updated SMT certificates

--- 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)
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+#1407 := (iff #717 #1406)
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+#1401 := (iff #700 #1400)
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+#1365 := [rewrite]: #1364
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+#1313 := (iff #143 #1312)
+#1314 := [rewrite]: #1313
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+#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
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+#1330 := [rewrite]: #1328
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+#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)
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+#1286 := (and #508 #1276)
+#1289 := (and #1283 #1286)
+#1293 := (iff #1289 #1292)
+#1294 := [rewrite]: #1293
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+#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)
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+#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)
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+#1244 := (and #1238 #429)
+#1247 := (and #1241 #1244)
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+#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)
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+#1215 := (iff #470 #1214)
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+#1206 := (and #1203 #429)
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+#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)
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-#1155 := (iff #266 #1152)
-#1148 := (implies #459 #1145)
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-#1146 := (iff #265 #1145)
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-#1136 := (implies #462 #1133)
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-#1142 := [rewrite]: #1141
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-#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
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+#1769 := [monotonicity #1162 #1766]: #1768
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+#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
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+#1159 := (iff #270 #1158)
+#1156 := (iff #269 #1146)
+#1151 := (implies true #1146)
+#1154 := (iff #1151 #1146)
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+#1139 := [rewrite]: #1138
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+#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)
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+#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)
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-#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)
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-#1054 := (implies #553 #1049)
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-#1060 := [rewrite]: #1059
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-#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
+#4357 := [quant-intro #4355]: #4356
+#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)
-#4363 := (iff #3369 #4362)
-#4360 := (iff #3368 #4359)
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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)
+#4348 := (iff #3358 #4347)
+#4345 := (iff #3357 #4344)
+#4342 := (iff #3350 #4341)
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+#4333 := (iff #3343 #4332)
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+#4321 := (iff #3307 #4320)
+#4318 := (iff #3301 #4315)
+#4316 := (iff #3296 #3296)
+#4317 := [refl]: #4316
+#4319 := [quant-intro #4317]: #4318
+#4322 := [monotonicity #4319]: #4321
+#4325 := [monotonicity #4322]: #4324
+#4328 := [monotonicity #4325]: #4327
+#4331 := [monotonicity #4328]: #4330
+#4334 := [monotonicity #4331]: #4333
+#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
-#4297 := [monotonicity #4294]: #4296
-#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
-#4280 := [monotonicity #4277]: #4279
-#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)
+#4299 := (iff #3248 #4298)
+#4296 := (iff #3242 #4293)
+#4294 := (iff #3231 #3231)
+#4295 := [refl]: #4294
+#4297 := [quant-intro #4295]: #4296
+#4300 := [monotonicity #4297]: #4299
+#4303 := [monotonicity #4300]: #4302
+#4306 := [monotonicity #4303]: #4305
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+#4286 := (iff #3227 #4283)
+#4284 := (iff #3216 #3216)
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+#4349 := [monotonicity #4290 #4346]: #4348
+#4352 := [monotonicity #4349]: #4351
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+#4277 := (iff #3213 #4274)
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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
+#4516 := [monotonicity #4248 #4256 #4265 #4273 #4281 #4513]: #4515
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+#4236 := [monotonicity #4233]: #4235
+#4239 := [monotonicity #4236]: #4238
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+#4220 := (iff #3087 #4217)
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+#4211 := (iff #3042 #4208)
+#4209 := (iff #3037 #3037)
+#4210 := [refl]: #4209
+#4212 := [quant-intro #4210]: #4211
+#4215 := [monotonicity #4212]: #4214
+#4540 := [monotonicity #4215 #4537]: #4539
+#4543 := [monotonicity #4540]: #4542
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+#4202 := (iff #1169 #4199)
+#4200 := (iff #1168 #1168)
+#4201 := [refl]: #4200
+#4203 := [quant-intro #4201]: #4202
+#4206 := [monotonicity #4203]: #4205
+#4552 := [monotonicity #4206 #4549]: #4551
 #4555 := [monotonicity #4552]: #4554
 #4558 := [monotonicity #4555]: #4557
 #4561 := [monotonicity #4558]: #4560
-#4238 := (iff #3651 #4237)
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-#4234 := [refl]: #4233
-#4236 := [quant-intro #4234]: #4235
-#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
-#4227 := [quant-intro #4225]: #4226
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-#2954 := (forall (vars (?v1 S3)) #2951)
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-#3004 := (and #181 #756 #1462 #1620 #1638 #1646 #2202 #2205 #2998)
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-#3521 := [quant-intro #3518]: #3520
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-#3498 := [monotonicity #3495]: #3497
-#3503 := [trans #3498 #3501]: #3502
-#3506 := [quant-intro #3503]: #3505
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-#3470 := (iff #3467 #3463)
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+#3373 := [quant-intro #3370]: #3372
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+#3315 := (not #3314)
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 #3322 := [rewrite]: #3321
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-#3309 := [rewrite]: #3308
-#3312 := [monotonicity #3309]: #3311
-#3316 := [trans #3312 #3314]: #3315
-#3319 := [monotonicity #3316]: #3318
-#3324 := [trans #3319 #3322]: #3323
-#3327 := [quant-intro #3324]: #3326
-#3330 := [monotonicity #3327]: #3329
-#3337 := [trans #3330 #3335]: #3336
-#3362 := [monotonicity #3337 #3359]: #3361
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-#3282 := [rewrite]: #3281
-#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)
-#1964 := (+ #58 #1963)
-#1965 := (= #1964 0::Int)
-#1969 := (and #453 #1968 #1965)
-#1985 := (not #1969)
-#1988 := (forall (vars (?v1 S3)) #1985)
-#1974 := (= ?v0!5 f10)
-#1975 := (not #1974)
-#1976 := (and #1975 #1973)
-#1977 := (not #1976)
-#1982 := (not #1977)
-#1992 := (and #1982 #1988)
-#2473 := (or #1992 #2469)
-#2477 := (and #1244 #2473)
-#1937 := (and #1936 #1934)
-#1938 := (not #1937)
-#1941 := (+ #1940 #1930)
-#1943 := (+ #1942 #1941)
-#1944 := (>= #1943 0::Int)
-#1945 := (or #1944 #1938)
-#1946 := (not #1945)
-#2481 := (or #1946 #2477)
-#2485 := (and #1213 #2481)
-#1903 := (* -1::Int #1902)
-#1905 := (+ #1904 #1903)
-#1906 := (>= #1905 0::Int)
-#1912 := (and #1911 #1908)
-#1913 := (not #1912)
-#1914 := (or #1913 #1906)
-#1915 := (not #1914)
-#2489 := (or #1915 #2485)
-#2493 := (and #1193 #2489)
-#2497 := (or #1888 #2493)
-#1851 := (not #1187)
-#2501 := (and #1851 #2497)
-#2505 := (or #1187 #2501)
-#3045 := (iff #2505 #3044)
-#3042 := (iff #2501 #3041)
-#3039 := (iff #2497 #3038)
-#3036 := (iff #2493 #3035)
-#3033 := (iff #2489 #3032)
-#3030 := (iff #2485 #3029)
-#3027 := (iff #2481 #3026)
-#3024 := (iff #2477 #3023)
-#3021 := (iff #2473 #3020)
-#3018 := (iff #2469 #3015)
-#3012 := (and #100 #2644 #2684 #3009 #1705 #1721 #1730)
-#3016 := (iff #3012 #3015)
-#3017 := [rewrite]: #3016
-#3013 := (iff #2469 #3012)
-#3010 := (iff #2444 #3009)
-#3007 := (iff #2440 #3004)
-#3001 := (and #181 #756 #2206 #1462 #2998 #1620 #1638 #1646)
-#3005 := (iff #3001 #3004)
-#3006 := [rewrite]: #3005
-#3002 := (iff #2440 #3001)
-#2999 := (iff #2420 #2998)
-#2996 := (iff #2416 #2995)
-#2993 := (iff #2412 #2992)
-#2990 := (iff #2408 #2989)
-#2987 := (iff #2404 #2986)
-#2984 := (iff #2400 #2983)
-#2981 := (iff #2396 #2980)
-#2978 := (iff #2392 #2977)
-#2975 := (iff #2388 #2974)
-#2972 := (iff #2384 #2971)
-#2969 := (iff #2380 #2968)
-#2966 := (iff #2376 #2963)
-#2926 := (and #2351 #2920)
-#2957 := (and #2926 #2954)
-#2960 := (and #1530 #2957)
-#2964 := (iff #2960 #2963)
-#2965 := [rewrite]: #2964
-#2961 := (iff #2376 #2960)
-#2958 := (iff #2371 #2957)
-#2955 := (iff #2367 #2954)
-#2952 := (iff #2364 #2951)
-#2949 := (iff #2347 #2948)
-#2946 := (iff #2344 #2945)
-#2943 := (= #2343 #2942)
-#2944 := [rewrite]: #2943
-#2947 := [monotonicity #2944]: #2946
-#2950 := [monotonicity #2947]: #2949
-#2953 := [monotonicity #2950]: #2952
-#2956 := [quant-intro #2953]: #2955
-#2939 := (iff #2361 #2926)
-#2931 := (not #2926)
-#2934 := (not #2931)
-#2937 := (iff #2934 #2926)
-#2938 := [rewrite]: #2937
-#2935 := (iff #2361 #2934)
-#2932 := (iff #2355 #2931)
-#2929 := (iff #2354 #2926)
-#2923 := (and #2920 #2351)
-#2927 := (iff #2923 #2926)
-#2928 := [rewrite]: #2927
-#2924 := (iff #2354 #2923)
-#2921 := (iff #2353 #2920)
-#2918 := (iff #2352 #2917)
-#2919 := [rewrite]: #2918
-#2922 := [monotonicity #2919]: #2921
-#2925 := [monotonicity #2922]: #2924
-#2930 := [trans #2925 #2928]: #2929
-#2933 := [monotonicity #2930]: #2932
-#2936 := [monotonicity #2933]: #2935
-#2940 := [trans #2936 #2938]: #2939
-#2959 := [monotonicity #2940 #2956]: #2958
-#2962 := [monotonicity #2959]: #2961
-#2967 := [trans #2962 #2965]: #2966
-#2915 := (iff #2325 #2914)
-#2912 := (iff #2324 #2911)
-#2909 := (iff #2315 #2906)
-#2896 := (+ #2310 #2313)
-#2897 := (+ #2309 #2896)
-#2900 := (>= #2897 0::Int)
-#2907 := (iff #2900 #2906)
-#2908 := [rewrite]: #2907
-#2901 := (iff #2315 #2900)
-#2898 := (= #2314 #2897)
-#2899 := [rewrite]: #2898
-#2902 := [monotonicity #2899]: #2901
-#2910 := [trans #2902 #2908]: #2909
-#2894 := (iff #2323 #2893)
-#2891 := (iff #2322 #2890)
-#2892 := [rewrite]: #2891
-#2895 := [monotonicity #2892]: #2894
-#2913 := [monotonicity #2895 #2910]: #2912
-#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
+#3113 := (iff #2576 #3110)
+#3105 := (and #1949 #2536 #3102)
+#3111 := (iff #3105 #3110)
+#3112 := [rewrite]: #3111
+#3106 := (iff #2576 #3105)
+#3103 := (iff #2570 #3102)
+#3100 := (iff #2567 #3091)
+#3092 := (not #3091)
+#3095 := (not #3092)
+#3098 := (iff #3095 #3091)
+#3099 := [rewrite]: #3098
+#3096 := (iff #2567 #3095)
+#3093 := (iff #2564 #3092)
+#3094 := [rewrite]: #3093
+#3097 := [monotonicity #3094]: #3096
+#3101 := [trans #3097 #3099]: #3100
+#3104 := [quant-intro #3101]: #3103
+#3107 := [monotonicity #3104]: #3106
+#3114 := [trans #3107 #3112]: #3113
+#3609 := [monotonicity #3114 #3606]: #3608
+#3088 := (iff #1220 #3087)
+#3085 := (iff #1217 #3082)
+#3068 := (or #432 #1202)
+#3079 := (or #1197 #3068)
+#3083 := (iff #3079 #3082)
+#3084 := [rewrite]: #3083
+#3080 := (iff #1217 #3079)
+#3077 := (iff #1214 #3068)
+#3069 := (not #3068)
+#3072 := (not #3069)
+#3075 := (iff #3072 #3068)
+#3076 := [rewrite]: #3075
+#3073 := (iff #1214 #3072)
+#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
+#3612 := [monotonicity #3089 #3609]: #3611
+#3620 := [trans #3612 #3618]: #3619
+#3066 := (iff #2530 #3065)
+#3063 := (iff #2527 #3060)
+#3046 := (or #1909 #3045)
+#3057 := (or #2518 #3046)
+#3061 := (iff #3057 #3060)
+#3062 := [rewrite]: #3061
+#3058 := (iff #2527 #3057)
+#3055 := (iff #2524 #3046)
+#3047 := (not #3046)
+#3050 := (not #3047)
+#3053 := (iff #3050 #3046)
+#3054 := [rewrite]: #3053
+#3051 := (iff #2524 #3050)
+#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
+#3623 := [monotonicity #3067 #3620]: #3622
+#3043 := (iff #1189 #3042)
+#3040 := (iff #1184 #3037)
+#3023 := (or #429 #2486)
+#3034 := (or #3023 #1177)
+#3038 := (iff #3034 #3037)
+#3039 := [rewrite]: #3038
+#3035 := (iff #1184 #3034)
+#3032 := (iff #450 #3023)
+#3024 := (not #3023)
+#3027 := (not #3024)
+#3030 := (iff #3027 #3023)
+#3031 := [rewrite]: #3030
+#3028 := (iff #450 #3027)
+#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)
+#1894 := (or #2131 #1886)
+#2274 := (or #1894 #2503)
+#2305 := (iff #2274 #2304)
+#1867 := [rewrite]: #2305
+#2185 := (iff #2508 #2274)
+#2096 := (iff #2492 #1894)
+#1831 := (not #1894)
+#2206 := (not #1831)
+#1926 := (iff #2206 #1894)
+#2095 := [rewrite]: #1926
+#2207 := (iff #2492 #2206)
+#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)
+#2320 := (= #2319 0::Int)
+#2323 := (and #774 #2322 #2320)
+#2340 := (not #2323)
+#2343 := (forall (vars (?v1 S2)) #2340)
+#2328 := (= ?v0!20 f10)
+#2329 := (not #2328)
+#2330 := (and #2329 #2327)
+#2331 := (not #2330)
+#2337 := (not #2331)
+#2347 := (and #2337 #2343)
+#2352 := (and #1506 #2347)
+#2285 := (* -1::Int #2284)
+#2287 := (+ #2286 #2285)
+#2290 := (+ #2289 #2287)
+#2291 := (>= #2290 0::Int)
+#2298 := (and #2297 #2295)
+#2299 := (not #2298)
+#2300 := (or #2299 #2291)
+#2301 := (not #2300)
+#2356 := (or #2301 #2352)
+#2360 := (and #1482 #2356)
+#2258 := (* -1::Int #2257)
+#2260 := (+ #2259 #2258)
+#2261 := (>= #2260 0::Int)
+#2267 := (and #2266 #2263)
+#2268 := (not #2267)
+#2269 := (or #2268 #2261)
+#2270 := (not #2269)
+#2364 := (or #2270 #2360)
+#2368 := (and #1463 #2364)
+#2372 := (or #2243 #2368)
+#2237 := (not #1457)
+#2376 := (and #2237 #2372)
+#2380 := (or #1457 #2376)
+#2384 := (and #786 #2380)
+#2221 := (= #2220 #2219)
+#2222 := (or #2221 #2218)
+#2223 := (not #2222)
+#2388 := (or #2223 #2384)
+#2392 := (and #1449 #2388)
+#2199 := (* -1::Int #2198)
+#2201 := (+ #2200 #2199)
+#2202 := (>= #2201 0::Int)
+#2203 := (not #2202)
+#2396 := (or #2203 #2392)
+#2182 := (and #2181 #2178)
+#2168 := (not #962)
+#2416 := (and #2168 #732 #2182 #1438 #2396 #1596 #1614 #1622)
+#2109 := (* -1::Int #2108)
+#2111 := (+ #2110 #2109)
+#2114 := (+ #2113 #2111)
+#2115 := (>= #2114 0::Int)
+#2124 := (and #2123 #2119)
+#2125 := (not #2124)
+#2126 := (or #2125 #2115)
+#2127 := (not #2126)
+#2146 := (or #2127 #2142)
+#2085 := (+ #2084 #1309)
+#2088 := (+ #2087 #2085)
+#2089 := (= #2088 0::Int)
+#2090 := (>= #2085 0::Int)
+#2091 := (not #2090)
+#2092 := (and #2091 #2089)
+#2097 := (or #1318 #2092)
+#2100 := (forall (vars (?v0 S2)) #2097)
+#2150 := (and #2100 #2146)
+#2049 := (+ #2048 #2046)
+#2050 := (= #2049 0::Int)
+#2053 := (and #2052 #2050)
+#2069 := (not #2053)
+#2072 := (forall (vars (?v1 S2)) #2069)
+#2058 := (= ?v0!8 f10)
+#2059 := (not #2058)
+#2060 := (and #2059 #2057)
+#2061 := (not #2060)
+#2066 := (not #2061)
+#2076 := (and #2066 #2072)
+#2154 := (or #2076 #2150)
+#2040 := (not #690)
+#2037 := (not #708)
+#2034 := (not #681)
+#2031 := (not #699)
+#2164 := (and #2031 #2034 #2037 #2040 #2154 #2161)
+#2420 := (or #2164 #2416)
+#2008 := (+ #2007 #1264)
+#2009 := (>= #2008 0::Int)
+#2010 := (not #2009)
+#2013 := (+ #2012 #2008)
+#2014 := (= #2013 0::Int)
+#2017 := (and #2016 #2014 #2010)
+#2022 := (or #1273 #2017)
+#2025 := (forall (vars (?v0 S2)) #2022)
+#1981 := (+ #1226 #1980)
+#1983 := (+ #1982 #1981)
+#1984 := (= #1983 0::Int)
