updated SMT certificates
authorboehmes
Tue, 31 May 2011 19:28:03 +0200
changeset 43118 e3c7b07704bc
parent 43117 5de84843685f
child 43119 1286e56edf06
updated SMT certificates
src/HOL/Boogie/Examples/Boogie_Dijkstra.certs
src/HOL/Boogie/Examples/Boogie_Max.certs
src/HOL/Boogie/Examples/VCC_Max.certs
src/HOL/Multivariate_Analysis/Integration.certs
src/HOL/SMT_Examples/SMT_Examples.certs
src/HOL/SMT_Examples/SMT_Tests.certs
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Tue May 31 19:27:19 2011 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Tue May 31 19:28:03 2011 +0200
@@ -1,814 +1,728 @@
-b9c818fc8db5c62ae4864b1c933f204656ce6c70 7184 0
+9404399607250187a35291f0e20ac6b62142fe20 6771 0
 #2 := false
-decl f13 :: (-> S5 S3 Int)
-decl f22 :: S3
+#8 := 0::Int
+decl f4 :: (-> S3 Int)
+decl f5 :: (-> S2 S2 S3)
+decl ?v0!20 :: S2
+#2313 := ?v0!20
+decl f22 :: S2
 #170 := f22
+#14159 := (f5 f22 ?v0!20)
+#14160 := (f4 #14159)
+#1175 := -1::Int
+#14164 := (* -1::Int #14160)
+decl f3 :: Int
+#9 := f3
+#14168 := (+ f3 #14164)
+#14169 := (<= #14168 0::Int)
+#12854 := (not #14169)
+decl f13 :: (-> S5 S2 Int)
 decl f14 :: S5
 #98 := f14
+#14126 := (f13 f14 ?v0!20)
+#14143 := (* -1::Int #14126)
+#14178 := (+ #14143 #14160)
 #174 := (f13 f14 f22)
-decl f10 :: S3
-#56 := f10
-#99 := (f13 f14 f10)
-#7788 := (= #99 #174)
-#7816 := (= #174 #99)
-#6077 := (= f22 f10)
-#6079 := (= f10 f22)
-decl f3 :: (-> S2 S3 S1)
-decl ?v1!7 :: (-> S3 S3)
-#6060 := (?v1!7 f22)
-decl f15 :: S2
+#14179 := (+ #174 #14178)
+#14180 := (>= #14179 0::Int)
+#14215 := (or #14169 #14180)
+#14218 := (not #14215)
+decl f24 :: (-> S2 Int)
+#2314 := (f24 ?v0!20)
+#14212 := (= #2314 #14126)
+#22951 := (not #14212)
+#14144 := (+ #2314 #14143)
+#19137 := (>= #14144 0::Int)
+#22448 := (not #19137)
+decl f8 :: (-> S4 S2 S1)
+decl ?v1!7 :: (-> S2 S2)
+#14273 := (?v1!7 ?v0!20)
+decl f15 :: S4
 #104 := f15
-#6072 := (f3 f15 #6060)
+#14285 := (f8 f15 #14273)
 decl f1 :: S1
 #4 := f1
-#6073 := (= f1 #6072)
-#6074 := (not #6073)
-#44 := 0::Int
-decl f9 :: (-> S4 Int)
-decl f5 :: (-> S3 S3 S4)
-#6065 := (f5 #6060 f22)
-#6066 := (f9 #6065)
-#1199 := -1::Int
-#6067 := (* -1::Int #6066)
-#6061 := (f13 f14 #6060)
-#6062 := (* -1::Int #6061)
-#6068 := (+ #6062 #6067)
-#6069 := (+ #174 #6068)
-#6070 := (= #6069 0::Int)
-#6071 := (not #6070)
-#6063 := (+ #174 #6062)
-#6064 := (<= #6063 0::Int)
-#6082 := (or #6064 #6071 #6074)
-decl f24 :: (-> S3 Int)
-decl ?v0!15 :: S3
-#2264 := ?v0!15
-#2265 := (f24 ?v0!15)
-#2266 := (>= #2265 0::Int)
-#2267 := (not #2266)
-decl ?v0!20 :: S3
-#2337 := ?v0!20
-#12 := (:var 0 S3)
-#2341 := (f5 #12 ?v0!20)
-#4445 := (pattern #2341)
-#188 := (f24 #12)
-#4385 := (pattern #188)
-decl f23 :: S2
+#14286 := (= f1 #14285)
+decl f9 :: (-> S4 S2 S1 S4)
+#180 := (f9 f15 f22 f1)
+#5830 := (f8 #180 f22)
+#5831 := (= f1 #5830)
+decl f6 :: (-> S3 S2)
+decl f10 :: S2
+#56 := f10
+#5873 := (f5 f22 f10)
+#6386 := (f6 #5873)
+#22127 := (= #6386 #14273)
+#22119 := (ite #22127 #5831 #14286)
+#22149 := (not #22119)
+#7238 := (f9 f15 #6386 #5830)
+#22125 := (f8 #7238 #14273)
+#22126 := (= f1 #22125)
+#22140 := (iff #22119 #22126)
+#12 := (:var 0 S2)
+#45 := (:var 1 S1)
+#44 := (:var 2 S2)
+#43 := (:var 3 S4)
+#46 := (f9 #43 #44 #45)
+#47 := (f8 #46 #12)
+#4178 := (pattern #47)
+#51 := (f8 #43 #12)
+#387 := (= f1 #51)
+#384 := (= f1 #45)
+#49 := (= #12 #44)
+#390 := (ite #49 #384 #387)
+#380 := (= f1 #47)
+#393 := (iff #380 #390)
+#4179 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #4178) #393)
+#396 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) #393)
+#4182 := (iff #396 #4179)
+#4180 := (iff #393 #393)
+#4181 := [refl]: #4180
+#4183 := [quant-intro #4181]: #4182
+#1821 := (~ #396 #396)
+#1849 := (~ #393 #393)
+#1850 := [refl]: #1849
+#1822 := [nnf-pos #1850]: #1821
+#52 := (= #51 f1)
+#50 := (= #45 f1)
+#53 := (ite #49 #50 #52)
+#48 := (= #47 f1)
+#54 := (iff #48 #53)
+#55 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) #54)
+#397 := (iff #55 #396)
+#394 := (iff #54 #393)
+#391 := (iff #53 #390)
+#388 := (iff #52 #387)
+#389 := [rewrite]: #388
+#385 := (iff #50 #384)
+#386 := [rewrite]: #385
+#392 := [monotonicity #386 #389]: #391
+#382 := (iff #48 #380)
+#383 := [rewrite]: #382
+#395 := [monotonicity #383 #392]: #394
+#398 := [quant-intro #395]: #397
+#379 := [asserted]: #55
+#401 := [mp #379 #398]: #396
+#1851 := [mp~ #401 #1822]: #396
+#4184 := [mp #1851 #4183]: #4179
+#6238 := (not #4179)
+#22056 := (or #6238 #22140)
+#22120 := (= #14273 #6386)
+#22122 := (ite #22120 #5831 #14286)
+#22124 := (iff #22126 #22122)
+#22094 := (or #6238 #22124)
+#22055 := (iff #22094 #22056)
+#22097 := (iff #22056 #22056)
+#22093 := [rewrite]: #22097
+#22057 := (iff #22124 #22140)
+#22130 := (iff #22126 #22119)
+#22141 := (iff #22130 #22140)
+#22139 := [rewrite]: #22141
+#22131 := (iff #22124 #22130)
+#22123 := (iff #22122 #22119)
+#22121 := (iff #22120 #22127)
+#22128 := [rewrite]: #22121
+#22129 := [monotonicity #22128]: #22123
+#22118 := [monotonicity #22129]: #22131
+#22088 := [trans #22118 #22139]: #22057
+#22096 := [monotonicity #22088]: #22055
+#22144 := [trans #22096 #22093]: #22055
+#22095 := [quant-inst #104 #6386 #5830 #14273]: #22094
+#22148 := [mp #22095 #22144]: #22056
+#22563 := [unit-resolution #22148 #4184]: #22140
+#22266 := (not #22126)
+decl f23 :: S4
 #179 := f23
-#198 := (f3 f23 #12)
-#4411 := (pattern #198)
-#2342 := (f9 #2341)
-#2338 := (f24 ?v0!20)
-#2339 := (* -1::Int #2338)
-#2941 := (+ #2339 #2342)
-#2942 := (+ #188 #2941)
-#2945 := (= #2942 0::Int)
-#3507 := (not #2945)
-#2340 := (+ #188 #2339)
-#2345 := (>= #2340 0::Int)
-#798 := (= f1 #198)
-#804 := (not #798)
-#3508 := (or #804 #2345 #3507)
-#4446 := (forall (vars (?v1 S3)) (:pat #4411 #4385 #4445) #3508)
-#4451 := (not #4446)
-#23 := (:var 1 S3)
-#81 := (f5 #12 #23)
-#4240 := (pattern #81)
-#210 := (f24 #23)
-#1494 := (* -1::Int #210)
-#1495 := (+ #188 #1494)
-#82 := (f9 #81)
-#1525 := (+ #82 #1495)
-#1523 := (>= #1525 0::Int)
-#1222 := (* -1::Int #82)
-decl f8 :: Int
-#45 := f8
-#1225 := (+ f8 #1222)
-#1226 := (<= #1225 0::Int)
-#3499 := (or #804 #1226 #1523)
-#4437 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3499)
-#4442 := (not #4437)
-#2917 := (= f10 ?v0!20)
-#2349 := (+ f8 #2339)
-#2350 := (<= #2349 0::Int)
-#4454 := (or #2350 #2917 #4442 #4451)
+#19072 := (f8 f23 #14273)
+#19073 := (= f1 #19072)
+#19080 := (not #19073)
+#22994 := (iff #19080 #22266)
+#22987 := (iff #19073 #22126)
+#23020 := (iff #22126 #19073)
+#23000 := (= #22125 #19072)
+#8697 := (= #7238 f23)
+#8695 := (= #180 f23)
+#181 := (= f23 #180)
+#2317 := (f5 #12 ?v0!20)
+#4421 := (pattern #2317)
+#188 := (f24 #12)
+#4361 := (pattern #188)
+#198 := (f8 f23 #12)
+#4387 := (pattern #198)
+#2318 := (f4 #2317)
+#2315 := (* -1::Int #2314)
+#2917 := (+ #2315 #2318)
+#2918 := (+ #188 #2917)
+#2921 := (= #2918 0::Int)
+#3483 := (not #2921)
+#2316 := (+ #188 #2315)
+#2321 := (>= #2316 0::Int)
+#774 := (= f1 #198)
+#780 := (not #774)
+#3484 := (or #780 #2321 #3483)
+#4422 := (forall (vars (?v1 S2)) (:pat #4387 #4361 #4421) #3484)
+#4427 := (not #4422)
+#11 := (:var 1 S2)
+#81 := (f5 #12 #11)
+#4216 := (pattern #81)
+#210 := (f24 #11)
+#1470 := (* -1::Int #210)
+#1471 := (+ #188 #1470)
+#82 := (f4 #81)
+#1501 := (+ #82 #1471)
+#1499 := (>= #1501 0::Int)
+#1198 := (* -1::Int #82)
+#1201 := (+ f3 #1198)
+#1202 := (<= #1201 0::Int)
+#3475 := (or #780 #1202 #1499)
+#4413 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4216) #3475)
+#4418 := (not #4413)
+#2893 := (= f10 ?v0!20)
+#2325 := (+ f3 #2315)
+#2326 := (<= #2325 0::Int)
+#4430 := (or #2326 #2893 #4418 #4427)
+#4433 := (not #4430)
+decl ?v0!19 :: S2
+#2283 := ?v0!19
+decl ?v1!18 :: S2
+#2282 := ?v1!18
+#2288 := (f5 ?v1!18 ?v0!19)
+#2289 := (f4 #2288)
+#2292 := (* -1::Int #2289)
+#2286 := (f24 ?v1!18)
+#2879 := (* -1::Int #2286)
+#2880 := (+ #2879 #2292)
+#2284 := (f24 ?v0!19)
+#2881 := (+ #2284 #2880)
+#2882 := (<= #2881 0::Int)
+#2296 := (f8 f23 ?v1!18)
+#2297 := (= f1 #2296)
+#3438 := (not #2297)
+#2293 := (+ f3 #2292)
+#2294 := (<= #2293 0::Int)
+#3453 := (or #2294 #3438 #2882)
+#3458 := (not #3453)
+#4436 := (or #3458 #4433)
+#4439 := (not #4436)
+#4404 := (pattern #188 #210)
+#1469 := (>= #1471 0::Int)
+#207 := (f8 f23 #11)
+#794 := (= f1 #207)
+#3415 := (not #794)
+#3430 := (or #774 #3415 #1469)
+#4405 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4404) #3430)
+#4410 := (not #4405)
+#4442 := (or #4410 #4439)
+#4445 := (not #4442)
+decl ?v1!16 :: S2
+#2255 := ?v1!16
+#2259 := (f24 ?v1!16)
+#2853 := (* -1::Int #2259)
+decl ?v0!17 :: S2
+#2256 := ?v0!17
+#2257 := (f24 ?v0!17)
+#2854 := (+ #2257 #2853)
+#2855 := (<= #2854 0::Int)
+#2264 := (f8 f23 ?v1!16)
+#2265 := (= f1 #2264)
+#2262 := (f8 f23 ?v0!17)
+#2263 := (= f1 #2262)
+#3392 := (not #2263)
+#3407 := (or #3392 #2265 #2855)
+#3412 := (not #3407)
+#4448 := (or #3412 #4445)
+#4451 := (not #4448)
+#1460 := (>= #188 0::Int)
+#4396 := (forall (vars (?v0 S2)) (:pat #4361) #1460)
+#4401 := (not #4396)
+#4454 := (or #4401 #4451)
 #4457 := (not #4454)
-decl ?v0!19 :: S3
-#2307 := ?v0!19
-decl ?v1!18 :: S3
-#2306 := ?v1!18
-#2312 := (f5 ?v1!18 ?v0!19)
-#2313 := (f9 #2312)
-#2316 := (* -1::Int #2313)
-#2310 := (f24 ?v1!18)
-#2903 := (* -1::Int #2310)
-#2904 := (+ #2903 #2316)
-#2308 := (f24 ?v0!19)
-#2905 := (+ #2308 #2904)
-#2906 := (<= #2905 0::Int)
-#2320 := (f3 f23 ?v1!18)
-#2321 := (= f1 #2320)
-#3462 := (not #2321)
-#2317 := (+ f8 #2316)
-#2318 := (<= #2317 0::Int)
-#3477 := (or #2318 #3462 #2906)
-#3482 := (not #3477)
-#4460 := (or #3482 #4457)
+decl ?v0!15 :: S2
+#2240 := ?v0!15
+#2241 := (f24 ?v0!15)
+#2242 := (>= #2241 0::Int)
+#2243 := (not #2242)
+#4460 := (or #2243 #4457)
 #4463 := (not #4460)
-#4428 := (pattern #188 #210)
-#1493 := (>= #1495 0::Int)
-#207 := (f3 f23 #23)
-#818 := (= f1 #207)
-#3439 := (not #818)
-#3454 := (or #798 #3439 #1493)
-#4429 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4428) #3454)
-#4434 := (not #4429)
-#4466 := (or #4434 #4463)
-#4469 := (not #4466)
-decl ?v1!16 :: S3
-#2279 := ?v1!16
-#2283 := (f24 ?v1!16)
-#2877 := (* -1::Int #2283)
-decl ?v0!17 :: S3
-#2280 := ?v0!17
-#2281 := (f24 ?v0!17)
-#2878 := (+ #2281 #2877)
-#2879 := (<= #2878 0::Int)
-#2288 := (f3 f23 ?v1!16)
-#2289 := (= f1 #2288)
-#2286 := (f3 f23 ?v0!17)
-#2287 := (= f1 #2286)
-#3416 := (not #2287)
-#3431 := (or #3416 #2289 #2879)
-#3436 := (not #3431)
-#4472 := (or #3436 #4469)
-#4475 := (not #4472)
-#1484 := (>= #188 0::Int)
-#4420 := (forall (vars (?v0 S3)) (:pat #4385) #1484)
-#4425 := (not #4420)
-#4478 := (or #4425 #4475)
-decl f6 :: (-> S4 S3)
-decl f7 :: (-> S4 S3)
-#5986 := (f5 f22 f22)
-#7202 := (f7 #5986)
-#14202 := (f5 #7202 ?v0!20)
-#24383 := (f7 #14202)
-#14765 := (?v1!7 ?v0!20)
-#24660 := (f5 #14765 #24383)
-#25033 := (f6 #24660)
-#26204 := (f3 f15 #25033)
-#26205 := (= f1 #26204)
-#14777 := (f3 f15 #14765)
-#27697 := (= #14777 #26204)
-#27694 := (= #26204 #14777)
-#29042 := (= #25033 #14765)
-#14770 := (f5 #14765 ?v0!20)
-#19029 := (f6 #14770)
-#26809 := (= #19029 #14765)
-#19034 := (= #14765 #19029)
-#37 := (f5 #23 #12)
-#4184 := (pattern #37)
-#41 := (f6 #37)
-#343 := (= #23 #41)
-#4191 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #343)
-#347 := (forall (vars (?v0 S3) (?v1 S3)) #343)
-#4194 := (iff #347 #4191)
-#4192 := (iff #343 #343)
-#4193 := [refl]: #4192
-#4195 := [quant-intro #4193]: #4194
-#1839 := (~ #347 #347)
-#1869 := (~ #343 #343)
-#1870 := [refl]: #1869
-#1840 := [nnf-pos #1870]: #1839
-#42 := (= #41 #23)
-#43 := (forall (vars (?v0 S3) (?v1 S3)) #42)
-#348 := (iff #43 #347)
-#345 := (iff #42 #343)
-#346 := [rewrite]: #345
-#349 := [quant-intro #346]: #348
-#342 := [asserted]: #43
-#352 := [mp #342 #349]: #347
-#1871 := [mp~ #352 #1840]: #347
-#4196 := [mp #1871 #4195]: #4191
-#6820 := (not #4191)
-#8621 := (or #6820 #19034)
-#13585 := [quant-inst #14765 #2337]: #8621
-#26765 := [unit-resolution #13585 #4196]: #19034
-#26807 := [symm #26765]: #26809
-#26817 := (= #25033 #19029)
-#26814 := (= #24660 #14770)
-#27246 := (= #24383 ?v0!20)
-#19033 := (f7 #14770)
-#25085 := (= #19033 ?v0!20)
-#19028 := (= ?v0!20 #19033)
-#38 := (f7 #37)
-#335 := (= #12 #38)
-#4185 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #335)
-#339 := (forall (vars (?v0 S3) (?v1 S3)) #335)
-#4188 := (iff #339 #4185)
-#4186 := (iff #335 #335)
-#4187 := [refl]: #4186
-#4189 := [quant-intro #4187]: #4188
-#1837 := (~ #339 #339)
-#1866 := (~ #335 #335)
-#1867 := [refl]: #1866
-#1838 := [nnf-pos #1867]: #1837
-#39 := (= #38 #12)
-#40 := (forall (vars (?v0 S3) (?v1 S3)) #39)
-#340 := (iff #40 #339)
-#337 := (iff #39 #335)
-#338 := [rewrite]: #337
-#341 := [quant-intro #338]: #340
-#334 := [asserted]: #40
-#344 := [mp #334 #341]: #339
-#1868 := [mp~ #344 #1838]: #339
-#4190 := [mp #1868 #4189]: #4185
-#6815 := (not #4185)
-#19035 := (or #6815 #19028)
-#19036 := [quant-inst #14765 #2337]: #19035
-#25084 := [unit-resolution #19036 #4190]: #19028
-#25086 := [symm #25084]: #25085
-#26786 := (= #24383 #19033)
-#23171 := (f5 #7202 #19033)
-#23290 := (f7 #23171)
-#26798 := (= #23290 #19033)
-#23296 := (= #19033 #23290)
-#26708 := (or #6815 #23296)
-#26711 := [quant-inst #7202 #19033]: #26708
-#26794 := [unit-resolution #26711 #4190]: #23296
-#26799 := [symm #26794]: #26798
-#26795 := (= #24383 #23290)
-#26792 := (= #23290 #24383)
-#26790 := (= #23171 #14202)
-#14122 := (f5 f22 ?v0!20)
-#26764 := (= #14122 #14202)
-#24019 := (= #14202 #14122)
-#7775 := (= #7202 f22)
-#7203 := (= f22 #7202)
-#7254 := (or #6815 #7203)
-#7255 := [quant-inst #170 #170]: #7254
-#7780 := [unit-resolution #7255 #4190]: #7203
-#7781 := [symm #7780]: #7775
-#24020 := [monotonicity #7781]: #24019
-#26706 := [symm #24020]: #26764
-#26768 := (= #23171 #14122)
-#26767 := (= #14122 #23171)
-#26743 := [monotonicity #7780 #25084]: #26767
-#26769 := [symm #26743]: #26768
-#26793 := [trans #26769 #26706]: #26790
-#26796 := [monotonicity #26793]: #26792
-#26797 := [symm #26796]: #26795
-#26813 := [trans #26797 #26799]: #26786
-#26787 := [trans #26813 #25086]: #27246
-#26815 := [monotonicity #26787]: #26814
-#26808 := [monotonicity #26815]: #26817
-#26810 := [trans #26808 #26807]: #29042
-#26805 := [monotonicity #26810]: #27694
-#26819 := [symm #26805]: #27697
-#14778 := (= f1 #14777)
-#14779 := (not #14778)
-#14771 := (f9 #14770)
-#14772 := (* -1::Int #14771)
-#14766 := (f13 f14 #14765)
-#14767 := (* -1::Int #14766)
-#14773 := (+ #14767 #14772)
-#14065 := (f13 f14 ?v0!20)
-#14774 := (+ #14065 #14773)
-#14775 := (= #14774 0::Int)
-#14776 := (not #14775)
-#14768 := (+ #14065 #14767)
-#14769 := (<= #14768 0::Int)
-#14785 := (or #14769 #14776 #14779)
-#14788 := (not #14785)
-#14106 := (* -1::Int #14065)
-#14782 := (+ f8 #14106)
-#14783 := (<= #14782 0::Int)
-#21426 := (not #14783)
-#2351 := (not #2350)
-#19774 := [hypothesis]: #2351
-#14107 := (+ #2338 #14106)
-#19558 := (>= #14107 0::Int)
-#14076 := (= #2338 #14065)
-#14123 := (f9 #14122)
-#14141 := (+ #14106 #14123)
-#14142 := (+ #174 #14141)
-#14143 := (>= #14142 0::Int)
-#14127 := (* -1::Int #14123)
-#14131 := (+ f8 #14127)
-#14132 := (<= #14131 0::Int)
-#14174 := (or #14132 #14143)
-#4481 := (not #4478)
-#1444 := (* -1::Int #174)
-#5904 := (+ #99 #1444)
-#7789 := (<= #5904 0::Int)
-#27725 := (or #6064 #2350)
-#25038 := (= #14765 #25033)
-#23328 := (or #6820 #25038)
-#23329 := [quant-inst #14765 #24383]: #23328
-#28975 := [unit-resolution #23329 #4196]: #25038
-#29053 := [symm #28975]: #29042
-#27689 := [monotonicity #29053]: #27694
-#27709 := [symm #27689]: #27697
-#6109 := (not #6064)
-#10065 := [hypothesis]: #6109
-#23165 := (or #14143 #6064)
-#11105 := (or #2266 #6064)
-#7527 := (f13 f14 ?v0!15)
-#7748 := (>= #7527 0::Int)
-#101 := (f13 f14 #12)
-#4264 := (pattern #101)
-#1727 := (>= #101 0::Int)
-#4265 := (forall (vars (?v0 S3)) (:pat #4264) #1727)
-#4484 := (or #2267 #4481)
-#4487 := (not #4484)
 #202 := (f24 f10)
 #203 := (= #202 0::Int)
-#1481 := (not #203)
-#4490 := (or #1481 #4487)
+#1457 := (not #203)
+#4466 := (or #1457 #4463)
+#4469 := (not #4466)
+#4472 := (or #1457 #4469)
+#4475 := (not #4472)
+#101 := (f13 f14 #12)
+#4240 := (pattern #101)
+#760 := (= #101 #188)
+#781 := (or #760 #780)
+#4388 := (forall (vars (?v0 S2)) (:pat #4240 #4361 #4387) #781)
+#4393 := (not #4388)
+#4478 := (or #4393 #4475)
+#4481 := (not #4478)
+decl ?v0!14 :: S2
+#2215 := ?v0!14
+#2220 := (f13 f14 ?v0!14)
+#2219 := (f24 ?v0!14)
+#2825 := (= #2219 #2220)
+#2216 := (f8 f23 ?v0!14)
+#2217 := (= f1 #2216)
+#2218 := (not #2217)
+#2831 := (or #2218 #2825)
+#2836 := (not #2831)
+#4484 := (or #2836 #4481)
+#4487 := (not #4484)
+#1445 := (* -1::Int #188)
+#1446 := (+ #101 #1445)
+#1444 := (>= #1446 0::Int)
+#4379 := (forall (vars (?v0 S2)) (:pat #4240 #4361) #1444)
+#4384 := (not #4379)
+#4490 := (or #4384 #4487)
 #4493 := (not #4490)
-#4496 := (or #1481 #4493)
+decl ?v0!13 :: S2
+#2197 := ?v0!13
+#2200 := (f13 f14 ?v0!13)
+#2815 := (* -1::Int #2200)
+#2198 := (f24 ?v0!13)
+#2816 := (+ #2198 #2815)
+#2817 := (<= #2816 0::Int)
+#2822 := (not #2817)
+#4496 := (or #2822 #4493)
 #4499 := (not #4496)
-#784 := (= #101 #188)
-#805 := (or #784 #804)
-#4412 := (forall (vars (?v0 S3)) (:pat #4264 #4385 #4411) #805)
-#4417 := (not #4412)
-#4502 := (or #4417 #4499)
-#4505 := (not #4502)
-decl ?v0!14 :: S3
-#2239 := ?v0!14
-#2244 := (f13 f14 ?v0!14)
-#2243 := (f24 ?v0!14)
-#2849 := (= #2243 #2244)
-#2240 := (f3 f23 ?v0!14)
-#2241 := (= f1 #2240)
-#2242 := (not #2241)
-#2855 := (or #2242 #2849)
-#2860 := (not #2855)
-#4508 := (or #2860 #4505)
-#4511 := (not #4508)
-#1469 := (* -1::Int #188)
-#1470 := (+ #101 #1469)
-#1468 := (>= #1470 0::Int)
-#4403 := (forall (vars (?v0 S3)) (:pat #4264 #4385) #1468)
-#4408 := (not #4403)
-#4514 := (or #4408 #4511)
-#4517 := (not #4514)
-decl ?v0!13 :: S3
-#2221 := ?v0!13
-#2224 := (f13 f14 ?v0!13)
-#2839 := (* -1::Int #2224)
-#2222 := (f24 ?v0!13)
-#2840 := (+ #2222 #2839)
-#2841 := (<= #2840 0::Int)
-#2846 := (not #2841)
-#4520 := (or #2846 #4517)
-#4523 := (not #4520)
 #182 := (f5 f22 #12)
-#4386 := (pattern #182)
-#183 := (f9 #182)
-#1612 := (+ #183 #1469)
-#1613 := (+ #174 #1612)
-#1614 := (= #1613 0::Int)
-#1438 := (* -1::Int #183)
-#1445 := (+ #1444 #1438)
-#1446 := (+ #101 #1445)
-#1447 := (<= #1446 0::Int)
-#1439 := (+ f8 #1438)
-#1440 := (<= #1439 0::Int)
-#3408 := (or #1440 #1447 #1614)
-#4395 := (forall (vars (?v0 S3)) (:pat #4386 #4264 #4385) #3408)
-#4400 := (not #4395)
-#3388 := (or #1440 #1447)
-#3389 := (not #3388)
-#3392 := (or #784 #3389)
-#4387 := (forall (vars (?v0 S3)) (:pat #4264 #4385 #4386) #3392)
-#4392 := (not #4387)
-decl ?v0!12 :: S3
-#2197 := ?v0!12
-#2203 := (f3 f15 ?v0!12)
-#2204 := (= f1 #2203)
-#2198 := (f13 f14 ?v0!12)
-#2199 := (* -1::Int #2198)
-#2200 := (+ f8 #2199)
-#2201 := (<= #2200 0::Int)
-#1644 := (+ f8 #1444)
-#1645 := (<= #1644 0::Int)
-#105 := (f3 f15 #12)
-#4306 := (pattern #105)
-#1627 := (+ #101 #1444)
-#1626 := (>= #1627 0::Int)
-#532 := (= f1 #105)
-#1633 := (or #532 #1626)
-#4377 := (forall (vars (?v0 S3)) (:pat #4306 #4264) #1633)
-#4382 := (not #4377)
-#171 := (f3 f15 f22)
-#753 := (= f1 #171)
-decl f4 :: (-> S2 S3 S1 S2)
-#180 := (f4 f15 f22 f1)
-#181 := (= f23 #180)
-#986 := (not #181)
-#4526 := (or #986 #753 #4382 #1645 #2201 #2204 #4392 #4400 #4523)
-#4529 := (not #4526)
-decl ?v0!11 :: S3
-#2131 := ?v0!11
-decl ?v1!10 :: S3
-#2130 := ?v1!10
-#2136 := (f5 ?v1!10 ?v0!11)
-#2137 := (f9 #2136)
-#2144 := (* -1::Int #2137)
+#4362 := (pattern #182)
+#183 := (f4 #182)
+#1588 := (+ #183 #1445)
+#1589 := (+ #174 #1588)
+#1590 := (= #1589 0::Int)
+#1414 := (* -1::Int #183)
+#1420 := (* -1::Int #174)
+#1421 := (+ #1420 #1414)
+#1422 := (+ #101 #1421)
+#1423 := (<= #1422 0::Int)
+#1415 := (+ f3 #1414)
+#1416 := (<= #1415 0::Int)
+#3384 := (or #1416 #1423 #1590)
+#4371 := (forall (vars (?v0 S2)) (:pat #4362 #4240 #4361) #3384)
+#4376 := (not #4371)
+#3364 := (or #1416 #1423)
+#3365 := (not #3364)
+#3368 := (or #760 #3365)
+#4363 := (forall (vars (?v0 S2)) (:pat #4240 #4361 #4362) #3368)
+#4368 := (not #4363)
+decl ?v0!12 :: S2
+#2173 := ?v0!12
+#2179 := (f8 f15 ?v0!12)
+#2180 := (= f1 #2179)
+#2174 := (f13 f14 ?v0!12)
+#2175 := (* -1::Int #2174)
+#2176 := (+ f3 #2175)
+#2177 := (<= #2176 0::Int)
+#1620 := (+ f3 #1420)
+#1621 := (<= #1620 0::Int)
+#105 := (f8 f15 #12)
+#4282 := (pattern #105)
+#1603 := (+ #101 #1420)
+#1602 := (>= #1603 0::Int)
+#508 := (= f1 #105)
+#1609 := (or #508 #1602)
+#4353 := (forall (vars (?v0 S2)) (:pat #4282 #4240) #1609)
+#4358 := (not #4353)
+#171 := (f8 f15 f22)
+#729 := (= f1 #171)
+#962 := (not #181)
+#4502 := (or #962 #729 #4358 #1621 #2177 #2180 #4368 #4376 #4499)
+#4505 := (not #4502)
+decl ?v0!11 :: S2
+#2107 := ?v0!11
+decl ?v1!10 :: S2
+#2106 := ?v1!10
+#2112 := (f5 ?v1!10 ?v0!11)
+#2113 := (f4 #2112)
+#2120 := (* -1::Int #2113)
 decl f19 :: S5
 #137 := f19
-#2134 := (f13 f19 ?v1!10)
-#2140 := (* -1::Int #2134)
-#2796 := (+ #2140 #2144)
-#2132 := (f13 f19 ?v0!11)
-#2797 := (+ #2132 #2796)
-#2798 := (<= #2797 0::Int)
-#2145 := (+ f8 #2144)
-#2146 := (<= #2145 0::Int)
-#2141 := (+ f8 #2140)
-#2142 := (<= #2141 0::Int)
-#3352 := (or #2142 #2146 #2798)
-#3357 := (not #3352)
-#145 := (f13 f19 #23)
-#1346 := (* -1::Int #145)
+#2110 := (f13 f19 ?v1!10)
+#2116 := (* -1::Int #2110)
+#2772 := (+ #2116 #2120)
+#2108 := (f13 f19 ?v0!11)
+#2773 := (+ #2108 #2772)
+#2774 := (<= #2773 0::Int)
+#2121 := (+ f3 #2120)
+#2122 := (<= #2121 0::Int)
+#2117 := (+ f3 #2116)
+#2118 := (<= #2117 0::Int)
+#3328 := (or #2118 #2122 #2774)
+#3333 := (not #3328)
+#145 := (f13 f19 #11)
+#1322 := (* -1::Int #145)
 #142 := (f13 f19 #12)
-#1347 := (+ #142 #1346)
-#1353 := (+ #82 #1347)
-#1376 := (>= #1353 0::Int)
-#1333 := (* -1::Int #142)
-#1334 := (+ f8 #1333)
-#1335 := (<= #1334 0::Int)
-#3320 := (or #1226 #1335 #1376)
-#4339 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3320)
-#4344 := (not #4339)
+#1323 := (+ #142 #1322)
+#1329 := (+ #82 #1323)
+#1352 := (>= #1329 0::Int)
+#1309 := (* -1::Int #142)
+#1310 := (+ f3 #1309)
+#1311 := (<= #1310 0::Int)
+#3296 := (or #1202 #1311 #1352)
+#4315 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4216) #3296)
+#4320 := (not #4315)
 #157 := (f13 f19 f10)
 #158 := (= #157 0::Int)
-#4347 := (or #158 #4344)
-#4350 := (not #4347)
-#4353 := (or #4350 #3357)
-#4356 := (not #4353)
-#4315 := (pattern #142)
-decl ?v1!9 :: (-> S3 S3)
-#2107 := (?v1!9 #12)
-#2110 := (f5 #2107 #12)
-#2111 := (f9 #2110)
-#2766 := (* -1::Int #2111)
-#2108 := (f13 f19 #2107)
-#2749 := (* -1::Int #2108)
-#2767 := (+ #2749 #2766)
-#2768 := (+ #142 #2767)
-#2769 := (= #2768 0::Int)
-#3290 := (not #2769)
-#2750 := (+ #142 #2749)
-#2751 := (<= #2750 0::Int)
-#3291 := (or #2751 #3290)
-#3292 := (not #3291)
+#4323 := (or #158 #4320)
+#4326 := (not #4323)
+#4329 := (or #4326 #3333)
+#4332 := (not #4329)
+#4291 := (pattern #142)
+decl ?v1!9 :: (-> S2 S2)
+#2083 := (?v1!9 #12)
+#2086 := (f5 #2083 #12)
+#2087 := (f4 #2086)
+#2742 := (* -1::Int #2087)
+#2084 := (f13 f19 #2083)
+#2725 := (* -1::Int #2084)
+#2743 := (+ #2725 #2742)
+#2744 := (+ #142 #2743)
+#2745 := (= #2744 0::Int)
+#3266 := (not #2745)
+#2726 := (+ #142 #2725)
+#2727 := (<= #2726 0::Int)
+#3267 := (or #2727 #3266)
+#3268 := (not #3267)
 #57 := (= #12 f10)
-#3298 := (or #57 #1335 #3292)
-#4331 := (forall (vars (?v0 S3)) (:pat #4315) #3298)
-#4336 := (not #4331)
-#4359 := (or #4336 #4356)
-#4362 := (not #4359)
-decl ?v0!8 :: S3
-#2067 := ?v0!8
-#2071 := (f5 #12 ?v0!8)
-#4316 := (pattern #2071)
-#2072 := (f9 #2071)
-#2068 := (f13 f19 ?v0!8)
-#2069 := (* -1::Int #2068)
-#2719 := (+ #2069 #2072)
-#2720 := (+ #142 #2719)
-#2723 := (= #2720 0::Int)
-#3254 := (not #2723)
-#2070 := (+ #142 #2069)
-#2075 := (>= #2070 0::Int)
-#3255 := (or #2075 #3254)
-#4317 := (forall (vars (?v1 S3)) (:pat #4315 #4316) #3255)
-#4322 := (not #4317)
-#2695 := (= f10 ?v0!8)
-#2079 := (+ f8 #2069)
-#2080 := (<= #2079 0::Int)
-#4325 := (or #2080 #2695 #4322)
-#4328 := (not #4325)
-#4365 := (or #4328 #4362)
-#4368 := (not #4365)
-#1288 := (* -1::Int #101)
-#1289 := (+ f8 #1288)
-#1290 := (<= #1289 0::Int)
-#3240 := (or #532 #1290)
-#4307 := (forall (vars (?v0 S3)) (:pat #4306 #4264) #3240)
+#3274 := (or #57 #1311 #3268)
+#4307 := (forall (vars (?v0 S2)) (:pat #4291) #3274)
 #4312 := (not #4307)
-#623 := (= f14 f19)
-#714 := (not #623)
-decl f16 :: S2
+#4335 := (or #4312 #4332)
+#4338 := (not #4335)
+decl ?v0!8 :: S2
+#2043 := ?v0!8
+#2047 := (f5 #12 ?v0!8)
+#4292 := (pattern #2047)
+#2048 := (f4 #2047)
+#2044 := (f13 f19 ?v0!8)
+#2045 := (* -1::Int #2044)
+#2695 := (+ #2045 #2048)
+#2696 := (+ #142 #2695)
+#2699 := (= #2696 0::Int)
+#3230 := (not #2699)
+#2046 := (+ #142 #2045)
+#2051 := (>= #2046 0::Int)
+#3231 := (or #2051 #3230)
+#4293 := (forall (vars (?v1 S2)) (:pat #4291 #4292) #3231)
+#4298 := (not #4293)
+#2671 := (= f10 ?v0!8)
+#2055 := (+ f3 #2045)
+#2056 := (<= #2055 0::Int)
+#4301 := (or #2056 #2671 #4298)
+#4304 := (not #4301)
+#4341 := (or #4304 #4338)
+#4344 := (not #4341)
+#1264 := (* -1::Int #101)
+#1265 := (+ f3 #1264)
+#1266 := (<= #1265 0::Int)
+#3216 := (or #508 #1266)
+#4283 := (forall (vars (?v0 S2)) (:pat #4282 #4240) #3216)
+#4288 := (not #4283)
+#599 := (= f14 f19)
+#690 := (not #599)
+decl f16 :: S4
 #132 := f16
-#620 := (= f15 f16)
-#732 := (not #620)
+#596 := (= f15 f16)
+#708 := (not #596)
 decl f21 :: S5
 #140 := f21
 decl f20 :: S5
 #139 := f20
 #141 := (= f20 f21)
-#705 := (not #141)
-decl f18 :: S3
+#681 := (not #141)
+decl f18 :: S2
 #135 := f18
-decl f17 :: S3
+decl f17 :: S2
 #134 := f17
 #136 := (= f17 f18)
-#723 := (not #136)
-#4371 := (or #723 #705 #732 #714 #4312 #4368)
-#4374 := (not #4371)
-#4532 := (or #4374 #4529)
-#4535 := (not #4532)
-#2030 := (?v1!7 #12)
-#2031 := (f13 f14 #2030)
-#2654 := (* -1::Int #2031)
-#2669 := (+ #101 #2654)
-#2670 := (<= #2669 0::Int)
-#2035 := (f5 #2030 #12)
-#2036 := (f9 #2035)
-#2655 := (* -1::Int #2036)
-#2656 := (+ #2654 #2655)
-#2657 := (+ #101 #2656)
-#2658 := (= #2657 0::Int)
-#3224 := (not #2658)
-#2039 := (f3 f15 #2030)
-#2040 := (= f1 #2039)
-#3223 := (not #2040)
-#3225 := (or #3223 #3224 #2670)
-#3226 := (not #3225)
-#3232 := (or #57 #1290 #3226)
-#4298 := (forall (vars (?v0 S3)) (:pat #4264) #3232)
-#4303 := (not #4298)
-decl f11 :: (-> S3 Int)
+#699 := (not #136)
+#4347 := (or #699 #681 #708 #690 #4288 #4344)
+#4350 := (not #4347)
+#4508 := (or #4350 #4505)
+#4511 := (not #4508)
+#2006 := (?v1!7 #12)
+#2007 := (f13 f14 #2006)
+#2630 := (* -1::Int #2007)
+#2645 := (+ #101 #2630)
+#2646 := (<= #2645 0::Int)
+#2011 := (f5 #2006 #12)
+#2012 := (f4 #2011)
+#2631 := (* -1::Int #2012)
+#2632 := (+ #2630 #2631)
+#2633 := (+ #101 #2632)
+#2634 := (= #2633 0::Int)
+#3200 := (not #2634)
+#2015 := (f8 f15 #2006)
+#2016 := (= f1 #2015)
+#3199 := (not #2016)
+#3201 := (or #3199 #3200 #2646)
+#3202 := (not #3201)
+#3208 := (or #57 #1266 #3202)
+#4274 := (forall (vars (?v0 S2)) (:pat #4240) #3208)
+#4279 := (not #4274)
+decl f11 :: (-> S2 Int)
 #58 := (f11 #12)
-#4209 := (pattern #58)
-decl ?v1!6 :: (-> S3 S3)
-#2002 := (?v1!6 #12)
-#2006 := (f11 #2002)
-#2613 := (* -1::Int #2006)
-#2003 := (f5 #2002 #12)
-#2004 := (f9 #2003)
-#2630 := (* -1::Int #2004)
-#2631 := (+ #2630 #2613)
-#2632 := (+ #58 #2631)
-#2633 := (= #2632 0::Int)
-#3196 := (not #2633)
-#2614 := (+ #58 #2613)
-#2615 := (<= #2614 0::Int)
-decl f12 :: (-> S3 S1)
-#2012 := (f12 #2002)
-#2013 := (= f1 #2012)
-#3195 := (not #2013)
-#3197 := (or #3195 #2615 #3196)
-#3198 := (not #3197)
-#1250 := (* -1::Int #58)
-#1251 := (+ f8 #1250)
-#1252 := (<= #1251 0::Int)
-#3204 := (or #57 #1252 #3198)
-#4290 := (forall (vars (?v0 S3)) (:pat #4209) #3204)
-#4295 := (not #4290)
-#108 := (f3 f15 #23)
-#4281 := (pattern #105 #108)
-#111 := (f13 f14 #23)
-#1302 := (* -1::Int #111)
-#1303 := (+ #101 #1302)
-#1306 := (>= #1303 0::Int)
-#538 := (= f1 #108)
-#3161 := (not #538)
-#3176 := (or #532 #3161 #1306)
-#4282 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4281) #3176)
-#4287 := (not #4282)
-#1304 := (+ #82 #1303)
-#1699 := (>= #1304 0::Int)
-#535 := (not #532)
-#3153 := (or #535 #1226 #1699)
-#4273 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3153)
-#4278 := (not #4273)
-#4270 := (not #4265)
+#4185 := (pattern #58)
+decl ?v1!6 :: (-> S2 S2)
+#1978 := (?v1!6 #12)
+#1982 := (f11 #1978)
+#2589 := (* -1::Int #1982)
+#1979 := (f5 #1978 #12)
+#1980 := (f4 #1979)
+#2606 := (* -1::Int #1980)
+#2607 := (+ #2606 #2589)
+#2608 := (+ #58 #2607)
+#2609 := (= #2608 0::Int)
+#3172 := (not #2609)
+#2590 := (+ #58 #2589)
+#2591 := (<= #2590 0::Int)
+decl f12 :: (-> S2 S1)
+#1988 := (f12 #1978)
+#1989 := (= f1 #1988)
+#3171 := (not #1989)
+#3173 := (or #3171 #2591 #3172)
+#3174 := (not #3173)
+#1226 := (* -1::Int #58)
+#1227 := (+ f3 #1226)
+#1228 := (<= #1227 0::Int)
+#3180 := (or #57 #1228 #3174)
+#4266 := (forall (vars (?v0 S2)) (:pat #4185) #3180)
+#4271 := (not #4266)
+#108 := (f8 f15 #11)
+#4257 := (pattern #105 #108)
+#111 := (f13 f14 #11)
+#1278 := (* -1::Int #111)
+#1279 := (+ #101 #1278)
+#1282 := (>= #1279 0::Int)
+#514 := (= f1 #108)
+#3137 := (not #514)
+#3152 := (or #508 #3137 #1282)
+#4258 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4257) #3152)
+#4263 := (not #4258)
+#1280 := (+ #82 #1279)
+#1675 := (>= #1280 0::Int)
+#511 := (not #508)
+#3129 := (or #511 #1202 #1675)
+#4249 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4216) #3129)
+#4254 := (not #4249)
+#1703 := (>= #101 0::Int)
+#4241 := (forall (vars (?v0 S2)) (:pat #4240) #1703)
+#4246 := (not #4241)
+#99 := (f13 f14 f10)
 #100 := (= #99 0::Int)
-#1738 := (not #100)
-#4538 := (or #1738 #4270 #4278 #4287 #4295 #4303 #4535)
-#4541 := (not #4538)
-decl ?v0!5 :: S3
-#1958 := ?v0!5
-#1959 := (f5 #12 ?v0!5)
-#4249 := (pattern #1959)
+#1714 := (not #100)
+#4514 := (or #1714 #4246 #4254 #4263 #4271 #4279 #4511)
+#4517 := (not #4514)
+decl ?v0!5 :: S2
+#1934 := ?v0!5
+#1935 := (f5 #12 ?v0!5)
+#4225 := (pattern #1935)
 #66 := (f12 #12)
-#4216 := (pattern #66)
-#1961 := (f11 ?v0!5)
-#1962 := (* -1::Int #1961)
-#1960 := (f9 #1959)
-#2581 := (+ #1960 #1962)
-#2582 := (+ #58 #2581)
-#2585 := (= #2582 0::Int)
-#3114 := (not #2585)
-#1966 := (+ #58 #1962)
-#1967 := (>= #1966 0::Int)
-#453 := (= f1 #66)
-#456 := (not #453)
-#3115 := (or #456 #1967 #3114)
-#4250 := (forall (vars (?v1 S3)) (:pat #4216 #4209 #4249) #3115)
-#4255 := (not #4250)
-#2557 := (= f10 ?v0!5)
-#1971 := (+ f8 #1962)
-#1972 := (<= #1971 0::Int)
-#4258 := (or #1972 #2557 #4255)
-#4261 := (not #4258)
-#4544 := (or #4261 #4541)
-#4547 := (not #4544)
-#77 := (f11 #23)
-#1202 := (* -1::Int #77)
-#1223 := (+ #1202 #82)
-#1224 := (+ #58 #1223)
-#1221 := (>= #1224 0::Int)
-#3106 := (or #456 #1221 #1226)
-#4241 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4240) #3106)
-#4246 := (not #4241)
-#4550 := (or #4246 #4547)
-#4553 := (not #4550)
-decl ?v1!3 :: S3
-#1927 := ?v1!3
-#1942 := (f11 ?v1!3)
-decl ?v0!4 :: S3
-#1928 := ?v0!4
-#1939 := (f11 ?v0!4)
-#1940 := (* -1::Int #1939)
-#2538 := (+ #1940 #1942)
-#1929 := (f5 ?v1!3 ?v0!4)
-#1930 := (f9 #1929)
-#2539 := (+ #1930 #2538)
-#2542 := (>= #2539 0::Int)
-#1935 := (f12 ?v1!3)
-#1936 := (= f1 #1935)
-#3069 := (not #1936)
-#1931 := (* -1::Int #1930)
-#1932 := (+ f8 #1931)
-#1933 := (<= #1932 0::Int)
-#3084 := (or #1933 #3069 #2542)
-#5213 := [hypothesis]: #1936
-#4217 := (forall (vars (?v0 S3)) (:pat #4216) #456)
-#459 := (forall (vars (?v0 S3)) #456)
-#4220 := (iff #459 #4217)
-#4218 := (iff #456 #456)
-#4219 := [refl]: #4218
-#4221 := [quant-intro #4219]: #4220
-#1849 := (~ #459 #459)
-#1879 := (~ #456 #456)
-#1880 := [refl]: #1879
-#1850 := [nnf-pos #1880]: #1849
+#4192 := (pattern #66)
+#1937 := (f11 ?v0!5)
+#1938 := (* -1::Int #1937)
+#1936 := (f4 #1935)
+#2557 := (+ #1936 #1938)
+#2558 := (+ #58 #2557)
+#2561 := (= #2558 0::Int)
+#3090 := (not #2561)
+#1942 := (+ #58 #1938)
+#1943 := (>= #1942 0::Int)
+#429 := (= f1 #66)
+#432 := (not #429)
+#3091 := (or #432 #1943 #3090)
+#4226 := (forall (vars (?v1 S2)) (:pat #4192 #4185 #4225) #3091)
+#4231 := (not #4226)
+#2533 := (= f10 ?v0!5)
+#1947 := (+ f3 #1938)
+#1948 := (<= #1947 0::Int)
+#4234 := (or #1948 #2533 #4231)
+#5626 := (= f3 #1937)
+#5735 := (not #5626)
+#1949 := (not #1948)
+#4237 := (not #4234)
+#5733 := [hypothesis]: #4237
+#4126 := (or #4234 #1949)
+#3800 := [def-axiom]: #4126
+#5734 := [unit-resolution #3800 #5733]: #1949
+#5736 := (or #5735 #1948)
+#5737 := [th-lemma arith triangle-eq]: #5736
+#5738 := [unit-resolution #5737 #5734]: #5735
+#2536 := (not #2533)
+#3801 := (or #4234 #2536)
+#4133 := [def-axiom]: #3801
+#5739 := [unit-resolution #4133 #5733]: #2536
+#415 := (= f3 #58)
+#421 := (or #57 #415)
+#4186 := (forall (vars (?v0 S2)) (:pat #4185) #421)
+#426 := (forall (vars (?v0 S2)) #421)
+#4189 := (iff #426 #4186)
+#4187 := (iff #421 #421)
+#4188 := [refl]: #4187
+#4190 := [quant-intro #4188]: #4189
+#1823 := (~ #426 #426)
+#1852 := (~ #421 #421)
+#1853 := [refl]: #1852
+#1824 := [nnf-pos #1853]: #1823
 #59 := (= #58 0::Int)
 #62 := (not #57)
-#1796 := (or #62 #59)
-#1799 := (forall (vars (?v0 S3)) #1796)
-#1802 := (not #1799)
-#1730 := (forall (vars (?v0 S3)) #1727)
-#1733 := (not #1730)
-#541 := (and #535 #538)
-#547 := (not #541)
-#1716 := (or #547 #1306)
-#1721 := (forall (vars (?v0 S3) (?v1 S3)) #1716)
-#1724 := (not #1721)
-#1227 := (not #1226)
-#1691 := (and #532 #1227)
-#1696 := (not #1691)
-#1702 := (or #1696 #1699)
-#1705 := (forall (vars (?v0 S3) (?v1 S3)) #1702)
-#1708 := (not #1705)
-#1638 := (forall (vars (?v0 S3)) #1633)
-#1641 := (not #1638)
-#1448 := (not #1447)
-#1441 := (not #1440)
-#1451 := (and #1441 #1448)
-#1609 := (not #1451)
-#1617 := (or #1609 #1614)
-#1620 := (forall (vars (?v0 S3)) #1617)
-#1623 := (not #1620)
-#1547 := (= #1525 0::Int)
-#1550 := (not #1493)
-#1559 := (and #798 #1550 #1547)
-#1564 := (exists (vars (?v1 S3)) #1559)
-#1536 := (+ f8 #1469)
-#1537 := (<= #1536 0::Int)
-#1538 := (not #1537)
-#1541 := (and #62 #1538)
-#1544 := (not #1541)
-#1567 := (or #1544 #1564)
-#1570 := (forall (vars (?v0 S3)) #1567)
-#1515 := (and #798 #1227)
-#1520 := (not #1515)
-#1527 := (or #1520 #1523)
-#1530 := (forall (vars (?v0 S3) (?v1 S3)) #1527)
-#1533 := (not #1530)
-#1573 := (or #1533 #1570)
-#1576 := (and #1530 #1573)
-#821 := (and #804 #818)
-#827 := (not #821)
-#1501 := (or #827 #1493)
-#1506 := (forall (vars (?v0 S3) (?v1 S3)) #1501)
+#1772 := (or #62 #59)
+#1775 := (forall (vars (?v0 S2)) #1772)
+#1778 := (not #1775)
+#1706 := (forall (vars (?v0 S2)) #1703)
+#1709 := (not #1706)
+#517 := (and #511 #514)
+#523 := (not #517)
+#1692 := (or #523 #1282)
+#1697 := (forall (vars (?v0 S2) (?v1 S2)) #1692)
+#1700 := (not #1697)
+#1203 := (not #1202)
+#1667 := (and #508 #1203)
+#1672 := (not #1667)
+#1678 := (or #1672 #1675)
+#1681 := (forall (vars (?v0 S2) (?v1 S2)) #1678)
+#1684 := (not #1681)
+#1614 := (forall (vars (?v0 S2)) #1609)
+#1617 := (not #1614)
+#1424 := (not #1423)
+#1417 := (not #1416)
+#1427 := (and #1417 #1424)
+#1585 := (not #1427)
+#1593 := (or #1585 #1590)
+#1596 := (forall (vars (?v0 S2)) #1593)
+#1599 := (not #1596)
