src/HOL/Multivariate_Analysis/Integration_MV.cert

Renamed Multivariate-Analysis/Integration to Multivariate-Analysis/Integration_MV to avoid name clash with Integration.

tB2Atlor9W4pSnrAz5nHpw 907 0
#2 := false
#299 := 0::real
decl uf_1 :: (-> T3 T2 real)
decl uf_10 :: (-> T4 T2)
decl uf_7 :: T4
#15 := uf_7
#22 := (uf_10 uf_7)
decl uf_2 :: (-> T1 T3)
decl uf_4 :: T1
#11 := uf_4
#91 := (uf_2 uf_4)
#902 := (uf_1 #91 #22)
#297 := -1::real
#1084 := (* -1::real #902)
decl uf_16 :: T1
#50 := uf_16
#78 := (uf_2 uf_16)
#799 := (uf_1 #78 #22)
#1267 := (+ #799 #1084)
#1272 := (>= #1267 0::real)
#1266 := (= #799 #902)
decl uf_9 :: T3
#21 := uf_9
#23 := (uf_1 uf_9 #22)
#905 := (= #23 #902)
decl uf_11 :: T3
#24 := uf_11
#850 := (uf_1 uf_11 #22)
#904 := (= #850 #902)
decl uf_6 :: (-> T2 T4)
#74 := (uf_6 #22)
#281 := (= uf_7 #74)
#922 := (ite #281 #905 #904)
decl uf_8 :: T3
#18 := uf_8
#848 := (uf_1 uf_8 #22)
#903 := (= #848 #902)
#60 := 0::int
decl uf_5 :: (-> T4 int)
#803 := (uf_5 #74)
#117 := -1::int
#813 := (* -1::int #803)
#16 := (uf_5 uf_7)
#916 := (+ #16 #813)
#917 := (<= #916 0::int)
#925 := (ite #917 #922 #903)
#6 := (:var 0 T2)
#19 := (uf_1 uf_8 #6)
#544 := (pattern #19)
#25 := (uf_1 uf_11 #6)
#543 := (pattern #25)
#92 := (uf_1 #91 #6)
#542 := (pattern #92)
#13 := (uf_6 #6)
#541 := (pattern #13)
#447 := (= #19 #92)
#445 := (= #25 #92)
#444 := (= #23 #92)
#20 := (= #13 uf_7)
#446 := (ite #20 #444 #445)
#120 := (* -1::int #16)
#14 := (uf_5 #13)
#121 := (+ #14 #120)
#119 := (>= #121 0::int)
#448 := (ite #119 #446 #447)
#545 := (forall (vars (?x3 T2)) (:pat #541 #542 #543 #544) #448)
#451 := (forall (vars (?x3 T2)) #448)
#548 := (iff #451 #545)
#546 := (iff #448 #448)
#547 := [refl]: #546
#549 := [quant-intro #547]: #548
#26 := (ite #20 #23 #25)
#127 := (ite #119 #26 #19)
#368 := (= #92 #127)
#369 := (forall (vars (?x3 T2)) #368)
#452 := (iff #369 #451)
#449 := (iff #368 #448)
#450 := [rewrite]: #449
#453 := [quant-intro #450]: #452
#392 := (~ #369 #369)
#390 := (~ #368 #368)
#391 := [refl]: #390
#366 := [nnf-pos #391]: #392
decl uf_3 :: (-> T1 T2 real)
#12 := (uf_3 uf_4 #6)
#132 := (= #12 #127)
#135 := (forall (vars (?x3 T2)) #132)
#370 := (iff #135 #369)
#4 := (:var 1 T1)
#8 := (uf_3 #4 #6)
#5 := (uf_2 #4)
#7 := (uf_1 #5 #6)
#9 := (= #7 #8)
#10 := (forall (vars (?x1 T1) (?x2 T2)) #9)
#113 := [asserted]: #10
#371 := [rewrite* #113]: #370
#17 := (< #14 #16)
#27 := (ite #17 #19 #26)
#28 := (= #12 #27)
#29 := (forall (vars (?x3 T2)) #28)
#136 := (iff #29 #135)
#133 := (iff #28 #132)
#130 := (= #27 #127)
#118 := (not #119)
#124 := (ite #118 #19 #26)
#128 := (= #124 #127)
#129 := [rewrite]: #128
#125 := (= #27 #124)
#122 := (iff #17 #118)
#123 := [rewrite]: #122
#126 := [monotonicity #123]: #125
#131 := [trans #126 #129]: #130
#134 := [monotonicity #131]: #133
#137 := [quant-intro #134]: #136
#114 := [asserted]: #29
#138 := [mp #114 #137]: #135
#372 := [mp #138 #371]: #369
#367 := [mp~ #372 #366]: #369
#454 := [mp #367 #453]: #451
#550 := [mp #454 #549]: #545
#738 := (not #545)
#928 := (or #738 #925)
#75 := (= #74 uf_7)
#906 := (ite #75 #905 #904)
#907 := (+ #803 #120)
#908 := (>= #907 0::int)
#909 := (ite #908 #906 #903)
#929 := (or #738 #909)
#931 := (iff #929 #928)
#933 := (iff #928 #928)
#934 := [rewrite]: #933
#926 := (iff #909 #925)
#923 := (iff #906 #922)
#283 := (iff #75 #281)
#284 := [rewrite]: #283
#924 := [monotonicity #284]: #923
#920 := (iff #908 #917)
#910 := (+ #120 #803)
#913 := (>= #910 0::int)
#918 := (iff #913 #917)
#919 := [rewrite]: #918
#914 := (iff #908 #913)
#911 := (= #907 #910)
#912 := [rewrite]: #911
#915 := [monotonicity #912]: #914
#921 := [trans #915 #919]: #920
#927 := [monotonicity #921 #924]: #926
#932 := [monotonicity #927]: #931
#935 := [trans #932 #934]: #931
#930 := [quant-inst]: #929
#936 := [mp #930 #935]: #928
#1300 := [unit-resolution #936 #550]: #925
#989 := (= #16 #803)
#1277 := (= #803 #16)
#280 := [asserted]: #75
#287 := [mp #280 #284]: #281
#1276 := [symm #287]: #75
#1278 := [monotonicity #1276]: #1277
#1301 := [symm #1278]: #989
#1302 := (not #989)
#1303 := (or #1302 #917)
#1304 := [th-lemma]: #1303
#1305 := [unit-resolution #1304 #1301]: #917
#950 := (not #917)
#949 := (not #925)
#951 := (or #949 #950 #922)
#952 := [def-axiom]: #951
#1306 := [unit-resolution #952 #1305 #1300]: #922
#937 := (not #922)
#1307 := (or #937 #905)
#938 := (not #281)
#939 := (or #937 #938 #905)
#940 := [def-axiom]: #939
#1308 := [unit-resolution #940 #287]: #1307
#1309 := [unit-resolution #1308 #1306]: #905
#1356 := (= #799 #23)
#800 := (= #23 #799)
decl uf_15 :: T4
#40 := uf_15
#41 := (uf_5 uf_15)
#814 := (+ #41 #813)
#815 := (<= #814 0::int)
#836 := (not #815)
#158 := (* -1::int #41)
#1270 := (+ #16 #158)
#1265 := (>= #1270 0::int)
#1339 := (not #1265)
#1269 := (= #16 #41)
#1298 := (not #1269)
#286 := (= uf_7 uf_15)
#44 := (uf_10 uf_15)
#72 := (uf_6 #44)
#73 := (= #72 uf_15)
#277 := (= uf_15 #72)
#278 := (iff #73 #277)
#279 := [rewrite]: #278
#276 := [asserted]: #73
#282 := [mp #276 #279]: #277
#1274 := [symm #282]: #73
#729 := (= uf_7 #72)
decl uf_17 :: (-> int T4)
#611 := (uf_5 #72)
#991 := (uf_17 #611)
#1289 := (= #991 #72)
#992 := (= #72 #991)
#55 := (:var 0 T4)
#56 := (uf_5 #55)
#574 := (pattern #56)
#57 := (uf_17 #56)
#177 := (= #55 #57)
#575 := (forall (vars (?x7 T4)) (:pat #574) #177)
#195 := (forall (vars (?x7 T4)) #177)
#578 := (iff #195 #575)
#576 := (iff #177 #177)
#577 := [refl]: #576
#579 := [quant-intro #577]: #578
#405 := (~ #195 #195)
#403 := (~ #177 #177)
#404 := [refl]: #403
#406 := [nnf-pos #404]: #405
#58 := (= #57 #55)
#59 := (forall (vars (?x7 T4)) #58)
#196 := (iff #59 #195)
#193 := (iff #58 #177)
#194 := [rewrite]: #193
#197 := [quant-intro #194]: #196
#155 := [asserted]: #59
#200 := [mp #155 #197]: #195
#407 := [mp~ #200 #406]: #195
#580 := [mp #407 #579]: #575
#995 := (not #575)
#996 := (or #995 #992)
#997 := [quant-inst]: #996
#1273 := [unit-resolution #997 #580]: #992
#1290 := [symm #1273]: #1289
#1293 := (= uf_7 #991)
#993 := (uf_17 #803)
#1287 := (= #993 #991)
#1284 := (= #803 #611)
#987 := (= #41 #611)
#1279 := (= #611 #41)
#1280 := [monotonicity #1274]: #1279
#1281 := [symm #1280]: #987
#1282 := (= #803 #41)
#1275 := [hypothesis]: #1269
#1283 := [trans #1278 #1275]: #1282
#1285 := [trans #1283 #1281]: #1284
#1288 := [monotonicity #1285]: #1287
#1291 := (= uf_7 #993)
#994 := (= #74 #993)
#1000 := (or #995 #994)
#1001 := [quant-inst]: #1000
#1286 := [unit-resolution #1001 #580]: #994
#1292 := [trans #287 #1286]: #1291
#1294 := [trans #1292 #1288]: #1293
#1295 := [trans #1294 #1290]: #729
#1296 := [trans #1295 #1274]: #286
#290 := (not #286)
#76 := (= uf_15 uf_7)
#77 := (not #76)
#291 := (iff #77 #290)
#288 := (iff #76 #286)
#289 := [rewrite]: #288
#292 := [monotonicity #289]: #291
#285 := [asserted]: #77
#295 := [mp #285 #292]: #290
#1297 := [unit-resolution #295 #1296]: false
#1299 := [lemma #1297]: #1298
#1342 := (or #1269 #1339)
#1271 := (<= #1270 0::int)
#621 := (* -1::int #611)
#723 := (+ #16 #621)
#724 := (<= #723 0::int)
decl uf_12 :: T1
#30 := uf_12
#88 := (uf_2 uf_12)
#771 := (uf_1 #88 #44)
#45 := (uf_1 uf_9 #44)
#772 := (= #45 #771)
#796 := (not #772)
decl uf_14 :: T1
#38 := uf_14
#83 := (uf_2 uf_14)
#656 := (uf_1 #83 #44)
#1239 := (= #656 #771)
#1252 := (not #1239)
#1324 := (iff #1252 #796)
#1322 := (iff #1239 #772)
#1320 := (= #656 #45)
#661 := (= #45 #656)
#659 := (uf_1 uf_11 #44)
#664 := (= #656 #659)
#667 := (ite #277 #661 #664)
#657 := (uf_1 uf_8 #44)
#670 := (= #656 #657)
#622 := (+ #41 #621)
#623 := (<= #622 0::int)
#673 := (ite #623 #667 #670)
#84 := (uf_1 #83 #6)
#560 := (pattern #84)
#467 := (= #19 #84)
#465 := (= #25 #84)
#464 := (= #45 #84)
#43 := (= #13 uf_15)
#466 := (ite #43 #464 #465)
#159 := (+ #14 #158)
#157 := (>= #159 0::int)
#468 := (ite #157 #466 #467)
#561 := (forall (vars (?x5 T2)) (:pat #541 #560 #543 #544) #468)
#471 := (forall (vars (?x5 T2)) #468)
#564 := (iff #471 #561)
#562 := (iff #468 #468)
#563 := [refl]: #562
#565 := [quant-intro #563]: #564
#46 := (ite #43 #45 #25)
#165 := (ite #157 #46 #19)
#378 := (= #84 #165)
#379 := (forall (vars (?x5 T2)) #378)
#472 := (iff #379 #471)
#469 := (iff #378 #468)
#470 := [rewrite]: #469
#473 := [quant-intro #470]: #472
#359 := (~ #379 #379)
#361 := (~ #378 #378)
#358 := [refl]: #361
#356 := [nnf-pos #358]: #359
#39 := (uf_3 uf_14 #6)
#170 := (= #39 #165)
#173 := (forall (vars (?x5 T2)) #170)
#380 := (iff #173 #379)
#381 := [rewrite* #113]: #380
#42 := (< #14 #41)
#47 := (ite #42 #19 #46)
#48 := (= #39 #47)
#49 := (forall (vars (?x5 T2)) #48)
#174 := (iff #49 #173)
#171 := (iff #48 #170)
#168 := (= #47 #165)
#156 := (not #157)
#162 := (ite #156 #19 #46)
#166 := (= #162 #165)
#167 := [rewrite]: #166
#163 := (= #47 #162)
#160 := (iff #42 #156)
#161 := [rewrite]: #160
#164 := [monotonicity #161]: #163
#169 := [trans #164 #167]: #168
#172 := [monotonicity #169]: #171
#175 := [quant-intro #172]: #174
#116 := [asserted]: #49
#176 := [mp #116 #175]: #173
#382 := [mp #176 #381]: #379
#357 := [mp~ #382 #356]: #379
#474 := [mp #357 #473]: #471
#566 := [mp #474 #565]: #561
#676 := (not #561)
#677 := (or #676 #673)
#658 := (= #657 #656)
#660 := (= #659 #656)
#662 := (ite #73 #661 #660)
#612 := (+ #611 #158)
#613 := (>= #612 0::int)
#663 := (ite #613 #662 #658)
#678 := (or #676 #663)
#680 := (iff #678 #677)
#682 := (iff #677 #677)
#683 := [rewrite]: #682
#674 := (iff #663 #673)
#671 := (iff #658 #670)
#672 := [rewrite]: #671
#668 := (iff #662 #667)
#665 := (iff #660 #664)
#666 := [rewrite]: #665
#669 := [monotonicity #279 #666]: #668
#626 := (iff #613 #623)
#615 := (+ #158 #611)
#618 := (>= #615 0::int)
#624 := (iff #618 #623)
#625 := [rewrite]: #624
#619 := (iff #613 #618)
#616 := (= #612 #615)
#617 := [rewrite]: #616
#620 := [monotonicity #617]: #619
#627 := [trans #620 #625]: #626
#675 := [monotonicity #627 #669 #672]: #674
#681 := [monotonicity #675]: #680
#684 := [trans #681 #683]: #680
#679 := [quant-inst]: #678
#685 := [mp #679 #684]: #677
#1311 := [unit-resolution #685 #566]: #673
#1312 := (not #987)
#1313 := (or #1312 #623)
#1314 := [th-lemma]: #1313
#1315 := [unit-resolution #1314 #1281]: #623
#645 := (not #623)
#698 := (not #673)
#699 := (or #698 #645 #667)
#700 := [def-axiom]: #699
#1316 := [unit-resolution #700 #1315 #1311]: #667
#686 := (not #667)