+#1985 := (+ #1982 #1226)
+#1986 := (>= #1985 0::Int)
+#1987 := (not #1986)
+#1990 := (and #1989 #1987 #1984)
+#1995 := (or #1235 #1990)
+#1998 := (forall (vars (?v0 S2)) #1995)
+#1973 := (not #1714)
+#2445 := (and #1973 #1998 #2025 #2420 #1681 #1697 #1706)
+#1939 := (+ #1938 #1936)
+#1940 := (+ #58 #1939)
+#1941 := (= #1940 0::Int)
+#1945 := (and #429 #1944 #1941)
+#1961 := (not #1945)
+#1964 := (forall (vars (?v1 S2)) #1961)
+#1951 := (not #1950)
+#1952 := (and #1951 #1949)
+#1953 := (not #1952)
+#1958 := (not #1953)
+#1968 := (and #1958 #1964)
+#2449 := (or #1968 #2445)
+#2453 := (and #1220 #2449)
+#1913 := (and #1912 #1910)
+#1914 := (not #1913)
+#1917 := (+ #1916 #1906)
+#1919 := (+ #1918 #1917)
+#1920 := (>= #1919 0::Int)
+#1921 := (or #1920 #1914)
+#1922 := (not #1921)
+#2457 := (or #1922 #2453)
+#2461 := (and #1189 #2457)
+#1879 := (* -1::Int #1878)
+#1881 := (+ #1880 #1879)
+#1882 := (>= #1881 0::Int)
+#1888 := (and #1887 #1884)
+#1889 := (not #1888)
+#1890 := (or #1889 #1882)
+#1891 := (not #1890)
+#2465 := (or #1891 #2461)
+#2469 := (and #1169 #2465)
+#2473 := (or #1864 #2469)
+#1827 := (not #1163)
+#2477 := (and #1827 #2473)
+#2481 := (or #1163 #2477)
+#3021 := (iff #2481 #3020)
+#3018 := (iff #2477 #3017)
+#3015 := (iff #2473 #3014)
+#3012 := (iff #2469 #3011)
+#3009 := (iff #2465 #3008)
+#3006 := (iff #2461 #3005)
+#3003 := (iff #2457 #3002)
+#3000 := (iff #2453 #2999)
+#2997 := (iff #2449 #2996)
+#2994 := (iff #2445 #2991)
+#2988 := (and #100 #2620 #2660 #2985 #1681 #1697 #1706)
+#2992 := (iff #2988 #2991)
+#2993 := [rewrite]: #2992
+#2989 := (iff #2445 #2988)
+#2986 := (iff #2420 #2985)
+#2983 := (iff #2416 #2980)
+#2977 := (and #181 #732 #2182 #1438 #2974 #1596 #1614 #1622)
+#2981 := (iff #2977 #2980)
+#2982 := [rewrite]: #2981
+#2978 := (iff #2416 #2977)
+#2975 := (iff #2396 #2974)
+#2972 := (iff #2392 #2971)
+#2969 := (iff #2388 #2968)
+#2966 := (iff #2384 #2965)
+#2963 := (iff #2380 #2962)
+#2960 := (iff #2376 #2959)
+#2957 := (iff #2372 #2956)
+#2954 := (iff #2368 #2953)
+#2951 := (iff #2364 #2950)
+#2948 := (iff #2360 #2947)
+#2945 := (iff #2356 #2944)
+#2942 := (iff #2352 #2939)
+#2902 := (and #2327 #2896)
+#2933 := (and #2902 #2930)
+#2936 := (and #1506 #2933)
+#2940 := (iff #2936 #2939)
+#2941 := [rewrite]: #2940
+#2937 := (iff #2352 #2936)
+#2934 := (iff #2347 #2933)
+#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)
+#2905 := (iff #2330 #2902)
+#2899 := (and #2896 #2327)
+#2903 := (iff #2899 #2902)
+#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
-#4014 := (or #4538 #4532)
-#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
-#4949 := [th-lemma arith farkas 1 -1 1 1 #4948 #4947 #4946 #4945]: false
-#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
-#5755 := (or #4628 #4846)
-#3811 := (or #4325 #2698)
-#3816 := [def-axiom]: #3811
-#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)
-#4849 := (or #2695 #4628 #4846)
-#4854 := (or #4303 #4849)
-#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)
-#5040 := (<= #5017 0::Int)
-#5226 := (<= #5222 0::Int)
-#5759 := (or #5714 #5226)
-#5760 := [th-lemma arith triangle-eq]: #5759
-#5761 := [unit-resolution #5760 #5713]: #5226
-#4877 := (<= #4782 0::Int)
-#4896 := (or #4772 #4764)
-#4898 := [def-axiom]: #4896
-#5762 := [unit-resolution #4898 #5757]: #4764
-#5763 := (or #4767 #4877)
-#5764 := [th-lemma arith triangle-eq]: #5763
-#5765 := [unit-resolution #5764 #5762]: #4877
-#4978 := (<= #4977 0::Int)
-#5408 := (or #5407 #4978)
-#5409 := [th-lemma arith triangle-eq]: #5408
-#5766 := [unit-resolution #5409 #5743]: #4978
-#5350 := (not #5226)
-#5349 := (not #4877)
-#5348 := (not #4978)
-#5351 := (or #5040 #5348 #5349 #5350)
-#5342 := [hypothesis]: #5226
-#5343 := [hypothesis]: #4877
-#5344 := [hypothesis]: #4978
-#5345 := (not #5040)
-#5346 := [hypothesis]: #5345
-#5347 := [th-lemma arith farkas -1 1 1 1 #5346 #5344 #5343 #5342]: false
-#5352 := [lemma #5347]: #5351
-#5767 := [unit-resolution #5352 #5766 #5765 #5761]: #5040
-#5041 := (>= #5017 0::Int)
-#4878 := (>= #4782 0::Int)
-#5768 := (or #4767 #4878)
-#5769 := [th-lemma arith triangle-eq]: #5768
-#5770 := [unit-resolution #5769 #5762]: #4878
-#5750 := (not #5227)
-#5390 := (not #4878)
-#5751 := (or #5041 #4985 #5390 #5750)
-#5746 := [hypothesis]: #5227
-#5386 := [hypothesis]: #4878
-#5747 := (not #5041)
-#5748 := [hypothesis]: #5747
-#5749 := [th-lemma arith farkas -1 1 1 1 #5748 #4982 #5386 #5746]: false
-#5752 := [lemma #5749]: #5751
-#5771 := [unit-resolution #5752 #5744 #5770 #5729]: #5041
-#5772 := (or #5018 #5345 #5747)
-#5773 := [th-lemma arith triangle-eq]: #5772
-#5774 := [unit-resolution #5773 #5771 #5767]: #5018
-#5023 := (not #5018)
-#5026 := (or #5004 #5023)
-#4152 := (or #4325 #4317)
-#3812 := [def-axiom]: #4152
-#5775 := [unit-resolution #3812 #5740]: #4317
-#5029 := (or #4322 #5004 #5023)
-#4988 := (+ #2069 #4700)
-#4990 := (+ #4989 #4988)
-#4991 := (= #4990 0::Int)
-#4992 := (not #4991)
-#4993 := (+ #4989 #2069)
-#4994 := (>= #4993 0::Int)
-#4995 := (or #4994 #4992)
-#5030 := (or #4322 #4995)
-#5037 := (iff #5030 #5029)
-#5032 := (or #4322 #5026)
-#5035 := (iff #5032 #5029)
-#5036 := [rewrite]: #5035
-#5033 := (iff #5030 #5032)
-#5027 := (iff #4995 #5026)
-#5024 := (iff #4992 #5023)
-#5021 := (iff #4991 #5018)
-#5009 := (+ #4700 #4989)
-#5010 := (+ #2069 #5009)
-#5013 := (= #5010 0::Int)
-#5019 := (iff #5013 #5018)
-#5020 := [rewrite]: #5019
-#5014 := (iff #4991 #5013)
-#5011 := (= #4990 #5010)
-#5012 := [rewrite]: #5011
-#5015 := [monotonicity #5012]: #5014
-#5022 := [trans #5015 #5020]: #5021
-#5025 := [monotonicity #5022]: #5024
-#5007 := (iff #4994 #5004)
-#4996 := (+ #2069 #4989)
-#4999 := (>= #4996 0::Int)
-#5005 := (iff #4999 #5004)
-#5006 := [rewrite]: #5005
-#5000 := (iff #4994 #4999)
-#4997 := (= #4993 #4996)
-#4998 := [rewrite]: #4997
-#5001 := [monotonicity #4998]: #5000
-#5008 := [trans #5001 #5006]: #5007
-#5028 := [monotonicity #5008 #5025]: #5027
-#5034 := [monotonicity #5028]: #5033
-#5038 := [trans #5034 #5036]: #5037
-#5031 := [quant-inst #4713]: #5030
-#5039 := [mp #5031 #5038]: #5029
-#5776 := [unit-resolution #5039 #5775]: #5026
-#5777 := [unit-resolution #5776 #5774]: #5004
-#5778 := [th-lemma arith farkas 1 -1 1 1 #5744 #5777 #5758 #5729]: false
-#5780 := [lemma #5778]: #5779
-#6499 := [unit-resolution #5780 #6498]: #4529
-#4035 := (or #4526 #4387)
-#4030 := [def-axiom]: #4035
-#6500 := [unit-resolution #4030 #6499]: #4387
-#9490 := (or #4392 #7530 #7632)
-#7583 := (+ #1444 #7582)
-#7584 := (+ #7527 #7583)
-#7585 := (<= #7584 0::Int)
-#7626 := (or #7587 #7585)
-#7627 := (not #7626)
-#7528 := (= #7527 #2265)
-#7628 := (or #7528 #7627)
-#9491 := (or #4392 #7628)
-#9498 := (iff #9491 #9490)
-#9493 := (or #4392 #7635)
-#9496 := (iff #9493 #9490)
-#9497 := [rewrite]: #9496
-#9494 := (iff #9491 #9493)
-#7636 := (iff #7628 #7635)
-#7633 := (iff #7627 #7632)
-#7630 := (iff #7626 #7629)
-#7601 := (iff #7585 #7598)
-#7589 := (+ #7527 #7582)
-#7590 := (+ #1444 #7589)
-#7593 := (<= #7590 0::Int)
-#7599 := (iff #7593 #7598)
-#7600 := [rewrite]: #7599
-#7594 := (iff #7585 #7593)
-#7591 := (= #7584 #7590)
-#7592 := [rewrite]: #7591
-#7595 := [monotonicity #7592]: #7594
-#7602 := [trans #7595 #7600]: #7601
-#7631 := [monotonicity #7602]: #7630
-#7634 := [monotonicity #7631]: #7633
-#7531 := (iff #7528 #7530)
-#7532 := [rewrite]: #7531
-#7637 := [monotonicity #7532 #7634]: #7636
-#9495 := [monotonicity #7637]: #9494
-#9499 := [trans #9495 #9497]: #9498
-#9492 := [quant-inst #2264]: #9491
-#9500 := [mp #9492 #9499]: #9490
-#10068 := [unit-resolution #9500 #6500]: #7635
-#10069 := [unit-resolution #10068 #10067]: #7632
-#9502 := (or #7629 #9501)
-#9503 := [def-axiom]: #9502
-#10070 := [unit-resolution #9503 #10069]: #9501
-#9504 := (not #7598)
-#9505 := (or #7629 #9504)
-#9506 := [def-axiom]: #9505
-#10071 := [unit-resolution #9506 #10069]: #9504
-#7610 := (or #7587 #7598 #7607)
-#4036 := (or #4526 #4395)
-#4009 := [def-axiom]: #4036
-#6504 := [unit-resolution #4009 #6499]: #4395
-#9477 := (or #4400 #7587 #7598 #7607)
-#7579 := (+ #7578 #7552)
-#7580 := (+ #174 #7579)
-#7581 := (= #7580 0::Int)
-#7588 := (or #7587 #7585 #7581)
-#9478 := (or #4400 #7588)
-#9485 := (iff #9478 #9477)
-#9480 := (or #4400 #7610)
-#9483 := (iff #9480 #9477)
-#9484 := [rewrite]: #9483
-#9481 := (iff #9478 #9480)
-#7611 := (iff #7588 #7610)
-#7608 := (iff #7581 #7607)
-#7605 := (= #7580 #7604)
-#7606 := [rewrite]: #7605
-#7609 := [monotonicity #7606]: #7608
-#7612 := [monotonicity #7602 #7609]: #7611
-#9482 := [monotonicity #7612]: #9481
-#9486 := [trans #9482 #9484]: #9485
-#9479 := [quant-inst #2264]: #9478
-#9487 := [mp #9479 #9486]: #9477
-#10072 := [unit-resolution #9487 #6504]: #7610
-#10073 := [unit-resolution #10072 #10071 #10070]: #7607
-#10074 := (not #7607)
-#10075 := (or #10074 #9488)
-#10076 := [th-lemma arith triangle-eq]: #10075
-#10077 := [unit-resolution #10076 #10073]: #9488
-#10041 := (>= #9980 0::Int)
-#10016 := (<= #9980 0::Int)
-#10017 := (not #10016)
-#9940 := (= ?v0!15 #7202)
-#9959 := (not #9940)
-#7659 := (f3 f15 ?v0!15)
-#7660 := (= f1 #7659)
-#5882 := (f3 #180 f22)
-#5883 := (= f1 #5882)
-#9943 := (ite #9940 #5883 #7660)
-#9958 := (not #9943)
-#8433 := (f4 f15 #7202 #5882)
-#9937 := (f3 #8433 ?v0!15)
-#9938 := (= f1 #9937)
-#9946 := (iff #9938 #9943)
-#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)
-#294 := (= #9 #12)
-#303 := (ite #294 #297 #300)
-#291 := (= f1 #13)
-#306 := (iff #291 #303)
-#4163 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) (:pat #4162) #306)
-#309 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S1) (?v3 S3)) #306)
-#4166 := (iff #309 #4163)
-#4164 := (iff #306 #306)
-#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 := [monotonicity #7370]: #7538
+#7541 := [trans #7539 #5538]: #7540
+#7544 := [monotonicity #7541]: #7543
+#7548 := [trans #7544 #7546]: #7547
+#7553 := [monotonicity #7548]: #7552
+#7556 := [trans #7553 #7555]: #7552
+#7551 := [quant-inst #6386 #6386]: #7550
+#7557 := [mp #7551 #7556]: #7549
+#7575 := [unit-resolution #7557 #4144]: #7533
+#7576 := (not #7533)
+#7577 := (or #7576 #7505)
+#7578 := [th-lemma arith triangle-eq]: #7577
+#7579 := [unit-resolution #7578 #7575]: #7505
+#5991 := (not #5963)
+#7580 := [hypothesis]: #5991
+#7581 := [th-lemma arith farkas -1 1 1 #7580 #7579 #7574]: false
+#7582 := [lemma #7581]: #5963
+#5992 := (or #5968 #5991)
+#5993 := [def-axiom]: #5992
+#8785 := [unit-resolution #5993 #7582]: #5968
+#5971 := (not #5968)
+#5974 := (or #5956 #5971)
+#5977 := (or #4368 #5956 #5971)
+#5948 := (+ #1420 #5947)
+#5949 := (+ #174 #5948)
+#5950 := (<= #5949 0::Int)
+#5953 := (or #5952 #5950)
+#5954 := (not #5953)
+#5957 := (or #5956 #5954)
+#5978 := (or #4368 #5957)
+#5985 := (iff #5978 #5977)
+#5980 := (or #4368 #5974)
+#5983 := (iff #5980 #5977)
+#5984 := [rewrite]: #5983
+#5981 := (iff #5978 #5980)
+#5975 := (iff #5957 #5974)
+#5972 := (iff #5954 #5971)
+#5969 := (iff #5953 #5968)
+#5966 := (iff #5950 #5963)
+#5960 := (<= #5947 0::Int)
+#5964 := (iff #5960 #5963)
+#5965 := [rewrite]: #5964
+#5961 := (iff #5950 #5960)
+#5958 := (= #5949 #5947)
+#5959 := [rewrite]: #5958
+#5962 := [monotonicity #5959]: #5961
+#5967 := [trans #5962 #5965]: #5966
+#5970 := [monotonicity #5967]: #5969
+#5973 := [monotonicity #5970]: #5972
+#5976 := [monotonicity #5973]: #5975
+#5982 := [monotonicity #5976]: #5981
+#5986 := [trans #5982 #5984]: #5985
+#5979 := [quant-inst #170]: #5978
+#5987 := [mp #5979 #5986]: #5977
+#8793 := [unit-resolution #5987 #6477]: #5974
+#8794 := [unit-resolution #8793 #8785]: #5956
+#8806 := [symm #8794]: #8792
+#8795 := (= #2219 #5955)
+#8788 := (= ?v0!14 f22)
+#7663 := [trans #7662 #7565]: #8788
+#7981 := [monotonicity #7663]: #8795
+#8725 := [trans #7981 #8806]: #8811
+#8173 := [trans #8725 #8735]: #8813
+#8678 := [trans #8173 #8736]: #2825
+#7979 := [unit-resolution #7694 #8678]: false
+#8048 := [lemma #7979]: #2831
+#4031 := (or #4490 #4484)
+#4032 := [def-axiom]: #4031
+#8651 := [unit-resolution #4032 #8738]: #4484
+#4027 := (or #4487 #2836 #4481)
 #4028 := [def-axiom]: #4027
-#7821 := [unit-resolution #4028 #6499]: #1646
-#12689 := (or #12688 #1645 #6064)
-#12690 := [th-lemma arith assign-bounds 1 1]: #12689
-#12692 := [unit-resolution #12690 #7821]: #12691
-#12693 := [unit-resolution #12692 #10065]: #12688
-#12656 := [unit-resolution #4008 #6498]: #4298
-#9202 := (or #4303 #7307 #7310 #7316)
-#7304 := (or #7303 #7300 #7293)
-#7305 := (not #7304)
-#7309 := (or #7308 #7307 #7305)
-#9439 := (or #4303 #7309)
-#9452 := (iff #9439 #9202)
-#7322 := (or #7307 #7310 #7316)
-#9445 := (or #4303 #7322)
-#9450 := (iff #9445 #9202)
-#9451 := [rewrite]: #9450
-#9447 := (iff #9439 #9445)
-#7325 := (iff #7309 #7322)
-#7319 := (or #7310 #7307 #7316)
-#7323 := (iff #7319 #7322)
-#7324 := [rewrite]: #7323
-#7320 := (iff #7309 #7319)
-#7317 := (iff #7305 #7316)
-#7314 := (iff #7304 #7313)
-#7315 := [rewrite]: #7314
-#7318 := [monotonicity #7315]: #7317
-#7311 := (iff #7308 #7310)
-#7312 := [rewrite]: #7311
-#7321 := [monotonicity #7312 #7318]: #7320
-#7326 := [trans #7321 #7324]: #7325
-#9449 := [monotonicity #7326]: #9447
-#9453 := [trans #9449 #9451]: #9452
-#9444 := [quant-inst #6060]: #9439
-#9469 := [mp #9444 #9453]: #9202
-#12695 := [unit-resolution #9469 #12656 #12693]: #12694
-#11942 := [unit-resolution #12695 #11944]: #7310
-#11945 := [symm #11942]: #7308
-#9272 := (= #8208 #6060)
-#9273 := [symm #9271]: #9272
-#11946 := [trans #9273 #11945]: #10688
-#11948 := [monotonicity #11946]: #11947
-#11949 := [symm #11948]: #10866
-#11935 := (not #10866)
-#11950 := (or #11935 #10869)
-#11951 := [th-lemma arith triangle-eq]: #11950
-#11952 := [unit-resolution #11951 #11949]: #10869
-#3908 := (>= #99 0::Int)
-#7114 := [unit-resolution #4024 #6498]: #100
-#6980 := (or #1738 #3908)
-#6981 := [th-lemma arith triangle-eq]: #6980
-#6982 := [unit-resolution #6981 #7114]: #3908
-#11972 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 #10099 #10078 #10077 #10065 #6982 #11952 #11941 #10062]: false
-#11977 := [lemma #11972]: #11976
-#11100 := [unit-resolution #11977 #10078 #10065]: #7530
-#11954 := (not #9572)
-#11908 := [hypothesis]: #11954
-#11909 := [hypothesis]: #7530
-#11910 := [unit-resolution #9579 #11909 #11908]: false
-#11911 := [lemma #11910]: #9578
-#11101 := [unit-resolution #11911 #11100]: #9572
-#11104 := [th-lemma arith farkas -1 1 1 #10078 #11101 #9571]: false
-#11103 := [lemma #11104]: #11105
-#23121 := [unit-resolution #11103 #10065]: #2266
-#4064 := (or #4502 #4496)
-#4065 := [def-axiom]: #4064
-#12699 := [unit-resolution #4065 #7090]: #4496
-#5923 := (= #99 #202)
-#12703 := (iff #5923 #203)
-#12702 := [commutativity]: #1479
-#12700 := (iff #5923 #813)
-#12701 := [monotonicity #7114]: #12700
-#12704 := [trans #12701 #12702]: #12703
-#5907 := (f5 f22 f10)
-#5908 := (f9 #5907)
-#7050 := (<= #5908 0::Int)
-#7051 := (not #7050)
-#6758 := (not #6079)
-#3925 := (f3 f15 f10)
-#3928 := (= f1 #3925)
-#6709 := (ite #6079 #5883 #3928)
-#6757 := (not #6709)
-#6689 := (f3 #6260 f10)
-#6690 := (= f1 #6689)
-#6714 := (iff #6690 #6709)
-#6721 := (or #6281 #6714)
-#6674 := (ite #6077 #5883 #3928)
-#6708 := (iff #6690 #6674)
-#6722 := (or #6281 #6708)
-#6724 := (iff #6722 #6721)
-#6726 := (iff #6721 #6721)
-#6754 := [rewrite]: #6726
-#6715 := (iff #6708 #6714)
-#6712 := (iff #6674 #6709)
-#6080 := (iff #6077 #6079)
-#6081 := [rewrite]: #6080
-#6713 := [monotonicity #6081]: #6712
-#6716 := [monotonicity #6713]: #6715
-#6725 := [monotonicity #6716]: #6724
-#6755 := [trans #6725 #6754]: #6724
-#6723 := [quant-inst #104 #170 #5882 #56]: #6722
-#6756 := [mp #6723 #6755]: #6721
-#7082 := [unit-resolution #6756 #4168]: #6714
-#6974 := (not #6690)
-#6349 := (f3 f23 f10)
-#6467 := (= f1 #6349)
-#6536 := (not #6467)
-#7100 := (iff #6536 #6974)
-#7098 := (iff #6467 #6690)
-#7096 := (iff #6690 #6467)
-#7094 := (= #6689 #6349)
-#7095 := [monotonicity #6998]: #7094
-#7097 := [monotonicity #7095]: #7096
-#7099 := [symm #7097]: #7098
-#7101 := [monotonicity #7099]: #7100