+#1523 := (= #1501 0::Int)
+#1526 := (not #1469)
+#1535 := (and #774 #1526 #1523)
+#1540 := (exists (vars (?v1 S2)) #1535)
+#1512 := (+ f3 #1445)
+#1513 := (<= #1512 0::Int)
+#1514 := (not #1513)
+#1517 := (and #62 #1514)
+#1520 := (not #1517)
+#1543 := (or #1520 #1540)
+#1546 := (forall (vars (?v0 S2)) #1543)
+#1491 := (and #774 #1203)
+#1496 := (not #1491)
+#1503 := (or #1496 #1499)
+#1506 := (forall (vars (?v0 S2) (?v1 S2)) #1503)
 #1509 := (not #1506)
-#1579 := (or #1509 #1576)
-#1582 := (and #1506 #1579)
-#1487 := (forall (vars (?v0 S3)) #1484)
-#1490 := (not #1487)
-#1585 := (or #1490 #1582)
-#1588 := (and #1487 #1585)
-#1591 := (or #1481 #1588)
-#1594 := (and #203 #1591)
-#810 := (forall (vars (?v0 S3)) #805)
-#944 := (not #810)
-#1597 := (or #944 #1594)
-#1600 := (and #810 #1597)
-#1473 := (forall (vars (?v0 S3)) #1468)
-#1476 := (not #1473)
-#1603 := (or #1476 #1600)
-#1606 := (and #1473 #1603)
-#1457 := (or #784 #1451)
-#1462 := (forall (vars (?v0 S3)) #1457)
-#1465 := (not #1462)
-#1291 := (not #1290)
-#1410 := (and #535 #1291)
-#1415 := (exists (vars (?v0 S3)) #1410)
-#1656 := (not #1415)
-#1680 := (or #986 #753 #1656 #1465 #1606 #1623 #1641 #1645)
-#1336 := (not #1335)
-#1370 := (and #1227 #1336)
-#1373 := (not #1370)
-#1379 := (or #1373 #1376)
-#1382 := (forall (vars (?v0 S3) (?v1 S3)) #1379)
-#1385 := (not #1382)
-#1393 := (or #158 #1385)
-#1398 := (and #1382 #1393)
-#1351 := (= #1353 0::Int)
-#1345 := (>= #1347 0::Int)
-#1348 := (not #1345)
-#1355 := (and #1348 #1351)
-#1358 := (exists (vars (?v1 S3)) #1355)
-#1339 := (and #62 #1336)
-#1342 := (not #1339)
-#1361 := (or #1342 #1358)
-#1364 := (forall (vars (?v0 S3)) #1361)
-#1367 := (not #1364)
-#1401 := (or #1367 #1398)
-#1404 := (and #1364 #1401)
-#1433 := (or #723 #705 #732 #714 #1404 #1415)
-#1685 := (and #1433 #1680)
-#1307 := (not #1306)
-#1300 := (= #1304 0::Int)
-#1316 := (and #532 #1300 #1307)
-#1321 := (exists (vars (?v1 S3)) #1316)
-#1294 := (and #62 #1291)
-#1297 := (not #1294)
-#1324 := (or #1297 #1321)
-#1327 := (forall (vars (?v0 S3)) #1324)
-#1330 := (not #1327)
-#1262 := (= #1224 0::Int)
-#1203 := (+ #58 #1202)
-#1201 := (>= #1203 0::Int)
-#1265 := (not #1201)
-#1274 := (and #453 #1265 #1262)
-#1279 := (exists (vars (?v1 S3)) #1274)
-#1253 := (not #1252)
-#1256 := (and #62 #1253)
-#1259 := (not #1256)
-#1282 := (or #1259 #1279)
-#1285 := (forall (vars (?v0 S3)) #1282)
-#1741 := (not #1285)
-#1762 := (or #1738 #1741 #1330 #1685 #1708 #1724 #1733)
-#1767 := (and #1285 #1762)
-#1233 := (and #453 #1227)
-#1238 := (not #1233)
-#1241 := (or #1221 #1238)
-#1244 := (forall (vars (?v0 S3) (?v1 S3)) #1241)
-#1247 := (not #1244)
-#1770 := (or #1247 #1767)
-#1773 := (and #1244 #1770)
-#74 := (f12 #23)
-#465 := (= f1 #74)
-#468 := (and #456 #465)
-#474 := (not #468)
-#1208 := (or #474 #1201)
-#1213 := (forall (vars (?v0 S3) (?v1 S3)) #1208)
-#1216 := (not #1213)
-#1776 := (or #1216 #1773)
-#1779 := (and #1213 #1776)
-#1192 := (>= #58 0::Int)
-#1193 := (forall (vars (?v0 S3)) #1192)
-#1196 := (not #1193)
-#1782 := (or #1196 #1779)
-#1785 := (and #1193 #1782)
+#1549 := (or #1509 #1546)
+#1552 := (and #1506 #1549)
+#797 := (and #780 #794)
+#803 := (not #797)
+#1477 := (or #803 #1469)
+#1482 := (forall (vars (?v0 S2) (?v1 S2)) #1477)
+#1485 := (not #1482)
+#1555 := (or #1485 #1552)
+#1558 := (and #1482 #1555)
+#1463 := (forall (vars (?v0 S2)) #1460)
+#1466 := (not #1463)
+#1561 := (or #1466 #1558)
+#1564 := (and #1463 #1561)
+#1567 := (or #1457 #1564)
+#1570 := (and #203 #1567)
+#786 := (forall (vars (?v0 S2)) #781)
+#920 := (not #786)
+#1573 := (or #920 #1570)
+#1576 := (and #786 #1573)
+#1449 := (forall (vars (?v0 S2)) #1444)
+#1452 := (not #1449)
+#1579 := (or #1452 #1576)
+#1582 := (and #1449 #1579)
+#1433 := (or #760 #1427)
+#1438 := (forall (vars (?v0 S2)) #1433)
+#1441 := (not #1438)
+#1267 := (not #1266)
+#1386 := (and #511 #1267)
+#1391 := (exists (vars (?v0 S2)) #1386)
+#1632 := (not #1391)
+#1656 := (or #962 #729 #1632 #1441 #1582 #1599 #1617 #1621)
+#1312 := (not #1311)
+#1346 := (and #1203 #1312)
+#1349 := (not #1346)
+#1355 := (or #1349 #1352)
+#1358 := (forall (vars (?v0 S2) (?v1 S2)) #1355)
+#1361 := (not #1358)
+#1369 := (or #158 #1361)
+#1374 := (and #1358 #1369)
+#1327 := (= #1329 0::Int)
+#1321 := (>= #1323 0::Int)
+#1324 := (not #1321)
+#1331 := (and #1324 #1327)
+#1334 := (exists (vars (?v1 S2)) #1331)
+#1315 := (and #62 #1312)
+#1318 := (not #1315)
+#1337 := (or #1318 #1334)
+#1340 := (forall (vars (?v0 S2)) #1337)
+#1343 := (not #1340)
+#1377 := (or #1343 #1374)
+#1380 := (and #1340 #1377)
+#1409 := (or #699 #681 #708 #690 #1380 #1391)
+#1661 := (and #1409 #1656)
+#1283 := (not #1282)
+#1276 := (= #1280 0::Int)
+#1292 := (and #508 #1276 #1283)
+#1297 := (exists (vars (?v1 S2)) #1292)
+#1270 := (and #62 #1267)
+#1273 := (not #1270)
+#1300 := (or #1273 #1297)
+#1303 := (forall (vars (?v0 S2)) #1300)
+#1306 := (not #1303)
+#77 := (f11 #11)
+#1178 := (* -1::Int #77)
+#1199 := (+ #1178 #82)
+#1200 := (+ #58 #1199)
+#1238 := (= #1200 0::Int)
+#1179 := (+ #58 #1178)
+#1177 := (>= #1179 0::Int)
+#1241 := (not #1177)
+#1250 := (and #429 #1241 #1238)
+#1255 := (exists (vars (?v1 S2)) #1250)
+#1229 := (not #1228)
+#1232 := (and #62 #1229)
+#1235 := (not #1232)
+#1258 := (or #1235 #1255)
+#1261 := (forall (vars (?v0 S2)) #1258)
+#1717 := (not #1261)
+#1738 := (or #1714 #1717 #1306 #1661 #1684 #1700 #1709)
+#1743 := (and #1261 #1738)
+#1209 := (and #429 #1203)
+#1214 := (not #1209)
+#1197 := (>= #1200 0::Int)
+#1217 := (or #1197 #1214)
+#1220 := (forall (vars (?v0 S2) (?v1 S2)) #1217)
+#1223 := (not #1220)
+#1746 := (or #1223 #1743)
+#1749 := (and #1220 #1746)
+#74 := (f12 #11)
+#441 := (= f1 #74)
+#444 := (and #432 #441)
+#450 := (not #444)
+#1184 := (or #450 #1177)
+#1189 := (forall (vars (?v0 S2) (?v1 S2)) #1184)
+#1192 := (not #1189)
+#1752 := (or #1192 #1749)
+#1755 := (and #1189 #1752)
+#1168 := (>= #58 0::Int)
+#1169 := (forall (vars (?v0 S2)) #1168)
+#1172 := (not #1169)
+#1758 := (or #1172 #1755)
+#1761 := (and #1169 #1758)
 #70 := (f11 f10)
 #71 := (= #70 0::Int)
-#1187 := (not #71)
-#1788 := (or #1187 #1785)
-#1791 := (and #71 #1788)
-#1151 := (not #459)
-#439 := (= f8 #58)
-#445 := (or #57 #439)
-#450 := (forall (vars (?v0 S3)) #445)
-#1160 := (not #450)
-#1814 := (or #1160 #1151 #1791 #1802)
-#1819 := (not #1814)
+#1163 := (not #71)
+#1764 := (or #1163 #1761)
+#1767 := (and #71 #1764)
+#435 := (forall (vars (?v0 S2)) #432)
+#1127 := (not #435)
+#1136 := (not #426)
+#1790 := (or #1136 #1127 #1767 #1778)
+#1795 := (not #1790)
 #1 := true
 #215 := (+ #188 #82)
 #222 := (= #210 #215)
@@ -816,17 +730,17 @@
 #223 := (and #199 #222)
 #221 := (< #188 #210)
 #224 := (and #221 #223)
-#225 := (exists (vars (?v1 S3)) #224)
-#219 := (< #188 f8)
+#225 := (exists (vars (?v1 S2)) #224)
+#219 := (< #188 f3)
 #220 := (and #62 #219)
 #226 := (implies #220 #225)
-#227 := (forall (vars (?v0 S3)) #226)
+#227 := (forall (vars (?v0 S2)) #226)
 #228 := (and #227 true)
 #216 := (<= #210 #215)
-#83 := (< #82 f8)
+#83 := (< #82 f3)
 #214 := (and #199 #83)
 #217 := (implies #214 #216)
-#218 := (forall (vars (?v0 S3) (?v1 S3)) #217)
+#218 := (forall (vars (?v0 S2) (?v1 S2)) #217)
 #229 := (implies #218 #228)
 #230 := (and #218 #229)
 #211 := (<= #210 #188)
@@ -834,69 +748,69 @@
 #206 := (not #199)
 #209 := (and #206 #208)
 #212 := (implies #209 #211)
-#213 := (forall (vars (?v0 S3) (?v1 S3)) #212)
+#213 := (forall (vars (?v0 S2) (?v1 S2)) #212)
 #231 := (implies #213 #230)
 #232 := (and #213 #231)
 #204 := (<= 0::Int #188)
-#205 := (forall (vars (?v0 S3)) #204)
+#205 := (forall (vars (?v0 S2)) #204)
 #233 := (implies #205 #232)
 #234 := (and #205 #233)
 #235 := (implies #203 #234)
 #236 := (and #203 #235)
 #193 := (= #188 #101)
 #200 := (implies #199 #193)
-#201 := (forall (vars (?v0 S3)) #200)
+#201 := (forall (vars (?v0 S2)) #200)
 #237 := (implies #201 #236)
 #238 := (and #201 #237)
 #196 := (<= #188 #101)
-#197 := (forall (vars (?v0 S3)) #196)
+#197 := (forall (vars (?v0 S2)) #196)
 #239 := (implies #197 #238)
 #240 := (and #197 #239)
 #185 := (+ #174 #183)
 #186 := (< #185 #101)
-#184 := (< #183 f8)
+#184 := (< #183 f3)
 #187 := (and #184 #186)
 #192 := (not #187)
 #194 := (implies #192 #193)
-#195 := (forall (vars (?v0 S3)) #194)
+#195 := (forall (vars (?v0 S2)) #194)
 #241 := (implies #195 #240)
 #189 := (= #188 #185)
 #190 := (implies #187 #189)
-#191 := (forall (vars (?v0 S3)) #190)
+#191 := (forall (vars (?v0 S2)) #190)
 #242 := (implies #191 #241)
 #243 := (implies #181 #242)
 #176 := (<= #174 #101)
 #106 := (= #105 f1)
 #107 := (not #106)
 #177 := (implies #107 #176)
-#178 := (forall (vars (?v0 S3)) #177)
+#178 := (forall (vars (?v0 S2)) #177)
 #244 := (implies #178 #243)
-#175 := (< #174 f8)
+#175 := (< #174 f3)
 #245 := (implies #175 #244)
 #172 := (= #171 f1)
 #173 := (not #172)
 #246 := (implies #173 #245)
-#120 := (< #101 f8)
+#120 := (< #101 f3)
 #129 := (and #107 #120)
-#130 := (exists (vars (?v0 S3)) #129)
+#130 := (exists (vars (?v0 S2)) #129)
 #247 := (implies #130 #246)
 #248 := (implies true #247)
 #159 := (and #158 true)
 #147 := (+ #142 #82)
 #154 := (<= #145 #147)
-#143 := (< #142 f8)
+#143 := (< #142 f3)
 #153 := (and #143 #83)
 #155 := (implies #153 #154)
-#156 := (forall (vars (?v0 S3) (?v1 S3)) #155)
+#156 := (forall (vars (?v0 S2) (?v1 S2)) #155)
 #160 := (implies #156 #159)
 #161 := (and #156 #160)
 #148 := (= #145 #147)
 #146 := (< #142 #145)
 #149 := (and #146 #148)
-#150 := (exists (vars (?v1 S3)) #149)
+#150 := (exists (vars (?v1 S2)) #149)
 #144 := (and #62 #143)
 #151 := (implies #144 #150)
-#152 := (forall (vars (?v0 S3)) #151)
+#152 := (forall (vars (?v0 S2)) #151)
 #162 := (implies #152 #161)
 #163 := (and #152 #162)
 #164 := (implies #141 #163)
@@ -914,24 +828,24 @@
 #124 := (and #106 #123)
 #122 := (< #101 #111)
 #125 := (and #122 #124)
-#126 := (exists (vars (?v1 S3)) #125)
+#126 := (exists (vars (?v1 S2)) #125)
 #121 := (and #62 #120)
 #127 := (implies #121 #126)
-#128 := (forall (vars (?v0 S3)) #127)
+#128 := (forall (vars (?v0 S2)) #127)
 #250 := (implies #128 #249)
 #117 := (<= #111 #116)
 #115 := (and #106 #83)
 #118 := (implies #115 #117)
-#119 := (forall (vars (?v0 S3) (?v1 S3)) #118)
+#119 := (forall (vars (?v0 S2) (?v1 S2)) #118)
 #251 := (implies #119 #250)
 #112 := (<= #111 #101)
 #109 := (= #108 f1)
 #110 := (and #107 #109)
 #113 := (implies #110 #112)
-#114 := (forall (vars (?v0 S3) (?v1 S3)) #113)
+#114 := (forall (vars (?v0 S2) (?v1 S2)) #113)
 #252 := (implies #114 #251)
 #102 := (<= 0::Int #101)
-#103 := (forall (vars (?v0 S3)) #102)
+#103 := (forall (vars (?v0 S2)) #102)
 #253 := (implies #103 #252)
 #254 := (implies #100 #253)
 #255 := (implies true #254)
@@ -941,17 +855,17 @@
 #93 := (and #67 #92)
 #91 := (< #58 #77)
 #94 := (and #91 #93)
-#95 := (exists (vars (?v1 S3)) #94)
-#89 := (< #58 f8)
+#95 := (exists (vars (?v1 S2)) #94)
+#89 := (< #58 f3)
 #90 := (and #62 #89)
 #96 := (implies #90 #95)
-#97 := (forall (vars (?v0 S3)) #96)
+#97 := (forall (vars (?v0 S2)) #96)
 #256 := (implies #97 #255)
 #257 := (and #97 #256)
 #86 := (<= #77 #85)
 #84 := (and #67 #83)
 #87 := (implies #84 #86)
-#88 := (forall (vars (?v0 S3) (?v1 S3)) #87)
+#88 := (forall (vars (?v0 S2) (?v1 S2)) #87)
 #258 := (implies #88 #257)
 #259 := (and #88 #258)
 #78 := (<= #77 #58)
@@ -959,6227 +873,5900 @@
 #68 := (not #67)
 #76 := (and #68 #75)
 #79 := (implies #76 #78)
-#80 := (forall (vars (?v0 S3) (?v1 S3)) #79)
+#80 := (forall (vars (?v0 S2) (?v1 S2)) #79)
 #260 := (implies #80 #259)
 #261 := (and #80 #260)
 #72 := (<= 0::Int #58)
-#73 := (forall (vars (?v0 S3)) #72)
+#73 := (forall (vars (?v0 S2)) #72)
 #262 := (implies #73 #261)
 #263 := (and #73 #262)
 #264 := (implies #71 #263)
 #265 := (and #71 #264)
-#69 := (forall (vars (?v0 S3)) #68)
+#69 := (forall (vars (?v0 S2)) #68)
 #266 := (implies #69 #265)
-#63 := (= #58 f8)
+#63 := (= #58 f3)
 #64 := (implies #62 #63)
-#65 := (forall (vars (?v0 S3)) #64)
+#65 := (forall (vars (?v0 S2)) #64)
 #267 := (implies #65 #266)
 #60 := (implies #57 #59)
-#61 := (forall (vars (?v0 S3)) #60)
+#61 := (forall (vars (?v0 S2)) #60)
 #268 := (implies #61 #267)
 #269 := (implies true #268)
 #270 := (not #269)
-#1822 := (iff #270 #1819)
-#844 := (+ #82 #188)
-#862 := (= #210 #844)
-#865 := (and #798 #862)
-#868 := (and #221 #865)
-#871 := (exists (vars (?v1 S3)) #868)
-#877 := (not #220)
-#878 := (or #877 #871)
-#883 := (forall (vars (?v0 S3)) #878)
-#847 := (<= #210 #844)
-#839 := (and #83 #798)
-#853 := (not #839)
+#1798 := (iff #270 #1795)
+#820 := (+ #82 #188)
+#838 := (= #210 #820)
+#841 := (and #774 #838)
+#844 := (and #221 #841)
+#847 := (exists (vars (?v1 S2)) #844)
+#853 := (not #220)
 #854 := (or #853 #847)
-#859 := (forall (vars (?v0 S3) (?v1 S3)) #854)
-#896 := (not #859)
-#897 := (or #896 #883)
-#902 := (and #859 #897)
-#828 := (or #211 #827)
-#833 := (forall (vars (?v0 S3) (?v1 S3)) #828)
-#908 := (not #833)
+#859 := (forall (vars (?v0 S2)) #854)
+#823 := (<= #210 #820)
+#815 := (and #83 #774)
+#829 := (not #815)
+#830 := (or #829 #823)
+#835 := (forall (vars (?v0 S2) (?v1 S2)) #830)
+#872 := (not #835)
+#873 := (or #872 #859)
+#878 := (and #835 #873)
+#804 := (or #211 #803)
+#809 := (forall (vars (?v0 S2) (?v1 S2)) #804)
+#884 := (not #809)
+#885 := (or #884 #878)
+#890 := (and #809 #885)
+#896 := (not #205)
+#897 := (or #896 #890)
+#902 := (and #205 #897)
+#789 := (= 0::Int #202)
+#908 := (not #789)
 #909 := (or #908 #902)
-#914 := (and #833 #909)
-#920 := (not #205)
+#914 := (and #789 #909)
 #921 := (or #920 #914)
-#926 := (and #205 #921)
-#813 := (= 0::Int #202)
-#932 := (not #813)
+#926 := (and #786 #921)
+#932 := (not #197)
 #933 := (or #932 #926)
-#938 := (and #813 #933)
+#938 := (and #197 #933)
+#766 := (or #187 #760)
+#771 := (forall (vars (?v0 S2)) #766)
+#944 := (not #771)
 #945 := (or #944 #938)
-#950 := (and #810 #945)
-#956 := (not #197)
-#957 := (or #956 #950)
-#962 := (and #197 #957)
-#790 := (or #187 #784)
-#795 := (forall (vars (?v0 S3)) #790)
-#968 := (not #795)
-#969 := (or #968 #962)
-#770 := (= #185 #188)
-#776 := (or #192 #770)
-#781 := (forall (vars (?v0 S3)) #776)
-#977 := (not #781)
-#978 := (or #977 #969)
-#987 := (or #986 #978)
-#762 := (or #176 #532)
-#767 := (forall (vars (?v0 S3)) #762)
-#995 := (not #767)
-#996 := (or #995 #987)
-#1004 := (not #175)
-#1005 := (or #1004 #996)
-#1013 := (or #753 #1005)
-#609 := (and #120 #535)
-#614 := (exists (vars (?v0 S3)) #609)
-#617 := (not #614)
-#1021 := (or #617 #1013)
-#668 := (= 0::Int #157)
-#626 := (+ #82 #142)
-#653 := (<= #145 #626)
-#650 := (and #83 #143)
-#659 := (not #650)
-#660 := (or #659 #653)
-#665 := (forall (vars (?v0 S3) (?v1 S3)) #660)
-#681 := (not #665)
-#682 := (or #681 #668)
-#687 := (and #665 #682)
-#629 := (= #145 #626)
-#632 := (and #146 #629)
-#635 := (exists (vars (?v1 S3)) #632)
-#641 := (not #144)
-#642 := (or #641 #635)
-#647 := (forall (vars (?v0 S3)) #642)
-#693 := (not #647)
-#694 := (or #693 #687)
-#699 := (and #647 #694)
-#706 := (or #705 #699)
-#715 := (or #714 #706)
-#724 := (or #723 #715)
-#733 := (or #732 #724)
-#741 := (or #614 #733)
-#1033 := (and #741 #1021)
-#564 := (+ #82 #101)
-#582 := (= #111 #564)
-#585 := (and #532 #582)
-#588 := (and #122 #585)
-#591 := (exists (vars (?v1 S3)) #588)
-#597 := (not #121)
-#598 := (or #597 #591)
-#603 := (forall (vars (?v0 S3)) #598)
-#1039 := (not #603)
-#1040 := (or #1039 #1033)
-#567 := (<= #111 #564)
-#559 := (and #83 #532)
-#573 := (not #559)
+#746 := (= #185 #188)
+#752 := (or #192 #746)
+#757 := (forall (vars (?v0 S2)) #752)
+#953 := (not #757)
+#954 := (or #953 #945)
+#963 := (or #962 #954)
+#738 := (or #176 #508)
+#743 := (forall (vars (?v0 S2)) #738)
+#971 := (not #743)
+#972 := (or #971 #963)
+#980 := (not #175)
+#981 := (or #980 #972)
+#989 := (or #729 #981)
+#585 := (and #120 #511)
+#590 := (exists (vars (?v0 S2)) #585)
+#593 := (not #590)
+#997 := (or #593 #989)
+#644 := (= 0::Int #157)
+#602 := (+ #82 #142)
+#629 := (<= #145 #602)
+#626 := (and #83 #143)
+#635 := (not #626)
+#636 := (or #635 #629)
+#641 := (forall (vars (?v0 S2) (?v1 S2)) #636)
+#657 := (not #641)
+#658 := (or #657 #644)
+#663 := (and #641 #658)
+#605 := (= #145 #602)
+#608 := (and #146 #605)
+#611 := (exists (vars (?v1 S2)) #608)
+#617 := (not #144)
+#618 := (or #617 #611)
+#623 := (forall (vars (?v0 S2)) #618)
+#669 := (not #623)
+#670 := (or #669 #663)
+#675 := (and #623 #670)
+#682 := (or #681 #675)
+#691 := (or #690 #682)
+#700 := (or #699 #691)
+#709 := (or #708 #700)
+#717 := (or #590 #709)
+#1009 := (and #717 #997)
+#540 := (+ #82 #101)
+#558 := (= #111 #540)
+#561 := (and #508 #558)
+#564 := (and #122 #561)
+#567 := (exists (vars (?v1 S2)) #564)
+#573 := (not #121)
 #574 := (or #573 #567)
-#579 := (forall (vars (?v0 S3) (?v1 S3)) #574)
-#1048 := (not #579)
-#1049 := (or #1048 #1040)
-#548 := (or #112 #547)
-#553 := (forall (vars (?v0 S3) (?v1 S3)) #548)
-#1057 := (not #553)
-#1058 := (or #1057 #1049)
-#1066 := (not #103)
-#1067 := (or #1066 #1058)
-#529 := (= 0::Int #99)
-#1075 := (not #529)
-#1076 := (or #1075 #1067)
-#506 := (and #92 #453)
-#511 := (and #91 #506)
-#514 := (exists (vars (?v1 S3)) #511)
-#520 := (not #90)
-#521 := (or #520 #514)
-#526 := (forall (vars (?v0 S3)) #521)
-#1091 := (not #526)
-#1092 := (or #1091 #1076)
-#1097 := (and #526 #1092)
-#486 := (and #83 #453)
-#494 := (not #486)
-#495 := (or #86 #494)
-#500 := (forall (vars (?v0 S3) (?v1 S3)) #495)
-#1103 := (not #500)
+#579 := (forall (vars (?v0 S2)) #574)
+#1015 := (not #579)
+#1016 := (or #1015 #1009)
+#543 := (<= #111 #540)
+#535 := (and #83 #508)
+#549 := (not #535)
+#550 := (or #549 #543)
+#555 := (forall (vars (?v0 S2) (?v1 S2)) #550)
+#1024 := (not #555)
+#1025 := (or #1024 #1016)
+#524 := (or #112 #523)
+#529 := (forall (vars (?v0 S2) (?v1 S2)) #524)
+#1033 := (not #529)
+#1034 := (or #1033 #1025)
+#1042 := (not #103)
+#1043 := (or #1042 #1034)
+#505 := (= 0::Int #99)
+#1051 := (not #505)
+#1052 := (or #1051 #1043)
+#482 := (and #92 #429)
+#487 := (and #91 #482)
+#490 := (exists (vars (?v1 S2)) #487)
+#496 := (not #90)
+#497 := (or #496 #490)
+#502 := (forall (vars (?v0 S2)) #497)
+#1067 := (not #502)
+#1068 := (or #1067 #1052)
+#1073 := (and #502 #1068)
+#462 := (and #83 #429)
+#470 := (not #462)
+#471 := (or #86 #470)
+#476 := (forall (vars (?v0 S2) (?v1 S2)) #471)
+#1079 := (not #476)
+#1080 := (or #1079 #1073)
+#1085 := (and #476 #1080)
+#451 := (or #78 #450)
+#456 := (forall (vars (?v0 S2) (?v1 S2)) #451)
+#1091 := (not #456)
+#1092 := (or #1091 #1085)
+#1097 := (and #456 #1092)
+#1103 := (not #73)
 #1104 := (or #1103 #1097)
-#1109 := (and #500 #1104)
-#475 := (or #78 #474)
-#480 := (forall (vars (?v0 S3) (?v1 S3)) #475)
-#1115 := (not #480)
+#1109 := (and #73 #1104)
+#438 := (= 0::Int #70)
+#1115 := (not #438)
 #1116 := (or #1115 #1109)
-#1121 := (and #480 #1116)
-#1127 := (not #73)
+#1121 := (and #438 #1116)
 #1128 := (or #1127 #1121)
-#1133 := (and #73 #1128)
-#462 := (= 0::Int #70)
-#1139 := (not #462)
-#1140 := (or #1139 #1133)
-#1145 := (and #462 #1140)
-#1152 := (or #1151 #1145)
-#1161 := (or #1160 #1152)
-#425 := (= 0::Int #58)
-#431 := (or #62 #425)
-#436 := (forall (vars (?v0 S3)) #431)
-#1169 := (not #436)
-#1170 := (or #1169 #1161)
-#1182 := (not #1170)
-#1820 := (iff #1182 #1819)
-#1817 := (iff #1170 #1814)
-#1805 := (or #1151 #1791)
-#1808 := (or #1160 #1805)
-#1811 := (or #1802 #1808)
-#1815 := (iff #1811 #1814)
-#1816 := [rewrite]: #1815
-#1812 := (iff #1170 #1811)
-#1809 := (iff #1161 #1808)
-#1806 := (iff #1152 #1805)
-#1792 := (iff #1145 #1791)
-#1789 := (iff #1140 #1788)
-#1786 := (iff #1133 #1785)
-#1783 := (iff #1128 #1782)
-#1780 := (iff #1121 #1779)
-#1777 := (iff #1116 #1776)
-#1774 := (iff #1109 #1773)
-#1771 := (iff #1104 #1770)
-#1768 := (iff #1097 #1767)
-#1765 := (iff #1092 #1762)
-#1744 := (or #1330 #1685)
-#1747 := (or #1708 #1744)
-#1750 := (or #1724 #1747)
-#1753 := (or #1733 #1750)
-#1756 := (or #1738 #1753)
-#1759 := (or #1741 #1756)
-#1763 := (iff #1759 #1762)
-#1764 := [rewrite]: #1763
-#1760 := (iff #1092 #1759)
-#1757 := (iff #1076 #1756)
-#1754 := (iff #1067 #1753)
-#1751 := (iff #1058 #1750)
-#1748 := (iff #1049 #1747)
-#1745 := (iff #1040 #1744)
-#1686 := (iff #1033 #1685)
-#1683 := (iff #1021 #1680)
-#1659 := (or #1465 #1606)
-#1662 := (or #1623 #1659)
-#1665 := (or #986 #1662)
-#1668 := (or #1641 #1665)
-#1671 := (or #1645 #1668)
-#1674 := (or #753 #1671)
-#1677 := (or #1656 #1674)
-#1681 := (iff #1677 #1680)
-#1682 := [rewrite]: #1681
-#1678 := (iff #1021 #1677)
-#1675 := (iff #1013 #1674)
-#1672 := (iff #1005 #1671)
-#1669 := (iff #996 #1668)
-#1666 := (iff #987 #1665)
-#1663 := (iff #978 #1662)
-#1660 := (iff #969 #1659)
-#1607 := (iff #962 #1606)
-#1604 := (iff #957 #1603)
-#1601 := (iff #950 #1600)
-#1598 := (iff #945 #1597)
-#1595 := (iff #938 #1594)
-#1592 := (iff #933 #1591)
-#1589 := (iff #926 #1588)
-#1586 := (iff #921 #1585)
-#1583 := (iff #914 #1582)
-#1580 := (iff #909 #1579)
-#1577 := (iff #902 #1576)
-#1574 := (iff #897 #1573)
-#1571 := (iff #883 #1570)
-#1568 := (iff #878 #1567)
-#1565 := (iff #871 #1564)
-#1562 := (iff #868 #1559)
-#1553 := (and #798 #1547)
-#1556 := (and #1550 #1553)
-#1560 := (iff #1556 #1559)
-#1561 := [rewrite]: #1560
-#1557 := (iff #868 #1556)
-#1554 := (iff #865 #1553)
-#1548 := (iff #862 #1547)
-#1549 := [rewrite]: #1548
-#1555 := [monotonicity #1549]: #1554
-#1551 := (iff #221 #1550)
-#1552 := [rewrite]: #1551
-#1558 := [monotonicity #1552 #1555]: #1557
-#1563 := [trans #1558 #1561]: #1562
-#1566 := [quant-intro #1563]: #1565
-#1545 := (iff #877 #1544)
-#1542 := (iff #220 #1541)
-#1539 := (iff #219 #1538)
-#1540 := [rewrite]: #1539
-#1543 := [monotonicity #1540]: #1542
-#1546 := [monotonicity #1543]: #1545
-#1569 := [monotonicity #1546 #1566]: #1568
-#1572 := [quant-intro #1569]: #1571
-#1534 := (iff #896 #1533)
-#1531 := (iff #859 #1530)
-#1528 := (iff #854 #1527)
-#1524 := (iff #847 #1523)
-#1526 := [rewrite]: #1524
+#1137 := (or #1136 #1128)
+#400 := (= 0::Int #58)
+#407 := (or #62 #400)
+#412 := (forall (vars (?v0 S2)) #407)
+#1145 := (not #412)
+#1146 := (or #1145 #1137)
+#1158 := (not #1146)
+#1796 := (iff #1158 #1795)
+#1793 := (iff #1146 #1790)
+#1781 := (or #1127 #1767)
+#1784 := (or #1136 #1781)
+#1787 := (or #1778 #1784)
+#1791 := (iff #1787 #1790)
+#1792 := [rewrite]: #1791
+#1788 := (iff #1146 #1787)
+#1785 := (iff #1137 #1784)
+#1782 := (iff #1128 #1781)
+#1768 := (iff #1121 #1767)
+#1765 := (iff #1116 #1764)
+#1762 := (iff #1109 #1761)
+#1759 := (iff #1104 #1758)
+#1756 := (iff #1097 #1755)
+#1753 := (iff #1092 #1752)
+#1750 := (iff #1085 #1749)
+#1747 := (iff #1080 #1746)
+#1744 := (iff #1073 #1743)
+#1741 := (iff #1068 #1738)
+#1720 := (or #1306 #1661)
+#1723 := (or #1684 #1720)
+#1726 := (or #1700 #1723)
+#1729 := (or #1709 #1726)
+#1732 := (or #1714 #1729)
+#1735 := (or #1717 #1732)
+#1739 := (iff #1735 #1738)
+#1740 := [rewrite]: #1739
+#1736 := (iff #1068 #1735)
+#1733 := (iff #1052 #1732)
+#1730 := (iff #1043 #1729)
+#1727 := (iff #1034 #1726)
+#1724 := (iff #1025 #1723)
+#1721 := (iff #1016 #1720)
+#1662 := (iff #1009 #1661)
+#1659 := (iff #997 #1656)
+#1635 := (or #1441 #1582)
+#1638 := (or #1599 #1635)
+#1641 := (or #962 #1638)
+#1644 := (or #1617 #1641)
+#1647 := (or #1621 #1644)
+#1650 := (or #729 #1647)
+#1653 := (or #1632 #1650)
+#1657 := (iff #1653 #1656)
+#1658 := [rewrite]: #1657
+#1654 := (iff #997 #1653)
+#1651 := (iff #989 #1650)
+#1648 := (iff #981 #1647)
+#1645 := (iff #972 #1644)
+#1642 := (iff #963 #1641)
+#1639 := (iff #954 #1638)
+#1636 := (iff #945 #1635)
+#1583 := (iff #938 #1582)
+#1580 := (iff #933 #1579)
+#1577 := (iff #926 #1576)
+#1574 := (iff #921 #1573)
+#1571 := (iff #914 #1570)
+#1568 := (iff #909 #1567)
+#1565 := (iff #902 #1564)
+#1562 := (iff #897 #1561)
+#1559 := (iff #890 #1558)
+#1556 := (iff #885 #1555)
+#1553 := (iff #878 #1552)
+#1550 := (iff #873 #1549)
+#1547 := (iff #859 #1546)
+#1544 := (iff #854 #1543)
+#1541 := (iff #847 #1540)
+#1538 := (iff #844 #1535)
+#1529 := (and #774 #1523)
+#1532 := (and #1526 #1529)
+#1536 := (iff #1532 #1535)
+#1537 := [rewrite]: #1536
+#1533 := (iff #844 #1532)
+#1530 := (iff #841 #1529)
+#1524 := (iff #838 #1523)
+#1525 := [rewrite]: #1524
+#1531 := [monotonicity #1525]: #1530
+#1527 := (iff #221 #1526)
+#1528 := [rewrite]: #1527
+#1534 := [monotonicity #1528 #1531]: #1533
+#1539 := [trans #1534 #1537]: #1538
+#1542 := [quant-intro #1539]: #1541
 #1521 := (iff #853 #1520)
-#1518 := (iff #839 #1515)
-#1512 := (and #1227 #798)
-#1516 := (iff #1512 #1515)
-#1517 := [rewrite]: #1516
-#1513 := (iff #839 #1512)
-#1228 := (iff #83 #1227)
-#1229 := [rewrite]: #1228
-#1514 := [monotonicity #1229]: #1513
-#1519 := [trans #1514 #1517]: #1518
+#1518 := (iff #220 #1517)
+#1515 := (iff #219 #1514)
+#1516 := [rewrite]: #1515
+#1519 := [monotonicity #1516]: #1518
 #1522 := [monotonicity #1519]: #1521
-#1529 := [monotonicity #1522 #1526]: #1528
-#1532 := [quant-intro #1529]: #1531
-#1535 := [monotonicity #1532]: #1534
-#1575 := [monotonicity #1535 #1572]: #1574
-#1578 := [monotonicity #1532 #1575]: #1577
-#1510 := (iff #908 #1509)
-#1507 := (iff #833 #1506)
-#1504 := (iff #828 #1501)
-#1498 := (or #1493 #827)
-#1502 := (iff #1498 #1501)
-#1503 := [rewrite]: #1502
-#1499 := (iff #828 #1498)
-#1496 := (iff #211 #1493)
-#1497 := [rewrite]: #1496
-#1500 := [monotonicity #1497]: #1499
-#1505 := [trans #1500 #1503]: #1504
+#1545 := [monotonicity #1522 #1542]: #1544
+#1548 := [quant-intro #1545]: #1547
+#1510 := (iff #872 #1509)
+#1507 := (iff #835 #1506)
+#1504 := (iff #830 #1503)
+#1500 := (iff #823 #1499)
+#1502 := [rewrite]: #1500
+#1497 := (iff #829 #1496)
+#1494 := (iff #815 #1491)
+#1488 := (and #1203 #774)
+#1492 := (iff #1488 #1491)
+#1493 := [rewrite]: #1492
+#1489 := (iff #815 #1488)
+#1204 := (iff #83 #1203)
+#1205 := [rewrite]: #1204
+#1490 := [monotonicity #1205]: #1489
+#1495 := [trans #1490 #1493]: #1494
+#1498 := [monotonicity #1495]: #1497
+#1505 := [monotonicity #1498 #1502]: #1504
 #1508 := [quant-intro #1505]: #1507
 #1511 := [monotonicity #1508]: #1510
-#1581 := [monotonicity #1511 #1578]: #1580
-#1584 := [monotonicity #1508 #1581]: #1583
-#1491 := (iff #920 #1490)
-#1488 := (iff #205 #1487)
-#1485 := (iff #204 #1484)
-#1486 := [rewrite]: #1485
-#1489 := [quant-intro #1486]: #1488
-#1492 := [monotonicity #1489]: #1491
-#1587 := [monotonicity #1492 #1584]: #1586
-#1590 := [monotonicity #1489 #1587]: #1589
-#1482 := (iff #932 #1481)
-#1479 := (iff #813 #203)
-#1480 := [rewrite]: #1479
-#1483 := [monotonicity #1480]: #1482
-#1593 := [monotonicity #1483 #1590]: #1592
-#1596 := [monotonicity #1480 #1593]: #1595
-#1599 := [monotonicity #1596]: #1598
-#1602 := [monotonicity #1599]: #1601
-#1477 := (iff #956 #1476)
-#1474 := (iff #197 #1473)
-#1471 := (iff #196 #1468)
-#1472 := [rewrite]: #1471
-#1475 := [quant-intro #1472]: #1474
-#1478 := [monotonicity #1475]: #1477
-#1605 := [monotonicity #1478 #1602]: #1604
-#1608 := [monotonicity #1475 #1605]: #1607
-#1466 := (iff #968 #1465)
-#1463 := (iff #795 #1462)
-#1460 := (iff #790 #1457)
-#1454 := (or #1451 #784)
-#1458 := (iff #1454 #1457)
-#1459 := [rewrite]: #1458
-#1455 := (iff #790 #1454)
-#1452 := (iff #187 #1451)
-#1449 := (iff #186 #1448)
-#1450 := [rewrite]: #1449
-#1442 := (iff #184 #1441)
-#1443 := [rewrite]: #1442
-#1453 := [monotonicity #1443 #1450]: #1452
-#1456 := [monotonicity #1453]: #1455
-#1461 := [trans #1456 #1459]: #1460
-#1464 := [quant-intro #1461]: #1463
-#1467 := [monotonicity #1464]: #1466
-#1661 := [monotonicity #1467 #1608]: #1660
-#1624 := (iff #977 #1623)
-#1621 := (iff #781 #1620)
-#1618 := (iff #776 #1617)
-#1615 := (iff #770 #1614)
-#1616 := [rewrite]: #1615
-#1610 := (iff #192 #1609)
-#1611 := [monotonicity #1453]: #1610
-#1619 := [monotonicity #1611 #1616]: #1618
-#1622 := [quant-intro #1619]: #1621
-#1625 := [monotonicity #1622]: #1624
-#1664 := [monotonicity #1625 #1661]: #1663
-#1667 := [monotonicity #1664]: #1666
-#1642 := (iff #995 #1641)
-#1639 := (iff #767 #1638)
-#1636 := (iff #762 #1633)
-#1630 := (or #1626 #532)
-#1634 := (iff #1630 #1633)
-#1635 := [rewrite]: #1634
-#1631 := (iff #762 #1630)
-#1628 := (iff #176 #1626)
-#1629 := [rewrite]: #1628
-#1632 := [monotonicity #1629]: #1631
-#1637 := [trans #1632 #1635]: #1636
-#1640 := [quant-intro #1637]: #1639
-#1643 := [monotonicity #1640]: #1642
-#1670 := [monotonicity #1643 #1667]: #1669
-#1654 := (iff #1004 #1645)
-#1646 := (not #1645)
-#1649 := (not #1646)
-#1652 := (iff #1649 #1645)
-#1653 := [rewrite]: #1652
-#1650 := (iff #1004 #1649)
-#1647 := (iff #175 #1646)
-#1648 := [rewrite]: #1647
-#1651 := [monotonicity #1648]: #1650
-#1655 := [trans #1651 #1653]: #1654
-#1673 := [monotonicity #1655 #1670]: #1672
-#1676 := [monotonicity #1673]: #1675
-#1657 := (iff #617 #1656)
-#1416 := (iff #614 #1415)
-#1413 := (iff #609 #1410)
-#1407 := (and #1291 #535)
-#1411 := (iff #1407 #1410)
-#1412 := [rewrite]: #1411
-#1408 := (iff #609 #1407)
-#1292 := (iff #120 #1291)
-#1293 := [rewrite]: #1292
-#1409 := [monotonicity #1293]: #1408
-#1414 := [trans #1409 #1412]: #1413
-#1417 := [quant-intro #1414]: #1416
-#1658 := [monotonicity #1417]: #1657
-#1679 := [monotonicity #1658 #1676]: #1678
-#1684 := [trans #1679 #1682]: #1683
-#1436 := (iff #741 #1433)
-#1418 := (or #705 #1404)
-#1421 := (or #714 #1418)
-#1424 := (or #723 #1421)
-#1427 := (or #732 #1424)
-#1430 := (or #1415 #1427)
+#1551 := [monotonicity #1511 #1548]: #1550
+#1554 := [monotonicity #1508 #1551]: #1553
+#1486 := (iff #884 #1485)
+#1483 := (iff #809 #1482)
+#1480 := (iff #804 #1477)
+#1474 := (or #1469 #803)
+#1478 := (iff #1474 #1477)
+#1479 := [rewrite]: #1478
+#1475 := (iff #804 #1474)
+#1472 := (iff #211 #1469)
+#1473 := [rewrite]: #1472
+#1476 := [monotonicity #1473]: #1475
+#1481 := [trans #1476 #1479]: #1480
+#1484 := [quant-intro #1481]: #1483
+#1487 := [monotonicity #1484]: #1486
+#1557 := [monotonicity #1487 #1554]: #1556
+#1560 := [monotonicity #1484 #1557]: #1559
+#1467 := (iff #896 #1466)
+#1464 := (iff #205 #1463)
+#1461 := (iff #204 #1460)
+#1462 := [rewrite]: #1461
+#1465 := [quant-intro #1462]: #1464
+#1468 := [monotonicity #1465]: #1467
+#1563 := [monotonicity #1468 #1560]: #1562
+#1566 := [monotonicity #1465 #1563]: #1565
+#1458 := (iff #908 #1457)
+#1455 := (iff #789 #203)
+#1456 := [rewrite]: #1455
+#1459 := [monotonicity #1456]: #1458
+#1569 := [monotonicity #1459 #1566]: #1568
+#1572 := [monotonicity #1456 #1569]: #1571
+#1575 := [monotonicity #1572]: #1574
+#1578 := [monotonicity #1575]: #1577
+#1453 := (iff #932 #1452)
+#1450 := (iff #197 #1449)
+#1447 := (iff #196 #1444)
+#1448 := [rewrite]: #1447
+#1451 := [quant-intro #1448]: #1450
+#1454 := [monotonicity #1451]: #1453
+#1581 := [monotonicity #1454 #1578]: #1580
+#1584 := [monotonicity #1451 #1581]: #1583
+#1442 := (iff #944 #1441)
+#1439 := (iff #771 #1438)
+#1436 := (iff #766 #1433)
+#1430 := (or #1427 #760)
 #1434 := (iff #1430 #1433)
 #1435 := [rewrite]: #1434
-#1431 := (iff #741 #1430)
-#1428 := (iff #733 #1427)
-#1425 := (iff #724 #1424)
-#1422 := (iff #715 #1421)
-#1419 := (iff #706 #1418)
-#1405 := (iff #699 #1404)
-#1402 := (iff #694 #1401)
-#1399 := (iff #687 #1398)
-#1396 := (iff #682 #1393)
-#1390 := (or #1385 #158)
-#1394 := (iff #1390 #1393)
-#1395 := [rewrite]: #1394
-#1391 := (iff #682 #1390)
-#1388 := (iff #668 #158)
-#1389 := [rewrite]: #1388
-#1386 := (iff #681 #1385)
-#1383 := (iff #665 #1382)
-#1380 := (iff #660 #1379)
-#1377 := (iff #653 #1376)
-#1378 := [rewrite]: #1377
-#1374 := (iff #659 #1373)
-#1371 := (iff #650 #1370)
-#1337 := (iff #143 #1336)
-#1338 := [rewrite]: #1337
-#1372 := [monotonicity #1229 #1338]: #1371
-#1375 := [monotonicity #1372]: #1374
-#1381 := [monotonicity #1375 #1378]: #1380
-#1384 := [quant-intro #1381]: #1383
-#1387 := [monotonicity #1384]: #1386
-#1392 := [monotonicity #1387 #1389]: #1391
-#1397 := [trans #1392 #1395]: #1396
-#1400 := [monotonicity #1384 #1397]: #1399
-#1368 := (iff #693 #1367)
-#1365 := (iff #647 #1364)
-#1362 := (iff #642 #1361)
-#1359 := (iff #635 #1358)
-#1356 := (iff #632 #1355)
-#1352 := (iff #629 #1351)
-#1354 := [rewrite]: #1352
-#1349 := (iff #146 #1348)
-#1350 := [rewrite]: #1349
-#1357 := [monotonicity #1350 #1354]: #1356
-#1360 := [quant-intro #1357]: #1359
-#1343 := (iff #641 #1342)
-#1340 := (iff #144 #1339)
-#1341 := [monotonicity #1338]: #1340
-#1344 := [monotonicity #1341]: #1343
-#1363 := [monotonicity #1344 #1360]: #1362
-#1366 := [quant-intro #1363]: #1365
-#1369 := [monotonicity #1366]: #1368
-#1403 := [monotonicity #1369 #1400]: #1402
-#1406 := [monotonicity #1366 #1403]: #1405
-#1420 := [monotonicity #1406]: #1419
-#1423 := [monotonicity #1420]: #1422
-#1426 := [monotonicity #1423]: #1425
-#1429 := [monotonicity #1426]: #1428
-#1432 := [monotonicity #1417 #1429]: #1431
+#1431 := (iff #766 #1430)
+#1428 := (iff #187 #1427)
+#1425 := (iff #186 #1424)
+#1426 := [rewrite]: #1425
+#1418 := (iff #184 #1417)
+#1419 := [rewrite]: #1418
+#1429 := [monotonicity #1419 #1426]: #1428
+#1432 := [monotonicity #1429]: #1431
 #1437 := [trans #1432 #1435]: #1436
-#1687 := [monotonicity #1437 #1684]: #1686
-#1331 := (iff #1039 #1330)
-#1328 := (iff #603 #1327)
-#1325 := (iff #598 #1324)
-#1322 := (iff #591 #1321)
-#1319 := (iff #588 #1316)
-#1310 := (and #532 #1300)
-#1313 := (and #1307 #1310)
-#1317 := (iff #1313 #1316)
-#1318 := [rewrite]: #1317
-#1314 := (iff #588 #1313)
-#1311 := (iff #585 #1310)
-#1301 := (iff #582 #1300)
-#1305 := [rewrite]: #1301
-#1312 := [monotonicity #1305]: #1311
-#1308 := (iff #122 #1307)
-#1309 := [rewrite]: #1308
-#1315 := [monotonicity #1309 #1312]: #1314
-#1320 := [trans #1315 #1318]: #1319
-#1323 := [quant-intro #1320]: #1322
-#1298 := (iff #597 #1297)
-#1295 := (iff #121 #1294)
-#1296 := [monotonicity #1293]: #1295
-#1299 := [monotonicity #1296]: #1298
-#1326 := [monotonicity #1299 #1323]: #1325
-#1329 := [quant-intro #1326]: #1328
-#1332 := [monotonicity #1329]: #1331
-#1746 := [monotonicity #1332 #1687]: #1745
-#1709 := (iff #1048 #1708)
-#1706 := (iff #579 #1705)
-#1703 := (iff #574 #1702)
-#1700 := (iff #567 #1699)
-#1701 := [rewrite]: #1700
-#1697 := (iff #573 #1696)
-#1694 := (iff #559 #1691)
-#1688 := (and #1227 #532)
-#1692 := (iff #1688 #1691)
-#1693 := [rewrite]: #1692
-#1689 := (iff #559 #1688)
-#1690 := [monotonicity #1229]: #1689
-#1695 := [trans #1690 #1693]: #1694
-#1698 := [monotonicity #1695]: #1697
-#1704 := [monotonicity #1698 #1701]: #1703
-#1707 := [quant-intro #1704]: #1706
-#1710 := [monotonicity #1707]: #1709
-#1749 := [monotonicity #1710 #1746]: #1748
-#1725 := (iff #1057 #1724)
-#1722 := (iff #553 #1721)
-#1719 := (iff #548 #1716)
-#1713 := (or #1306 #547)
-#1717 := (iff #1713 #1716)
-#1718 := [rewrite]: #1717
-#1714 := (iff #548 #1713)
-#1711 := (iff #112 #1306)
-#1712 := [rewrite]: #1711
-#1715 := [monotonicity #1712]: #1714
-#1720 := [trans #1715 #1718]: #1719
-#1723 := [quant-intro #1720]: #1722
-#1726 := [monotonicity #1723]: #1725
-#1752 := [monotonicity #1726 #1749]: #1751
-#1734 := (iff #1066 #1733)
-#1731 := (iff #103 #1730)