#1317 := (or #686 #661)
#687 := (not #277)
#688 := (or #686 #687 #661)
#689 := [def-axiom]: #688
#1318 := [unit-resolution #689 #282]: #1317
#1319 := [unit-resolution #1318 #1316]: #661
#1321 := [symm #1319]: #1320
#1323 := [monotonicity #1321]: #1322
#1325 := [monotonicity #1323]: #1324
#1145 := (* -1::real #771)
#1240 := (+ #656 #1145)
#1241 := (<= #1240 0::real)
#1249 := (not #1241)
#1243 := [hypothesis]: #1241
decl uf_18 :: T3
#80 := uf_18
#1040 := (uf_1 uf_18 #44)
#1043 := (* -1::real #1040)
#1156 := (+ #771 #1043)
#1157 := (>= #1156 0::real)
#1189 := (not #1157)
#708 := (uf_1 #91 #44)
#1168 := (+ #708 #1043)
#1169 := (<= #1168 0::real)
#1174 := (or #1157 #1169)
#1177 := (not #1174)
#89 := (uf_1 #88 #6)
#552 := (pattern #89)
#81 := (uf_1 uf_18 #6)
#594 := (pattern #81)
#324 := (* -1::real #92)
#325 := (+ #81 #324)
#323 := (>= #325 0::real)
#317 := (* -1::real #89)
#318 := (+ #81 #317)
#319 := (<= #318 0::real)
#436 := (or #319 #323)
#437 := (not #436)
#601 := (forall (vars (?x11 T2)) (:pat #594 #552 #542) #437)
#440 := (forall (vars (?x11 T2)) #437)
#604 := (iff #440 #601)
#602 := (iff #437 #437)
#603 := [refl]: #602
#605 := [quant-intro #603]: #604
#326 := (not #323)
#320 := (not #319)
#329 := (and #320 #326)
#332 := (forall (vars (?x11 T2)) #329)
#441 := (iff #332 #440)
#438 := (iff #329 #437)
#439 := [rewrite]: #438
#442 := [quant-intro #439]: #441
#425 := (~ #332 #332)
#423 := (~ #329 #329)
#424 := [refl]: #423
#426 := [nnf-pos #424]: #425
#306 := (* -1::real #84)
#307 := (+ #81 #306)
#305 := (>= #307 0::real)
#308 := (not #305)
#301 := (* -1::real #81)
#79 := (uf_1 #78 #6)
#302 := (+ #79 #301)
#300 := (>= #302 0::real)
#298 := (not #300)
#311 := (and #298 #308)
#314 := (forall (vars (?x10 T2)) #311)
#335 := (and #314 #332)
#93 := (< #81 #92)
#90 := (< #89 #81)
#94 := (and #90 #93)
#95 := (forall (vars (?x11 T2)) #94)
#85 := (< #81 #84)
#82 := (< #79 #81)
#86 := (and #82 #85)
#87 := (forall (vars (?x10 T2)) #86)
#96 := (and #87 #95)
#336 := (iff #96 #335)
#333 := (iff #95 #332)
#330 := (iff #94 #329)
#327 := (iff #93 #326)
#328 := [rewrite]: #327
#321 := (iff #90 #320)
#322 := [rewrite]: #321
#331 := [monotonicity #322 #328]: #330
#334 := [quant-intro #331]: #333
#315 := (iff #87 #314)
#312 := (iff #86 #311)
#309 := (iff #85 #308)
#310 := [rewrite]: #309
#303 := (iff #82 #298)
#304 := [rewrite]: #303
#313 := [monotonicity #304 #310]: #312
#316 := [quant-intro #313]: #315
#337 := [monotonicity #316 #334]: #336
#293 := [asserted]: #96
#338 := [mp #293 #337]: #335
#340 := [and-elim #338]: #332
#427 := [mp~ #340 #426]: #332
#443 := [mp #427 #442]: #440
#606 := [mp #443 #605]: #601
#1124 := (not #601)
#1180 := (or #1124 #1177)
#1142 := (* -1::real #708)
#1143 := (+ #1040 #1142)
#1144 := (>= #1143 0::real)
#1146 := (+ #1040 #1145)
#1147 := (<= #1146 0::real)
#1148 := (or #1147 #1144)
#1149 := (not #1148)
#1181 := (or #1124 #1149)
#1183 := (iff #1181 #1180)
#1185 := (iff #1180 #1180)
#1186 := [rewrite]: #1185
#1178 := (iff #1149 #1177)
#1175 := (iff #1148 #1174)
#1172 := (iff #1144 #1169)
#1162 := (+ #1142 #1040)
#1165 := (>= #1162 0::real)
#1170 := (iff #1165 #1169)
#1171 := [rewrite]: #1170
#1166 := (iff #1144 #1165)
#1163 := (= #1143 #1162)
#1164 := [rewrite]: #1163
#1167 := [monotonicity #1164]: #1166
#1173 := [trans #1167 #1171]: #1172
#1160 := (iff #1147 #1157)
#1150 := (+ #1145 #1040)
#1153 := (<= #1150 0::real)
#1158 := (iff #1153 #1157)
#1159 := [rewrite]: #1158
#1154 := (iff #1147 #1153)
#1151 := (= #1146 #1150)
#1152 := [rewrite]: #1151
#1155 := [monotonicity #1152]: #1154
#1161 := [trans #1155 #1159]: #1160
#1176 := [monotonicity #1161 #1173]: #1175
#1179 := [monotonicity #1176]: #1178
#1184 := [monotonicity #1179]: #1183
#1187 := [trans #1184 #1186]: #1183
#1182 := [quant-inst]: #1181
#1188 := [mp #1182 #1187]: #1180
#1244 := [unit-resolution #1188 #606]: #1177
#1190 := (or #1174 #1189)
#1191 := [def-axiom]: #1190
#1245 := [unit-resolution #1191 #1244]: #1189
#1054 := (+ #656 #1043)
#1055 := (<= #1054 0::real)
#1079 := (not #1055)
#607 := (uf_1 #78 #44)
#1044 := (+ #607 #1043)
#1045 := (>= #1044 0::real)
#1060 := (or #1045 #1055)
#1063 := (not #1060)
#567 := (pattern #79)
#428 := (or #300 #305)
#429 := (not #428)
#595 := (forall (vars (?x10 T2)) (:pat #567 #594 #560) #429)
#432 := (forall (vars (?x10 T2)) #429)
#598 := (iff #432 #595)
#596 := (iff #429 #429)
#597 := [refl]: #596
#599 := [quant-intro #597]: #598
#433 := (iff #314 #432)
#430 := (iff #311 #429)
#431 := [rewrite]: #430
#434 := [quant-intro #431]: #433
#420 := (~ #314 #314)
#418 := (~ #311 #311)
#419 := [refl]: #418
#421 := [nnf-pos #419]: #420
#339 := [and-elim #338]: #314
#422 := [mp~ #339 #421]: #314
#435 := [mp #422 #434]: #432
#600 := [mp #435 #599]: #595
#1066 := (not #595)
#1067 := (or #1066 #1063)
#1039 := (* -1::real #656)
#1041 := (+ #1040 #1039)
#1042 := (>= #1041 0::real)
#1046 := (or #1045 #1042)
#1047 := (not #1046)
#1068 := (or #1066 #1047)
#1070 := (iff #1068 #1067)
#1072 := (iff #1067 #1067)
#1073 := [rewrite]: #1072
#1064 := (iff #1047 #1063)
#1061 := (iff #1046 #1060)
#1058 := (iff #1042 #1055)
#1048 := (+ #1039 #1040)
#1051 := (>= #1048 0::real)
#1056 := (iff #1051 #1055)
#1057 := [rewrite]: #1056
#1052 := (iff #1042 #1051)
#1049 := (= #1041 #1048)
#1050 := [rewrite]: #1049
#1053 := [monotonicity #1050]: #1052
#1059 := [trans #1053 #1057]: #1058
#1062 := [monotonicity #1059]: #1061
#1065 := [monotonicity #1062]: #1064
#1071 := [monotonicity #1065]: #1070
#1074 := [trans #1071 #1073]: #1070
#1069 := [quant-inst]: #1068
#1075 := [mp #1069 #1074]: #1067
#1246 := [unit-resolution #1075 #600]: #1063
#1080 := (or #1060 #1079)
#1081 := [def-axiom]: #1080
#1247 := [unit-resolution #1081 #1246]: #1079
#1248 := [th-lemma #1247 #1245 #1243]: false
#1250 := [lemma #1248]: #1249
#1253 := (or #1252 #1241)
#1254 := [th-lemma]: #1253
#1310 := [unit-resolution #1254 #1250]: #1252
#1326 := [mp #1310 #1325]: #796
#1328 := (or #724 #772)
decl uf_13 :: T3
#33 := uf_13
#609 := (uf_1 uf_13 #44)
#773 := (= #609 #771)
#775 := (ite #724 #773 #772)
#32 := (uf_1 uf_9 #6)
#553 := (pattern #32)
#34 := (uf_1 uf_13 #6)
#551 := (pattern #34)
#456 := (= #32 #89)
#455 := (= #34 #89)
#457 := (ite #119 #455 #456)
#554 := (forall (vars (?x4 T2)) (:pat #541 #551 #552 #553) #457)
#460 := (forall (vars (?x4 T2)) #457)
#557 := (iff #460 #554)
#555 := (iff #457 #457)
#556 := [refl]: #555
#558 := [quant-intro #556]: #557
#143 := (ite #119 #34 #32)
#373 := (= #89 #143)
#374 := (forall (vars (?x4 T2)) #373)
#461 := (iff #374 #460)
#458 := (iff #373 #457)
#459 := [rewrite]: #458
#462 := [quant-intro #459]: #461
#362 := (~ #374 #374)
#364 := (~ #373 #373)
#365 := [refl]: #364
#363 := [nnf-pos #365]: #362
#31 := (uf_3 uf_12 #6)
#148 := (= #31 #143)
#151 := (forall (vars (?x4 T2)) #148)
#375 := (iff #151 #374)
#376 := [rewrite* #113]: #375
#35 := (ite #17 #32 #34)
#36 := (= #31 #35)
#37 := (forall (vars (?x4 T2)) #36)
#152 := (iff #37 #151)
#149 := (iff #36 #148)
#146 := (= #35 #143)
#140 := (ite #118 #32 #34)
#144 := (= #140 #143)
#145 := [rewrite]: #144
#141 := (= #35 #140)
#142 := [monotonicity #123]: #141
#147 := [trans #142 #145]: #146
#150 := [monotonicity #147]: #149
#153 := [quant-intro #150]: #152
#115 := [asserted]: #37
#154 := [mp #115 #153]: #151
#377 := [mp #154 #376]: #374
#360 := [mp~ #377 #363]: #374
#463 := [mp #360 #462]: #460
#559 := [mp #463 #558]: #554
#778 := (not #554)
#779 := (or #778 #775)
#714 := (+ #611 #120)
#715 := (>= #714 0::int)
#774 := (ite #715 #773 #772)
#780 := (or #778 #774)
#782 := (iff #780 #779)
#784 := (iff #779 #779)
#785 := [rewrite]: #784
#776 := (iff #774 #775)
#727 := (iff #715 #724)
#717 := (+ #120 #611)
#720 := (>= #717 0::int)
#725 := (iff #720 #724)
#726 := [rewrite]: #725
#721 := (iff #715 #720)
#718 := (= #714 #717)
#719 := [rewrite]: #718
#722 := [monotonicity #719]: #721
#728 := [trans #722 #726]: #727
#777 := [monotonicity #728]: #776
#783 := [monotonicity #777]: #782
#786 := [trans #783 #785]: #782
#781 := [quant-inst]: #780
#787 := [mp #781 #786]: #779
#1327 := [unit-resolution #787 #559]: #775
#788 := (not #775)
#791 := (or #788 #724 #772)
#792 := [def-axiom]: #791
#1329 := [unit-resolution #792 #1327]: #1328
#1330 := [unit-resolution #1329 #1326]: #724
#988 := (>= #622 0::int)
#1331 := (or #1312 #988)
#1332 := [th-lemma]: #1331
#1333 := [unit-resolution #1332 #1281]: #988
#761 := (not #724)
#1334 := (not #988)
#1335 := (or #1271 #1334 #761)
#1336 := [th-lemma]: #1335
#1337 := [unit-resolution #1336 #1333 #1330]: #1271
#1338 := (not #1271)
#1340 := (or #1269 #1338 #1339)
#1341 := [th-lemma]: #1340
#1343 := [unit-resolution #1341 #1337]: #1342
#1344 := [unit-resolution #1343 #1299]: #1339
#990 := (>= #916 0::int)
#1345 := (or #1302 #990)
#1346 := [th-lemma]: #1345
#1347 := [unit-resolution #1346 #1301]: #990
#1348 := (not #990)
#1349 := (or #836 #1348 #1265)
#1350 := [th-lemma]: #1349
#1351 := [unit-resolution #1350 #1347 #1344]: #836
#1353 := (or #815 #800)
#801 := (uf_1 uf_13 #22)
#820 := (= #799 #801)
#823 := (ite #815 #820 #800)
#476 := (= #32 #79)
#475 := (= #34 #79)
#477 := (ite #157 #475 #476)
#568 := (forall (vars (?x6 T2)) (:pat #541 #551 #567 #553) #477)
#480 := (forall (vars (?x6 T2)) #477)
#571 := (iff #480 #568)
#569 := (iff #477 #477)
#570 := [refl]: #569
#572 := [quant-intro #570]: #571
#181 := (ite #157 #34 #32)
#383 := (= #79 #181)
#384 := (forall (vars (?x6 T2)) #383)
#481 := (iff #384 #480)
#478 := (iff #383 #477)
#479 := [rewrite]: #478
#482 := [quant-intro #479]: #481
#352 := (~ #384 #384)
#354 := (~ #383 #383)
#355 := [refl]: #354
#353 := [nnf-pos #355]: #352
#51 := (uf_3 uf_16 #6)
#186 := (= #51 #181)
#189 := (forall (vars (?x6 T2)) #186)
#385 := (iff #189 #384)
#386 := [rewrite* #113]: #385
#52 := (ite #42 #32 #34)
#53 := (= #51 #52)
#54 := (forall (vars (?x6 T2)) #53)
#190 := (iff #54 #189)
#187 := (iff #53 #186)
#184 := (= #52 #181)
#178 := (ite #156 #32 #34)
#182 := (= #178 #181)
#183 := [rewrite]: #182
#179 := (= #52 #178)
#180 := [monotonicity #161]: #179
#185 := [trans #180 #183]: #184
#188 := [monotonicity #185]: #187
#191 := [quant-intro #188]: #190
#139 := [asserted]: #54
#192 := [mp #139 #191]: #189
#387 := [mp #192 #386]: #384
#402 := [mp~ #387 #353]: #384
#483 := [mp #402 #482]: #480
#573 := [mp #483 #572]: #568
#634 := (not #568)
#826 := (or #634 #823)