-#7083 := (not #5923)
-#7086 := [hypothesis]: #7083
-#6537 := (or #5923 #6536)
-#6540 := (or #4417 #5923 #6536)
-#6535 := (or #4417 #6537)
-#6542 := (iff #6535 #6540)
-#6543 := [rewrite]: #6542
-#6541 := [quant-inst #56]: #6535
-#6544 := [mp #6541 #6543]: #6540
-#7092 := [unit-resolution #6544 #7091]: #6537
-#7093 := [unit-resolution #7092 #7086]: #6536
-#7102 := [mp #7093 #7101]: #6974
-#6977 := (not #6714)
-#6978 := (or #6977 #6690 #6757)
-#6979 := [def-axiom]: #6978
-#7103 := [unit-resolution #6979 #7102 #7082]: #6757
-#7104 := (or #6709 #6758)
-#6762 := (or #6709 #6758 #6295)
-#6763 := [def-axiom]: #6762
-#7105 := [unit-resolution #6763 #6990]: #7104
-#7106 := [unit-resolution #7105 #7103]: #6758
-#7052 := (or #6079 #7051)
-#7055 := (or #6773 #6079 #7051)
-#7056 := (or #6773 #7052)
-#7058 := (iff #7056 #7055)
-#7059 := [rewrite]: #7058
-#7057 := [quant-inst #170 #56]: #7056
-#7060 := [mp #7057 #7059]: #7055
-#7107 := [unit-resolution #7060 #4208]: #7052
-#7108 := [unit-resolution #7107 #7106]: #7051
-#5915 := (* -1::Int #5908)
-#5916 := (+ #1444 #5915)
-#5917 := (+ #99 #5916)
-#5918 := (<= #5917 0::Int)
-#5945 := (not #5918)
-#5919 := (+ f8 #5915)
-#5920 := (<= #5919 0::Int)
-#5925 := (or #5918 #5920)
-#5928 := (not #5925)
-#5931 := (or #5923 #5928)
-#5934 := (or #4392 #5923 #5928)
-#5921 := (or #5920 #5918)
-#5922 := (not #5921)
-#5924 := (or #5923 #5922)
-#5935 := (or #4392 #5924)
-#5942 := (iff #5935 #5934)
-#5937 := (or #4392 #5931)
-#5940 := (iff #5937 #5934)
-#5941 := [rewrite]: #5940
-#5938 := (iff #5935 #5937)
-#5932 := (iff #5924 #5931)
-#5929 := (iff #5922 #5928)
-#5926 := (iff #5921 #5925)
-#5927 := [rewrite]: #5926
-#5930 := [monotonicity #5927]: #5929
-#5933 := [monotonicity #5930]: #5932
-#5939 := [monotonicity #5933]: #5938
-#5943 := [trans #5939 #5941]: #5942
-#5936 := [quant-inst #56]: #5935
-#5944 := [mp #5936 #5943]: #5934
-#7109 := [unit-resolution #5944 #6500]: #5931
-#7110 := [unit-resolution #7109 #7086]: #5928
-#5946 := (or #5925 #5945)
-#5947 := [def-axiom]: #5946
-#7111 := [unit-resolution #5947 #7110]: #5945
-#6118 := (>= #174 0::Int)
-#6121 := (or #4270 #6118)
-#6122 := [quant-inst #170]: #6121
-#7113 := [unit-resolution #6122 #7112]: #6118
-#3911 := (<= #99 0::Int)
-#7115 := (or #1738 #3911)
-#7116 := [th-lemma arith triangle-eq]: #7115
-#7117 := [unit-resolution #7116 #7114]: #3911
-#7118 := [th-lemma arith farkas 1 1 1 1 #7117 #7113 #7111 #7108]: false
-#7119 := [lemma #7118]: #5923
-#12705 := [mp #7119 #12704]: #203
-#4074 := (or #4499 #1481 #4493)
-#4060 := [def-axiom]: #4074
-#12706 := [unit-resolution #4060 #12705 #12699]: #4493
-#4083 := (or #4490 #4484)
-#4067 := [def-axiom]: #4083
-#12707 := [unit-resolution #4067 #12706]: #4484
-#4080 := (or #4487 #2267 #4481)
-#4081 := [def-axiom]: #4080
-#12708 := [unit-resolution #4081 #12707]: #4484
-#23122 := [unit-resolution #12708 #23121]: #4481
-#4075 := (or #4478 #4472)
+#8737 := [unit-resolution #4028 #8651]: #4484
+#8043 := [unit-resolution #8737 #8048]: #4481
+#4037 := (or #4478 #4388)
+#4039 := [def-axiom]: #4037
+#8044 := [unit-resolution #4039 #8043]: #4388
+#11868 := (or #4393 #3438 #11825)
+#11823 := (= #11822 #2286)
+#11824 := (or #11823 #3438)
+#11883 := (or #4393 #11824)
+#11839 := (iff #11883 #11868)
+#11831 := (or #3438 #11825)
+#11930 := (or #4393 #11831)
+#11783 := (iff #11930 #11868)
+#11840 := [rewrite]: #11783
+#11837 := (iff #11883 #11930)
+#11834 := (iff #11824 #11831)
+#11828 := (or #11825 #3438)
+#11832 := (iff #11828 #11831)
+#11833 := [rewrite]: #11832
+#11829 := (iff #11824 #11828)
+#11826 := (iff #11823 #11825)
+#11827 := [rewrite]: #11826
+#11830 := [monotonicity #11827]: #11829
+#11835 := [trans #11830 #11833]: #11834
+#11838 := [monotonicity #11835]: #11837
+#11799 := [trans #11838 #11840]: #11839
+#11903 := [quant-inst #2282]: #11883
+#11841 := [mp #11903 #11799]: #11868
+#14128 := [unit-resolution #11841 #8044 #14152]: #11825
+#14123 := (not #11825)
+#14129 := (or #14123 #12288)
+#14127 := [th-lemma arith triangle-eq]: #14129
+#14130 := [unit-resolution #14127 #14128]: #12288
+#15883 := (not #12288)
+#15884 := (or #15882 #15883 #2882)
+#15862 := [hypothesis]: #4089
+#15863 := [hypothesis]: #12288
+#12524 := (f7 #2288)
+#12647 := (f13 f14 #12524)
+#12661 := (* -1::Int #12647)
+#12311 := (+ #12339 #12661)
+#12316 := (>= #12311 0::Int)
+#12295 := (= #12339 #12647)
+#12525 := (= ?v0!19 #12524)
+#12287 := (or #5129 #12525)
+#12294 := [quant-inst #2282 #2283]: #12287
+#15864 := [unit-resolution #12294 #4162]: #12525
+#15865 := [monotonicity #15864]: #12295
+#15866 := (not #12295)
+#15867 := (or #15866 #12316)
+#15868 := [th-lemma arith triangle-eq]: #15867
+#15869 := [unit-resolution #15868 #15865]: #12316
+#15870 := [hypothesis]: #12472
+#12979 := (f24 #12524)
+#12996 := (* -1::Int #12979)
+#12997 := (+ #12647 #12996)
+#12998 := (>= #12997 0::Int)
+#12522 := (or #4384 #12998)
+#12541 := [quant-inst #12524]: #12522
+#15871 := [unit-resolution #12541 #10275]: #12998
+#13229 := (+ #2284 #12996)
+#13230 := (<= #13229 0::Int)
+#13224 := (= #2284 #12979)
+#15874 := (= #12979 #2284)
+#15872 := (= #12524 ?v0!19)
+#15873 := [symm #15864]: #15872
+#15875 := [monotonicity #15873]: #15874
+#15876 := [symm #15875]: #13224
+#15877 := (not #13224)
+#15878 := (or #15877 #13230)
+#15879 := [th-lemma arith triangle-eq]: #15878
+#15880 := [unit-resolution #15879 #15876]: #13230
+#15881 := [th-lemma arith farkas -1 1 1 1 1 1 #15880 #15871 #15870 #15869 #15863 #15862]: false
+#15885 := [lemma #15881]: #15884
+#14106 := [unit-resolution #15885 #14130 #14107]: #15882
+#14132 := (or #11874 #12472)
+#14131 := [unit-resolution #3982 #6450]: #4249
+#12193 := (or #4254 #2294 #11874 #12472)
+#12473 := (or #11874 #2294 #12472)
+#12255 := (or #4254 #12473)
+#12219 := (iff #12255 #12193)
+#12474 := (or #2294 #11874 #12472)
+#12259 := (or #4254 #12474)
+#12134 := (iff #12259 #12193)
+#12194 := [rewrite]: #12134
+#12279 := (iff #12255 #12259)
+#12475 := (iff #12473 #12474)
+#12476 := [rewrite]: #12475
+#12280 := [monotonicity #12476]: #12279
+#12220 := [trans #12280 #12194]: #12219
+#12258 := [quant-inst #2283 #2282]: #12255
+#12215 := [mp #12258 #12220]: #12193
+#14135 := [unit-resolution #12215 #14131 #14196]: #14132
+#14151 := [unit-resolution #14135 #14106]: #11874
+#12108 := (not #11850)
+#12130 := (or #12108 #11849 #11848)
+#12131 := [def-axiom]: #12130
+#14134 := [unit-resolution #12131 #14151 #14226]: #11849
+#14154 := [trans #14134 #7565]: #14153
+#14156 := [monotonicity #14154]: #14155
+#14150 := [monotonicity #14156]: #14020
+#14157 := (not #14020)
+#14231 := (or #14157 #14056)
+#14203 := [th-lemma arith triangle-eq]: #14231
+#14229 := [unit-resolution #14203 #14150]: #14056
+#15334 := (not #14056)
+#15340 := (or #11456 #15334 #2294)
+#15336 := [hypothesis]: #2295
+#15337 := [hypothesis]: #14056
+#15338 := [hypothesis]: #12400
+#15339 := [th-lemma arith farkas -1 1 1 #15338 #15337 #15336]: false
+#15341 := [lemma #15339]: #15340
+#14204 := [unit-resolution #15341 #14229 #14196]: #11456
+#12409 := (+ #12374 #12391)
+#12410 := (+ #174 #12409)
+#12411 := (>= #12410 0::Int)
+#11381 := (not #12411)
+#12526 := (f6 #2288)
+#12547 := (f13 f14 #12526)
+#12565 := (* -1::Int #12547)
+#15720 := (+ #6404 #12565)
+#14007 := (<= #15720 0::Int)
+#13983 := (= #6404 #12547)
+#14240 := (= #12547 #6404)
+#12777 := (= #12526 #6386)
+#14238 := (= #12526 ?v1!18)
+#12527 := (= ?v1!18 #12526)
+#12285 := (or #6389 #12527)
+#12296 := [quant-inst #2282 #2283]: #12285
+#14515 := [unit-resolution #12296 #4156]: #12527
+#14239 := [symm #14515]: #14238
+#14230 := [trans #14239 #14134]: #12777
+#14241 := [monotonicity #14230]: #14240
+#14242 := [symm #14241]: #13983
+#14202 := (not #13983)
+#14224 := (or #14202 #14007)
+#14234 := [th-lemma arith triangle-eq]: #14224
+#14263 := [unit-resolution #14234 #14242]: #14007
+#14478 := (not #14007)
+#14523 := (or #11381 #15334 #2882 #15883 #14478)
+#12375 := (+ #2284 #12374)
+#12376 := (<= #12375 0::Int)
+#11370 := (or #4384 #12376)
+#12366 := (+ #12339 #2285)
+#12367 := (>= #12366 0::Int)
+#11369 := (or #4384 #12367)
+#11352 := (iff #11369 #11370)
+#11356 := (iff #11370 #11370)
+#11363 := [rewrite]: #11356
+#12379 := (iff #12367 #12376)
+#12368 := (+ #2285 #12339)
+#12371 := (>= #12368 0::Int)
+#12377 := (iff #12371 #12376)
+#12378 := [rewrite]: #12377
+#12372 := (iff #12367 #12371)
+#12369 := (= #12366 #12368)
+#12370 := [rewrite]: #12369
+#12373 := [monotonicity #12370]: #12372
+#12380 := [trans #12373 #12378]: #12379
+#11355 := [monotonicity #12380]: #11352
+#11365 := [trans #11355 #11363]: #11352
+#11354 := [quant-inst #2283]: #11369
+#11366 := [mp #11354 #11365]: #11370
+#14491 := [unit-resolution #11366 #10275]: #12376
+#12321 := (+ #11822 #12565)
+#12328 := (>= #12321 0::Int)
+#12320 := (= #11822 #12547)
+#14518 := [monotonicity #14515]: #12320
+#14519 := (not #12320)
+#14532 := (or #14519 #12328)
+#14533 := [th-lemma arith triangle-eq]: #14532
+#14559 := [unit-resolution #14533 #14518]: #12328
+#6512 := (<= #6751 0::Int)
+#14565 := (or #8151 #6512)
+#14566 := [th-lemma arith triangle-eq]: #14565
+#14567 := [unit-resolution #14566 #8807]: #6512
+#14568 := [hypothesis]: #14007
+#14479 := [hypothesis]: #12411
+#14522 := [th-lemma arith farkas -1 -1 -1 -1 1 1 -1 1 #15337 #14479 #15862 #15863 #14568 #14567 #14559 #14491]: false
+#14524 := [lemma #14522]: #14523
+#14264 := [unit-resolution #14524 #14229 #14107 #14130 #14263]: #11381
+#12423 := (or #12400 #12411 #12420)
+#11389 := (or #4376 #12400 #12411 #12420)
+#12392 := (+ #12391 #2285)
+#12393 := (+ #174 #12392)
+#12394 := (= #12393 0::Int)
+#12396 := (+ #1420 #12395)
+#12397 := (+ #12339 #12396)
+#12398 := (<= #12397 0::Int)
+#12401 := (or #12400 #12398 #12394)
+#11357 := (or #4376 #12401)
+#11458 := (iff #11357 #11389)
+#11390 := (or #4376 #12423)
+#11391 := (iff #11390 #11389)
+#11392 := [rewrite]: #11391
+#11364 := (iff #11357 #11390)
+#12424 := (iff #12401 #12423)
+#12421 := (iff #12394 #12420)
+#12418 := (= #12393 #12417)
+#12419 := [rewrite]: #12418
+#12422 := [monotonicity #12419]: #12421
+#12414 := (iff #12398 #12411)
+#12402 := (+ #12339 #12395)
+#12403 := (+ #1420 #12402)
+#12406 := (<= #12403 0::Int)
+#12412 := (iff #12406 #12411)
+#12413 := [rewrite]: #12412
+#12407 := (iff #12398 #12406)
+#12404 := (= #12397 #12403)
+#12405 := [rewrite]: #12404
+#12408 := [monotonicity #12405]: #12407
+#12415 := [trans #12408 #12413]: #12414
+#12425 := [monotonicity #12415 #12422]: #12424
+#11383 := [monotonicity #12425]: #11364
+#11459 := [trans #11383 #11392]: #11458
+#11404 := [quant-inst #2283]: #11357
+#11457 := [mp #11404 #11459]: #11389
+#14265 := [unit-resolution #11457 #6291]: #12423
+#14266 := [unit-resolution #14265 #14264 #14204]: #12420
+#14268 := (not #12420)
+#14319 := (or #14268 #11416)
+#14320 := [th-lemma arith triangle-eq]: #14319
+#14321 := [unit-resolution #14320 #14266]: #11416
+#14267 := [th-lemma arith farkas 1 1 1 -1 -1 1 1 #14229 #14107 #14130 #14263 #14567 #14559 #14321]: false
+#14262 := [lemma #14267]: #3453
+#4040 := (or #4478 #4472)
+#4041 := [def-axiom]: #4040
+#13724 := [unit-resolution #4041 #8043]: #4472
+#13668 := (or #4475 #4469)
+#5880 := (= #99 #202)
+#13485 := (iff #5880 #203)
+#13484 := [commutativity]: #1455
+#13287 := (iff #5880 #789)
+#6483 := [unit-resolution #4000 #6450]: #100
+#13293 := [monotonicity #6483]: #13287
+#13489 := [trans #13293 #13484]: #13485
+#5756 := (f4 #5873)
+#5811 := (* -1::Int #5756)
+#5876 := (+ f3 #5811)
+#5877 := (<= #5876 0::Int)
+#5832 := (+ #1420 #5811)
+#5862 := (+ #99 #5832)
+#5875 := (<= #5862 0::Int)
+#5882 := (or #5875 #5877)
+#6510 := (>= #5756 0::Int)
+#6390 := (= #5756 0::Int)
+#7055 := (not #6390)
+#7416 := (not #6510)
+#7054 := [hypothesis]: #7416
+#7053 := (or #7055 #6510)
+#7056 := [th-lemma arith triangle-eq]: #7053
+#7057 := [unit-resolution #7056 #7054]: #7055
+#6036 := (= f10 f22)
+#6413 := (<= #5756 0::Int)
+#7058 := (or #6510 #6413)
+#7059 := [th-lemma arith farkas 1 1]: #7058
+#7060 := [unit-resolution #7059 #7054]: #6413
+#6415 := (not #6413)
+#6417 := (or #6036 #6415)
+#6421 := (or #6420 #6036 #6415)
+#6034 := (= f22 f10)
+#6416 := (or #6034 #6415)
+#6422 := (or #6420 #6416)
+#6429 := (iff #6422 #6421)
+#6424 := (or #6420 #6417)
+#6427 := (iff #6424 #6421)
+#6428 := [rewrite]: #6427
+#6425 := (iff #6422 #6424)
+#6418 := (iff #6416 #6417)
+#6037 := (iff #6034 #6036)
+#6038 := [rewrite]: #6037
+#6419 := [monotonicity #6038]: #6418
+#6426 := [monotonicity #6419]: #6425
+#6430 := [trans #6426 #6428]: #6429
+#6423 := [quant-inst #170 #56]: #6422
+#6431 := [mp #6423 #6430]: #6421
+#6475 := [unit-resolution #6431 #4150]: #6417
+#7061 := [unit-resolution #6475 #7060]: #6036
+#6322 := (not #6036)
+#6398 := (or #6322 #6390)
+#6381 := (or #6380 #6322 #6390)
+#6391 := (not #6034)
+#6395 := (or #6391 #6390)
+#6392 := (or #6380 #6395)
+#6508 := (iff #6392 #6381)
+#6394 := (or #6380 #6398)
+#6506 := (iff #6394 #6381)
+#6507 := [rewrite]: #6506
+#6401 := (iff #6392 #6394)
+#6399 := (iff #6395 #6398)
+#6396 := (iff #6391 #6322)
+#6397 := [monotonicity #6038]: #6396
+#6400 := [monotonicity #6397]: #6399
+#6505 := [monotonicity #6400]: #6401
+#6509 := [trans #6505 #6507]: #6508
+#6393 := [quant-inst #170 #56]: #6392
+#6504 := [mp #6393 #6509]: #6381
+#7083 := [unit-resolution #6504 #4144]: #6398
+#7084 := [unit-resolution #7083 #7061 #7057]: false
+#7085 := [lemma #7084]: #6510
+#7417 := (or #7416 #5875)
+#6075 := (>= #174 0::Int)
+#4001 := (or #4514 #4241)
+#3997 := [def-axiom]: #4001
+#6481 := [unit-resolution #3997 #6450]: #4241
+#6078 := (or #4246 #6075)
+#6079 := [quant-inst #170]: #6078
+#6482 := [unit-resolution #6079 #6481]: #6075
+#5902 := (not #5875)
+#7413 := [hypothesis]: #5902
+#3887 := (<= #99 0::Int)
+#6484 := (or #1714 #3887)
+#6485 := [th-lemma arith triangle-eq]: #6484
+#6486 := [unit-resolution #6485 #6483]: #3887
+#7414 := [hypothesis]: #6510
+#7415 := [th-lemma arith farkas 1 -1 1 1 #7414 #6486 #7413 #6482]: false
+#7418 := [lemma #7415]: #7417
+#13236 := [unit-resolution #7418 #7085]: #5875
+#5903 := (or #5882 #5902)
+#5904 := [def-axiom]: #5903
+#13280 := [unit-resolution #5904 #13236]: #5882
+#5885 := (not #5882)
+#5888 := (or #5880 #5885)
+#5891 := (or #4368 #5880 #5885)
+#5878 := (or #5877 #5875)
+#5879 := (not #5878)
+#5881 := (or #5880 #5879)
+#5892 := (or #4368 #5881)
+#5899 := (iff #5892 #5891)
+#5894 := (or #4368 #5888)
+#5897 := (iff #5894 #5891)
+#5898 := [rewrite]: #5897
+#5895 := (iff #5892 #5894)
+#5889 := (iff #5881 #5888)
+#5886 := (iff #5879 #5885)
+#5883 := (iff #5878 #5882)
+#5884 := [rewrite]: #5883
+#5887 := [monotonicity #5884]: #5886
+#5890 := [monotonicity #5887]: #5889
+#5896 := [monotonicity #5890]: #5895
+#5900 := [trans #5896 #5898]: #5899
+#5893 := [quant-inst #56]: #5892
+#5901 := [mp #5893 #5900]: #5891
+#13235 := [unit-resolution #5901 #6477]: #5888
+#13281 := [unit-resolution #13235 #13280]: #5880
+#13667 := [mp #13281 #13489]: #203
+#4050 := (or #4475 #1457 #4469)
+#4036 := [def-axiom]: #4050
+#13464 := [unit-resolution #4036 #13667]: #13668
+#13680 := [unit-resolution #13464 #13724]: #4469
+#4059 := (or #4466 #4460)
+#4043 := [def-axiom]: #4059
+#13681 := [unit-resolution #4043 #13680]: #4460
+#7879 := (f5 f22 ?v0!15)
+#7880 := (f4 #7879)
+#7854 := (* -1::Int #2241)
+#7905 := (+ #7854 #7880)
+#7906 := (+ #174 #7905)
+#7926 := (<= #7906 0::Int)
+#7909 := (= #7906 0::Int)
+#7884 := (* -1::Int #7880)
+#7888 := (+ f3 #7884)
+#7889 := (<= #7888 0::Int)
+#7951 := (not #7889)
+#7829 := (f13 f14 ?v0!15)
+#7863 := (* -1::Int #7829)
+#7898 := (+ #7863 #7880)
+#7899 := (+ #174 #7898)
+#7900 := (>= #7899 0::Int)
+#7931 := (or #7889 #7900)
+#7934 := (not #7931)
+#7832 := (= #2241 #7829)
+#8564 := (not #7832)
+#7864 := (+ #2241 #7863)
+#8554 := (>= #7864 0::Int)
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+#8592 := [hypothesis]: #2243
+#8251 := (or #8594 #2242)
+#8050 := (>= #7829 0::Int)
+#8053 := (or #4246 #8050)
+#8054 := [quant-inst #2240]: #8053
+#8252 := [unit-resolution #8054 #6481]: #8050
