242)
2866 #247 := [def-axiom]: #246
2867 #304 := [unit-resolution #247 #303]: #145
2869 #244 := (or #243 #241)
2870 #245 := [def-axiom]: #244
2871 #305 := [unit-resolution #245 #304]: #241
2873 #307 := (or #306 #281)
2874 #308 := [th-lemma]: #307
2875 [unit-resolution #308 #305 #290]: false
2877 hwh3oeLAWt56hnKIa8Wuow 248 0
2880 decl uf_2 :: (-> T2 T1 real)
2885 #18 := (uf_2 uf_6 uf_5)
2888 #16 := (uf_2 uf_4 uf_5)
2890 #137 := (* -1::real #16)
2891 #138 := (+ #137 #18)
2894 #80 := (* -1::real #18)
2896 #201 := (+ uf_1 #81)
2897 #202 := (<= #201 0::real)
2898 #205 := (ite #202 uf_1 #138)
2899 #352 := (* -1::real #205)
2900 #353 := (+ uf_1 #352)
2901 #354 := (<= #353 0::real)
2904 #244 := (* 1/2::real #205)
2905 #322 := (<= #244 0::real)
2906 #245 := (= #244 0::real)
2908 #208 := (* -1/2::real #205)
2909 #211 := (+ #18 #208)
2912 #20 := (uf_2 uf_3 uf_5)
2914 #85 := (* -1::real #20)
2916 #188 := (+ uf_1 #86)
2917 #189 := (<= #188 0::real)
2918 #192 := (ite #189 uf_1 #117)
2919 #195 := (* 1/2::real #192)
2920 #198 := (+ #18 #195)
2921 #97 := (* 1/2::real #20)
2923 #96 := (* 1/2::real #16)
2924 #110 := (+ #96 #109)
2925 #107 := (>= #110 0::real)
2926 #214 := (ite #107 #198 #211)
2927 #217 := (= #18 #214)
2928 #248 := (iff #217 #245)
2929 #241 := (= #18 #211)
2930 #246 := (iff #241 #245)
2931 #247 := [rewrite]: #246
2932 #242 := (iff #217 #241)
2933 #239 := (= #214 #211)
2934 #234 := (ite false #198 #211)
2935 #237 := (= #234 #211)
2936 #238 := [rewrite]: #237
2937 #235 := (= #214 #234)
2938 #232 := (iff #107 false)
2942 #25 := (/ #23 2::real)
2944 #108 := (iff #26 #104)
2947 #106 := (iff #101 #104)
2948 #105 := [rewrite]: #106
2949 #102 := (iff #26 #101)
2951 #100 := [rewrite]: #99
2952 #103 := [monotonicity #100]: #102
2953 #111 := [trans #103 #105]: #108
2954 #65 := [asserted]: #26
2955 #112 := [mp #65 #111]: #104
2956 #233 := [iff-false #112]: #232
2957 #236 := [monotonicity #233]: #235
2958 #240 := [trans #236 #238]: #239
2959 #243 := [monotonicity #240]: #242
2960 #249 := [trans #243 #247]: #248
2962 #34 := (<= uf_1 #33)
2963 #35 := (ite #34 uf_1 #33)
2964 #36 := (/ #35 2::real)
2967 #29 := (<= uf_1 #28)
2968 #30 := (ite #29 uf_1 #28)
2969 #31 := (/ #30 2::real)
2972 #38 := (ite #27 #32 #37)
2976 #220 := (iff #41 #217)
2977 #141 := (<= uf_1 #138)
2978 #144 := (ite #141 uf_1 #138)
2979 #159 := (* -1/2::real #144)
2980 #160 := (+ #18 #159)
2981 #120 := (<= uf_1 #117)
2982 #123 := (ite #120 uf_1 #117)
2983 #129 := (* 1/2::real #123)
2984 #134 := (+ #18 #129)
2985 #114 := (<= #18 #98)
2986 #165 := (ite #114 #134 #160)
2987 #171 := (= #18 #165)
2988 #218 := (iff #171 #217)
2989 #215 := (= #165 #214)
2990 #212 := (= #160 #211)
2991 #209 := (= #159 #208)
2992 #206 := (= #144 #205)
2993 #203 := (iff #141 #202)
2994 #204 := [rewrite]: #203
2995 #207 := [monotonicity #204]: #206
2996 #210 := [monotonicity #207]: #209
2997 #213 := [monotonicity #210]: #212
2998 #199 := (= #134 #198)
2999 #196 := (= #129 #195)
3000 #193 := (= #123 #192)
3001 #190 := (iff #120 #189)
3002 #191 := [rewrite]: #190
3003 #194 := [monotonicity #191]: #193
3004 #197 := [monotonicity #194]: #196
3005 #200 := [monotonicity #197]: #199
3006 #187 := (iff #114 #107)
3007 #186 := [rewrite]: #187