#802 := (= #801 #799)
#804 := (+ #803 #158)
#805 := (>= #804 0::int)
#806 := (ite #805 #802 #800)
#827 := (or #634 #806)
#829 := (iff #827 #826)
#831 := (iff #826 #826)
#832 := [rewrite]: #831
#824 := (iff #806 #823)
#821 := (iff #802 #820)
#822 := [rewrite]: #821
#818 := (iff #805 #815)
#807 := (+ #158 #803)
#810 := (>= #807 0::int)
#816 := (iff #810 #815)
#817 := [rewrite]: #816
#811 := (iff #805 #810)
#808 := (= #804 #807)
#809 := [rewrite]: #808
#812 := [monotonicity #809]: #811
#819 := [trans #812 #817]: #818
#825 := [monotonicity #819 #822]: #824
#830 := [monotonicity #825]: #829
#833 := [trans #830 #832]: #829
#828 := [quant-inst]: #827
#834 := [mp #828 #833]: #826
#1352 := [unit-resolution #834 #573]: #823
#835 := (not #823)
#839 := (or #835 #815 #800)
#840 := [def-axiom]: #839
#1354 := [unit-resolution #840 #1352]: #1353
#1355 := [unit-resolution #1354 #1351]: #800
#1357 := [symm #1355]: #1356
#1358 := [trans #1357 #1309]: #1266
#1359 := (not #1266)
#1360 := (or #1359 #1272)
#1361 := [th-lemma]: #1360
#1362 := [unit-resolution #1361 #1358]: #1272
#1085 := (uf_1 uf_18 #22)
#1099 := (* -1::real #1085)
#1112 := (+ #902 #1099)
#1113 := (<= #1112 0::real)
#1137 := (not #1113)
#960 := (uf_1 #88 #22)
#1100 := (+ #960 #1099)
#1101 := (>= #1100 0::real)
#1118 := (or #1101 #1113)
#1121 := (not #1118)
#1125 := (or #1124 #1121)
#1086 := (+ #1085 #1084)
#1087 := (>= #1086 0::real)
#1088 := (* -1::real #960)
#1089 := (+ #1085 #1088)
#1090 := (<= #1089 0::real)
#1091 := (or #1090 #1087)
#1092 := (not #1091)
#1126 := (or #1124 #1092)
#1128 := (iff #1126 #1125)
#1130 := (iff #1125 #1125)
#1131 := [rewrite]: #1130
#1122 := (iff #1092 #1121)
#1119 := (iff #1091 #1118)
#1116 := (iff #1087 #1113)
#1106 := (+ #1084 #1085)
#1109 := (>= #1106 0::real)
#1114 := (iff #1109 #1113)
#1115 := [rewrite]: #1114
#1110 := (iff #1087 #1109)
#1107 := (= #1086 #1106)
#1108 := [rewrite]: #1107
#1111 := [monotonicity #1108]: #1110
#1117 := [trans #1111 #1115]: #1116
#1104 := (iff #1090 #1101)
#1093 := (+ #1088 #1085)
#1096 := (<= #1093 0::real)
#1102 := (iff #1096 #1101)
#1103 := [rewrite]: #1102
#1097 := (iff #1090 #1096)
#1094 := (= #1089 #1093)
#1095 := [rewrite]: #1094
#1098 := [monotonicity #1095]: #1097
#1105 := [trans #1098 #1103]: #1104
#1120 := [monotonicity #1105 #1117]: #1119
#1123 := [monotonicity #1120]: #1122
#1129 := [monotonicity #1123]: #1128
#1132 := [trans #1129 #1131]: #1128
#1127 := [quant-inst]: #1126
#1133 := [mp #1127 #1132]: #1125
#1363 := [unit-resolution #1133 #606]: #1121
#1138 := (or #1118 #1137)
#1139 := [def-axiom]: #1138
#1364 := [unit-resolution #1139 #1363]: #1137
#1200 := (+ #799 #1099)
#1201 := (>= #1200 0::real)
#1231 := (not #1201)
#847 := (uf_1 #83 #22)
#1210 := (+ #847 #1099)
#1211 := (<= #1210 0::real)
#1216 := (or #1201 #1211)
#1219 := (not #1216)
#1222 := (or #1066 #1219)
#1197 := (* -1::real #847)
#1198 := (+ #1085 #1197)
#1199 := (>= #1198 0::real)
#1202 := (or #1201 #1199)
#1203 := (not #1202)
#1223 := (or #1066 #1203)
#1225 := (iff #1223 #1222)
#1227 := (iff #1222 #1222)
#1228 := [rewrite]: #1227
#1220 := (iff #1203 #1219)
#1217 := (iff #1202 #1216)
#1214 := (iff #1199 #1211)
#1204 := (+ #1197 #1085)
#1207 := (>= #1204 0::real)
#1212 := (iff #1207 #1211)
#1213 := [rewrite]: #1212
#1208 := (iff #1199 #1207)
#1205 := (= #1198 #1204)
#1206 := [rewrite]: #1205
#1209 := [monotonicity #1206]: #1208
#1215 := [trans #1209 #1213]: #1214
#1218 := [monotonicity #1215]: #1217
#1221 := [monotonicity #1218]: #1220
#1226 := [monotonicity #1221]: #1225
#1229 := [trans #1226 #1228]: #1225
#1224 := [quant-inst]: #1223
#1230 := [mp #1224 #1229]: #1222
#1365 := [unit-resolution #1230 #600]: #1219
#1232 := (or #1216 #1231)
#1233 := [def-axiom]: #1232
#1366 := [unit-resolution #1233 #1365]: #1231
[th-lemma #1366 #1364 #1362]: false
unsat
NQHwTeL311Tq3wf2s5BReA 419 0
#2 := false
#194 := 0::real
decl uf_4 :: (-> T2 T3 real)
decl uf_6 :: (-> T1 T3)
decl uf_3 :: T1
#21 := uf_3
#25 := (uf_6 uf_3)
decl uf_5 :: T2
#24 := uf_5
#26 := (uf_4 uf_5 #25)
decl uf_7 :: T2
#27 := uf_7
#28 := (uf_4 uf_7 #25)
decl uf_10 :: T1
#38 := uf_10
#42 := (uf_6 uf_10)
decl uf_9 :: T2
#33 := uf_9
#43 := (uf_4 uf_9 #42)
#41 := (= uf_3 uf_10)
#44 := (ite #41 #43 #28)
#9 := 0::int
decl uf_2 :: (-> T1 int)
#39 := (uf_2 uf_10)
#226 := -1::int
#229 := (* -1::int #39)
#22 := (uf_2 uf_3)
#230 := (+ #22 #229)
#228 := (>= #230 0::int)
#236 := (ite #228 #44 #26)
#192 := -1::real
#244 := (* -1::real #236)
#642 := (+ #26 #244)
#643 := (<= #642 0::real)
#567 := (= #26 #236)
#227 := (not #228)
decl uf_1 :: (-> int T1)
#593 := (uf_1 #39)
#660 := (= #593 uf_10)
#594 := (= uf_10 #593)
#4 := (:var 0 T1)
#5 := (uf_2 #4)
#546 := (pattern #5)
#6 := (uf_1 #5)
#93 := (= #4 #6)
#547 := (forall (vars (?x1 T1)) (:pat #546) #93)
#96 := (forall (vars (?x1 T1)) #93)
#550 := (iff #96 #547)
#548 := (iff #93 #93)
#549 := [refl]: #548
#551 := [quant-intro #549]: #550
#448 := (~ #96 #96)
#450 := (~ #93 #93)
#451 := [refl]: #450
#449 := [nnf-pos #451]: #448
#7 := (= #6 #4)
#8 := (forall (vars (?x1 T1)) #7)
#97 := (iff #8 #96)
#94 := (iff #7 #93)
#95 := [rewrite]: #94
#98 := [quant-intro #95]: #97
#92 := [asserted]: #8
#101 := [mp #92 #98]: #96
#446 := [mp~ #101 #449]: #96
#552 := [mp #446 #551]: #547
#595 := (not #547)
#600 := (or #595 #594)
#601 := [quant-inst]: #600
#654 := [unit-resolution #601 #552]: #594
#680 := [symm #654]: #660
#681 := (= uf_3 #593)
#591 := (uf_1 #22)
#658 := (= #591 #593)
#656 := (= #593 #591)
#652 := (= #39 #22)
#647 := (= #22 #39)
#290 := (<= #230 0::int)
#70 := (<= #22 #39)
#388 := (iff #70 #290)
#389 := [rewrite]: #388
#341 := [asserted]: #70
#390 := [mp #341 #389]: #290
#646 := [hypothesis]: #228
#648 := [th-lemma #646 #390]: #647
#653 := [symm #648]: #652
#657 := [monotonicity #653]: #656
#659 := [symm #657]: #658
#592 := (= uf_3 #591)
#596 := (or #595 #592)
#597 := [quant-inst]: #596
#655 := [unit-resolution #597 #552]: #592
#682 := [trans #655 #659]: #681
#683 := [trans #682 #680]: #41
#570 := (not #41)
decl uf_11 :: T2
#47 := uf_11
#59 := (uf_4 uf_11 #42)
#278 := (ite #41 #26 #59)
#459 := (* -1::real #278)
#637 := (+ #26 #459)
#639 := (>= #637 0::real)
#585 := (= #26 #278)
#661 := [hypothesis]: #41
#587 := (or #570 #585)
#588 := [def-axiom]: #587
#662 := [unit-resolution #588 #661]: #585
#663 := (not #585)
#664 := (or #663 #639)
#665 := [th-lemma]: #664
#666 := [unit-resolution #665 #662]: #639
decl uf_8 :: T2
#30 := uf_8
#56 := (uf_4 uf_8 #42)
#357 := (* -1::real #56)
#358 := (+ #43 #357)
#356 := (>= #358 0::real)
#355 := (not #356)
#374 := (* -1::real #59)
#375 := (+ #56 #374)
#373 := (>= #375 0::real)
#376 := (not #373)
#381 := (and #355 #376)
#64 := (< #39 #39)
#67 := (ite #64 #43 #59)
#68 := (< #56 #67)
#53 := (uf_4 uf_5 #42)
#65 := (ite #64 #53 #43)
#66 := (< #65 #56)
#69 := (and #66 #68)
#382 := (iff #69 #381)
#379 := (iff #68 #376)
#370 := (< #56 #59)
#377 := (iff #370 #376)
#378 := [rewrite]: #377
#371 := (iff #68 #370)
#368 := (= #67 #59)
#363 := (ite false #43 #59)
#366 := (= #363 #59)
#367 := [rewrite]: #366
#364 := (= #67 #363)
#343 := (iff #64 false)
#344 := [rewrite]: #343
#365 := [monotonicity #344]: #364
#369 := [trans #365 #367]: #368
#372 := [monotonicity #369]: #371
#380 := [trans #372 #378]: #379
#361 := (iff #66 #355)
#352 := (< #43 #56)
#359 := (iff #352 #355)
#360 := [rewrite]: #359
#353 := (iff #66 #352)
#350 := (= #65 #43)
#345 := (ite false #53 #43)
#348 := (= #345 #43)
#349 := [rewrite]: #348
#346 := (= #65 #345)
#347 := [monotonicity #344]: #346
#351 := [trans #347 #349]: #350
#354 := [monotonicity #351]: #353
#362 := [trans #354 #360]: #361
#383 := [monotonicity #362 #380]: #382
#340 := [asserted]: #69
#384 := [mp #340 #383]: #381
#385 := [and-elim #384]: #355
#394 := (* -1::real #53)
#395 := (+ #43 #394)
#393 := (>= #395 0::real)
#54 := (uf_4 uf_7 #42)
#402 := (* -1::real #54)
#403 := (+ #53 #402)
#401 := (>= #403 0::real)
#397 := (+ #43 #374)
#398 := (<= #397 0::real)
#412 := (and #393 #398 #401)
#73 := (<= #43 #59)
#72 := (<= #53 #43)
#74 := (and #72 #73)
#71 := (<= #54 #53)
#75 := (and #71 #74)
#415 := (iff #75 #412)
#406 := (and #393 #398)
#409 := (and #401 #406)
#413 := (iff #409 #412)
#414 := [rewrite]: #413
#410 := (iff #75 #409)
#407 := (iff #74 #406)
#399 := (iff #73 #398)
#400 := [rewrite]: #399
#392 := (iff #72 #393)
#396 := [rewrite]: #392
#408 := [monotonicity #396 #400]: #407
#404 := (iff #71 #401)
#405 := [rewrite]: #404
#411 := [monotonicity #405 #408]: #410
#416 := [trans #411 #414]: #415
#342 := [asserted]: #75
#417 := [mp #342 #416]: #412
#418 := [and-elim #417]: #393
#650 := (+ #26 #394)
#651 := (<= #650 0::real)
#649 := (= #26 #53)
#671 := (= #53 #26)
#669 := (= #42 #25)
#667 := (= #25 #42)
#668 := [monotonicity #661]: #667
#670 := [symm #668]: #669
#672 := [monotonicity #670]: #671
#673 := [symm #672]: #649
#674 := (not #649)
#675 := (or #674 #651)
#676 := [th-lemma]: #675
#677 := [unit-resolution #676 #673]: #651
#462 := (+ #56 #459)
#465 := (>= #462 0::real)
#438 := (not #465)
#316 := (ite #290 #278 #43)
#326 := (* -1::real #316)
#327 := (+ #56 #326)
#325 := (>= #327 0::real)
#324 := (not #325)
#439 := (iff #324 #438)
#466 := (iff #325 #465)
#463 := (= #327 #462)
#460 := (= #326 #459)
#457 := (= #316 #278)
#1 := true
#452 := (ite true #278 #43)
#455 := (= #452 #278)
#456 := [rewrite]: #455
#453 := (= #316 #452)
#444 := (iff #290 true)
#445 := [iff-true #390]: #444
#454 := [monotonicity #445]: #453
#458 := [trans #454 #456]: #457
#461 := [monotonicity #458]: #460
#464 := [monotonicity #461]: #463
#467 := [monotonicity #464]: #466
#468 := [monotonicity #467]: #439
#297 := (ite #290 #54 #53)
#305 := (* -1::real #297)
#306 := (+ #56 #305)
#307 := (<= #306 0::real)
#308 := (not #307)
#332 := (and #308 #324)
#58 := (= uf_10 uf_3)
#60 := (ite #58 #26 #59)
#52 := (< #39 #22)
#61 := (ite #52 #43 #60)
#62 := (< #56 #61)
#55 := (ite #52 #53 #54)
#57 := (< #55 #56)
#63 := (and #57 #62)
#335 := (iff #63 #332)
#281 := (ite #52 #43 #278)
#284 := (< #56 #281)
#287 := (and #57 #284)
#333 := (iff #287 #332)
#330 := (iff #284 #324)
#321 := (< #56 #316)
#328 := (iff #321 #324)
#329 := [rewrite]: #328
#322 := (iff #284 #321)
#319 := (= #281 #316)
#291 := (not #290)
#313 := (ite #291 #43 #278)
#317 := (= #313 #316)
#318 := [rewrite]: #317
#314 := (= #281 #313)
#292 := (iff #52 #291)