+#8589 := [hypothesis]: #8554
+#8253 := [th-lemma arith farkas -1 1 1 #8592 #8589 #8252]: false
+#8255 := [lemma #8253]: #8251
+#8761 := [unit-resolution #8255 #8592]: #8594
+#8565 := (or #8564 #8554)
+#8572 := [th-lemma arith triangle-eq]: #8565
+#8206 := [unit-resolution #8572 #8761]: #8564
+#7940 := (or #4368 #7832 #7934)
+#7885 := (+ #1420 #7884)
+#7886 := (+ #7829 #7885)
+#7887 := (<= #7886 0::Int)
+#7928 := (or #7889 #7887)
+#7929 := (not #7928)
+#7830 := (= #7829 #2241)
+#7930 := (or #7830 #7929)
+#7941 := (or #4368 #7930)
+#7948 := (iff #7941 #7940)
+#7937 := (or #7832 #7934)
+#7943 := (or #4368 #7937)
+#7946 := (iff #7943 #7940)
+#7947 := [rewrite]: #7946
+#7944 := (iff #7941 #7943)
+#7938 := (iff #7930 #7937)
+#7935 := (iff #7929 #7934)
+#7932 := (iff #7928 #7931)
+#7903 := (iff #7887 #7900)
+#7891 := (+ #7829 #7884)
+#7892 := (+ #1420 #7891)
+#7895 := (<= #7892 0::Int)
+#7901 := (iff #7895 #7900)
+#7902 := [rewrite]: #7901
+#7896 := (iff #7887 #7895)
+#7893 := (= #7886 #7892)
+#7894 := [rewrite]: #7893
+#7897 := [monotonicity #7894]: #7896
+#7904 := [trans #7897 #7902]: #7903
+#7933 := [monotonicity #7904]: #7932
+#7936 := [monotonicity #7933]: #7935
+#7833 := (iff #7830 #7832)
+#7834 := [rewrite]: #7833
+#7939 := [monotonicity #7834 #7936]: #7938
+#7945 := [monotonicity #7939]: #7944
+#7949 := [trans #7945 #7947]: #7948
+#7942 := [quant-inst #2240]: #7941
+#7950 := [mp #7942 #7949]: #7940
+#8744 := [unit-resolution #7950 #6477 #8206]: #7934
+#7952 := (or #7931 #7951)
+#7953 := [def-axiom]: #7952
+#8722 := [unit-resolution #7953 #8744]: #7951
+#7954 := (not #7900)
+#7955 := (or #7931 #7954)
+#7956 := [def-axiom]: #7955
+#8745 := [unit-resolution #7956 #8744]: #7954
+#7912 := (or #7889 #7900 #7909)
+#7915 := (or #4376 #7889 #7900 #7909)
+#7881 := (+ #7880 #7854)
+#7882 := (+ #174 #7881)
+#7883 := (= #7882 0::Int)
+#7890 := (or #7889 #7887 #7883)
+#7916 := (or #4376 #7890)
+#7923 := (iff #7916 #7915)
+#7918 := (or #4376 #7912)
+#7921 := (iff #7918 #7915)
+#7922 := [rewrite]: #7921
+#7919 := (iff #7916 #7918)
+#7913 := (iff #7890 #7912)
+#7910 := (iff #7883 #7909)
+#7907 := (= #7882 #7906)
+#7908 := [rewrite]: #7907
+#7911 := [monotonicity #7908]: #7910
+#7914 := [monotonicity #7904 #7911]: #7913
+#7920 := [monotonicity #7914]: #7919
+#7924 := [trans #7920 #7922]: #7923
+#7917 := [quant-inst #2240]: #7916
+#7925 := [mp #7917 #7924]: #7915
+#8767 := [unit-resolution #7925 #6291]: #7912
+#8747 := [unit-resolution #8767 #8745 #8722]: #7909
+#8769 := (not #7909)
+#8770 := (or #8769 #7926)
+#8771 := [th-lemma arith triangle-eq]: #8770
+#8748 := [unit-resolution #8771 #8747]: #7926
+#8336 := (f5 #6386 ?v0!15)
+#8325 := (f4 #8336)
+#8083 := (* -1::Int #8325)
+#8200 := (+ #7880 #8083)
+#8207 := (>= #8200 0::Int)
+#8199 := (= #7880 #8325)
+#8754 := (= #8325 #7880)
+#8752 := (= #8336 #7879)
+#8753 := [monotonicity #7565]: #8752
+#8755 := [monotonicity #8753]: #8754
+#8756 := [symm #8755]: #8199
+#8757 := (not #8199)
+#8758 := (or #8757 #8207)
+#8759 := [th-lemma arith triangle-eq]: #8758
+#8760 := [unit-resolution #8759 #8756]: #8207
+#8403 := (<= #8325 0::Int)
+#8404 := (not #8403)
+#8239 := (= ?v0!15 #6386)
+#8270 := (not #8239)
+#7961 := (f8 f15 ?v0!15)
+#7962 := (= f1 #7961)
+#8240 := (ite #8239 #5831 #7962)
+#8269 := (not #8240)
+#7826 := (f8 f23 ?v0!15)
+#7827 := (= f1 #7826)
+#7828 := (not #7827)
+#7843 := (or #4393 #7828 #7832)
+#7831 := (or #7830 #7828)
+#7844 := (or #4393 #7831)
+#7851 := (iff #7844 #7843)
+#7838 := (or #7828 #7832)
+#7846 := (or #4393 #7838)
+#7849 := (iff #7846 #7843)
+#7850 := [rewrite]: #7849
+#7847 := (iff #7844 #7846)
+#7841 := (iff #7831 #7838)
+#7835 := (or #7832 #7828)
+#7839 := (iff #7835 #7838)
+#7840 := [rewrite]: #7839
+#7836 := (iff #7831 #7835)
+#7837 := [monotonicity #7834]: #7836
+#7842 := [trans #7837 #7840]: #7841
+#7848 := [monotonicity #7842]: #7847
+#7852 := [trans #7848 #7850]: #7851
+#7845 := [quant-inst #2240]: #7844
+#7853 := [mp #7845 #7852]: #7843
+#8042 := [unit-resolution #7853 #8044 #8206]: #7828
+#8496 := (or #7827 #8269)
+#8238 := (f8 #7238 ?v0!15)
+#8493 := (= #8238 #7826)
+#8490 := (= #7826 #8238)
+#8530 := (= f23 #7238)
+#8528 := (= #180 #7238)
+#8529 := [symm #8694]: #8528
+#8525 := [trans #8689 #8529]: #8530
+#8491 := [monotonicity #8525]: #8490
+#8488 := [symm #8491]: #8493
+#8241 := (= f1 #8238)
+#8243 := (iff #8240 #8241)
+#8278 := (or #6238 #8243)
+#8242 := (iff #8241 #8240)
+#8284 := (or #6238 #8242)
+#8329 := (iff #8284 #8278)
+#8331 := (iff #8278 #8278)
+#8332 := [rewrite]: #8331
+#8249 := (iff #8242 #8243)
+#8250 := [rewrite]: #8249
+#8330 := [monotonicity #8250]: #8329
+#8333 := [trans #8330 #8332]: #8329
+#8285 := [quant-inst #104 #6386 #5830 #2240]: #8284
+#8334 := [mp #8285 #8333]: #8278
+#8498 := [unit-resolution #8334 #4184]: #8243
+#8335 := (not #8243)
+#8508 := (or #8335 #8241)
+#8507 := [hypothesis]: #8240
+#8248 := (or #8335 #8269 #8241)
+#8254 := [def-axiom]: #8248
+#8526 := [unit-resolution #8254 #8507]: #8508
+#8527 := [unit-resolution #8526 #8498]: #8241
+#8494 := [trans #8527 #8488]: #7827
+#8497 := [hypothesis]: #7828
+#8495 := [unit-resolution #8497 #8494]: false
+#8639 := [lemma #8495]: #8496
+#8045 := [unit-resolution #8639 #8042]: #8269
+#8654 := (or #8240 #8270)
+#6252 := (not #5831)
+#8274 := (or #8240 #8270 #6252)
+#8275 := [def-axiom]: #8274
+#8655 := [unit-resolution #8275 #8690]: #8654
+#8046 := [unit-resolution #8655 #8045]: #8270
+#8156 := (or #6420 #8239 #8404)
+#8324 := (= #6386 ?v0!15)
+#8405 := (or #8324 #8404)
+#8159 := (or #6420 #8405)
+#8178 := (iff #8159 #8156)
+#8406 := (or #8239 #8404)
+#8170 := (or #6420 #8406)
+#8177 := (iff #8170 #8156)
+#8175 := [rewrite]: #8177
+#8171 := (iff #8159 #8170)
+#8407 := (iff #8405 #8406)
+#8354 := (iff #8324 #8239)
+#8355 := [rewrite]: #8354
+#8402 := [monotonicity #8355]: #8407
+#8176 := [monotonicity #8402]: #8171
+#8179 := [trans #8176 #8175]: #8178
+#8169 := [quant-inst #6386 #2240]: #8159
+#8180 := [mp #8169 #8179]: #8156
+#8047 := [unit-resolution #8180 #4150 #8046]: #8404
+#7817 := [th-lemma arith farkas 1 1 1 1 1 #8047 #8760 #8592 #8748 #6482]: false
+#7872 := [lemma #7817]: #2242
+#4056 := (or #4463 #2243 #4457)
+#4057 := [def-axiom]: #4056
+#13740 := [unit-resolution #4057 #7872 #13681]: #4457
+#4051 := (or #4454 #4448)
+#4053 := [def-axiom]: #4051
+#20485 := [unit-resolution #4053 #13740]: #4448
+#9206 := (f5 f22 ?v1!16)
+#9207 := (f4 #9206)
+#9232 := (+ #2853 #9207)
+#9233 := (+ #174 #9232)
+#9253 := (<= #9233 0::Int)
+#9236 := (= #9233 0::Int)
+#9179 := (f13 f14 ?v1!16)
+#9190 := (* -1::Int #9179)
+#9225 := (+ #9190 #9207)
+#9226 := (+ #174 #9225)
+#9227 := (>= #9226 0::Int)
+#9211 := (* -1::Int #9207)
+#9215 := (+ f3 #9211)
+#9216 := (<= #9215 0::Int)
+#9262 := (or #9216 #9227)
+#9265 := (not #9262)
+#9259 := (= #2259 #9179)
+#10308 := (not #9259)
+#9191 := (+ #2259 #9190)
+#9282 := (>= #9191 0::Int)
+#10279 := (not #9282)
+#5996 := (* -1::Int #5955)
+#9612 := (+ #2257 #5996)
+#9617 := (<= #9612 0::Int)
+#9606 := (= #2257 #5955)
+#10953 := (= ?v0!17 f22)
+#9033 := (= ?v0!17 #6386)
+#9031 := (f8 f15 ?v0!17)
+#9032 := (= f1 #9031)
+#9034 := (ite #9033 #5831 #9032)
+#9035 := (f8 #7238 ?v0!17)
+#9036 := (= f1 #9035)
+#9038 := (iff #9034 #9036)
+#9041 := (or #6238 #9038)
+#9037 := (iff #9036 #9034)
+#9042 := (or #6238 #9037)
+#9044 := (iff #9042 #9041)
+#9046 := (iff #9041 #9041)
+#9047 := [rewrite]: #9046
+#9039 := (iff #9037 #9038)
+#9040 := [rewrite]: #9039
+#9045 := [monotonicity #9040]: #9044
+#9048 := [trans #9045 #9047]: #9044
+#9043 := [quant-inst #104 #6386 #5830 #2256]: #9042
+#9049 := [mp #9043 #9048]: #9041
+#9688 := [unit-resolution #9049 #4184]: #9038
+#9681 := (= #2262 #9035)
+#9666 := (= #9035 #2262)
+#9676 := [monotonicity #8698]: #9666
+#9682 := [symm #9676]: #9681
+#9664 := [hypothesis]: #3412
+#4098 := (or #3407 #2263)
+#3939 := [def-axiom]: #4098
+#9665 := [unit-resolution #3939 #9664]: #2263
+#9675 := [trans #9665 #9682]: #9036
+#9062 := (not #9036)
+#9061 := (not #9038)
+#9063 := (or #9061 #9034 #9062)
+#9064 := [def-axiom]: #9063
+#9683 := [unit-resolution #9064 #9675 #9688]: #9034
+#9058 := (not #9032)
+#9006 := (f13 f14 ?v0!17)
+#9082 := (* -1::Int #9006)
+#9966 := (+ #6404 #9082)
+#9961 := (>= #9966 0::Int)
+#10276 := (not #9961)
+#9393 := (+ #174 #9190)
+#9394 := (<= #9393 0::Int)
+#8966 := (f8 f15 ?v1!16)
+#8967 := (= f1 #8966)
+#8993 := (not #8967)
+#8968 := (= ?v1!16 #6386)
+#8969 := (ite #8968 #5831 #8967)
+#8985 := (not #8969)
+#8970 := (f8 #7238 ?v1!16)
+#8971 := (= f1 #8970)
+#8973 := (iff #8969 #8971)
+#8976 := (or #6238 #8973)
+#8972 := (iff #8971 #8969)
+#8977 := (or #6238 #8972)
+#8979 := (iff #8977 #8976)
+#8981 := (iff #8976 #8976)
+#8982 := [rewrite]: #8981
+#8974 := (iff #8972 #8973)
+#8975 := [rewrite]: #8974
+#8980 := [monotonicity #8975]: #8979
+#8983 := [trans #8980 #8982]: #8979
+#8978 := [quant-inst #104 #6386 #5830 #2255]: #8977
+#8984 := [mp #8978 #8983]: #8976
+#9684 := [unit-resolution #8984 #4184]: #8973
+#8997 := (not #8971)
+#9695 := (iff #2266 #8997)
+#9696 := (iff #2265 #8971)
+#9668 := (iff #8971 #2265)
+#9686 := (= #8970 #2264)
+#9687 := [monotonicity #8698]: #9686
+#9669 := [monotonicity #9687]: #9668
+#9697 := [symm #9669]: #9696
+#9667 := [monotonicity #9697]: #9695
+#3940 := (or #3407 #2266)
+#3941 := [def-axiom]: #3940
+#9685 := [unit-resolution #3941 #9664]: #2266
+#9698 := [mp #9685 #9667]: #8997
+#8996 := (not #8973)
+#9000 := (or #8996 #8985 #8971)
+#9001 := [def-axiom]: #9000
+#9699 := [unit-resolution #9001 #9698 #9684]: #8985
+#8986 := (not #8968)
+#9700 := (or #8969 #8986)
+#8991 := (or #8969 #8986 #6252)
+#8992 := [def-axiom]: #8991
+#9724 := [unit-resolution #8992 #8690]: #9700
+#9725 := [unit-resolution #9724 #9699]: #8986
+#8994 := (or #8969 #8968 #8993)
+#8995 := [def-axiom]: #8994
+#9763 := [unit-resolution #8995 #9725 #9699]: #8993
+#9399 := (or #8967 #9394)
+#4021 := (or #4502 #4353)
+#4007 := [def-axiom]: #4021
+#9764 := [unit-resolution #4007 #6451]: #4353
+#9402 := (or #4358 #8967 #9394)
+#9382 := (+ #9179 #1420)
+#9383 := (>= #9382 0::Int)
+#9386 := (or #8967 #9383)
+#9403 := (or #4358 #9386)
+#9410 := (iff #9403 #9402)
+#9405 := (or #4358 #9399)
+#9408 := (iff #9405 #9402)
+#9409 := [rewrite]: #9408
+#9406 := (iff #9403 #9405)
+#9400 := (iff #9386 #9399)
+#9397 := (iff #9383 #9394)
+#9387 := (+ #1420 #9179)
+#9390 := (>= #9387 0::Int)
+#9395 := (iff #9390 #9394)
+#9396 := [rewrite]: #9395
+#9391 := (iff #9383 #9390)
+#9388 := (= #9382 #9387)
+#9389 := [rewrite]: #9388
+#9392 := [monotonicity #9389]: #9391
+#9398 := [trans #9392 #9396]: #9397
+#9401 := [monotonicity #9398]: #9400
+#9407 := [monotonicity #9401]: #9406
+#9411 := [trans #9407 #9409]: #9410
+#9404 := [quant-inst #2255]: #9403
+#9412 := [mp #9404 #9411]: #9402
+#9765 := [unit-resolution #9412 #9764]: #9399
+#9766 := [unit-resolution #9765 #9763]: #9394
+#4083 := (not #2855)
+#4084 := (or #3407 #4083)
+#4085 := [def-axiom]: #4084
+#9767 := [unit-resolution #4085 #9664]: #4083
+#10304 := (not #9394)
+#10397 := (or #10276 #2855 #8968 #10304)
+#10273 := [unit-resolution #8182 #8735]: #6759
+#10274 := [hypothesis]: #9394
+#10269 := [hypothesis]: #4083
+#9083 := (+ #2257 #9082)
+#9084 := (<= #9083 0::Int)
+#9089 := (or #4384 #9084)
+#9072 := (+ #9006 #2258)
+#9073 := (>= #9072 0::Int)
+#9090 := (or #4384 #9073)
+#9092 := (iff #9090 #9089)
+#9094 := (iff #9089 #9089)
+#9095 := [rewrite]: #9094
+#9087 := (iff #9073 #9084)
+#9076 := (+ #2258 #9006)
+#9079 := (>= #9076 0::Int)
+#9085 := (iff #9079 #9084)
+#9086 := [rewrite]: #9085
+#9080 := (iff #9073 #9079)
+#9077 := (= #9072 #9076)
+#9078 := [rewrite]: #9077
+#9081 := [monotonicity #9078]: #9080
+#9088 := [trans #9081 #9086]: #9087
+#9093 := [monotonicity #9088]: #9092
+#9096 := [trans #9093 #9095]: #9092
+#9091 := [quant-inst #2256]: #9090
+#9097 := [mp #9091 #9096]: #9089
+#10277 := [unit-resolution #9097 #10275]: #9084
+#10278 := [hypothesis]: #9961
+#10305 := (not #6759)
+#10303 := (not #9084)
+#10306 := (or #10279 #10303 #2855 #10304 #10276 #10305)
+#10307 := [th-lemma arith assign-bounds -1 1 -1 1 1]: #10306
+#10302 := [unit-resolution #10307 #10278 #10277 #10269 #10274 #10273]: #10279
+#10311 := (or #10308 #9282)
+#10312 := [th-lemma arith triangle-eq]: #10311
+#10366 := [unit-resolution #10312 #10302]: #10308
+#9268 := (or #9259 #9265)
+#9271 := (or #4368 #9259 #9265)
+#9212 := (+ #1420 #9211)
+#9213 := (+ #9179 #9212)
+#9214 := (<= #9213 0::Int)
+#9255 := (or #9216 #9214)
+#9256 := (not #9255)
+#9257 := (= #9179 #2259)
+#9258 := (or #9257 #9256)
+#9272 := (or #4368 #9258)
+#9279 := (iff #9272 #9271)
+#9274 := (or #4368 #9268)
+#9277 := (iff #9274 #9271)
+#9278 := [rewrite]: #9277
+#9275 := (iff #9272 #9274)
+#9269 := (iff #9258 #9268)
+#9266 := (iff #9256 #9265)
+#9263 := (iff #9255 #9262)
+#9230 := (iff #9214 #9227)
+#9218 := (+ #9179 #9211)
+#9219 := (+ #1420 #9218)
+#9222 := (<= #9219 0::Int)
+#9228 := (iff #9222 #9227)
+#9229 := [rewrite]: #9228
+#9223 := (iff #9214 #9222)
+#9220 := (= #9213 #9219)
+#9221 := [rewrite]: #9220
+#9224 := [monotonicity #9221]: #9223
+#9231 := [trans #9224 #9229]: #9230
+#9264 := [monotonicity #9231]: #9263
+#9267 := [monotonicity #9264]: #9266
+#9260 := (iff #9257 #9259)
+#9261 := [rewrite]: #9260
+#9270 := [monotonicity #9261 #9267]: #9269
+#9276 := [monotonicity #9270]: #9275
+#9280 := [trans #9276 #9278]: #9279
+#9273 := [quant-inst #2255]: #9272
+#9281 := [mp #9273 #9280]: #9271
+#10367 := [unit-resolution #9281 #6477]: #9268
+#10369 := [unit-resolution #10367 #10366]: #9265
+#10870 := (or #9262 #9236)
+#10863 := (not #9236)
+#10864 := [hypothesis]: #10863
+#9283 := (not #9216)
+#10865 := [hypothesis]: #9265
+#9284 := (or #9262 #9283)
+#9285 := [def-axiom]: #9284
+#10866 := [unit-resolution #9285 #10865]: #9283
+#9286 := (not #9227)
+#9287 := (or #9262 #9286)
+#9288 := [def-axiom]: #9287
+#10867 := [unit-resolution #9288 #10865]: #9286
+#9239 := (or #9216 #9227 #9236)
+#9242 := (or #4376 #9216 #9227 #9236)
+#9208 := (+ #9207 #2853)
+#9209 := (+ #174 #9208)
+#9210 := (= #9209 0::Int)
+#9217 := (or #9216 #9214 #9210)
+#9243 := (or #4376 #9217)
+#9250 := (iff #9243 #9242)
+#9245 := (or #4376 #9239)
+#9248 := (iff #9245 #9242)
+#9249 := [rewrite]: #9248
+#9246 := (iff #9243 #9245)
+#9240 := (iff #9217 #9239)
+#9237 := (iff #9210 #9236)
+#9234 := (= #9209 #9233)
+#9235 := [rewrite]: #9234
+#9238 := [monotonicity #9235]: #9237
+#9241 := [monotonicity #9231 #9238]: #9240
+#9247 := [monotonicity #9241]: #9246
+#9251 := [trans #9247 #9249]: #9250
+#9244 := [quant-inst #2255]: #9243
+#9252 := [mp #9244 #9251]: #9242
+#10868 := [unit-resolution #9252 #6291]: #9239
+#10869 := [unit-resolution #10868 #10867 #10866 #10864]: false
+#10871 := [lemma #10869]: #10870
+#10370 := [unit-resolution #10871 #10369]: #9236
+#10368 := (or #10863 #9253)
+#10371 := [th-lemma arith triangle-eq]: #10368
+#10372 := [unit-resolution #10371 #10370]: #9253
+#10104 := (f5 #6386 ?v1!16)
+#10119 := (f4 #10104)
+#10120 := (* -1::Int #10119)
+#10271 := (+ #9207 #10120)
+#10272 := (>= #10271 0::Int)
+#10270 := (= #9207 #10119)
+#10355 := (= #10119 #9207)
+#10373 := (= #10104 #9206)
+#10354 := [monotonicity #7565]: #10373
+#10374 := [monotonicity #10354]: #10355
+#10356 := [symm #10374]: #10270
+#10357 := (not #10270)
+#10358 := (or #10357 #10272)
+#10353 := [th-lemma arith triangle-eq]: #10358
+#10359 := [unit-resolution #10353 #10356]: #10272
+#10229 := (<= #10119 0::Int)
+#10280 := (not #10229)
+#10401 := [hypothesis]: #8986
+#10204 := (or #6420 #8968 #10280)
+#10228 := (= #6386 ?v1!16)
+#10281 := (or #10228 #10280)
+#10209 := (or #6420 #10281)
+#10283 := (iff #10209 #10204)
+#10206 := (or #8968 #10280)
+#10221 := (or #6420 #10206)
+#10284 := (iff #10221 #10204)
+#10285 := [rewrite]: #10284
+#10222 := (iff #10209 #10221)
+#10207 := (iff #10281 #10206)
+#10199 := (iff #10228 #8968)
+#10205 := [rewrite]: #10199
+#10208 := [monotonicity #10205]: #10207
+#10223 := [monotonicity #10208]: #10222