-#1728 := (iff #102 #1727)
-#1729 := [rewrite]: #1728
-#1732 := [quant-intro #1729]: #1731
-#1735 := [monotonicity #1732]: #1734
-#1755 := [monotonicity #1735 #1752]: #1754
-#1739 := (iff #1075 #1738)
-#1736 := (iff #529 #100)
-#1737 := [rewrite]: #1736
-#1740 := [monotonicity #1737]: #1739
-#1758 := [monotonicity #1740 #1755]: #1757
-#1742 := (iff #1091 #1741)
-#1286 := (iff #526 #1285)
-#1283 := (iff #521 #1282)
-#1280 := (iff #514 #1279)
-#1277 := (iff #511 #1274)
-#1268 := (and #1262 #453)
-#1271 := (and #1265 #1268)
-#1275 := (iff #1271 #1274)
-#1276 := [rewrite]: #1275
-#1272 := (iff #511 #1271)
-#1269 := (iff #506 #1268)
-#1263 := (iff #92 #1262)
-#1264 := [rewrite]: #1263
-#1270 := [monotonicity #1264]: #1269
-#1266 := (iff #91 #1265)
-#1267 := [rewrite]: #1266
-#1273 := [monotonicity #1267 #1270]: #1272
-#1278 := [trans #1273 #1276]: #1277
-#1281 := [quant-intro #1278]: #1280
-#1260 := (iff #520 #1259)
-#1257 := (iff #90 #1256)
-#1254 := (iff #89 #1253)
-#1255 := [rewrite]: #1254
-#1258 := [monotonicity #1255]: #1257
-#1261 := [monotonicity #1258]: #1260
-#1284 := [monotonicity #1261 #1281]: #1283
-#1287 := [quant-intro #1284]: #1286
-#1743 := [monotonicity #1287]: #1742
-#1761 := [monotonicity #1743 #1758]: #1760
-#1766 := [trans #1761 #1764]: #1765
-#1769 := [monotonicity #1287 #1766]: #1768
-#1248 := (iff #1103 #1247)
-#1245 := (iff #500 #1244)
-#1242 := (iff #495 #1241)
-#1239 := (iff #494 #1238)
-#1236 := (iff #486 #1233)
-#1230 := (and #1227 #453)
-#1234 := (iff #1230 #1233)
-#1235 := [rewrite]: #1234
-#1231 := (iff #486 #1230)
-#1232 := [monotonicity #1229]: #1231
-#1237 := [trans #1232 #1235]: #1236
-#1240 := [monotonicity #1237]: #1239
-#1220 := (iff #86 #1221)
-#1219 := [rewrite]: #1220
-#1243 := [monotonicity #1219 #1240]: #1242
-#1246 := [quant-intro #1243]: #1245
-#1249 := [monotonicity #1246]: #1248
-#1772 := [monotonicity #1249 #1769]: #1771
-#1775 := [monotonicity #1246 #1772]: #1774
-#1217 := (iff #1115 #1216)
-#1214 := (iff #480 #1213)
-#1211 := (iff #475 #1208)
-#1205 := (or #1201 #474)
-#1209 := (iff #1205 #1208)
-#1210 := [rewrite]: #1209
-#1206 := (iff #475 #1205)
-#1200 := (iff #78 #1201)
-#1204 := [rewrite]: #1200
-#1207 := [monotonicity #1204]: #1206
-#1212 := [trans #1207 #1210]: #1211
-#1215 := [quant-intro #1212]: #1214
-#1218 := [monotonicity #1215]: #1217
-#1778 := [monotonicity #1218 #1775]: #1777
-#1781 := [monotonicity #1215 #1778]: #1780
-#1197 := (iff #1127 #1196)
-#1194 := (iff #73 #1193)
-#1190 := (iff #72 #1192)
-#1191 := [rewrite]: #1190
-#1195 := [quant-intro #1191]: #1194
-#1198 := [monotonicity #1195]: #1197
-#1784 := [monotonicity #1198 #1781]: #1783
-#1787 := [monotonicity #1195 #1784]: #1786
-#1188 := (iff #1139 #1187)
-#1185 := (iff #462 #71)
+#1440 := [quant-intro #1437]: #1439
+#1443 := [monotonicity #1440]: #1442
+#1637 := [monotonicity #1443 #1584]: #1636
+#1600 := (iff #953 #1599)
+#1597 := (iff #757 #1596)
+#1594 := (iff #752 #1593)
+#1591 := (iff #746 #1590)
+#1592 := [rewrite]: #1591
+#1586 := (iff #192 #1585)
+#1587 := [monotonicity #1429]: #1586
+#1595 := [monotonicity #1587 #1592]: #1594
+#1598 := [quant-intro #1595]: #1597
+#1601 := [monotonicity #1598]: #1600
+#1640 := [monotonicity #1601 #1637]: #1639
+#1643 := [monotonicity #1640]: #1642
+#1618 := (iff #971 #1617)
+#1615 := (iff #743 #1614)
+#1612 := (iff #738 #1609)
+#1606 := (or #1602 #508)
+#1610 := (iff #1606 #1609)
+#1611 := [rewrite]: #1610
+#1607 := (iff #738 #1606)
+#1604 := (iff #176 #1602)
+#1605 := [rewrite]: #1604
+#1608 := [monotonicity #1605]: #1607
+#1613 := [trans #1608 #1611]: #1612
+#1616 := [quant-intro #1613]: #1615
+#1619 := [monotonicity #1616]: #1618
+#1646 := [monotonicity #1619 #1643]: #1645
+#1630 := (iff #980 #1621)
+#1622 := (not #1621)
+#1625 := (not #1622)
+#1628 := (iff #1625 #1621)
+#1629 := [rewrite]: #1628
+#1626 := (iff #980 #1625)
+#1623 := (iff #175 #1622)
+#1624 := [rewrite]: #1623
+#1627 := [monotonicity #1624]: #1626
+#1631 := [trans #1627 #1629]: #1630
+#1649 := [monotonicity #1631 #1646]: #1648
+#1652 := [monotonicity #1649]: #1651
+#1633 := (iff #593 #1632)
+#1392 := (iff #590 #1391)
+#1389 := (iff #585 #1386)
+#1383 := (and #1267 #511)
+#1387 := (iff #1383 #1386)
+#1388 := [rewrite]: #1387
+#1384 := (iff #585 #1383)
+#1268 := (iff #120 #1267)
+#1269 := [rewrite]: #1268
+#1385 := [monotonicity #1269]: #1384
+#1390 := [trans #1385 #1388]: #1389
+#1393 := [quant-intro #1390]: #1392
+#1634 := [monotonicity #1393]: #1633
+#1655 := [monotonicity #1634 #1652]: #1654
+#1660 := [trans #1655 #1658]: #1659
+#1412 := (iff #717 #1409)
+#1394 := (or #681 #1380)
+#1397 := (or #690 #1394)
+#1400 := (or #699 #1397)
+#1403 := (or #708 #1400)
+#1406 := (or #1391 #1403)
+#1410 := (iff #1406 #1409)
+#1411 := [rewrite]: #1410
+#1407 := (iff #717 #1406)
+#1404 := (iff #709 #1403)
+#1401 := (iff #700 #1400)
+#1398 := (iff #691 #1397)
+#1395 := (iff #682 #1394)
+#1381 := (iff #675 #1380)
+#1378 := (iff #670 #1377)
+#1375 := (iff #663 #1374)
+#1372 := (iff #658 #1369)
+#1366 := (or #1361 #158)
+#1370 := (iff #1366 #1369)
+#1371 := [rewrite]: #1370
+#1367 := (iff #658 #1366)
+#1364 := (iff #644 #158)
+#1365 := [rewrite]: #1364
+#1362 := (iff #657 #1361)
+#1359 := (iff #641 #1358)
+#1356 := (iff #636 #1355)
+#1353 := (iff #629 #1352)
+#1354 := [rewrite]: #1353
+#1350 := (iff #635 #1349)
+#1347 := (iff #626 #1346)
+#1313 := (iff #143 #1312)
+#1314 := [rewrite]: #1313
+#1348 := [monotonicity #1205 #1314]: #1347
+#1351 := [monotonicity #1348]: #1350
+#1357 := [monotonicity #1351 #1354]: #1356
+#1360 := [quant-intro #1357]: #1359
+#1363 := [monotonicity #1360]: #1362
+#1368 := [monotonicity #1363 #1365]: #1367
+#1373 := [trans #1368 #1371]: #1372
+#1376 := [monotonicity #1360 #1373]: #1375
+#1344 := (iff #669 #1343)
+#1341 := (iff #623 #1340)
+#1338 := (iff #618 #1337)
+#1335 := (iff #611 #1334)
+#1332 := (iff #608 #1331)
+#1328 := (iff #605 #1327)
+#1330 := [rewrite]: #1328
+#1325 := (iff #146 #1324)
+#1326 := [rewrite]: #1325
+#1333 := [monotonicity #1326 #1330]: #1332
+#1336 := [quant-intro #1333]: #1335
+#1319 := (iff #617 #1318)
+#1316 := (iff #144 #1315)
+#1317 := [monotonicity #1314]: #1316
+#1320 := [monotonicity #1317]: #1319
+#1339 := [monotonicity #1320 #1336]: #1338
+#1342 := [quant-intro #1339]: #1341
+#1345 := [monotonicity #1342]: #1344
+#1379 := [monotonicity #1345 #1376]: #1378
+#1382 := [monotonicity #1342 #1379]: #1381
+#1396 := [monotonicity #1382]: #1395
+#1399 := [monotonicity #1396]: #1398
+#1402 := [monotonicity #1399]: #1401
+#1405 := [monotonicity #1402]: #1404
+#1408 := [monotonicity #1393 #1405]: #1407
+#1413 := [trans #1408 #1411]: #1412
+#1663 := [monotonicity #1413 #1660]: #1662
+#1307 := (iff #1015 #1306)
+#1304 := (iff #579 #1303)
+#1301 := (iff #574 #1300)
+#1298 := (iff #567 #1297)
+#1295 := (iff #564 #1292)
+#1286 := (and #508 #1276)
+#1289 := (and #1283 #1286)
+#1293 := (iff #1289 #1292)
+#1294 := [rewrite]: #1293
+#1290 := (iff #564 #1289)
+#1287 := (iff #561 #1286)
+#1277 := (iff #558 #1276)
+#1281 := [rewrite]: #1277
+#1288 := [monotonicity #1281]: #1287
+#1284 := (iff #122 #1283)
+#1285 := [rewrite]: #1284
+#1291 := [monotonicity #1285 #1288]: #1290
+#1296 := [trans #1291 #1294]: #1295
+#1299 := [quant-intro #1296]: #1298
+#1274 := (iff #573 #1273)
+#1271 := (iff #121 #1270)
+#1272 := [monotonicity #1269]: #1271
+#1275 := [monotonicity #1272]: #1274
+#1302 := [monotonicity #1275 #1299]: #1301
+#1305 := [quant-intro #1302]: #1304
+#1308 := [monotonicity #1305]: #1307
+#1722 := [monotonicity #1308 #1663]: #1721
+#1685 := (iff #1024 #1684)
+#1682 := (iff #555 #1681)
+#1679 := (iff #550 #1678)
+#1676 := (iff #543 #1675)
+#1677 := [rewrite]: #1676
+#1673 := (iff #549 #1672)
+#1670 := (iff #535 #1667)
+#1664 := (and #1203 #508)
+#1668 := (iff #1664 #1667)
+#1669 := [rewrite]: #1668
+#1665 := (iff #535 #1664)
+#1666 := [monotonicity #1205]: #1665
+#1671 := [trans #1666 #1669]: #1670
+#1674 := [monotonicity #1671]: #1673
+#1680 := [monotonicity #1674 #1677]: #1679
+#1683 := [quant-intro #1680]: #1682
+#1686 := [monotonicity #1683]: #1685
+#1725 := [monotonicity #1686 #1722]: #1724
+#1701 := (iff #1033 #1700)
+#1698 := (iff #529 #1697)
+#1695 := (iff #524 #1692)
+#1689 := (or #1282 #523)
+#1693 := (iff #1689 #1692)
+#1694 := [rewrite]: #1693
+#1690 := (iff #524 #1689)
+#1687 := (iff #112 #1282)
+#1688 := [rewrite]: #1687
+#1691 := [monotonicity #1688]: #1690
+#1696 := [trans #1691 #1694]: #1695
+#1699 := [quant-intro #1696]: #1698
+#1702 := [monotonicity #1699]: #1701
+#1728 := [monotonicity #1702 #1725]: #1727
+#1710 := (iff #1042 #1709)
+#1707 := (iff #103 #1706)
+#1704 := (iff #102 #1703)
+#1705 := [rewrite]: #1704
+#1708 := [quant-intro #1705]: #1707
+#1711 := [monotonicity #1708]: #1710
+#1731 := [monotonicity #1711 #1728]: #1730
+#1715 := (iff #1051 #1714)
+#1712 := (iff #505 #100)
+#1713 := [rewrite]: #1712
+#1716 := [monotonicity #1713]: #1715
+#1734 := [monotonicity #1716 #1731]: #1733
+#1718 := (iff #1067 #1717)
+#1262 := (iff #502 #1261)
+#1259 := (iff #497 #1258)
+#1256 := (iff #490 #1255)
+#1253 := (iff #487 #1250)
+#1244 := (and #1238 #429)
+#1247 := (and #1241 #1244)
+#1251 := (iff #1247 #1250)
+#1252 := [rewrite]: #1251
+#1248 := (iff #487 #1247)
+#1245 := (iff #482 #1244)
+#1239 := (iff #92 #1238)
+#1240 := [rewrite]: #1239
+#1246 := [monotonicity #1240]: #1245
+#1242 := (iff #91 #1241)
+#1243 := [rewrite]: #1242
+#1249 := [monotonicity #1243 #1246]: #1248
+#1254 := [trans #1249 #1252]: #1253
+#1257 := [quant-intro #1254]: #1256
+#1236 := (iff #496 #1235)
+#1233 := (iff #90 #1232)
+#1230 := (iff #89 #1229)
+#1231 := [rewrite]: #1230
+#1234 := [monotonicity #1231]: #1233
+#1237 := [monotonicity #1234]: #1236
+#1260 := [monotonicity #1237 #1257]: #1259
+#1263 := [quant-intro #1260]: #1262
+#1719 := [monotonicity #1263]: #1718
+#1737 := [monotonicity #1719 #1734]: #1736
+#1742 := [trans #1737 #1740]: #1741
+#1745 := [monotonicity #1263 #1742]: #1744
+#1224 := (iff #1079 #1223)
+#1221 := (iff #476 #1220)
+#1218 := (iff #471 #1217)
+#1215 := (iff #470 #1214)
+#1212 := (iff #462 #1209)
+#1206 := (and #1203 #429)
+#1210 := (iff #1206 #1209)
+#1211 := [rewrite]: #1210
+#1207 := (iff #462 #1206)
+#1208 := [monotonicity #1205]: #1207
+#1213 := [trans #1208 #1211]: #1212
+#1216 := [monotonicity #1213]: #1215
+#1196 := (iff #86 #1197)
+#1195 := [rewrite]: #1196
+#1219 := [monotonicity #1195 #1216]: #1218
+#1222 := [quant-intro #1219]: #1221
+#1225 := [monotonicity #1222]: #1224
+#1748 := [monotonicity #1225 #1745]: #1747
+#1751 := [monotonicity #1222 #1748]: #1750
+#1193 := (iff #1091 #1192)
+#1190 := (iff #456 #1189)
+#1187 := (iff #451 #1184)
+#1181 := (or #1177 #450)
+#1185 := (iff #1181 #1184)
 #1186 := [rewrite]: #1185
-#1189 := [monotonicity #1186]: #1188
-#1790 := [monotonicity #1189 #1787]: #1789
-#1793 := [monotonicity #1186 #1790]: #1792
-#1807 := [monotonicity #1793]: #1806
-#1810 := [monotonicity #1807]: #1809
-#1803 := (iff #1169 #1802)
-#1800 := (iff #436 #1799)
-#1797 := (iff #431 #1796)
-#1794 := (iff #425 #59)
-#1795 := [rewrite]: #1794
-#1798 := [monotonicity #1795]: #1797
-#1801 := [quant-intro #1798]: #1800
-#1804 := [monotonicity #1801]: #1803
-#1813 := [monotonicity #1804 #1810]: #1812
-#1818 := [trans #1813 #1816]: #1817
-#1821 := [monotonicity #1818]: #1820
-#1183 := (iff #270 #1182)
-#1180 := (iff #269 #1170)
-#1175 := (implies true #1170)
-#1178 := (iff #1175 #1170)
-#1179 := [rewrite]: #1178
-#1176 := (iff #269 #1175)
-#1173 := (iff #268 #1170)
-#1166 := (implies #436 #1161)
-#1171 := (iff #1166 #1170)
-#1172 := [rewrite]: #1171
-#1167 := (iff #268 #1166)
-#1164 := (iff #267 #1161)
-#1157 := (implies #450 #1152)
-#1162 := (iff #1157 #1161)
-#1163 := [rewrite]: #1162
-#1158 := (iff #267 #1157)
-#1155 := (iff #266 #1152)
-#1148 := (implies #459 #1145)
-#1153 := (iff #1148 #1152)
-#1154 := [rewrite]: #1153
-#1149 := (iff #266 #1148)
-#1146 := (iff #265 #1145)
-#1143 := (iff #264 #1140)
-#1136 := (implies #462 #1133)
-#1141 := (iff #1136 #1140)
-#1142 := [rewrite]: #1141
-#1137 := (iff #264 #1136)
-#1134 := (iff #263 #1133)
-#1131 := (iff #262 #1128)
-#1124 := (implies #73 #1121)
+#1182 := (iff #451 #1181)
+#1176 := (iff #78 #1177)
+#1180 := [rewrite]: #1176
+#1183 := [monotonicity #1180]: #1182
+#1188 := [trans #1183 #1186]: #1187
+#1191 := [quant-intro #1188]: #1190
+#1194 := [monotonicity #1191]: #1193
+#1754 := [monotonicity #1194 #1751]: #1753
+#1757 := [monotonicity #1191 #1754]: #1756
+#1173 := (iff #1103 #1172)
+#1170 := (iff #73 #1169)
+#1166 := (iff #72 #1168)
+#1167 := [rewrite]: #1166
+#1171 := [quant-intro #1167]: #1170
+#1174 := [monotonicity #1171]: #1173
+#1760 := [monotonicity #1174 #1757]: #1759
+#1763 := [monotonicity #1171 #1760]: #1762
+#1164 := (iff #1115 #1163)
+#1161 := (iff #438 #71)
+#1162 := [rewrite]: #1161
+#1165 := [monotonicity #1162]: #1164
+#1766 := [monotonicity #1165 #1763]: #1765
+#1769 := [monotonicity #1162 #1766]: #1768
+#1783 := [monotonicity #1769]: #1782
+#1786 := [monotonicity #1783]: #1785
+#1779 := (iff #1145 #1778)
+#1776 := (iff #412 #1775)
+#1773 := (iff #407 #1772)
+#1770 := (iff #400 #59)
+#1771 := [rewrite]: #1770
+#1774 := [monotonicity #1771]: #1773
+#1777 := [quant-intro #1774]: #1776
+#1780 := [monotonicity #1777]: #1779
+#1789 := [monotonicity #1780 #1786]: #1788
+#1794 := [trans #1789 #1792]: #1793
+#1797 := [monotonicity #1794]: #1796
+#1159 := (iff #270 #1158)
+#1156 := (iff #269 #1146)
+#1151 := (implies true #1146)
+#1154 := (iff #1151 #1146)
+#1155 := [rewrite]: #1154
+#1152 := (iff #269 #1151)
+#1149 := (iff #268 #1146)
+#1142 := (implies #412 #1137)
+#1147 := (iff #1142 #1146)
+#1148 := [rewrite]: #1147
+#1143 := (iff #268 #1142)
+#1140 := (iff #267 #1137)
+#1133 := (implies #426 #1128)
+#1138 := (iff #1133 #1137)
+#1139 := [rewrite]: #1138
+#1134 := (iff #267 #1133)
+#1131 := (iff #266 #1128)
+#1124 := (implies #435 #1121)
 #1129 := (iff #1124 #1128)
 #1130 := [rewrite]: #1129
-#1125 := (iff #262 #1124)
-#1122 := (iff #261 #1121)
-#1119 := (iff #260 #1116)
-#1112 := (implies #480 #1109)
+#1125 := (iff #266 #1124)
+#1122 := (iff #265 #1121)
+#1119 := (iff #264 #1116)
+#1112 := (implies #438 #1109)
 #1117 := (iff #1112 #1116)
 #1118 := [rewrite]: #1117
-#1113 := (iff #260 #1112)
-#1110 := (iff #259 #1109)
-#1107 := (iff #258 #1104)
-#1100 := (implies #500 #1097)
+#1113 := (iff #264 #1112)
+#1110 := (iff #263 #1109)
+#1107 := (iff #262 #1104)
+#1100 := (implies #73 #1097)
 #1105 := (iff #1100 #1104)
 #1106 := [rewrite]: #1105
-#1101 := (iff #258 #1100)
-#1098 := (iff #257 #1097)
-#1095 := (iff #256 #1092)
-#1088 := (implies #526 #1076)
+#1101 := (iff #262 #1100)
+#1098 := (iff #261 #1097)
+#1095 := (iff #260 #1092)
+#1088 := (implies #456 #1085)
 #1093 := (iff #1088 #1092)
 #1094 := [rewrite]: #1093
-#1089 := (iff #256 #1088)
-#1086 := (iff #255 #1076)
-#1081 := (implies true #1076)
-#1084 := (iff #1081 #1076)
-#1085 := [rewrite]: #1084
-#1082 := (iff #255 #1081)
-#1079 := (iff #254 #1076)
-#1072 := (implies #529 #1067)
-#1077 := (iff #1072 #1076)
-#1078 := [rewrite]: #1077
-#1073 := (iff #254 #1072)
-#1070 := (iff #253 #1067)
-#1063 := (implies #103 #1058)
-#1068 := (iff #1063 #1067)
-#1069 := [rewrite]: #1068
-#1064 := (iff #253 #1063)
-#1061 := (iff #252 #1058)
-#1054 := (implies #553 #1049)
-#1059 := (iff #1054 #1058)
-#1060 := [rewrite]: #1059
-#1055 := (iff #252 #1054)
-#1052 := (iff #251 #1049)
-#1045 := (implies #579 #1040)
-#1050 := (iff #1045 #1049)
-#1051 := [rewrite]: #1050
-#1046 := (iff #251 #1045)
-#1043 := (iff #250 #1040)
-#1036 := (implies #603 #1033)
-#1041 := (iff #1036 #1040)
-#1042 := [rewrite]: #1041
-#1037 := (iff #250 #1036)
-#1034 := (iff #249 #1033)
-#1031 := (iff #248 #1021)
-#1026 := (implies true #1021)
-#1029 := (iff #1026 #1021)
-#1030 := [rewrite]: #1029
-#1027 := (iff #248 #1026)
-#1024 := (iff #247 #1021)
-#1018 := (implies #614 #1013)
-#1022 := (iff #1018 #1021)
-#1023 := [rewrite]: #1022
-#1019 := (iff #247 #1018)
-#1016 := (iff #246 #1013)
-#756 := (not #753)
-#1010 := (implies #756 #1005)
-#1014 := (iff #1010 #1013)
-#1015 := [rewrite]: #1014
-#1011 := (iff #246 #1010)
-#1008 := (iff #245 #1005)
-#1001 := (implies #175 #996)
-#1006 := (iff #1001 #1005)
-#1007 := [rewrite]: #1006
-#1002 := (iff #245 #1001)
-#999 := (iff #244 #996)
-#992 := (implies #767 #987)
-#997 := (iff #992 #996)
-#998 := [rewrite]: #997
-#993 := (iff #244 #992)
-#990 := (iff #243 #987)
-#983 := (implies #181 #978)
-#988 := (iff #983 #987)
-#989 := [rewrite]: #988
-#984 := (iff #243 #983)
-#981 := (iff #242 #978)
-#974 := (implies #781 #969)
-#979 := (iff #974 #978)
-#980 := [rewrite]: #979
-#975 := (iff #242 #974)
-#972 := (iff #241 #969)
-#965 := (implies #795 #962)
-#970 := (iff #965 #969)
-#971 := [rewrite]: #970
-#966 := (iff #241 #965)
-#963 := (iff #240 #962)
-#960 := (iff #239 #957)
-#953 := (implies #197 #950)
-#958 := (iff #953 #957)
-#959 := [rewrite]: #958
-#954 := (iff #239 #953)
-#951 := (iff #238 #950)
-#948 := (iff #237 #945)
-#941 := (implies #810 #938)
+#1089 := (iff #260 #1088)
+#1086 := (iff #259 #1085)
+#1083 := (iff #258 #1080)
+#1076 := (implies #476 #1073)
+#1081 := (iff #1076 #1080)
+#1082 := [rewrite]: #1081
+#1077 := (iff #258 #1076)
+#1074 := (iff #257 #1073)
+#1071 := (iff #256 #1068)
+#1064 := (implies #502 #1052)
+#1069 := (iff #1064 #1068)
+#1070 := [rewrite]: #1069
+#1065 := (iff #256 #1064)
+#1062 := (iff #255 #1052)
+#1057 := (implies true #1052)
+#1060 := (iff #1057 #1052)
+#1061 := [rewrite]: #1060
+#1058 := (iff #255 #1057)
+#1055 := (iff #254 #1052)
+#1048 := (implies #505 #1043)
+#1053 := (iff #1048 #1052)
+#1054 := [rewrite]: #1053
+#1049 := (iff #254 #1048)
+#1046 := (iff #253 #1043)
+#1039 := (implies #103 #1034)
+#1044 := (iff #1039 #1043)
+#1045 := [rewrite]: #1044
+#1040 := (iff #253 #1039)
+#1037 := (iff #252 #1034)
+#1030 := (implies #529 #1025)
+#1035 := (iff #1030 #1034)
+#1036 := [rewrite]: #1035
+#1031 := (iff #252 #1030)
+#1028 := (iff #251 #1025)
+#1021 := (implies #555 #1016)
+#1026 := (iff #1021 #1025)
+#1027 := [rewrite]: #1026
+#1022 := (iff #251 #1021)
+#1019 := (iff #250 #1016)
+#1012 := (implies #579 #1009)
+#1017 := (iff #1012 #1016)
+#1018 := [rewrite]: #1017
+#1013 := (iff #250 #1012)
+#1010 := (iff #249 #1009)
+#1007 := (iff #248 #997)
+#1002 := (implies true #997)
+#1005 := (iff #1002 #997)
+#1006 := [rewrite]: #1005
+#1003 := (iff #248 #1002)
+#1000 := (iff #247 #997)
+#994 := (implies #590 #989)
+#998 := (iff #994 #997)
+#999 := [rewrite]: #998
+#995 := (iff #247 #994)
+#992 := (iff #246 #989)
+#732 := (not #729)
+#986 := (implies #732 #981)
+#990 := (iff #986 #989)
+#991 := [rewrite]: #990
+#987 := (iff #246 #986)
+#984 := (iff #245 #981)
+#977 := (implies #175 #972)
+#982 := (iff #977 #981)
+#983 := [rewrite]: #982
+#978 := (iff #245 #977)
+#975 := (iff #244 #972)
+#968 := (implies #743 #963)
+#973 := (iff #968 #972)
+#974 := [rewrite]: #973
+#969 := (iff #244 #968)
+#966 := (iff #243 #963)
+#959 := (implies #181 #954)
+#964 := (iff #959 #963)
+#965 := [rewrite]: #964
+#960 := (iff #243 #959)
+#957 := (iff #242 #954)
+#950 := (implies #757 #945)
+#955 := (iff #950 #954)
+#956 := [rewrite]: #955
+#951 := (iff #242 #950)
+#948 := (iff #241 #945)
+#941 := (implies #771 #938)
 #946 := (iff #941 #945)
 #947 := [rewrite]: #946
-#942 := (iff #237 #941)
-#939 := (iff #236 #938)
-#936 := (iff #235 #933)
-#929 := (implies #813 #926)
+#942 := (iff #241 #941)
+#939 := (iff #240 #938)
+#936 := (iff #239 #933)
+#929 := (implies #197 #926)
 #934 := (iff #929 #933)
 #935 := [rewrite]: #934
-#930 := (iff #235 #929)
-#927 := (iff #234 #926)
-#924 := (iff #233 #921)
-#917 := (implies #205 #914)
+#930 := (iff #239 #929)
+#927 := (iff #238 #926)
+#924 := (iff #237 #921)
+#917 := (implies #786 #914)
 #922 := (iff #917 #921)
 #923 := [rewrite]: #922
-#918 := (iff #233 #917)
-#915 := (iff #232 #914)
-#912 := (iff #231 #909)
-#905 := (implies #833 #902)
+#918 := (iff #237 #917)
+#915 := (iff #236 #914)
+#912 := (iff #235 #909)
+#905 := (implies #789 #902)
 #910 := (iff #905 #909)
 #911 := [rewrite]: #910
-#906 := (iff #231 #905)
-#903 := (iff #230 #902)
-#900 := (iff #229 #897)
-#893 := (implies #859 #883)
+#906 := (iff #235 #905)
+#903 := (iff #234 #902)
+#900 := (iff #233 #897)
+#893 := (implies #205 #890)
 #898 := (iff #893 #897)
 #899 := [rewrite]: #898
-#894 := (iff #229 #893)
-#891 := (iff #228 #883)
-#886 := (and #883 true)
-#889 := (iff #886 #883)
-#890 := [rewrite]: #889
-#887 := (iff #228 #886)
-#884 := (iff #227 #883)
-#881 := (iff #226 #878)
-#874 := (implies #220 #871)
-#879 := (iff #874 #878)
-#880 := [rewrite]: #879
-#875 := (iff #226 #874)
-#872 := (iff #225 #871)
-#869 := (iff #224 #868)
-#866 := (iff #223 #865)
-#863 := (iff #222 #862)
-#845 := (= #215 #844)
-#846 := [rewrite]: #845
-#864 := [monotonicity #846]: #863
-#799 := (iff #199 #798)
-#800 := [rewrite]: #799
-#867 := [monotonicity #800 #864]: #866
-#870 := [monotonicity #867]: #869
-#873 := [quant-intro #870]: #872
-#876 := [monotonicity #873]: #875
-#882 := [trans #876 #880]: #881
-#885 := [quant-intro #882]: #884
-#888 := [monotonicity #885]: #887
-#892 := [trans #888 #890]: #891
-#860 := (iff #218 #859)
-#857 := (iff #217 #854)
-#850 := (implies #839 #847)
+#894 := (iff #233 #893)
+#891 := (iff #232 #890)
+#888 := (iff #231 #885)
+#881 := (implies #809 #878)
+#886 := (iff #881 #885)
+#887 := [rewrite]: #886
+#882 := (iff #231 #881)
+#879 := (iff #230 #878)
+#876 := (iff #229 #873)
+#869 := (implies #835 #859)
+#874 := (iff #869 #873)
+#875 := [rewrite]: #874
+#870 := (iff #229 #869)
+#867 := (iff #228 #859)
+#862 := (and #859 true)
+#865 := (iff #862 #859)
+#866 := [rewrite]: #865
+#863 := (iff #228 #862)
+#860 := (iff #227 #859)
+#857 := (iff #226 #854)
+#850 := (implies #220 #847)
 #855 := (iff #850 #854)
 #856 := [rewrite]: #855
-#851 := (iff #217 #850)
-#848 := (iff #216 #847)
-#849 := [monotonicity #846]: #848
-#842 := (iff #214 #839)
-#836 := (and #798 #83)
-#840 := (iff #836 #839)
-#841 := [rewrite]: #840
-#837 := (iff #214 #836)
-#838 := [monotonicity #800]: #837
-#843 := [trans #838 #841]: #842
-#852 := [monotonicity #843 #849]: #851
+#851 := (iff #226 #850)
+#848 := (iff #225 #847)
+#845 := (iff #224 #844)
+#842 := (iff #223 #841)
+#839 := (iff #222 #838)
+#821 := (= #215 #820)
+#822 := [rewrite]: #821
+#840 := [monotonicity #822]: #839
+#775 := (iff #199 #774)
+#776 := [rewrite]: #775
+#843 := [monotonicity #776 #840]: #842
+#846 := [monotonicity #843]: #845
+#849 := [quant-intro #846]: #848
+#852 := [monotonicity #849]: #851
 #858 := [trans #852 #856]: #857
 #861 := [quant-intro #858]: #860
-#895 := [monotonicity #861 #892]: #894
+#864 := [monotonicity #861]: #863
+#868 := [trans #864 #866]: #867
+#836 := (iff #218 #835)
+#833 := (iff #217 #830)
+#826 := (implies #815 #823)
+#831 := (iff #826 #830)
+#832 := [rewrite]: #831
+#827 := (iff #217 #826)
+#824 := (iff #216 #823)
+#825 := [monotonicity #822]: #824
+#818 := (iff #214 #815)
+#812 := (and #774 #83)
+#816 := (iff #812 #815)
+#817 := [rewrite]: #816
+#813 := (iff #214 #812)
+#814 := [monotonicity #776]: #813
+#819 := [trans #814 #817]: #818
+#828 := [monotonicity #819 #825]: #827
+#834 := [trans #828 #832]: #833
+#837 := [quant-intro #834]: #836
+#871 := [monotonicity #837 #868]: #870
+#877 := [trans #871 #875]: #876
+#880 := [monotonicity #837 #877]: #879
+#810 := (iff #213 #809)
+#807 := (iff #212 #804)
+#800 := (implies #797 #211)
+#805 := (iff #800 #804)
+#806 := [rewrite]: #805
+#801 := (iff #212 #800)
+#798 := (iff #209 #797)
+#795 := (iff #208 #794)
+#796 := [rewrite]: #795
+#792 := (iff #206 #780)
+#793 := [monotonicity #776]: #792
+#799 := [monotonicity #793 #796]: #798
+#802 := [monotonicity #799]: #801
+#808 := [trans #802 #806]: #807
+#811 := [quant-intro #808]: #810
+#883 := [monotonicity #811 #880]: #882
+#889 := [trans #883 #887]: #888
+#892 := [monotonicity #811 #889]: #891
+#895 := [monotonicity #892]: #894
 #901 := [trans #895 #899]: #900
-#904 := [monotonicity #861 #901]: #903
-#834 := (iff #213 #833)
-#831 := (iff #212 #828)
-#824 := (implies #821 #211)
-#829 := (iff #824 #828)
-#830 := [rewrite]: #829
-#825 := (iff #212 #824)
-#822 := (iff #209 #821)
-#819 := (iff #208 #818)
-#820 := [rewrite]: #819
-#816 := (iff #206 #804)
-#817 := [monotonicity #800]: #816
-#823 := [monotonicity #817 #820]: #822
-#826 := [monotonicity #823]: #825
-#832 := [trans #826 #830]: #831
-#835 := [quant-intro #832]: #834
-#907 := [monotonicity #835 #904]: #906
+#904 := [monotonicity #901]: #903
+#790 := (iff #203 #789)
+#791 := [rewrite]: #790
+#907 := [monotonicity #791 #904]: #906
 #913 := [trans #907 #911]: #912
-#916 := [monotonicity #835 #913]: #915
-#919 := [monotonicity #916]: #918
+#916 := [monotonicity #791 #913]: #915
+#787 := (iff #201 #786)
+#784 := (iff #200 #781)
+#777 := (implies #774 #760)
+#782 := (iff #777 #781)
+#783 := [rewrite]: #782
+#778 := (iff #200 #777)
+#761 := (iff #193 #760)
+#762 := [rewrite]: #761
+#779 := [monotonicity #776 #762]: #778
+#785 := [trans #779 #783]: #784
+#788 := [quant-intro #785]: #787
+#919 := [monotonicity #788 #916]: #918
 #925 := [trans #919 #923]: #924
-#928 := [monotonicity #925]: #927
-#814 := (iff #203 #813)
-#815 := [rewrite]: #814
-#931 := [monotonicity #815 #928]: #930
+#928 := [monotonicity #788 #925]: #927
+#931 := [monotonicity #928]: #930
 #937 := [trans #931 #935]: #936
-#940 := [monotonicity #815 #937]: #939
-#811 := (iff #201 #810)
-#808 := (iff #200 #805)
-#801 := (implies #798 #784)
-#806 := (iff #801 #805)
-#807 := [rewrite]: #806
-#802 := (iff #200 #801)
-#785 := (iff #193 #784)
-#786 := [rewrite]: #785
-#803 := [monotonicity #800 #786]: #802
-#809 := [trans #803 #807]: #808
-#812 := [quant-intro #809]: #811
-#943 := [monotonicity #812 #940]: #942
+#940 := [monotonicity #937]: #939
+#772 := (iff #195 #771)
+#769 := (iff #194 #766)
+#763 := (implies #192 #760)
+#767 := (iff #763 #766)
+#768 := [rewrite]: #767
+#764 := (iff #194 #763)
+#765 := [monotonicity #762]: #764
+#770 := [trans #765 #768]: #769
+#773 := [quant-intro #770]: #772
+#943 := [monotonicity #773 #940]: #942
 #949 := [trans #943 #947]: #948
-#952 := [monotonicity #812 #949]: #951
-#955 := [monotonicity #952]: #954
-#961 := [trans #955 #959]: #960
-#964 := [monotonicity #961]: #963
-#796 := (iff #195 #795)
-#793 := (iff #194 #790)
-#787 := (implies #192 #784)
-#791 := (iff #787 #790)
-#792 := [rewrite]: #791
-#788 := (iff #194 #787)
-#789 := [monotonicity #786]: #788
-#794 := [trans #789 #792]: #793
-#797 := [quant-intro #794]: #796
-#967 := [monotonicity #797 #964]: #966
-#973 := [trans #967 #971]: #972
-#782 := (iff #191 #781)
-#779 := (iff #190 #776)
-#773 := (implies #187 #770)
-#777 := (iff #773 #776)
-#778 := [rewrite]: #777
-#774 := (iff #190 #773)
-#771 := (iff #189 #770)
-#772 := [rewrite]: #771
-#775 := [monotonicity #772]: #774
-#780 := [trans #775 #778]: #779
-#783 := [quant-intro #780]: #782
-#976 := [monotonicity #783 #973]: #975
-#982 := [trans #976 #980]: #981
-#985 := [monotonicity #982]: #984
-#991 := [trans #985 #989]: #990
-#768 := (iff #178 #767)
-#765 := (iff #177 #762)
-#759 := (implies #535 #176)
-#763 := (iff #759 #762)
-#764 := [rewrite]: #763
-#760 := (iff #177 #759)
-#536 := (iff #107 #535)
-#533 := (iff #106 #532)
-#534 := [rewrite]: #533
-#537 := [monotonicity #534]: #536
-#761 := [monotonicity #537]: #760
-#766 := [trans #761 #764]: #765
-#769 := [quant-intro #766]: #768
-#994 := [monotonicity #769 #991]: #993
-#1000 := [trans #994 #998]: #999
-#1003 := [monotonicity #1000]: #1002
-#1009 := [trans #1003 #1007]: #1008
-#757 := (iff #173 #756)
-#754 := (iff #172 #753)
-#755 := [rewrite]: #754
-#758 := [monotonicity #755]: #757
-#1012 := [monotonicity #758 #1009]: #1011
-#1017 := [trans #1012 #1015]: #1016
-#615 := (iff #130 #614)
-#612 := (iff #129 #609)
-#606 := (and #535 #120)
-#610 := (iff #606 #609)
-#611 := [rewrite]: #610
-#607 := (iff #129 #606)
-#608 := [monotonicity #537]: #607
-#613 := [trans #608 #611]: #612
-#616 := [quant-intro #613]: #615
-#1020 := [monotonicity #616 #1017]: #1019
-#1025 := [trans #1020 #1023]: #1024
-#1028 := [monotonicity #1025]: #1027
-#1032 := [trans #1028 #1030]: #1031
-#751 := (iff #169 #741)
-#746 := (implies true #741)
-#749 := (iff #746 #741)
-#750 := [rewrite]: #749
-#747 := (iff #169 #746)
-#744 := (iff #168 #741)
-#738 := (implies #617 #733)
-#742 := (iff #738 #741)
-#743 := [rewrite]: #742
-#739 := (iff #168 #738)
-#736 := (iff #167 #733)
-#729 := (implies #620 #724)
-#734 := (iff #729 #733)
-#735 := [rewrite]: #734
-#730 := (iff #167 #729)
-#727 := (iff #166 #724)
-#720 := (implies #136 #715)
-#725 := (iff #720 #724)
+#758 := (iff #191 #757)
+#755 := (iff #190 #752)
+#749 := (implies #187 #746)
+#753 := (iff #749 #752)
+#754 := [rewrite]: #753
+#750 := (iff #190 #749)
+#747 := (iff #189 #746)
+#748 := [rewrite]: #747
+#751 := [monotonicity #748]: #750
+#756 := [trans #751 #754]: #755
+#759 := [quant-intro #756]: #758
+#952 := [monotonicity #759 #949]: #951
+#958 := [trans #952 #956]: #957
+#961 := [monotonicity #958]: #960
+#967 := [trans #961 #965]: #966
+#744 := (iff #178 #743)
+#741 := (iff #177 #738)
+#735 := (implies #511 #176)
+#739 := (iff #735 #738)
+#740 := [rewrite]: #739
+#736 := (iff #177 #735)
+#512 := (iff #107 #511)
+#509 := (iff #106 #508)
+#510 := [rewrite]: #509
+#513 := [monotonicity #510]: #512
+#737 := [monotonicity #513]: #736
+#742 := [trans #737 #740]: #741
+#745 := [quant-intro #742]: #744
+#970 := [monotonicity #745 #967]: #969
+#976 := [trans #970 #974]: #975
+#979 := [monotonicity #976]: #978
+#985 := [trans #979 #983]: #984
+#733 := (iff #173 #732)
+#730 := (iff #172 #729)
+#731 := [rewrite]: #730
+#734 := [monotonicity #731]: #733
+#988 := [monotonicity #734 #985]: #987
+#993 := [trans #988 #991]: #992
+#591 := (iff #130 #590)
+#588 := (iff #129 #585)
+#582 := (and #511 #120)
+#586 := (iff #582 #585)
+#587 := [rewrite]: #586
+#583 := (iff #129 #582)
+#584 := [monotonicity #513]: #583
+#589 := [trans #584 #587]: #588
+#592 := [quant-intro #589]: #591
+#996 := [monotonicity #592 #993]: #995
+#1001 := [trans #996 #999]: #1000
+#1004 := [monotonicity #1001]: #1003
+#1008 := [trans #1004 #1006]: #1007
+#727 := (iff #169 #717)
+#722 := (implies true #717)
+#725 := (iff #722 #717)
 #726 := [rewrite]: #725
-#721 := (iff #166 #720)
-#718 := (iff #165 #715)
-#711 := (implies #623 #706)
-#716 := (iff #711 #715)
-#717 := [rewrite]: #716
-#712 := (iff #165 #711)
-#709 := (iff #164 #706)
-#702 := (implies #141 #699)
-#707 := (iff #702 #706)
-#708 := [rewrite]: #707
-#703 := (iff #164 #702)
-#700 := (iff #163 #699)
-#697 := (iff #162 #694)
-#690 := (implies #647 #687)
-#695 := (iff #690 #694)
-#696 := [rewrite]: #695
-#691 := (iff #162 #690)
-#688 := (iff #161 #687)
-#685 := (iff #160 #682)
-#678 := (implies #665 #668)
+#723 := (iff #169 #722)
+#720 := (iff #168 #717)
+#714 := (implies #593 #709)
+#718 := (iff #714 #717)
+#719 := [rewrite]: #718
+#715 := (iff #168 #714)
+#712 := (iff #167 #709)
+#705 := (implies #596 #700)
+#710 := (iff #705 #709)
+#711 := [rewrite]: #710
+#706 := (iff #167 #705)
+#703 := (iff #166 #700)
+#696 := (implies #136 #691)
+#701 := (iff #696 #700)
+#702 := [rewrite]: #701
+#697 := (iff #166 #696)
+#694 := (iff #165 #691)
+#687 := (implies #599 #682)
+#692 := (iff #687 #691)
+#693 := [rewrite]: #692
+#688 := (iff #165 #687)
+#685 := (iff #164 #682)
+#678 := (implies #141 #675)
 #683 := (iff #678 #682)
 #684 := [rewrite]: #683
-#679 := (iff #160 #678)
-#676 := (iff #159 #668)
-#671 := (and #668 true)
-#674 := (iff #671 #668)
-#675 := [rewrite]: #674
-#672 := (iff #159 #671)
-#669 := (iff #158 #668)
-#670 := [rewrite]: #669
-#673 := [monotonicity #670]: #672
-#677 := [trans #673 #675]: #676
-#666 := (iff #156 #665)
-#663 := (iff #155 #660)
-#656 := (implies #650 #653)
-#661 := (iff #656 #660)
-#662 := [rewrite]: #661
-#657 := (iff #155 #656)
-#654 := (iff #154 #653)
-#627 := (= #147 #626)
+#679 := (iff #164 #678)
+#676 := (iff #163 #675)
+#673 := (iff #162 #670)
+#666 := (implies #623 #663)
+#671 := (iff #666 #670)
+#672 := [rewrite]: #671
+#667 := (iff #162 #666)
+#664 := (iff #161 #663)
+#661 := (iff #160 #658)
+#654 := (implies #641 #644)
+#659 := (iff #654 #658)
+#660 := [rewrite]: #659
+#655 := (iff #160 #654)
+#652 := (iff #159 #644)
+#647 := (and #644 true)
+#650 := (iff #647 #644)
+#651 := [rewrite]: #650
+#648 := (iff #159 #647)
+#645 := (iff #158 #644)
+#646 := [rewrite]: #645
+#649 := [monotonicity #646]: #648
+#653 := [trans #649 #651]: #652
+#642 := (iff #156 #641)
+#639 := (iff #155 #636)
+#632 := (implies #626 #629)
+#637 := (iff #632 #636)
+#638 := [rewrite]: #637
+#633 := (iff #155 #632)
+#630 := (iff #154 #629)
+#603 := (= #147 #602)
+#604 := [rewrite]: #603
+#631 := [monotonicity #604]: #630
+#627 := (iff #153 #626)
 #628 := [rewrite]: #627
-#655 := [monotonicity #628]: #654
-#651 := (iff #153 #650)
-#652 := [rewrite]: #651
-#658 := [monotonicity #652 #655]: #657
-#664 := [trans #658 #662]: #663
-#667 := [quant-intro #664]: #666
-#680 := [monotonicity #667 #677]: #679
+#634 := [monotonicity #628 #631]: #633
+#640 := [trans #634 #638]: #639
+#643 := [quant-intro #640]: #642
+#656 := [monotonicity #643 #653]: #655
+#662 := [trans #656 #660]: #661
+#665 := [monotonicity #643 #662]: #664
+#624 := (iff #152 #623)
+#621 := (iff #151 #618)
+#614 := (implies #144 #611)
+#619 := (iff #614 #618)
+#620 := [rewrite]: #619
+#615 := (iff #151 #614)
+#612 := (iff #150 #611)
+#609 := (iff #149 #608)
+#606 := (iff #148 #605)
+#607 := [monotonicity #604]: #606
+#610 := [monotonicity #607]: #609
+#613 := [quant-intro #610]: #612
+#616 := [monotonicity #613]: #615
+#622 := [trans #616 #620]: #621
+#625 := [quant-intro #622]: #624
+#668 := [monotonicity #625 #665]: #667
+#674 := [trans #668 #672]: #673
+#677 := [monotonicity #625 #674]: #676
+#680 := [monotonicity #677]: #679
 #686 := [trans #680 #684]: #685
-#689 := [monotonicity #667 #686]: #688
-#648 := (iff #152 #647)
-#645 := (iff #151 #642)
-#638 := (implies #144 #635)
-#643 := (iff #638 #642)
-#644 := [rewrite]: #643
-#639 := (iff #151 #638)
-#636 := (iff #150 #635)
-#633 := (iff #149 #632)
-#630 := (iff #148 #629)
-#631 := [monotonicity #628]: #630
-#634 := [monotonicity #631]: #633
-#637 := [quant-intro #634]: #636
-#640 := [monotonicity #637]: #639
-#646 := [trans #640 #644]: #645
-#649 := [quant-intro #646]: #648
-#692 := [monotonicity #649 #689]: #691
-#698 := [trans #692 #696]: #697
-#701 := [monotonicity #649 #698]: #700
-#704 := [monotonicity #701]: #703
-#710 := [trans #704 #708]: #709
-#624 := (iff #138 #623)
-#625 := [rewrite]: #624
-#713 := [monotonicity #625 #710]: #712
-#719 := [trans #713 #717]: #718
-#722 := [monotonicity #719]: #721
-#728 := [trans #722 #726]: #727
-#621 := (iff #133 #620)
-#622 := [rewrite]: #621
-#731 := [monotonicity #622 #728]: #730
-#737 := [trans #731 #735]: #736
-#618 := (iff #131 #617)
-#619 := [monotonicity #616]: #618
-#740 := [monotonicity #619 #737]: #739
-#745 := [trans #740 #743]: #744
-#748 := [monotonicity #745]: #747
-#752 := [trans #748 #750]: #751
-#1035 := [monotonicity #752 #1032]: #1034
