src/HOL/Multivariate_Analysis/Integration.cert

   val!5 -> val!6
   val!4 -> val!7
   else -> val!7
 }
 sat
+qkVrmXMcHAG5MLuJ9d8jXQ 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