#293 := [rewrite]: #292
#315 := [monotonicity #293]: #314
#320 := [trans #315 #318]: #319
#323 := [monotonicity #320]: #322
#331 := [trans #323 #329]: #330
#311 := (iff #57 #308)
#302 := (< #297 #56)
#309 := (iff #302 #308)
#310 := [rewrite]: #309
#303 := (iff #57 #302)
#300 := (= #55 #297)
#294 := (ite #291 #53 #54)
#298 := (= #294 #297)
#299 := [rewrite]: #298
#295 := (= #55 #294)
#296 := [monotonicity #293]: #295
#301 := [trans #296 #299]: #300
#304 := [monotonicity #301]: #303
#312 := [trans #304 #310]: #311
#334 := [monotonicity #312 #331]: #333
#288 := (iff #63 #287)
#285 := (iff #62 #284)
#282 := (= #61 #281)
#279 := (= #60 #278)
#225 := (iff #58 #41)
#277 := [rewrite]: #225
#280 := [monotonicity #277]: #279
#283 := [monotonicity #280]: #282
#286 := [monotonicity #283]: #285
#289 := [monotonicity #286]: #288
#336 := [trans #289 #334]: #335
#179 := [asserted]: #63
#337 := [mp #179 #336]: #332
#339 := [and-elim #337]: #324
#469 := [mp #339 #468]: #438
#678 := [th-lemma #469 #677 #418 #385 #666]: false
#679 := [lemma #678]: #570
#684 := [unit-resolution #679 #683]: false
#685 := [lemma #684]: #227
#577 := (or #228 #567)
#578 := [def-axiom]: #577
#645 := [unit-resolution #578 #685]: #567
#686 := (not #567)
#687 := (or #686 #643)
#688 := [th-lemma]: #687
#689 := [unit-resolution #688 #645]: #643
#31 := (uf_4 uf_8 #25)
#245 := (+ #31 #244)
#246 := (<= #245 0::real)
#247 := (not #246)
#34 := (uf_4 uf_9 #25)
#48 := (uf_4 uf_11 #25)
#255 := (ite #228 #48 #34)
#264 := (* -1::real #255)
#265 := (+ #31 #264)
#263 := (>= #265 0::real)
#266 := (not #263)
#271 := (and #247 #266)
#40 := (< #22 #39)
#49 := (ite #40 #34 #48)
#50 := (< #31 #49)
#45 := (ite #40 #26 #44)
#46 := (< #45 #31)
#51 := (and #46 #50)
#272 := (iff #51 #271)
#269 := (iff #50 #266)
#260 := (< #31 #255)
#267 := (iff #260 #266)
#268 := [rewrite]: #267
#261 := (iff #50 #260)
#258 := (= #49 #255)
#252 := (ite #227 #34 #48)
#256 := (= #252 #255)
#257 := [rewrite]: #256
#253 := (= #49 #252)
#231 := (iff #40 #227)
#232 := [rewrite]: #231
#254 := [monotonicity #232]: #253
#259 := [trans #254 #257]: #258
#262 := [monotonicity #259]: #261
#270 := [trans #262 #268]: #269
#250 := (iff #46 #247)
#241 := (< #236 #31)
#248 := (iff #241 #247)
#249 := [rewrite]: #248
#242 := (iff #46 #241)
#239 := (= #45 #236)
#233 := (ite #227 #26 #44)
#237 := (= #233 #236)
#238 := [rewrite]: #237
#234 := (= #45 #233)
#235 := [monotonicity #232]: #234
#240 := [trans #235 #238]: #239
#243 := [monotonicity #240]: #242
#251 := [trans #243 #249]: #250
#273 := [monotonicity #251 #270]: #272
#178 := [asserted]: #51
#274 := [mp #178 #273]: #271
#275 := [and-elim #274]: #247
#196 := (* -1::real #31)
#212 := (+ #26 #196)
#213 := (<= #212 0::real)
#214 := (not #213)
#197 := (+ #28 #196)
#195 := (>= #197 0::real)
#193 := (not #195)
#219 := (and #193 #214)
#23 := (< #22 #22)
#35 := (ite #23 #34 #26)
#36 := (< #31 #35)
#29 := (ite #23 #26 #28)
#32 := (< #29 #31)
#37 := (and #32 #36)
#220 := (iff #37 #219)
#217 := (iff #36 #214)
#209 := (< #31 #26)
#215 := (iff #209 #214)
#216 := [rewrite]: #215
#210 := (iff #36 #209)
#207 := (= #35 #26)
#202 := (ite false #34 #26)
#205 := (= #202 #26)
#206 := [rewrite]: #205
#203 := (= #35 #202)
#180 := (iff #23 false)
#181 := [rewrite]: #180
#204 := [monotonicity #181]: #203
#208 := [trans #204 #206]: #207
#211 := [monotonicity #208]: #210
#218 := [trans #211 #216]: #217
#200 := (iff #32 #193)
#189 := (< #28 #31)
#198 := (iff #189 #193)
#199 := [rewrite]: #198
#190 := (iff #32 #189)
#187 := (= #29 #28)
#182 := (ite false #26 #28)
#185 := (= #182 #28)
#186 := [rewrite]: #185
#183 := (= #29 #182)
#184 := [monotonicity #181]: #183
#188 := [trans #184 #186]: #187
#191 := [monotonicity #188]: #190
#201 := [trans #191 #199]: #200
#221 := [monotonicity #201 #218]: #220
#177 := [asserted]: #37
#222 := [mp #177 #221]: #219
#224 := [and-elim #222]: #214
[th-lemma #224 #275 #689]: false
unsat
NX/HT1QOfbspC2LtZNKpBA 428 0
#2 := false
decl uf_10 :: T1
#38 := uf_10
decl uf_3 :: T1
#21 := uf_3
#45 := (= uf_3 uf_10)
decl uf_1 :: (-> int T1)
decl uf_2 :: (-> T1 int)
#39 := (uf_2 uf_10)
#588 := (uf_1 #39)
#686 := (= #588 uf_10)
#589 := (= uf_10 #588)
#4 := (:var 0 T1)
#5 := (uf_2 #4)
#541 := (pattern #5)
#6 := (uf_1 #5)
#93 := (= #4 #6)
#542 := (forall (vars (?x1 T1)) (:pat #541) #93)
#96 := (forall (vars (?x1 T1)) #93)
#545 := (iff #96 #542)
#543 := (iff #93 #93)
#544 := [refl]: #543
#546 := [quant-intro #544]: #545
#454 := (~ #96 #96)
#456 := (~ #93 #93)
#457 := [refl]: #456
#455 := [nnf-pos #457]: #454
#7 := (= #6 #4)
#8 := (forall (vars (?x1 T1)) #7)
#97 := (iff #8 #96)
#94 := (iff #7 #93)
#95 := [rewrite]: #94
#98 := [quant-intro #95]: #97
#92 := [asserted]: #8
#101 := [mp #92 #98]: #96
#452 := [mp~ #101 #455]: #96
#547 := [mp #452 #546]: #542
#590 := (not #542)
#595 := (or #590 #589)
#596 := [quant-inst]: #595
#680 := [unit-resolution #596 #547]: #589
#687 := [symm #680]: #686
#688 := (= uf_3 #588)
#22 := (uf_2 uf_3)
#586 := (uf_1 #22)
#684 := (= #586 #588)
#682 := (= #588 #586)
#678 := (= #39 #22)
#676 := (= #22 #39)
#9 := 0::int
#227 := -1::int
#230 := (* -1::int #39)
#231 := (+ #22 #230)
#296 := (<= #231 0::int)
#70 := (<= #22 #39)
#393 := (iff #70 #296)
#394 := [rewrite]: #393
#347 := [asserted]: #70
#395 := [mp #347 #394]: #296
#229 := (>= #231 0::int)
decl uf_4 :: (-> T2 T3 real)
decl uf_6 :: (-> T1 T3)
#25 := (uf_6 uf_3)
decl uf_7 :: T2
#27 := uf_7
#28 := (uf_4 uf_7 #25)
decl uf_9 :: T2
#33 := uf_9
#34 := (uf_4 uf_9 #25)
#46 := (uf_6 uf_10)
decl uf_5 :: T2
#24 := uf_5
#47 := (uf_4 uf_5 #46)
#48 := (ite #45 #47 #34)
#256 := (ite #229 #48 #28)
#568 := (= #28 #256)
#648 := (not #568)
#194 := 0::real
#192 := -1::real
#265 := (* -1::real #256)
#640 := (+ #28 #265)
#642 := (>= #640 0::real)
#645 := (not #642)
#643 := [hypothesis]: #642
decl uf_8 :: T2
#30 := uf_8
#31 := (uf_4 uf_8 #25)
#266 := (+ #31 #265)
#264 := (>= #266 0::real)
#267 := (not #264)
#26 := (uf_4 uf_5 #25)
decl uf_11 :: T2
#41 := uf_11
#42 := (uf_4 uf_11 #25)
#237 := (ite #229 #42 #26)
#245 := (* -1::real #237)
#246 := (+ #31 #245)
#247 := (<= #246 0::real)
#248 := (not #247)
#272 := (and #248 #267)
#40 := (< #22 #39)
#49 := (ite #40 #28 #48)
#50 := (< #31 #49)
#43 := (ite #40 #26 #42)
#44 := (< #43 #31)
#51 := (and #44 #50)
#273 := (iff #51 #272)
#270 := (iff #50 #267)
#261 := (< #31 #256)
#268 := (iff #261 #267)
#269 := [rewrite]: #268
#262 := (iff #50 #261)
#259 := (= #49 #256)
#228 := (not #229)
#253 := (ite #228 #28 #48)
#257 := (= #253 #256)
#258 := [rewrite]: #257
#254 := (= #49 #253)
#232 := (iff #40 #228)
#233 := [rewrite]: #232
#255 := [monotonicity #233]: #254
#260 := [trans #255 #258]: #259
#263 := [monotonicity #260]: #262
#271 := [trans #263 #269]: #270
#251 := (iff #44 #248)
#242 := (< #237 #31)
#249 := (iff #242 #248)
#250 := [rewrite]: #249
#243 := (iff #44 #242)
#240 := (= #43 #237)
#234 := (ite #228 #26 #42)
#238 := (= #234 #237)
#239 := [rewrite]: #238
#235 := (= #43 #234)
#236 := [monotonicity #233]: #235
#241 := [trans #236 #239]: #240
#244 := [monotonicity #241]: #243
#252 := [trans #244 #250]: #251
#274 := [monotonicity #252 #271]: #273
#178 := [asserted]: #51
#275 := [mp #178 #274]: #272
#277 := [and-elim #275]: #267
#196 := (* -1::real #31)
#197 := (+ #28 #196)
#195 := (>= #197 0::real)
#193 := (not #195)
#213 := (* -1::real #34)
#214 := (+ #31 #213)
#212 := (>= #214 0::real)
#215 := (not #212)
#220 := (and #193 #215)
#23 := (< #22 #22)
#35 := (ite #23 #28 #34)
#36 := (< #31 #35)
#29 := (ite #23 #26 #28)
#32 := (< #29 #31)
#37 := (and #32 #36)
#221 := (iff #37 #220)
#218 := (iff #36 #215)
#209 := (< #31 #34)
#216 := (iff #209 #215)
#217 := [rewrite]: #216
#210 := (iff #36 #209)
#207 := (= #35 #34)
#202 := (ite false #28 #34)
#205 := (= #202 #34)
#206 := [rewrite]: #205
#203 := (= #35 #202)
#180 := (iff #23 false)
#181 := [rewrite]: #180
#204 := [monotonicity #181]: #203
#208 := [trans #204 #206]: #207
#211 := [monotonicity #208]: #210
#219 := [trans #211 #217]: #218
#200 := (iff #32 #193)
#189 := (< #28 #31)
#198 := (iff #189 #193)
#199 := [rewrite]: #198
#190 := (iff #32 #189)
#187 := (= #29 #28)
#182 := (ite false #26 #28)
#185 := (= #182 #28)
#186 := [rewrite]: #185
#183 := (= #29 #182)
#184 := [monotonicity #181]: #183
#188 := [trans #184 #186]: #187
#191 := [monotonicity #188]: #190
#201 := [trans #191 #199]: #200
#222 := [monotonicity #201 #219]: #221
#177 := [asserted]: #37
#223 := [mp #177 #222]: #220
#224 := [and-elim #223]: #193
#644 := [th-lemma #224 #277 #643]: false
#646 := [lemma #644]: #645
#647 := [hypothesis]: #568
#649 := (or #648 #642)
#650 := [th-lemma]: #649
#651 := [unit-resolution #650 #647 #646]: false
#652 := [lemma #651]: #648
#578 := (or #229 #568)
#579 := [def-axiom]: #578
#675 := [unit-resolution #579 #652]: #229
#677 := [th-lemma #675 #395]: #676
#679 := [symm #677]: #678
#683 := [monotonicity #679]: #682
#685 := [symm #683]: #684
#587 := (= uf_3 #586)
#591 := (or #590 #587)
#592 := [quant-inst]: #591
#681 := [unit-resolution #592 #547]: #587
#689 := [trans #681 #685]: #688
#690 := [trans #689 #687]: #45
#571 := (not #45)
#54 := (uf_4 uf_11 #46)
#279 := (ite #45 #28 #54)
#465 := (* -1::real #279)
#632 := (+ #28 #465)
#633 := (<= #632 0::real)
#580 := (= #28 #279)
#656 := [hypothesis]: #45
#582 := (or #571 #580)
#583 := [def-axiom]: #582
#657 := [unit-resolution #583 #656]: #580
#658 := (not #580)
#659 := (or #658 #633)
#660 := [th-lemma]: #659
#661 := [unit-resolution #660 #657]: #633
#57 := (uf_4 uf_8 #46)
#363 := (* -1::real #57)
#379 := (+ #47 #363)
#380 := (<= #379 0::real)
#381 := (not #380)
#364 := (+ #54 #363)
#362 := (>= #364 0::real)
#361 := (not #362)
#386 := (and #361 #381)
#59 := (uf_4 uf_7 #46)
#64 := (< #39 #39)
#67 := (ite #64 #59 #47)
#68 := (< #57 #67)
#65 := (ite #64 #47 #54)
#66 := (< #65 #57)
#69 := (and #66 #68)
#387 := (iff #69 #386)
#384 := (iff #68 #381)
#376 := (< #57 #47)
#382 := (iff #376 #381)
#383 := [rewrite]: #382
#377 := (iff #68 #376)
#374 := (= #67 #47)
#369 := (ite false #59 #47)
#372 := (= #369 #47)
#373 := [rewrite]: #372
#370 := (= #67 #369)
#349 := (iff #64 false)
#350 := [rewrite]: #349
#371 := [monotonicity #350]: #370
#375 := [trans #371 #373]: #374
#378 := [monotonicity #375]: #377
#385 := [trans #378 #383]: #384
#367 := (iff #66 #361)
#358 := (< #54 #57)
#365 := (iff #358 #361)