-#604 := (iff #128 #603)
-#601 := (iff #127 #598)
-#594 := (implies #121 #591)
-#599 := (iff #594 #598)
-#600 := [rewrite]: #599
-#595 := (iff #127 #594)
-#592 := (iff #126 #591)
-#589 := (iff #125 #588)
-#586 := (iff #124 #585)
-#583 := (iff #123 #582)
-#565 := (= #116 #564)
-#566 := [rewrite]: #565
-#584 := [monotonicity #566]: #583
-#587 := [monotonicity #534 #584]: #586
-#590 := [monotonicity #587]: #589
-#593 := [quant-intro #590]: #592
-#596 := [monotonicity #593]: #595
-#602 := [trans #596 #600]: #601
-#605 := [quant-intro #602]: #604
-#1038 := [monotonicity #605 #1035]: #1037
-#1044 := [trans #1038 #1042]: #1043
-#580 := (iff #119 #579)
-#577 := (iff #118 #574)
-#570 := (implies #559 #567)
+#600 := (iff #138 #599)
+#601 := [rewrite]: #600
+#689 := [monotonicity #601 #686]: #688
+#695 := [trans #689 #693]: #694
+#698 := [monotonicity #695]: #697
+#704 := [trans #698 #702]: #703
+#597 := (iff #133 #596)
+#598 := [rewrite]: #597
+#707 := [monotonicity #598 #704]: #706
+#713 := [trans #707 #711]: #712
+#594 := (iff #131 #593)
+#595 := [monotonicity #592]: #594
+#716 := [monotonicity #595 #713]: #715
+#721 := [trans #716 #719]: #720
+#724 := [monotonicity #721]: #723
+#728 := [trans #724 #726]: #727
+#1011 := [monotonicity #728 #1008]: #1010
+#580 := (iff #128 #579)
+#577 := (iff #127 #574)
+#570 := (implies #121 #567)
 #575 := (iff #570 #574)
 #576 := [rewrite]: #575
-#571 := (iff #118 #570)
-#568 := (iff #117 #567)
-#569 := [monotonicity #566]: #568
-#562 := (iff #115 #559)
-#556 := (and #532 #83)
-#560 := (iff #556 #559)
-#561 := [rewrite]: #560
-#557 := (iff #115 #556)
-#558 := [monotonicity #534]: #557
-#563 := [trans #558 #561]: #562
-#572 := [monotonicity #563 #569]: #571
+#571 := (iff #127 #570)
+#568 := (iff #126 #567)
+#565 := (iff #125 #564)
+#562 := (iff #124 #561)
+#559 := (iff #123 #558)
+#541 := (= #116 #540)
+#542 := [rewrite]: #541
+#560 := [monotonicity #542]: #559
+#563 := [monotonicity #510 #560]: #562
+#566 := [monotonicity #563]: #565
+#569 := [quant-intro #566]: #568
+#572 := [monotonicity #569]: #571
 #578 := [trans #572 #576]: #577
 #581 := [quant-intro #578]: #580
-#1047 := [monotonicity #581 #1044]: #1046
-#1053 := [trans #1047 #1051]: #1052
-#554 := (iff #114 #553)
-#551 := (iff #113 #548)
-#544 := (implies #541 #112)
-#549 := (iff #544 #548)
-#550 := [rewrite]: #549
-#545 := (iff #113 #544)
-#542 := (iff #110 #541)
-#539 := (iff #109 #538)
-#540 := [rewrite]: #539
-#543 := [monotonicity #537 #540]: #542
-#546 := [monotonicity #543]: #545
-#552 := [trans #546 #550]: #551
-#555 := [quant-intro #552]: #554
-#1056 := [monotonicity #555 #1053]: #1055
-#1062 := [trans #1056 #1060]: #1061
-#1065 := [monotonicity #1062]: #1064
-#1071 := [trans #1065 #1069]: #1070
-#530 := (iff #100 #529)
-#531 := [rewrite]: #530
-#1074 := [monotonicity #531 #1071]: #1073
-#1080 := [trans #1074 #1078]: #1079
-#1083 := [monotonicity #1080]: #1082
-#1087 := [trans #1083 #1085]: #1086
-#527 := (iff #97 #526)
-#524 := (iff #96 #521)
-#517 := (implies #90 #514)
-#522 := (iff #517 #521)
-#523 := [rewrite]: #522
-#518 := (iff #96 #517)
-#515 := (iff #95 #514)
-#512 := (iff #94 #511)
-#509 := (iff #93 #506)
-#503 := (and #453 #92)
-#507 := (iff #503 #506)
-#508 := [rewrite]: #507
-#504 := (iff #93 #503)
-#454 := (iff #67 #453)
-#455 := [rewrite]: #454
-#505 := [monotonicity #455]: #504
-#510 := [trans #505 #508]: #509
-#513 := [monotonicity #510]: #512
-#516 := [quant-intro #513]: #515
-#519 := [monotonicity #516]: #518
-#525 := [trans #519 #523]: #524
-#528 := [quant-intro #525]: #527
-#1090 := [monotonicity #528 #1087]: #1089
+#1014 := [monotonicity #581 #1011]: #1013
+#1020 := [trans #1014 #1018]: #1019
+#556 := (iff #119 #555)
+#553 := (iff #118 #550)
+#546 := (implies #535 #543)
+#551 := (iff #546 #550)
+#552 := [rewrite]: #551
+#547 := (iff #118 #546)
+#544 := (iff #117 #543)
+#545 := [monotonicity #542]: #544
+#538 := (iff #115 #535)
+#532 := (and #508 #83)
+#536 := (iff #532 #535)
+#537 := [rewrite]: #536
+#533 := (iff #115 #532)
+#534 := [monotonicity #510]: #533
+#539 := [trans #534 #537]: #538
+#548 := [monotonicity #539 #545]: #547
+#554 := [trans #548 #552]: #553
+#557 := [quant-intro #554]: #556
+#1023 := [monotonicity #557 #1020]: #1022
+#1029 := [trans #1023 #1027]: #1028
+#530 := (iff #114 #529)
+#527 := (iff #113 #524)
+#520 := (implies #517 #112)
+#525 := (iff #520 #524)
+#526 := [rewrite]: #525
+#521 := (iff #113 #520)
+#518 := (iff #110 #517)
+#515 := (iff #109 #514)
+#516 := [rewrite]: #515
+#519 := [monotonicity #513 #516]: #518
+#522 := [monotonicity #519]: #521
+#528 := [trans #522 #526]: #527
+#531 := [quant-intro #528]: #530
+#1032 := [monotonicity #531 #1029]: #1031
+#1038 := [trans #1032 #1036]: #1037
+#1041 := [monotonicity #1038]: #1040
+#1047 := [trans #1041 #1045]: #1046
+#506 := (iff #100 #505)
+#507 := [rewrite]: #506
+#1050 := [monotonicity #507 #1047]: #1049
+#1056 := [trans #1050 #1054]: #1055
+#1059 := [monotonicity #1056]: #1058
+#1063 := [trans #1059 #1061]: #1062
+#503 := (iff #97 #502)
+#500 := (iff #96 #497)
+#493 := (implies #90 #490)
+#498 := (iff #493 #497)
+#499 := [rewrite]: #498
+#494 := (iff #96 #493)
+#491 := (iff #95 #490)
+#488 := (iff #94 #487)
+#485 := (iff #93 #482)
+#479 := (and #429 #92)
+#483 := (iff #479 #482)
+#484 := [rewrite]: #483
+#480 := (iff #93 #479)
+#430 := (iff #67 #429)
+#431 := [rewrite]: #430
+#481 := [monotonicity #431]: #480
+#486 := [trans #481 #484]: #485
+#489 := [monotonicity #486]: #488
+#492 := [quant-intro #489]: #491
+#495 := [monotonicity #492]: #494
+#501 := [trans #495 #499]: #500
+#504 := [quant-intro #501]: #503
+#1066 := [monotonicity #504 #1063]: #1065
+#1072 := [trans #1066 #1070]: #1071
+#1075 := [monotonicity #504 #1072]: #1074
+#477 := (iff #88 #476)
+#474 := (iff #87 #471)
+#467 := (implies #462 #86)
+#472 := (iff #467 #471)
+#473 := [rewrite]: #472
+#468 := (iff #87 #467)
+#465 := (iff #84 #462)
+#459 := (and #429 #83)
+#463 := (iff #459 #462)
+#464 := [rewrite]: #463
+#460 := (iff #84 #459)
+#461 := [monotonicity #431]: #460
+#466 := [trans #461 #464]: #465
+#469 := [monotonicity #466]: #468
+#475 := [trans #469 #473]: #474
+#478 := [quant-intro #475]: #477
+#1078 := [monotonicity #478 #1075]: #1077
+#1084 := [trans #1078 #1082]: #1083
+#1087 := [monotonicity #478 #1084]: #1086
+#457 := (iff #80 #456)
+#454 := (iff #79 #451)
+#447 := (implies #444 #78)
+#452 := (iff #447 #451)
+#453 := [rewrite]: #452
+#448 := (iff #79 #447)
+#445 := (iff #76 #444)
+#442 := (iff #75 #441)
+#443 := [rewrite]: #442
+#433 := (iff #68 #432)
+#434 := [monotonicity #431]: #433
+#446 := [monotonicity #434 #443]: #445
+#449 := [monotonicity #446]: #448
+#455 := [trans #449 #453]: #454
+#458 := [quant-intro #455]: #457
+#1090 := [monotonicity #458 #1087]: #1089
 #1096 := [trans #1090 #1094]: #1095
-#1099 := [monotonicity #528 #1096]: #1098
-#501 := (iff #88 #500)
-#498 := (iff #87 #495)
-#491 := (implies #486 #86)
-#496 := (iff #491 #495)
-#497 := [rewrite]: #496
-#492 := (iff #87 #491)
-#489 := (iff #84 #486)
-#483 := (and #453 #83)
-#487 := (iff #483 #486)
-#488 := [rewrite]: #487
-#484 := (iff #84 #483)
-#485 := [monotonicity #455]: #484
-#490 := [trans #485 #488]: #489
-#493 := [monotonicity #490]: #492
-#499 := [trans #493 #497]: #498
-#502 := [quant-intro #499]: #501
-#1102 := [monotonicity #502 #1099]: #1101
+#1099 := [monotonicity #458 #1096]: #1098
+#1102 := [monotonicity #1099]: #1101
 #1108 := [trans #1102 #1106]: #1107
-#1111 := [monotonicity #502 #1108]: #1110
-#481 := (iff #80 #480)
-#478 := (iff #79 #475)
-#471 := (implies #468 #78)
-#476 := (iff #471 #475)
-#477 := [rewrite]: #476
-#472 := (iff #79 #471)
-#469 := (iff #76 #468)
-#466 := (iff #75 #465)
-#467 := [rewrite]: #466
-#457 := (iff #68 #456)
-#458 := [monotonicity #455]: #457
-#470 := [monotonicity #458 #467]: #469
-#473 := [monotonicity #470]: #472
-#479 := [trans #473 #477]: #478
-#482 := [quant-intro #479]: #481
-#1114 := [monotonicity #482 #1111]: #1113
+#1111 := [monotonicity #1108]: #1110
+#439 := (iff #71 #438)
+#440 := [rewrite]: #439
+#1114 := [monotonicity #440 #1111]: #1113
 #1120 := [trans #1114 #1118]: #1119
-#1123 := [monotonicity #482 #1120]: #1122
-#1126 := [monotonicity #1123]: #1125
+#1123 := [monotonicity #440 #1120]: #1122
+#436 := (iff #69 #435)
+#437 := [quant-intro #434]: #436
+#1126 := [monotonicity #437 #1123]: #1125
 #1132 := [trans #1126 #1130]: #1131
-#1135 := [monotonicity #1132]: #1134
-#463 := (iff #71 #462)
-#464 := [rewrite]: #463
-#1138 := [monotonicity #464 #1135]: #1137
-#1144 := [trans #1138 #1142]: #1143
-#1147 := [monotonicity #464 #1144]: #1146
-#460 := (iff #69 #459)
-#461 := [quant-intro #458]: #460
-#1150 := [monotonicity #461 #1147]: #1149
-#1156 := [trans #1150 #1154]: #1155
-#451 := (iff #65 #450)
-#448 := (iff #64 #445)
-#442 := (implies #62 #439)
-#446 := (iff #442 #445)
-#447 := [rewrite]: #446
-#443 := (iff #64 #442)
-#440 := (iff #63 #439)
-#441 := [rewrite]: #440
-#444 := [monotonicity #441]: #443
-#449 := [trans #444 #447]: #448
-#452 := [quant-intro #449]: #451
-#1159 := [monotonicity #452 #1156]: #1158
-#1165 := [trans #1159 #1163]: #1164
-#437 := (iff #61 #436)
-#434 := (iff #60 #431)
-#428 := (implies #57 #425)
-#432 := (iff #428 #431)
-#433 := [rewrite]: #432
-#429 := (iff #60 #428)
-#426 := (iff #59 #425)
-#427 := [rewrite]: #426
-#430 := [monotonicity #427]: #429
-#435 := [trans #430 #433]: #434
-#438 := [quant-intro #435]: #437
-#1168 := [monotonicity #438 #1165]: #1167
-#1174 := [trans #1168 #1172]: #1173
-#1177 := [monotonicity #1174]: #1176
-#1181 := [trans #1177 #1179]: #1180
-#1184 := [monotonicity #1181]: #1183
-#1823 := [trans #1184 #1821]: #1822
-#424 := [asserted]: #270
-#1824 := [mp #424 #1823]: #1819
-#1826 := [not-or-elim #1824]: #459
-#1881 := [mp~ #1826 #1850]: #459
-#4222 := [mp #1881 #4221]: #4217
-#5520 := (not #4217)
-#5521 := (or #5520 #3069)
-#5516 := [quant-inst #1927]: #5521
-#5328 := [unit-resolution #5516 #4222 #5213]: false
-#5336 := [lemma #5328]: #3069
-#3836 := (or #3084 #1936)
-#3840 := [def-axiom]: #3836
-#6486 := [unit-resolution #3840 #5336]: #3084
-#3089 := (not #3084)
-#4556 := (or #3089 #4553)
+#427 := (iff #65 #426)
+#424 := (iff #64 #421)
+#418 := (implies #62 #415)
+#422 := (iff #418 #421)
+#423 := [rewrite]: #422
+#419 := (iff #64 #418)
+#416 := (iff #63 #415)
+#417 := [rewrite]: #416
+#420 := [monotonicity #417]: #419
+#425 := [trans #420 #423]: #424
+#428 := [quant-intro #425]: #427
+#1135 := [monotonicity #428 #1132]: #1134
+#1141 := [trans #1135 #1139]: #1140
+#413 := (iff #61 #412)
+#410 := (iff #60 #407)
+#404 := (implies #57 #400)
+#408 := (iff #404 #407)
+#409 := [rewrite]: #408
+#405 := (iff #60 #404)
+#402 := (iff #59 #400)
+#403 := [rewrite]: #402
+#406 := [monotonicity #403]: #405
+#411 := [trans #406 #409]: #410
+#414 := [quant-intro #411]: #413
+#1144 := [monotonicity #414 #1141]: #1143
+#1150 := [trans #1144 #1148]: #1149
+#1153 := [monotonicity #1150]: #1152
+#1157 := [trans #1153 #1155]: #1156
+#1160 := [monotonicity #1157]: #1159
+#1799 := [trans #1160 #1797]: #1798
+#399 := [asserted]: #270
+#1800 := [mp #399 #1799]: #1795
+#1801 := [not-or-elim #1800]: #426
+#1854 := [mp~ #1801 #1824]: #426
+#4191 := [mp #1854 #4190]: #4186
+#4925 := (not #4186)
+#5686 := (or #4925 #2533 #5626)
+#1950 := (= ?v0!5 f10)
+#5627 := (or #1950 #5626)
+#5687 := (or #4925 #5627)
+#5694 := (iff #5687 #5686)
+#5630 := (or #2533 #5626)
+#5689 := (or #4925 #5630)
+#5692 := (iff #5689 #5686)
+#5693 := [rewrite]: #5692
+#5690 := (iff #5687 #5689)
+#5631 := (iff #5627 #5630)
+#2534 := (iff #1950 #2533)
+#2535 := [rewrite]: #2534
+#5632 := [monotonicity #2535]: #5631
+#5691 := [monotonicity #5632]: #5690
+#5695 := [trans #5691 #5693]: #5694
+#5688 := [quant-inst #1934]: #5687
+#5696 := [mp #5688 #5695]: #5686
+#5740 := [unit-resolution #5696 #4191 #5739 #5738]: false
+#5741 := [lemma #5740]: #4234
+#4520 := (or #4237 #4517)
+#4523 := (not #4520)
+#3082 := (or #432 #1197 #1202)
+#4217 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4216) #3082)
+#4222 := (not #4217)
+#4526 := (or #4222 #4523)
+#4529 := (not #4526)
+decl ?v1!3 :: S2
+#1903 := ?v1!3
+#1918 := (f11 ?v1!3)
+decl ?v0!4 :: S2
+#1904 := ?v0!4
+#1915 := (f11 ?v0!4)
+#1916 := (* -1::Int #1915)
+#2514 := (+ #1916 #1918)
+#1905 := (f5 ?v1!3 ?v0!4)
+#1906 := (f4 #1905)
+#2515 := (+ #1906 #2514)
+#2518 := (>= #2515 0::Int)
+#1911 := (f12 ?v1!3)
+#1912 := (= f1 #1911)
+#3045 := (not #1912)
+#1907 := (* -1::Int #1906)
+#1908 := (+ f3 #1907)
+#1909 := (<= #1908 0::Int)
+#3060 := (or #1909 #3045 #2518)
+#3065 := (not #3060)
+#4532 := (or #3065 #4529)
+#4535 := (not #4532)
+#4207 := (pattern #66 #74)
+#2486 := (not #441)
+#3037 := (or #429 #2486 #1177)
+#4208 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4207) #3037)
+#4213 := (not #4208)
+#4538 := (or #4213 #4535)
+#4541 := (not #4538)
+decl ?v1!1 :: S2
+#1876 := ?v1!1
+#1880 := (f11 ?v1!1)
+#2501 := (* -1::Int #1880)
+decl ?v0!2 :: S2
+#1877 := ?v0!2
+#1878 := (f11 ?v0!2)
+#2502 := (+ #1878 #2501)
+#2503 := (<= #2502 0::Int)
+#1885 := (f12 ?v1!1)
+#1886 := (= f1 #1885)
+#1883 := (f12 ?v0!2)
+#1884 := (= f1 #1883)
+#2131 := (not #1884)
+#2304 := (or #2131 #1886 #2503)
+#2021 := (not #2304)
+#4544 := (or #2021 #4541)
+#4547 := (not #4544)
+#4199 := (forall (vars (?v0 S2)) (:pat #4185) #1168)
+#4204 := (not #4199)
+#4550 := (or #4204 #4547)
+#4553 := (not #4550)
+decl ?v0!0 :: S2
+#1861 := ?v0!0
+#1862 := (f11 ?v0!0)
+#1863 := (>= #1862 0::Int)
+#293 := (<= f3 0::Int)
+#294 := (not #293)
+#10 := (< 0::Int f3)
+#295 := (iff #10 #294)
+#296 := [rewrite]: #295
+#290 := [asserted]: #10
+#297 := [mp #290 #296]: #294
+#5160 := (* -1::Int #1862)
+#5161 := (+ f3 #5160)
+#5182 := (<= #5161 0::Int)
+#3882 := (= f3 #1862)
+#4613 := (= f10 ?v0!0)
+#5181 := (not #4613)
+#5246 := (= #1862 0::Int)
+#4859 := (not #5246)
+#1864 := (not #1863)
+#4858 := [hypothesis]: #1864
+#5157 := (or #4859 #1863)
+#5253 := [th-lemma arith triangle-eq]: #5157
+#5254 := [unit-resolution #5253 #4858]: #4859
+#4572 := (forall (vars (?v0 S2)) (:pat #4185) #1772)
+#4575 := (iff #1775 #4572)
+#4573 := (iff #1772 #1772)
+#4574 := [refl]: #4573
+#4576 := [quant-intro #4574]: #4575
+#2226 := (~ #1775 #1775)
+#1993 := (~ #1772 #1772)
+#1994 := [refl]: #1993
+#2227 := [nnf-pos #1994]: #2226
+#1805 := [not-or-elim #1800]: #1775
+#2130 := [mp~ #1805 #2227]: #1775
+#4577 := [mp #2130 #4576]: #4572
+#5440 := (not #4572)
+#5441 := (or #5440 #5181 #5246)
+#3894 := (= ?v0!0 f10)
+#5247 := (not #3894)
+#5248 := (or #5247 #5246)
+#5442 := (or #5440 #5248)
+#5447 := (iff #5442 #5441)
+#5245 := (or #5181 #5246)
+#5444 := (or #5440 #5245)
+#5445 := (iff #5444 #5441)
+#5446 := [rewrite]: #5445
+#5275 := (iff #5442 #5444)
+#5251 := (iff #5248 #5245)
+#5249 := (iff #5247 #5181)
+#4628 := (iff #3894 #4613)
+#4629 := [rewrite]: #4628
+#5250 := [monotonicity #4629]: #5249
+#5252 := [monotonicity #5250]: #5251
+#5439 := [monotonicity #5252]: #5275
+#5448 := [trans #5439 #5446]: #5447
+#5443 := [quant-inst #1861]: #5442
+#3896 := [mp #5443 #5448]: #5441
+#5255 := [unit-resolution #3896 #4577 #5254]: #5181
+#4685 := (or #3882 #4613)
+#4927 := (or #4925 #3882 #4613)
+#4611 := (or #3894 #3882)
+#4928 := (or #4925 #4611)
+#5153 := (iff #4928 #4927)
+#3819 := (or #4925 #4685)
+#5042 := (iff #3819 #4927)
+#5136 := [rewrite]: #5042
+#3829 := (iff #4928 #3819)
+#4688 := (iff #4611 #4685)
+#4610 := (or #4613 #3882)
+#4686 := (iff #4610 #4685)
+#4687 := [rewrite]: #4686
+#4684 := (iff #4611 #4610)
+#4612 := [monotonicity #4629]: #4684
+#4856 := [trans #4612 #4687]: #4688
+#4926 := [monotonicity #4856]: #3829
+#5155 := [trans #4926 #5136]: #5153
+#3914 := [quant-inst #1861]: #4928
+#5156 := [mp #3914 #5155]: #4927
+#5449 := [unit-resolution #5156 #4191]: #4685
+#5509 := [unit-resolution #5449 #5255]: #3882
+#5510 := (not #3882)
+#5511 := (or #5510 #5182)
+#5491 := [th-lemma arith triangle-eq]: #5511
+#5492 := [unit-resolution #5491 #5509]: #5182
+#4857 := (<= #1862 0::Int)
+#5493 := (or #4857 #1863)
+#5494 := [th-lemma arith farkas 1 1]: #5493
+#5495 := [unit-resolution #5494 #4858]: #4857
+#5490 := [th-lemma arith farkas 1 -1 1 #5495 #5492 #297]: false
+#5496 := [lemma #5490]: #1863
+#4556 := (or #1864 #4553)
 #4559 := (not #4556)
-#4231 := (pattern #66 #74)
-#2510 := (not #465)
-#3061 := (or #453 #2510 #1201)
-#4232 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4231) #3061)
-#4237 := (not #4232)
-#4562 := (or #4237 #4559)
+#4562 := (or #1163 #4559)
 #4565 := (not #4562)
-decl ?v1!1 :: S3
-#1900 := ?v1!1
-#1904 := (f11 ?v1!1)
-#2525 := (* -1::Int #1904)
-decl ?v0!2 :: S3
-#1901 := ?v0!2
-#1902 := (f11 ?v0!2)
-#2526 := (+ #1902 #2525)
-#2527 := (<= #2526 0::Int)
-#1909 := (f12 ?v1!1)
-#1910 := (= f1 #1909)
-#1907 := (f12 ?v0!2)
-#1908 := (= f1 #1907)
-#2210 := (not #1908)
-#2119 := (or #2210 #1910 #2527)
-#2018 := (not #2119)
-#4568 := (or #2018 #4565)
-#4571 := (not #4568)
-#4223 := (forall (vars (?v0 S3)) (:pat #4209) #1192)
-#4228 := (not #4223)
-#4574 := (or #4228 #4571)
-#4577 := (not #4574)
-decl ?v0!0 :: S3
-#1885 := ?v0!0
-#1886 := (f11 ?v0!0)
-#1887 := (>= #1886 0::Int)
-#1888 := (not #1887)
-#4580 := (or #1888 #4577)
-#4583 := (not #4580)
-#4586 := (or #1187 #4583)
-#4589 := (not #4586)
-#4596 := (forall (vars (?v0 S3)) (:pat #4209) #1796)
-#4599 := (iff #1799 #4596)
-#4597 := (iff #1796 #1796)
-#4598 := [refl]: #4597
-#4600 := [quant-intro #4598]: #4599
-#2044 := (~ #1799 #1799)
-#1891 := (~ #1796 #1796)
-#1892 := [refl]: #1891
-#2045 := [nnf-pos #1892]: #2044
-#1829 := [not-or-elim #1824]: #1799
-#2209 := [mp~ #1829 #2045]: #1799
-#4601 := [mp #2209 #4600]: #4596
-#5315 := [hypothesis]: #1187
-#4775 := (not #4596)
-#5251 := (or #4775 #71)
-#5135 := (= f10 f10)
-#5136 := (not #5135)
-#5138 := (or #5136 #71)
-#5219 := (or #4775 #5138)
-#5253 := (iff #5219 #5251)
-#5255 := (iff #5251 #5251)
-#5250 := [rewrite]: #5255
-#5224 := (iff #5138 #71)
-#5192 := (or false #71)
-#5220 := (iff #5192 #71)
-#5223 := [rewrite]: #5220
-#5193 := (iff #5138 #5192)
-#5190 := (iff #5136 false)
-#5187 := (not true)
-#5184 := (iff #5187 false)
-#5185 := [rewrite]: #5184
-#5188 := (iff #5136 #5187)
-#5139 := (iff #5135 true)
-#5186 := [rewrite]: #5139
-#5189 := [monotonicity #5186]: #5188
-#5191 := [trans #5189 #5185]: #5190
-#5194 := [monotonicity #5191]: #5193
-#5225 := [trans #5194 #5223]: #5224
-#5254 := [monotonicity #5225]: #5253
-#5260 := [trans #5254 #5250]: #5253
-#5252 := [quant-inst #56]: #5219
-#5286 := [mp #5252 #5260]: #5251
-#5316 := [unit-resolution #5286 #5315 #4601]: false
-#5311 := [lemma #5316]: #71
-#4592 := (or #1187 #4589)
-#3519 := (forall (vars (?v1 S3)) #3508)
-#3526 := (not #3519)
-#3504 := (forall (vars (?v0 S3) (?v1 S3)) #3499)
-#3525 := (not #3504)
-#3527 := (or #2350 #2917 #3525 #3526)
-#3528 := (not #3527)
-#3533 := (or #3482 #3528)
-#3540 := (not #3533)
-#3459 := (forall (vars (?v0 S3) (?v1 S3)) #3454)
-#3539 := (not #3459)
-#3541 := (or #3539 #3540)
-#3542 := (not #3541)
-#3547 := (or #3436 #3542)
-#3553 := (not #3547)
-#3554 := (or #1490 #3553)
-#3555 := (not #3554)
-#3560 := (or #2267 #3555)
-#3566 := (not #3560)
-#3567 := (or #1481 #3566)
-#3568 := (not #3567)
-#3573 := (or #1481 #3568)
-#3579 := (not #3573)
-#3580 := (or #944 #3579)
-#3581 := (not #3580)
-#3586 := (or #2860 #3581)
-#3592 := (not #3586)
-#3593 := (or #1476 #3592)
-#3594 := (not #3593)
-#3599 := (or #2846 #3594)
-#3607 := (not #3599)
-#3413 := (forall (vars (?v0 S3)) #3408)
-#3606 := (not #3413)
-#3395 := (forall (vars (?v0 S3)) #3392)
-#3605 := (not #3395)
-#3608 := (or #986 #753 #1641 #1645 #2201 #2204 #3605 #3606 #3607)
-#3609 := (not #3608)
-#3325 := (forall (vars (?v0 S3) (?v1 S3)) #3320)
-#3331 := (not #3325)
-#3332 := (or #158 #3331)
-#3333 := (not #3332)
-#3360 := (or #3333 #3357)
-#3367 := (not #3360)
-#3303 := (forall (vars (?v0 S3)) #3298)
-#3366 := (not #3303)
-#3368 := (or #3366 #3367)
-#3369 := (not #3368)
-#3266 := (forall (vars (?v1 S3)) #3255)
-#3272 := (not #3266)
-#3273 := (or #2080 #2695 #3272)
-#3274 := (not #3273)
-#3374 := (or #3274 #3369)
-#3381 := (not #3374)
-#3251 := (forall (vars (?v0 S3)) #3240)
-#3380 := (not #3251)
-#3382 := (or #723 #705 #732 #714 #3380 #3381)
-#3383 := (not #3382)
-#3614 := (or #3383 #3609)
-#3624 := (not #3614)
-#3237 := (forall (vars (?v0 S3)) #3232)
-#3623 := (not #3237)
-#3209 := (forall (vars (?v0 S3)) #3204)
-#3622 := (not #3209)
-#3181 := (forall (vars (?v0 S3) (?v1 S3)) #3176)
-#3621 := (not #3181)
-#3158 := (forall (vars (?v0 S3) (?v1 S3)) #3153)
-#3620 := (not #3158)
-#3625 := (or #1738 #1733 #3620 #3621 #3622 #3623 #3624)
-#3626 := (not #3625)
-#3126 := (forall (vars (?v1 S3)) #3115)
-#3132 := (not #3126)
-#3133 := (or #1972 #2557 #3132)
-#3134 := (not #3133)
-#3631 := (or #3134 #3626)
-#3638 := (not #3631)
-#3111 := (forall (vars (?v0 S3) (?v1 S3)) #3106)
-#3637 := (not #3111)
-#3639 := (or #3637 #3638)
-#3640 := (not #3639)
-#3645 := (or #3089 #3640)
-#3652 := (not #3645)
-#3066 := (forall (vars (?v0 S3) (?v1 S3)) #3061)
-#3651 := (not #3066)
-#3653 := (or #3651 #3652)
-#3654 := (not #3653)
-#3659 := (or #2018 #3654)
-#3665 := (not #3659)
-#3666 := (or #1196 #3665)
-#3667 := (not #3666)
-#3672 := (or #1888 #3667)
-#3678 := (not #3672)
-#3679 := (or #1187 #3678)
-#3680 := (not #3679)
-#3685 := (or #1187 #3680)
-#4593 := (iff #3685 #4592)
-#4590 := (iff #3680 #4589)
-#4587 := (iff #3679 #4586)
-#4584 := (iff #3678 #4583)
-#4581 := (iff #3672 #4580)
-#4578 := (iff #3667 #4577)
-#4575 := (iff #3666 #4574)
-#4572 := (iff #3665 #4571)
-#4569 := (iff #3659 #4568)
-#4566 := (iff #3654 #4565)
-#4563 := (iff #3653 #4562)
-#4560 := (iff #3652 #4559)
-#4557 := (iff #3645 #4556)
-#4554 := (iff #3640 #4553)
-#4551 := (iff #3639 #4550)
-#4548 := (iff #3638 #4547)
-#4545 := (iff #3631 #4544)
-#4542 := (iff #3626 #4541)
-#4539 := (iff #3625 #4538)
-#4536 := (iff #3624 #4535)
-#4533 := (iff #3614 #4532)
-#4530 := (iff #3609 #4529)
-#4527 := (iff #3608 #4526)
-#4524 := (iff #3607 #4523)
-#4521 := (iff #3599 #4520)
-#4518 := (iff #3594 #4517)
-#4515 := (iff #3593 #4514)
-#4512 := (iff #3592 #4511)
-#4509 := (iff #3586 #4508)
-#4506 := (iff #3581 #4505)
-#4503 := (iff #3580 #4502)
-#4500 := (iff #3579 #4499)
-#4497 := (iff #3573 #4496)
-#4494 := (iff #3568 #4493)
-#4491 := (iff #3567 #4490)
-#4488 := (iff #3566 #4487)
-#4485 := (iff #3560 #4484)
-#4482 := (iff #3555 #4481)
-#4479 := (iff #3554 #4478)
-#4476 := (iff #3553 #4475)
-#4473 := (iff #3547 #4472)
-#4470 := (iff #3542 #4469)
-#4467 := (iff #3541 #4466)
-#4464 := (iff #3540 #4463)
-#4461 := (iff #3533 #4460)
-#4458 := (iff #3528 #4457)
-#4455 := (iff #3527 #4454)
-#4452 := (iff #3526 #4451)
-#4449 := (iff #3519 #4446)
-#4447 := (iff #3508 #3508)
-#4448 := [refl]: #4447
-#4450 := [quant-intro #4448]: #4449
+#5587 := [hypothesis]: #1163
+#5579 := (or #5440 #71)
+#3879 := (= f10 f10)
+#5183 := (not #3879)
+#5497 := (or #5183 #71)
+#5580 := (or #5440 #5497)
+#5582 := (iff #5580 #5579)
+#5578 := (iff #5579 #5579)
+#5584 := [rewrite]: #5578
+#5545 := (iff #5497 #71)
+#5541 := (or false #71)
+#5543 := (iff #5541 #71)
+#5544 := [rewrite]: #5543
+#5536 := (iff #5497 #5541)
+#5539 := (iff #5183 false)
+#5500 := (not true)
+#5537 := (iff #5500 false)
+#5538 := [rewrite]: #5537
+#5515 := (iff #5183 #5500)
+#5498 := (iff #3879 true)
+#5499 := [rewrite]: #5498
+#5516 := [monotonicity #5499]: #5515
+#5540 := [trans #5516 #5538]: #5539
+#5542 := [monotonicity #5540]: #5536
+#5546 := [trans #5542 #5544]: #5545
+#5583 := [monotonicity #5546]: #5582
+#5585 := [trans #5583 #5584]: #5582
+#5581 := [quant-inst #56]: #5580
+#5586 := [mp #5581 #5585]: #5579
+#5588 := [unit-resolution #5586 #5587 #4577]: false
+#5593 := [lemma #5588]: #71
+#4568 := (or #1163 #4565)
+#3495 := (forall (vars (?v1 S2)) #3484)
+#3502 := (not #3495)
+#3480 := (forall (vars (?v0 S2) (?v1 S2)) #3475)
+#3501 := (not #3480)
+#3503 := (or #2326 #2893 #3501 #3502)
+#3504 := (not #3503)
+#3509 := (or #3458 #3504)
+#3516 := (not #3509)
+#3435 := (forall (vars (?v0 S2) (?v1 S2)) #3430)
+#3515 := (not #3435)
+#3517 := (or #3515 #3516)
+#3518 := (not #3517)
+#3523 := (or #3412 #3518)
+#3529 := (not #3523)
+#3530 := (or #1466 #3529)
+#3531 := (not #3530)
+#3536 := (or #2243 #3531)
+#3542 := (not #3536)
+#3543 := (or #1457 #3542)
+#3544 := (not #3543)
+#3549 := (or #1457 #3544)
+#3555 := (not #3549)
+#3556 := (or #920 #3555)
+#3557 := (not #3556)
+#3562 := (or #2836 #3557)
+#3568 := (not #3562)
+#3569 := (or #1452 #3568)
+#3570 := (not #3569)
+#3575 := (or #2822 #3570)
+#3583 := (not #3575)
+#3389 := (forall (vars (?v0 S2)) #3384)
+#3582 := (not #3389)
+#3371 := (forall (vars (?v0 S2)) #3368)
+#3581 := (not #3371)
+#3584 := (or #962 #729 #1617 #1621 #2177 #2180 #3581 #3582 #3583)
+#3585 := (not #3584)
+#3301 := (forall (vars (?v0 S2) (?v1 S2)) #3296)
+#3307 := (not #3301)
+#3308 := (or #158 #3307)
+#3309 := (not #3308)
+#3336 := (or #3309 #3333)
+#3343 := (not #3336)
+#3279 := (forall (vars (?v0 S2)) #3274)
+#3342 := (not #3279)
+#3344 := (or #3342 #3343)
+#3345 := (not #3344)
+#3242 := (forall (vars (?v1 S2)) #3231)
+#3248 := (not #3242)
+#3249 := (or #2056 #2671 #3248)
+#3250 := (not #3249)
+#3350 := (or #3250 #3345)
+#3357 := (not #3350)
+#3227 := (forall (vars (?v0 S2)) #3216)
+#3356 := (not #3227)
+#3358 := (or #699 #681 #708 #690 #3356 #3357)
+#3359 := (not #3358)
+#3590 := (or #3359 #3585)
+#3600 := (not #3590)
+#3213 := (forall (vars (?v0 S2)) #3208)
+#3599 := (not #3213)
+#3185 := (forall (vars (?v0 S2)) #3180)
+#3598 := (not #3185)
+#3157 := (forall (vars (?v0 S2) (?v1 S2)) #3152)
+#3597 := (not #3157)
+#3134 := (forall (vars (?v0 S2) (?v1 S2)) #3129)
+#3596 := (not #3134)
+#3601 := (or #1714 #1709 #3596 #3597 #3598 #3599 #3600)
+#3602 := (not #3601)
+#3102 := (forall (vars (?v1 S2)) #3091)
+#3108 := (not #3102)
+#3109 := (or #1948 #2533 #3108)
+#3110 := (not #3109)
+#3607 := (or #3110 #3602)
+#3614 := (not #3607)
+#3087 := (forall (vars (?v0 S2) (?v1 S2)) #3082)
+#3613 := (not #3087)
+#3615 := (or #3613 #3614)
+#3616 := (not #3615)
+#3621 := (or #3065 #3616)
+#3628 := (not #3621)
+#3042 := (forall (vars (?v0 S2) (?v1 S2)) #3037)
+#3627 := (not #3042)
+#3629 := (or #3627 #3628)
+#3630 := (not #3629)
+#3635 := (or #2021 #3630)
+#3641 := (not #3635)
+#3642 := (or #1172 #3641)
+#3643 := (not #3642)
+#3648 := (or #1864 #3643)
+#3654 := (not #3648)
+#3655 := (or #1163 #3654)
+#3656 := (not #3655)
+#3661 := (or #1163 #3656)
+#4569 := (iff #3661 #4568)
+#4566 := (iff #3656 #4565)
+#4563 := (iff #3655 #4562)
+#4560 := (iff #3654 #4559)
+#4557 := (iff #3648 #4556)
+#4554 := (iff #3643 #4553)
+#4551 := (iff #3642 #4550)
+#4548 := (iff #3641 #4547)
+#4545 := (iff #3635 #4544)
+#4542 := (iff #3630 #4541)
+#4539 := (iff #3629 #4538)
+#4536 := (iff #3628 #4535)
+#4533 := (iff #3621 #4532)
+#4530 := (iff #3616 #4529)
+#4527 := (iff #3615 #4526)
+#4524 := (iff #3614 #4523)
+#4521 := (iff #3607 #4520)
+#4518 := (iff #3602 #4517)
+#4515 := (iff #3601 #4514)
+#4512 := (iff #3600 #4511)
+#4509 := (iff #3590 #4508)
+#4506 := (iff #3585 #4505)
+#4503 := (iff #3584 #4502)
+#4500 := (iff #3583 #4499)
+#4497 := (iff #3575 #4496)
+#4494 := (iff #3570 #4493)
+#4491 := (iff #3569 #4490)
+#4488 := (iff #3568 #4487)
+#4485 := (iff #3562 #4484)
+#4482 := (iff #3557 #4481)
+#4479 := (iff #3556 #4478)
+#4476 := (iff #3555 #4475)
+#4473 := (iff #3549 #4472)
+#4470 := (iff #3544 #4469)
+#4467 := (iff #3543 #4466)
+#4464 := (iff #3542 #4463)
+#4461 := (iff #3536 #4460)
+#4458 := (iff #3531 #4457)
+#4455 := (iff #3530 #4454)
+#4452 := (iff #3529 #4451)
+#4449 := (iff #3523 #4448)
+#4446 := (iff #3518 #4445)
+#4443 := (iff #3517 #4442)
+#4440 := (iff #3516 #4439)
+#4437 := (iff #3509 #4436)
+#4434 := (iff #3504 #4433)
+#4431 := (iff #3503 #4430)
+#4428 := (iff #3502 #4427)
+#4425 := (iff #3495 #4422)
+#4423 := (iff #3484 #3484)
+#4424 := [refl]: #4423
+#4426 := [quant-intro #4424]: #4425
+#4429 := [monotonicity #4426]: #4428
+#4419 := (iff #3501 #4418)
+#4416 := (iff #3480 #4413)
+#4414 := (iff #3475 #3475)
+#4415 := [refl]: #4414
+#4417 := [quant-intro #4415]: #4416
+#4420 := [monotonicity #4417]: #4419
+#4432 := [monotonicity #4420 #4429]: #4431
+#4435 := [monotonicity #4432]: #4434
+#4438 := [monotonicity #4435]: #4437
+#4441 := [monotonicity #4438]: #4440
+#4411 := (iff #3515 #4410)
+#4408 := (iff #3435 #4405)
+#4406 := (iff #3430 #3430)
+#4407 := [refl]: #4406
+#4409 := [quant-intro #4407]: #4408
+#4412 := [monotonicity #4409]: #4411
+#4444 := [monotonicity #4412 #4441]: #4443
+#4447 := [monotonicity #4444]: #4446
+#4450 := [monotonicity #4447]: #4449
 #4453 := [monotonicity #4450]: #4452
-#4443 := (iff #3525 #4442)
-#4440 := (iff #3504 #4437)
-#4438 := (iff #3499 #3499)
-#4439 := [refl]: #4438
-#4441 := [quant-intro #4439]: #4440
-#4444 := [monotonicity #4441]: #4443
-#4456 := [monotonicity #4444 #4453]: #4455
+#4402 := (iff #1466 #4401)
+#4399 := (iff #1463 #4396)
+#4397 := (iff #1460 #1460)
+#4398 := [refl]: #4397
+#4400 := [quant-intro #4398]: #4399
+#4403 := [monotonicity #4400]: #4402
+#4456 := [monotonicity #4403 #4453]: #4455
 #4459 := [monotonicity #4456]: #4458
 #4462 := [monotonicity #4459]: #4461
 #4465 := [monotonicity #4462]: #4464
-#4435 := (iff #3539 #4434)
-#4432 := (iff #3459 #4429)
-#4430 := (iff #3454 #3454)
-#4431 := [refl]: #4430
-#4433 := [quant-intro #4431]: #4432
-#4436 := [monotonicity #4433]: #4435
-#4468 := [monotonicity #4436 #4465]: #4467
+#4468 := [monotonicity #4465]: #4467
 #4471 := [monotonicity #4468]: #4470
 #4474 := [monotonicity #4471]: #4473
 #4477 := [monotonicity #4474]: #4476
-#4426 := (iff #1490 #4425)
-#4423 := (iff #1487 #4420)
-#4421 := (iff #1484 #1484)
-#4422 := [refl]: #4421
-#4424 := [quant-intro #4422]: #4423
-#4427 := [monotonicity #4424]: #4426
-#4480 := [monotonicity #4427 #4477]: #4479
+#4394 := (iff #920 #4393)
+#4391 := (iff #786 #4388)
+#4389 := (iff #781 #781)
+#4390 := [refl]: #4389
+#4392 := [quant-intro #4390]: #4391
+#4395 := [monotonicity #4392]: #4394
+#4480 := [monotonicity #4395 #4477]: #4479
 #4483 := [monotonicity #4480]: #4482
 #4486 := [monotonicity #4483]: #4485
 #4489 := [monotonicity #4486]: #4488
-#4492 := [monotonicity #4489]: #4491
+#4385 := (iff #1452 #4384)
+#4382 := (iff #1449 #4379)
+#4380 := (iff #1444 #1444)
+#4381 := [refl]: #4380
+#4383 := [quant-intro #4381]: #4382
+#4386 := [monotonicity #4383]: #4385
+#4492 := [monotonicity #4386 #4489]: #4491
 #4495 := [monotonicity #4492]: #4494
 #4498 := [monotonicity #4495]: #4497
 #4501 := [monotonicity #4498]: #4500
-#4418 := (iff #944 #4417)
-#4415 := (iff #810 #4412)
-#4413 := (iff #805 #805)
-#4414 := [refl]: #4413
-#4416 := [quant-intro #4414]: #4415
-#4419 := [monotonicity #4416]: #4418
-#4504 := [monotonicity #4419 #4501]: #4503
+#4377 := (iff #3582 #4376)
+#4374 := (iff #3389 #4371)
+#4372 := (iff #3384 #3384)
+#4373 := [refl]: #4372
+#4375 := [quant-intro #4373]: #4374
+#4378 := [monotonicity #4375]: #4377
+#4369 := (iff #3581 #4368)
+#4366 := (iff #3371 #4363)
+#4364 := (iff #3368 #3368)
+#4365 := [refl]: #4364
+#4367 := [quant-intro #4365]: #4366
+#4370 := [monotonicity #4367]: #4369
+#4359 := (iff #1617 #4358)
+#4356 := (iff #1614 #4353)
+#4354 := (iff #1609 #1609)
+#4355 := [refl]: #4354
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+#4360 := [monotonicity #4357]: #4359
+#4504 := [monotonicity #4360 #4370 #4378 #4501]: #4503
 #4507 := [monotonicity #4504]: #4506
-#4510 := [monotonicity #4507]: #4509
-#4513 := [monotonicity #4510]: #4512
-#4409 := (iff #1476 #4408)
-#4406 := (iff #1473 #4403)
-#4404 := (iff #1468 #1468)
-#4405 := [refl]: #4404
-#4407 := [quant-intro #4405]: #4406
-#4410 := [monotonicity #4407]: #4409
-#4516 := [monotonicity #4410 #4513]: #4515
-#4519 := [monotonicity #4516]: #4518
-#4522 := [monotonicity #4519]: #4521
-#4525 := [monotonicity #4522]: #4524
-#4401 := (iff #3606 #4400)
-#4398 := (iff #3413 #4395)
-#4396 := (iff #3408 #3408)
-#4397 := [refl]: #4396
-#4399 := [quant-intro #4397]: #4398
-#4402 := [monotonicity #4399]: #4401
-#4393 := (iff #3605 #4392)
-#4390 := (iff #3395 #4387)
-#4388 := (iff #3392 #3392)
-#4389 := [refl]: #4388
-#4391 := [quant-intro #4389]: #4390
-#4394 := [monotonicity #4391]: #4393
-#4383 := (iff #1641 #4382)
-#4380 := (iff #1638 #4377)
-#4378 := (iff #1633 #1633)
-#4379 := [refl]: #4378
-#4381 := [quant-intro #4379]: #4380
-#4384 := [monotonicity #4381]: #4383
-#4528 := [monotonicity #4384 #4394 #4402 #4525]: #4527
-#4531 := [monotonicity #4528]: #4530
-#4375 := (iff #3383 #4374)
-#4372 := (iff #3382 #4371)
-#4369 := (iff #3381 #4368)
-#4366 := (iff #3374 #4365)
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-#4342 := (iff #3325 #4339)
-#4340 := (iff #3320 #3320)
-#4341 := [refl]: #4340
-#4343 := [quant-intro #4341]: #4342
-#4346 := [monotonicity #4343]: #4345
-#4349 := [monotonicity #4346]: #4348
-#4352 := [monotonicity #4349]: #4351
-#4355 := [monotonicity #4352]: #4354
-#4358 := [monotonicity #4355]: #4357
-#4337 := (iff #3366 #4336)
-#4334 := (iff #3303 #4331)
-#4332 := (iff #3298 #3298)
-#4333 := [refl]: #4332
-#4335 := [quant-intro #4333]: #4334
-#4338 := [monotonicity #4335]: #4337
-#4361 := [monotonicity #4338 #4358]: #4360
-#4364 := [monotonicity #4361]: #4363
-#4329 := (iff #3274 #4328)
-#4326 := (iff #3273 #4325)
-#4323 := (iff #3272 #4322)
-#4320 := (iff #3266 #4317)
-#4318 := (iff #3255 #3255)
-#4319 := [refl]: #4318
-#4321 := [quant-intro #4319]: #4320
-#4324 := [monotonicity #4321]: #4323
-#4327 := [monotonicity #4324]: #4326
-#4330 := [monotonicity #4327]: #4329
-#4367 := [monotonicity #4330 #4364]: #4366
-#4370 := [monotonicity #4367]: #4369
-#4313 := (iff #3380 #4312)
-#4310 := (iff #3251 #4307)
-#4308 := (iff #3240 #3240)
+#4351 := (iff #3359 #4350)
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+#4317 := [refl]: #4316
+#4319 := [quant-intro #4317]: #4318
+#4322 := [monotonicity #4319]: #4321
+#4325 := [monotonicity #4322]: #4324
+#4328 := [monotonicity #4325]: #4327
+#4331 := [monotonicity #4328]: #4330
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+#4313 := (iff #3342 #4312)
+#4310 := (iff #3279 #4307)
+#4308 := (iff #3274 #3274)
 #4309 := [refl]: #4308
 #4311 := [quant-intro #4309]: #4310
 #4314 := [monotonicity #4311]: #4313
-#4373 := [monotonicity #4314 #4370]: #4372
-#4376 := [monotonicity #4373]: #4375
-#4534 := [monotonicity #4376 #4531]: #4533
-#4537 := [monotonicity #4534]: #4536
-#4304 := (iff #3623 #4303)
-#4301 := (iff #3237 #4298)
-#4299 := (iff #3232 #3232)
-#4300 := [refl]: #4299
-#4302 := [quant-intro #4300]: #4301
-#4305 := [monotonicity #4302]: #4304
-#4296 := (iff #3622 #4295)
-#4293 := (iff #3209 #4290)
-#4291 := (iff #3204 #3204)
-#4292 := [refl]: #4291
-#4294 := [quant-intro #4292]: #4293
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-#4288 := (iff #3621 #4287)
-#4285 := (iff #3181 #4282)
-#4283 := (iff #3176 #3176)
-#4284 := [refl]: #4283
-#4286 := [quant-intro #4284]: #4285
-#4289 := [monotonicity #4286]: #4288
-#4279 := (iff #3620 #4278)
-#4276 := (iff #3158 #4273)
-#4274 := (iff #3153 #3153)
-#4275 := [refl]: #4274