+#10286 := [trans #10223 #10285]: #10283
+#10220 := [quant-inst #6386 #2255]: #10209
+#10287 := [mp #10220 #10286]: #10204
+#10402 := [unit-resolution #10287 #4150 #10401]: #10280
+#10400 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10277 #10269 #10278 #10273 #10402 #10359 #10372]: false
+#10403 := [lemma #10400]: #10397
+#9778 := [unit-resolution #10403 #9767 #9725 #9766]: #10276
+#9641 := (or #9058 #9961)
+#9636 := [hypothesis]: #10276
+#9637 := [hypothesis]: #9032
+#9611 := (or #4263 #6402 #9058 #9961)
+#9967 := (or #6402 #9058 #9961)
+#9613 := (or #4263 #9967)
+#9614 := (iff #9613 #9611)
+#9615 := [rewrite]: #9614
+#9601 := [quant-inst #2256 #6386]: #9613
+#9616 := [mp #9601 #9615]: #9611
+#9638 := [unit-resolution #9616 #7878 #8069 #9637 #9636]: false
+#9639 := [lemma #9638]: #9641
+#9779 := [unit-resolution #9639 #9778]: #9058
+#9050 := (not #9034)
+#9054 := (or #9050 #9033 #9032)
+#9055 := [def-axiom]: #9054
+#9780 := [unit-resolution #9055 #9779 #9683]: #9033
+#9781 := [trans #9780 #7565]: #10953
+#9723 := [monotonicity #9781]: #9606
+#9729 := (not #9606)
+#9730 := (or #9729 #9617)
+#9731 := [th-lemma arith triangle-eq]: #9730
+#9732 := [unit-resolution #9731 #9723]: #9617
+#6267 := (+ #174 #5996)
+#6268 := (>= #6267 0::Int)
+#6333 := (or #4384 #6268)
+#6324 := [quant-inst #170]: #6333
+#9728 := [unit-resolution #6324 #10275]: #6268
+#9758 := (not #6268)
+#9733 := (not #9617)
+#9759 := (or #10279 #9733 #2855 #10304 #9758)
+#9760 := [th-lemma arith assign-bounds -1 1 -1 1]: #9759
+#9761 := [unit-resolution #9760 #9767 #9728 #9766 #9732]: #10279
+#9783 := [unit-resolution #10312 #9761]: #10308
+#9784 := [unit-resolution #10367 #9783]: #9265
+#9777 := [unit-resolution #10871 #9784]: #9236
+#9785 := [unit-resolution #10371 #9777]: #9253
+#9786 := [unit-resolution #10287 #4150 #9725]: #10280
+#9787 := [th-lemma arith farkas 1 1 1 1 1 1 #9732 #9767 #9728 #9786 #10359 #9785]: false
+#9793 := [lemma #9787]: #3407
+#4073 := (or #4451 #3412 #4445)
+#4060 := [def-axiom]: #4073
+#20486 := [unit-resolution #4060 #9793 #20485]: #4445
+#3967 := (or #4442 #4436)
+#3975 := [def-axiom]: #3967
+#19065 := [unit-resolution #3975 #20486]: #4436
+#3956 := (or #4439 #3458 #4433)
+#3971 := [def-axiom]: #3956
+#18975 := [unit-resolution #3971 #19065]: #4436
+#19059 := [unit-resolution #18975 #14262]: #4433
+#4075 := (or #4430 #2327)
 #4077 := [def-axiom]: #4075
-#23130 := [unit-resolution #4077 #23122]: #4472
-#12711 := (or #4475 #4469)
-#10279 := [hypothesis]: #3436
-#3964 := (or #3431 #2290)
-#3965 := [def-axiom]: #3964
-#9749 := [unit-resolution #3965 #10279]: #2290
-#10370 := (or #3431 #2289)
-#10555 := (f5 #7202 ?v1!16)
-#10556 := (f9 #10555)
-#10573 := (* -1::Int #10556)
-#8682 := (f5 f22 ?v1!16)
-#8683 := (f9 #8682)
-#10576 := (+ #8683 #10573)
-#10578 := (>= #10576 0::Int)
-#10572 := (= #8683 #10556)
-#10583 := (= #10556 #8683)
-#10581 := (= #10555 #8682)
-#10582 := [monotonicity #7781]: #10581
-#10584 := [monotonicity #10582]: #10583
-#10585 := [symm #10584]: #10572
-#10586 := (not #10572)
-#10587 := (or #10586 #10578)
-#10588 := [th-lemma arith triangle-eq]: #10587
-#10589 := [unit-resolution #10588 #10585]: #10578
-#5998 := (f24 f22)
-#6039 := (* -1::Int #5998)
-#6408 := (+ #174 #6039)
-#6409 := (>= #6408 0::Int)
-#4053 := (or #4514 #4403)
-#4054 := [def-axiom]: #4053
-#8184 := [unit-resolution #4054 #7088]: #4403
-#6413 := (or #4408 #6409)
-#6414 := [quant-inst #170]: #6413
-#8185 := [unit-resolution #6414 #8184]: #6409
-#4107 := (not #2879)
-#4108 := (or #3431 #4107)
-#4109 := [def-axiom]: #4108
-#10282 := [unit-resolution #4109 #10279]: #4107
-#10214 := (+ #2281 #6039)
-#10215 := (<= #10214 0::Int)
-#10203 := (= #2281 #5998)
-#10471 := (= ?v0!17 f22)
-#8508 := (= ?v0!17 #7202)
-#8501 := (f3 f15 ?v0!17)
-#8502 := (= f1 #8501)
-#8511 := (ite #8508 #5883 #8502)
-#8505 := (f3 #8433 ?v0!17)
-#8506 := (= f1 #8505)
-#8514 := (iff #8506 #8511)
-#9702 := (or #6281 #8514)
-#8503 := (= #7202 ?v0!17)
-#8504 := (ite #8503 #5883 #8502)
-#8507 := (iff #8506 #8504)
-#9697 := (or #6281 #8507)
-#9704 := (iff #9697 #9702)
-#9706 := (iff #9702 #9702)
-#9707 := [rewrite]: #9706
-#8515 := (iff #8507 #8514)
-#8512 := (iff #8504 #8511)
-#8509 := (iff #8503 #8508)
-#8510 := [rewrite]: #8509
-#8513 := [monotonicity #8510]: #8512
-#8516 := [monotonicity #8513]: #8515
-#9705 := [monotonicity #8516]: #9704
-#9713 := [trans #9705 #9707]: #9704
-#9703 := [quant-inst #104 #7202 #5882 #2280]: #9697
-#9714 := [mp #9703 #9713]: #9702
-#10283 := [unit-resolution #9714 #4168]: #8514
-#10312 := (= #2286 #8505)
-#10285 := (= #8505 #2286)
-#10222 := [monotonicity #9277]: #10285
-#10313 := [symm #10222]: #10312
-#4122 := (or #3431 #2287)
-#3963 := [def-axiom]: #4122
-#10284 := [unit-resolution #3963 #10279]: #2287
-#10314 := [trans #10284 #10313]: #8506
-#9723 := (not #8506)
-#9726 := (not #8514)
-#9729 := (or #9726 #9723 #8511)
-#9730 := [def-axiom]: #9729
-#10315 := [unit-resolution #9730 #10314 #10283]: #8511
-#9722 := (not #8502)
-#8476 := (f13 f14 ?v0!17)
-#8558 := (* -1::Int #8476)
-#7504 := (f13 f14 #7202)
-#10477 := (+ #7504 #8558)
-#10478 := (>= #10477 0::Int)
-#10603 := (not #10478)
-#8437 := (= ?v1!16 #7202)
-#9607 := (not #8437)
-#8429 := (f3 f15 ?v1!16)
-#8430 := (= f1 #8429)
-#8440 := (ite #8437 #5883 #8430)
-#9606 := (not #8440)
-#8434 := (f3 #8433 ?v1!16)
-#8435 := (= f1 #8434)
-#8443 := (iff #8435 #8440)
-#9575 := (or #6281 #8443)
-#8431 := (= #7202 ?v1!16)
-#8432 := (ite #8431 #5883 #8430)
-#8436 := (iff #8435 #8432)
-#9576 := (or #6281 #8436)
-#9601 := (iff #9576 #9575)
-#9597 := (iff #9575 #9575)
-#9603 := [rewrite]: #9597
-#8444 := (iff #8436 #8443)
-#8441 := (iff #8432 #8440)
-#8438 := (iff #8431 #8437)
-#8439 := [rewrite]: #8438
-#8442 := [monotonicity #8439]: #8441
-#8445 := [monotonicity #8442]: #8444
-#9602 := [monotonicity #8445]: #9601
-#9604 := [trans #9602 #9603]: #9601
-#9600 := [quant-inst #104 #7202 #5882 #2279]: #9576
-#9605 := [mp #9600 #9604]: #9575
-#10316 := [unit-resolution #9605 #4168]: #8443
-#9639 := (not #8435)
-#10324 := (iff #2290 #9639)
-#10322 := (iff #2289 #8435)
-#10320 := (iff #8435 #2289)
-#10318 := (= #8434 #2288)
-#10319 := [monotonicity #9277]: #10318
-#10321 := [monotonicity #10319]: #10320
-#10323 := [symm #10321]: #10322
-#10325 := [monotonicity #10323]: #10324
-#10317 := [hypothesis]: #2290
-#10326 := [mp #10317 #10325]: #9639
-#9631 := (not #8443)
-#9632 := (or #9631 #8435 #9606)
-#9638 := [def-axiom]: #9632
-#10327 := [unit-resolution #9638 #10326 #10316]: #9606
-#10328 := (or #8440 #9607)
-#9627 := (or #8440 #9607 #6295)
-#9622 := [def-axiom]: #9627
-#10329 := [unit-resolution #9622 #6990]: #10328
-#10330 := [unit-resolution #10329 #10327]: #9607
-#8655 := (f13 f14 ?v1!16)
-#8666 := (* -1::Int #8655)
-#8914 := (+ #174 #8666)
-#8915 := (<= #8914 0::Int)
-#9628 := (not #8430)
-#9629 := (or #8440 #8437 #9628)
-#9630 := [def-axiom]: #9629
-#10299 := [unit-resolution #9630 #10330 #10327]: #9628
-#8920 := (or #8430 #8915)
-#4045 := (or #4526 #4377)
-#4031 := [def-axiom]: #4045
-#10304 := [unit-resolution #4031 #6499]: #4377
-#9975 := (or #4382 #8430 #8915)
-#8903 := (+ #8655 #1444)
-#8904 := (>= #8903 0::Int)
-#8907 := (or #8430 #8904)
-#9976 := (or #4382 #8907)
-#10011 := (iff #9976 #9975)
-#10007 := (or #4382 #8920)
-#10010 := (iff #10007 #9975)
-#10005 := [rewrite]: #10010
-#10008 := (iff #9976 #10007)
-#8921 := (iff #8907 #8920)
-#8918 := (iff #8904 #8915)
-#8908 := (+ #1444 #8655)
-#8911 := (>= #8908 0::Int)
-#8916 := (iff #8911 #8915)
-#8917 := [rewrite]: #8916
-#8912 := (iff #8904 #8911)
-#8909 := (= #8903 #8908)
-#8910 := [rewrite]: #8909
-#8913 := [monotonicity #8910]: #8912
-#8919 := [trans #8913 #8917]: #8918
-#8922 := [monotonicity #8919]: #8921
-#10009 := [monotonicity #8922]: #10008
-#10012 := [trans #10009 #10005]: #10011
-#10006 := [quant-inst #2279]: #9976
-#10013 := [mp #10006 #10012]: #9975
-#10298 := [unit-resolution #10013 #10304]: #8920
-#10305 := [unit-resolution #10298 #10299]: #8915
-#10577 := (not #8915)
-#10624 := (or #10603 #10577 #2879 #8437)
-#8708 := (+ #2877 #8683)
-#8709 := (+ #174 #8708)
-#8712 := (= #8709 0::Int)
-#10609 := (not #8712)
-#9826 := (<= #8709 0::Int)
-#10602 := (not #9826)
-#10590 := [hypothesis]: #9607
-#10592 := [hypothesis]: #4107
-#10579 := [hypothesis]: #10478
-#10604 := (or #10602 #2879 #10603 #8437)
-#10580 := [hypothesis]: #9826
-#10557 := (<= #10556 0::Int)
-#10558 := (not #10557)
-#10562 := (or #6773 #8437 #10558)
-#10559 := (or #8437 #10558)
-#10563 := (or #6773 #10559)
-#10565 := (iff #10563 #10562)
-#10566 := [rewrite]: #10565
-#10564 := [quant-inst #7202 #2279]: #10563
-#10567 := [mp #10564 #10566]: #10562
-#10591 := [unit-resolution #10567 #4208 #10590]: #10558
-#8559 := (+ #2281 #8558)
-#8560 := (<= #8559 0::Int)
-#9739 := (or #4408 #8560)
-#8548 := (+ #8476 #2282)
-#8549 := (>= #8548 0::Int)
-#9742 := (or #4408 #8549)
-#9757 := (iff #9742 #9739)
-#9759 := (iff #9739 #9739)
-#9760 := [rewrite]: #9759
-#8563 := (iff #8549 #8560)
-#8552 := (+ #2282 #8476)
-#8555 := (>= #8552 0::Int)
-#8561 := (iff #8555 #8560)
-#8562 := [rewrite]: #8561
-#8556 := (iff #8549 #8555)
-#8553 := (= #8548 #8552)
-#8554 := [rewrite]: #8553
-#8557 := [monotonicity #8554]: #8556
-#8564 := [trans #8557 #8562]: #8563
-#9758 := [monotonicity #8564]: #9757
-#9761 := [trans #9758 #9760]: #9757
-#9756 := [quant-inst #2280]: #9742
-#9762 := [mp #9756 #9761]: #9739
-#10593 := [unit-resolution #9762 #8184]: #8560
-#7520 := (* -1::Int #7504)
-#8414 := (+ #174 #7520)
-#8420 := (>= #8414 0::Int)
-#7327 := (= #174 #7504)
-#10594 := (= #7504 #174)
-#10595 := [monotonicity #7781]: #10594
-#10596 := [symm #10595]: #7327
-#10597 := (not #7327)
-#10598 := (or #10597 #8420)
-#10599 := [th-lemma arith triangle-eq]: #10598
-#10600 := [unit-resolution #10599 #10596]: #8420
-#10601 := [th-lemma arith farkas 1 1 1 1 1 1 1 #10600 #10593 #10592 #10591 #10589 #10580 #10579]: false
-#10605 := [lemma #10601]: #10604
-#10608 := [unit-resolution #10605 #10579 #10592 #10590]: #10602
-#10610 := (or #10609 #9826)
-#10611 := [th-lemma arith triangle-eq]: #10610
-#10612 := [unit-resolution #10611 #10608]: #10609
-#8687 := (* -1::Int #8683)
-#8691 := (+ f8 #8687)
-#8692 := (<= #8691 0::Int)
-#9840 := (not #8692)
-#8701 := (+ #8666 #8683)
-#8702 := (+ #174 #8701)
-#8703 := (>= #8702 0::Int)
-#8738 := (or #8692 #8703)
-#8741 := (not #8738)
-#8735 := (= #2283 #8655)
-#10614 := (not #8735)
-#8667 := (+ #2283 #8666)
-#9839 := (>= #8667 0::Int)
-#10575 := (not #9839)
-#10570 := [hypothesis]: #8915
-#10606 := (or #10575 #2879 #10577 #10603)
-#10571 := [hypothesis]: #9839
-#10574 := [th-lemma arith farkas 1 -1 1 1 -1 1 #10600 #10593 #10592 #10571 #10570 #10579]: false
-#10607 := [lemma #10574]: #10606
-#10613 := [unit-resolution #10607 #10579 #10570 #10592]: #10575
-#10615 := (or #10614 #9839)
-#10616 := [th-lemma arith triangle-eq]: #10615
-#10617 := [unit-resolution #10616 #10613]: #10614
-#8744 := (or #8735 #8741)
-#9828 := (or #4392 #8735 #8741)
-#8688 := (+ #1444 #8687)
-#8689 := (+ #8655 #8688)
-#8690 := (<= #8689 0::Int)
-#8731 := (or #8692 #8690)
-#8732 := (not #8731)
-#8733 := (= #8655 #2283)
-#8734 := (or #8733 #8732)
-#9829 := (or #4392 #8734)
-#9836 := (iff #9829 #9828)
-#9830 := (or #4392 #8744)
-#9833 := (iff #9830 #9828)
-#9834 := [rewrite]: #9833
-#9831 := (iff #9829 #9830)
-#8745 := (iff #8734 #8744)
-#8742 := (iff #8732 #8741)
-#8739 := (iff #8731 #8738)
-#8706 := (iff #8690 #8703)
-#8694 := (+ #8655 #8687)
-#8695 := (+ #1444 #8694)
-#8698 := (<= #8695 0::Int)
-#8704 := (iff #8698 #8703)
-#8705 := [rewrite]: #8704
-#8699 := (iff #8690 #8698)
-#8696 := (= #8689 #8695)
-#8697 := [rewrite]: #8696
-#8700 := [monotonicity #8697]: #8699
-#8707 := [trans #8700 #8705]: #8706
-#8740 := [monotonicity #8707]: #8739
-#8743 := [monotonicity #8740]: #8742
-#8736 := (iff #8733 #8735)
-#8737 := [rewrite]: #8736
-#8746 := [monotonicity #8737 #8743]: #8745
-#9832 := [monotonicity #8746]: #9831
-#9837 := [trans #9832 #9834]: #9836
-#9808 := [quant-inst #2279]: #9829
-#9838 := [mp #9808 #9837]: #9828
-#10618 := [unit-resolution #9838 #6500]: #8744
-#10619 := [unit-resolution #10618 #10617]: #8741
-#9835 := (or #8738 #9840)
-#9841 := [def-axiom]: #9835
-#10620 := [unit-resolution #9841 #10619]: #9840
-#9842 := (not #8703)
-#9843 := (or #8738 #9842)
-#9844 := [def-axiom]: #9843
-#10621 := [unit-resolution #9844 #10619]: #9842
-#8715 := (or #8692 #8703 #8712)
-#9814 := (or #4400 #8692 #8703 #8712)
-#8684 := (+ #8683 #2877)
-#8685 := (+ #174 #8684)
-#8686 := (= #8685 0::Int)
-#8693 := (or #8692 #8690 #8686)
-#9815 := (or #4400 #8693)
-#9821 := (iff #9815 #9814)
-#9817 := (or #4400 #8715)
-#9819 := (iff #9817 #9814)
-#9820 := [rewrite]: #9819
-#9812 := (iff #9815 #9817)
-#8716 := (iff #8693 #8715)
-#8713 := (iff #8686 #8712)
-#8710 := (= #8685 #8709)
-#8711 := [rewrite]: #8710
-#8714 := [monotonicity #8711]: #8713
-#8717 := [monotonicity #8707 #8714]: #8716
-#9818 := [monotonicity #8717]: #9812
-#9822 := [trans #9818 #9820]: #9821
-#9816 := [quant-inst #2279]: #9815
-#9825 := [mp #9816 #9822]: #9814
-#10622 := [unit-resolution #9825 #6504]: #8715
-#10623 := [unit-resolution #10622 #10621 #10620 #10612]: false
-#10625 := [lemma #10623]: #10624
-#10306 := [unit-resolution #10625 #10305 #10282 #10330]: #10603
-#10301 := (or #9722 #10478)
-#10286 := [hypothesis]: #10603
-#10288 := [hypothesis]: #8502
-#7506 := (f3 f15 #7202)
-#7507 := (= f1 #7506)
-#10294 := (not #7507)
-#10295 := (iff #756 #10294)
-#10287 := (iff #753 #7507)
-#10291 := (iff #7507 #753)
-#10289 := (= #7506 #171)
-#10290 := [monotonicity #7781]: #10289
-#10292 := [monotonicity #10290]: #10291
-#10293 := [symm #10292]: #10287
-#10296 := [monotonicity #10293]: #10295
-#10297 := [mp #6917 #10296]: #10294
-#10224 := (or #4287 #7507 #9722 #10478)
-#10485 := (or #7507 #9722 #10478)
-#10230 := (or #4287 #10485)
-#10232 := (iff #10230 #10224)
-#10233 := [rewrite]: #10232
-#10231 := [quant-inst #2280 #7202]: #10230
-#10234 := [mp #10231 #10233]: #10224
-#10300 := [unit-resolution #10234 #6928 #10297 #10288 #10286]: false
-#10302 := [lemma #10300]: #10301
-#10307 := [unit-resolution #10302 #10306]: #9722
-#9715 := (not #8511)
-#9718 := (or #9715 #8508 #8502)
-#9719 := [def-axiom]: #9718
-#10308 := [unit-resolution #9719 #10307 #10315]: #8508
-#10309 := [trans #10308 #7781]: #10471
-#10310 := [monotonicity #10309]: #10203
-#10337 := (not #10203)
-#10338 := (or #10337 #10215)
-#10336 := [th-lemma arith triangle-eq]: #10338
-#10339 := [unit-resolution #10336 #10310]: #10215
-#10341 := (not #6409)
-#10340 := (not #10215)
-#10346 := (or #10575 #10340 #2879 #10577 #10341)
-#10347 := [th-lemma arith assign-bounds -1 1 -1 1]: #10346
-#10345 := [unit-resolution #10347 #10282 #8185 #10305 #10339]: #10575
-#10348 := [unit-resolution #10616 #10345]: #10614
-#10349 := [unit-resolution #10618 #10348]: #8741
-#10174 := (or #8738 #8712)
-#10170 := [hypothesis]: #10609
-#10171 := [hypothesis]: #8741
-#10172 := [unit-resolution #9841 #10171]: #9840
-#10167 := [unit-resolution #9844 #10171]: #9842
-#10173 := [unit-resolution #10622 #10167 #10172 #10170]: false
-#10175 := [lemma #10173]: #10174
-#10350 := [unit-resolution #10175 #10349]: #8712
-#10367 := [unit-resolution #10611 #10350]: #9826
-#10368 := [unit-resolution #10567 #4208 #10330]: #10558
-#10369 := [th-lemma arith farkas 1 1 1 1 1 1 #10368 #10367 #10339 #10282 #8185 #10589]: false
-#10371 := [lemma #10369]: #10370
-#9750 := [unit-resolution #10371 #9749 #10279]: false
-#9751 := [lemma #9750]: #3431
-#4097 := (or #4475 #3436 #4469)
-#4084 := [def-axiom]: #4097
-#12712 := [unit-resolution #4084 #9751]: #12711
-#23123 := [unit-resolution #12712 #23130]: #4469
-#3991 := (or #4466 #4460)
-#3999 := [def-axiom]: #3991
-#23124 := [unit-resolution #3999 #23123]: #4460
-#23125 := (or #4463 #4457)
-#14662 := (f5 f22 ?v0!19)
-#14663 := (f9 #14662)
-#14458 := (f13 f14 ?v0!19)
-#14594 := (* -1::Int #14458)
-#14710 := (+ #14594 #14663)
-#14711 := (+ #174 #14710)
-#14712 := (>= #14711 0::Int)