#366 := [rewrite]: #365
#359 := (iff #66 #358)
#356 := (= #65 #54)
#351 := (ite false #47 #54)
#354 := (= #351 #54)
#355 := [rewrite]: #354
#352 := (= #65 #351)
#353 := [monotonicity #350]: #352
#357 := [trans #353 #355]: #356
#360 := [monotonicity #357]: #359
#368 := [trans #360 #366]: #367
#388 := [monotonicity #368 #385]: #387
#346 := [asserted]: #69
#389 := [mp #346 #388]: #386
#391 := [and-elim #389]: #381
#397 := (* -1::real #59)
#398 := (+ #47 #397)
#399 := (<= #398 0::real)
#409 := (* -1::real #54)
#410 := (+ #47 #409)
#408 := (>= #410 0::real)
#60 := (uf_4 uf_9 #46)
#402 := (* -1::real #60)
#403 := (+ #59 #402)
#404 := (<= #403 0::real)
#418 := (and #399 #404 #408)
#73 := (<= #59 #60)
#72 := (<= #47 #59)
#74 := (and #72 #73)
#71 := (<= #54 #47)
#75 := (and #71 #74)
#421 := (iff #75 #418)
#412 := (and #399 #404)
#415 := (and #408 #412)
#419 := (iff #415 #418)
#420 := [rewrite]: #419
#416 := (iff #75 #415)
#413 := (iff #74 #412)
#405 := (iff #73 #404)
#406 := [rewrite]: #405
#400 := (iff #72 #399)
#401 := [rewrite]: #400
#414 := [monotonicity #401 #406]: #413
#407 := (iff #71 #408)
#411 := [rewrite]: #407
#417 := [monotonicity #411 #414]: #416
#422 := [trans #417 #420]: #421
#348 := [asserted]: #75
#423 := [mp #348 #422]: #418
#424 := [and-elim #423]: #399
#637 := (+ #28 #397)
#639 := (>= #637 0::real)
#636 := (= #28 #59)
#666 := (= #59 #28)
#664 := (= #46 #25)
#662 := (= #25 #46)
#663 := [monotonicity #656]: #662
#665 := [symm #663]: #664
#667 := [monotonicity #665]: #666
#668 := [symm #667]: #636
#669 := (not #636)
#670 := (or #669 #639)
#671 := [th-lemma]: #670
#672 := [unit-resolution #671 #668]: #639
#468 := (+ #57 #465)
#471 := (<= #468 0::real)
#444 := (not #471)
#322 := (ite #296 #279 #47)
#330 := (* -1::real #322)
#331 := (+ #57 #330)
#332 := (<= #331 0::real)
#333 := (not #332)
#445 := (iff #333 #444)
#472 := (iff #332 #471)
#469 := (= #331 #468)
#466 := (= #330 #465)
#463 := (= #322 #279)
#1 := true
#458 := (ite true #279 #47)
#461 := (= #458 #279)
#462 := [rewrite]: #461
#459 := (= #322 #458)
#450 := (iff #296 true)
#451 := [iff-true #395]: #450
#460 := [monotonicity #451]: #459
#464 := [trans #460 #462]: #463
#467 := [monotonicity #464]: #466
#470 := [monotonicity #467]: #469
#473 := [monotonicity #470]: #472
#474 := [monotonicity #473]: #445
#303 := (ite #296 #60 #59)
#313 := (* -1::real #303)
#314 := (+ #57 #313)
#312 := (>= #314 0::real)
#311 := (not #312)
#338 := (and #311 #333)
#52 := (< #39 #22)
#61 := (ite #52 #59 #60)
#62 := (< #57 #61)
#53 := (= uf_10 uf_3)
#55 := (ite #53 #28 #54)
#56 := (ite #52 #47 #55)
#58 := (< #56 #57)
#63 := (and #58 #62)
#341 := (iff #63 #338)
#282 := (ite #52 #47 #279)
#285 := (< #282 #57)
#291 := (and #62 #285)
#339 := (iff #291 #338)
#336 := (iff #285 #333)
#327 := (< #322 #57)
#334 := (iff #327 #333)
#335 := [rewrite]: #334
#328 := (iff #285 #327)
#325 := (= #282 #322)
#297 := (not #296)
#319 := (ite #297 #47 #279)
#323 := (= #319 #322)
#324 := [rewrite]: #323
#320 := (= #282 #319)
#298 := (iff #52 #297)
#299 := [rewrite]: #298
#321 := [monotonicity #299]: #320
#326 := [trans #321 #324]: #325
#329 := [monotonicity #326]: #328
#337 := [trans #329 #335]: #336
#317 := (iff #62 #311)
#308 := (< #57 #303)
#315 := (iff #308 #311)
#316 := [rewrite]: #315
#309 := (iff #62 #308)
#306 := (= #61 #303)
#300 := (ite #297 #59 #60)
#304 := (= #300 #303)
#305 := [rewrite]: #304
#301 := (= #61 #300)
#302 := [monotonicity #299]: #301
#307 := [trans #302 #305]: #306
#310 := [monotonicity #307]: #309
#318 := [trans #310 #316]: #317
#340 := [monotonicity #318 #337]: #339
#294 := (iff #63 #291)
#288 := (and #285 #62)
#292 := (iff #288 #291)
#293 := [rewrite]: #292
#289 := (iff #63 #288)
#286 := (iff #58 #285)
#283 := (= #56 #282)
#280 := (= #55 #279)
#226 := (iff #53 #45)
#278 := [rewrite]: #226
#281 := [monotonicity #278]: #280
#284 := [monotonicity #281]: #283
#287 := [monotonicity #284]: #286
#290 := [monotonicity #287]: #289
#295 := [trans #290 #293]: #294
#342 := [trans #295 #340]: #341
#179 := [asserted]: #63
#343 := [mp #179 #342]: #338
#345 := [and-elim #343]: #333
#475 := [mp #345 #474]: #444
#673 := [th-lemma #475 #672 #424 #391 #661]: false
#674 := [lemma #673]: #571
[unit-resolution #674 #690]: false
unsat
IL2powemHjRpCJYwmXFxyw 211 0
#2 := false
#33 := 0::real
decl uf_11 :: (-> T5 T6 real)
decl uf_15 :: T6
#28 := uf_15
decl uf_16 :: T5
#30 := uf_16
#31 := (uf_11 uf_16 uf_15)
decl uf_12 :: (-> T7 T8 T5)
decl uf_14 :: T8
#26 := uf_14
decl uf_13 :: (-> T1 T7)
decl uf_8 :: T1
#16 := uf_8
#25 := (uf_13 uf_8)
#27 := (uf_12 #25 uf_14)
#29 := (uf_11 #27 uf_15)
#73 := -1::real
#84 := (* -1::real #29)
#85 := (+ #84 #31)
#74 := (* -1::real #31)
#75 := (+ #29 #74)
#112 := (>= #75 0::real)
#119 := (ite #112 #75 #85)
#127 := (* -1::real #119)
decl uf_17 :: T5
#37 := uf_17
#38 := (uf_11 uf_17 uf_15)
#102 := -1/3::real
#103 := (* -1/3::real #38)
#128 := (+ #103 #127)
#100 := 1/3::real
#101 := (* 1/3::real #31)
#129 := (+ #101 #128)
#130 := (<= #129 0::real)
#131 := (not #130)
#40 := 3::real
#39 := (- #31 #38)
#41 := (/ #39 3::real)
#32 := (- #29 #31)
#35 := (- #32)
#34 := (< #32 0::real)
#36 := (ite #34 #35 #32)
#42 := (< #36 #41)
#136 := (iff #42 #131)
#104 := (+ #101 #103)
#78 := (< #75 0::real)
#90 := (ite #78 #85 #75)
#109 := (< #90 #104)
#134 := (iff #109 #131)
#124 := (< #119 #104)
#132 := (iff #124 #131)
#133 := [rewrite]: #132
#125 := (iff #109 #124)
#122 := (= #90 #119)
#113 := (not #112)
#116 := (ite #113 #85 #75)
#120 := (= #116 #119)
#121 := [rewrite]: #120
#117 := (= #90 #116)
#114 := (iff #78 #113)
#115 := [rewrite]: #114
#118 := [monotonicity #115]: #117
#123 := [trans #118 #121]: #122
#126 := [monotonicity #123]: #125
#135 := [trans #126 #133]: #134
#110 := (iff #42 #109)
#107 := (= #41 #104)
#93 := (* -1::real #38)
#94 := (+ #31 #93)
#97 := (/ #94 3::real)
#105 := (= #97 #104)
#106 := [rewrite]: #105
#98 := (= #41 #97)
#95 := (= #39 #94)
#96 := [rewrite]: #95
#99 := [monotonicity #96]: #98
#108 := [trans #99 #106]: #107
#91 := (= #36 #90)
#76 := (= #32 #75)
#77 := [rewrite]: #76
#88 := (= #35 #85)
#81 := (- #75)
#86 := (= #81 #85)
#87 := [rewrite]: #86
#82 := (= #35 #81)
#83 := [monotonicity #77]: #82
#89 := [trans #83 #87]: #88
#79 := (iff #34 #78)
#80 := [monotonicity #77]: #79
#92 := [monotonicity #80 #89 #77]: #91
#111 := [monotonicity #92 #108]: #110
#137 := [trans #111 #135]: #136
#72 := [asserted]: #42
#138 := [mp #72 #137]: #131
decl uf_1 :: T1
#4 := uf_1
#43 := (uf_13 uf_1)
#44 := (uf_12 #43 uf_14)
#45 := (uf_11 #44 uf_15)
#149 := (* -1::real #45)
#150 := (+ #38 #149)
#140 := (+ #93 #45)
#161 := (<= #150 0::real)
#168 := (ite #161 #140 #150)
#176 := (* -1::real #168)
#177 := (+ #103 #176)
#178 := (+ #101 #177)
#179 := (<= #178 0::real)
#180 := (not #179)
#46 := (- #45 #38)
#48 := (- #46)
#47 := (< #46 0::real)
#49 := (ite #47 #48 #46)
#50 := (< #49 #41)
#185 := (iff #50 #180)
#143 := (< #140 0::real)
#155 := (ite #143 #150 #140)
#158 := (< #155 #104)
#183 := (iff #158 #180)
#173 := (< #168 #104)
#181 := (iff #173 #180)
#182 := [rewrite]: #181
#174 := (iff #158 #173)
#171 := (= #155 #168)
#162 := (not #161)
#165 := (ite #162 #150 #140)
#169 := (= #165 #168)
#170 := [rewrite]: #169
#166 := (= #155 #165)
#163 := (iff #143 #162)
#164 := [rewrite]: #163
#167 := [monotonicity #164]: #166
#172 := [trans #167 #170]: #171
#175 := [monotonicity #172]: #174
#184 := [trans #175 #182]: #183
#159 := (iff #50 #158)
#156 := (= #49 #155)
#141 := (= #46 #140)
#142 := [rewrite]: #141
#153 := (= #48 #150)
#146 := (- #140)
#151 := (= #146 #150)
#152 := [rewrite]: #151
#147 := (= #48 #146)
#148 := [monotonicity #142]: #147
#154 := [trans #148 #152]: #153
#144 := (iff #47 #143)
#145 := [monotonicity #142]: #144
#157 := [monotonicity #145 #154 #142]: #156
#160 := [monotonicity #157 #108]: #159
#186 := [trans #160 #184]: #185
#139 := [asserted]: #50
#187 := [mp #139 #186]: #180
#299 := (+ #140 #176)
#300 := (<= #299 0::real)
#290 := (= #140 #168)
#329 := [hypothesis]: #162
#191 := (+ #29 #149)
#192 := (<= #191 0::real)
#51 := (<= #29 #45)
#193 := (iff #51 #192)
#194 := [rewrite]: #193
#188 := [asserted]: #51
#195 := [mp #188 #194]: #192
#298 := (+ #75 #127)
#301 := (<= #298 0::real)
#284 := (= #75 #119)
#302 := [hypothesis]: #113
#296 := (+ #85 #127)
#297 := (<= #296 0::real)
#285 := (= #85 #119)
#288 := (or #112 #285)
#289 := [def-axiom]: #288
#303 := [unit-resolution #289 #302]: #285
#304 := (not #285)
#305 := (or #304 #297)
#306 := [th-lemma]: #305
#307 := [unit-resolution #306 #303]: #297
#315 := (not #290)
#310 := (not #300)
#311 := (or #310 #112)
#308 := [hypothesis]: #300
#309 := [th-lemma #308 #307 #138 #302 #187 #195]: false
#312 := [lemma #309]: #311
#322 := [unit-resolution #312 #302]: #310
#316 := (or #315 #300)
#313 := [hypothesis]: #310
#314 := [hypothesis]: #290
#317 := [th-lemma]: #316
#318 := [unit-resolution #317 #314 #313]: false
#319 := [lemma #318]: #316
#323 := [unit-resolution #319 #322]: #315
#292 := (or #162 #290)
#293 := [def-axiom]: #292
#324 := [unit-resolution #293 #323]: #162
#325 := [th-lemma #324 #307 #138 #302 #195]: false
#326 := [lemma #325]: #112
#286 := (or #113 #284)
#287 := [def-axiom]: #286
#330 := [unit-resolution #287 #326]: #284
#331 := (not #284)
#332 := (or #331 #301)
#333 := [th-lemma]: #332
#334 := [unit-resolution #333 #330]: #301
#335 := [th-lemma #326 #334 #195 #329 #138]: false
#336 := [lemma #335]: #161
#327 := [unit-resolution #293 #336]: #290
#328 := [unit-resolution #319 #327]: #300
[th-lemma #326 #334 #195 #328 #187 #138]: false
unsat
GX51o3DUO/UBS3eNP2P9kA 285 0
#2 := false
#7 := 0::real
decl uf_4 :: real
#16 := uf_4
#40 := -1::real
#116 := (* -1::real uf_4)
decl uf_3 :: real
#11 := uf_3
#117 := (+ uf_3 #116)
#128 := (<= #117 0::real)
#129 := (not #128)
#220 := 2/3::real
#221 := (* 2/3::real uf_3)
#222 := (+ #221 #116)
decl uf_2 :: real
#5 := uf_2
#67 := 1/3::real
#68 := (* 1/3::real uf_2)
#233 := (+ #68 #222)
#243 := (<= #233 0::real)
#268 := (not #243)
#287 := [hypothesis]: #268
#41 := (* -1::real uf_2)
decl uf_1 :: real
#4 := uf_1
#42 := (+ uf_1 #41)
#79 := (>= #42 0::real)
#80 := (not #79)
#297 := (or #80 #243)
#158 := (+ uf_1 #116)
#159 := (<= #158 0::real)
#22 := (<= uf_1 uf_4)
#160 := (iff #22 #159)
#161 := [rewrite]: #160
#155 := [asserted]: #22
#162 := [mp #155 #161]: #159