-#4277 := [quant-intro #4275]: #4276
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-#4271 := (iff #1733 #4270)
-#4268 := (iff #1730 #4265)
-#4266 := (iff #1727 #1727)
-#4267 := [refl]: #4266
-#4269 := [quant-intro #4267]: #4268
-#4272 := [monotonicity #4269]: #4271
-#4540 := [monotonicity #4272 #4280 #4289 #4297 #4305 #4537]: #4539
-#4543 := [monotonicity #4540]: #4542
-#4262 := (iff #3134 #4261)
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-#4253 := (iff #3126 #4250)
-#4251 := (iff #3115 #3115)
-#4252 := [refl]: #4251
-#4254 := [quant-intro #4252]: #4253
-#4257 := [monotonicity #4254]: #4256
-#4260 := [monotonicity #4257]: #4259
-#4263 := [monotonicity #4260]: #4262
-#4546 := [monotonicity #4263 #4543]: #4545
-#4549 := [monotonicity #4546]: #4548
-#4247 := (iff #3637 #4246)
-#4244 := (iff #3111 #4241)
-#4242 := (iff #3106 #3106)
+#4337 := [monotonicity #4314 #4334]: #4336
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+#4302 := (iff #3249 #4301)
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+#4296 := (iff #3242 #4293)
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+#4303 := [monotonicity #4300]: #4302
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+#4286 := (iff #3227 #4283)
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+#4352 := [monotonicity #4349]: #4351
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+#4250 := (iff #3129 #3129)
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+#4244 := (iff #1706 #4241)
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 #4243 := [refl]: #4242
 #4245 := [quant-intro #4243]: #4244
 #4248 := [monotonicity #4245]: #4247
-#4552 := [monotonicity #4248 #4549]: #4551
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+#4239 := [monotonicity #4236]: #4238
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+#4219 := [refl]: #4218
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+#4540 := [monotonicity #4215 #4537]: #4539
+#4543 := [monotonicity #4540]: #4542
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+#4200 := (iff #1168 #1168)
+#4201 := [refl]: #4200
+#4203 := [quant-intro #4201]: #4202
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 #4555 := [monotonicity #4552]: #4554
 #4558 := [monotonicity #4555]: #4557
 #4561 := [monotonicity #4558]: #4560
-#4238 := (iff #3651 #4237)
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-#4234 := [refl]: #4233
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-#4239 := [monotonicity #4236]: #4238
-#4564 := [monotonicity #4239 #4561]: #4563
+#4564 := [monotonicity #4561]: #4563
 #4567 := [monotonicity #4564]: #4566
 #4570 := [monotonicity #4567]: #4569
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-#4224 := (iff #1192 #1192)
-#4225 := [refl]: #4224
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-#3521 := [quant-intro #3518]: #3520
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-#3495 := [trans #3491 #3493]: #3494
-#3498 := [monotonicity #3495]: #3497
-#3503 := [trans #3498 #3501]: #3502
-#3506 := [quant-intro #3503]: #3505
-#3524 := [monotonicity #3506 #3521]: #3523
-#3532 := [trans #3524 #3530]: #3531
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 #3322 := [rewrite]: #3321
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-#3285 := [monotonicity #3282]: #3284
-#3289 := [trans #3285 #3287]: #3288
-#3297 := [monotonicity #3289 #3294]: #3296
-#3302 := [trans #3297 #3300]: #3301
-#3305 := [quant-intro #3302]: #3304
-#3365 := [monotonicity #3305 #3362]: #3364
-#3373 := [trans #3365 #3371]: #3372
-#3277 := (iff #2738 #3274)
-#3269 := (and #2081 #2698 #3266)
-#3275 := (iff #3269 #3274)
+#3319 := (iff #2762 #3318)
+#3316 := (iff #2759 #3315)
+#3317 := [rewrite]: #3316
+#3320 := [monotonicity #3317]: #3319
+#3324 := [trans #3320 #3322]: #3323
+#3327 := [monotonicity #3324]: #3326
+#3332 := [trans #3327 #3330]: #3331
+#3335 := [monotonicity #3332]: #3334
+#3312 := (iff #2142 #3309)
+#3304 := (and #2132 #3301)
+#3310 := (iff #3304 #3309)
+#3311 := [rewrite]: #3310
+#3305 := (iff #2142 #3304)
+#3302 := (iff #1358 #3301)
+#3299 := (iff #1355 #3296)
+#3282 := (or #1202 #1311)
+#3293 := (or #3282 #1352)
+#3297 := (iff #3293 #3296)
+#3298 := [rewrite]: #3297
+#3294 := (iff #1355 #3293)
+#3291 := (iff #1349 #3282)
+#3283 := (not #3282)
+#3286 := (not #3283)
+#3289 := (iff #3286 #3282)
+#3290 := [rewrite]: #3289
+#3287 := (iff #1349 #3286)
+#3284 := (iff #1346 #3283)
+#3285 := [rewrite]: #3284
+#3288 := [monotonicity #3285]: #3287
+#3292 := [trans #3288 #3290]: #3291
+#3295 := [monotonicity #3292]: #3294
+#3300 := [trans #3295 #3298]: #3299
+#3303 := [quant-intro #3300]: #3302
+#3306 := [monotonicity #3303]: #3305
+#3313 := [trans #3306 #3311]: #3312
+#3338 := [monotonicity #3313 #3335]: #3337
+#3280 := (iff #2756 #3279)
+#3277 := (iff #2753 #3274)
+#3255 := (or #57 #1311)
+#3271 := (or #3255 #3268)
+#3275 := (iff #3271 #3274)
 #3276 := [rewrite]: #3275
-#3270 := (iff #2738 #3269)
-#3267 := (iff #2732 #3266)
-#3264 := (iff #2729 #3255)
+#3272 := (iff #2753 #3271)
+#3269 := (iff #2750 #3268)
+#3270 := [rewrite]: #3269
+#3264 := (iff #1318 #3255)
 #3256 := (not #3255)
 #3259 := (not #3256)
 #3262 := (iff #3259 #3255)
 #3263 := [rewrite]: #3262
-#3260 := (iff #2729 #3259)
-#3257 := (iff #2726 #3256)
+#3260 := (iff #1318 #3259)
+#3257 := (iff #1315 #3256)
 #3258 := [rewrite]: #3257
 #3261 := [monotonicity #3258]: #3260
 #3265 := [trans #3261 #3263]: #3264
-#3268 := [quant-intro #3265]: #3267
-#3271 := [monotonicity #3268]: #3270
-#3278 := [trans #3271 #3276]: #3277
-#3376 := [monotonicity #3278 #3373]: #3375
-#3252 := (iff #2185 #3251)
-#3249 := (iff #2182 #3240)
-#3241 := (not #3240)
-#3244 := (not #3241)
-#3247 := (iff #3244 #3240)
-#3248 := [rewrite]: #3247
-#3245 := (iff #2182 #3244)
-#3242 := (iff #1410 #3241)
-#3243 := [rewrite]: #3242
-#3246 := [monotonicity #3243]: #3245
-#3250 := [trans #3246 #3248]: #3249
-#3253 := [quant-intro #3250]: #3252
-#3379 := [monotonicity #3253 #3376]: #3378
-#3387 := [trans #3379 #3385]: #3386
-#3616 := [monotonicity #3387 #3613]: #3615
-#3238 := (iff #2684 #3237)
-#3235 := (iff #2681 #3232)
-#3212 := (or #57 #1290)
-#3229 := (or #3212 #3226)
-#3233 := (iff #3229 #3232)
+#3273 := [monotonicity #3265 #3270]: #3272
+#3278 := [trans #3273 #3276]: #3277
+#3281 := [quant-intro #3278]: #3280
+#3341 := [monotonicity #3281 #3338]: #3340
+#3349 := [trans #3341 #3347]: #3348
+#3253 := (iff #2714 #3250)
+#3245 := (and #2057 #2674 #3242)
+#3251 := (iff #3245 #3250)
+#3252 := [rewrite]: #3251
+#3246 := (iff #2714 #3245)
+#3243 := (iff #2708 #3242)
+#3240 := (iff #2705 #3231)
+#3232 := (not #3231)
+#3235 := (not #3232)
+#3238 := (iff #3235 #3231)
+#3239 := [rewrite]: #3238
+#3236 := (iff #2705 #3235)
+#3233 := (iff #2702 #3232)
 #3234 := [rewrite]: #3233
-#3230 := (iff #2681 #3229)
-#3227 := (iff #2678 #3226)
-#3228 := [rewrite]: #3227
-#3221 := (iff #1297 #3212)
-#3213 := (not #3212)
-#3216 := (not #3213)
-#3219 := (iff #3216 #3212)
-#3220 := [rewrite]: #3219
-#3217 := (iff #1297 #3216)
-#3214 := (iff #1294 #3213)
-#3215 := [rewrite]: #3214
-#3218 := [monotonicity #3215]: #3217
-#3222 := [trans #3218 #3220]: #3221
-#3231 := [monotonicity #3222 #3228]: #3230
-#3236 := [trans #3231 #3234]: #3235
-#3239 := [quant-intro #3236]: #3238
-#3210 := (iff #2644 #3209)
-#3207 := (iff #2641 #3204)
-#3184 := (or #57 #1252)
-#3201 := (or #3184 #3198)
-#3205 := (iff #3201 #3204)
-#3206 := [rewrite]: #3205
-#3202 := (iff #2641 #3201)
-#3199 := (iff #2638 #3198)
-#3200 := [rewrite]: #3199
-#3193 := (iff #1259 #3184)
-#3185 := (not #3184)
-#3188 := (not #3185)
-#3191 := (iff #3188 #3184)
-#3192 := [rewrite]: #3191
-#3189 := (iff #1259 #3188)
-#3186 := (iff #1256 #3185)
-#3187 := [rewrite]: #3186
-#3190 := [monotonicity #3187]: #3189
-#3194 := [trans #3190 #3192]: #3193
-#3203 := [monotonicity #3194 #3200]: #3202
-#3208 := [trans #3203 #3206]: #3207
-#3211 := [quant-intro #3208]: #3210
-#3182 := (iff #1721 #3181)
-#3179 := (iff #1716 #3176)
-#3162 := (or #532 #3161)
-#3173 := (or #3162 #1306)
-#3177 := (iff #3173 #3176)
-#3178 := [rewrite]: #3177
-#3174 := (iff #1716 #3173)
-#3171 := (iff #547 #3162)
-#3163 := (not #3162)
-#3166 := (not #3163)
-#3169 := (iff #3166 #3162)
-#3170 := [rewrite]: #3169
-#3167 := (iff #547 #3166)
-#3164 := (iff #541 #3163)
-#3165 := [rewrite]: #3164
-#3168 := [monotonicity #3165]: #3167
-#3172 := [trans #3168 #3170]: #3171
-#3175 := [monotonicity #3172]: #3174
-#3180 := [trans #3175 #3178]: #3179
-#3183 := [quant-intro #3180]: #3182
-#3159 := (iff #1705 #3158)
-#3156 := (iff #1702 #3153)
-#3139 := (or #535 #1226)
-#3150 := (or #3139 #1699)
-#3154 := (iff #3150 #3153)
-#3155 := [rewrite]: #3154
-#3151 := (iff #1702 #3150)
-#3148 := (iff #1696 #3139)
-#3140 := (not #3139)
-#3143 := (not #3140)
-#3146 := (iff #3143 #3139)
-#3147 := [rewrite]: #3146
-#3144 := (iff #1696 #3143)
-#3141 := (iff #1691 #3140)
-#3142 := [rewrite]: #3141
-#3145 := [monotonicity #3142]: #3144
-#3149 := [trans #3145 #3147]: #3148
-#3152 := [monotonicity #3149]: #3151
-#3157 := [trans #3152 #3155]: #3156
-#3160 := [quant-intro #3157]: #3159
-#3619 := [monotonicity #3160 #3183 #3211 #3239 #3616]: #3618
-#3630 := [trans #3619 #3628]: #3629
-#3137 := (iff #2600 #3134)
-#3129 := (and #1973 #2560 #3126)
-#3135 := (iff #3129 #3134)
-#3136 := [rewrite]: #3135
-#3130 := (iff #2600 #3129)
-#3127 := (iff #2594 #3126)
-#3124 := (iff #2591 #3115)
+#3237 := [monotonicity #3234]: #3236
+#3241 := [trans #3237 #3239]: #3240
+#3244 := [quant-intro #3241]: #3243
+#3247 := [monotonicity #3244]: #3246
+#3254 := [trans #3247 #3252]: #3253
+#3352 := [monotonicity #3254 #3349]: #3351
+#3228 := (iff #2161 #3227)
+#3225 := (iff #2158 #3216)
+#3217 := (not #3216)
+#3220 := (not #3217)
+#3223 := (iff #3220 #3216)
+#3224 := [rewrite]: #3223
+#3221 := (iff #2158 #3220)
+#3218 := (iff #1386 #3217)
+#3219 := [rewrite]: #3218
+#3222 := [monotonicity #3219]: #3221
+#3226 := [trans #3222 #3224]: #3225
+#3229 := [quant-intro #3226]: #3228
+#3355 := [monotonicity #3229 #3352]: #3354
+#3363 := [trans #3355 #3361]: #3362
+#3592 := [monotonicity #3363 #3589]: #3591
+#3214 := (iff #2660 #3213)
+#3211 := (iff #2657 #3208)
+#3188 := (or #57 #1266)
+#3205 := (or #3188 #3202)
+#3209 := (iff #3205 #3208)
+#3210 := [rewrite]: #3209
+#3206 := (iff #2657 #3205)
+#3203 := (iff #2654 #3202)
+#3204 := [rewrite]: #3203
+#3197 := (iff #1273 #3188)
+#3189 := (not #3188)
+#3192 := (not #3189)
+#3195 := (iff #3192 #3188)
+#3196 := [rewrite]: #3195
+#3193 := (iff #1273 #3192)
+#3190 := (iff #1270 #3189)
+#3191 := [rewrite]: #3190
+#3194 := [monotonicity #3191]: #3193
+#3198 := [trans #3194 #3196]: #3197
+#3207 := [monotonicity #3198 #3204]: #3206
+#3212 := [trans #3207 #3210]: #3211
+#3215 := [quant-intro #3212]: #3214
+#3186 := (iff #2620 #3185)
+#3183 := (iff #2617 #3180)
+#3160 := (or #57 #1228)
+#3177 := (or #3160 #3174)
+#3181 := (iff #3177 #3180)
+#3182 := [rewrite]: #3181
+#3178 := (iff #2617 #3177)
+#3175 := (iff #2614 #3174)
+#3176 := [rewrite]: #3175
+#3169 := (iff #1235 #3160)
+#3161 := (not #3160)
+#3164 := (not #3161)
+#3167 := (iff #3164 #3160)
+#3168 := [rewrite]: #3167
+#3165 := (iff #1235 #3164)
+#3162 := (iff #1232 #3161)
+#3163 := [rewrite]: #3162
+#3166 := [monotonicity #3163]: #3165
+#3170 := [trans #3166 #3168]: #3169
+#3179 := [monotonicity #3170 #3176]: #3178
+#3184 := [trans #3179 #3182]: #3183
+#3187 := [quant-intro #3184]: #3186
+#3158 := (iff #1697 #3157)
+#3155 := (iff #1692 #3152)
+#3138 := (or #508 #3137)
+#3149 := (or #3138 #1282)
+#3153 := (iff #3149 #3152)
+#3154 := [rewrite]: #3153
+#3150 := (iff #1692 #3149)
+#3147 := (iff #523 #3138)
+#3139 := (not #3138)
+#3142 := (not #3139)
+#3145 := (iff #3142 #3138)
+#3146 := [rewrite]: #3145
+#3143 := (iff #523 #3142)
+#3140 := (iff #517 #3139)
+#3141 := [rewrite]: #3140
+#3144 := [monotonicity #3141]: #3143
+#3148 := [trans #3144 #3146]: #3147
+#3151 := [monotonicity #3148]: #3150
+#3156 := [trans #3151 #3154]: #3155
+#3159 := [quant-intro #3156]: #3158
+#3135 := (iff #1681 #3134)
+#3132 := (iff #1678 #3129)
+#3115 := (or #511 #1202)
+#3126 := (or #3115 #1675)
+#3130 := (iff #3126 #3129)
+#3131 := [rewrite]: #3130
+#3127 := (iff #1678 #3126)
+#3124 := (iff #1672 #3115)
 #3116 := (not #3115)
 #3119 := (not #3116)
 #3122 := (iff #3119 #3115)
 #3123 := [rewrite]: #3122
-#3120 := (iff #2591 #3119)
-#3117 := (iff #2588 #3116)
+#3120 := (iff #1672 #3119)
+#3117 := (iff #1667 #3116)
 #3118 := [rewrite]: #3117
 #3121 := [monotonicity #3118]: #3120
 #3125 := [trans #3121 #3123]: #3124
-#3128 := [quant-intro #3125]: #3127
-#3131 := [monotonicity #3128]: #3130
-#3138 := [trans #3131 #3136]: #3137
-#3633 := [monotonicity #3138 #3630]: #3632
-#3112 := (iff #1244 #3111)
-#3109 := (iff #1241 #3106)
-#3092 := (or #456 #1226)
-#3103 := (or #1221 #3092)
-#3107 := (iff #3103 #3106)
-#3108 := [rewrite]: #3107
-#3104 := (iff #1241 #3103)
-#3101 := (iff #1238 #3092)
-#3093 := (not #3092)
-#3096 := (not #3093)
-#3099 := (iff #3096 #3092)
-#3100 := [rewrite]: #3099
-#3097 := (iff #1238 #3096)
-#3094 := (iff #1233 #3093)
-#3095 := [rewrite]: #3094
-#3098 := [monotonicity #3095]: #3097
-#3102 := [trans #3098 #3100]: #3101
-#3105 := [monotonicity #3102]: #3104
-#3110 := [trans #3105 #3108]: #3109
-#3113 := [quant-intro #3110]: #3112
-#3636 := [monotonicity #3113 #3633]: #3635
-#3644 := [trans #3636 #3642]: #3643
-#3090 := (iff #2554 #3089)
-#3087 := (iff #2551 #3084)
-#3070 := (or #1933 #3069)
-#3081 := (or #2542 #3070)
-#3085 := (iff #3081 #3084)
-#3086 := [rewrite]: #3085
-#3082 := (iff #2551 #3081)
-#3079 := (iff #2548 #3070)
-#3071 := (not #3070)
-#3074 := (not #3071)
-#3077 := (iff #3074 #3070)
-#3078 := [rewrite]: #3077
-#3075 := (iff #2548 #3074)
-#3072 := (iff #2545 #3071)
-#3073 := [rewrite]: #3072
-#3076 := [monotonicity #3073]: #3075
-#3080 := [trans #3076 #3078]: #3079
-#3083 := [monotonicity #3080]: #3082
-#3088 := [trans #3083 #3086]: #3087
-#3091 := [monotonicity #3088]: #3090
-#3647 := [monotonicity #3091 #3644]: #3646
-#3067 := (iff #1213 #3066)
-#3064 := (iff #1208 #3061)
-#3047 := (or #453 #2510)
-#3058 := (or #3047 #1201)
-#3062 := (iff #3058 #3061)
-#3063 := [rewrite]: #3062
-#3059 := (iff #1208 #3058)
-#3056 := (iff #474 #3047)
-#3048 := (not #3047)
-#3051 := (not #3048)
-#3054 := (iff #3051 #3047)
-#3055 := [rewrite]: #3054
-#3052 := (iff #474 #3051)
-#3049 := (iff #468 #3048)
-#3050 := [rewrite]: #3049
-#3053 := [monotonicity #3050]: #3052
-#3057 := [trans #3053 #3055]: #3056
-#3060 := [monotonicity #3057]: #3059
-#3065 := [trans #3060 #3063]: #3064
-#3068 := [quant-intro #3065]: #3067
-#3650 := [monotonicity #3068 #3647]: #3649
-#3658 := [trans #3650 #3656]: #3657
-#2250 := (iff #2535 #2018)
-#2329 := (iff #2532 #2119)
-#2297 := (or #2210 #1910)
-#2231 := (or #2297 #2527)
-#2120 := (iff #2231 #2119)
-#2328 := [rewrite]: #2120
-#1918 := (iff #2532 #2231)
-#2271 := (iff #2516 #2297)
-#1855 := (not #2297)
-#2154 := (not #1855)
-#1950 := (iff #2154 #2297)
-#2270 := [rewrite]: #1950
-#2155 := (iff #2516 #2154)
-#1856 := (iff #2513 #1855)
-#2298 := [rewrite]: #1856
-#1949 := [monotonicity #2298]: #2155
-#2230 := [trans #1949 #2270]: #2271
-#1919 := [monotonicity #2230]: #1918
-#2017 := [trans #1919 #2328]: #2329
-#2251 := [monotonicity #2017]: #2250
-#3661 := [monotonicity #2251 #3658]: #3660
-#3664 := [monotonicity #3661]: #3663
-#3671 := [trans #3664 #3669]: #3670
-#3674 := [monotonicity #3671]: #3673
-#3677 := [monotonicity #3674]: #3676
-#3684 := [trans #3677 #3682]: #3683
-#3687 := [monotonicity #3684]: #3686
-#2343 := (+ #2342 #2340)
-#2344 := (= #2343 0::Int)
-#2347 := (and #798 #2346 #2344)
-#2364 := (not #2347)
-#2367 := (forall (vars (?v1 S3)) #2364)
-#2352 := (= ?v0!20 f10)
-#2353 := (not #2352)
-#2354 := (and #2353 #2351)
-#2355 := (not #2354)
-#2361 := (not #2355)
-#2371 := (and #2361 #2367)
-#2376 := (and #1530 #2371)
-#2309 := (* -1::Int #2308)
-#2311 := (+ #2310 #2309)
-#2314 := (+ #2313 #2311)
-#2315 := (>= #2314 0::Int)
-#2322 := (and #2321 #2319)
-#2323 := (not #2322)
-#2324 := (or #2323 #2315)
-#2325 := (not #2324)
-#2380 := (or #2325 #2376)
-#2384 := (and #1506 #2380)
-#2282 := (* -1::Int #2281)
-#2284 := (+ #2283 #2282)
-#2285 := (>= #2284 0::Int)
-#2291 := (and #2290 #2287)
-#2292 := (not #2291)
-#2293 := (or #2292 #2285)
-#2294 := (not #2293)
-#2388 := (or #2294 #2384)
-#2392 := (and #1487 #2388)
-#2396 := (or #2267 #2392)
-#2261 := (not #1481)
-#2400 := (and #2261 #2396)
-#2404 := (or #1481 #2400)
-#2408 := (and #810 #2404)
-#2245 := (= #2244 #2243)
-#2246 := (or #2245 #2242)
-#2247 := (not #2246)
-#2412 := (or #2247 #2408)
-#2416 := (and #1473 #2412)
-#2223 := (* -1::Int #2222)
-#2225 := (+ #2224 #2223)
-#2226 := (>= #2225 0::Int)
-#2227 := (not #2226)
-#2420 := (or #2227 #2416)
-#2206 := (and #2205 #2202)
-#2192 := (not #986)
-#2440 := (and #2192 #756 #2206 #1462 #2420 #1620 #1638 #1646)
-#2133 := (* -1::Int #2132)
-#2135 := (+ #2134 #2133)
-#2138 := (+ #2137 #2135)
-#2139 := (>= #2138 0::Int)
-#2148 := (and #2147 #2143)
-#2149 := (not #2148)
-#2150 := (or #2149 #2139)
-#2151 := (not #2150)
-#2170 := (or #2151 #2166)
-#2109 := (+ #2108 #1333)
-#2112 := (+ #2111 #2109)
-#2113 := (= #2112 0::Int)
-#2114 := (>= #2109 0::Int)
-#2115 := (not #2114)
-#2116 := (and #2115 #2113)
-#2121 := (or #1342 #2116)
-#2124 := (forall (vars (?v0 S3)) #2121)
-#2174 := (and #2124 #2170)
-#2073 := (+ #2072 #2070)
-#2074 := (= #2073 0::Int)
-#2077 := (and #2076 #2074)
-#2093 := (not #2077)
-#2096 := (forall (vars (?v1 S3)) #2093)
-#2082 := (= ?v0!8 f10)
-#2083 := (not #2082)
-#2084 := (and #2083 #2081)
-#2085 := (not #2084)
-#2090 := (not #2085)
-#2100 := (and #2090 #2096)
-#2178 := (or #2100 #2174)
-#2064 := (not #714)
-#2061 := (not #732)
-#2058 := (not #705)
-#2055 := (not #723)
-#2188 := (and #2055 #2058 #2061 #2064 #2178 #2185)
-#2444 := (or #2188 #2440)
-#2032 := (+ #2031 #1288)
-#2033 := (>= #2032 0::Int)
-#2034 := (not #2033)
-#2037 := (+ #2036 #2032)
-#2038 := (= #2037 0::Int)
-#2041 := (and #2040 #2038 #2034)
-#2046 := (or #1297 #2041)
-#2049 := (forall (vars (?v0 S3)) #2046)
-#2005 := (+ #1250 #2004)
-#2007 := (+ #2006 #2005)
-#2008 := (= #2007 0::Int)
-#2009 := (+ #2006 #1250)
-#2010 := (>= #2009 0::Int)
-#2011 := (not #2010)
-#2014 := (and #2013 #2011 #2008)
-#2019 := (or #1259 #2014)
-#2022 := (forall (vars (?v0 S3)) #2019)
-#1997 := (not #1738)
-#2469 := (and #1997 #2022 #2049 #2444 #1705 #1721 #1730)
-#1963 := (+ #1962 #1960)
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-#1937 := (and #1936 #1934)
-#1938 := (not #1937)
-#1941 := (+ #1940 #1930)
-#1943 := (+ #1942 #1941)
-#1944 := (>= #1943 0::Int)
-#1945 := (or #1944 #1938)
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-#1905 := (+ #1904 #1903)
-#1906 := (>= #1905 0::Int)
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-#2946 := (iff #2344 #2945)
-#2943 := (= #2343 #2942)
-#2944 := [rewrite]: #2943
-#2947 := [monotonicity #2944]: #2946
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-#2953 := [monotonicity #2950]: #2952
-#2956 := [quant-intro #2953]: #2955
-#2939 := (iff #2361 #2926)
-#2931 := (not #2926)
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-#2937 := (iff #2934 #2926)
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-#2929 := (iff #2354 #2926)
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-#2921 := (iff #2353 #2920)
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-#2919 := [rewrite]: #2918
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-#2925 := [monotonicity #2922]: #2924
-#2930 := [trans #2925 #2928]: #2929
-#2933 := [monotonicity #2930]: #2932
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-#2962 := [monotonicity #2959]: #2961
-#2967 := [trans #2962 #2965]: #2966
-#2915 := (iff #2325 #2914)
-#2912 := (iff #2324 #2911)
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-#2896 := (+ #2310 #2313)
-#2897 := (+ #2309 #2896)
-#2900 := (>= #2897 0::Int)
-#2907 := (iff #2900 #2906)
-#2908 := [rewrite]: #2907
-#2901 := (iff #2315 #2900)
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-#2899 := [rewrite]: #2898
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-#2910 := [trans #2902 #2908]: #2909
-#2894 := (iff #2323 #2893)
-#2891 := (iff #2322 #2890)
-#2892 := [rewrite]: #2891
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-#2916 := [monotonicity #2913]: #2915
-#2970 := [monotonicity #2916 #2967]: #2969
+#3128 := [monotonicity #3125]: #3127
+#3133 := [trans #3128 #3131]: #3132
+#3136 := [quant-intro #3133]: #3135
+#3595 := [monotonicity #3136 #3159 #3187 #3215 #3592]: #3594
+#3606 := [trans #3595 #3604]: #3605
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+#3094 := [rewrite]: #3093
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+#3104 := [quant-intro #3101]: #3103
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+#3114 := [trans #3107 #3112]: #3113
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+#3088 := (iff #1220 #3087)
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+#3070 := (iff #1209 #3069)
+#3071 := [rewrite]: #3070
+#3074 := [monotonicity #3071]: #3073
+#3078 := [trans #3074 #3076]: #3077
+#3081 := [monotonicity #3078]: #3080
+#3086 := [trans #3081 #3084]: #3085
+#3089 := [quant-intro #3086]: #3088
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+#3620 := [trans #3612 #3618]: #3619
+#3066 := (iff #2530 #3065)
+#3063 := (iff #2527 #3060)
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+#3048 := (iff #2521 #3047)
+#3049 := [rewrite]: #3048
+#3052 := [monotonicity #3049]: #3051
+#3056 := [trans #3052 #3054]: #3055
+#3059 := [monotonicity #3056]: #3058
+#3064 := [trans #3059 #3062]: #3063
+#3067 := [monotonicity #3064]: #3066
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+#3043 := (iff #1189 #3042)
+#3040 := (iff #1184 #3037)
+#3023 := (or #429 #2486)
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+#3027 := (not #3024)
+#3030 := (iff #3027 #3023)
+#3031 := [rewrite]: #3030
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+#3025 := (iff #444 #3024)
+#3026 := [rewrite]: #3025
+#3029 := [monotonicity #3026]: #3028
+#3033 := [trans #3029 #3031]: #3032
+#3036 := [monotonicity #3033]: #3035
+#3041 := [trans #3036 #3039]: #3040
+#3044 := [quant-intro #3041]: #3043
+#3626 := [monotonicity #3044 #3623]: #3625
+#3634 := [trans #3626 #3632]: #3633
+#2246 := (iff #2511 #2021)
+#1868 := (iff #2508 #2304)
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+#2206 := (not #1831)
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+#2095 := [rewrite]: #1926
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+#1832 := (iff #2489 #1831)
+#1895 := [rewrite]: #1832
+#1925 := [monotonicity #1895]: #2207
+#2273 := [trans #1925 #2095]: #2096
+#2186 := [monotonicity #2273]: #2185
+#2020 := [trans #2186 #1867]: #1868
+#2247 := [monotonicity #2020]: #2246
+#3637 := [monotonicity #2247 #3634]: #3636
+#3640 := [monotonicity #3637]: #3639
+#3647 := [trans #3640 #3645]: #3646
+#3650 := [monotonicity #3647]: #3649
+#3653 := [monotonicity #3650]: #3652
+#3660 := [trans #3653 #3658]: #3659
+#3663 := [monotonicity #3660]: #3662
+#2319 := (+ #2318 #2316)
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+#2323 := (and #774 #2322 #2320)
+#2340 := (not #2323)
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+#2328 := (= ?v0!20 f10)
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+#2285 := (* -1::Int #2284)
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+#2008 := (+ #2007 #1264)
+#2009 := (>= #2008 0::Int)
+#2010 := (not #2009)
+#2013 := (+ #2012 #2008)
+#2014 := (= #2013 0::Int)
+#2017 := (and #2016 #2014 #2010)
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+#1981 := (+ #1226 #1980)
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+#1985 := (+ #1982 #1226)
+#1986 := (>= #1985 0::Int)
+#1987 := (not #1986)
+#1990 := (and #1989 #1987 #1984)
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+#2445 := (and #1973 #1998 #2025 #2420 #1681 #1697 #1706)
+#1939 := (+ #1938 #1936)
+#1940 := (+ #58 #1939)
+#1941 := (= #1940 0::Int)
+#1945 := (and #429 #1944 #1941)
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+#1917 := (+ #1916 #1906)
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+#1920 := (>= #1919 0::Int)
+#1921 := (or #1920 #1914)
+#1922 := (not #1921)
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+#2461 := (and #1189 #2457)
+#1879 := (* -1::Int #1878)
+#1881 := (+ #1880 #1879)
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+#1888 := (and #1887 #1884)
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+#2988 := (and #100 #2620 #2660 #2985 #1681 #1697 #1706)
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+#2989 := (iff #2445 #2988)
+#2986 := (iff #2420 #2985)
+#2983 := (iff #2416 #2980)
+#2977 := (and #181 #732 #2182 #1438 #2974 #1596 #1614 #1622)
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+#2982 := [rewrite]: #2981
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+#2975 := (iff #2396 #2974)
+#2972 := (iff #2392 #2971)
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+#2931 := (iff #2343 #2930)
+#2928 := (iff #2340 #2927)
+#2925 := (iff #2323 #2924)
+#2922 := (iff #2320 #2921)
+#2919 := (= #2319 #2918)
+#2920 := [rewrite]: #2919
+#2923 := [monotonicity #2920]: #2922
+#2926 := [monotonicity #2923]: #2925
+#2929 := [monotonicity #2926]: #2928
+#2932 := [quant-intro #2929]: #2931
+#2915 := (iff #2337 #2902)
+#2907 := (not #2902)
+#2910 := (not #2907)
+#2913 := (iff #2910 #2902)
+#2914 := [rewrite]: #2913
+#2911 := (iff #2337 #2910)
+#2908 := (iff #2331 #2907)
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+#2899 := (and #2896 #2327)
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+#2904 := [rewrite]: #2903
+#2900 := (iff #2330 #2899)
+#2897 := (iff #2329 #2896)
+#2894 := (iff #2328 #2893)
+#2895 := [rewrite]: #2894
+#2898 := [monotonicity #2895]: #2897
+#2901 := [monotonicity #2898]: #2900
+#2906 := [trans #2901 #2904]: #2905
+#2909 := [monotonicity #2906]: #2908
+#2912 := [monotonicity #2909]: #2911
+#2916 := [trans #2912 #2914]: #2915
+#2935 := [monotonicity #2916 #2932]: #2934
+#2938 := [monotonicity #2935]: #2937
+#2943 := [trans #2938 #2941]: #2942
+#2891 := (iff #2301 #2890)
+#2888 := (iff #2300 #2887)
+#2885 := (iff #2291 #2882)
+#2872 := (+ #2286 #2289)
+#2873 := (+ #2285 #2872)
+#2876 := (>= #2873 0::Int)
+#2883 := (iff #2876 #2882)
+#2884 := [rewrite]: #2883
+#2877 := (iff #2291 #2876)
+#2874 := (= #2290 #2873)
+#2875 := [rewrite]: #2874
+#2878 := [monotonicity #2875]: #2877
+#2886 := [trans #2878 #2884]: #2885
+#2870 := (iff #2299 #2869)
+#2867 := (iff #2298 #2866)
+#2868 := [rewrite]: #2867
+#2871 := [monotonicity #2868]: #2870
+#2889 := [monotonicity #2871 #2886]: #2888
+#2892 := [monotonicity #2889]: #2891
+#2946 := [monotonicity #2892 #2943]: #2945
+#2949 := [monotonicity #2946]: #2948
+#2864 := (iff #2270 #2863)
+#2861 := (iff #2269 #2860)
+#2858 := (iff #2261 #2855)
+#2847 := (+ #2258 #2259)
+#2850 := (>= #2847 0::Int)
+#2856 := (iff #2850 #2855)
+#2857 := [rewrite]: #2856
+#2851 := (iff #2261 #2850)
+#2848 := (= #2260 #2847)
+#2849 := [rewrite]: #2848
+#2852 := [monotonicity #2849]: #2851
+#2859 := [trans #2852 #2857]: #2858
+#2845 := (iff #2268 #2844)
+#2842 := (iff #2267 #2841)
+#2843 := [rewrite]: #2842
+#2846 := [monotonicity #2843]: #2845
+#2862 := [monotonicity #2846 #2859]: #2861
+#2865 := [monotonicity #2862]: #2864
+#2952 := [monotonicity #2865 #2949]: #2951
+#2955 := [monotonicity #2952]: #2954
+#2958 := [monotonicity #2955]: #2957
+#2839 := (iff #2237 #203)
+#2840 := [rewrite]: #2839
+#2961 := [monotonicity #2840 #2958]: #2960
+#2964 := [monotonicity #2961]: #2963
+#2967 := [monotonicity #2964]: #2966
+#2837 := (iff #2223 #2836)
+#2834 := (iff #2222 #2831)
+#2828 := (or #2825 #2218)
+#2832 := (iff #2828 #2831)
+#2833 := [rewrite]: #2832
+#2829 := (iff #2222 #2828)
+#2826 := (iff #2221 #2825)
+#2827 := [rewrite]: #2826
+#2830 := [monotonicity #2827]: #2829
+#2835 := [trans #2830 #2833]: #2834
+#2838 := [monotonicity #2835]: #2837
+#2970 := [monotonicity #2838 #2967]: #2969
 #2973 := [monotonicity #2970]: #2972
-#2888 := (iff #2294 #2887)
-#2885 := (iff #2293 #2884)
-#2882 := (iff #2285 #2879)
-#2871 := (+ #2282 #2283)
-#2874 := (>= #2871 0::Int)
-#2880 := (iff #2874 #2879)
-#2881 := [rewrite]: #2880
-#2875 := (iff #2285 #2874)
-#2872 := (= #2284 #2871)
-#2873 := [rewrite]: #2872
-#2876 := [monotonicity #2873]: #2875
-#2883 := [trans #2876 #2881]: #2882
-#2869 := (iff #2292 #2868)
-#2866 := (iff #2291 #2865)
-#2867 := [rewrite]: #2866
-#2870 := [monotonicity #2867]: #2869
-#2886 := [monotonicity #2870 #2883]: #2885
-#2889 := [monotonicity #2886]: #2888
-#2976 := [monotonicity #2889 #2973]: #2975
-#2979 := [monotonicity #2976]: #2978
-#2982 := [monotonicity #2979]: #2981
-#2863 := (iff #2261 #203)
-#2864 := [rewrite]: #2863
-#2985 := [monotonicity #2864 #2982]: #2984
-#2988 := [monotonicity #2985]: #2987
-#2991 := [monotonicity #2988]: #2990
-#2861 := (iff #2247 #2860)
-#2858 := (iff #2246 #2855)
-#2852 := (or #2849 #2242)
-#2856 := (iff #2852 #2855)
-#2857 := [rewrite]: #2856
-#2853 := (iff #2246 #2852)
-#2850 := (iff #2245 #2849)
-#2851 := [rewrite]: #2850
-#2854 := [monotonicity #2851]: #2853
-#2859 := [trans #2854 #2857]: #2858
-#2862 := [monotonicity #2859]: #2861
-#2994 := [monotonicity #2862 #2991]: #2993
-#2997 := [monotonicity #2994]: #2996
-#2847 := (iff #2227 #2846)
-#2844 := (iff #2226 #2841)
-#2833 := (+ #2223 #2224)
-#2836 := (>= #2833 0::Int)
-#2842 := (iff #2836 #2841)
-#2843 := [rewrite]: #2842
-#2837 := (iff #2226 #2836)
-#2834 := (= #2225 #2833)
-#2835 := [rewrite]: #2834
-#2838 := [monotonicity #2835]: #2837
-#2845 := [trans #2838 #2843]: #2844
-#2848 := [monotonicity #2845]: #2847
-#3000 := [monotonicity #2848 #2997]: #2999
-#2831 := (iff #2192 #181)
-#2832 := [rewrite]: #2831
-#3003 := [monotonicity #2832 #3000]: #3002
-#3008 := [trans #3003 #3006]: #3007
-#2829 := (iff #2188 #2826)
-#2823 := (and #136 #141 #620 #623 #2820 #2185)
-#2827 := (iff #2823 #2826)
-#2828 := [rewrite]: #2827
-#2824 := (iff #2188 #2823)
-#2821 := (iff #2178 #2820)
-#2818 := (iff #2174 #2817)
-#2815 := (iff #2170 #2812)
-#2809 := (or #2806 #2166)
-#2813 := (iff #2809 #2812)
-#2814 := [rewrite]: #2813
-#2810 := (iff #2170 #2809)
-#2807 := (iff #2151 #2806)
-#2804 := (iff #2150 #2803)
-#2801 := (iff #2139 #2798)
-#2789 := (+ #2134 #2137)
-#2790 := (+ #2133 #2789)
-#2793 := (>= #2790 0::Int)
-#2799 := (iff #2793 #2798)
-#2800 := [rewrite]: #2799
-#2794 := (iff #2139 #2793)
-#2791 := (= #2138 #2790)
-#2792 := [rewrite]: #2791
-#2795 := [monotonicity #2792]: #2794
-#2802 := [trans #2795 #2800]: #2801
-#2787 := (iff #2149 #2786)
-#2784 := (iff #2148 #2783)
-#2785 := [rewrite]: #2784
-#2788 := [monotonicity #2785]: #2787
-#2805 := [monotonicity #2788 #2802]: #2804
-#2808 := [monotonicity #2805]: #2807
-#2811 := [monotonicity #2808]: #2810
-#2816 := [trans #2811 #2814]: #2815
-#2781 := (iff #2124 #2780)
-#2778 := (iff #2121 #2777)
-#2775 := (iff #2116 #2774)
-#2772 := (iff #2113 #2769)
-#2759 := (+ #2108 #2111)
-#2760 := (+ #1333 #2759)
-#2763 := (= #2760 0::Int)
-#2770 := (iff #2763 #2769)
-#2771 := [rewrite]: #2770
-#2764 := (iff #2113 #2763)
-#2761 := (= #2112 #2760)
-#2762 := [rewrite]: #2761
-#2765 := [monotonicity #2762]: #2764
-#2773 := [trans #2765 #2771]: #2772
-#2757 := (iff #2115 #2756)
-#2754 := (iff #2114 #2751)
-#2743 := (+ #1333 #2108)
-#2746 := (>= #2743 0::Int)
-#2752 := (iff #2746 #2751)
-#2753 := [rewrite]: #2752
-#2747 := (iff #2114 #2746)
-#2744 := (= #2109 #2743)
-#2745 := [rewrite]: #2744
-#2748 := [monotonicity #2745]: #2747
-#2755 := [trans #2748 #2753]: #2754
-#2758 := [monotonicity #2755]: #2757
-#2776 := [monotonicity #2758 #2773]: #2775
-#2779 := [monotonicity #2776]: #2778
-#2782 := [quant-intro #2779]: #2781
-#2819 := [monotonicity #2782 #2816]: #2818
-#2741 := (iff #2100 #2738)
-#2704 := (and #2081 #2698)
-#2735 := (and #2704 #2732)
-#2739 := (iff #2735 #2738)
-#2740 := [rewrite]: #2739
-#2736 := (iff #2100 #2735)
-#2733 := (iff #2096 #2732)
-#2730 := (iff #2093 #2729)
-#2727 := (iff #2077 #2726)
-#2724 := (iff #2074 #2723)
-#2721 := (= #2073 #2720)
-#2722 := [rewrite]: #2721
-#2725 := [monotonicity #2722]: #2724
-#2728 := [monotonicity #2725]: #2727
-#2731 := [monotonicity #2728]: #2730
-#2734 := [quant-intro #2731]: #2733
-#2717 := (iff #2090 #2704)
-#2709 := (not #2704)
-#2712 := (not #2709)
-#2715 := (iff #2712 #2704)
+#2823 := (iff #2203 #2822)
+#2820 := (iff #2202 #2817)
+#2809 := (+ #2199 #2200)
+#2812 := (>= #2809 0::Int)
+#2818 := (iff #2812 #2817)
+#2819 := [rewrite]: #2818
+#2813 := (iff #2202 #2812)
+#2810 := (= #2201 #2809)
+#2811 := [rewrite]: #2810
+#2814 := [monotonicity #2811]: #2813
+#2821 := [trans #2814 #2819]: #2820
+#2824 := [monotonicity #2821]: #2823
+#2976 := [monotonicity #2824 #2973]: #2975
+#2807 := (iff #2168 #181)
+#2808 := [rewrite]: #2807
+#2979 := [monotonicity #2808 #2976]: #2978
+#2984 := [trans #2979 #2982]: #2983
+#2805 := (iff #2164 #2802)
+#2799 := (and #136 #141 #596 #599 #2796 #2161)
+#2803 := (iff #2799 #2802)
+#2804 := [rewrite]: #2803
+#2800 := (iff #2164 #2799)
+#2797 := (iff #2154 #2796)
+#2794 := (iff #2150 #2793)
+#2791 := (iff #2146 #2788)
+#2785 := (or #2782 #2142)
+#2789 := (iff #2785 #2788)
+#2790 := [rewrite]: #2789
+#2786 := (iff #2146 #2785)
+#2783 := (iff #2127 #2782)
+#2780 := (iff #2126 #2779)
+#2777 := (iff #2115 #2774)
+#2765 := (+ #2110 #2113)
+#2766 := (+ #2109 #2765)
+#2769 := (>= #2766 0::Int)
+#2775 := (iff #2769 #2774)
+#2776 := [rewrite]: #2775
+#2770 := (iff #2115 #2769)
+#2767 := (= #2114 #2766)
+#2768 := [rewrite]: #2767
+#2771 := [monotonicity #2768]: #2770
+#2778 := [trans #2771 #2776]: #2777
+#2763 := (iff #2125 #2762)
+#2760 := (iff #2124 #2759)
+#2761 := [rewrite]: #2760
+#2764 := [monotonicity #2761]: #2763
+#2781 := [monotonicity #2764 #2778]: #2780
+#2784 := [monotonicity #2781]: #2783
+#2787 := [monotonicity #2784]: #2786
+#2792 := [trans #2787 #2790]: #2791
+#2757 := (iff #2100 #2756)
+#2754 := (iff #2097 #2753)
+#2751 := (iff #2092 #2750)
+#2748 := (iff #2089 #2745)
+#2735 := (+ #2084 #2087)
+#2736 := (+ #1309 #2735)
+#2739 := (= #2736 0::Int)
+#2746 := (iff #2739 #2745)
+#2747 := [rewrite]: #2746
+#2740 := (iff #2089 #2739)
+#2737 := (= #2088 #2736)
+#2738 := [rewrite]: #2737
+#2741 := [monotonicity #2738]: #2740
+#2749 := [trans #2741 #2747]: #2748
+#2733 := (iff #2091 #2732)
+#2730 := (iff #2090 #2727)
+#2719 := (+ #1309 #2084)
+#2722 := (>= #2719 0::Int)
+#2728 := (iff #2722 #2727)
+#2729 := [rewrite]: #2728
+#2723 := (iff #2090 #2722)
+#2720 := (= #2085 #2719)
+#2721 := [rewrite]: #2720
+#2724 := [monotonicity #2721]: #2723
+#2731 := [trans #2724 #2729]: #2730
+#2734 := [monotonicity #2731]: #2733
+#2752 := [monotonicity #2734 #2749]: #2751
+#2755 := [monotonicity #2752]: #2754
+#2758 := [quant-intro #2755]: #2757
+#2795 := [monotonicity #2758 #2792]: #2794
+#2717 := (iff #2076 #2714)
+#2680 := (and #2057 #2674)
+#2711 := (and #2680 #2708)
+#2715 := (iff #2711 #2714)
 #2716 := [rewrite]: #2715