3008 #216 := [monotonicity #186 #200 #213]: #215
3009 #219 := [monotonicity #216]: #218
3010 #184 := (iff #41 #171)
3013 #182 := (iff #179 #171)
3014 #183 := [rewrite]: #182
3015 #180 := (iff #41 #179)
3016 #177 := (iff #40 #176)
3017 #174 := (iff #39 #171)
3018 #168 := (= #165 #18)
3019 #172 := (iff #168 #171)
3020 #173 := [rewrite]: #172
3021 #169 := (iff #39 #168)
3022 #166 := (= #38 #165)
3023 #163 := (= #37 #160)
3024 #150 := (* 1/2::real #144)
3025 #155 := (- #18 #150)
3026 #161 := (= #155 #160)
3027 #162 := [rewrite]: #161
3028 #156 := (= #37 #155)
3029 #153 := (= #36 #150)
3030 #147 := (/ #144 2::real)
3031 #151 := (= #147 #150)
3032 #152 := [rewrite]: #151
3033 #148 := (= #36 #147)
3034 #145 := (= #35 #144)
3035 #139 := (= #33 #138)
3036 #140 := [rewrite]: #139
3037 #142 := (iff #34 #141)
3038 #143 := [monotonicity #140]: #142
3039 #146 := [monotonicity #143 #140]: #145
3040 #149 := [monotonicity #146]: #148
3041 #154 := [trans #149 #152]: #153
3042 #157 := [monotonicity #154]: #156
3043 #164 := [trans #157 #162]: #163
3044 #135 := (= #32 #134)
3045 #132 := (= #31 #129)
3046 #126 := (/ #123 2::real)
3047 #130 := (= #126 #129)
3048 #131 := [rewrite]: #130
3049 #127 := (= #31 #126)
3050 #124 := (= #30 #123)
3051 #118 := (= #28 #117)
3052 #119 := [rewrite]: #118
3053 #121 := (iff #29 #120)
3054 #122 := [monotonicity #119]: #121
3055 #125 := [monotonicity #122 #119]: #124
3056 #128 := [monotonicity #125]: #127
3057 #133 := [trans #128 #131]: #132
3058 #136 := [monotonicity #133]: #135
3059 #115 := (iff #27 #114)
3060 #116 := [monotonicity #100]: #115
3061 #167 := [monotonicity #116 #136 #164]: #166
3062 #170 := [monotonicity #167]: #169
3063 #175 := [trans #170 #173]: #174
3064 #178 := [monotonicity #175]: #177
3065 #181 := [monotonicity #178]: #180
3066 #185 := [trans #181 #183]: #184
3067 #221 := [trans #185 #219]: #220
3068 #113 := [asserted]: #41
3069 #222 := [mp #113 #221]: #217
3070 #250 := [mp #222 #249]: #245
3072 #357 := (or #356 #322)
3073 #358 := [th-lemma]: #357
3074 #359 := [unit-resolution #358 #250]: #322
3075 #360 := [hypothesis]: #354
3076 #60 := (<= uf_1 0::real)
3078 #6 := (< 0::real uf_1)
3080 #63 := [rewrite]: #62
3081 #57 := [asserted]: #6
3082 #64 := [mp #57 #63]: #61
3083 #361 := [th-lemma #64 #360 #359]: false
3084 #363 := [lemma #361]: #362
3085 #315 := (= uf_1 #205)
3086 #316 := (= #138 #205)
3088 #355 := (+ #138 #352)
3089 #364 := (<= #355 0::real)
3091 #87 := (<= #86 0::real)
3092 #82 := (<= #81 0::real)
3093 #90 := (and #82 #87)
3096 #22 := (and #19 #21)
3097 #91 := (iff #22 #90)
3098 #88 := (iff #21 #87)
3099 #89 := [rewrite]: #88
3100 #83 := (iff #19 #82)
3101 #84 := [rewrite]: #83
3102 #92 := [monotonicity #84 #89]: #91
3103 #59 := [asserted]: #22
3104 #93 := [mp #59 #92]: #90
3105 #95 := [and-elim #93]: #87
3106 #366 := [hypothesis]: #364
3107 #367 := [th-lemma #366 #95 #112 #359]: false
3108 #369 := [lemma #367]: #368
3109 #370 := [hypothesis]: #316
3110 #372 := (or #371 #364)
3111 #373 := [th-lemma]: #372
3112 #374 := [unit-resolution #373 #370 #369]: false
3113 #375 := [lemma #374]: #371
3114 #320 := (or #202 #316)
3115 #321 := [def-axiom]: #320
3116 #376 := [unit-resolution #321 #375]: #202
3118 #318 := (or #317 #315)
3119 #319 := [def-axiom]: #318