#200 := (* 1/3::real uf_3)
#198 := -4/3::real
#199 := (* -4/3::real uf_2)
#201 := (+ #199 #200)
#202 := (+ uf_1 #201)
#203 := (>= #202 0::real)
#258 := (not #203)
#292 := [hypothesis]: #79
#293 := (or #80 #258)
#69 := -1/3::real
#70 := (* -1/3::real uf_3)
#186 := -2/3::real
#187 := (* -2/3::real uf_2)
#188 := (+ #187 #70)
#189 := (+ uf_1 #188)
#204 := (<= #189 0::real)
#205 := (ite #79 #203 #204)
#210 := (not #205)
#51 := (* -1::real uf_1)
#52 := (+ #51 uf_2)
#86 := (ite #79 #42 #52)
#94 := (* -1::real #86)
#95 := (+ #70 #94)
#96 := (+ #68 #95)
#97 := (<= #96 0::real)
#98 := (not #97)
#211 := (iff #98 #210)
#208 := (iff #97 #205)
#182 := 4/3::real
#183 := (* 4/3::real uf_2)
#184 := (+ #183 #70)
#185 := (+ #51 #184)
#190 := (ite #79 #185 #189)
#195 := (<= #190 0::real)
#206 := (iff #195 #205)
#207 := [rewrite]: #206
#196 := (iff #97 #195)
#193 := (= #96 #190)
#172 := (+ #41 #70)
#173 := (+ uf_1 #172)
#170 := (+ uf_2 #70)
#171 := (+ #51 #170)
#174 := (ite #79 #171 #173)
#179 := (+ #68 #174)
#191 := (= #179 #190)
#192 := [rewrite]: #191
#180 := (= #96 #179)
#177 := (= #95 #174)
#164 := (ite #79 #52 #42)
#167 := (+ #70 #164)
#175 := (= #167 #174)
#176 := [rewrite]: #175
#168 := (= #95 #167)
#156 := (= #94 #164)
#165 := [rewrite]: #156
#169 := [monotonicity #165]: #168
#178 := [trans #169 #176]: #177
#181 := [monotonicity #178]: #180
#194 := [trans #181 #192]: #193
#197 := [monotonicity #194]: #196
#209 := [trans #197 #207]: #208
#212 := [monotonicity #209]: #211
#13 := 3::real
#12 := (- uf_2 uf_3)
#14 := (/ #12 3::real)
#6 := (- uf_1 uf_2)
#9 := (- #6)
#8 := (< #6 0::real)
#10 := (ite #8 #9 #6)
#15 := (< #10 #14)
#103 := (iff #15 #98)
#71 := (+ #68 #70)
#45 := (< #42 0::real)
#57 := (ite #45 #52 #42)
#76 := (< #57 #71)
#101 := (iff #76 #98)
#91 := (< #86 #71)
#99 := (iff #91 #98)
#100 := [rewrite]: #99
#92 := (iff #76 #91)
#89 := (= #57 #86)
#83 := (ite #80 #52 #42)
#87 := (= #83 #86)
#88 := [rewrite]: #87
#84 := (= #57 #83)
#81 := (iff #45 #80)
#82 := [rewrite]: #81
#85 := [monotonicity #82]: #84
#90 := [trans #85 #88]: #89
#93 := [monotonicity #90]: #92
#102 := [trans #93 #100]: #101
#77 := (iff #15 #76)
#74 := (= #14 #71)
#60 := (* -1::real uf_3)
#61 := (+ uf_2 #60)
#64 := (/ #61 3::real)
#72 := (= #64 #71)
#73 := [rewrite]: #72
#65 := (= #14 #64)
#62 := (= #12 #61)
#63 := [rewrite]: #62
#66 := [monotonicity #63]: #65
#75 := [trans #66 #73]: #74
#58 := (= #10 #57)
#43 := (= #6 #42)
#44 := [rewrite]: #43
#55 := (= #9 #52)
#48 := (- #42)
#53 := (= #48 #52)
#54 := [rewrite]: #53
#49 := (= #9 #48)
#50 := [monotonicity #44]: #49
#56 := [trans #50 #54]: #55
#46 := (iff #8 #45)
#47 := [monotonicity #44]: #46
#59 := [monotonicity #47 #56 #44]: #58
#78 := [monotonicity #59 #75]: #77
#104 := [trans #78 #102]: #103
#39 := [asserted]: #15
#105 := [mp #39 #104]: #98
#213 := [mp #105 #212]: #210
#259 := (or #205 #80 #258)
#260 := [def-axiom]: #259
#294 := [unit-resolution #260 #213]: #293
#295 := [unit-resolution #294 #292]: #258
#296 := [th-lemma #287 #292 #295 #162]: false
#298 := [lemma #296]: #297
#299 := [unit-resolution #298 #287]: #80
#261 := (not #204)
#281 := (or #79 #261)
#262 := (or #205 #79 #261)
#263 := [def-axiom]: #262
#282 := [unit-resolution #263 #213]: #281
#300 := [unit-resolution #282 #299]: #261
#290 := (or #79 #204 #243)
#276 := [hypothesis]: #261
#288 := [hypothesis]: #80
#289 := [th-lemma #288 #276 #162 #287]: false
#291 := [lemma #289]: #290
#301 := [unit-resolution #291 #300 #299 #287]: false
#302 := [lemma #301]: #243
#303 := (or #129 #268)
#223 := (* -4/3::real uf_3)
#224 := (+ #223 uf_4)
#234 := (+ #68 #224)
#244 := (<= #234 0::real)
#245 := (ite #128 #243 #244)
#250 := (not #245)
#107 := (+ #60 uf_4)
#135 := (ite #128 #107 #117)
#143 := (* -1::real #135)
#144 := (+ #70 #143)
#145 := (+ #68 #144)
#146 := (<= #145 0::real)
#147 := (not #146)
#251 := (iff #147 #250)
#248 := (iff #146 #245)
#235 := (ite #128 #233 #234)
#240 := (<= #235 0::real)
#246 := (iff #240 #245)
#247 := [rewrite]: #246
#241 := (iff #146 #240)
#238 := (= #145 #235)
#225 := (ite #128 #222 #224)
#230 := (+ #68 #225)
#236 := (= #230 #235)
#237 := [rewrite]: #236
#231 := (= #145 #230)
#228 := (= #144 #225)
#214 := (ite #128 #117 #107)
#217 := (+ #70 #214)
#226 := (= #217 #225)
#227 := [rewrite]: #226
#218 := (= #144 #217)
#215 := (= #143 #214)
#216 := [rewrite]: #215
#219 := [monotonicity #216]: #218
#229 := [trans #219 #227]: #228
#232 := [monotonicity #229]: #231
#239 := [trans #232 #237]: #238
#242 := [monotonicity #239]: #241
#249 := [trans #242 #247]: #248
#252 := [monotonicity #249]: #251
#17 := (- uf_4 uf_3)
#19 := (- #17)
#18 := (< #17 0::real)
#20 := (ite #18 #19 #17)
#21 := (< #20 #14)
#152 := (iff #21 #147)
#110 := (< #107 0::real)
#122 := (ite #110 #117 #107)
#125 := (< #122 #71)
#150 := (iff #125 #147)
#140 := (< #135 #71)
#148 := (iff #140 #147)
#149 := [rewrite]: #148
#141 := (iff #125 #140)
#138 := (= #122 #135)
#132 := (ite #129 #117 #107)
#136 := (= #132 #135)
#137 := [rewrite]: #136
#133 := (= #122 #132)
#130 := (iff #110 #129)
#131 := [rewrite]: #130
#134 := [monotonicity #131]: #133
#139 := [trans #134 #137]: #138
#142 := [monotonicity #139]: #141
#151 := [trans #142 #149]: #150
#126 := (iff #21 #125)
#123 := (= #20 #122)
#108 := (= #17 #107)
#109 := [rewrite]: #108
#120 := (= #19 #117)
#113 := (- #107)
#118 := (= #113 #117)
#119 := [rewrite]: #118
#114 := (= #19 #113)
#115 := [monotonicity #109]: #114
#121 := [trans #115 #119]: #120
#111 := (iff #18 #110)
#112 := [monotonicity #109]: #111
#124 := [monotonicity #112 #121 #109]: #123
#127 := [monotonicity #124 #75]: #126
#153 := [trans #127 #151]: #152
#106 := [asserted]: #21
#154 := [mp #106 #153]: #147
#253 := [mp #154 #252]: #250
#269 := (or #245 #129 #268)
#270 := [def-axiom]: #269
#304 := [unit-resolution #270 #253]: #303
#305 := [unit-resolution #304 #302]: #129
#271 := (not #244)
#306 := (or #128 #271)
#272 := (or #245 #128 #271)
#273 := [def-axiom]: #272
#307 := [unit-resolution #273 #253]: #306
#308 := [unit-resolution #307 #305]: #271
#285 := (or #128 #244)
#274 := [hypothesis]: #271
#275 := [hypothesis]: #129
#278 := (or #204 #128 #244)
#277 := [th-lemma #276 #275 #274 #162]: false
#279 := [lemma #277]: #278
#280 := [unit-resolution #279 #275 #274]: #204
#283 := [unit-resolution #282 #280]: #79
#284 := [th-lemma #275 #274 #283 #162]: false
#286 := [lemma #284]: #285
[unit-resolution #286 #308 #305]: false
unsat
cebG074uorSr8ODzgTmcKg 97 0
#2 := false
#18 := 0::real
decl uf_1 :: (-> T2 T1 real)
decl uf_5 :: T1
#11 := uf_5
decl uf_2 :: T2
#4 := uf_2
#20 := (uf_1 uf_2 uf_5)
#42 := -1::real
#53 := (* -1::real #20)
decl uf_3 :: T2
#7 := uf_3
#19 := (uf_1 uf_3 uf_5)
#54 := (+ #19 #53)
#63 := (<= #54 0::real)
#21 := (- #19 #20)
#22 := (< 0::real #21)
#23 := (not #22)
#74 := (iff #23 #63)
#57 := (< 0::real #54)
#60 := (not #57)
#72 := (iff #60 #63)
#64 := (not #63)
#67 := (not #64)
#70 := (iff #67 #63)
#71 := [rewrite]: #70
#68 := (iff #60 #67)
#65 := (iff #57 #64)
#66 := [rewrite]: #65
#69 := [monotonicity #66]: #68
#73 := [trans #69 #71]: #72
#61 := (iff #23 #60)
#58 := (iff #22 #57)
#55 := (= #21 #54)
#56 := [rewrite]: #55
#59 := [monotonicity #56]: #58
#62 := [monotonicity #59]: #61
#75 := [trans #62 #73]: #74
#41 := [asserted]: #23
#76 := [mp #41 #75]: #63
#5 := (:var 0 T1)
#8 := (uf_1 uf_3 #5)
#141 := (pattern #8)
#6 := (uf_1 uf_2 #5)
#140 := (pattern #6)
#45 := (* -1::real #8)
#46 := (+ #6 #45)
#44 := (>= #46 0::real)
#43 := (not #44)
#142 := (forall (vars (?x1 T1)) (:pat #140 #141) #43)
#49 := (forall (vars (?x1 T1)) #43)
#145 := (iff #49 #142)
#143 := (iff #43 #43)
#144 := [refl]: #143
#146 := [quant-intro #144]: #145
#80 := (~ #49 #49)
#82 := (~ #43 #43)
#83 := [refl]: #82
#81 := [nnf-pos #83]: #80
#9 := (< #6 #8)
#10 := (forall (vars (?x1 T1)) #9)
#50 := (iff #10 #49)
#47 := (iff #9 #43)
#48 := [rewrite]: #47
#51 := [quant-intro #48]: #50
#39 := [asserted]: #10
#52 := [mp #39 #51]: #49
#79 := [mp~ #52 #81]: #49
#147 := [mp #79 #146]: #142
#164 := (not #142)
#165 := (or #164 #64)
#148 := (* -1::real #19)
#149 := (+ #20 #148)
#150 := (>= #149 0::real)
#151 := (not #150)
#166 := (or #164 #151)
#168 := (iff #166 #165)
#170 := (iff #165 #165)
#171 := [rewrite]: #170
#162 := (iff #151 #64)
#160 := (iff #150 #63)
#152 := (+ #148 #20)
#155 := (>= #152 0::real)
#158 := (iff #155 #63)
#159 := [rewrite]: #158
#156 := (iff #150 #155)
#153 := (= #149 #152)
#154 := [rewrite]: #153
#157 := [monotonicity #154]: #156
#161 := [trans #157 #159]: #160
#163 := [monotonicity #161]: #162
#169 := [monotonicity #163]: #168
#172 := [trans #169 #171]: #168
#167 := [quant-inst]: #166
#173 := [mp #167 #172]: #165
[unit-resolution #173 #147 #76]: false
unsat
DKRtrJ2XceCkITuNwNViRw 57 0
#2 := false
#4 := 0::real
decl uf_1 :: (-> T2 real)
decl uf_2 :: (-> T1 T1 T2)
decl uf_12 :: (-> T4 T1)
decl uf_4 :: T4
#11 := uf_4
#39 := (uf_12 uf_4)
decl uf_10 :: T4
#27 := uf_10
#38 := (uf_12 uf_10)
#40 := (uf_2 #38 #39)
#41 := (uf_1 #40)
#264 := (>= #41 0::real)
#266 := (not #264)
#43 := (= #41 0::real)
#44 := (not #43)
#131 := [asserted]: #44
#272 := (or #43 #266)
#42 := (<= #41 0::real)
#130 := [asserted]: #42
#265 := (not #42)
#270 := (or #43 #265 #266)
#271 := [th-lemma]: #270
#273 := [unit-resolution #271 #130]: #272
#274 := [unit-resolution #273 #131]: #266
#6 := (:var 0 T1)
#5 := (:var 1 T1)
#7 := (uf_2 #5 #6)
#241 := (pattern #7)
#8 := (uf_1 #7)
#65 := (>= #8 0::real)
#242 := (forall (vars (?x1 T1) (?x2 T1)) (:pat #241) #65)
#66 := (forall (vars (?x1 T1) (?x2 T1)) #65)
#245 := (iff #66 #242)
#243 := (iff #65 #65)
#244 := [refl]: #243
#246 := [quant-intro #244]: #245
#149 := (~ #66 #66)
#151 := (~ #65 #65)
#152 := [refl]: #151
#150 := [nnf-pos #152]: #149
#9 := (<= 0::real #8)
#10 := (forall (vars (?x1 T1) (?x2 T1)) #9)
#67 := (iff #10 #66)
#63 := (iff #9 #65)
#64 := [rewrite]: #63
#68 := [quant-intro #64]: #67
#60 := [asserted]: #10
#69 := [mp #60 #68]: #66
#147 := [mp~ #69 #150]: #66
#247 := [mp #147 #246]: #242
#267 := (not #242)
#268 := (or #267 #264)
#269 := [quant-inst]: #268
[unit-resolution #269 #247 #274]: false
unsat
97KJAJfUio+nGchEHWvgAw 91 0
#2 := false
#38 := 0::real
decl uf_1 :: (-> T1 T2 real)
decl uf_3 :: T2
#5 := uf_3
decl uf_4 :: T1
#7 := uf_4
#8 := (uf_1 uf_4 uf_3)
#35 := -1::real
#36 := (* -1::real #8)
decl uf_2 :: T1
#4 := uf_2