-#2713 := (iff #2090 #2712)
-#2710 := (iff #2085 #2709)
-#2707 := (iff #2084 #2704)
-#2701 := (and #2698 #2081)
-#2705 := (iff #2701 #2704)
-#2706 := [rewrite]: #2705
-#2702 := (iff #2084 #2701)
-#2699 := (iff #2083 #2698)
-#2696 := (iff #2082 #2695)
-#2697 := [rewrite]: #2696
-#2700 := [monotonicity #2697]: #2699
-#2703 := [monotonicity #2700]: #2702
-#2708 := [trans #2703 #2706]: #2707
-#2711 := [monotonicity #2708]: #2710
-#2714 := [monotonicity #2711]: #2713
-#2718 := [trans #2714 #2716]: #2717
-#2737 := [monotonicity #2718 #2734]: #2736
-#2742 := [trans #2737 #2740]: #2741
-#2822 := [monotonicity #2742 #2819]: #2821
-#2693 := (iff #2064 #623)
-#2694 := [rewrite]: #2693
-#2691 := (iff #2061 #620)
+#2712 := (iff #2076 #2711)
+#2709 := (iff #2072 #2708)
+#2706 := (iff #2069 #2705)
+#2703 := (iff #2053 #2702)
+#2700 := (iff #2050 #2699)
+#2697 := (= #2049 #2696)
+#2698 := [rewrite]: #2697
+#2701 := [monotonicity #2698]: #2700
+#2704 := [monotonicity #2701]: #2703
+#2707 := [monotonicity #2704]: #2706
+#2710 := [quant-intro #2707]: #2709
+#2693 := (iff #2066 #2680)
+#2685 := (not #2680)
+#2688 := (not #2685)
+#2691 := (iff #2688 #2680)
 #2692 := [rewrite]: #2691
-#2689 := (iff #2058 #141)
-#2690 := [rewrite]: #2689
-#2687 := (iff #2055 #136)
-#2688 := [rewrite]: #2687
-#2825 := [monotonicity #2688 #2690 #2692 #2694 #2822]: #2824
-#2830 := [trans #2825 #2828]: #2829
-#3011 := [monotonicity #2830 #3008]: #3010
-#2685 := (iff #2049 #2684)
-#2682 := (iff #2046 #2681)
-#2679 := (iff #2041 #2678)
-#2676 := (iff #2034 #2675)
-#2673 := (iff #2033 #2670)
-#2663 := (+ #1288 #2031)
-#2666 := (>= #2663 0::Int)
-#2671 := (iff #2666 #2670)
-#2672 := [rewrite]: #2671
-#2667 := (iff #2033 #2666)
-#2664 := (= #2032 #2663)
-#2665 := [rewrite]: #2664
-#2668 := [monotonicity #2665]: #2667
-#2674 := [trans #2668 #2672]: #2673
-#2677 := [monotonicity #2674]: #2676
-#2661 := (iff #2038 #2658)
-#2647 := (+ #2031 #2036)
-#2648 := (+ #1288 #2647)
-#2651 := (= #2648 0::Int)
-#2659 := (iff #2651 #2658)
-#2660 := [rewrite]: #2659
-#2652 := (iff #2038 #2651)
-#2649 := (= #2037 #2648)
-#2650 := [rewrite]: #2649
+#2689 := (iff #2066 #2688)
+#2686 := (iff #2061 #2685)
+#2683 := (iff #2060 #2680)
+#2677 := (and #2674 #2057)
+#2681 := (iff #2677 #2680)
+#2682 := [rewrite]: #2681
+#2678 := (iff #2060 #2677)
+#2675 := (iff #2059 #2674)
+#2672 := (iff #2058 #2671)
+#2673 := [rewrite]: #2672
+#2676 := [monotonicity #2673]: #2675
+#2679 := [monotonicity #2676]: #2678
+#2684 := [trans #2679 #2682]: #2683
+#2687 := [monotonicity #2684]: #2686
+#2690 := [monotonicity #2687]: #2689
+#2694 := [trans #2690 #2692]: #2693
+#2713 := [monotonicity #2694 #2710]: #2712
+#2718 := [trans #2713 #2716]: #2717
+#2798 := [monotonicity #2718 #2795]: #2797
+#2669 := (iff #2040 #599)
+#2670 := [rewrite]: #2669
+#2667 := (iff #2037 #596)
+#2668 := [rewrite]: #2667
+#2665 := (iff #2034 #141)
+#2666 := [rewrite]: #2665
+#2663 := (iff #2031 #136)
+#2664 := [rewrite]: #2663
+#2801 := [monotonicity #2664 #2666 #2668 #2670 #2798]: #2800
+#2806 := [trans #2801 #2804]: #2805
+#2987 := [monotonicity #2806 #2984]: #2986
+#2661 := (iff #2025 #2660)
+#2658 := (iff #2022 #2657)
+#2655 := (iff #2017 #2654)
+#2652 := (iff #2010 #2651)
+#2649 := (iff #2009 #2646)
+#2639 := (+ #1264 #2007)
+#2642 := (>= #2639 0::Int)
+#2647 := (iff #2642 #2646)
+#2648 := [rewrite]: #2647
+#2643 := (iff #2009 #2642)
+#2640 := (= #2008 #2639)
+#2641 := [rewrite]: #2640
+#2644 := [monotonicity #2641]: #2643
+#2650 := [trans #2644 #2648]: #2649
 #2653 := [monotonicity #2650]: #2652
-#2662 := [trans #2653 #2660]: #2661
-#2680 := [monotonicity #2662 #2677]: #2679
-#2683 := [monotonicity #2680]: #2682
-#2686 := [quant-intro #2683]: #2685
-#2645 := (iff #2022 #2644)
-#2642 := (iff #2019 #2641)
-#2639 := (iff #2014 #2638)
-#2636 := (iff #2008 #2633)
-#2623 := (+ #2004 #2006)
-#2624 := (+ #1250 #2623)
+#2637 := (iff #2014 #2634)
+#2623 := (+ #2007 #2012)
+#2624 := (+ #1264 #2623)
 #2627 := (= #2624 0::Int)
-#2634 := (iff #2627 #2633)
-#2635 := [rewrite]: #2634
-#2628 := (iff #2008 #2627)
-#2625 := (= #2007 #2624)
+#2635 := (iff #2627 #2634)
+#2636 := [rewrite]: #2635
+#2628 := (iff #2014 #2627)
+#2625 := (= #2013 #2624)
 #2626 := [rewrite]: #2625
 #2629 := [monotonicity #2626]: #2628
-#2637 := [trans #2629 #2635]: #2636
-#2621 := (iff #2011 #2620)
-#2618 := (iff #2010 #2615)
-#2607 := (+ #1250 #2006)
-#2610 := (>= #2607 0::Int)
-#2616 := (iff #2610 #2615)
-#2617 := [rewrite]: #2616
-#2611 := (iff #2010 #2610)
-#2608 := (= #2009 #2607)
-#2609 := [rewrite]: #2608
-#2612 := [monotonicity #2609]: #2611
-#2619 := [trans #2612 #2617]: #2618
-#2622 := [monotonicity #2619]: #2621
-#2640 := [monotonicity #2622 #2637]: #2639
-#2643 := [monotonicity #2640]: #2642
-#2646 := [quant-intro #2643]: #2645
-#2605 := (iff #1997 #100)
-#2606 := [rewrite]: #2605
-#3014 := [monotonicity #2606 #2646 #2686 #3011]: #3013
-#3019 := [trans #3014 #3017]: #3018
-#2603 := (iff #1992 #2600)
-#2566 := (and #1973 #2560)
-#2597 := (and #2566 #2594)
-#2601 := (iff #2597 #2600)
+#2638 := [trans #2629 #2636]: #2637
+#2656 := [monotonicity #2638 #2653]: #2655
+#2659 := [monotonicity #2656]: #2658
+#2662 := [quant-intro #2659]: #2661
+#2621 := (iff #1998 #2620)
+#2618 := (iff #1995 #2617)
+#2615 := (iff #1990 #2614)
+#2612 := (iff #1984 #2609)
+#2599 := (+ #1980 #1982)
+#2600 := (+ #1226 #2599)
+#2603 := (= #2600 0::Int)
+#2610 := (iff #2603 #2609)
+#2611 := [rewrite]: #2610
+#2604 := (iff #1984 #2603)
+#2601 := (= #1983 #2600)
 #2602 := [rewrite]: #2601
-#2598 := (iff #1992 #2597)
-#2595 := (iff #1988 #2594)
-#2592 := (iff #1985 #2591)
-#2589 := (iff #1969 #2588)
-#2586 := (iff #1965 #2585)
-#2583 := (= #1964 #2582)
-#2584 := [rewrite]: #2583
-#2587 := [monotonicity #2584]: #2586
-#2590 := [monotonicity #2587]: #2589
-#2593 := [monotonicity #2590]: #2592
-#2596 := [quant-intro #2593]: #2595
-#2579 := (iff #1982 #2566)
-#2571 := (not #2566)
-#2574 := (not #2571)
-#2577 := (iff #2574 #2566)
+#2605 := [monotonicity #2602]: #2604
+#2613 := [trans #2605 #2611]: #2612
+#2597 := (iff #1987 #2596)
+#2594 := (iff #1986 #2591)
+#2583 := (+ #1226 #1982)
+#2586 := (>= #2583 0::Int)
+#2592 := (iff #2586 #2591)
+#2593 := [rewrite]: #2592
+#2587 := (iff #1986 #2586)
+#2584 := (= #1985 #2583)
+#2585 := [rewrite]: #2584
+#2588 := [monotonicity #2585]: #2587
+#2595 := [trans #2588 #2593]: #2594
+#2598 := [monotonicity #2595]: #2597
+#2616 := [monotonicity #2598 #2613]: #2615
+#2619 := [monotonicity #2616]: #2618
+#2622 := [quant-intro #2619]: #2621
+#2581 := (iff #1973 #100)
+#2582 := [rewrite]: #2581
+#2990 := [monotonicity #2582 #2622 #2662 #2987]: #2989
+#2995 := [trans #2990 #2993]: #2994
+#2579 := (iff #1968 #2576)
+#2542 := (and #1949 #2536)
+#2573 := (and #2542 #2570)
+#2577 := (iff #2573 #2576)
 #2578 := [rewrite]: #2577
-#2575 := (iff #1982 #2574)
-#2572 := (iff #1977 #2571)
-#2569 := (iff #1976 #2566)
-#2563 := (and #2560 #1973)
-#2567 := (iff #2563 #2566)
-#2568 := [rewrite]: #2567
-#2564 := (iff #1976 #2563)
-#2561 := (iff #1975 #2560)
-#2558 := (iff #1974 #2557)
-#2559 := [rewrite]: #2558
-#2562 := [monotonicity #2559]: #2561
-#2565 := [monotonicity #2562]: #2564
-#2570 := [trans #2565 #2568]: #2569
-#2573 := [monotonicity #2570]: #2572
-#2576 := [monotonicity #2573]: #2575
-#2580 := [trans #2576 #2578]: #2579
-#2599 := [monotonicity #2580 #2596]: #2598
-#2604 := [trans #2599 #2602]: #2603
-#3022 := [monotonicity #2604 #3019]: #3021
-#3025 := [monotonicity #3022]: #3024
-#2555 := (iff #1946 #2554)
-#2552 := (iff #1945 #2551)
-#2549 := (iff #1938 #2548)
-#2546 := (iff #1937 #2545)
-#2547 := [rewrite]: #2546
-#2550 := [monotonicity #2547]: #2549
-#2543 := (iff #1944 #2542)
-#2540 := (= #1943 #2539)
-#2541 := [rewrite]: #2540
-#2544 := [monotonicity #2541]: #2543
-#2553 := [monotonicity #2544 #2550]: #2552
-#2556 := [monotonicity #2553]: #2555
-#3028 := [monotonicity #2556 #3025]: #3027
-#3031 := [monotonicity #3028]: #3030
-#2536 := (iff #1915 #2535)
-#2533 := (iff #1914 #2532)
-#2530 := (iff #1906 #2527)
-#2519 := (+ #1903 #1904)
-#2522 := (>= #2519 0::Int)
-#2528 := (iff #2522 #2527)
-#2529 := [rewrite]: #2528
-#2523 := (iff #1906 #2522)
-#2520 := (= #1905 #2519)
-#2521 := [rewrite]: #2520
-#2524 := [monotonicity #2521]: #2523
-#2531 := [trans #2524 #2529]: #2530
-#2517 := (iff #1913 #2516)
-#2514 := (iff #1912 #2513)
-#2515 := [rewrite]: #2514
-#2518 := [monotonicity #2515]: #2517
-#2534 := [monotonicity #2518 #2531]: #2533
-#2537 := [monotonicity #2534]: #2536
-#3034 := [monotonicity #2537 #3031]: #3033
-#3037 := [monotonicity #3034]: #3036
-#3040 := [monotonicity #3037]: #3039
-#2511 := (iff #1851 #71)
-#2512 := [rewrite]: #2511
-#3043 := [monotonicity #2512 #3040]: #3042
-#3046 := [monotonicity #3043]: #3045
-#1827 := (not #1791)
-#2506 := (~ #1827 #2505)
-#2502 := (not #1788)
-#2503 := (~ #2502 #2501)
-#2498 := (not #1785)
-#2499 := (~ #2498 #2497)
-#2494 := (not #1782)
-#2495 := (~ #2494 #2493)
-#2490 := (not #1779)
-#2491 := (~ #2490 #2489)
-#2486 := (not #1776)
-#2487 := (~ #2486 #2485)
-#2482 := (not #1773)
-#2483 := (~ #2482 #2481)
-#2478 := (not #1770)
+#2574 := (iff #1968 #2573)
+#2571 := (iff #1964 #2570)
+#2568 := (iff #1961 #2567)
+#2565 := (iff #1945 #2564)
+#2562 := (iff #1941 #2561)
+#2559 := (= #1940 #2558)
+#2560 := [rewrite]: #2559
+#2563 := [monotonicity #2560]: #2562
+#2566 := [monotonicity #2563]: #2565
+#2569 := [monotonicity #2566]: #2568
+#2572 := [quant-intro #2569]: #2571
+#2555 := (iff #1958 #2542)
+#2547 := (not #2542)
+#2550 := (not #2547)
+#2553 := (iff #2550 #2542)
+#2554 := [rewrite]: #2553
+#2551 := (iff #1958 #2550)
+#2548 := (iff #1953 #2547)
+#2545 := (iff #1952 #2542)
+#2539 := (and #2536 #1949)
+#2543 := (iff #2539 #2542)
+#2544 := [rewrite]: #2543
+#2540 := (iff #1952 #2539)
+#2537 := (iff #1951 #2536)
+#2538 := [monotonicity #2535]: #2537
+#2541 := [monotonicity #2538]: #2540
+#2546 := [trans #2541 #2544]: #2545
+#2549 := [monotonicity #2546]: #2548
+#2552 := [monotonicity #2549]: #2551
+#2556 := [trans #2552 #2554]: #2555
+#2575 := [monotonicity #2556 #2572]: #2574
+#2580 := [trans #2575 #2578]: #2579
+#2998 := [monotonicity #2580 #2995]: #2997
+#3001 := [monotonicity #2998]: #3000
+#2531 := (iff #1922 #2530)
+#2528 := (iff #1921 #2527)
+#2525 := (iff #1914 #2524)
+#2522 := (iff #1913 #2521)
+#2523 := [rewrite]: #2522
+#2526 := [monotonicity #2523]: #2525
+#2519 := (iff #1920 #2518)
+#2516 := (= #1919 #2515)
+#2517 := [rewrite]: #2516
+#2520 := [monotonicity #2517]: #2519
+#2529 := [monotonicity #2520 #2526]: #2528
+#2532 := [monotonicity #2529]: #2531
+#3004 := [monotonicity #2532 #3001]: #3003
+#3007 := [monotonicity #3004]: #3006
+#2512 := (iff #1891 #2511)
+#2509 := (iff #1890 #2508)
+#2506 := (iff #1882 #2503)
+#2495 := (+ #1879 #1880)
+#2498 := (>= #2495 0::Int)
+#2504 := (iff #2498 #2503)
+#2505 := [rewrite]: #2504
+#2499 := (iff #1882 #2498)
+#2496 := (= #1881 #2495)
+#2497 := [rewrite]: #2496
+#2500 := [monotonicity #2497]: #2499
+#2507 := [trans #2500 #2505]: #2506
+#2493 := (iff #1889 #2492)
+#2490 := (iff #1888 #2489)
+#2491 := [rewrite]: #2490
+#2494 := [monotonicity #2491]: #2493
+#2510 := [monotonicity #2494 #2507]: #2509
+#2513 := [monotonicity #2510]: #2512
+#3010 := [monotonicity #2513 #3007]: #3009
+#3013 := [monotonicity #3010]: #3012
+#3016 := [monotonicity #3013]: #3015
+#2487 := (iff #1827 #71)
+#2488 := [rewrite]: #2487
+#3019 := [monotonicity #2488 #3016]: #3018
+#3022 := [monotonicity #3019]: #3021
+#1803 := (not #1767)
+#2482 := (~ #1803 #2481)
+#2478 := (not #1764)
 #2479 := (~ #2478 #2477)
-#2474 := (not #1767)
+#2474 := (not #1761)
 #2475 := (~ #2474 #2473)
-#2470 := (not #1762)
+#2470 := (not #1758)
 #2471 := (~ #2470 #2469)
-#2466 := (not #1733)
-#2467 := (~ #2466 #1730)
-#2464 := (~ #1730 #1730)
-#2462 := (~ #1727 #1727)
-#2463 := [refl]: #2462
-#2465 := [nnf-pos #2463]: #2464
-#2468 := [nnf-neg #2465]: #2467
-#2459 := (not #1724)
-#2460 := (~ #2459 #1721)
-#2457 := (~ #1721 #1721)
-#2455 := (~ #1716 #1716)
-#2456 := [refl]: #2455
-#2458 := [nnf-pos #2456]: #2457
-#2461 := [nnf-neg #2458]: #2460
-#2452 := (not #1708)
-#2453 := (~ #2452 #1705)
-#2450 := (~ #1705 #1705)
-#2448 := (~ #1702 #1702)
-#2449 := [refl]: #2448
-#2451 := [nnf-pos #2449]: #2450
-#2454 := [nnf-neg #2451]: #2453
-#2445 := (not #1685)
-#2446 := (~ #2445 #2444)
-#2441 := (not #1680)
-#2442 := (~ #2441 #2440)
-#2438 := (~ #1646 #1646)
+#2466 := (not #1755)
+#2467 := (~ #2466 #2465)
+#2462 := (not #1752)
+#2463 := (~ #2462 #2461)
+#2458 := (not #1749)
+#2459 := (~ #2458 #2457)
+#2454 := (not #1746)
+#2455 := (~ #2454 #2453)
+#2450 := (not #1743)
+#2451 := (~ #2450 #2449)
+#2446 := (not #1738)
+#2447 := (~ #2446 #2445)
+#2442 := (not #1709)
+#2443 := (~ #2442 #1706)
+#2440 := (~ #1706 #1706)
+#2438 := (~ #1703 #1703)
 #2439 := [refl]: #2438
-#2435 := (not #1641)
-#2436 := (~ #2435 #1638)
-#2433 := (~ #1638 #1638)
-#2431 := (~ #1633 #1633)
+#2441 := [nnf-pos #2439]: #2440
+#2444 := [nnf-neg #2441]: #2443
+#2435 := (not #1700)
+#2436 := (~ #2435 #1697)
+#2433 := (~ #1697 #1697)
+#2431 := (~ #1692 #1692)
 #2432 := [refl]: #2431
 #2434 := [nnf-pos #2432]: #2433
 #2437 := [nnf-neg #2434]: #2436
-#2428 := (not #1623)
-#2429 := (~ #2428 #1620)
-#2426 := (~ #1620 #1620)
-#2424 := (~ #1617 #1617)
+#2428 := (not #1684)
+#2429 := (~ #2428 #1681)
+#2426 := (~ #1681 #1681)
+#2424 := (~ #1678 #1678)
 #2425 := [refl]: #2424
 #2427 := [nnf-pos #2425]: #2426
 #2430 := [nnf-neg #2427]: #2429
-#2421 := (not #1606)
+#2421 := (not #1661)
 #2422 := (~ #2421 #2420)
-#2417 := (not #1603)
+#2417 := (not #1656)
 #2418 := (~ #2417 #2416)
-#2413 := (not #1600)
-#2414 := (~ #2413 #2412)
-#2409 := (not #1597)
-#2410 := (~ #2409 #2408)
-#2405 := (not #1594)
-#2406 := (~ #2405 #2404)
-#2401 := (not #1591)
-#2402 := (~ #2401 #2400)
-#2397 := (not #1588)
+#2414 := (~ #1622 #1622)
+#2415 := [refl]: #2414
+#2411 := (not #1617)
+#2412 := (~ #2411 #1614)
+#2409 := (~ #1614 #1614)
+#2407 := (~ #1609 #1609)
+#2408 := [refl]: #2407
+#2410 := [nnf-pos #2408]: #2409
+#2413 := [nnf-neg #2410]: #2412
+#2404 := (not #1599)
+#2405 := (~ #2404 #1596)
+#2402 := (~ #1596 #1596)
+#2400 := (~ #1593 #1593)
+#2401 := [refl]: #2400
+#2403 := [nnf-pos #2401]: #2402
+#2406 := [nnf-neg #2403]: #2405
+#2397 := (not #1582)
 #2398 := (~ #2397 #2396)
-#2393 := (not #1585)
+#2393 := (not #1579)
 #2394 := (~ #2393 #2392)
-#2389 := (not #1582)
+#2389 := (not #1576)
 #2390 := (~ #2389 #2388)
-#2385 := (not #1579)
+#2385 := (not #1573)
 #2386 := (~ #2385 #2384)
-#2381 := (not #1576)
+#2381 := (not #1570)
 #2382 := (~ #2381 #2380)
-#2377 := (not #1573)
+#2377 := (not #1567)
 #2378 := (~ #2377 #2376)
-#2358 := (not #1570)
-#2374 := (~ #2358 #2371)
-#2348 := (exists (vars (?v1 S3)) #2347)
-#2356 := (or #2355 #2348)
-#2357 := (not #2356)
-#2372 := (~ #2357 #2371)
-#2368 := (not #2348)
-#2369 := (~ #2368 #2367)
-#2365 := (~ #2364 #2364)
-#2366 := [refl]: #2365
-#2370 := [nnf-neg #2366]: #2369
-#2362 := (~ #2361 #2361)
-#2363 := [refl]: #2362
-#2373 := [nnf-neg #2363 #2370]: #2372
-#2359 := (~ #2358 #2357)
-#2360 := [sk]: #2359
-#2375 := [trans #2360 #2373]: #2374
-#2334 := (not #1533)
-#2335 := (~ #2334 #1530)
-#2332 := (~ #1530 #1530)
-#2330 := (~ #1527 #1527)
-#2331 := [refl]: #2330
-#2333 := [nnf-pos #2331]: #2332
-#2336 := [nnf-neg #2333]: #2335
-#2379 := [nnf-neg #2336 #2375]: #2378
-#2326 := (~ #1533 #2325)
-#2327 := [sk]: #2326
-#2383 := [nnf-neg #2327 #2379]: #2382
-#2303 := (not #1509)
-#2304 := (~ #2303 #1506)
-#2301 := (~ #1506 #1506)
-#2299 := (~ #1501 #1501)
-#2300 := [refl]: #2299
-#2302 := [nnf-pos #2300]: #2301
-#2305 := [nnf-neg #2302]: #2304
-#2387 := [nnf-neg #2305 #2383]: #2386
-#2295 := (~ #1509 #2294)
-#2296 := [sk]: #2295
-#2391 := [nnf-neg #2296 #2387]: #2390
-#2276 := (not #1490)
-#2277 := (~ #2276 #1487)
-#2274 := (~ #1487 #1487)
-#2272 := (~ #1484 #1484)
-#2273 := [refl]: #2272
-#2275 := [nnf-pos #2273]: #2274
-#2278 := [nnf-neg #2275]: #2277
-#2395 := [nnf-neg #2278 #2391]: #2394
-#2268 := (~ #1490 #2267)
-#2269 := [sk]: #2268
-#2399 := [nnf-neg #2269 #2395]: #2398
-#2262 := (~ #2261 #2261)
-#2263 := [refl]: #2262
-#2403 := [nnf-neg #2263 #2399]: #2402
-#2259 := (~ #1481 #1481)
-#2260 := [refl]: #2259
-#2407 := [nnf-neg #2260 #2403]: #2406
-#2256 := (not #944)
-#2257 := (~ #2256 #810)
-#2254 := (~ #810 #810)
-#2252 := (~ #805 #805)
-#2253 := [refl]: #2252
-#2255 := [nnf-pos #2253]: #2254
-#2258 := [nnf-neg #2255]: #2257
-#2411 := [nnf-neg #2258 #2407]: #2410
-#2248 := (~ #944 #2247)
-#2249 := [sk]: #2248
-#2415 := [nnf-neg #2249 #2411]: #2414
-#2236 := (not #1476)
-#2237 := (~ #2236 #1473)
-#2234 := (~ #1473 #1473)
-#2232 := (~ #1468 #1468)
-#2233 := [refl]: #2232
-#2235 := [nnf-pos #2233]: #2234
-#2238 := [nnf-neg #2235]: #2237
-#2419 := [nnf-neg #2238 #2415]: #2418
-#2228 := (~ #1476 #2227)
-#2229 := [sk]: #2228
-#2423 := [nnf-neg #2229 #2419]: #2422
-#2218 := (not #1465)
-#2219 := (~ #2218 #1462)
-#2216 := (~ #1462 #1462)
-#2214 := (~ #1457 #1457)
-#2215 := [refl]: #2214
-#2217 := [nnf-pos #2215]: #2216
-#2220 := [nnf-neg #2217]: #2219
-#2211 := (not #1656)
-#2212 := (~ #2211 #2206)
-#2207 := (~ #1415 #2206)
-#2208 := [sk]: #2207
-#2213 := [nnf-neg #2208]: #2212
-#2195 := (~ #756 #756)
-#2196 := [refl]: #2195
-#2193 := (~ #2192 #2192)
-#2194 := [refl]: #2193
-#2443 := [nnf-neg #2194 #2196 #2213 #2220 #2423 #2430 #2437 #2439]: #2442
-#2189 := (not #1433)
-#2190 := (~ #2189 #2188)
-#2186 := (~ #1656 #2185)
-#2183 := (~ #2182 #2182)
-#2184 := [refl]: #2183
-#2187 := [nnf-neg #2184]: #2186
-#2179 := (not #1404)
-#2180 := (~ #2179 #2178)
-#2175 := (not #1401)
-#2176 := (~ #2175 #2174)
-#2171 := (not #1398)
-#2172 := (~ #2171 #2170)
-#2167 := (not #1393)
-#2168 := (~ #2167 #2166)
-#2163 := (not #1385)
-#2164 := (~ #2163 #1382)
-#2161 := (~ #1382 #1382)
-#2159 := (~ #1379 #1379)
+#2373 := (not #1564)
+#2374 := (~ #2373 #2372)
+#2369 := (not #1561)
+#2370 := (~ #2369 #2368)
+#2365 := (not #1558)
+#2366 := (~ #2365 #2364)
+#2361 := (not #1555)
+#2362 := (~ #2361 #2360)
+#2357 := (not #1552)
+#2358 := (~ #2357 #2356)
+#2353 := (not #1549)
+#2354 := (~ #2353 #2352)
+#2334 := (not #1546)
+#2350 := (~ #2334 #2347)
+#2324 := (exists (vars (?v1 S2)) #2323)
+#2332 := (or #2331 #2324)
+#2333 := (not #2332)
+#2348 := (~ #2333 #2347)
+#2344 := (not #2324)
+#2345 := (~ #2344 #2343)
+#2341 := (~ #2340 #2340)
+#2342 := [refl]: #2341
+#2346 := [nnf-neg #2342]: #2345
+#2338 := (~ #2337 #2337)
+#2339 := [refl]: #2338
+#2349 := [nnf-neg #2339 #2346]: #2348
+#2335 := (~ #2334 #2333)
+#2336 := [sk]: #2335
+#2351 := [trans #2336 #2349]: #2350
+#2310 := (not #1509)
+#2311 := (~ #2310 #1506)
+#2308 := (~ #1506 #1506)
+#2306 := (~ #1503 #1503)
+#2307 := [refl]: #2306
+#2309 := [nnf-pos #2307]: #2308
+#2312 := [nnf-neg #2309]: #2311
+#2355 := [nnf-neg #2312 #2351]: #2354
+#2302 := (~ #1509 #2301)
+#2303 := [sk]: #2302
+#2359 := [nnf-neg #2303 #2355]: #2358
+#2279 := (not #1485)
+#2280 := (~ #2279 #1482)
+#2277 := (~ #1482 #1482)
+#2275 := (~ #1477 #1477)
+#2276 := [refl]: #2275
+#2278 := [nnf-pos #2276]: #2277
+#2281 := [nnf-neg #2278]: #2280
+#2363 := [nnf-neg #2281 #2359]: #2362
+#2271 := (~ #1485 #2270)
+#2272 := [sk]: #2271
+#2367 := [nnf-neg #2272 #2363]: #2366
+#2252 := (not #1466)
+#2253 := (~ #2252 #1463)
+#2250 := (~ #1463 #1463)
+#2248 := (~ #1460 #1460)
+#2249 := [refl]: #2248
+#2251 := [nnf-pos #2249]: #2250
+#2254 := [nnf-neg #2251]: #2253
+#2371 := [nnf-neg #2254 #2367]: #2370
+#2244 := (~ #1466 #2243)
+#2245 := [sk]: #2244
+#2375 := [nnf-neg #2245 #2371]: #2374
+#2238 := (~ #2237 #2237)
+#2239 := [refl]: #2238
+#2379 := [nnf-neg #2239 #2375]: #2378
+#2235 := (~ #1457 #1457)
+#2236 := [refl]: #2235
+#2383 := [nnf-neg #2236 #2379]: #2382
+#2232 := (not #920)
+#2233 := (~ #2232 #786)
+#2230 := (~ #786 #786)
+#2228 := (~ #781 #781)
+#2229 := [refl]: #2228
+#2231 := [nnf-pos #2229]: #2230
+#2234 := [nnf-neg #2231]: #2233
+#2387 := [nnf-neg #2234 #2383]: #2386
+#2224 := (~ #920 #2223)
+#2225 := [sk]: #2224
+#2391 := [nnf-neg #2225 #2387]: #2390
+#2212 := (not #1452)
+#2213 := (~ #2212 #1449)
+#2210 := (~ #1449 #1449)
+#2208 := (~ #1444 #1444)
+#2209 := [refl]: #2208
+#2211 := [nnf-pos #2209]: #2210
+#2214 := [nnf-neg #2211]: #2213
+#2395 := [nnf-neg #2214 #2391]: #2394
+#2204 := (~ #1452 #2203)
+#2205 := [sk]: #2204
+#2399 := [nnf-neg #2205 #2395]: #2398
+#2194 := (not #1441)
+#2195 := (~ #2194 #1438)
+#2192 := (~ #1438 #1438)
+#2190 := (~ #1433 #1433)
+#2191 := [refl]: #2190
+#2193 := [nnf-pos #2191]: #2192
+#2196 := [nnf-neg #2193]: #2195
+#2187 := (not #1632)
+#2188 := (~ #2187 #2182)
+#2183 := (~ #1391 #2182)
+#2184 := [sk]: #2183
+#2189 := [nnf-neg #2184]: #2188
+#2171 := (~ #732 #732)
+#2172 := [refl]: #2171
+#2169 := (~ #2168 #2168)
+#2170 := [refl]: #2169
+#2419 := [nnf-neg #2170 #2172 #2189 #2196 #2399 #2406 #2413 #2415]: #2418
+#2165 := (not #1409)
+#2166 := (~ #2165 #2164)
+#2162 := (~ #1632 #2161)
+#2159 := (~ #2158 #2158)
 #2160 := [refl]: #2159
-#2162 := [nnf-pos #2160]: #2161
-#2165 := [nnf-neg #2162]: #2164
-#2157 := (~ #2156 #2156)
-#2158 := [refl]: #2157
-#2169 := [nnf-neg #2158 #2165]: #2168
-#2152 := (~ #1385 #2151)
-#2153 := [sk]: #2152
-#2173 := [nnf-neg #2153 #2169]: #2172
-#2127 := (not #1367)
-#2128 := (~ #2127 #2124)
-#2125 := (~ #1364 #2124)
-#2122 := (~ #1361 #2121)
-#2117 := (~ #1358 #2116)
-#2118 := [sk]: #2117
-#2105 := (~ #1342 #1342)
-#2106 := [refl]: #2105
-#2123 := [monotonicity #2106 #2118]: #2122
-#2126 := [nnf-pos #2123]: #2125
-#2129 := [nnf-neg #2126]: #2128
-#2177 := [nnf-neg #2129 #2173]: #2176
-#2103 := (~ #1367 #2100)
-#2078 := (exists (vars (?v1 S3)) #2077)
-#2086 := (or #2085 #2078)
-#2087 := (not #2086)
-#2101 := (~ #2087 #2100)
-#2097 := (not #2078)
-#2098 := (~ #2097 #2096)
-#2094 := (~ #2093 #2093)
-#2095 := [refl]: #2094
-#2099 := [nnf-neg #2095]: #2098
-#2091 := (~ #2090 #2090)
-#2092 := [refl]: #2091
-#2102 := [nnf-neg #2092 #2099]: #2101
-#2088 := (~ #1367 #2087)
-#2089 := [sk]: #2088
-#2104 := [trans #2089 #2102]: #2103
-#2181 := [nnf-neg #2104 #2177]: #2180
-#2065 := (~ #2064 #2064)
-#2066 := [refl]: #2065
-#2062 := (~ #2061 #2061)
-#2063 := [refl]: #2062
-#2059 := (~ #2058 #2058)
-#2060 := [refl]: #2059
-#2056 := (~ #2055 #2055)
-#2057 := [refl]: #2056
-#2191 := [nnf-neg #2057 #2060 #2063 #2066 #2181 #2187]: #2190
-#2447 := [nnf-neg #2191 #2443]: #2446
-#2052 := (not #1330)
-#2053 := (~ #2052 #2049)
-#2050 := (~ #1327 #2049)
-#2047 := (~ #1324 #2046)
-#2042 := (~ #1321 #2041)
-#2043 := [sk]: #2042
-#2028 := (~ #1297 #1297)
-#2029 := [refl]: #2028
-#2048 := [monotonicity #2029 #2043]: #2047
-#2051 := [nnf-pos #2048]: #2050
-#2054 := [nnf-neg #2051]: #2053
-#2025 := (not #1741)
-#2026 := (~ #2025 #2022)
-#2023 := (~ #1285 #2022)
-#2020 := (~ #1282 #2019)
-#2015 := (~ #1279 #2014)
-#2016 := [sk]: #2015
-#2000 := (~ #1259 #1259)
-#2001 := [refl]: #2000
-#2021 := [monotonicity #2001 #2016]: #2020
-#2024 := [nnf-pos #2021]: #2023
-#2027 := [nnf-neg #2024]: #2026
-#1998 := (~ #1997 #1997)
-#1999 := [refl]: #1998
-#2472 := [nnf-neg #1999 #2027 #2054 #2447 #2454 #2461 #2468]: #2471
-#1995 := (~ #1741 #1992)
-#1970 := (exists (vars (?v1 S3)) #1969)
-#1978 := (or #1977 #1970)
-#1979 := (not #1978)
-#1993 := (~ #1979 #1992)
-#1989 := (not #1970)
-#1990 := (~ #1989 #1988)
-#1986 := (~ #1985 #1985)
-#1987 := [refl]: #1986
-#1991 := [nnf-neg #1987]: #1990
-#1983 := (~ #1982 #1982)
-#1984 := [refl]: #1983
-#1994 := [nnf-neg #1984 #1991]: #1993
-#1980 := (~ #1741 #1979)
-#1981 := [sk]: #1980
-#1996 := [trans #1981 #1994]: #1995
-#2476 := [nnf-neg #1996 #2472]: #2475
-#1955 := (not #1247)
-#1956 := (~ #1955 #1244)
-#1953 := (~ #1244 #1244)
-#1951 := (~ #1241 #1241)
-#1952 := [refl]: #1951
-#1954 := [nnf-pos #1952]: #1953
-#1957 := [nnf-neg #1954]: #1956
-#2480 := [nnf-neg #1957 #2476]: #2479
-#1947 := (~ #1247 #1946)
-#1948 := [sk]: #1947
-#2484 := [nnf-neg #1948 #2480]: #2483
-#1924 := (not #1216)
-#1925 := (~ #1924 #1213)
-#1922 := (~ #1213 #1213)
-#1920 := (~ #1208 #1208)
-#1921 := [refl]: #1920
-#1923 := [nnf-pos #1921]: #1922
-#1926 := [nnf-neg #1923]: #1925
-#2488 := [nnf-neg #1926 #2484]: #2487
-#1916 := (~ #1216 #1915)
-#1917 := [sk]: #1916
-#2492 := [nnf-neg #1917 #2488]: #2491
-#1897 := (not #1196)
-#1898 := (~ #1897 #1193)
-#1895 := (~ #1193 #1193)
-#1893 := (~ #1192 #1192)
-#1894 := [refl]: #1893
-#1896 := [nnf-pos #1894]: #1895
-#1899 := [nnf-neg #1896]: #1898
-#2496 := [nnf-neg #1899 #2492]: #2495
-#1889 := (~ #1196 #1888)
-#1890 := [sk]: #1889
-#2500 := [nnf-neg #1890 #2496]: #2499
-#1852 := (~ #1851 #1851)
-#1884 := [refl]: #1852
-#2504 := [nnf-neg #1884 #2500]: #2503
-#1882 := (~ #1187 #1187)
-#1883 := [refl]: #1882
-#2507 := [nnf-neg #1883 #2504]: #2506
-#1828 := [not-or-elim #1824]: #1827
-#2508 := [mp~ #1828 #2507]: #2505
-#2509 := [mp #2508 #3046]: #3044
-#3688 := [mp #2509 #3687]: #3685
-#4595 := [mp #3688 #4594]: #4592
-#6487 := [unit-resolution #4595 #5311]: #4589
-#3934 := (or #4586 #4580)
-#3935 := [def-axiom]: #3934
-#6488 := [unit-resolution #3935 #6487]: #4580
-#6489 := (or #4583 #4577)
-#5098 := [hypothesis]: #1888
-#5097 := (<= #1886 0::Int)
-#4712 := (or #5097 #1887)
-#5130 := [th-lemma arith farkas 1 1]: #4712
-#5131 := [unit-resolution #5130 #5098]: #5097
-#5090 := (not #5097)
-#5105 := (or #5090 #1887)
-#354 := (<= f8 0::Int)
-#355 := (not #354)
-#46 := (< 0::Int f8)
-#356 := (iff #46 #355)
-#357 := [rewrite]: #356
-#350 := [asserted]: #46
-#358 := [mp #350 #357]: #355
-#4709 := (* -1::Int #1886)
-#4710 := (+ f8 #4709)
-#4711 := (<= #4710 0::Int)
-#3924 := (= f8 #1886)
-#3903 := (= f10 ?v0!0)
-#4902 := (not #3903)
-#4899 := (= #1886 0::Int)
-#5099 := (not #4899)
-#5100 := (or #5099 #1887)
-#5101 := [th-lemma arith triangle-eq]: #5100
-#5081 := [unit-resolution #5101 #5098]: #5099
-#4908 := (or #4775 #4902 #4899)
-#3923 := (= ?v0!0 f10)
-#4900 := (not #3923)
-#4901 := (or #4900 #4899)
-#4639 := (or #4775 #4901)
-#5094 := (iff #4639 #4908)
-#4706 := (or #4902 #4899)
-#4925 := (or #4775 #4706)
-#4971 := (iff #4925 #4908)
-#5093 := [rewrite]: #4971
-#4969 := (iff #4639 #4925)
-#4707 := (iff #4901 #4706)
-#4905 := (iff #4900 #4902)
-#3905 := (iff #3923 #3903)
-#3906 := [rewrite]: #3905
-#4906 := [monotonicity #3906]: #4905
-#4774 := [monotonicity #4906]: #4707
-#4970 := [monotonicity #4774]: #4969
-#5095 := [trans #4970 #5093]: #5094
-#4922 := [quant-inst #1885]: #4639
-#5096 := [mp #4922 #5095]: #4908
-#5082 := [unit-resolution #5096 #4601 #5081]: #4902
-#3918 := (or #3903 #3924)
-#4210 := (forall (vars (?v0 S3)) (:pat #4209) #445)
-#4213 := (iff #450 #4210)
-#4211 := (iff #445 #445)
-#4212 := [refl]: #4211
-#4214 := [quant-intro #4212]: #4213
-#1847 := (~ #450 #450)
-#1876 := (~ #445 #445)
-#1877 := [refl]: #1876
-#1848 := [nnf-pos #1877]: #1847
-#1825 := [not-or-elim #1824]: #450
-#1878 := [mp~ #1825 #1848]: #450
-#4215 := [mp #1878 #4214]: #4210
-#3914 := (not #4210)
-#3907 := (or #3914 #3903 #3924)
-#3913 := (or #3923 #3924)
-#3915 := (or #3914 #3913)
-#4653 := (iff #3915 #3907)
-#3900 := (or #3914 #3918)
-#4637 := (iff #3900 #3907)
-#4652 := [rewrite]: #4637
-#4635 := (iff #3915 #3900)
-#3909 := (iff #3913 #3918)
-#3910 := [monotonicity #3906]: #3909
-#4636 := [monotonicity #3910]: #4635
-#4634 := [trans #4636 #4652]: #4653
-#3898 := [quant-inst #1885]: #3915
-#4708 := [mp #3898 #4634]: #3907
-#5083 := [unit-resolution #4708 #4215]: #3918
-#5084 := [unit-resolution #5083 #5082]: #3924
-#5085 := (not #3924)
-#5080 := (or #5085 #4711)
-#5086 := [th-lemma arith triangle-eq]: #5080
-#5087 := [unit-resolution #5086 #5084]: #4711
-#5088 := [hypothesis]: #5097
-#5089 := [th-lemma arith farkas 1 -1 1 #5088 #5087 #358]: false
-#5106 := [lemma #5089]: #5105
-#5132 := [unit-resolution #5106 #5131 #5098]: false
-#5133 := [lemma #5132]: #1887
-#3929 := (or #4583 #1888 #4577)
+#2163 := [nnf-neg #2160]: #2162
+#2155 := (not #1380)
+#2156 := (~ #2155 #2154)
+#2151 := (not #1377)
+#2152 := (~ #2151 #2150)
+#2147 := (not #1374)
+#2148 := (~ #2147 #2146)
+#2143 := (not #1369)
+#2144 := (~ #2143 #2142)
+#2139 := (not #1361)
+#2140 := (~ #2139 #1358)
+#2137 := (~ #1358 #1358)
+#2135 := (~ #1355 #1355)
+#2136 := [refl]: #2135
+#2138 := [nnf-pos #2136]: #2137
+#2141 := [nnf-neg #2138]: #2140
+#2133 := (~ #2132 #2132)
+#2134 := [refl]: #2133
+#2145 := [nnf-neg #2134 #2141]: #2144
+#2128 := (~ #1361 #2127)
+#2129 := [sk]: #2128
+#2149 := [nnf-neg #2129 #2145]: #2148
+#2103 := (not #1343)
+#2104 := (~ #2103 #2100)
+#2101 := (~ #1340 #2100)
+#2098 := (~ #1337 #2097)
+#2093 := (~ #1334 #2092)
+#2094 := [sk]: #2093
+#2081 := (~ #1318 #1318)
+#2082 := [refl]: #2081
+#2099 := [monotonicity #2082 #2094]: #2098
+#2102 := [nnf-pos #2099]: #2101
+#2105 := [nnf-neg #2102]: #2104
+#2153 := [nnf-neg #2105 #2149]: #2152
+#2079 := (~ #1343 #2076)
+#2054 := (exists (vars (?v1 S2)) #2053)
+#2062 := (or #2061 #2054)
+#2063 := (not #2062)
+#2077 := (~ #2063 #2076)
+#2073 := (not #2054)
+#2074 := (~ #2073 #2072)
+#2070 := (~ #2069 #2069)
+#2071 := [refl]: #2070
+#2075 := [nnf-neg #2071]: #2074
+#2067 := (~ #2066 #2066)
+#2068 := [refl]: #2067
+#2078 := [nnf-neg #2068 #2075]: #2077
+#2064 := (~ #1343 #2063)
+#2065 := [sk]: #2064
+#2080 := [trans #2065 #2078]: #2079
+#2157 := [nnf-neg #2080 #2153]: #2156
+#2041 := (~ #2040 #2040)
+#2042 := [refl]: #2041
+#2038 := (~ #2037 #2037)
+#2039 := [refl]: #2038
+#2035 := (~ #2034 #2034)
+#2036 := [refl]: #2035
+#2032 := (~ #2031 #2031)
+#2033 := [refl]: #2032
+#2167 := [nnf-neg #2033 #2036 #2039 #2042 #2157 #2163]: #2166
+#2423 := [nnf-neg #2167 #2419]: #2422
+#2028 := (not #1306)
+#2029 := (~ #2028 #2025)
+#2026 := (~ #1303 #2025)
+#2023 := (~ #1300 #2022)
+#2018 := (~ #1297 #2017)
+#2019 := [sk]: #2018
+#2004 := (~ #1273 #1273)
+#2005 := [refl]: #2004
+#2024 := [monotonicity #2005 #2019]: #2023
+#2027 := [nnf-pos #2024]: #2026
+#2030 := [nnf-neg #2027]: #2029
+#2001 := (not #1717)
+#2002 := (~ #2001 #1998)
+#1999 := (~ #1261 #1998)
+#1996 := (~ #1258 #1995)
+#1991 := (~ #1255 #1990)
+#1992 := [sk]: #1991
+#1976 := (~ #1235 #1235)
+#1977 := [refl]: #1976
+#1997 := [monotonicity #1977 #1992]: #1996
+#2000 := [nnf-pos #1997]: #1999
+#2003 := [nnf-neg #2000]: #2002
+#1974 := (~ #1973 #1973)
+#1975 := [refl]: #1974
+#2448 := [nnf-neg #1975 #2003 #2030 #2423 #2430 #2437 #2444]: #2447
+#1971 := (~ #1717 #1968)
+#1946 := (exists (vars (?v1 S2)) #1945)
+#1954 := (or #1953 #1946)
+#1955 := (not #1954)
+#1969 := (~ #1955 #1968)
+#1965 := (not #1946)
+#1966 := (~ #1965 #1964)
+#1962 := (~ #1961 #1961)
+#1963 := [refl]: #1962
+#1967 := [nnf-neg #1963]: #1966
+#1959 := (~ #1958 #1958)
+#1960 := [refl]: #1959
+#1970 := [nnf-neg #1960 #1967]: #1969
+#1956 := (~ #1717 #1955)
+#1957 := [sk]: #1956
+#1972 := [trans #1957 #1970]: #1971
+#2452 := [nnf-neg #1972 #2448]: #2451
+#1931 := (not #1223)
+#1932 := (~ #1931 #1220)
+#1929 := (~ #1220 #1220)
+#1927 := (~ #1217 #1217)
+#1928 := [refl]: #1927
+#1930 := [nnf-pos #1928]: #1929
+#1933 := [nnf-neg #1930]: #1932
+#2456 := [nnf-neg #1933 #2452]: #2455
+#1923 := (~ #1223 #1922)
+#1924 := [sk]: #1923
+#2460 := [nnf-neg #1924 #2456]: #2459
+#1900 := (not #1192)
+#1901 := (~ #1900 #1189)
+#1898 := (~ #1189 #1189)
+#1896 := (~ #1184 #1184)
+#1897 := [refl]: #1896
+#1899 := [nnf-pos #1897]: #1898
+#1902 := [nnf-neg #1899]: #1901
+#2464 := [nnf-neg #1902 #2460]: #2463
+#1892 := (~ #1192 #1891)
+#1893 := [sk]: #1892
+#2468 := [nnf-neg #1893 #2464]: #2467
+#1873 := (not #1172)
+#1874 := (~ #1873 #1169)
+#1871 := (~ #1169 #1169)
+#1869 := (~ #1168 #1168)
+#1870 := [refl]: #1869
+#1872 := [nnf-pos #1870]: #1871
+#1875 := [nnf-neg #1872]: #1874
+#2472 := [nnf-neg #1875 #2468]: #2471
+#1865 := (~ #1172 #1864)
+#1866 := [sk]: #1865
+#2476 := [nnf-neg #1866 #2472]: #2475
+#1828 := (~ #1827 #1827)
+#1860 := [refl]: #1828
+#2480 := [nnf-neg #1860 #2476]: #2479
+#1858 := (~ #1163 #1163)
+#1859 := [refl]: #1858
+#2483 := [nnf-neg #1859 #2480]: #2482
+#1804 := [not-or-elim #1800]: #1803
+#2484 := [mp~ #1804 #2483]: #2481
+#2485 := [mp #2484 #3022]: #3020
+#3664 := [mp #2485 #3663]: #3661
+#4571 := [mp #3664 #4570]: #4568
+#6438 := [unit-resolution #4571 #5593]: #4565
+#3910 := (or #4562 #4556)
+#3911 := [def-axiom]: #3910
+#6439 := [unit-resolution #3911 #6438]: #4556
+#3905 := (or #4559 #1864 #4553)
+#3906 := [def-axiom]: #3905
+#6440 := [unit-resolution #3906 #6439 #5496]: #4553
+#3929 := (or #4550 #4544)
 #3930 := [def-axiom]: #3929
-#6490 := [unit-resolution #3930 #5133]: #6489
-#6491 := [unit-resolution #6490 #6488]: #4577
-#3953 := (or #4574 #4568)
-#3954 := [def-axiom]: #3953
-#6492 := [unit-resolution #3954 #6491]: #4568
-#5808 := [hypothesis]: #1908
-#5321 := (or #5520 #2210)
-#5326 := [quant-inst #1901]: #5321
-#5809 := [unit-resolution #5326 #4222 #5808]: false
-#5810 := [lemma #5809]: #2210
-#3746 := (or #2119 #1908)
-#3833 := [def-axiom]: #3746
-#6493 := [unit-resolution #3833 #5810]: #2119
-#3947 := (or #4571 #2018 #4565)
-#3949 := [def-axiom]: #3947
-#6494 := [unit-resolution #3949 #6493 #6492]: #4565
-#3974 := (or #4562 #4556)
-#3975 := [def-axiom]: #3974
-#6495 := [unit-resolution #3975 #6494]: #4556
-#3970 := (or #4559 #3089 #4553)
-#3971 := [def-axiom]: #3970
-#6496 := [unit-resolution #3971 #6495 #6486]: #4553
-#3984 := (or #4550 #4544)
-#4005 := [def-axiom]: #3984
-#6497 := [unit-resolution #4005 #6496]: #4544
-#5781 := (= f8 #1961)
-#5845 := (not #5781)
-#5843 := [hypothesis]: #4261
-#4150 := (or #4258 #1973)
-#3824 := [def-axiom]: #4150
-#5844 := [unit-resolution #3824 #5843]: #1973
-#5846 := (or #5845 #1972)
-#5847 := [th-lemma arith triangle-eq]: #5846
-#5848 := [unit-resolution #5847 #5844]: #5845
-#3825 := (or #4258 #2560)
-#4157 := [def-axiom]: #3825
-#5849 := [unit-resolution #4157 #5843]: #2560
-#5801 := (or #3914 #2557 #5781)
-#5782 := (or #1974 #5781)
-#5796 := (or #3914 #5782)
-#5660 := (iff #5796 #5801)
-#5798 := (or #2557 #5781)
-#5803 := (or #3914 #5798)
-#5806 := (iff #5803 #5801)
-#5659 := [rewrite]: #5806
-#5804 := (iff #5796 #5803)
-#5799 := (iff #5782 #5798)
-#5800 := [monotonicity #2559]: #5799
-#5805 := [monotonicity #5800]: #5804
-#5661 := [trans #5805 #5659]: #5660
-#5802 := [quant-inst #1958]: #5796
-#5466 := [mp #5802 #5661]: #5801
-#5850 := [unit-resolution #5466 #4215 #5849 #5848]: false
-#5851 := [lemma #5850]: #4258
-#3992 := (or #4547 #4261 #4541)
-#3993 := [def-axiom]: #3992
-#6498 := [unit-resolution #3993 #5851 #6497]: #4541
-#4025 := (or #4538 #4265)
-#4021 := [def-axiom]: #4025
-#7112 := [unit-resolution #4021 #6498]: #4265
-#9544 := (or #4270 #7748)
-#9545 := [quant-inst #2264]: #9544
-#9571 := [unit-resolution #9545 #7112]: #7748
-#7561 := (* -1::Int #7527)
-#7562 := (+ #2265 #7561)
-#9572 := (>= #7562 0::Int)
-#7530 := (= #2265 #7527)
-#10078 := [hypothesis]: #2267
-#11976 := (or #7530 #2266 #6064)
-#9979 := (f5 #7202 ?v0!15)
-#9980 := (f9 #9979)
-#9981 := (* -1::Int #9980)
-#7577 := (f5 f22 ?v0!15)
-#7578 := (f9 #7577)
-#10049 := (+ #7578 #9981)
-#10053 := (>= #10049 0::Int)
-#10048 := (= #7578 #9980)
-#10056 := (= #9980 #7578)
-#10054 := (= #9979 #7577)
-#10055 := [monotonicity #7781]: #10054