-#14951 := (not #14712)
-#14666 := (* -1::Int #14663)
-#15450 := (+ #2313 #14666)
-#15451 := (>= #15450 0::Int)
-#15449 := (= #2313 #14663)
-#15659 := (= #2312 #14662)
-#15686 := (= ?v1!18 f22)
-#13656 := (= ?v1!18 #7202)
-#13649 := (f3 f15 ?v1!18)
-#13650 := (= f1 #13649)
-#13793 := (not #13650)
-#13789 := (f13 f14 ?v1!18)
-#14914 := (+ #13789 #14594)
-#14915 := (+ #2313 #14914)
-#14910 := (>= #14915 0::Int)
-#15610 := (not #14910)
-#14595 := (+ #2308 #14594)
-#14596 := (<= #14595 0::Int)
-#14809 := (or #4408 #14596)
-#14561 := (+ #14458 #2309)
-#14588 := (>= #14561 0::Int)
-#14810 := (or #4408 #14588)
-#14812 := (iff #14810 #14809)
-#14814 := (iff #14809 #14809)
-#14815 := [rewrite]: #14814
-#14613 := (iff #14588 #14596)
-#14589 := (+ #2309 #14458)
-#14592 := (>= #14589 0::Int)
-#14597 := (iff #14592 #14596)
-#14612 := [rewrite]: #14597
-#14587 := (iff #14588 #14592)
-#14590 := (= #14561 #14589)
-#14591 := [rewrite]: #14590
-#14593 := [monotonicity #14591]: #14587
-#14614 := [trans #14593 #14612]: #14613
-#14813 := [monotonicity #14614]: #14812
-#14763 := [trans #14813 #14815]: #14812
-#14811 := [quant-inst #2307]: #14810
-#14882 := [mp #14811 #14763]: #14809
-#15599 := [unit-resolution #14882 #8184]: #14596
-#4113 := (not #2906)
-#15600 := [hypothesis]: #3482
-#3942 := (or #3477 #4113)
-#3944 := [def-axiom]: #3942
-#15598 := [unit-resolution #3944 #15600]: #4113
-#13806 := (* -1::Int #13789)
-#13807 := (+ #2310 #13806)
-#13535 := (>= #13807 0::Int)
-#13875 := (= #2310 #13789)
-#4112 := (or #3477 #2321)
-#4106 := [def-axiom]: #4112
-#15601 := [unit-resolution #4106 #15600]: #2321
-#13767 := (or #4417 #3462 #13875)
-#13873 := (= #13789 #2310)
-#13743 := (or #13873 #3462)
-#13768 := (or #4417 #13743)
-#13790 := (iff #13768 #13767)
-#13741 := (or #3462 #13875)
-#13782 := (or #4417 #13741)
-#13792 := (iff #13782 #13767)
-#13784 := [rewrite]: #13792
-#13787 := (iff #13768 #13782)
-#13749 := (iff #13743 #13741)
-#13744 := (or #13875 #3462)
-#13747 := (iff #13744 #13741)
-#13748 := [rewrite]: #13747
-#13745 := (iff #13743 #13744)
-#13876 := (iff #13873 #13875)
-#13877 := [rewrite]: #13876
-#13746 := [monotonicity #13877]: #13745
-#13750 := [trans #13746 #13748]: #13749
-#13791 := [monotonicity #13750]: #13787
-#13794 := [trans #13791 #13784]: #13790
-#13786 := [quant-inst #2306]: #13768
-#13795 := [mp #13786 #13794]: #13767
-#15606 := [unit-resolution #13795 #7091 #15601]: #13875
-#15607 := (not #13875)
-#15608 := (or #15607 #13535)
-#15592 := [th-lemma arith triangle-eq]: #15608
-#15609 := [unit-resolution #15592 #15606]: #13535
-#15605 := (not #14596)
-#15602 := (not #13535)
-#15611 := (or #15610 #15602 #15605 #2906)
-#15613 := [th-lemma arith assign-bounds 1 -1 1]: #15611
-#15614 := [unit-resolution #15613 #15609 #15598 #15599]: #15610
-#15619 := (or #13793 #14910)
-#4105 := (or #3477 #2319)
-#4111 := [def-axiom]: #4105
-#15617 := [unit-resolution #4111 #15600]: #2319
-#15618 := [unit-resolution #4006 #6498]: #4273
-#13302 := (or #4278 #2318 #13793 #14910)
-#14916 := (or #13793 #2318 #14910)
-#13531 := (or #4278 #14916)
-#15117 := (iff #13531 #13302)
-#14917 := (or #2318 #13793 #14910)
-#13537 := (or #4278 #14917)
-#15115 := (iff #13537 #13302)
-#15116 := [rewrite]: #15115
-#13639 := (iff #13531 #13537)
-#14918 := (iff #14916 #14917)
-#14919 := [rewrite]: #14918
-#15114 := [monotonicity #14919]: #13639
-#15118 := [trans #15114 #15116]: #15117
-#13534 := [quant-inst #2307 #2306]: #13531
-#15119 := [mp #13534 #15118]: #13302
-#15612 := [unit-resolution #15119 #15618 #15617]: #15619
-#15620 := [unit-resolution #15612 #15614]: #13793
-#13659 := (ite #13656 #5883 #13650)
-#13653 := (f3 #8433 ?v1!18)
-#13654 := (= f1 #13653)
-#13662 := (iff #13654 #13659)
-#15003 := (or #6281 #13662)
-#13651 := (= #7202 ?v1!18)
-#13652 := (ite #13651 #5883 #13650)
-#13655 := (iff #13654 #13652)
-#15008 := (or #6281 #13655)
-#14881 := (iff #15008 #15003)
-#15034 := (iff #15003 #15003)
-#15035 := [rewrite]: #15034
-#13663 := (iff #13655 #13662)
-#13660 := (iff #13652 #13659)
-#13657 := (iff #13651 #13656)
-#13658 := [rewrite]: #13657
-#13661 := [monotonicity #13658]: #13660
-#13664 := [monotonicity #13661]: #13663
-#15010 := [monotonicity #13664]: #14881
-#15051 := [trans #15010 #15035]: #14881
-#15009 := [quant-inst #104 #7202 #5882 #2306]: #15008
-#14880 := [mp #15009 #15051]: #15003
-#15621 := [unit-resolution #14880 #4168]: #13662
-#15681 := (= #2320 #13653)
-#15615 := (= #13653 #2320)
-#15616 := [monotonicity #9277]: #15615
-#15683 := [symm #15616]: #15681
-#15684 := [trans #15601 #15683]: #13654
-#13228 := (not #13654)
-#12821 := (not #13662)
-#12779 := (or #12821 #13228 #13659)
-#13241 := [def-axiom]: #12779
-#15685 := [unit-resolution #13241 #15684 #15621]: #13659
-#15052 := (not #13659)
-#15050 := (or #15052 #13656 #13650)
-#15058 := [def-axiom]: #15050
-#15679 := [unit-resolution #15058 #15685 #15620]: #13656
-#15658 := [trans #15679 #7781]: #15686
-#15657 := [monotonicity #15658]: #15659
-#15661 := [monotonicity #15657]: #15449
-#15663 := (not #15449)
-#15664 := (or #15663 #15451)
-#15665 := [th-lemma arith triangle-eq]: #15664
-#15660 := [unit-resolution #15665 #15661]: #15451
-#15229 := (+ #2310 #6039)
-#15231 := (>= #15229 0::Int)
-#15441 := (= #2310 #5998)
-#15752 := [monotonicity #15658]: #15441
-#15662 := (not #15441)
-#15758 := (or #15662 #15231)
-#15759 := [th-lemma arith triangle-eq]: #15758
-#15760 := [unit-resolution #15759 #15752]: #15231
-#6665 := (<= #6408 0::Int)
-#5999 := (= #174 #5998)
-#6538 := (f3 f23 f22)
-#6539 := (= f1 #6538)
-#8175 := (= #5882 #6538)
-#8173 := (= #6538 #5882)
-#8174 := [monotonicity #6989]: #8173
-#8176 := [symm #8174]: #8175
-#8177 := [trans #6990 #8176]: #6539
-#6545 := (not #6539)
-#6597 := (or #5999 #6545)
-#6678 := (or #4417 #5999 #6545)
-#6679 := (or #4417 #6597)
-#6681 := (iff #6679 #6678)
-#6682 := [rewrite]: #6681
-#6680 := [quant-inst #170]: #6679
-#6683 := [mp #6680 #6682]: #6678
-#8178 := [unit-resolution #6683 #7091]: #6597
-#8179 := [unit-resolution #8178 #8177]: #5999
-#8180 := (not #5999)
-#8181 := (or #8180 #6665)
-#8182 := [th-lemma arith triangle-eq]: #8181
-#8183 := [unit-resolution #8182 #8179]: #6665
-#16330 := (not #15451)
-#12643 := (not #6665)
-#15761 := (not #15231)
-#15757 := (or #14951 #15605 #2906 #15761 #12643 #16330)
-#15765 := [th-lemma arith assign-bounds -1 1 1 -1 1]: #15757
-#15766 := [unit-resolution #15765 #15599 #8183 #15760 #15598 #15660]: #14951
-#14670 := (+ f8 #14666)
-#14722 := (<= #14670 0::Int)
-#15005 := (not #14722)
-#16331 := (or #15005 #16330 #2318)
-#16327 := [hypothesis]: #2319
-#16322 := [hypothesis]: #14722
-#16328 := [hypothesis]: #15451
-#16329 := [th-lemma arith farkas 1 -1 1 #16328 #16322 #16327]: false
-#16332 := [lemma #16329]: #16331
-#15767 := [unit-resolution #16332 #15660 #15617]: #15005
-#14716 := (+ #2309 #14663)
-#14717 := (+ #174 #14716)
-#14734 := (= #14717 0::Int)
-#15802 := (not #14734)
-#14848 := (>= #14717 0::Int)
-#15763 := (not #14848)
-#15784 := (or #15763 #2906 #15761 #12643 #16330)
-#15796 := [th-lemma arith assign-bounds 1 1 -1 1]: #15784
-#15797 := [unit-resolution #15796 #15760 #8183 #15598 #15660]: #15763
-#15803 := (or #15802 #14848)
-#15804 := [th-lemma arith triangle-eq]: #15803
-#15838 := [unit-resolution #15804 #15797]: #15802
-#14759 := (or #14712 #14722 #14734)
-#14883 := (or #4400 #14712 #14722 #14734)
-#14664 := (+ #14663 #2309)
-#14665 := (+ #174 #14664)
-#14660 := (= #14665 0::Int)
-#14667 := (+ #1444 #14666)
-#14668 := (+ #14458 #14667)
-#14669 := (<= #14668 0::Int)
-#14723 := (or #14722 #14669 #14660)
-#14884 := (or #4400 #14723)
-#14851 := (iff #14884 #14883)
-#14886 := (or #4400 #14759)
-#14849 := (iff #14886 #14883)
-#14850 := [rewrite]: #14849
-#14912 := (iff #14884 #14886)
-#14761 := (iff #14723 #14759)
-#14756 := (or #14722 #14712 #14734)
-#14754 := (iff #14756 #14759)
-#14760 := [rewrite]: #14754
-#14757 := (iff #14723 #14756)
-#14735 := (iff #14660 #14734)
-#14718 := (= #14665 #14717)
-#14719 := [rewrite]: #14718
-#14755 := [monotonicity #14719]: #14735
-#14709 := (iff #14669 #14712)
-#14724 := (+ #14458 #14666)
-#14725 := (+ #1444 #14724)
-#14728 := (<= #14725 0::Int)
-#14713 := (iff #14728 #14712)
-#14714 := [rewrite]: #14713
-#14729 := (iff #14669 #14728)
-#14726 := (= #14668 #14725)
-#14727 := [rewrite]: #14726
-#14730 := [monotonicity #14727]: #14729
-#14715 := [trans #14730 #14714]: #14709
-#14758 := [monotonicity #14715 #14755]: #14757
-#14762 := [trans #14758 #14760]: #14761
-#14913 := [monotonicity #14762]: #14912
-#14911 := [trans #14913 #14850]: #14851
-#14885 := [quant-inst #2307]: #14884
-#14852 := [mp #14885 #14911]: #14883
-#15836 := [unit-resolution #14852 #6504]: #14759
-#15837 := [unit-resolution #15836 #15838 #15767 #15766]: false
-#15833 := [lemma #15837]: #3477
-#3980 := (or #4463 #3482 #4457)
-#3995 := [def-axiom]: #3980
-#23140 := [unit-resolution #3995 #15833]: #23125
-#23141 := [unit-resolution #23140 #23124]: #4457
-#4099 := (or #4454 #2351)
-#4101 := [def-axiom]: #4099
-#23142 := [unit-resolution #4101 #23141]: #2351
-#23143 := (= #9072 #6061)
-#23144 := [monotonicity #9273]: #23143
-#23146 := [symm #23144]: #9852
-#23147 := [unit-resolution #11940 #23146]: #9448
-#9809 := (<= #9446 0::Int)
-#23139 := (or #11936 #9809)
-#23145 := [th-lemma arith triangle-eq]: #23139
-#23148 := [unit-resolution #23145 #23146]: #9809
-#23149 := (not #9809)
-#23155 := (or #10869 #23149)
-#7349 := (>= #6061 0::Int)
-#7287 := (not #7349)
-#7288 := [hypothesis]: #7287
-#7969 := (or #4270 #7349)
-#7970 := [quant-inst #6060]: #7969
-#7475 := [unit-resolution #7970 #7112 #7288]: false
-#7479 := [lemma #7475]: #7349
-#7044 := (not #3911)
-#23150 := (or #10869 #7044 #7287 #23149)
-#23152 := [th-lemma arith assign-bounds -1 1 -1]: #23150
-#23156 := [unit-resolution #23152 #7479 #7117]: #23155
-#23154 := [unit-resolution #23156 #23148]: #10869
-#3986 := (or #4454 #4446)
-#3987 := [def-axiom]: #3986
-#23157 := [unit-resolution #3987 #23141]: #4446
-#24096 := (or #14174 #4451)
-#8769 := (f24 #7202)
-#9535 := (* -1::Int #8769)
-#14029 := (+ #2338 #9535)
-#14217 := (<= #14029 0::Int)
-#10155 := (f3 f23 #7202)
-#10156 := (= f1 #10155)
-#11801 := (= #5882 #10155)
-#11794 := (= #10155 #5882)
-#11800 := [monotonicity #6989 #7781]: #11794
-#11802 := [symm #11800]: #11801
-#11803 := [trans #6990 #11802]: #10156
-#14203 := (f9 #14202)
-#14229 := (* -1::Int #14203)
-#14230 := (+ #9535 #14229)
-#14231 := (+ #2338 #14230)
-#14232 := (= #14231 0::Int)
-#15147 := (>= #14231 0::Int)
-#14148 := (+ #2339 #14123)
-#14149 := (+ #174 #14148)
-#14418 := (<= #14149 0::Int)
-#14152 := (= #14149 0::Int)
-#14177 := (not #14174)
-#21302 := [hypothesis]: #14177
-#21307 := (or #14174 #14152)
-#21296 := (not #14152)
-#21297 := [hypothesis]: #21296
-#12463 := (not #14132)
-#12470 := (or #14174 #12463)
-#12471 := [def-axiom]: #12470
-#21303 := [unit-resolution #12471 #21302]: #12463
-#12460 := (not #14143)
-#12469 := (or #14174 #12460)
-#12472 := [def-axiom]: #12469
-#21304 := [unit-resolution #12472 #21302]: #12460
-#14155 := (or #14132 #14143 #14152)
-#12402 := (or #4400 #14132 #14143 #14152)
-#14124 := (+ #14123 #2339)
-#14125 := (+ #174 #14124)
-#14126 := (= #14125 0::Int)
-#14128 := (+ #1444 #14127)
-#14129 := (+ #14065 #14128)
-#14130 := (<= #14129 0::Int)
-#14133 := (or #14132 #14130 #14126)
-#12426 := (or #4400 #14133)
-#12431 := (iff #12426 #12402)
-#12399 := (or #4400 #14155)
-#12430 := (iff #12399 #12402)
-#12425 := [rewrite]: #12430
-#12428 := (iff #12426 #12399)
-#14156 := (iff #14133 #14155)
-#14153 := (iff #14126 #14152)
-#14150 := (= #14125 #14149)
-#14151 := [rewrite]: #14150
-#14154 := [monotonicity #14151]: #14153
-#14146 := (iff #14130 #14143)
-#14134 := (+ #14065 #14127)
-#14135 := (+ #1444 #14134)
-#14138 := (<= #14135 0::Int)
-#14144 := (iff #14138 #14143)
-#14145 := [rewrite]: #14144
-#14139 := (iff #14130 #14138)
-#14136 := (= #14129 #14135)
-#14137 := [rewrite]: #14136
-#14140 := [monotonicity #14137]: #14139
-#14147 := [trans #14140 #14145]: #14146
-#14157 := [monotonicity #14147 #14154]: #14156
-#12429 := [monotonicity #14157]: #12428
-#12433 := [trans #12429 #12425]: #12431
-#12427 := [quant-inst #2337]: #12426
-#12434 := [mp #12427 #12433]: #12402
-#21305 := [unit-resolution #12434 #6504]: #14155
-#21306 := [unit-resolution #21305 #21304 #21303 #21297]: false
-#21308 := [lemma #21306]: #21307
-#24013 := [unit-resolution #21308 #21302]: #14152
-#24014 := (or #21296 #14418)
-#24015 := [th-lemma arith triangle-eq]: #24014
-#24016 := [unit-resolution #24015 #24013]: #14418
-#17675 := (not #14418)
-#24037 := (or #15147 #17675)
-#9536 := (+ #5998 #9535)
-#7436 := (>= #9536 0::Int)
-#9534 := (= #5998 #8769)
-#11865 := (= #8769 #5998)
-#11866 := [monotonicity #7781]: #11865
-#11867 := [symm #11866]: #9534
-#11868 := (not #9534)
-#24011 := (or #11868 #7436)
-#24017 := [th-lemma arith triangle-eq]: #24011
-#24018 := [unit-resolution #24017 #11867]: #7436
-#13344 := (+ #14123 #14229)
-#13577 := (>= #13344 0::Int)
-#7914 := (= #14123 #14203)
-#24021 := (= #14203 #14123)
-#24028 := [monotonicity #24020]: #24021
-#24029 := [symm #24028]: #7914
-#24027 := (not #7914)
-#24030 := (or #24027 #13577)
-#24031 := [th-lemma arith triangle-eq]: #24030
-#24032 := [unit-resolution #24031 #24029]: #13577
-#24035 := (not #13577)
-#24034 := (not #7436)
-#24033 := (or #15147 #24034 #10341 #24035 #17675)
-#24036 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24033
-#24038 := [unit-resolution #24036 #24032 #24018 #8185]: #24037
-#24026 := [unit-resolution #24038 #24016]: #15147
-#15125 := (<= #14231 0::Int)
-#14419 := (>= #14149 0::Int)
-#24039 := (or #21296 #14419)
-#24040 := [th-lemma arith triangle-eq]: #24039
-#24041 := [unit-resolution #24040 #24013]: #14419
-#24045 := (not #14419)
-#24049 := (or #15125 #24045)
-#9537 := (<= #9536 0::Int)
-#11869 := (or #11868 #9537)
-#11870 := [th-lemma arith triangle-eq]: #11869
-#11871 := [unit-resolution #11870 #11867]: #9537
-#13345 := (<= #13344 0::Int)
-#24042 := (or #24027 #13345)
-#24025 := [th-lemma arith triangle-eq]: #24042
-#24043 := [unit-resolution #24025 #24029]: #13345
-#24044 := (not #13345)
-#12642 := (not #9537)
-#24046 := (or #15125 #12642 #12643 #24044 #24045)
-#24047 := [th-lemma arith assign-bounds -1 -1 -1 1]: #24046
-#24050 := [unit-resolution #24047 #24043 #11871 #8183]: #24049
-#24051 := [unit-resolution #24050 #24041]: #15125
-#24053 := (not #15147)
-#24052 := (not #15125)
-#24048 := (or #14232 #24052 #24053)
-#24054 := [th-lemma arith triangle-eq]: #24048
-#24055 := [unit-resolution #24054 #24051 #24026]: #14232
-#14237 := (not #14232)
-#10168 := (not #10156)
-#14240 := (or #10168 #14217 #14237)
-#24056 := [hypothesis]: #4446
-#12768 := (or #4451 #10168 #14217 #14237)
-#14204 := (+ #2339 #14203)
-#14205 := (+ #8769 #14204)
-#14206 := (= #14205 0::Int)
-#14207 := (not #14206)
-#14208 := (+ #8769 #2339)
-#14209 := (>= #14208 0::Int)
-#14210 := (or #10168 #14209 #14207)
-#12775 := (or #4451 #14210)
-#12828 := (iff #12775 #12768)
-#12839 := (or #4451 #14240)
-#12862 := (iff #12839 #12768)
-#12868 := [rewrite]: #12862
-#12866 := (iff #12775 #12839)
-#14241 := (iff #14210 #14240)
-#14238 := (iff #14207 #14237)
-#14235 := (iff #14206 #14232)
-#14222 := (+ #8769 #14203)
-#14223 := (+ #2339 #14222)
-#14226 := (= #14223 0::Int)
-#14233 := (iff #14226 #14232)
-#14234 := [rewrite]: #14233
-#14227 := (iff #14206 #14226)
-#14224 := (= #14205 #14223)
-#14225 := [rewrite]: #14224
-#14228 := [monotonicity #14225]: #14227
-#14236 := [trans #14228 #14234]: #14235
-#14239 := [monotonicity #14236]: #14238
-#14220 := (iff #14209 #14217)
-#14211 := (+ #2339 #8769)
-#14214 := (>= #14211 0::Int)
-#14218 := (iff #14214 #14217)
-#14219 := [rewrite]: #14218
-#14215 := (iff #14209 #14214)
-#14212 := (= #14208 #14211)
-#14213 := [rewrite]: #14212
-#14216 := [monotonicity #14213]: #14215
-#14221 := [trans #14216 #14219]: #14220
-#14242 := [monotonicity #14221 #14239]: #14241
-#12867 := [monotonicity #14242]: #12866
-#12894 := [trans #12867 #12868]: #12828