3120 #377 := [unit-resolution #319 #376]: #315
3122 #379 := (or #378 #354)
3123 #380 := [th-lemma]: #379
3124 [unit-resolution #380 #377 #363]: false
3126 WdMJH3tkMv/rps8y9Ukq5Q 86 0
3129 decl uf_2 :: (-> T2 T1 real)
3134 #13 := (uf_2 uf_3 uf_4)
3136 #140 := (* -1::real #13)
3139 #141 := (+ uf_1 #140)
3140 #143 := (>= #141 0::real)
3142 #7 := (uf_2 uf_3 #6)
3143 #127 := (pattern #7)
3144 #35 := (* -1::real #7)
3146 #47 := (>= #36 0::real)
3147 #134 := (forall (vars (?x2 T1)) (:pat #127) #47)
3148 #49 := (forall (vars (?x2 T1)) #47)
3149 #137 := (iff #49 #134)
3150 #135 := (iff #47 #47)
3151 #136 := [refl]: #135
3152 #138 := [quant-intro #136]: #137
3156 #68 := [nnf-pos #66]: #67
3158 #11 := (forall (vars (?x2 T1)) #10)
3159 #50 := (iff #11 #49)
3160 #46 := (iff #10 #47)
3161 #48 := [rewrite]: #46
3162 #51 := [quant-intro #48]: #50
3163 #32 := [asserted]: #11
3164 #52 := [mp #32 #51]: #49
3165 #69 := [mp~ #52 #68]: #49
3166 #139 := [mp #69 #138]: #134
3168 #150 := (or #149 #143)
3169 #151 := [quant-inst]: #150
3170 #144 := [unit-resolution #151 #139]: #143
3171 #142 := (<= #141 0::real)
3172 #38 := (<= #36 0::real)
3173 #128 := (forall (vars (?x1 T1)) (:pat #127) #38)
3174 #41 := (forall (vars (?x1 T1)) #38)
3175 #131 := (iff #41 #128)
3176 #129 := (iff #38 #38)
3177 #130 := [refl]: #129
3178 #132 := [quant-intro #130]: #131
3182 #63 := [nnf-pos #65]: #62
3184 #9 := (forall (vars (?x1 T1)) #8)
3187 #40 := [rewrite]: #39
3188 #43 := [quant-intro #40]: #42
3189 #31 := [asserted]: #9
3190 #44 := [mp #31 #43]: #41
3191 #61 := [mp~ #44 #63]: #41
3192 #133 := [mp #61 #132]: #128
3194 #146 := (or #145 #142)
3195 #147 := [quant-inst]: #146
3196 #148 := [unit-resolution #147 #133]: #142
3201 #56 := (iff #15 #55)
3202 #53 := (iff #14 #45)
3203 #54 := [rewrite]: #53
3204 #57 := [monotonicity #54]: #56
3205 #33 := [asserted]: #15
3206 #60 := [mp #33 #57]: #55
3209 #154 := (or #45 #152 #153)
3210 #155 := [th-lemma]: #154
3211 [unit-resolution #155 #60 #148 #144]: false
3213 V+IAyBZU/6QjYs6JkXx8LQ 57 0
3216 decl uf_1 :: (-> T2 real)
3217 decl uf_2 :: (-> T1 T1 T2)
3218 decl uf_12 :: (-> T4 T1)
3224 #38 := (uf_12 uf_10)
3225 #40 := (uf_2 #38 #39)
3227 #264 := (>= #41 0::real)
3229 #43 := (= #41 0::real)
3231 #131 := [asserted]: #44
3232 #272 := (or #43 #266)
3233 #42 := (<= #41 0::real)
3234 #130 := [asserted]: #42
3236 #270 := (or #43 #265 #266)
3237 #271 := [th-lemma]: #270
3238 #273 := [unit-resolution #271 #130]: #272
3239 #274 := [unit-resolution #273 #131]: #266
3243 #241 := (pattern #7)
3245 #65 := (>= #8 0::real)
3246 #242 := (forall (vars (?x1 T1) (?x2 T1)) (:pat #241) #65)
3247 #66 := (forall (vars (?x1 T1) (?x2 T1)) #65)
3248 #245 := (iff #66 #242)
3249 #243 := (iff #65 #65)
3250 #244 := [refl]: #243
3251 #246 := [quant-intro #244]: #245
3254 #152 := [refl]: #151
3255 #150 := [nnf-pos #152]: #149
3256 #9 := (<= 0::real #8)
3257 #10 := (forall (vars (?x1 T1) (?x2 T1)) #9)
3258 #67 := (iff #10 #66)
3260 #64 := [rewrite]: #63
3261 #68 := [quant-intro #64]: #67
3262 #60 := [asserted]: #10
3263 #69 := [mp #60 #68]: #66
3264 #147 := [mp~ #69 #150]: #66
3265 #247 := [mp #147 #246]: #242
3267 #268 := (or #267 #264)
3268 #269 := [quant-inst]: #268
3269 [unit-resolution #269 #247 #274]: false