#6 := (uf_1 uf_2 uf_3)
#37 := (+ #6 #36)
#130 := (>= #37 0::real)
#155 := (not #130)
#43 := (= #6 #8)
#55 := (not #43)
#15 := (= #8 #6)
#16 := (not #15)
#56 := (iff #16 #55)
#53 := (iff #15 #43)
#54 := [rewrite]: #53
#57 := [monotonicity #54]: #56
#34 := [asserted]: #16
#60 := [mp #34 #57]: #55
#158 := (or #43 #155)
#39 := (<= #37 0::real)
#9 := (<= #6 #8)
#40 := (iff #9 #39)
#41 := [rewrite]: #40
#32 := [asserted]: #9
#42 := [mp #32 #41]: #39
#154 := (not #39)
#156 := (or #43 #154 #155)
#157 := [th-lemma]: #156
#159 := [unit-resolution #157 #42]: #158
#160 := [unit-resolution #159 #60]: #155
#10 := (:var 0 T2)
#12 := (uf_1 uf_2 #10)
#123 := (pattern #12)
#11 := (uf_1 uf_4 #10)
#122 := (pattern #11)
#44 := (* -1::real #12)
#45 := (+ #11 #44)
#46 := (<= #45 0::real)
#124 := (forall (vars (?x1 T2)) (:pat #122 #123) #46)
#49 := (forall (vars (?x1 T2)) #46)
#127 := (iff #49 #124)
#125 := (iff #46 #46)
#126 := [refl]: #125
#128 := [quant-intro #126]: #127
#62 := (~ #49 #49)
#64 := (~ #46 #46)
#65 := [refl]: #64
#63 := [nnf-pos #65]: #62
#13 := (<= #11 #12)
#14 := (forall (vars (?x1 T2)) #13)
#50 := (iff #14 #49)
#47 := (iff #13 #46)
#48 := [rewrite]: #47
#51 := [quant-intro #48]: #50
#33 := [asserted]: #14
#52 := [mp #33 #51]: #49
#61 := [mp~ #52 #63]: #49
#129 := [mp #61 #128]: #124
#144 := (not #124)
#145 := (or #144 #130)
#131 := (* -1::real #6)
#132 := (+ #8 #131)
#133 := (<= #132 0::real)
#146 := (or #144 #133)
#148 := (iff #146 #145)
#150 := (iff #145 #145)
#151 := [rewrite]: #150
#142 := (iff #133 #130)
#134 := (+ #131 #8)
#137 := (<= #134 0::real)
#140 := (iff #137 #130)
#141 := [rewrite]: #140
#138 := (iff #133 #137)
#135 := (= #132 #134)
#136 := [rewrite]: #135
#139 := [monotonicity #136]: #138
#143 := [trans #139 #141]: #142
#149 := [monotonicity #143]: #148
#152 := [trans #149 #151]: #148
#147 := [quant-inst]: #146
#153 := [mp #147 #152]: #145
[unit-resolution #153 #129 #160]: false
unsat
flJYbeWfe+t2l/zsRqdujA 149 0
#2 := false
#19 := 0::real
decl uf_1 :: (-> T1 T2 real)
decl uf_3 :: T2
#5 := uf_3
decl uf_4 :: T1
#7 := uf_4
#8 := (uf_1 uf_4 uf_3)
#44 := -1::real
#156 := (* -1::real #8)
decl uf_2 :: T1
#4 := uf_2
#6 := (uf_1 uf_2 uf_3)
#203 := (+ #6 #156)
#205 := (>= #203 0::real)
#9 := (= #6 #8)
#40 := [asserted]: #9
#208 := (not #9)
#209 := (or #208 #205)
#210 := [th-lemma]: #209
#211 := [unit-resolution #210 #40]: #205
decl uf_5 :: T1
#12 := uf_5
#22 := (uf_1 uf_5 uf_3)
#160 := (* -1::real #22)
#161 := (+ #6 #160)
#207 := (>= #161 0::real)
#222 := (not #207)
#206 := (= #6 #22)
#216 := (not #206)
#62 := (= #8 #22)
#70 := (not #62)
#217 := (iff #70 #216)
#214 := (iff #62 #206)
#212 := (iff #206 #62)
#213 := [monotonicity #40]: #212
#215 := [symm #213]: #214
#218 := [monotonicity #215]: #217
#23 := (= #22 #8)
#24 := (not #23)
#71 := (iff #24 #70)
#68 := (iff #23 #62)
#69 := [rewrite]: #68
#72 := [monotonicity #69]: #71
#43 := [asserted]: #24
#75 := [mp #43 #72]: #70
#219 := [mp #75 #218]: #216
#225 := (or #206 #222)
#162 := (<= #161 0::real)
#172 := (+ #8 #160)
#173 := (>= #172 0::real)
#178 := (not #173)
#163 := (not #162)
#181 := (or #163 #178)
#184 := (not #181)
#10 := (:var 0 T2)
#15 := (uf_1 uf_4 #10)
#149 := (pattern #15)
#13 := (uf_1 uf_5 #10)
#148 := (pattern #13)
#11 := (uf_1 uf_2 #10)
#147 := (pattern #11)
#50 := (* -1::real #15)
#51 := (+ #13 #50)
#52 := (<= #51 0::real)
#76 := (not #52)
#45 := (* -1::real #13)
#46 := (+ #11 #45)
#47 := (<= #46 0::real)
#78 := (not #47)
#73 := (or #78 #76)
#83 := (not #73)
#150 := (forall (vars (?x1 T2)) (:pat #147 #148 #149) #83)
#86 := (forall (vars (?x1 T2)) #83)
#153 := (iff #86 #150)
#151 := (iff #83 #83)
#152 := [refl]: #151
#154 := [quant-intro #152]: #153
#55 := (and #47 #52)
#58 := (forall (vars (?x1 T2)) #55)
#87 := (iff #58 #86)
#84 := (iff #55 #83)
#85 := [rewrite]: #84
#88 := [quant-intro #85]: #87
#79 := (~ #58 #58)
#81 := (~ #55 #55)
#82 := [refl]: #81
#80 := [nnf-pos #82]: #79
#16 := (<= #13 #15)
#14 := (<= #11 #13)
#17 := (and #14 #16)
#18 := (forall (vars (?x1 T2)) #17)
#59 := (iff #18 #58)
#56 := (iff #17 #55)
#53 := (iff #16 #52)
#54 := [rewrite]: #53
#48 := (iff #14 #47)
#49 := [rewrite]: #48
#57 := [monotonicity #49 #54]: #56
#60 := [quant-intro #57]: #59
#41 := [asserted]: #18
#61 := [mp #41 #60]: #58
#77 := [mp~ #61 #80]: #58
#89 := [mp #77 #88]: #86
#155 := [mp #89 #154]: #150
#187 := (not #150)
#188 := (or #187 #184)
#157 := (+ #22 #156)
#158 := (<= #157 0::real)
#159 := (not #158)
#164 := (or #163 #159)
#165 := (not #164)
#189 := (or #187 #165)
#191 := (iff #189 #188)
#193 := (iff #188 #188)
#194 := [rewrite]: #193
#185 := (iff #165 #184)
#182 := (iff #164 #181)
#179 := (iff #159 #178)
#176 := (iff #158 #173)
#166 := (+ #156 #22)
#169 := (<= #166 0::real)
#174 := (iff #169 #173)
#175 := [rewrite]: #174
#170 := (iff #158 #169)
#167 := (= #157 #166)
#168 := [rewrite]: #167
#171 := [monotonicity #168]: #170
#177 := [trans #171 #175]: #176
#180 := [monotonicity #177]: #179
#183 := [monotonicity #180]: #182
#186 := [monotonicity #183]: #185
#192 := [monotonicity #186]: #191
#195 := [trans #192 #194]: #191
#190 := [quant-inst]: #189
#196 := [mp #190 #195]: #188
#220 := [unit-resolution #196 #155]: #184
#197 := (or #181 #162)
#198 := [def-axiom]: #197
#221 := [unit-resolution #198 #220]: #162
#223 := (or #206 #163 #222)
#224 := [th-lemma]: #223
#226 := [unit-resolution #224 #221]: #225
#227 := [unit-resolution #226 #219]: #222
#199 := (or #181 #173)
#200 := [def-axiom]: #199
#228 := [unit-resolution #200 #220]: #173
[th-lemma #228 #227 #211]: false
unsat
rbrrQuQfaijtLkQizgEXnQ 222 0
#2 := false
#4 := 0::real
decl uf_2 :: (-> T2 T1 real)
decl uf_5 :: T1
#15 := uf_5
decl uf_3 :: T2
#7 := uf_3
#20 := (uf_2 uf_3 uf_5)
decl uf_6 :: T2
#17 := uf_6
#18 := (uf_2 uf_6 uf_5)
#59 := -1::real
#73 := (* -1::real #18)
#106 := (+ #73 #20)
decl uf_1 :: real
#5 := uf_1
#78 := (* -1::real #20)
#79 := (+ #18 #78)
#144 := (+ uf_1 #79)
#145 := (<= #144 0::real)
#148 := (ite #145 uf_1 #106)
#279 := (* -1::real #148)
#280 := (+ uf_1 #279)
#281 := (<= #280 0::real)
#289 := (not #281)
#72 := 1/2::real
#151 := (* 1/2::real #148)
#248 := (<= #151 0::real)
#162 := (= #151 0::real)
#24 := 2::real
#27 := (- #20 #18)
#28 := (<= uf_1 #27)
#29 := (ite #28 uf_1 #27)
#30 := (/ #29 2::real)
#31 := (+ #18 #30)
#32 := (= #31 #18)
#33 := (not #32)
#34 := (not #33)
#165 := (iff #34 #162)
#109 := (<= uf_1 #106)
#112 := (ite #109 uf_1 #106)
#118 := (* 1/2::real #112)
#123 := (+ #18 #118)
#129 := (= #18 #123)
#163 := (iff #129 #162)
#154 := (+ #18 #151)
#157 := (= #18 #154)
#160 := (iff #157 #162)
#161 := [rewrite]: #160
#158 := (iff #129 #157)
#155 := (= #123 #154)
#152 := (= #118 #151)
#149 := (= #112 #148)
#146 := (iff #109 #145)
#147 := [rewrite]: #146
#150 := [monotonicity #147]: #149
#153 := [monotonicity #150]: #152
#156 := [monotonicity #153]: #155
#159 := [monotonicity #156]: #158
#164 := [trans #159 #161]: #163
#142 := (iff #34 #129)
#134 := (not #129)
#137 := (not #134)
#140 := (iff #137 #129)
#141 := [rewrite]: #140
#138 := (iff #34 #137)
#135 := (iff #33 #134)
#132 := (iff #32 #129)
#126 := (= #123 #18)
#130 := (iff #126 #129)
#131 := [rewrite]: #130
#127 := (iff #32 #126)
#124 := (= #31 #123)
#121 := (= #30 #118)
#115 := (/ #112 2::real)
#119 := (= #115 #118)
#120 := [rewrite]: #119
#116 := (= #30 #115)
#113 := (= #29 #112)
#107 := (= #27 #106)
#108 := [rewrite]: #107
#110 := (iff #28 #109)
#111 := [monotonicity #108]: #110
#114 := [monotonicity #111 #108]: #113
#117 := [monotonicity #114]: #116
#122 := [trans #117 #120]: #121
#125 := [monotonicity #122]: #124
#128 := [monotonicity #125]: #127
#133 := [trans #128 #131]: #132
#136 := [monotonicity #133]: #135
#139 := [monotonicity #136]: #138
#143 := [trans #139 #141]: #142
#166 := [trans #143 #164]: #165
#105 := [asserted]: #34
#167 := [mp #105 #166]: #162
#283 := (not #162)
#284 := (or #283 #248)
#285 := [th-lemma]: #284
#286 := [unit-resolution #285 #167]: #248
#287 := [hypothesis]: #281
#53 := (<= uf_1 0::real)
#54 := (not #53)
#6 := (< 0::real uf_1)
#55 := (iff #6 #54)
#56 := [rewrite]: #55
#50 := [asserted]: #6
#57 := [mp #50 #56]: #54
#288 := [th-lemma #57 #287 #286]: false
#290 := [lemma #288]: #289
#241 := (= uf_1 #148)
#242 := (= #106 #148)
#299 := (not #242)
#282 := (+ #106 #279)
#291 := (<= #282 0::real)
#296 := (not #291)
decl uf_4 :: T2
#10 := uf_4
#16 := (uf_2 uf_4 uf_5)
#260 := (+ #16 #78)
#261 := (>= #260 0::real)
#266 := (not #261)
#8 := (:var 0 T1)
#11 := (uf_2 uf_4 #8)
#234 := (pattern #11)
#9 := (uf_2 uf_3 #8)
#233 := (pattern #9)
#60 := (* -1::real #11)
#61 := (+ #9 #60)
#62 := (<= #61 0::real)
#179 := (not #62)
#235 := (forall (vars (?x1 T1)) (:pat #233 #234) #179)
#178 := (forall (vars (?x1 T1)) #179)
#238 := (iff #178 #235)
#236 := (iff #179 #179)
#237 := [refl]: #236
#239 := [quant-intro #237]: #238
#65 := (exists (vars (?x1 T1)) #62)
#68 := (not #65)
#175 := (~ #68 #178)
#180 := (~ #179 #179)
#177 := [refl]: #180
#176 := [nnf-neg #177]: #175
#12 := (<= #9 #11)
#13 := (exists (vars (?x1 T1)) #12)
#14 := (not #13)
#69 := (iff #14 #68)
#66 := (iff #13 #65)
#63 := (iff #12 #62)
#64 := [rewrite]: #63
#67 := [quant-intro #64]: #66
#70 := [monotonicity #67]: #69
#51 := [asserted]: #14
#71 := [mp #51 #70]: #68
#173 := [mp~ #71 #176]: #178
#240 := [mp #173 #239]: #235
#269 := (not #235)
#270 := (or #269 #266)
#250 := (* -1::real #16)
#251 := (+ #20 #250)
#252 := (<= #251 0::real)
#253 := (not #252)
#271 := (or #269 #253)
#273 := (iff #271 #270)
#275 := (iff #270 #270)
#276 := [rewrite]: #275
#267 := (iff #253 #266)
#264 := (iff #252 #261)
#254 := (+ #250 #20)
#257 := (<= #254 0::real)
#262 := (iff #257 #261)
#263 := [rewrite]: #262
#258 := (iff #252 #257)
#255 := (= #251 #254)
#256 := [rewrite]: #255
#259 := [monotonicity #256]: #258
#265 := [trans #259 #263]: #264
#268 := [monotonicity #265]: #267
#274 := [monotonicity #268]: #273
#277 := [trans #274 #276]: #273
#272 := [quant-inst]: #271
#278 := [mp #272 #277]: #270
#293 := [unit-resolution #278 #240]: #266
#90 := (* 1/2::real #20)
#102 := (+ #73 #90)
#89 := (* 1/2::real #16)
#103 := (+ #89 #102)
#100 := (>= #103 0::real)
#23 := (+ #16 #20)
#25 := (/ #23 2::real)
#26 := (<= #18 #25)
#98 := (iff #26 #100)
#91 := (+ #89 #90)
#94 := (<= #18 #91)
#97 := (iff #94 #100)
#99 := [rewrite]: #97
#95 := (iff #26 #94)
#92 := (= #25 #91)