-#12832 := [quant-inst #7202]: #12775
-#12895 := [mp #12832 #12894]: #12768
-#24057 := [unit-resolution #12895 #24056]: #14240
-#24058 := [unit-resolution #24057 #24055 #11803]: #14217
-#12478 := (f5 f10 ?v0!20)
-#17146 := (f7 #12478)
-#22307 := (f5 #7202 #17146)
-#22316 := (f9 #22307)
-#22319 := (* -1::Int #22316)
-#22448 := (+ #14123 #22319)
-#17182 := (>= #22448 0::Int)
-#17168 := (= #14123 #22316)
-#24059 := (= #22316 #14123)
-#24063 := (= #22307 #14122)
-#24061 := (= #17146 ?v0!20)
-#17147 := (= ?v0!20 #17146)
-#17170 := (or #6815 #17147)
-#17171 := [quant-inst #56 #2337]: #17170
-#24060 := [unit-resolution #17171 #4190]: #17147
-#24062 := [symm #24060]: #24061
-#24064 := [monotonicity #7781 #24062]: #24063
-#24065 := [monotonicity #24064]: #24059
-#24066 := [symm #24065]: #17168
-#24067 := (not #17168)
-#24068 := (or #24067 #17182)
-#24069 := [th-lemma arith triangle-eq]: #24068
-#24071 := [unit-resolution #24069 #24066]: #17182
-#22375 := (<= #22316 0::Int)
-#22355 := (not #22375)
-#22358 := (= #7202 #17146)
-#22388 := (not #22358)
-#20545 := (f3 f15 #17146)
-#20562 := (= f1 #20545)
-#23972 := (ite #22358 #5883 #20562)
-#23992 := (not #23972)
-#23973 := (f3 #8433 #17146)
-#23978 := (= f1 #23973)
-#23980 := (iff #23972 #23978)
-#23984 := (or #6281 #23980)
-#23979 := (iff #23978 #23972)
-#23985 := (or #6281 #23979)
-#23987 := (iff #23985 #23984)
-#23983 := (iff #23984 #23984)
-#23989 := [rewrite]: #23983
-#23981 := (iff #23979 #23980)
-#23982 := [rewrite]: #23981
-#23988 := [monotonicity #23982]: #23987
-#23990 := [trans #23988 #23989]: #23987
-#23986 := [quant-inst #104 #7202 #5882 #17146]: #23985
-#23991 := [mp #23986 #23990]: #23984
-#24072 := [unit-resolution #23991 #4168]: #23980
-#24004 := (not #23978)
-#10237 := (f3 f23 ?v0!20)
-#10238 := (= f1 #10237)
-#10239 := (not #10238)
-#24085 := (iff #10239 #24004)
-#24083 := (iff #10238 #23978)
-#24080 := (iff #23978 #10238)
-#24078 := (= #23973 #10237)
-#24079 := [monotonicity #9277 #24062]: #24078
-#24082 := [monotonicity #24079]: #24080
-#24084 := [symm #24082]: #24083
-#24086 := [monotonicity #24084]: #24085
-#24699 := (not #14076)
-#21427 := (not #19558)
-#24073 := (or #14143 #21427 #24035 #24052 #24034 #10341)
-#24074 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #24073
-#24075 := [unit-resolution #24074 #24051 #24032 #21304 #24018 #8185]: #21427
-#24700 := (or #24699 #19558)
-#24687 := [hypothesis]: #21427
-#24688 := [hypothesis]: #14076
-#24701 := [th-lemma arith triangle-eq]: #24700
-#24702 := [unit-resolution #24701 #24688 #24687]: false
-#24703 := [lemma #24702]: #24700
-#24070 := [unit-resolution #24703 #24075]: #24699
-#14082 := (or #10239 #14076)
-#12325 := (or #4417 #10239 #14076)
-#14072 := (= #14065 #2338)
-#14075 := (or #14072 #10239)
-#12365 := (or #4417 #14075)
-#12373 := (iff #12365 #12325)
-#12368 := (or #4417 #14082)
-#12370 := (iff #12368 #12325)
-#12372 := [rewrite]: #12370
-#12369 := (iff #12365 #12368)
-#14085 := (iff #14075 #14082)
-#14079 := (or #14076 #10239)
-#14083 := (iff #14079 #14082)
-#14084 := [rewrite]: #14083
-#14080 := (iff #14075 #14079)
-#14077 := (iff #14072 #14076)
-#14078 := [rewrite]: #14077
-#14081 := [monotonicity #14078]: #14080
-#14086 := [trans #14081 #14084]: #14085
-#12364 := [monotonicity #14086]: #12369
-#12374 := [trans #12364 #12372]: #12373
-#12367 := [quant-inst #2337]: #12365
-#12393 := [mp #12367 #12374]: #12325
-#24076 := [unit-resolution #12393 #7091]: #14082
-#24077 := [unit-resolution #24076 #24070]: #10239
-#24081 := [mp #24077 #24086]: #24004
-#24003 := (not #23980)
-#24006 := (or #24003 #23992 #23978)
-#24007 := [def-axiom]: #24006
-#24087 := [unit-resolution #24007 #24081 #24072]: #23992
-#24088 := (or #23972 #22388)
-#23999 := (or #23972 #22388 #6295)
-#24000 := [def-axiom]: #23999
-#24089 := [unit-resolution #24000 #6990]: #24088
-#24090 := [unit-resolution #24089 #24087]: #22388
-#22360 := (or #22358 #22355)
-#23949 := (or #6773 #22358 #22355)
-#22356 := (= #17146 #7202)
-#22357 := (or #22356 #22355)
-#23950 := (or #6773 #22357)
-#23957 := (iff #23950 #23949)
-#23952 := (or #6773 #22360)
-#23955 := (iff #23952 #23949)
-#23956 := [rewrite]: #23955
-#23953 := (iff #23950 #23952)
-#22361 := (iff #22357 #22360)
-#22359 := (iff #22356 #22358)
-#22354 := [rewrite]: #22359
-#22362 := [monotonicity #22354]: #22361
-#23954 := [monotonicity #22362]: #23953
-#23958 := [trans #23954 #23956]: #23957
-#23951 := [quant-inst #7202 #17146]: #23950
-#23959 := [mp #23951 #23958]: #23949
-#24091 := [unit-resolution #23959 #4208]: #22360
-#24094 := [unit-resolution #24091 #24090]: #22355
-#24095 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #24018 #8185 #24094 #24071 #24016 #24058]: false
-#24097 := [lemma #24095]: #24096
-#23158 := [unit-resolution #24097 #23157]: #14174
-#23138 := [hypothesis]: #12460
-#12473 := (or #14177 #14132 #14143)
-#12474 := [def-axiom]: #12473
-#23151 := [unit-resolution #12474 #23138 #23158]: #14132
-#14180 := (or #14076 #14177)
-#12435 := (or #4392 #14076 #14177)
-#14171 := (or #14132 #14130)
-#14172 := (not #14171)
-#14173 := (or #14072 #14172)
-#12454 := (or #4392 #14173)
-#12459 := (iff #12454 #12435)
-#12432 := (or #4392 #14180)
-#12458 := (iff #12432 #12435)
-#12453 := [rewrite]: #12458
-#12456 := (iff #12454 #12432)
-#14181 := (iff #14173 #14180)
-#14178 := (iff #14172 #14177)
-#14175 := (iff #14171 #14174)
-#14176 := [monotonicity #14147]: #14175
-#14179 := [monotonicity #14176]: #14178
-#14182 := [monotonicity #14078 #14179]: #14181
-#12457 := [monotonicity #14182]: #12456
-#12461 := [trans #12457 #12453]: #12459
-#12455 := [quant-inst #2337]: #12454
-#12462 := [mp #12455 #12461]: #12435
-#23159 := [unit-resolution #12462 #6500]: #14180
-#23137 := [unit-resolution #23159 #23158]: #14076
-#23160 := [unit-resolution #24703 #23137]: #19558
-#23161 := [unit-resolution #24074 #23138 #24032 #23160 #24018 #8185]: #24052
-#23153 := (or #15125 #15147)
-#23162 := [th-lemma arith farkas 1 1]: #23153
-#23163 := [unit-resolution #23162 #23161]: #15147
-#23164 := [th-lemma arith farkas 1 1 1 1 1 1 1 1 1 1 #24043 #23163 #11871 #8183 #23151 #10065 #23154 #23147 #6982 #23142]: false
-#23166 := [lemma #23164]: #23165
-#27682 := [unit-resolution #23166 #10065]: #14143
-#27687 := [unit-resolution #12472 #27682]: #14174
-#27699 := [unit-resolution #12462 #6500 #27687]: #14076
-#27700 := [unit-resolution #24701 #27699]: #19558
-#21428 := (or #21426 #21427 #2350)
-#21421 := [hypothesis]: #19558
-#21422 := [hypothesis]: #14783
-#21425 := [th-lemma arith farkas -1 1 1 #21422 #21421 #19774]: false
-#21429 := [lemma #21425]: #21428
-#27701 := [unit-resolution #21429 #27700 #19774]: #21426
-#4102 := (or #4454 #2920)
-#4100 := [def-axiom]: #4102
-#27702 := [unit-resolution #4100 #23141]: #2920
-#24426 := (or #4303 #2917 #14783 #14788)
-#14780 := (or #14779 #14776 #14769)
-#14781 := (not #14780)
-#14784 := (or #2352 #14783 #14781)
-#24435 := (or #4303 #14784)
-#24441 := (iff #24435 #24426)
-#14791 := (or #2917 #14783 #14788)
-#24432 := (or #4303 #14791)
-#24440 := (iff #24432 #24426)
-#24436 := [rewrite]: #24440
-#24431 := (iff #24435 #24432)
-#14792 := (iff #14784 #14791)
-#14789 := (iff #14781 #14788)
-#14786 := (iff #14780 #14785)
-#14787 := [rewrite]: #14786
-#14790 := [monotonicity #14787]: #14789
-#14793 := [monotonicity #2919 #14790]: #14792
-#24438 := [monotonicity #14793]: #24431
-#24430 := [trans #24438 #24436]: #24441
-#24437 := [quant-inst #2337]: #24435
-#24453 := [mp #24437 #24430]: #24426
-#27704 := [unit-resolution #24453 #12656 #27702 #27701]: #14788
-#24457 := (or #14785 #14778)
-#24443 := [def-axiom]: #24457
-#27669 := [unit-resolution #24443 #27704]: #14778
-#27710 := [trans #27669 #27709]: #26205
-#26233 := (not #26205)
-#15527 := (>= #14774 0::Int)
-#24455 := (or #14785 #14775)
-#24456 := [def-axiom]: #24455
-#27706 := [unit-resolution #24456 #27704]: #14775
-#27707 := (or #14776 #15527)
-#27705 := [th-lemma arith triangle-eq]: #27707
-#27708 := [unit-resolution #27705 #27706]: #15527
-#24439 := (not #14769)
-#24454 := (or #14785 #24439)
-#24433 := [def-axiom]: #24454
-#27690 := [unit-resolution #24433 #27704]: #24439
-#15503 := (<= #14774 0::Int)
-#27688 := (or #14776 #15503)
-#27691 := [th-lemma arith triangle-eq]: #27688
-#27692 := [unit-resolution #27691 #27706]: #15503
-#28955 := (not #15527)
-#29072 := (not #15503)
-#29103 := (or #26233 #29072 #4451 #14769 #21427 #28955)
-#21407 := (f24 #14765)
-#21437 := (* -1::Int #21407)
-#21648 := (+ #14772 #21437)
-#21649 := (+ #2338 #21648)
-#17946 := (<= #21649 0::Int)
-#29055 := (not #17946)
-#18257 := (>= #21649 0::Int)
-#21438 := (+ #14766 #21437)
-#21439 := (>= #21438 0::Int)
-#25323 := (or #4408 #21439)
-#25330 := [quant-inst #14765]: #25323
-#28960 := [unit-resolution #25330 #8184]: #21439
-#28952 := [hypothesis]: #15527
-#28957 := (not #21439)
-#28958 := (or #18257 #28955 #21427 #28957)
-#28954 := [th-lemma arith assign-bounds -1 -1 -1]: #28958
-#28953 := [unit-resolution #28954 #28952 #21421 #28960]: #18257
-#21650 := (= #21649 0::Int)
-#21655 := (not #21650)
-#21635 := (+ #2338 #21437)
-#21636 := (<= #21635 0::Int)
-#28956 := (not #21636)
-#28959 := [hypothesis]: #24439
-#28976 := (or #28956 #14769 #21427 #28957)
-#28990 := [th-lemma arith assign-bounds -1 -1 -1]: #28976
-#29033 := [unit-resolution #28990 #28959 #21421 #28960]: #28956
-#21420 := (f3 f23 #14765)
-#21400 := (= f1 #21420)
-#25149 := (f3 f23 #25033)
-#25138 := (= f1 #25149)
-#29034 := (iff #25138 #21400)
-#29037 := (iff #21400 #25138)
-#29036 := (= #21420 #25149)
-#28991 := [monotonicity #28975]: #29036
-#29032 := [monotonicity #28991]: #29037
-#29040 := [symm #29032]: #29034
-#30417 := (= #7202 #25033)
-#30411 := (ite #30417 #5883 #26205)
-#30479 := [hypothesis]: #26205
-#30483 := (or #30411 #26233)
-#30455 := (not #30411)
-#30475 := [hypothesis]: #30455
-#30456 := (not #30417)
-#30476 := (or #30411 #30456)
-#30461 := (or #30411 #30456 #6295)
-#30462 := [def-axiom]: #30461
-#30477 := [unit-resolution #30462 #6990]: #30476
-#30478 := [unit-resolution #30477 #30475]: #30456
-#30480 := (or #30411 #30417)
-#30463 := (or #30411 #30417 #26233)
-#30464 := [def-axiom]: #30463
-#30481 := [unit-resolution #30464 #30479]: #30480
-#30482 := [unit-resolution #30481 #30478 #30475]: false
-#30484 := [lemma #30482]: #30483
-#28974 := [unit-resolution #30484 #30479]: #30411
-#30250 := (or #25138 #30455)
-#30440 := (f3 #8433 #25033)
-#30245 := (= #30440 #25149)
-#30241 := (= #25149 #30440)
-#18315 := (= f23 #8433)
-#18216 := (= #180 #8433)
-#18317 := [symm #9275]: #18216
-#18314 := [trans #6989 #18317]: #18315
-#30242 := [monotonicity #18314]: #30241
-#30247 := [symm #30242]: #30245
-#30441 := (= f1 #30440)
-#30443 := (iff #30411 #30441)
-#30185 := (or #6281 #30443)
-#30442 := (iff #30441 #30411)
-#30183 := (or #6281 #30442)
-#30190 := (iff #30183 #30185)
-#30192 := (iff #30185 #30185)
-#30181 := [rewrite]: #30192
-#30444 := (iff #30442 #30443)
-#30445 := [rewrite]: #30444
-#30191 := [monotonicity #30445]: #30190
-#30193 := [trans #30191 #30181]: #30190
-#30189 := [quant-inst #104 #7202 #5882 #25033]: #30183
-#30194 := [mp #30189 #30193]: #30185
-#30237 := [unit-resolution #30194 #4168]: #30443
-#30195 := (not #30443)
-#30239 := (or #30195 #30441)
-#30238 := [hypothesis]: #30411
-#30200 := (or #30195 #30455 #30441)
-#30201 := [def-axiom]: #30200
-#30240 := [unit-resolution #30201 #30238]: #30239
-#30231 := [unit-resolution #30240 #30237]: #30441
-#30248 := [trans #30231 #30247]: #25138
-#25150 := (not #25138)
-#30232 := [hypothesis]: #25150
-#30249 := [unit-resolution #30232 #30248]: false
-#30251 := [lemma #30249]: #30250
-#29035 := [unit-resolution #30251 #28974]: #25138
-#29041 := [mp #29035 #29040]: #21400
-#21406 := (not #21400)
-#21658 := (or #21406 #21636 #21655)
-#16831 := (or #4451 #21406 #21636 #21655)
-#21622 := (+ #2339 #14771)
-#21623 := (+ #21407 #21622)
-#21624 := (= #21623 0::Int)
-#21625 := (not #21624)
-#21626 := (+ #21407 #2339)
-#21627 := (>= #21626 0::Int)
-#21628 := (or #21406 #21627 #21625)
-#16832 := (or #4451 #21628)
-#16865 := (iff #16832 #16831)
-#16845 := (or #4451 #21658)
-#16848 := (iff #16845 #16831)
-#16843 := [rewrite]: #16848
-#16846 := (iff #16832 #16845)
-#21659 := (iff #21628 #21658)
-#21656 := (iff #21625 #21655)
-#21653 := (iff #21624 #21650)
-#21641 := (+ #14771 #21407)
-#21642 := (+ #2339 #21641)
-#21645 := (= #21642 0::Int)
-#21651 := (iff #21645 #21650)
-#21652 := [rewrite]: #21651
-#21646 := (iff #21624 #21645)
-#21643 := (= #21623 #21642)
-#21644 := [rewrite]: #21643
-#21647 := [monotonicity #21644]: #21646
-#21654 := [trans #21647 #21652]: #21653
-#21657 := [monotonicity #21654]: #21656
-#21639 := (iff #21627 #21636)
-#21629 := (+ #2339 #21407)
-#21632 := (>= #21629 0::Int)
-#21637 := (iff #21632 #21636)
-#21638 := [rewrite]: #21637
-#21633 := (iff #21627 #21632)
-#21630 := (= #21626 #21629)
-#21631 := [rewrite]: #21630
-#21634 := [monotonicity #21631]: #21633
-#21640 := [trans #21634 #21638]: #21639
-#21660 := [monotonicity #21640 #21657]: #21659
-#16853 := [monotonicity #21660]: #16846
-#16850 := [trans #16853 #16843]: #16865
-#16844 := [quant-inst #14765]: #16832
-#16894 := [mp #16844 #16850]: #16831
-#29052 := [unit-resolution #16894 #24056]: #21658
-#29050 := [unit-resolution #29052 #29041 #29033]: #21655
-#29039 := (not #18257)
-#29051 := (or #21650 #29055 #29039)
-#29054 := [th-lemma arith triangle-eq]: #29051
-#29062 := [unit-resolution #29054 #29050 #28953]: #29055
-#25320 := (<= #21438 0::Int)
-#21408 := (= #14766 #21407)
-#26200 := (f13 f14 #25033)
-#25139 := (f24 #25033)
-#26939 := (= #25139 #26200)
-#29146 := (iff #26939 #21408)
-#29068 := (= #21407 #14766)
-#29060 := (iff #29068 #21408)
-#29145 := [commutativity]: #29060
-#29071 := (iff #26939 #29068)
-#29069 := (= #26200 #14766)
-#29038 := [monotonicity #29053]: #29069
-#29064 := (= #25139 #21407)
-#24491 := (= #21407 #25139)
-#29070 := [monotonicity #28975]: #24491
-#29061 := [symm #29070]: #29064
-#29073 := [monotonicity #29061 #29038]: #29071
-#29144 := [trans #29073 #29145]: #29146
-#26979 := (or #25150 #26939)
-#26982 := (or #4417 #25150 #26939)
-#26973 := (= #26200 #25139)
-#26992 := (or #26973 #25150)
-#26999 := (or #4417 #26992)
-#27004 := (iff #26999 #26982)
-#27001 := (or #4417 #26979)
-#26957 := (iff #27001 #26982)
-#27003 := [rewrite]: #26957
-#26994 := (iff #26999 #27001)
-#26995 := (iff #26992 #26979)
-#26972 := (or #26939 #25150)
-#26980 := (iff #26972 #26979)
-#26981 := [rewrite]: #26980
-#26978 := (iff #26992 #26972)
-#26976 := (iff #26973 #26939)
-#26938 := [rewrite]: #26976
-#26977 := [monotonicity #26938]: #26978
-#26998 := [trans #26977 #26981]: #26995
-#27002 := [monotonicity #26998]: #26994
-#26956 := [trans #27002 #27003]: #27004
-#27000 := [quant-inst #25033]: #26999
-#27006 := [mp #27000 #26956]: #26982
-#29063 := [unit-resolution #27006 #7091]: #26979
-#29059 := [unit-resolution #29063 #29035]: #26939
-#29147 := [mp #29059 #29144]: #21408
-#29148 := (not #21408)
-#29149 := (or #29148 #25320)
-#29109 := [th-lemma arith triangle-eq]: #29149
-#29142 := [unit-resolution #29109 #29147]: #25320
-#14108 := (<= #14107 0::Int)
-#13512 := (or #4408 #14108)
-#14098 := (+ #14065 #2339)
-#14099 := (>= #14098 0::Int)
-#13542 := (or #4408 #14099)
-#13509 := (iff #13542 #13512)
-#13558 := (iff #13512 #13512)
-#13566 := [rewrite]: #13558
-#14111 := (iff #14099 #14108)
-#14100 := (+ #2339 #14065)
-#14103 := (>= #14100 0::Int)
-#14109 := (iff #14103 #14108)
-#14110 := [rewrite]: #14109
-#14104 := (iff #14099 #14103)
-#14101 := (= #14098 #14100)
-#14102 := [rewrite]: #14101
-#14105 := [monotonicity #14102]: #14104
-#14112 := [trans #14105 #14110]: #14111
-#13561 := [monotonicity #14112]: #13509
-#13569 := [trans #13561 #13566]: #13509
-#13552 := [quant-inst #2337]: #13542
-#13567 := [mp #13552 #13569]: #13512
-#29101 := [unit-resolution #13567 #8184]: #14108
-#29150 := [hypothesis]: #15503
-#29100 := [th-lemma arith farkas -1 -1 -1 1 #29150 #29101 #29142 #29062]: false
-#29104 := [lemma #29100]: #29103