-#10057 := [monotonicity #10055]: #10056
-#10058 := [symm #10057]: #10048
-#10059 := (not #10048)
-#10060 := (or #10059 #10053)
-#10061 := [th-lemma arith triangle-eq]: #10060
-#10062 := [unit-resolution #10061 #10058]: #10053
-#7959 := (f5 #6060 #7202)
-#8208 := (f6 #7959)
-#9072 := (f13 f14 #8208)
-#9073 := (* -1::Int #9072)
-#9446 := (+ #6061 #9073)
-#9448 := (>= #9446 0::Int)
-#9852 := (= #6061 #9072)
-#8209 := (= #6060 #8208)
-#8380 := (or #6820 #8209)
-#8381 := [quant-inst #6060 #7202]: #8380
-#9271 := [unit-resolution #8381 #4196]: #8209
-#11938 := [monotonicity #9271]: #9852
-#11936 := (not #9852)
-#11939 := (or #11936 #9448)
-#11940 := [th-lemma arith triangle-eq]: #11939
-#11941 := [unit-resolution #11940 #11938]: #9448
-#10857 := (+ #99 #9073)
-#10869 := (<= #10857 0::Int)
-#10866 := (= #99 #9072)
-#11947 := (= #9072 #99)
-#10688 := (= #8208 f10)
-#7308 := (= #6060 f10)
-#7310 := (= f10 #6060)
-#7289 := (?v1!7 #6060)
-#7301 := (f3 f15 #7289)
-#7302 := (= f1 #7301)
-#7303 := (not #7302)
-#7294 := (f5 #7289 #6060)
-#7295 := (f9 #7294)
-#7296 := (* -1::Int #7295)
-#7290 := (f13 f14 #7289)
-#7291 := (* -1::Int #7290)
-#7297 := (+ #7291 #7296)
-#7298 := (+ #6061 #7297)
-#7299 := (= #7298 0::Int)
-#7300 := (not #7299)
-#7292 := (+ #6061 #7291)
-#7293 := (<= #7292 0::Int)
-#7313 := (or #7293 #7300 #7303)
-#9598 := (or #2266 #6064 #7293)
-#8242 := (not #7293)
-#10063 := [hypothesis]: #8242
-#10101 := (or #7530 #2266 #6064 #7293)
-#9116 := (>= #7290 0::Int)
-#9119 := (or #4270 #9116)
-#9290 := [quant-inst #7289]: #9119
-#10064 := [unit-resolution #9290 #7112]: #9116
-#7552 := (* -1::Int #2265)
-#7603 := (+ #7552 #7578)
-#7604 := (+ #174 #7603)
-#9488 := (<= #7604 0::Int)
-#7607 := (= #7604 0::Int)
-#7582 := (* -1::Int #7578)
-#7586 := (+ f8 #7582)
-#7587 := (<= #7586 0::Int)
-#9501 := (not #7587)
-#7596 := (+ #7561 #7578)
-#7597 := (+ #174 #7596)
-#7598 := (>= #7597 0::Int)
-#7629 := (or #7587 #7598)
-#7632 := (not #7629)
-#10066 := (not #7530)
-#10067 := [hypothesis]: #10066
-#7635 := (or #7530 #7632)
-#5779 := (or #4538 #4529)
-#4713 := (?v1!7 ?v0!8)
-#4989 := (f13 f19 #4713)
-#5002 := (* -1::Int #4989)
-#4714 := (f13 f14 #4713)
-#5222 := (+ #4714 #5002)
-#5227 := (>= #5222 0::Int)
-#5221 := (= #4714 #4989)
-#5711 := (= #4989 #4714)
-#5706 := [hypothesis]: #4526
-#5707 := [hypothesis]: #4541
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-#3982 := [def-axiom]: #4014
-#5708 := [unit-resolution #3982 #5707]: #4532
-#4019 := (or #4535 #4374 #4529)
-#4020 := [def-axiom]: #4019
-#5709 := [unit-resolution #4020 #5708 #5706]: #4374
-#4125 := (or #4371 #623)
-#4126 := [def-axiom]: #4125
-#5710 := [unit-resolution #4126 #5709]: #623
-#5705 := [symm #5710]: #138
-#5712 := [monotonicity #5705]: #5711
-#5713 := [symm #5712]: #5221
-#5714 := (not #5221)
-#5715 := (or #5714 #5227)
-#5728 := [th-lemma arith triangle-eq]: #5715
-#5729 := [unit-resolution #5728 #5713]: #5227
-#4696 := (* -1::Int #4714)
-#4646 := (f13 f14 ?v0!8)
-#4697 := (+ #4646 #4696)
-#4698 := (<= #4697 0::Int)
-#4879 := (not #4698)
-#4705 := (f3 f15 #4713)
-#4776 := (= f1 #4705)
-#4777 := (not #4776)
-#4699 := (f5 #4713 ?v0!8)
-#4700 := (f9 #4699)
-#4695 := (* -1::Int #4700)
-#4781 := (+ #4695 #4696)
-#4782 := (+ #4646 #4781)
-#4764 := (= #4782 0::Int)
-#4767 := (not #4764)
-#4772 := (or #4698 #4767 #4777)
-#4846 := (not #4772)
-#4647 := (* -1::Int #4646)
-#4648 := (+ f8 #4647)
-#4628 := (<= #4648 0::Int)
-#4984 := (not #4628)
-#4127 := (or #4371 #4365)
-#4124 := [def-axiom]: #4127
-#5730 := [unit-resolution #4124 #5709]: #4365
-#4023 := (or #4538 #100)
-#4024 := [def-axiom]: #4023
-#5731 := [unit-resolution #4024 #5707]: #100
-#5732 := (= #157 #99)
-#5727 := [monotonicity #5705]: #5732
-#5733 := [trans #5727 #5731]: #158
-#4137 := (or #4347 #2156)
-#3800 := [def-axiom]: #4137
-#5734 := [unit-resolution #3800 #5733]: #4347
-#4026 := (or #4538 #4273)
-#4006 := [def-axiom]: #4026
-#5735 := [unit-resolution #4006 #5707]: #4273
-#3841 := (or #4371 #4307)
-#4123 := [def-axiom]: #3841
-#5736 := [unit-resolution #4123 #5709]: #4307
-#4967 := (or #3352 #4312 #4278 #714)
-#4940 := [hypothesis]: #3357
-#4140 := (or #3352 #2143)
-#4141 := [def-axiom]: #4140
-#4941 := [unit-resolution #4141 #4940]: #2143
-#4715 := (f13 f14 ?v1!10)
-#4716 := (* -1::Int #4715)
-#4717 := (+ f8 #4716)
-#4718 := (<= #4717 0::Int)
-#4719 := (f3 f15 ?v1!10)
-#4720 := (= f1 #4719)
-#4791 := (not #4720)
-#3828 := (f13 f14 ?v0!11)
-#3829 := (* -1::Int #3828)
-#4793 := (+ #3829 #4715)
-#4794 := (+ #2137 #4793)
-#4797 := (>= #4794 0::Int)
-#4950 := (not #4797)
-#4924 := (+ #2134 #4716)
-#4926 := (>= #4924 0::Int)
-#4923 := (= #2134 #4715)
-#4928 := (= #4715 #2134)
-#4927 := [hypothesis]: #623
-#4929 := [monotonicity #4927]: #4928
-#4930 := [symm #4929]: #4923
-#4931 := (not #4923)
-#4932 := (or #4931 #4926)
-#4933 := [th-lemma arith triangle-eq]: #4932
-#4934 := [unit-resolution #4933 #4930]: #4926
-#4138 := (not #2798)
-#4144 := (or #3352 #4138)
-#3782 := [def-axiom]: #4144
-#4935 := [unit-resolution #3782 #4940]: #4138
-#4917 := (+ #2132 #3829)
-#4921 := (<= #4917 0::Int)
-#4916 := (= #2132 #3828)
-#4938 := (= #3828 #2132)
-#4939 := [monotonicity #4927]: #4938
-#4942 := [symm #4939]: #4916
-#4943 := (not #4916)
-#4944 := (or #4943 #4921)
-#4955 := [th-lemma arith triangle-eq]: #4944
-#4956 := [unit-resolution #4955 #4942]: #4921
-#4952 := (not #4926)
-#4951 := (not #4921)
-#4953 := (or #4950 #4951 #2798 #4952)
-#4945 := [hypothesis]: #4926
-#4946 := [hypothesis]: #4138
-#4947 := [hypothesis]: #4921
-#4948 := [hypothesis]: #4797
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-#4954 := [lemma #4949]: #4953
-#4957 := [unit-resolution #4954 #4956 #4935 #4934]: #4950
-#4960 := (or #4791 #4797)
-#4142 := (or #3352 #2147)
-#4143 := [def-axiom]: #4142
-#4958 := [unit-resolution #4143 #4940]: #2147
-#4959 := [hypothesis]: #4273
-#4808 := (or #4278 #2146 #4791 #4797)
-#4786 := (+ #4715 #3829)
-#4787 := (+ #2137 #4786)
-#4790 := (>= #4787 0::Int)
-#4792 := (or #4791 #2146 #4790)
-#4809 := (or #4278 #4792)
-#4816 := (iff #4809 #4808)
-#4803 := (or #2146 #4791 #4797)
-#4811 := (or #4278 #4803)
-#4814 := (iff #4811 #4808)
-#4815 := [rewrite]: #4814
-#4812 := (iff #4809 #4811)
-#4806 := (iff #4792 #4803)
-#4800 := (or #4791 #2146 #4797)
-#4804 := (iff #4800 #4803)
-#4805 := [rewrite]: #4804
-#4801 := (iff #4792 #4800)
-#4798 := (iff #4790 #4797)
-#4795 := (= #4787 #4794)
-#4796 := [rewrite]: #4795
-#4799 := [monotonicity #4796]: #4798
-#4802 := [monotonicity #4799]: #4801
-#4807 := [trans #4802 #4805]: #4806
-#4813 := [monotonicity #4807]: #4812
-#4817 := [trans #4813 #4815]: #4816
-#4810 := [quant-inst #2131 #2130]: #4809
-#4818 := [mp #4810 #4817]: #4808
-#4961 := [unit-resolution #4818 #4959 #4958]: #4960
-#4962 := [unit-resolution #4961 #4957]: #4791
-#4722 := (or #4718 #4720)
-#4963 := [hypothesis]: #4307
-#4725 := (or #4312 #4718 #4720)
-#4721 := (or #4720 #4718)
-#4726 := (or #4312 #4721)
-#4733 := (iff #4726 #4725)
-#4728 := (or #4312 #4722)
-#4731 := (iff #4728 #4725)
-#4732 := [rewrite]: #4731
-#4729 := (iff #4726 #4728)
-#4723 := (iff #4721 #4722)
-#4724 := [rewrite]: #4723
-#4730 := [monotonicity #4724]: #4729
-#4734 := [trans #4730 #4732]: #4733
-#4727 := [quant-inst #2130]: #4726
-#4735 := [mp #4727 #4734]: #4725
-#4964 := [unit-resolution #4735 #4963]: #4722
-#4965 := [unit-resolution #4964 #4962]: #4718
-#4966 := [th-lemma arith farkas 1 -1 1 #4934 #4965 #4941]: false
-#4968 := [lemma #4966]: #4967
-#5737 := [unit-resolution #4968 #5736 #5735 #5710]: #3352
-#4149 := (or #4356 #4350 #3357)
-#4135 := [def-axiom]: #4149
-#5738 := [unit-resolution #4135 #5737 #5734]: #4356
-#3859 := (or #4359 #4353)
-#3860 := [def-axiom]: #3859
-#5739 := [unit-resolution #3860 #5738]: #4359
-#4129 := (or #4368 #4328 #4362)
-#4133 := [def-axiom]: #4129
-#5740 := [unit-resolution #4133 #5739 #5730]: #4328
-#4161 := (or #4325 #2081)
-#4151 := [def-axiom]: #4161
-#5741 := [unit-resolution #4151 #5740]: #2081
-#4977 := (+ #2068 #4647)
-#4979 := (>= #4977 0::Int)
-#4976 := (= #2068 #4646)
-#5404 := (= #4646 #2068)
-#5742 := [monotonicity #5710]: #5404
-#5743 := [symm #5742]: #4976
-#5407 := (not #4976)
-#5412 := (or #5407 #4979)
-#5413 := [th-lemma arith triangle-eq]: #5412
-#5744 := [unit-resolution #5413 #5743]: #4979
-#4985 := (not #4979)
-#4986 := (or #4984 #4985 #2080)
-#4980 := [hypothesis]: #2081
-#4981 := [hypothesis]: #4628
-#4982 := [hypothesis]: #4979
-#4983 := [th-lemma arith farkas 1 -1 1 #4982 #4981 #4980]: false
-#4987 := [lemma #4983]: #4986
-#5745 := [unit-resolution #4987 #5744 #5741]: #4984
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-#3811 := (or #4325 #2698)
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-#5753 := [unit-resolution #3816 #5740]: #2698
-#4013 := (or #4538 #4298)
-#4008 := [def-axiom]: #4013
-#5754 := [unit-resolution #4008 #5707]: #4298
-#4851 := (or #4303 #2695 #4628 #4846)
-#4701 := (+ #4696 #4695)
-#4702 := (+ #4646 #4701)
-#4703 := (= #4702 0::Int)
-#4704 := (not #4703)
-#4778 := (or #4777 #4704 #4698)
-#4779 := (not #4778)
-#4780 := (or #2082 #4628 #4779)
-#4852 := (or #4303 #4780)
-#4875 := (iff #4852 #4851)
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-#4873 := (iff #4854 #4851)
-#4874 := [rewrite]: #4873
-#4870 := (iff #4852 #4854)
-#4844 := (iff #4780 #4849)
-#4847 := (iff #4779 #4846)
-#4789 := (iff #4778 #4772)
-#4769 := (or #4777 #4767 #4698)
-#4773 := (iff #4769 #4772)
-#4788 := [rewrite]: #4773
-#4770 := (iff #4778 #4769)
-#4768 := (iff #4704 #4767)
-#4765 := (iff #4703 #4764)
-#4783 := (= #4702 #4782)
-#4784 := [rewrite]: #4783
-#4766 := [monotonicity #4784]: #4765
-#4763 := [monotonicity #4766]: #4768
-#4771 := [monotonicity #4763]: #4770
-#4845 := [trans #4771 #4788]: #4789
-#4848 := [monotonicity #4845]: #4847
-#4850 := [monotonicity #2697 #4848]: #4844
-#4872 := [monotonicity #4850]: #4870
-#4876 := [trans #4872 #4874]: #4875
-#4853 := [quant-inst #2067]: #4852
-#4871 := [mp #4853 #4876]: #4851
-#5756 := [unit-resolution #4871 #5754 #5753]: #5755
-#5757 := [unit-resolution #5756 #5745]: #4846
-#4880 := (or #4772 #4879)
-#4881 := [def-axiom]: #4880
-#5758 := [unit-resolution #4881 #5757]: #4879
-#5003 := (+ #2068 #5002)
-#5004 := (<= #5003 0::Int)
-#5016 := (+ #4695 #5002)
-#5017 := (+ #2068 #5016)
-#5018 := (= #5017 0::Int)
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-#5759 := (or #5714 #5226)
-#5760 := [th-lemma arith triangle-eq]: #5759
-#5761 := [unit-resolution #5760 #5713]: #5226
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-#4896 := (or #4772 #4764)
-#4898 := [def-axiom]: #4896
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-#5765 := [unit-resolution #5764 #5762]: #4877
-#4978 := (<= #4977 0::Int)
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-#5349 := (not #4877)
-#5348 := (not #4978)
-#5351 := (or #5040 #5348 #5349 #5350)
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-#5770 := [unit-resolution #5769 #5762]: #4878
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-#5390 := (not #4878)
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-#5029 := (or #4322 #5004 #5023)
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-#4991 := (= #4990 0::Int)
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-#4993 := (+ #4989 #2069)
-#4994 := (>= #4993 0::Int)
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-#5014 := (iff #4991 #5013)
-#5011 := (= #4990 #5010)
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-#4997 := (= #4993 #4996)
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-#5777 := [unit-resolution #5776 #5774]: #5004
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-#7528 := (= #7527 #2265)
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-#7591 := (= #7584 #7590)
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-#9503 := [def-axiom]: #9502
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-#9940 := (= ?v0!15 #7202)
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-#7659 := (f3 f15 ?v0!15)
-#7660 := (= f1 #7659)
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-#5883 := (= f1 #5882)
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-#9937 := (f3 #8433 ?v0!15)
-#9938 := (= f1 #9937)
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-#10 := (:var 1 S1)
-#9 := (:var 2 S3)
-#8 := (:var 3 S2)
-#11 := (f4 #8 #9 #10)
-#13 := (f3 #11 #12)
-#4162 := (pattern #13)
-#17 := (f3 #8 #12)
-#300 := (= f1 #17)
-#297 := (= f1 #10)
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-#303 := (ite #294 #297 #300)
-#291 := (= f1 #13)
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-#4166 := (iff #309 #4163)
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-#4165 := [refl]: #4164
-#4167 := [quant-intro #4165]: #4166
-#1859 := (~ #309 #309)
-#1857 := (~ #306 #306)
-#1858 := [refl]: #1857
-#1860 := [nnf-pos #1858]: #1859
-#18 := (= #17 f1)
-#16 := (= #10 f1)
-#15 := (= #12 #9)
-#19 := (ite #15 #16 #18)
-#14 := (= #13 f1)
-#20 := (iff #14 #19)
-#21 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #20)
-#310 := (iff #21 #309)
-#307 := (iff #20 #306)
-#304 := (iff #19 #303)
-#301 := (iff #18 #300)
-#302 := [rewrite]: #301
-#298 := (iff #16 #297)
-#299 := [rewrite]: #298
-#295 := (iff #15 #294)
-#296 := [rewrite]: #295
-#305 := [monotonicity #296 #299 #302]: #304
-#292 := (iff #14 #291)
-#293 := [rewrite]: #292
-#308 := [monotonicity #293 #305]: #307
-#311 := [quant-intro #308]: #310
-#290 := [asserted]: #21
-#314 := [mp #290 #311]: #309
-#1831 := [mp~ #314 #1860]: #309
-#4168 := [mp #1831 #4167]: #4163
-#6281 := (not #4163)
-#9949 := (or #6281 #9946)
-#9935 := (= #7202 ?v0!15)
-#9936 := (ite #9935 #5883 #7660)
-#9939 := (iff #9938 #9936)
-#9950 := (or #6281 #9939)
-#9952 := (iff #9950 #9949)
-#9954 := (iff #9949 #9949)
-#9955 := [rewrite]: #9954
-#9947 := (iff #9939 #9946)
-#9944 := (iff #9936 #9943)
-#9941 := (iff #9935 #9940)
-#9942 := [rewrite]: #9941
-#9945 := [monotonicity #9942]: #9944
-#9948 := [monotonicity #9945]: #9947
-#9953 := [monotonicity #9948]: #9952
-#9956 := [trans #9953 #9955]: #9952
-#9951 := [quant-inst #104 #7202 #5882 #2264]: #9950
-#9957 := [mp #9951 #9956]: #9949
-#10079 := [unit-resolution #9957 #4168]: #9946
-#9972 := (not #9938)
-#7524 := (f3 f23 ?v0!15)
-#7525 := (= f1 #7524)
-#7526 := (not #7525)
-#10088 := (iff #7526 #9972)
-#10086 := (iff #7525 #9938)
-#10084 := (iff #9938 #7525)
-#10082 := (= #9937 #7524)
-#9276 := (= #8433 f23)
-#6995 := (= #180 f23)
-#4042 := (or #4526 #181)
-#4043 := [def-axiom]: #4042
-#6989 := [unit-resolution #4043 #6499]: #181
-#6996 := [symm #6989]: #6995
-#9274 := (= #8433 #180)
-#6991 := (= #5882 f1)
-#24 := (:var 0 S1)
-#22 := (:var 2 S2)
-#25 := (f4 #22 #23 #24)
-#4169 := (pattern #25)
-#317 := (= f1 #24)
-#26 := (f3 #25 #23)
-#313 := (= f1 #26)
-#320 := (iff #313 #317)
-#4170 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) (:pat #4169) #320)
-#323 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #320)
-#4173 := (iff #323 #4170)
-#4171 := (iff #320 #320)
-#4172 := [refl]: #4171
-#4174 := [quant-intro #4172]: #4173
-#1833 := (~ #323 #323)
-#1832 := (~ #320 #320)
-#1861 := [refl]: #1832
-#1834 := [nnf-pos #1861]: #1833
-#28 := (= #24 f1)
-#27 := (= #26 f1)
-#29 := (iff #27 #28)
-#30 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1)) #29)
-#324 := (iff #30 #323)
-#321 := (iff #29 #320)
-#318 := (iff #28 #317)
-#319 := [rewrite]: #318
-#315 := (iff #27 #313)
-#316 := [rewrite]: #315
-#322 := [monotonicity #316 #319]: #321
-#325 := [quant-intro #322]: #324
-#312 := [asserted]: #30
-#328 := [mp #312 #325]: #323
-#1862 := [mp~ #328 #1834]: #323
-#4175 := [mp #1862 #4174]: #4170
-#5894 := (not #4170)
-#5895 := (or #5894 #5883)
-#5881 := (= f1 f1)
-#5884 := (iff #5883 #5881)
-#5896 := (or #5894 #5884)
-#5898 := (iff #5896 #5895)
-#5900 := (iff #5895 #5895)
-#5901 := [rewrite]: #5900
-#5892 := (iff #5884 #5883)
-#5887 := (iff #5883 true)
-#5890 := (iff #5887 #5883)
-#5891 := [rewrite]: #5890
-#5888 := (iff #5884 #5887)
-#5885 := (iff #5881 true)
-#5886 := [rewrite]: #5885
-#5889 := [monotonicity #5886]: #5888
-#5893 := [trans #5889 #5891]: #5892
-#5899 := [monotonicity #5893]: #5898
-#5902 := [trans #5899 #5901]: #5898
-#5897 := [quant-inst #104 #170 #4]: #5896
-#5903 := [mp #5897 #5902]: #5895
-#6990 := [unit-resolution #5903 #4175]: #5883
-#6992 := [symm #6990]: #6991
-#9275 := [monotonicity #7781 #6992]: #9274
-#9277 := [trans #9275 #6996]: #9276
-#10083 := [monotonicity #9277]: #10082
-#10085 := [monotonicity #10083]: #10084
-#10087 := [symm #10085]: #10086
-#10089 := [monotonicity #10087]: #10088
-#7536 := (or #7526 #7530)
-#4010 := (or #4526 #4520)
-#4011 := [def-axiom]: #4010
-#7087 := [unit-resolution #4011 #6499]: #4520
-#6302 := (f5 f22 ?v0!13)
-#6303 := (f9 #6302)
-#6328 := (+ #2223 #6303)
-#6329 := (+ #174 #6328)
-#6350 := (>= #6329 0::Int)
-#6332 := (= #6329 0::Int)
-#6307 := (* -1::Int #6303)
-#6311 := (+ f8 #6307)
-#6312 := (<= #6311 0::Int)
-#6379 := (not #6312)
-#6321 := (+ #2839 #6303)
-#6322 := (+ #174 #6321)
-#6323 := (>= #6322 0::Int)
-#6358 := (or #6312 #6323)
-#6361 := (not #6358)
-#6355 := (= #2222 #2224)
-#6480 := (not #6355)
-#6479 := [hypothesis]: #2846
-#6483 := (or #6480 #2841)
-#6484 := [th-lemma arith triangle-eq]: #6483
-#6485 := [unit-resolution #6484 #6479]: #6480
-#6367 := (or #4392 #6355 #6361)
-#6308 := (+ #1444 #6307)
-#6309 := (+ #2224 #6308)
-#6310 := (<= #6309 0::Int)
-#6351 := (or #6312 #6310)
-#6352 := (not #6351)
-#6353 := (= #2224 #2222)
-#6354 := (or #6353 #6352)
-#6368 := (or #4392 #6354)
-#6375 := (iff #6368 #6367)
-#6364 := (or #6355 #6361)
-#6370 := (or #4392 #6364)
-#6373 := (iff #6370 #6367)
-#6374 := [rewrite]: #6373
-#6371 := (iff #6368 #6370)
-#6365 := (iff #6354 #6364)
-#6362 := (iff #6352 #6361)
-#6359 := (iff #6351 #6358)
-#6326 := (iff #6310 #6323)
-#6314 := (+ #2224 #6307)
-#6315 := (+ #1444 #6314)
-#6318 := (<= #6315 0::Int)
-#6324 := (iff #6318 #6323)
-#6325 := [rewrite]: #6324
-#6319 := (iff #6310 #6318)
-#6316 := (= #6309 #6315)
-#6317 := [rewrite]: #6316
-#6320 := [monotonicity #6317]: #6319
-#6327 := [trans #6320 #6325]: #6326
-#6360 := [monotonicity #6327]: #6359
-#6363 := [monotonicity #6360]: #6362
-#6356 := (iff #6353 #6355)
-#6357 := [rewrite]: #6356
-#6366 := [monotonicity #6357 #6363]: #6365
-#6372 := [monotonicity #6366]: #6371
-#6376 := [trans #6372 #6374]: #6375
-#6369 := [quant-inst #2221]: #6368
-#6377 := [mp #6369 #6376]: #6367
-#6501 := [unit-resolution #6377 #6500 #6485]: #6361
-#6380 := (or #6358 #6379)
-#6381 := [def-axiom]: #6380
-#6502 := [unit-resolution #6381 #6501]: #6379
-#6382 := (not #6323)
-#6383 := (or #6358 #6382)
-#6384 := [def-axiom]: #6383
-#6503 := [unit-resolution #6384 #6501]: #6382
-#6335 := (or #6312 #6323 #6332)
-#6338 := (or #4400 #6312 #6323 #6332)
-#6304 := (+ #6303 #2223)
-#6305 := (+ #174 #6304)
-#6306 := (= #6305 0::Int)
-#6313 := (or #6312 #6310 #6306)
-#6339 := (or #4400 #6313)
-#6346 := (iff #6339 #6338)
-#6341 := (or #4400 #6335)
-#6344 := (iff #6341 #6338)
-#6345 := [rewrite]: #6344
-#6342 := (iff #6339 #6341)
-#6336 := (iff #6313 #6335)
-#6333 := (iff #6306 #6332)
-#6330 := (= #6305 #6329)
-#6331 := [rewrite]: #6330
-#6334 := [monotonicity #6331]: #6333
-#6337 := [monotonicity #6327 #6334]: #6336
-#6343 := [monotonicity #6337]: #6342
-#6347 := [trans #6343 #6345]: #6346
-#6340 := [quant-inst #2221]: #6339
-#6348 := [mp #6340 #6347]: #6338
-#6505 := [unit-resolution #6348 #6504]: #6335
-#6506 := [unit-resolution #6505 #6503 #6502]: #6332
-#6507 := (not #6332)
-#6508 := (or #6507 #6350)
-#6509 := [th-lemma arith triangle-eq]: #6508
-#6510 := [unit-resolution #6509 #6506]: #6350
-#6378 := (>= #2840 0::Int)
-#6511 := (or #6378 #2841)
-#6512 := [th-lemma arith farkas 1 1]: #6511
-#6513 := [unit-resolution #6512 #6479]: #6378
-#6514 := [th-lemma arith farkas 1 -1 1 #6513 #6503 #6510]: false
-#6515 := [lemma #6514]: #2841
-#4040 := (or #4523 #2846 #4517)
-#4041 := [def-axiom]: #4040
-#7088 := [unit-resolution #4041 #6515 #7087]: #4517
-#4055 := (or #4514 #4508)
-#4056 := [def-axiom]: #4055
-#7089 := [unit-resolution #4056 #7088]: #4508
-#6870 := (= #174 #2244)
-#6687 := (= f22 ?v0!14)
-#6517 := (f3 f15 ?v0!14)
-#6518 := (= f1 #6517)
-#6688 := (ite #6687 #5883 #6518)
-#6260 := (f4 f15 f22 #5882)
-#6691 := (f3 #6260 ?v0!14)
-#6692 := (= f1 #6691)
-#6694 := (iff #6688 #6692)
-#6697 := (or #6281 #6694)
-#6693 := (iff #6692 #6688)
-#6698 := (or #6281 #6693)
-#6700 := (iff #6698 #6697)
-#6702 := (iff #6697 #6697)
-#6703 := [rewrite]: #6702
-#6695 := (iff #6693 #6694)
-#6696 := [rewrite]: #6695
-#6701 := [monotonicity #6696]: #6700
-#6704 := [trans #6701 #6703]: #6700
-#6699 := [quant-inst #104 #170 #5882 #2239]: #6698
-#6705 := [mp #6699 #6704]: #6697
-#6987 := [unit-resolution #6705 #4168]: #6694
-#7003 := (= #2240 #6691)
-#6999 := (= #6691 #2240)
-#6997 := (= #6260 f23)
-#6993 := (= #6260 #180)
-#6994 := [monotonicity #6992]: #6993
-#6998 := [trans #6994 #6996]: #6997
-#7000 := [monotonicity #6998]: #6999
-#7004 := [symm #7000]: #7003
-#6985 := [hypothesis]: #2860
-#4118 := (or #2855 #2241)
+#6441 := [unit-resolution #3930 #6440]: #4544
+#6443 := (or #4547 #4541)
+#5503 := [hypothesis]: #1884
+#4193 := (forall (vars (?v0 S2)) (:pat #4192) #432)
+#4196 := (iff #435 #4193)
+#4194 := (iff #432 #432)
+#4195 := [refl]: #4194
+#4197 := [quant-intro #4195]: #4196
+#1825 := (~ #435 #435)
+#1855 := (~ #432 #432)
+#1856 := [refl]: #1855
+#1826 := [nnf-pos #1856]: #1825
+#1802 := [not-or-elim #1800]: #435
+#1857 := [mp~ #1802 #1826]: #435
+#4198 := [mp #1857 #4197]: #4193
+#5505 := (not #4193)
+#5506 := (or #5505 #2131)
+#5507 := [quant-inst #1877]: #5506
+#5504 := [unit-resolution #5507 #4198 #5503]: false
+#5508 := [lemma #5504]: #2131
+#3722 := (or #2304 #1884)
+#3809 := [def-axiom]: #3722
+#6442 := [unit-resolution #3809 #5508]: #2304
+#3923 := (or #4547 #2021 #4541)
+#3925 := [def-axiom]: #3923
+#6444 := [unit-resolution #3925 #6442]: #6443
+#6445 := [unit-resolution #6444 #6441]: #4541
+#3950 := (or #4538 #4532)
+#3951 := [def-axiom]: #3950
+#6446 := [unit-resolution #3951 #6445]: #4532
+#5865 := [hypothesis]: #1912
+#5721 := (or #5505 #3045)
+#5722 := [quant-inst #1903]: #5721
+#5866 := [unit-resolution #5722 #4198 #5865]: false
+#5874 := [lemma #5866]: #3045
+#3812 := (or #3060 #1912)
+#3816 := [def-axiom]: #3812
+#6447 := [unit-resolution #3816 #5874]: #3060
+#3946 := (or #4535 #3065 #4529)
+#3947 := [def-axiom]: #3946
+#6448 := [unit-resolution #3947 #6447 #6446]: #4529
+#3960 := (or #4526 #4520)
+#3981 := [def-axiom]: #3960
+#6449 := [unit-resolution #3981 #6448]: #4520
+#3968 := (or #4523 #4237 #4517)
+#3969 := [def-axiom]: #3968
+#6450 := [unit-resolution #3969 #6449 #5741]: #4517
+#5134 := (or #4514 #4505)
+#4689 := (?v1!7 ?v0!8)
+#4690 := (f13 f14 #4689)
+#4672 := (* -1::Int #4690)
+#4622 := (f13 f14 ?v0!8)
+#4673 := (+ #4622 #4672)
+#4674 := (<= #4673 0::Int)
+#5029 := [hypothesis]: #4502
+#5035 := [hypothesis]: #4517
+#3990 := (or #4514 #4508)
+#3958 := [def-axiom]: #3990
+#5036 := [unit-resolution #3958 #5035]: #4508
+#3995 := (or #4511 #4350 #4505)
+#3996 := [def-axiom]: #3995
+#5037 := [unit-resolution #3996 #5036 #5029]: #4350
+#4103 := (or #4347 #4341)
+#4100 := [def-axiom]: #4103
+#5038 := [unit-resolution #4100 #5037]: #4341
+#3999 := (or #4514 #100)
+#4000 := [def-axiom]: #3999
+#5039 := [unit-resolution #4000 #5035]: #100
+#5079 := (= #157 #99)
+#4101 := (or #4347 #599)
+#4102 := [def-axiom]: #4101
+#5054 := [unit-resolution #4102 #5037]: #599
+#5055 := [symm #5054]: #138
+#5080 := [monotonicity #5055]: #5079
+#5081 := [trans #5080 #5039]: #158
+#4113 := (or #4323 #2132)
+#3776 := [def-axiom]: #4113
+#5082 := [unit-resolution #3776 #5081]: #4323
+#4002 := (or #4514 #4249)
+#3982 := [def-axiom]: #4002
+#5083 := [unit-resolution #3982 #5035]: #4249
+#3817 := (or #4347 #4283)
+#4099 := [def-axiom]: #3817
+#5078 := [unit-resolution #4099 #5037]: #4283
+#4919 := (or #3328 #4288 #4254 #690)
+#4892 := [hypothesis]: #3333
+#4116 := (or #3328 #2119)
+#4117 := [def-axiom]: #4116
+#4893 := [unit-resolution #4117 #4892]: #2119
+#4691 := (f13 f14 ?v1!10)
+#4692 := (* -1::Int #4691)
+#4693 := (+ f3 #4692)
+#4694 := (<= #4693 0::Int)
+#4695 := (f8 f15 ?v1!10)
+#4696 := (= f1 #4695)
+#4767 := (not #4696)
+#3804 := (f13 f14 ?v0!11)
+#3805 := (* -1::Int #3804)
+#4769 := (+ #3805 #4691)
+#4770 := (+ #2113 #4769)
+#4773 := (>= #4770 0::Int)
+#4902 := (not #4773)
+#4876 := (+ #2110 #4692)
+#4878 := (>= #4876 0::Int)
+#4875 := (= #2110 #4691)
+#4880 := (= #4691 #2110)
+#4879 := [hypothesis]: #599
+#4881 := [monotonicity #4879]: #4880
+#4882 := [symm #4881]: #4875
+#4883 := (not #4875)
+#4884 := (or #4883 #4878)
+#4885 := [th-lemma arith triangle-eq]: #4884
+#4886 := [unit-resolution #4885 #4882]: #4878
+#4114 := (not #2774)
+#4120 := (or #3328 #4114)
+#3758 := [def-axiom]: #4120
+#4887 := [unit-resolution #3758 #4892]: #4114
+#4865 := (+ #2108 #3805)
+#4873 := (<= #4865 0::Int)
+#4864 := (= #2108 #3804)
+#4890 := (= #3804 #2108)
+#4891 := [monotonicity #4879]: #4890
+#4894 := [symm #4891]: #4864
+#4895 := (not #4864)
+#4896 := (or #4895 #4873)
+#4907 := [th-lemma arith triangle-eq]: #4896
+#4908 := [unit-resolution #4907 #4894]: #4873
+#4904 := (not #4878)
+#4903 := (not #4873)
+#4905 := (or #4902 #4903 #2774 #4904)
+#4897 := [hypothesis]: #4878
+#4898 := [hypothesis]: #4114
+#4899 := [hypothesis]: #4873
+#4900 := [hypothesis]: #4773
+#4901 := [th-lemma arith farkas 1 -1 1 1 #4900 #4899 #4898 #4897]: false
+#4906 := [lemma #4901]: #4905
+#4909 := [unit-resolution #4906 #4908 #4887 #4886]: #4902
+#4912 := (or #4767 #4773)
+#4118 := (or #3328 #2123)
 #4119 := [def-axiom]: #4118
-#6988 := [unit-resolution #4119 #6985]: #2241
-#7005 := [trans #6988 #7004]: #6692
-#6718 := (not #6692)
-#6717 := (not #6694)
-#6719 := (or #6717 #6688 #6718)
-#6720 := [def-axiom]: #6719
-#7006 := [unit-resolution #6720 #7005 #6987]: #6688
-#6546 := (f5 f22 ?v0!14)
-#6547 := (f9 #6546)
-#6477 := (* -1::Int #2244)
-#6564 := (+ #6477 #6547)
-#6565 := (+ #174 #6564)
-#6566 := (>= #6565 0::Int)
-#6594 := (not #6566)
-#6548 := (* -1::Int #6547)
-#6552 := (+ f8 #6548)
-#6553 := (<= #6552 0::Int)
-#6571 := (or #6553 #6566)
-#6574 := (not #6571)
-#4114 := (not #2849)
-#4115 := (or #2855 #4114)
-#4120 := [def-axiom]: #4115
-#6986 := [unit-resolution #4120 #6985]: #4114
-#6580 := (or #4392 #2849 #6574)
-#6549 := (+ #1444 #6548)
-#6550 := (+ #2244 #6549)
-#6551 := (<= #6550 0::Int)
-#6554 := (or #6553 #6551)
-#6555 := (not #6554)
-#6556 := (or #2245 #6555)
-#6581 := (or #4392 #6556)
-#6588 := (iff #6581 #6580)
-#6577 := (or #2849 #6574)
-#6583 := (or #4392 #6577)
-#6586 := (iff #6583 #6580)
-#6587 := [rewrite]: #6586
-#6584 := (iff #6581 #6583)
-#6578 := (iff #6556 #6577)
-#6575 := (iff #6555 #6574)
-#6572 := (iff #6554 #6571)
-#6569 := (iff #6551 #6566)
-#6557 := (+ #2244 #6548)
-#6558 := (+ #1444 #6557)
-#6561 := (<= #6558 0::Int)
-#6567 := (iff #6561 #6566)
-#6568 := [rewrite]: #6567
-#6562 := (iff #6551 #6561)
-#6559 := (= #6550 #6558)
-#6560 := [rewrite]: #6559
-#6563 := [monotonicity #6560]: #6562
-#6570 := [trans #6563 #6568]: #6569
-#6573 := [monotonicity #6570]: #6572
-#6576 := [monotonicity #6573]: #6575
-#6579 := [monotonicity #2851 #6576]: #6578
-#6585 := [monotonicity #6579]: #6584
-#6589 := [trans #6585 #6587]: #6588
-#6582 := [quant-inst #2239]: #6581
-#6590 := [mp #6582 #6589]: #6580
-#7007 := [unit-resolution #6590 #6500 #6986]: #6574
-#6595 := (or #6571 #6594)
-#6596 := [def-axiom]: #6595
-#7008 := [unit-resolution #6596 #7007]: #6594
-#6706 := (not #6688)
-#6932 := (or #6687 #6566 #6706)
-#6813 := (f6 #6546)
-#6823 := (f13 f14 #6813)
-#6838 := (* -1::Int #6823)
-#6878 := (+ #174 #6838)
-#6880 := (>= #6878 0::Int)
-#6877 := (= #174 #6823)
-#6884 := (= #6823 #174)
-#6882 := (= #6813 f22)
-#6814 := (= f22 #6813)
-#6821 := (or #6820 #6814)
-#6822 := [quant-inst #170 #2239]: #6821
-#6881 := [unit-resolution #6822 #4196]: #6814
-#6883 := [symm #6881]: #6882
-#6885 := [monotonicity #6883]: #6884
-#6886 := [symm #6885]: #6877
-#6887 := (not #6877)
-#6888 := (or #6887 #6880)
-#6889 := [th-lemma arith triangle-eq]: #6888
-#6890 := [unit-resolution #6889 #6886]: #6880
-#6891 := [hypothesis]: #6594
-#6810 := (>= #6547 0::Int)
-#6764 := (<= #6547 0::Int)
-#6765 := (not #6764)
-#6707 := (not #6687)
-#6892 := [hypothesis]: #6707
-#6770 := (or #6687 #6765)
-#48 := (f9 #37)
-#406 := (<= #48 0::Int)
-#407 := (not #406)
-#353 := (= #12 #23)
-#413 := (or #353 #407)
-#4203 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #413)
-#418 := (forall (vars (?v0 S3) (?v1 S3)) #413)
-#4206 := (iff #418 #4203)
-#4204 := (iff #413 #413)
-#4205 := [refl]: #4204
-#4207 := [quant-intro #4205]: #4206
-#1845 := (~ #418 #418)
-#1844 := (~ #413 #413)
-#1874 := [refl]: #1844
-#1846 := [nnf-pos #1874]: #1845
-#53 := (< 0::Int #48)
-#47 := (= #23 #12)
-#52 := (not #47)
-#54 := (implies #52 #53)
-#55 := (forall (vars (?v0 S3) (?v1 S3)) #54)
-#421 := (iff #55 #418)
-#398 := (or #53 #353)
-#403 := (forall (vars (?v0 S3) (?v1 S3)) #398)
-#419 := (iff #403 #418)
-#416 := (iff #398 #413)
-#410 := (or #407 #353)
-#414 := (iff #410 #413)
-#415 := [rewrite]: #414
-#411 := (iff #398 #410)
-#408 := (iff #53 #407)
-#409 := [rewrite]: #408
-#412 := [monotonicity #409]: #411
-#417 := [trans #412 #415]: #416
-#420 := [quant-intro #417]: #419
-#404 := (iff #55 #403)
-#401 := (iff #54 #398)
-#367 := (not #353)
-#395 := (implies #367 #53)
-#399 := (iff #395 #398)
-#400 := [rewrite]: #399
-#396 := (iff #54 #395)
-#393 := (iff #52 #367)
-#359 := (iff #47 #353)
-#360 := [rewrite]: #359
-#394 := [monotonicity #360]: #393
-#397 := [monotonicity #394]: #396
-#402 := [trans #397 #400]: #401
-#405 := [quant-intro #402]: #404
-#422 := [trans #405 #420]: #421
-#392 := [asserted]: #55
-#423 := [mp #392 #422]: #418
-#1875 := [mp~ #423 #1846]: #418
-#4208 := [mp #1875 #4207]: #4203
-#6773 := (not #4203)
-#6774 := (or #6773 #6687 #6765)
-#6766 := (= ?v0!14 f22)
-#6767 := (or #6766 #6765)
-#6775 := (or #6773 #6767)
-#6782 := (iff #6775 #6774)
-#6777 := (or #6773 #6770)
-#6780 := (iff #6777 #6774)
-#6781 := [rewrite]: #6780
-#6778 := (iff #6775 #6777)
-#6771 := (iff #6767 #6770)
-#6768 := (iff #6766 #6687)
-#6769 := [rewrite]: #6768
-#6772 := [monotonicity #6769]: #6771
-#6779 := [monotonicity #6772]: #6778
-#6783 := [trans #6779 #6781]: #6782
-#6776 := [quant-inst #170 #2239]: #6775
-#6784 := [mp #6776 #6783]: #6774
-#6893 := [unit-resolution #6784 #4208]: #6770
-#6894 := [unit-resolution #6893 #6892]: #6765
-#6895 := (or #6810 #6764)
-#6896 := [th-lemma arith farkas 1 1]: #6895
-#6897 := [unit-resolution #6896 #6894]: #6810
-#6811 := (f7 #6546)
-#6818 := (f13 f14 #6811)
-#6819 := (* -1::Int #6818)
-#6868 := (+ #2244 #6819)
-#6875 := (<= #6868 0::Int)
-#6867 := (= #2244 #6818)
-#6901 := (= #6818 #2244)
-#6899 := (= #6811 ?v0!14)
-#6812 := (= ?v0!14 #6811)
-#6816 := (or #6815 #6812)
-#6817 := [quant-inst #170 #2239]: #6816
-#6898 := [unit-resolution #6817 #4190]: #6812
-#6900 := [symm #6898]: #6899
-#6902 := [monotonicity #6900]: #6901
-#6903 := [symm #6902]: #6867
-#6904 := (not #6867)
-#6905 := (or #6904 #6875)
-#6906 := [th-lemma arith triangle-eq]: #6905
-#6907 := [unit-resolution #6906 #6903]: #6875
-#6839 := (+ #6818 #6838)
-#6840 := (<= #6839 0::Int)
-#6826 := (f3 f15 #6811)
-#6827 := (= f1 #6826)
-#6914 := (= #6517 #6826)
-#6910 := (= #6826 #6517)
-#6911 := [monotonicity #6900]: #6910
-#6915 := [symm #6911]: #6914
-#6908 := [hypothesis]: #6688
-#6710 := (or #6706 #6687 #6518)
-#6711 := [def-axiom]: #6710
-#6909 := [unit-resolution #6711 #6892 #6908]: #6518
-#6916 := [trans #6909 #6915]: #6827
-#6829 := (f3 f15 #6813)
-#6830 := (= f1 #6829)
-#6924 := (not #6830)
-#6925 := (iff #756 #6924)
-#6922 := (iff #753 #6830)
-#6920 := (iff #6830 #753)
-#6918 := (= #6829 #171)
-#6919 := [monotonicity #6883]: #6918
-#6921 := [monotonicity #6919]: #6920
-#6923 := [symm #6921]: #6922
-#6926 := [monotonicity #6923]: #6925
-#4044 := (or #4526 #756)
-#4039 := [def-axiom]: #4044
-#6917 := [unit-resolution #4039 #6499]: #756
-#6927 := [mp #6917 #6926]: #6924
-#6828 := (not #6827)
-#6848 := (or #6828 #6830 #6840)
-#3952 := (or #4538 #4282)
-#4007 := [def-axiom]: #3952
-#6928 := [unit-resolution #4007 #6498]: #4282
-#6853 := (or #4287 #6828 #6830 #6840)
-#6824 := (+ #6823 #6819)
-#6825 := (>= #6824 0::Int)
-#6831 := (or #6830 #6828 #6825)
-#6854 := (or #4287 #6831)
-#6861 := (iff #6854 #6853)
-#6856 := (or #4287 #6848)
-#6859 := (iff #6856 #6853)
-#6860 := [rewrite]: #6859
+#4910 := [unit-resolution #4119 #4892]: #2123
+#4911 := [hypothesis]: #4249
+#4784 := (or #4254 #2122 #4767 #4773)
+#4762 := (+ #4691 #3805)
+#4763 := (+ #2113 #4762)
+#4766 := (>= #4763 0::Int)
+#4768 := (or #4767 #2122 #4766)
+#4785 := (or #4254 #4768)
+#4792 := (iff #4785 #4784)
+#4779 := (or #2122 #4767 #4773)
+#4787 := (or #4254 #4779)
+#4790 := (iff #4787 #4784)
+#4791 := [rewrite]: #4790
+#4788 := (iff #4785 #4787)
+#4782 := (iff #4768 #4779)
+#4776 := (or #4767 #2122 #4773)
+#4780 := (iff #4776 #4779)
+#4781 := [rewrite]: #4780
+#4777 := (iff #4768 #4776)
+#4774 := (iff #4766 #4773)
+#4771 := (= #4763 #4770)
+#4772 := [rewrite]: #4771
+#4775 := [monotonicity #4772]: #4774
+#4778 := [monotonicity #4775]: #4777
+#4783 := [trans #4778 #4781]: #4782
+#4789 := [monotonicity #4783]: #4788
+#4793 := [trans #4789 #4791]: #4792
+#4786 := [quant-inst #2107 #2106]: #4785
+#4794 := [mp #4786 #4793]: #4784
+#4913 := [unit-resolution #4794 #4911 #4910]: #4912
+#4914 := [unit-resolution #4913 #4909]: #4767
+#4698 := (or #4694 #4696)
+#4915 := [hypothesis]: #4283
+#4701 := (or #4288 #4694 #4696)
+#4697 := (or #4696 #4694)
+#4702 := (or #4288 #4697)
+#4709 := (iff #4702 #4701)
+#4704 := (or #4288 #4698)
+#4707 := (iff #4704 #4701)
+#4708 := [rewrite]: #4707
+#4705 := (iff #4702 #4704)
+#4699 := (iff #4697 #4698)
+#4700 := [rewrite]: #4699
+#4706 := [monotonicity #4700]: #4705
+#4710 := [trans #4706 #4708]: #4709
+#4703 := [quant-inst #2106]: #4702
+#4711 := [mp #4703 #4710]: #4701
+#4916 := [unit-resolution #4711 #4915]: #4698
+#4917 := [unit-resolution #4916 #4914]: #4694
+#4918 := [th-lemma arith farkas 1 -1 1 #4886 #4917 #4893]: false
+#4920 := [lemma #4918]: #4919
+#5084 := [unit-resolution #4920 #5078 #5083 #5054]: #3328
+#4125 := (or #4332 #4326 #3333)
+#4111 := [def-axiom]: #4125
+#5085 := [unit-resolution #4111 #5084 #5082]: #4332
+#3835 := (or #4335 #4329)
+#3836 := [def-axiom]: #3835
+#5086 := [unit-resolution #3836 #5085]: #4335
+#4105 := (or #4344 #4304 #4338)
+#4109 := [def-axiom]: #4105
+#5087 := [unit-resolution #4109 #5086 #5038]: #4304
+#4137 := (or #4301 #2057)
+#4127 := [def-axiom]: #4137
+#5088 := [unit-resolution #4127 #5087]: #2057
+#4128 := (or #4301 #4293)
+#3788 := [def-axiom]: #4128
+#5115 := [unit-resolution #3788 #5087]: #4293
+#3787 := (or #4301 #2674)
+#3792 := [def-axiom]: #3787
+#5116 := [unit-resolution #3792 #5087]: #2674
+#3989 := (or #4514 #4274)
+#3984 := [def-axiom]: #3989
+#5117 := [unit-resolution #3984 #5035]: #4274
+#5033 := (or #4674 #4279 #2671 #4298 #690 #2056)