#93 := [rewrite]: #92
#96 := [monotonicity #93]: #95
#101 := [trans #96 #99]: #98
#58 := [asserted]: #26
#104 := [mp #58 #101]: #100
#294 := [hypothesis]: #291
#295 := [th-lemma #294 #104 #293 #286]: false
#297 := [lemma #295]: #296
#298 := [hypothesis]: #242
#300 := (or #299 #291)
#301 := [th-lemma]: #300
#302 := [unit-resolution #301 #298 #297]: false
#303 := [lemma #302]: #299
#246 := (or #145 #242)
#247 := [def-axiom]: #246
#304 := [unit-resolution #247 #303]: #145
#243 := (not #145)
#244 := (or #243 #241)
#245 := [def-axiom]: #244
#305 := [unit-resolution #245 #304]: #241
#306 := (not #241)
#307 := (or #306 #281)
#308 := [th-lemma]: #307
[unit-resolution #308 #305 #290]: false
unsat
hwh3oeLAWt56hnKIa8Wuow 248 0
#2 := false
#4 := 0::real
decl uf_2 :: (-> T2 T1 real)
decl uf_5 :: T1
#15 := uf_5
decl uf_6 :: T2
#17 := uf_6
#18 := (uf_2 uf_6 uf_5)
decl uf_4 :: T2
#10 := uf_4
#16 := (uf_2 uf_4 uf_5)
#66 := -1::real
#137 := (* -1::real #16)
#138 := (+ #137 #18)
decl uf_1 :: real
#5 := uf_1
#80 := (* -1::real #18)
#81 := (+ #16 #80)
#201 := (+ uf_1 #81)
#202 := (<= #201 0::real)
#205 := (ite #202 uf_1 #138)
#352 := (* -1::real #205)
#353 := (+ uf_1 #352)
#354 := (<= #353 0::real)
#362 := (not #354)
#79 := 1/2::real
#244 := (* 1/2::real #205)
#322 := (<= #244 0::real)
#245 := (= #244 0::real)
#158 := -1/2::real
#208 := (* -1/2::real #205)
#211 := (+ #18 #208)
decl uf_3 :: T2
#7 := uf_3
#20 := (uf_2 uf_3 uf_5)
#117 := (+ #80 #20)
#85 := (* -1::real #20)
#86 := (+ #18 #85)
#188 := (+ uf_1 #86)
#189 := (<= #188 0::real)
#192 := (ite #189 uf_1 #117)
#195 := (* 1/2::real #192)
#198 := (+ #18 #195)
#97 := (* 1/2::real #20)
#109 := (+ #80 #97)
#96 := (* 1/2::real #16)
#110 := (+ #96 #109)
#107 := (>= #110 0::real)
#214 := (ite #107 #198 #211)
#217 := (= #18 #214)
#248 := (iff #217 #245)
#241 := (= #18 #211)
#246 := (iff #241 #245)
#247 := [rewrite]: #246
#242 := (iff #217 #241)
#239 := (= #214 #211)
#234 := (ite false #198 #211)
#237 := (= #234 #211)
#238 := [rewrite]: #237
#235 := (= #214 #234)
#232 := (iff #107 false)
#104 := (not #107)
#24 := 2::real
#23 := (+ #16 #20)
#25 := (/ #23 2::real)
#26 := (< #25 #18)
#108 := (iff #26 #104)
#98 := (+ #96 #97)
#101 := (< #98 #18)
#106 := (iff #101 #104)
#105 := [rewrite]: #106
#102 := (iff #26 #101)
#99 := (= #25 #98)
#100 := [rewrite]: #99
#103 := [monotonicity #100]: #102
#111 := [trans #103 #105]: #108
#65 := [asserted]: #26
#112 := [mp #65 #111]: #104
#233 := [iff-false #112]: #232
#236 := [monotonicity #233]: #235
#240 := [trans #236 #238]: #239
#243 := [monotonicity #240]: #242
#249 := [trans #243 #247]: #248
#33 := (- #18 #16)
#34 := (<= uf_1 #33)
#35 := (ite #34 uf_1 #33)
#36 := (/ #35 2::real)
#37 := (- #18 #36)
#28 := (- #20 #18)
#29 := (<= uf_1 #28)
#30 := (ite #29 uf_1 #28)
#31 := (/ #30 2::real)
#32 := (+ #18 #31)
#27 := (<= #18 #25)
#38 := (ite #27 #32 #37)
#39 := (= #38 #18)
#40 := (not #39)
#41 := (not #40)
#220 := (iff #41 #217)
#141 := (<= uf_1 #138)
#144 := (ite #141 uf_1 #138)
#159 := (* -1/2::real #144)
#160 := (+ #18 #159)
#120 := (<= uf_1 #117)
#123 := (ite #120 uf_1 #117)
#129 := (* 1/2::real #123)
#134 := (+ #18 #129)
#114 := (<= #18 #98)
#165 := (ite #114 #134 #160)
#171 := (= #18 #165)
#218 := (iff #171 #217)
#215 := (= #165 #214)
#212 := (= #160 #211)
#209 := (= #159 #208)
#206 := (= #144 #205)
#203 := (iff #141 #202)
#204 := [rewrite]: #203
#207 := [monotonicity #204]: #206
#210 := [monotonicity #207]: #209
#213 := [monotonicity #210]: #212
#199 := (= #134 #198)
#196 := (= #129 #195)
#193 := (= #123 #192)
#190 := (iff #120 #189)
#191 := [rewrite]: #190
#194 := [monotonicity #191]: #193
#197 := [monotonicity #194]: #196
#200 := [monotonicity #197]: #199
#187 := (iff #114 #107)
#186 := [rewrite]: #187
#216 := [monotonicity #186 #200 #213]: #215
#219 := [monotonicity #216]: #218
#184 := (iff #41 #171)
#176 := (not #171)
#179 := (not #176)
#182 := (iff #179 #171)
#183 := [rewrite]: #182
#180 := (iff #41 #179)
#177 := (iff #40 #176)
#174 := (iff #39 #171)
#168 := (= #165 #18)
#172 := (iff #168 #171)
#173 := [rewrite]: #172
#169 := (iff #39 #168)
#166 := (= #38 #165)
#163 := (= #37 #160)
#150 := (* 1/2::real #144)
#155 := (- #18 #150)
#161 := (= #155 #160)
#162 := [rewrite]: #161
#156 := (= #37 #155)
#153 := (= #36 #150)
#147 := (/ #144 2::real)
#151 := (= #147 #150)
#152 := [rewrite]: #151
#148 := (= #36 #147)
#145 := (= #35 #144)
#139 := (= #33 #138)
#140 := [rewrite]: #139
#142 := (iff #34 #141)
#143 := [monotonicity #140]: #142
#146 := [monotonicity #143 #140]: #145
#149 := [monotonicity #146]: #148
#154 := [trans #149 #152]: #153
#157 := [monotonicity #154]: #156
#164 := [trans #157 #162]: #163
#135 := (= #32 #134)
#132 := (= #31 #129)
#126 := (/ #123 2::real)
#130 := (= #126 #129)
#131 := [rewrite]: #130
#127 := (= #31 #126)
#124 := (= #30 #123)
#118 := (= #28 #117)
#119 := [rewrite]: #118
#121 := (iff #29 #120)
#122 := [monotonicity #119]: #121
#125 := [monotonicity #122 #119]: #124
#128 := [monotonicity #125]: #127
#133 := [trans #128 #131]: #132
#136 := [monotonicity #133]: #135
#115 := (iff #27 #114)
#116 := [monotonicity #100]: #115
#167 := [monotonicity #116 #136 #164]: #166
#170 := [monotonicity #167]: #169
#175 := [trans #170 #173]: #174
#178 := [monotonicity #175]: #177
#181 := [monotonicity #178]: #180
#185 := [trans #181 #183]: #184
#221 := [trans #185 #219]: #220
#113 := [asserted]: #41
#222 := [mp #113 #221]: #217
#250 := [mp #222 #249]: #245
#356 := (not #245)
#357 := (or #356 #322)
#358 := [th-lemma]: #357
#359 := [unit-resolution #358 #250]: #322
#360 := [hypothesis]: #354
#60 := (<= uf_1 0::real)
#61 := (not #60)
#6 := (< 0::real uf_1)
#62 := (iff #6 #61)
#63 := [rewrite]: #62
#57 := [asserted]: #6
#64 := [mp #57 #63]: #61
#361 := [th-lemma #64 #360 #359]: false
#363 := [lemma #361]: #362
#315 := (= uf_1 #205)
#316 := (= #138 #205)
#371 := (not #316)
#355 := (+ #138 #352)
#364 := (<= #355 0::real)
#368 := (not #364)
#87 := (<= #86 0::real)
#82 := (<= #81 0::real)
#90 := (and #82 #87)
#21 := (<= #18 #20)
#19 := (<= #16 #18)
#22 := (and #19 #21)
#91 := (iff #22 #90)
#88 := (iff #21 #87)
#89 := [rewrite]: #88
#83 := (iff #19 #82)
#84 := [rewrite]: #83
#92 := [monotonicity #84 #89]: #91
#59 := [asserted]: #22
#93 := [mp #59 #92]: #90
#95 := [and-elim #93]: #87
#366 := [hypothesis]: #364
#367 := [th-lemma #366 #95 #112 #359]: false
#369 := [lemma #367]: #368
#370 := [hypothesis]: #316
#372 := (or #371 #364)
#373 := [th-lemma]: #372
#374 := [unit-resolution #373 #370 #369]: false
#375 := [lemma #374]: #371
#320 := (or #202 #316)
#321 := [def-axiom]: #320
#376 := [unit-resolution #321 #375]: #202
#317 := (not #202)
#318 := (or #317 #315)
#319 := [def-axiom]: #318
#377 := [unit-resolution #319 #376]: #315
#378 := (not #315)
#379 := (or #378 #354)
#380 := [th-lemma]: #379
[unit-resolution #380 #377 #363]: false
unsat
WdMJH3tkMv/rps8y9Ukq5Q 86 0
#2 := false
#37 := 0::real
decl uf_2 :: (-> T2 T1 real)
decl uf_4 :: T1
#12 := uf_4
decl uf_3 :: T2
#5 := uf_3
#13 := (uf_2 uf_3 uf_4)
#34 := -1::real
#140 := (* -1::real #13)
decl uf_1 :: real
#4 := uf_1
#141 := (+ uf_1 #140)
#143 := (>= #141 0::real)
#6 := (:var 0 T1)
#7 := (uf_2 uf_3 #6)
#127 := (pattern #7)
#35 := (* -1::real #7)
#36 := (+ uf_1 #35)
#47 := (>= #36 0::real)
#134 := (forall (vars (?x2 T1)) (:pat #127) #47)
#49 := (forall (vars (?x2 T1)) #47)
#137 := (iff #49 #134)
#135 := (iff #47 #47)
#136 := [refl]: #135
#138 := [quant-intro #136]: #137
#67 := (~ #49 #49)
#58 := (~ #47 #47)
#66 := [refl]: #58
#68 := [nnf-pos #66]: #67
#10 := (<= #7 uf_1)
#11 := (forall (vars (?x2 T1)) #10)
#50 := (iff #11 #49)
#46 := (iff #10 #47)
#48 := [rewrite]: #46
#51 := [quant-intro #48]: #50
#32 := [asserted]: #11
#52 := [mp #32 #51]: #49
#69 := [mp~ #52 #68]: #49
#139 := [mp #69 #138]: #134
#149 := (not #134)
#150 := (or #149 #143)
#151 := [quant-inst]: #150
#144 := [unit-resolution #151 #139]: #143
#142 := (<= #141 0::real)
#38 := (<= #36 0::real)
#128 := (forall (vars (?x1 T1)) (:pat #127) #38)
#41 := (forall (vars (?x1 T1)) #38)
#131 := (iff #41 #128)
#129 := (iff #38 #38)
#130 := [refl]: #129
#132 := [quant-intro #130]: #131
#62 := (~ #41 #41)
#64 := (~ #38 #38)
#65 := [refl]: #64
#63 := [nnf-pos #65]: #62
#8 := (<= uf_1 #7)
#9 := (forall (vars (?x1 T1)) #8)
#42 := (iff #9 #41)
#39 := (iff #8 #38)
#40 := [rewrite]: #39
#43 := [quant-intro #40]: #42
#31 := [asserted]: #9
#44 := [mp #31 #43]: #41
#61 := [mp~ #44 #63]: #41
#133 := [mp #61 #132]: #128
#145 := (not #128)
#146 := (or #145 #142)
#147 := [quant-inst]: #146
#148 := [unit-resolution #147 #133]: #142
#45 := (= uf_1 #13)
#55 := (not #45)
#14 := (= #13 uf_1)
#15 := (not #14)
#56 := (iff #15 #55)
#53 := (iff #14 #45)
#54 := [rewrite]: #53
#57 := [monotonicity #54]: #56
#33 := [asserted]: #15
#60 := [mp #33 #57]: #55
#153 := (not #143)
#152 := (not #142)
#154 := (or #45 #152 #153)
#155 := [th-lemma]: #154
[unit-resolution #155 #60 #148 #144]: false
unsat
V+IAyBZU/6QjYs6JkXx8LQ 57 0
#2 := false
#4 := 0::real
decl uf_1 :: (-> T2 real)
decl uf_2 :: (-> T1 T1 T2)
decl uf_12 :: (-> T4 T1)
decl uf_4 :: T4
#11 := uf_4
#39 := (uf_12 uf_4)
decl uf_10 :: T4
#27 := uf_10
#38 := (uf_12 uf_10)
#40 := (uf_2 #38 #39)
#41 := (uf_1 #40)
#264 := (>= #41 0::real)
#266 := (not #264)
#43 := (= #41 0::real)
#44 := (not #43)
#131 := [asserted]: #44
#272 := (or #43 #266)
#42 := (<= #41 0::real)
#130 := [asserted]: #42
#265 := (not #42)
#270 := (or #43 #265 #266)
#271 := [th-lemma]: #270
#273 := [unit-resolution #271 #130]: #272
#274 := [unit-resolution #273 #131]: #266
#6 := (:var 0 T1)
#5 := (:var 1 T1)
#7 := (uf_2 #5 #6)
#241 := (pattern #7)
#8 := (uf_1 #7)
#65 := (>= #8 0::real)
#242 := (forall (vars (?x1 T1) (?x2 T1)) (:pat #241) #65)
#66 := (forall (vars (?x1 T1) (?x2 T1)) #65)
#245 := (iff #66 #242)
#243 := (iff #65 #65)
#244 := [refl]: #243
#246 := [quant-intro #244]: #245
#149 := (~ #66 #66)
#151 := (~ #65 #65)
#152 := [refl]: #151
#150 := [nnf-pos #152]: #149
#9 := (<= 0::real #8)
#10 := (forall (vars (?x1 T1) (?x2 T1)) #9)
#67 := (iff #10 #66)
#63 := (iff #9 #65)
#64 := [rewrite]: #63
#68 := [quant-intro #64]: #67
#60 := [asserted]: #10
#69 := [mp #60 #68]: #66
#147 := [mp~ #69 #150]: #66
#247 := [mp #147 #246]: #242
#267 := (not #242)
#268 := (or #267 #264)
#269 := [quant-inst]: #268
[unit-resolution #269 #247 #274]: false
unsat