+#4675 := (f5 #4689 ?v0!8)
+#4676 := (f4 #4675)
+#4671 := (* -1::Int #4676)
+#4757 := (+ #4671 #4672)
+#4758 := (+ #4622 #4757)
+#4740 := (= #4758 0::Int)
+#4743 := (not #4740)
+#5676 := [hypothesis]: #4293
+#4852 := (not #4674)
+#5671 := [hypothesis]: #4852
+#5684 := (or #4743 #4298 #4674 #690)
+#4938 := (f13 f19 #4689)
+#4951 := (* -1::Int #4938)
+#4965 := (+ #4671 #4951)
+#4966 := (+ #2044 #4965)
+#4990 := (>= #4966 0::Int)
+#5185 := (+ #4690 #4951)
+#5187 := (>= #5185 0::Int)
+#5184 := (= #4690 #4938)
+#5634 := (= #4938 #4690)
+#5633 := [symm #4879]: #138
+#5635 := [monotonicity #5633]: #5634
+#5636 := [symm #5635]: #5184
+#5637 := (not #5184)
+#5638 := (or #5637 #5187)
+#5639 := [th-lemma arith triangle-eq]: #5638
+#5640 := [unit-resolution #5639 #5636]: #5187
+#4623 := (* -1::Int #4622)
+#4934 := (+ #2044 #4623)
+#4936 := (>= #4934 0::Int)
+#4933 := (= #2044 #4622)
+#5641 := (= #4622 #2044)
+#5642 := [monotonicity #4879]: #5641
+#5643 := [symm #5642]: #4933
+#5644 := (not #4933)
+#5645 := (or #5644 #4936)
+#5646 := [th-lemma arith triangle-eq]: #5645
+#5647 := [unit-resolution #5646 #5643]: #4936
+#4851 := (>= #4758 0::Int)
+#5648 := [hypothesis]: #4740
+#5649 := (or #4743 #4851)
+#5650 := [th-lemma arith triangle-eq]: #5649
+#5651 := [unit-resolution #5650 #5648]: #4851
+#5652 := (not #5187)
+#5405 := (not #4936)
+#5403 := (not #4851)
+#5653 := (or #4990 #5403 #5405 #5652)
+#5654 := [th-lemma arith assign-bounds -1 -1 -1]: #5653
+#5655 := [unit-resolution #5654 #5651 #5647 #5640]: #4990
+#4989 := (<= #4966 0::Int)
+#5186 := (<= #5185 0::Int)
+#5656 := (or #5637 #5186)
+#5657 := [th-lemma arith triangle-eq]: #5656
+#5658 := [unit-resolution #5657 #5636]: #5186
+#4935 := (<= #4934 0::Int)
+#5659 := (or #5644 #4935)
+#5660 := [th-lemma arith triangle-eq]: #5659
+#5661 := [unit-resolution #5660 #5643]: #4935
+#4850 := (<= #4758 0::Int)
+#5662 := (or #4743 #4850)
+#5663 := [th-lemma arith triangle-eq]: #5662
+#5664 := [unit-resolution #5663 #5648]: #4850
+#5667 := (not #5186)
+#5666 := (not #4935)
+#5665 := (not #4850)
+#5668 := (or #4989 #5665 #5666 #5667)
+#5669 := [th-lemma arith assign-bounds -1 -1 -1]: #5668
+#5670 := [unit-resolution #5669 #5664 #5661 #5658]: #4989
+#4967 := (= #4966 0::Int)
+#4972 := (not #4967)
+#4952 := (+ #2044 #4951)
+#4953 := (<= #4952 0::Int)
+#5672 := (not #4953)
+#5673 := (or #5672 #5405 #4674 #5652)
+#5674 := [th-lemma arith assign-bounds -1 -1 -1]: #5673
+#5675 := [unit-resolution #5674 #5640 #5671 #5647]: #5672
+#4975 := (or #4953 #4972)
+#4978 := (or #4298 #4953 #4972)
+#4937 := (+ #2045 #4676)
+#4939 := (+ #4938 #4937)
+#4940 := (= #4939 0::Int)
+#4941 := (not #4940)
+#4942 := (+ #4938 #2045)
+#4943 := (>= #4942 0::Int)
+#4944 := (or #4943 #4941)
+#4979 := (or #4298 #4944)
+#4986 := (iff #4979 #4978)
+#4981 := (or #4298 #4975)
+#4984 := (iff #4981 #4978)
+#4985 := [rewrite]: #4984
+#4982 := (iff #4979 #4981)
+#4976 := (iff #4944 #4975)
+#4973 := (iff #4941 #4972)
+#4970 := (iff #4940 #4967)
+#4958 := (+ #4676 #4938)
+#4959 := (+ #2045 #4958)
+#4962 := (= #4959 0::Int)
+#4968 := (iff #4962 #4967)
+#4969 := [rewrite]: #4968
+#4963 := (iff #4940 #4962)
+#4960 := (= #4939 #4959)
+#4961 := [rewrite]: #4960
+#4964 := [monotonicity #4961]: #4963
+#4971 := [trans #4964 #4969]: #4970
+#4974 := [monotonicity #4971]: #4973
+#4956 := (iff #4943 #4953)
+#4945 := (+ #2045 #4938)
+#4948 := (>= #4945 0::Int)
+#4954 := (iff #4948 #4953)
+#4955 := [rewrite]: #4954
+#4949 := (iff #4943 #4948)
+#4946 := (= #4942 #4945)
+#4947 := [rewrite]: #4946
+#4950 := [monotonicity #4947]: #4949
+#4957 := [trans #4950 #4955]: #4956
+#4977 := [monotonicity #4957 #4974]: #4976
+#4983 := [monotonicity #4977]: #4982
+#4987 := [trans #4983 #4985]: #4986
+#4980 := [quant-inst #4689]: #4979
+#4988 := [mp #4980 #4987]: #4978
+#5677 := [unit-resolution #4988 #5676]: #4975
+#5678 := [unit-resolution #5677 #5675]: #4972
+#5680 := (not #4990)
+#5679 := (not #4989)
+#5681 := (or #4967 #5679 #5680)
+#5682 := [th-lemma arith triangle-eq]: #5681
+#5683 := [unit-resolution #5682 #5678 #5670 #5655]: false
+#5685 := [lemma #5683]: #5684
+#5043 := [unit-resolution #5685 #5671 #5676 #4879]: #4743
+#4681 := (f8 f15 #4689)
+#4752 := (= f1 #4681)
+#4753 := (not #4752)
+#4748 := (or #4674 #4743 #4753)
+#4822 := (not #4748)
+#4624 := (+ f3 #4623)
+#4604 := (<= #4624 0::Int)
+#5044 := (not #4604)
+#5298 := [hypothesis]: #2057
+#5045 := (or #5044 #2056 #5405)
+#5046 := [th-lemma arith assign-bounds -1 -1]: #5045
+#5047 := [unit-resolution #5046 #5298 #5647]: #5044
+#5050 := (or #4604 #4822)
+#5048 := [hypothesis]: #2674
+#5049 := [hypothesis]: #4274
+#4827 := (or #4279 #2671 #4604 #4822)
+#4677 := (+ #4672 #4671)
+#4678 := (+ #4622 #4677)
+#4679 := (= #4678 0::Int)
+#4680 := (not #4679)
+#4754 := (or #4753 #4680 #4674)
+#4755 := (not #4754)
+#4756 := (or #2058 #4604 #4755)
+#4828 := (or #4279 #4756)
+#4841 := (iff #4828 #4827)
+#4825 := (or #2671 #4604 #4822)
+#4830 := (or #4279 #4825)
+#4837 := (iff #4830 #4827)
+#4840 := [rewrite]: #4837
+#4835 := (iff #4828 #4830)
+#4820 := (iff #4756 #4825)
+#4823 := (iff #4755 #4822)
+#4765 := (iff #4754 #4748)
+#4745 := (or #4753 #4743 #4674)
+#4749 := (iff #4745 #4748)
+#4764 := [rewrite]: #4749
+#4746 := (iff #4754 #4745)
+#4744 := (iff #4680 #4743)
+#4741 := (iff #4679 #4740)
+#4759 := (= #4678 #4758)
+#4760 := [rewrite]: #4759
+#4742 := [monotonicity #4760]: #4741
+#4739 := [monotonicity #4742]: #4744
+#4747 := [monotonicity #4739]: #4746
+#4821 := [trans #4747 #4764]: #4765
+#4824 := [monotonicity #4821]: #4823
+#4826 := [monotonicity #2673 #4824]: #4820
+#4836 := [monotonicity #4826]: #4835
+#4842 := [trans #4836 #4840]: #4841
+#4829 := [quant-inst #2043]: #4828
+#4848 := [mp #4829 #4842]: #4827
+#5030 := [unit-resolution #4848 #5049 #5048]: #5050
+#5031 := [unit-resolution #5030 #5047]: #4822
+#4849 := (or #4748 #4740)
+#4855 := [def-axiom]: #4849
+#5032 := [unit-resolution #4855 #5031 #5043]: false
+#5034 := [lemma #5032]: #5033
+#5118 := [unit-resolution #5034 #5117 #5116 #5115 #5054 #5088]: #4674
+#5119 := [monotonicity #5054]: #5641
+#5114 := [symm #5119]: #4933
+#5120 := [unit-resolution #5646 #5114]: #4936
+#5121 := [unit-resolution #5046 #5088 #5120]: #5044
+#5122 := [unit-resolution #4848 #5117 #5116]: #5050
+#5123 := [unit-resolution #5122 #5121]: #4822
+#4853 := (or #4748 #4852)
+#4854 := [def-axiom]: #4853
+#5124 := [unit-resolution #4854 #5123 #5118]: false
+#5135 := [lemma #5124]: #5134
+#6451 := [unit-resolution #5135 #6450]: #4505
+#4018 := (or #4502 #181)
+#4019 := [def-axiom]: #4018
+#8689 := [unit-resolution #4019 #6451]: #181
+#8696 := [symm #8689]: #8695
+#8693 := (= #7238 #180)
+#8691 := (= #5830 f1)
+#36 := (:var 0 S1)
+#35 := (:var 2 S4)
+#37 := (f9 #35 #11 #36)
+#4171 := (pattern #37)
+#370 := (= f1 #36)
+#38 := (f8 #37 #11)
+#366 := (= f1 #38)
+#373 := (iff #366 #370)
+#4172 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) (:pat #4171) #373)
+#376 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) #373)
+#4175 := (iff #376 #4172)
+#4173 := (iff #373 #373)
+#4174 := [refl]: #4173
+#4176 := [quant-intro #4174]: #4175
+#1819 := (~ #376 #376)
+#1846 := (~ #373 #373)
+#1847 := [refl]: #1846
+#1820 := [nnf-pos #1847]: #1819
+#40 := (= #36 f1)
+#39 := (= #38 f1)
+#41 := (iff #39 #40)
+#42 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) #41)
+#377 := (iff #42 #376)
+#374 := (iff #41 #373)
+#371 := (iff #40 #370)
+#372 := [rewrite]: #371
+#368 := (iff #39 #366)
+#369 := [rewrite]: #368
+#375 := [monotonicity #369 #372]: #374
+#378 := [quant-intro #375]: #377
+#365 := [asserted]: #42
+#381 := [mp #365 #378]: #376
+#1848 := [mp~ #381 #1820]: #376
+#4177 := [mp #1848 #4176]: #4172
+#5855 := (not #4172)
+#5850 := (or #5855 #5831)
+#5829 := (= f1 f1)
+#5837 := (iff #5831 #5829)
+#5856 := (or #5855 #5837)
+#5858 := (iff #5856 #5850)
+#5860 := (iff #5850 #5850)
+#5867 := [rewrite]: #5860
+#5853 := (iff #5837 #5831)
+#5842 := (iff #5831 true)
+#5851 := (iff #5842 #5831)
+#5852 := [rewrite]: #5851
+#5843 := (iff #5837 #5842)
+#5838 := (iff #5829 true)
+#5841 := [rewrite]: #5838
+#5849 := [monotonicity #5841]: #5843
+#5854 := [trans #5849 #5852]: #5853
+#5859 := [monotonicity #5854]: #5858
+#5869 := [trans #5859 #5867]: #5858
+#5857 := [quant-inst #104 #170 #4]: #5856
+#5870 := [mp #5857 #5869]: #5850
+#8690 := [unit-resolution #5870 #4177]: #5831
+#8692 := [symm #8690]: #8691
+#7564 := (= #6386 f22)
+#6387 := (= f22 #6386)
+#14 := (f5 #11 #12)
+#4138 := (pattern #14)
+#23 := (f6 #14)
+#343 := (= #11 #23)
+#4151 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4138) #343)
+#346 := (forall (vars (?v0 S2) (?v1 S2)) #343)
+#4154 := (iff #346 #4151)
+#4152 := (iff #343 #343)
+#4153 := [refl]: #4152
+#4155 := [quant-intro #4153]: #4154
+#1813 := (~ #346 #346)
+#1837 := (~ #343 #343)
+#1838 := [refl]: #1837
+#1814 := [nnf-pos #1838]: #1813
+#24 := (= #23 #11)
+#25 := (forall (vars (?v0 S2) (?v1 S2)) #24)
+#347 := (iff #25 #346)
+#344 := (iff #24 #343)
+#345 := [rewrite]: #344
+#348 := [quant-intro #345]: #347
+#342 := [asserted]: #25
+#351 := [mp #342 #348]: #346
+#1839 := [mp~ #351 #1814]: #346
+#4156 := [mp #1839 #4155]: #4151
+#6389 := (not #4151)
+#6571 := (or #6389 #6387)
+#6572 := [quant-inst #170 #56]: #6571
+#7563 := [unit-resolution #6572 #4156]: #6387
+#7565 := [symm #7563]: #7564
+#8694 := [monotonicity #7565 #8692]: #8693
+#8698 := [trans #8694 #8696]: #8697
+#23017 := [monotonicity #8698]: #23000
+#23006 := [monotonicity #23017]: #23020
+#22998 := [symm #23006]: #22987
+#23007 := [monotonicity #22998]: #22994
+#19081 := (f24 #14273)
+#19098 := (* -1::Int #19081)
+#14278 := (f5 #14273 ?v0!20)
+#14279 := (f4 #14278)
+#14280 := (* -1::Int #14279)
+#19309 := (+ #14280 #19098)
+#19310 := (+ #2314 #19309)
+#19311 := (= #19310 0::Int)
+#10493 := (>= #19310 0::Int)
+#14274 := (f13 f14 #14273)
+#19099 := (+ #14274 #19098)
+#19100 := (>= #19099 0::Int)
+#3986 := (or #4502 #4496)
+#3987 := [def-axiom]: #3986
+#8746 := [unit-resolution #3987 #6451]: #4496
+#6803 := (f5 f22 ?v0!13)
+#6804 := (f4 #6803)
+#6829 := (+ #2199 #6804)
+#6830 := (+ #174 #6829)
+#6851 := (>= #6830 0::Int)
+#6833 := (= #6830 0::Int)
+#6808 := (* -1::Int #6804)
+#6812 := (+ f3 #6808)
+#6813 := (<= #6812 0::Int)
+#6880 := (not #6813)
+#6822 := (+ #2815 #6804)
+#6823 := (+ #174 #6822)
+#6824 := (>= #6823 0::Int)
+#6859 := (or #6813 #6824)
+#6862 := (not #6859)
+#6856 := (= #2198 #2200)
+#6981 := (not #6856)
+#6980 := [hypothesis]: #2822
+#6984 := (or #6981 #2817)
+#6985 := [th-lemma arith triangle-eq]: #6984
+#6986 := [unit-resolution #6985 #6980]: #6981
+#4011 := (or #4502 #4363)
+#4006 := [def-axiom]: #4011
+#6477 := [unit-resolution #4006 #6451]: #4363
+#6868 := (or #4368 #6856 #6862)
+#6809 := (+ #1420 #6808)
+#6810 := (+ #2200 #6809)
+#6811 := (<= #6810 0::Int)
+#6852 := (or #6813 #6811)
+#6853 := (not #6852)
+#6854 := (= #2200 #2198)
+#6855 := (or #6854 #6853)
+#6869 := (or #4368 #6855)
+#6876 := (iff #6869 #6868)
+#6865 := (or #6856 #6862)
+#6871 := (or #4368 #6865)
+#6874 := (iff #6871 #6868)
+#6875 := [rewrite]: #6874
+#6872 := (iff #6869 #6871)
+#6866 := (iff #6855 #6865)
+#6863 := (iff #6853 #6862)
+#6860 := (iff #6852 #6859)
+#6827 := (iff #6811 #6824)
+#6815 := (+ #2200 #6808)
+#6816 := (+ #1420 #6815)
+#6819 := (<= #6816 0::Int)
+#6825 := (iff #6819 #6824)
+#6826 := [rewrite]: #6825
+#6820 := (iff #6811 #6819)
+#6817 := (= #6810 #6816)
+#6818 := [rewrite]: #6817
+#6821 := [monotonicity #6818]: #6820
+#6828 := [trans #6821 #6826]: #6827
+#6861 := [monotonicity #6828]: #6860
+#6864 := [monotonicity #6861]: #6863
 #6857 := (iff #6854 #6856)
-#6851 := (iff #6831 #6848)
-#6845 := (or #6830 #6828 #6840)
-#6849 := (iff #6845 #6848)
-#6850 := [rewrite]: #6849
-#6846 := (iff #6831 #6845)
-#6843 := (iff #6825 #6840)
-#6832 := (+ #6819 #6823)
-#6835 := (>= #6832 0::Int)
-#6841 := (iff #6835 #6840)
-#6842 := [rewrite]: #6841
-#6836 := (iff #6825 #6835)
-#6833 := (= #6824 #6832)
-#6834 := [rewrite]: #6833
-#6837 := [monotonicity #6834]: #6836
-#6844 := [trans #6837 #6842]: #6843
-#6847 := [monotonicity #6844]: #6846
-#6852 := [trans #6847 #6850]: #6851
-#6858 := [monotonicity #6852]: #6857
-#6862 := [trans #6858 #6860]: #6861
-#6855 := [quant-inst #6811 #6813]: #6854
-#6863 := [mp #6855 #6862]: #6853
-#6929 := [unit-resolution #6863 #6928]: #6848
-#6930 := [unit-resolution #6929 #6927 #6916]: #6840
-#6931 := [th-lemma arith farkas 1 1 1 -1 1 #6930 #6907 #6897 #6891 #6890]: false
-#6933 := [lemma #6931]: #6932
-#7009 := [unit-resolution #6933 #7008 #7006]: #6687
-#7033 := [monotonicity #7009]: #6870
-#7031 := (= #2243 #174)
-#7029 := (= #174 #2243)
-#6786 := (= #6547 0::Int)
-#6793 := (or #6707 #6786)
-#49 := (= #48 0::Int)
-#381 := (or #49 #367)
-#4197 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #4184) #381)
-#386 := (forall (vars (?v0 S3) (?v1 S3)) #381)
-#4200 := (iff #386 #4197)
-#4198 := (iff #381 #381)
-#4199 := [refl]: #4198
-#4201 := [quant-intro #4199]: #4200
-#1841 := (~ #386 #386)
-#1872 := (~ #381 #381)
-#1873 := [refl]: #1872
-#1842 := [nnf-pos #1873]: #1841
-#50 := (implies #47 #49)
-#51 := (forall (vars (?v0 S3) (?v1 S3)) #50)
-#389 := (iff #51 #386)
-#361 := (= 0::Int #48)
-#368 := (or #367 #361)
-#373 := (forall (vars (?v0 S3) (?v1 S3)) #368)
-#387 := (iff #373 #386)
-#384 := (iff #368 #381)
-#378 := (or #367 #49)
-#382 := (iff #378 #381)
-#383 := [rewrite]: #382
-#379 := (iff #368 #378)
-#376 := (iff #361 #49)
-#377 := [rewrite]: #376
-#380 := [monotonicity #377]: #379
-#385 := [trans #380 #383]: #384
-#388 := [quant-intro #385]: #387
-#374 := (iff #51 #373)
-#371 := (iff #50 #368)
-#364 := (implies #353 #361)
-#369 := (iff #364 #368)
-#370 := [rewrite]: #369
-#365 := (iff #50 #364)
-#362 := (iff #49 #361)
-#363 := [rewrite]: #362
-#366 := [monotonicity #360 #363]: #365
-#372 := [trans #366 #370]: #371
-#375 := [quant-intro #372]: #374
-#390 := [trans #375 #388]: #389
-#351 := [asserted]: #51
-#391 := [mp #351 #390]: #386
-#1843 := [mp~ #391 #1842]: #386
-#4202 := [mp #1843 #4201]: #4197
-#6798 := (not #4197)
-#6799 := (or #6798 #6707 #6786)
-#6785 := (not #6766)
-#6787 := (or #6786 #6785)
-#6800 := (or #6798 #6787)
-#6807 := (iff #6800 #6799)
-#6802 := (or #6798 #6793)
-#6805 := (iff #6802 #6799)
-#6806 := [rewrite]: #6805
-#6803 := (iff #6800 #6802)
-#6796 := (iff #6787 #6793)
-#6790 := (or #6786 #6707)
-#6794 := (iff #6790 #6793)
-#6795 := [rewrite]: #6794
-#6791 := (iff #6787 #6790)
-#6788 := (iff #6785 #6707)
-#6789 := [monotonicity #6769]: #6788
-#6792 := [monotonicity #6789]: #6791
-#6797 := [trans #6792 #6795]: #6796
-#6804 := [monotonicity #6797]: #6803
-#6808 := [trans #6804 #6806]: #6807
-#6801 := [quant-inst #170 #2239]: #6800
-#6809 := [mp #6801 #6808]: #6799
-#7010 := [unit-resolution #6809 #4202]: #6793
-#7011 := [unit-resolution #7010 #7009]: #6786
-#7012 := (not #6786)
-#7013 := (or #7012 #6764)
-#7014 := [th-lemma arith triangle-eq]: #7013
-#7015 := [unit-resolution #7014 #7011]: #6764
-#7016 := (or #7012 #6810)
-#7017 := [th-lemma arith triangle-eq]: #7016
-#7018 := [unit-resolution #7017 #7011]: #6810
-#6415 := (* -1::Int #2243)
-#6603 := (+ #6415 #6547)
-#6604 := (+ #174 #6603)
-#6624 := (<= #6604 0::Int)
-#6607 := (= #6604 0::Int)
-#6591 := (not #6553)
-#6592 := (or #6571 #6591)
-#6593 := [def-axiom]: #6592
-#7019 := [unit-resolution #6593 #7007]: #6591
-#6610 := (or #6553 #6566 #6607)
-#6613 := (or #4400 #6553 #6566 #6607)
-#6599 := (+ #6547 #6415)
-#6600 := (+ #174 #6599)
-#6601 := (= #6600 0::Int)
-#6602 := (or #6553 #6551 #6601)
-#6614 := (or #4400 #6602)
-#6621 := (iff #6614 #6613)
-#6616 := (or #4400 #6610)
-#6619 := (iff #6616 #6613)
-#6620 := [rewrite]: #6619
-#6617 := (iff #6614 #6616)
-#6611 := (iff #6602 #6610)
-#6608 := (iff #6601 #6607)
-#6605 := (= #6600 #6604)
-#6606 := [rewrite]: #6605
-#6609 := [monotonicity #6606]: #6608
-#6612 := [monotonicity #6570 #6609]: #6611
-#6618 := [monotonicity #6612]: #6617
-#6622 := [trans #6618 #6620]: #6621
-#6615 := [quant-inst #2239]: #6614
-#6623 := [mp #6615 #6622]: #6613
-#7020 := [unit-resolution #6623 #6504]: #6610
-#7021 := [unit-resolution #7020 #7008 #7019]: #6607
-#7022 := (not #6607)
-#7023 := (or #7022 #6624)
-#7024 := [th-lemma arith triangle-eq]: #7023
-#7025 := [unit-resolution #7024 #7021]: #6624
-#6625 := (>= #6604 0::Int)
-#7026 := (or #7022 #6625)
-#7027 := [th-lemma arith triangle-eq]: #7026
-#7028 := [unit-resolution #7027 #7021]: #6625
-#7030 := [th-lemma arith eq-propagate 1 1 -1 -1 #7028 #7025 #7018 #7015]: #7029
-#7032 := [symm #7030]: #7031
-#7034 := [trans #7032 #7033]: #2849
-#7035 := [unit-resolution #6986 #7034]: false
-#7036 := [lemma #7035]: #2855
-#4051 := (or #4511 #2860 #4505)
-#4052 := [def-axiom]: #4051
-#7090 := [unit-resolution #4052 #7036 #7089]: #4505
-#4061 := (or #4502 #4412)
-#4063 := [def-axiom]: #4061
-#7091 := [unit-resolution #4063 #7090]: #4412
-#9457 := (or #4417 #7526 #7530)
-#7529 := (or #7528 #7526)
-#9458 := (or #4417 #7529)
-#9465 := (iff #9458 #9457)
-#9460 := (or #4417 #7536)
-#9463 := (iff #9460 #9457)
-#9464 := [rewrite]: #9463
-#9461 := (iff #9458 #9460)
-#7539 := (iff #7529 #7536)
-#7533 := (or #7530 #7526)
-#7537 := (iff #7533 #7536)
-#7538 := [rewrite]: #7537
-#7534 := (iff #7529 #7533)
-#7535 := [monotonicity #7532]: #7534
-#7540 := [trans #7535 #7538]: #7539
-#9462 := [monotonicity #7540]: #9461
-#9466 := [trans #9462 #9464]: #9465
-#9459 := [quant-inst #2264]: #9458
-#9467 := [mp #9459 #9466]: #9457
-#10080 := [unit-resolution #9467 #7091]: #7536
-#10081 := [unit-resolution #10080 #10067]: #7526
-#10090 := [mp #10081 #10089]: #9972
-#9969 := (not #9946)
-#9970 := (or #9969 #9938 #9958)
-#9971 := [def-axiom]: #9970
-#10091 := [unit-resolution #9971 #10090 #10079]: #9958
-#10092 := (or #9943 #9959)
-#6295 := (not #5883)
-#9964 := (or #9943 #9959 #6295)
-#9965 := [def-axiom]: #9964
-#10093 := [unit-resolution #9965 #6990]: #10092
-#10094 := [unit-resolution #10093 #10091]: #9959
-#10018 := (or #9940 #10017)
-#10021 := (or #6773 #9940 #10017)
-#10022 := (or #6773 #10018)
-#10024 := (iff #10022 #10021)
-#10025 := [rewrite]: #10024
-#10023 := [quant-inst #7202 #2264]: #10022
-#10026 := [mp #10023 #10025]: #10021
-#10095 := [unit-resolution #10026 #4208]: #10018
-#10096 := [unit-resolution #10095 #10094]: #10017
-#10097 := (or #10041 #10016)
-#10098 := [th-lemma arith farkas 1 1]: #10097
-#10099 := [unit-resolution #10098 #10096]: #10041
-#10100 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10099 #10078 #10077 #10065 #10064 #10063 #10062]: false
-#10102 := [lemma #10100]: #10101
-#9577 := [unit-resolution #10102 #10078 #10065 #10063]: #7530
-#9578 := (or #10066 #9572)
-#9579 := [th-lemma arith triangle-eq]: #9578
-#9580 := [unit-resolution #9579 #9577]: #9572
-#9581 := [th-lemma arith farkas -1 1 1 #10078 #9580 #9571]: false
-#9599 := [lemma #9581]: #9598
-#11943 := [unit-resolution #9599 #10078 #10065]: #7293
-#9470 := (or #7313 #8242)
-#9468 := [def-axiom]: #9470
-#11944 := [unit-resolution #9468 #11943]: #7313
-#7316 := (not #7313)
-#12694 := (or #7310 #7316)
-#7306 := (+ f8 #6062)
-#7307 := (<= #7306 0::Int)
-#12688 := (not #7307)
-#12691 := (or #12688 #6064)
-#4027 := (or #4526 #1646)
+#6858 := [rewrite]: #6857
+#6867 := [monotonicity #6858 #6864]: #6866
+#6873 := [monotonicity #6867]: #6872
+#6877 := [trans #6873 #6875]: #6876
+#6870 := [quant-inst #2197]: #6869
+#6878 := [mp #6870 #6877]: #6868
+#6987 := [unit-resolution #6878 #6477 #6986]: #6862
+#6881 := (or #6859 #6880)
+#6882 := [def-axiom]: #6881
+#6988 := [unit-resolution #6882 #6987]: #6880
+#6883 := (not #6824)
+#6884 := (or #6859 #6883)
+#6885 := [def-axiom]: #6884
+#6989 := [unit-resolution #6885 #6987]: #6883
+#6836 := (or #6813 #6824 #6833)
+#4012 := (or #4502 #4371)
+#3985 := [def-axiom]: #4012
+#6291 := [unit-resolution #3985 #6451]: #4371
+#6839 := (or #4376 #6813 #6824 #6833)
+#6805 := (+ #6804 #2199)
+#6806 := (+ #174 #6805)
+#6807 := (= #6806 0::Int)
+#6814 := (or #6813 #6811 #6807)
+#6840 := (or #4376 #6814)
+#6847 := (iff #6840 #6839)
+#6842 := (or #4376 #6836)
+#6845 := (iff #6842 #6839)
+#6846 := [rewrite]: #6845
+#6843 := (iff #6840 #6842)
+#6837 := (iff #6814 #6836)
+#6834 := (iff #6807 #6833)
+#6831 := (= #6806 #6830)
+#6832 := [rewrite]: #6831
+#6835 := [monotonicity #6832]: #6834
+#6838 := [monotonicity #6828 #6835]: #6837
+#6844 := [monotonicity #6838]: #6843
+#6848 := [trans #6844 #6846]: #6847
+#6841 := [quant-inst #2197]: #6840
+#6849 := [mp #6841 #6848]: #6839
+#6990 := [unit-resolution #6849 #6291]: #6836
+#6991 := [unit-resolution #6990 #6989 #6988]: #6833
+#6992 := (not #6833)
+#6993 := (or #6992 #6851)
+#6994 := [th-lemma arith triangle-eq]: #6993
+#6995 := [unit-resolution #6994 #6991]: #6851
+#6879 := (>= #2816 0::Int)
+#6996 := (or #6879 #2817)
+#6997 := [th-lemma arith farkas 1 1]: #6996
+#6998 := [unit-resolution #6997 #6980]: #6879
+#6999 := [th-lemma arith farkas 1 -1 1 #6998 #6989 #6995]: false
+#7000 := [lemma #6999]: #2817
+#4016 := (or #4499 #2822 #4493)
+#4017 := [def-axiom]: #4016
+#8738 := [unit-resolution #4017 #7000 #8746]: #4493
+#4029 := (or #4490 #4379)
+#4030 := [def-axiom]: #4029
+#10275 := [unit-resolution #4030 #8738]: #4379
+#15705 := (or #4384 #19100)
+#14698 := [quant-inst #14273]: #15705
+#29722 := [unit-resolution #14698 #10275]: #19100
+#14275 := (* -1::Int #14274)
+#14281 := (+ #14275 #14280)
+#14282 := (+ #14126 #14281)
+#8606 := (>= #14282 0::Int)
+#14283 := (= #14282 0::Int)
+#14287 := (not #14286)
+#14284 := (not #14283)
+#14276 := (+ #14126 #14275)
+#14277 := (<= #14276 0::Int)
+#14293 := (or #14277 #14284 #14287)
+#14296 := (not #14293)
+#14290 := (+ f3 #14143)
+#14291 := (<= #14290 0::Int)
+#22561 := (not #14291)
+#22543 := [hypothesis]: #19137
+#22806 := (or #22561 #22448)
+#12390 := (f5 f22 ?v0!19)
+#12391 := (f4 #12390)
+#12416 := (+ #2285 #12391)
+#12417 := (+ #174 #12416)
+#11416 := (>= #12417 0::Int)
+#12420 := (= #12417 0::Int)
+#12395 := (* -1::Int #12391)
+#12399 := (+ f3 #12395)
+#12400 := (<= #12399 0::Int)
+#11456 := (not #12400)
+#14158 := [hypothesis]: #3458
+#4081 := (or #3453 #2295)
+#4087 := [def-axiom]: #4081
+#14196 := [unit-resolution #4087 #14158]: #2295
+#14021 := (+ #2289 #12395)
+#14056 := (>= #14021 0::Int)
+#14020 := (= #2289 #12391)
+#14155 := (= #2288 #12390)
+#14153 := (= ?v1!18 f22)
+#11849 := (= ?v1!18 #6386)
+#11847 := (f8 f15 ?v1!18)
+#11848 := (= f1 #11847)
+#11850 := (ite #11849 #5831 #11848)
+#11851 := (f8 #7238 ?v1!18)
+#11852 := (= f1 #11851)
+#11854 := (iff #11850 #11852)
+#12005 := (or #6238 #11854)
+#11853 := (iff #11852 #11850)
+#12035 := (or #6238 #11853)
+#12030 := (iff #12035 #12005)
+#12106 := (iff #12005 #12005)
+#12107 := [rewrite]: #12106
+#11855 := (iff #11853 #11854)
+#11856 := [rewrite]: #11855
+#12104 := [monotonicity #11856]: #12030
+#12105 := [trans #12104 #12107]: #12030
+#12036 := [quant-inst #104 #6386 #5830 #2282]: #12035
+#12037 := [mp #12036 #12105]: #12005
+#14197 := [unit-resolution #12037 #4184]: #11854
+#14201 := (= #2296 #11851)
+#14198 := (= #11851 #2296)
+#14199 := [monotonicity #8698]: #14198
+#14243 := [symm #14199]: #14201
+#4088 := (or #3453 #2297)
+#4082 := [def-axiom]: #4088
+#14152 := [unit-resolution #4082 #14158]: #2297
+#14225 := [trans #14152 #14243]: #11852
+#12133 := (not #11852)
+#12138 := (not #11854)
+#12187 := (or #12138 #11850 #12133)
+#12137 := [def-axiom]: #12187
+#14226 := [unit-resolution #12137 #14225 #14197]: #11850
+#11874 := (not #11848)
+#12339 := (f13 f14 ?v0!19)
+#12374 := (* -1::Int #12339)
+#11822 := (f13 f14 ?v1!18)
+#12470 := (+ #11822 #12374)
+#12471 := (+ #2289 #12470)
+#12472 := (>= #12471 0::Int)
+#15882 := (not #12472)
+#4089 := (not #2882)
+#3918 := (or #3453 #4089)
+#3920 := [def-axiom]: #3918
+#14107 := [unit-resolution #3920 #14158]: #4089
+#12051 := (* -1::Int #11822)
+#12052 := (+ #2286 #12051)
+#12288 := (>= #12052 0::Int)
+#11825 := (= #2286 #11822)
+#6404 := (f13 f14 #6386)
+#8791 := (= #6404 #2220)
+#8808 := (= #2220 #6404)
+#7234 := (= ?v0!14 #6386)
+#7064 := (f8 f15 ?v0!14)
+#7065 := (= f1 #7064)
+#7235 := (ite #7234 #5831 #7065)
+#7239 := (f8 #7238 ?v0!14)
+#7240 := (= f1 #7239)
+#7242 := (iff #7235 #7240)
+#7258 := (or #6238 #7242)
+#7241 := (iff #7240 #7235)
+#7262 := (or #6238 #7241)
+#7261 := (iff #7262 #7258)
+#7267 := (iff #7258 #7258)
+#7268 := [rewrite]: #7267
+#7243 := (iff #7241 #7242)
+#7244 := [rewrite]: #7243
+#7266 := [monotonicity #7244]: #7261
+#7273 := [trans #7266 #7268]: #7261
+#7265 := [quant-inst #104 #6386 #5830 #2215]: #7262
+#7274 := [mp #7265 #7273]: #7258
+#7818 := [unit-resolution #7274 #4184]: #7242
+#7657 := (= #2216 #7239)
+#7793 := (= #7239 #2216)
+#7820 := [monotonicity #8698]: #7793
+#7658 := [symm #7820]: #7657
+#7693 := [hypothesis]: #2836
+#4094 := (or #2831 #2217)
+#4095 := [def-axiom]: #4094
+#7819 := [unit-resolution #4095 #7693]: #2217
+#7659 := [trans #7819 #7658]: #7240
+#7320 := (not #7240)
+#7324 := (not #7242)
+#7325 := (or #7324 #7235 #7320)
+#7336 := [def-axiom]: #7325
+#7660 := [unit-resolution #7336 #7659 #7818]: #7235
+#7093 := (f5 f22 ?v0!14)
+#7094 := (f4 #7093)
+#7046 := (* -1::Int #2220)
+#7111 := (+ #7046 #7094)
+#7112 := (+ #174 #7111)
+#7113 := (>= #7112 0::Int)
+#7082 := (not #7113)
+#7095 := (* -1::Int #7094)
+#7099 := (+ f3 #7095)
+#7100 := (<= #7099 0::Int)
+#7118 := (or #7100 #7113)
+#7121 := (not #7118)
+#4090 := (not #2825)
+#4091 := (or #2831 #4090)
+#4096 := [def-axiom]: #4091
+#7694 := [unit-resolution #4096 #7693]: #4090
+#6455 := (or #4368 #2825 #7121)
+#7096 := (+ #1420 #7095)
+#7097 := (+ #2220 #7096)
+#7098 := (<= #7097 0::Int)
+#7101 := (or #7100 #7098)
+#7102 := (not #7101)
+#7103 := (or #2221 #7102)
+#6460 := (or #4368 #7103)
+#7131 := (iff #6460 #6455)
+#7124 := (or #2825 #7121)
+#6462 := (or #4368 #7124)
+#7129 := (iff #6462 #6455)
+#7130 := [rewrite]: #7129
+#6463 := (iff #6460 #6462)
+#7125 := (iff #7103 #7124)
+#7122 := (iff #7102 #7121)
+#7119 := (iff #7101 #7118)
+#7116 := (iff #7098 #7113)
+#7104 := (+ #2220 #7095)
+#7105 := (+ #1420 #7104)
+#7108 := (<= #7105 0::Int)
+#7114 := (iff #7108 #7113)
+#7115 := [rewrite]: #7114
+#7109 := (iff #7098 #7108)
+#7106 := (= #7097 #7105)
+#7107 := [rewrite]: #7106
+#7110 := [monotonicity #7107]: #7109
+#7117 := [trans #7110 #7115]: #7116
+#7120 := [monotonicity #7117]: #7119
+#7123 := [monotonicity #7120]: #7122
+#7126 := [monotonicity #2827 #7123]: #7125
+#7128 := [monotonicity #7126]: #6463
+#7144 := [trans #7128 #7130]: #7131
+#6461 := [quant-inst #2215]: #6460
+#7132 := [mp #6461 #7144]: #6455
+#7661 := [unit-resolution #7132 #6477 #7694]: #7121
+#7090 := (or #7118 #7082)
+#7091 := [def-axiom]: #7090
+#7656 := [unit-resolution #7091 #7661]: #7082
+#7246 := (not #7235)
+#8732 := (or #7234 #7113 #7246)
+decl f7 :: (-> S3 S2)
+#7276 := (f5 #6386 ?v0!14)
+#7316 := (f7 #7276)
+#7666 := (f13 f14 #7316)
+#7695 := (* -1::Int #7666)
+#7696 := (+ #6404 #7695)
+#7697 := (>= #7696 0::Int)
+#7692 := (f8 f15 #7316)
+#7665 := (= f1 #7692)
+#7797 := (= #7064 #7692)
+#7786 := (= #7692 #7064)
+#7776 := (= #7316 ?v0!14)
+#7317 := (= ?v0!14 #7316)
+#26 := (f7 #14)
+#350 := (= #12 #26)
+#4157 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4138) #350)
+#354 := (forall (vars (?v0 S2) (?v1 S2)) #350)
+#4160 := (iff #354 #4157)
+#4158 := (iff #350 #350)
+#4159 := [refl]: #4158
+#4161 := [quant-intro #4159]: #4160
+#1815 := (~ #354 #354)
+#1840 := (~ #350 #350)
+#1841 := [refl]: #1840
+#1816 := [nnf-pos #1841]: #1815
+#27 := (= #26 #12)
+#28 := (forall (vars (?v0 S2) (?v1 S2)) #27)
+#355 := (iff #28 #354)
+#352 := (iff #27 #350)
+#353 := [rewrite]: #352
+#356 := [quant-intro #353]: #355
+#349 := [asserted]: #28
+#359 := [mp #349 #356]: #354
+#1842 := [mp~ #359 #1816]: #354
+#4162 := [mp #1842 #4161]: #4157
+#5129 := (not #4157)
+#7448 := (or #5129 #7317)
+#7479 := [quant-inst #6386 #2215]: #7448
+#7785 := [unit-resolution #7479 #4162]: #7317
+#7707 := [symm #7785]: #7776
+#7794 := [monotonicity #7707]: #7786
+#7984 := [symm #7794]: #7797
+#7708 := [hypothesis]: #7235
+#7255 := (not #7234)
+#7783 := [hypothesis]: #7255
+#7272 := (or #7246 #7234 #7065)
+#7245 := [def-axiom]: #7272
+#7784 := [unit-resolution #7245 #7783 #7708]: #7065
+#7985 := [trans #7784 #7984]: #7665
+#7698 := (not #7665)
+#8065 := (or #7698 #7697)
+#6407 := (f8 f15 #6386)
+#6402 := (= f1 #6407)
+#7988 := (not #6402)
+#7871 := (iff #732 #7988)
+#7824 := (iff #729 #6402)
+#7983 := (iff #6402 #729)
+#7989 := (= #6407 #171)
+#8060 := [monotonicity #7565]: #7989
+#7823 := [monotonicity #8060]: #7983
+#7825 := [symm #7823]: #7824
+#8068 := [monotonicity #7825]: #7871
+#4020 := (or #4502 #732)
+#4015 := [def-axiom]: #4020
+#7986 := [unit-resolution #4015 #6451]: #732
+#8069 := [mp #7986 #8068]: #7988
+#3928 := (or #4514 #4258)
+#3983 := [def-axiom]: #3928
+#7878 := [unit-resolution #3983 #6450]: #4258
+#7702 := (or #4263 #6402 #7698 #7697)
+#7699 := (or #6402 #7698 #7697)
+#7712 := (or #4263 #7699)
+#7711 := (iff #7712 #7702)
+#7778 := [rewrite]: #7711
+#7777 := [quant-inst #7316 #6386]: #7712
+#7779 := [mp #7777 #7778]: #7702
+#8070 := [unit-resolution #7779 #7878 #8069]: #8065
+#8066 := [unit-resolution #8070 #7985]: #7697
+#8133 := [hypothesis]: #7082
+#7277 := (f4 #7276)
+#7278 := (* -1::Int #7277)
+#7616 := (+ #7094 #7278)
+#7632 := (>= #7616 0::Int)
+#7615 := (= #7094 #7277)
+#7873 := (= #7277 #7094)
+#8134 := (= #7276 #7093)
+#8414 := [monotonicity #7565]: #8134
+#8135 := [monotonicity #8414]: #7873
+#8147 := [symm #8135]: #7615
+#8146 := (not #7615)
+#8629 := (or #8146 #7632)
+#7870 := [th-lemma arith triangle-eq]: #8629
+#8667 := [unit-resolution #7870 #8147]: #7632
+#7459 := (>= #7277 0::Int)
+#7346 := (<= #7277 0::Int)
+#7348 := (not #7346)
+#7350 := (or #7234 #7348)
+#15 := (f4 #14)
+#329 := (<= #15 0::Int)
+#330 := (not #329)
+#13 := (= #11 #12)
+#333 := (or #13 #330)
+#4145 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4138) #333)
+#336 := (forall (vars (?v0 S2) (?v1 S2)) #333)
+#4148 := (iff #336 #4145)
+#4146 := (iff #333 #333)
+#4147 := [refl]: #4146
+#4149 := [quant-intro #4147]: #4148
+#1811 := (~ #336 #336)
+#1810 := (~ #333 #333)
+#1807 := [refl]: #1810
+#1812 := [nnf-pos #1807]: #1811
+#20 := (< 0::Int #15)
+#19 := (not #13)
+#21 := (implies #19 #20)
+#22 := (forall (vars (?v0 S2) (?v1 S2)) #21)
+#339 := (iff #22 #336)
+#323 := (or #13 #20)
+#326 := (forall (vars (?v0 S2) (?v1 S2)) #323)
+#337 := (iff #326 #336)
+#334 := (iff #323 #333)
+#331 := (iff #20 #330)
+#332 := [rewrite]: #331
+#335 := [monotonicity #332]: #334
+#338 := [quant-intro #335]: #337
+#327 := (iff #22 #326)
+#324 := (iff #21 #323)
+#325 := [rewrite]: #324
+#328 := [quant-intro #325]: #327
+#340 := [trans #328 #338]: #339
+#322 := [asserted]: #22
+#341 := [mp #322 #340]: #336
+#1808 := [mp~ #341 #1812]: #336
+#4150 := [mp #1808 #4149]: #4145
+#6420 := (not #4145)
+#7437 := (or #6420 #7234 #7348)
+#7322 := (= #6386 ?v0!14)
+#7349 := (or #7322 #7348)
+#7441 := (or #6420 #7349)
+#7532 := (iff #7441 #7437)
+#7445 := (or #6420 #7350)
+#7526 := (iff #7445 #7437)
+#7531 := [rewrite]: #7526
+#7446 := (iff #7441 #7445)
+#7351 := (iff #7349 #7350)
+#7328 := (iff #7322 #7234)
+#7329 := [rewrite]: #7328
+#7352 := [monotonicity #7329]: #7351
+#7525 := [monotonicity #7352]: #7446
+#7523 := [trans #7525 #7531]: #7532
+#7442 := [quant-inst #6386 #2215]: #7441
+#7524 := [mp #7442 #7523]: #7437
+#8625 := [unit-resolution #7524 #4150]: #7350
+#8630 := [unit-resolution #8625 #7783]: #7348
+#8631 := (or #7459 #7346)
+#7957 := [th-lemma arith farkas 1 1]: #8631
+#8132 := [unit-resolution #7957 #8630]: #7459
+#7781 := (+ #2220 #7695)
+#7821 := (<= #7781 0::Int)
+#7782 := (= #2220 #7666)
+#8155 := (= #7666 #2220)
+#8650 := [monotonicity #7707]: #8155
+#8413 := [symm #8650]: #7782
+#8160 := (not #7782)
+#8167 := (or #8160 #7821)
+#8168 := [th-lemma arith triangle-eq]: #8167
+#8537 := [unit-resolution #8168 #8413]: #7821
+#6414 := (* -1::Int #6404)
+#6751 := (+ #174 #6414)
+#6759 := (>= #6751 0::Int)
+#6382 := (= #174 #6404)
+#8807 := [monotonicity #7563]: #6382
+#8151 := (not #6382)
+#8148 := (or #8151 #6759)
+#8182 := [th-lemma arith triangle-eq]: #8148
+#8183 := [unit-resolution #8182 #8807]: #6759
+#8724 := [th-lemma arith farkas 1 1 1 1 -1 1 #8183 #8537 #8132 #8667 #8133 #8066]: false
+#8733 := [lemma #8724]: #8732
+#7662 := [unit-resolution #8733 #7656 #7660]: #7234
+#7795 := [monotonicity #7662]: #8808
+#8736 := [symm #7795]: #8791
+#8813 := (= #2219 #6404)
+#7796 := (= #6404 #174)
+#8734 := [monotonicity #7565]: #7796
+#8735 := [symm #8734]: #6382
+#8811 := (= #2219 #174)
+#5955 := (f24 f22)
+#8792 := (= #5955 #174)
+#5956 := (= #174 #5955)
+#5943 := (f5 f22 f22)
+#5944 := (f4 #5943)
+#5963 := (>= #5944 0::Int)
+#5947 := (* -1::Int #5944)
+#5951 := (+ f3 #5947)
+#5952 := (<= #5951 0::Int)
+#5968 := (or #5952 #5963)
+#7494 := (f5 #6386 #6386)
+#7495 := (f4 #7494)
+#7496 := (* -1::Int #7495)
+#7560 := (+ #5944 #7496)
+#7562 := (>= #7560 0::Int)
+#7559 := (= #5944 #7495)
+#7568 := (= #5943 #7494)
+#7566 := (= #7494 #5943)
+#7567 := [monotonicity #7565 #7565]: #7566
+#7569 := [symm #7567]: #7568
+#7570 := [monotonicity #7569]: #7559
+#7571 := (not #7559)
+#7572 := (or #7571 #7562)
+#7573 := [th-lemma arith triangle-eq]: #7572
+#7574 := [unit-resolution #7573 #7570]: #7562
+#7505 := (>= #7495 0::Int)
+#7533 := (= #7495 0::Int)
+#16 := (= #15 0::Int)
+#313 := (or #19 #16)
+#4139 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4138) #313)
+#316 := (forall (vars (?v0 S2) (?v1 S2)) #313)
+#4142 := (iff #316 #4139)
+#4140 := (iff #313 #313)
+#4141 := [refl]: #4140
+#4143 := [quant-intro #4141]: #4142
+#1835 := (~ #316 #316)
+#1833 := (~ #313 #313)
+#1834 := [refl]: #1833
+#1836 := [nnf-pos #1834]: #1835
+#17 := (implies #13 #16)
+#18 := (forall (vars (?v0 S2) (?v1 S2)) #17)
+#319 := (iff #18 #316)
+#292 := (= 0::Int #15)
+#303 := (or #19 #292)
+#308 := (forall (vars (?v0 S2) (?v1 S2)) #303)
+#317 := (iff #308 #316)
+#314 := (iff #303 #313)
+#311 := (iff #292 #16)
+#312 := [rewrite]: #311
+#315 := [monotonicity #312]: #314
+#318 := [quant-intro #315]: #317
+#309 := (iff #18 #308)
+#306 := (iff #17 #303)
+#300 := (implies #13 #292)
+#304 := (iff #300 #303)
+#305 := [rewrite]: #304
+#301 := (iff #17 #300)
+#298 := (iff #16 #292)
+#299 := [rewrite]: #298
+#302 := [monotonicity #299]: #301
+#307 := [trans #302 #305]: #306
+#310 := [quant-intro #307]: #309
+#320 := [trans #310 #318]: #319
+#291 := [asserted]: #18
+#321 := [mp #291 #320]: #316
+#1809 := [mp~ #321 #1836]: #316
+#4144 := [mp #1809 #4143]: #4139
+#6380 := (not #4139)
+#7549 := (or #6380 #7533)
+#7364 := (= #6386 #6386)
+#7534 := (not #7364)
+#7537 := (or #7534 #7533)
+#7550 := (or #6380 #7537)
+#7552 := (iff #7550 #7549)
+#7554 := (iff #7549 #7549)
+#7555 := [rewrite]: #7554
+#7547 := (iff #7537 #7533)
+#7542 := (or false #7533)
+#7545 := (iff #7542 #7533)
+#7546 := [rewrite]: #7545
+#7543 := (iff #7537 #7542)
+#7540 := (iff #7534 false)
+#7538 := (iff #7534 #5500)
+#7369 := (iff #7364 true)
+#7370 := [rewrite]: #7369
+#7539 := [m