-#27693 := [unit-resolution #29104 #27692 #23157 #27690 #27700 #27708]: #26233
-#27711 := [unit-resolution #27693 #27710]: false
-#27726 := [lemma #27711]: #27725
-#26709 := [unit-resolution #27726 #19774]: #6064
-#6110 := (or #6082 #6109)
-#6111 := [def-axiom]: #6110
-#26710 := [unit-resolution #6111 #26709]: #6082
-#6085 := (not #6082)
-#12657 := (or #6079 #6085)
-#6096 := (or #4303 #1645 #6079 #6085)
-#6075 := (or #6074 #6071 #6064)
-#6076 := (not #6075)
-#6078 := (or #6077 #1645 #6076)
-#6097 := (or #4303 #6078)
-#6104 := (iff #6097 #6096)
-#6091 := (or #1645 #6079 #6085)
-#6099 := (or #4303 #6091)
-#6102 := (iff #6099 #6096)
-#6103 := [rewrite]: #6102
-#6100 := (iff #6097 #6099)
-#6094 := (iff #6078 #6091)
-#6088 := (or #6079 #1645 #6085)
-#6092 := (iff #6088 #6091)
-#6093 := [rewrite]: #6092
-#6089 := (iff #6078 #6088)
-#6086 := (iff #6076 #6085)
-#6083 := (iff #6075 #6082)
-#6084 := [rewrite]: #6083
-#6087 := [monotonicity #6084]: #6086
-#6090 := [monotonicity #6081 #6087]: #6089
-#6095 := [trans #6090 #6093]: #6094
-#6101 := [monotonicity #6095]: #6100
-#6105 := [trans #6101 #6103]: #6104
-#6098 := [quant-inst #170]: #6097
-#6106 := [mp #6098 #6105]: #6096
-#12658 := [unit-resolution #6106 #12656 #7821]: #12657
-#26756 := [unit-resolution #12658 #26710]: #6079
-#26757 := [symm #26756]: #6077
-#26753 := [monotonicity #26757]: #7816
-#26760 := [symm #26753]: #7788
-#7783 := (not #7788)
-#7813 := (or #7783 #7789)
-#7819 := [th-lemma arith triangle-eq]: #7813
-#26755 := [unit-resolution #7819 #26760]: #7789
-#9960 := (not #7789)
-#8355 := (or #2266 #9960)
-#9891 := (not #9488)
-#9573 := [hypothesis]: #7789
-#9645 := (or #9891 #2266 #9960)
-#10019 := (= #9980 0::Int)
-#9966 := (not #10019)
-#9776 := (not #10041)
-#9574 := [hypothesis]: #9488
-#6983 := (not #3908)
-#9890 := (not #10053)
-#9963 := (or #9776 #9890 #2266 #9891 #6983 #9960)
-#9883 := [th-lemma arith assign-bounds 1 -1 -1 1 -1]: #9963
-#9889 := [unit-resolution #9883 #9574 #6982 #10062 #10078 #9573]: #9776
-#9850 := (or #9966 #10041)
-#9962 := [th-lemma arith triangle-eq]: #9850
-#9644 := [unit-resolution #9962 #9889]: #9966
-#9961 := (or #10016 #9890 #2266 #9891 #6983 #9960)
-#10032 := [th-lemma arith assign-bounds 1 1 1 1 1]: #9961
-#10033 := [unit-resolution #10032 #9574 #6982 #10078 #10062 #9573]: #10016
-#9854 := [unit-resolution #10026 #4208 #10033]: #9940
-#9519 := (or #6798 #9959 #10019)
-#10020 := (or #10019 #9959)
-#9538 := (or #6798 #10020)
-#9792 := (iff #9538 #9519)
-#10027 := (or #9959 #10019)
-#9489 := (or #6798 #10027)
-#9526 := (iff #9489 #9519)
-#9791 := [rewrite]: #9526
-#9528 := (iff #9538 #9489)
-#10028 := (iff #10020 #10027)
-#10029 := [rewrite]: #10028
-#9532 := [monotonicity #10029]: #9528
-#9793 := [trans #9532 #9791]: #9792
-#9530 := [quant-inst #7202 #2264]: #9538
-#9752 := [mp #9530 #9793]: #9519
-#9853 := [unit-resolution #9752 #4202 #9854 #9644]: false
-#10133 := [lemma #9853]: #9645
-#9525 := [unit-resolution #10133 #10078 #9573]: #9891
-#9529 := [unit-resolution #10076 #9525]: #10074
-#8418 := (or #7629 #7607)
-#9089 := [hypothesis]: #10074
-#8415 := [hypothesis]: #7632
-#8417 := [unit-resolution #9503 #8415]: #9501
-#8457 := [unit-resolution #9506 #8415]: #9504
-#8458 := [unit-resolution #10072 #8457 #8417 #9089]: false
-#9334 := [lemma #8458]: #8418
-#9748 := [unit-resolution #9334 #9529]: #7629
-#9790 := [unit-resolution #10068 #9748]: #7530
-#9746 := [unit-resolution #11911 #9790]: #9572
-#9888 := [th-lemma arith farkas 1 -1 1 #9571 #10078 #9746]: false
-#8313 := [lemma #9888]: #8355
-#26761 := [unit-resolution #8313 #26755]: #2266
-#26759 := [unit-resolution #12708 #26761]: #4481
-#26762 := [unit-resolution #4077 #26759]: #4472
-#26758 := [unit-resolution #12712 #26762]: #4469
-#26763 := [unit-resolution #3999 #26758]: #4460
-#26771 := [unit-resolution #23140 #26763]: #4457
-#26773 := [unit-resolution #3987 #26771]: #4446
-#26770 := [unit-resolution #24097 #26773]: #14174
-#26774 := [unit-resolution #12462 #6500 #26770]: #14076
-#26772 := [unit-resolution #24701 #26774]: #19558
-#26788 := [unit-resolution #21429 #26772 #19774]: #21426
-#26791 := [unit-resolution #4100 #26771]: #2920
-#26783 := [unit-resolution #24453 #12656 #26791 #26788]: #14788
-#26766 := [unit-resolution #24443 #26783]: #14778
-#26825 := [trans #26766 #26819]: #26205
-#26789 := [unit-resolution #24456 #26783]: #14775
-#26784 := [unit-resolution #27691 #26789]: #15503
-#26782 := [unit-resolution #24433 #26783]: #24439
-#26785 := [unit-resolution #27705 #26789]: #15527
-#26781 := [unit-resolution #29104 #26785 #26773 #26782 #26772 #26784]: #26233
-#26820 := [unit-resolution #26781 #26825]: false
-#26821 := [lemma #26820]: #2350
-#8220 := [unit-resolution #4101 #26821]: #4454
-#8224 := [unit-resolution #23140 #8220]: #4463
-#8310 := [unit-resolution #3999 #8224]: #4466
-#8229 := [unit-resolution #12712 #8310]: #4475
-#8233 := [unit-resolution #4077 #8229]: #4478
-#8239 := [unit-resolution #12708 #8233]: #2267
-#8333 := [unit-resolution #11103 #8239]: #6064
-#8358 := [unit-resolution #6111 #8333]: #6082
-#8276 := [unit-resolution #12658 #8358]: #6079
-#8416 := [symm #8276]: #6077
-#8345 := [monotonicity #8416]: #7816
-#8349 := [symm #8345]: #7788
-#8351 := [unit-resolution #8313 #8239]: #9960
-[unit-resolution #7819 #8351 #8349]: false
+#29183 := [unit-resolution #4077 #19059]: #2327
+#22564 := (or #22561 #22448 #2326)
+#22565 := [th-lemma arith assign-bounds -1 -1]: #22564
+#22807 := [unit-resolution #22565 #29183]: #22806
+#22808 := [unit-resolution #22807 #22543]: #22561
+#22605 := (or #14291 #14296)
+#4078 := (or #4430 #2896)
+#4076 := [def-axiom]: #4078
+#22809 := [unit-resolution #4076 #19059]: #2896
+#12741 := [unit-resolution #3984 #6450]: #4274
+#8711 := (or #4279 #2893 #14291 #14296)
+#14288 := (or #14287 #14284 #14277)
+#14289 := (not #14288)
+#14292 := (or #2328 #14291 #14289)
+#10448 := (or #4279 #14292)
+#11789 := (iff #10448 #8711)
+#14299 := (or #2893 #14291 #14296)
+#10454 := (or #4279 #14299)
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+#10538 := (iff #10448 #10454)
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+#14297 := (iff #14289 #14296)
+#14294 := (iff #14288 #14293)
+#14295 := [rewrite]: #14294
+#14298 := [monotonicity #14295]: #14297
+#14301 := [monotonicity #2895 #14298]: #14300
+#10449 := [monotonicity #14301]: #10538
+#11798 := [trans #10449 #11372]: #11789
+#10447 := [quant-inst #2313]: #10448
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+#28118 := [unit-resolution #8713 #12741 #22809]: #22605
+#22606 := [unit-resolution #28118 #22808]: #14296
+#10476 := (or #14293 #14283)
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+#22805 := [unit-resolution #10439 #22606]: #14283
+#22811 := (or #14284 #8606)
+#22812 := [th-lemma arith triangle-eq]: #22811
+#22813 := [unit-resolution #22812 #22805]: #8606
+#29724 := (not #19100)
+#22839 := (not #8606)
+#22911 := (or #10493 #22839 #22448 #29724)
+#22905 := [th-lemma arith assign-bounds -1 -1 -1]: #22911
+#22815 := [unit-resolution #22905 #22543 #22813 #29722]: #10493
+#13447 := (<= #19310 0::Int)
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+#19082 := (= #14274 #19081)
+#18965 := (+ #6404 #14275)
+#18966 := (>= #18965 0::Int)
+#10474 := (or #14293 #14286)
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+#22912 := [unit-resolution #12249 #22606]: #14286
+#14738 := (or #4263 #6402 #14287 #18966)
+#18967 := (or #6402 #14287 #18966)
+#14207 := (or #4263 #18967)
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+#14721 := [rewrite]: #14695
+#15013 := [quant-inst #14273 #6386]: #14207
+#15330 := [mp #15013 #14721]: #14738
+#22914 := [unit-resolution #15330 #7878 #8069 #22912]: #18966
+#29729 := (not #18966)
+#29730 := (or #19082 #29729)
+#29708 := [hypothesis]: #18966
+#6521 := (f24 #6386)
+#6522 := (* -1::Int #6521)
+#6520 := (+ #6404 #6522)
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+#6658 := (= #6404 #6521)
+#18890 := (iff #5956 #6658)
+#18888 := (iff #6658 #5956)
+#18885 := (= #6521 #5955)
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+#19034 := [symm #19033]: #18890
+#19090 := [mp #8794 #19034]: #6658
+#18893 := (not #6658)
+#18894 := (or #18893 #6727)
+#18895 := [th-lemma arith triangle-eq]: #18894
+#19093 := [unit-resolution #18895 #19090]: #6727
+#19429 := (+ #6521 #19098)
+#19431 := (<= #19429 0::Int)
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+#29716 := [hypothesis]: #29709
+#19084 := (or #19080 #19082)
+#14673 := (or #4393 #19080 #19082)
+#19083 := (or #19082 #19080)
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+#15067 := (iff #14660 #14673)
+#15826 := (or #4393 #19084)
+#15471 := (iff #15826 #14673)
+#15714 := [rewrite]: #15471
+#15453 := (iff #14660 #15826)
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+#19086 := [rewrite]: #19085
+#15466 := [monotonicity #19086]: #15453
+#15472 := [trans #15466 #15714]: #15067
+#15726 := [quant-inst #14273]: #14660
+#15068 := [mp #15726 #15472]: #14673
+#29717 := [unit-resolution #15068 #8044]: #19084
+#29718 := [unit-resolution #29717 #29716]: #19080
+#29719 := (or #19073 #19431)
+#8990 := (f8 f23 #6386)
+#8998 := (= f1 #8990)
+#20482 := (= #5830 #8990)
+#20480 := (= #8990 #5830)
+#20481 := [monotonicity #8689 #7565]: #20480
+#20483 := [symm #20481]: #20482
+#20484 := [trans #8690 #20483]: #8998
+#3973 := (or #4442 #4405)
+#3974 := [def-axiom]: #3973
+#20487 := [unit-resolution #3974 #20486]: #4405
+#8999 := (not #8998)
+#19799 := (or #4410 #8999 #19073 #19431)
+#19920 := (+ #19081 #6522)
+#19927 := (>= #19920 0::Int)
+#19930 := (or #19073 #8999 #19927)
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+#19919 := (or #8999 #19073 #19431)
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+#19880 := (iff #19884 #19799)
+#19870 := [rewrite]: #19880
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+#19434 := (or #19073 #8999 #19431)
+#18974 := (iff #19434 #19919)
+#19239 := [rewrite]: #18974
+#19435 := (iff #19930 #19434)
+#19425 := (iff #19927 #19431)
+#19931 := (+ #6522 #19081)
+#19923 := (>= #19931 0::Int)
+#19418 := (iff #19923 #19431)
+#19432 := [rewrite]: #19418
+#19426 := (iff #19927 #19923)
+#19932 := (= #19920 #19931)
+#18964 := [rewrite]: #19932
+#19427 := [monotonicity #18964]: #19426
+#19433 := [trans #19427 #19432]: #19425
+#19918 := [monotonicity #19433]: #19435
+#19230 := [trans #19918 #19239]: #19240
+#19886 := [monotonicity #19230]: #19883
+#19885 := [trans #19886 #19870]: #19864
+#19803 := [quant-inst #6386 #14273]: #19881
+#19865 := [mp #19803 #19885]: #19799
+#29720 := [unit-resolution #19865 #20487 #20484]: #29719
+#29721 := [unit-resolution #29720 #29718]: #19431
+#29723 := (not #15911)
+#29725 := (or #19082 #29723 #29724)
+#29726 := [th-lemma arith triangle-eq]: #29725
+#29727 := [unit-resolution #29726 #29716 #29722]: #29723
+#29728 := [th-lemma arith farkas 1 -1 -1 1 #29727 #29721 #19093 #29708]: false
+#29731 := [lemma #29728]: #29730
+#22913 := [unit-resolution #29731 #22914]: #19082
+#22810 := (or #29709 #15911)
+#22910 := [th-lemma arith triangle-eq]: #22810
+#22915 := [unit-resolution #22910 #22913]: #15911
+#14145 := (<= #14144 0::Int)
+#12676 := (or #4384 #14145)
+#14133 := (+ #14126 #2315)
+#14136 := (>= #14133 0::Int)
+#12671 := (or #4384 #14136)
+#12728 := (iff #12671 #12676)
+#12004 := (iff #12676 #12676)
+#12577 := [rewrite]: #12004
+#14148 := (iff #14136 #14145)
+#14137 := (+ #2315 #14126)
+#14140 := (>= #14137 0::Int)
+#14146 := (iff #14140 #14145)
+#14147 := [rewrite]: #14146
+#14141 := (iff #14136 #14140)
+#14138 := (= #14133 #14137)
+#14139 := [rewrite]: #14138
+#14142 := [monotonicity #14139]: #14141
+#14149 := [trans #14142 #14147]: #14148
+#12643 := [monotonicity #14149]: #12728
+#12578 := [trans #12643 #12577]: #12728
+#12755 := [quant-inst #2313]: #12671
+#12429 := [mp #12755 #12578]: #12676
+#22939 := [unit-resolution #12429 #10275]: #14145
+#8607 := (<= #14282 0::Int)
+#22841 := (or #14284 #8607)
+#22842 := [th-lemma arith triangle-eq]: #22841
+#22940 := [unit-resolution #22842 #22805]: #8607
+#22942 := (not #14145)
+#22941 := (not #8607)
+#22993 := (or #13447 #22941 #22942 #29723)
+#22814 := [th-lemma arith assign-bounds -1 -1 -1]: #22993
+#22840 := [unit-resolution #22814 #22940 #22939 #22915]: #13447
+#22995 := (not #10493)
+#22996 := (not #13447)
+#22991 := (or #19311 #22996 #22995)
+#22997 := [th-lemma arith triangle-eq]: #22991
+#23002 := [unit-resolution #22997 #22840 #22815]: #19311
+#19296 := (+ #2314 #19098)
+#19297 := (<= #19296 0::Int)
+#23013 := (not #19297)
+#8707 := (not #14277)
+#10455 := (or #14293 #8707)
+#10458 := [def-axiom]: #10455
+#22992 := [unit-resolution #10458 #22606]: #8707
+#23014 := (or #23013 #14277 #22448 #29724)
+#23005 := [th-lemma arith assign-bounds -1 -1 -1]: #23014
+#23015 := [unit-resolution #23005 #22543 #22992 #29722]: #23013
+#19316 := (not #19311)
+#19319 := (or #19080 #19297 #19316)
+#3962 := (or #4430 #4422)
+#3963 := [def-axiom]: #3962
+#19076 := [unit-resolution #3963 #19059]: #4422
+#13449 := (or #4427 #19080 #19297 #19316)
+#19283 := (+ #2315 #14279)
+#19284 := (+ #19081 #19283)
+#19285 := (= #19284 0::Int)
+#19286 := (not #19285)
+#19287 := (+ #19081 #2315)
+#19288 := (>= #19287 0::Int)
+#19289 := (or #19080 #19288 #19286)
+#13900 := (or #4427 #19289)
+#10536 := (iff #13900 #13449)
+#11723 := (or #4427 #19319)
+#10535 := (iff #11723 #13449)
+#10532 := [rewrite]: #10535
+#10486 := (iff #13900 #11723)
+#19320 := (iff #19289 #19319)
+#19317 := (iff #19286 #19316)
+#19314 := (iff #19285 #19311)
+#19302 := (+ #14279 #19081)
+#19303 := (+ #2315 #19302)
+#19306 := (= #19303 0::Int)
+#19312 := (iff #19306 #19311)
+#19313 := [rewrite]: #19312
+#19307 := (iff #19285 #19306)
+#19304 := (= #19284 #19303)
+#19305 := [rewrite]: #19304
+#19308 := [monotonicity #19305]: #19307
+#19315 := [trans #19308 #19313]: #19314
+#19318 := [monotonicity #19315]: #19317
+#19300 := (iff #19288 #19297)
+#19290 := (+ #2315 #19081)
+#19293 := (>= #19290 0::Int)
+#19298 := (iff #19293 #19297)
+#19299 := [rewrite]: #19298
+#19294 := (iff #19288 #19293)
+#19291 := (= #19287 #19290)
+#19292 := [rewrite]: #19291
+#19295 := [monotonicity #19292]: #19294
+#19301 := [trans #19295 #19299]: #19300
+#19321 := [monotonicity #19301 #19318]: #19320
+#14052 := [monotonicity #19321]: #10486
+#10495 := [trans #14052 #10532]: #10536
+#13899 := [quant-inst #14273]: #13900
+#8714 := [mp #13899 #10495]: #13449
+#23016 := [unit-resolution #8714 #19076]: #19319
+#23001 := [unit-resolution #23016 #23015 #23002]: #19080
+#23008 := [mp #23001 #23007]: #22266
+#22265 := (not #22140)
+#22276 := (or #22265 #22149 #22126)
+#22277 := [def-axiom]: #22276
+#23019 := [unit-resolution #22277 #23008 #22563]: #22149
+#22260 := (not #22127)
+#23009 := (or #22119 #22260)
+#22153 := (or #22119 #22260 #6252)
+#22264 := [def-axiom]: #22153
+#23011 := [unit-resolution #22264 #8690]: #23009
+#23012 := [unit-resolution #23011 #23019]: #22260
+#23074 := (or #22119 #22127)
+#22261 := (or #22119 #22127 #14287)
+#22258 := [def-axiom]: #22261
+#23072 := [unit-resolution #22258 #22912]: #23074
+#23073 := [unit-resolution #23072 #23012 #23019]: false
+#22988 := [lemma #23073]: #22448
+#22954 := (or #22951 #19137)
+#22449 := [hypothesis]: #22448
+#22950 := [hypothesis]: #14212
+#22955 := [th-lemma arith triangle-eq]: #22954
+#22956 := [unit-resolution #22955 #22950 #22449]: false
+#22957 := [lemma #22956]: #22954
+#13336 := [unit-resolution #22957 #22988]: #22951
+#14221 := (or #14212 #14218)
+#12780 := (or #4368 #14212 #14218)
+#14165 := (+ #1420 #14164)
+#14166 := (+ #14126 #14165)
+#14167 := (<= #14166 0::Int)
+#14208 := (or #14169 #14167)
+#14209 := (not #14208)
+#14210 := (= #14126 #2314)
+#14211 := (or #14210 #14209)
+#12763 := (or #4368 #14211)
+#12775 := (iff #12763 #12780)
+#12856 := (or #4368 #14221)
+#12859 := (iff #12856 #12780)
+#12862 := [rewrite]: #12859
+#12857 := (iff #12763 #12856)
+#14222 := (iff #14211 #14221)
+#14219 := (iff #14209 #14218)
+#14216 := (iff #14208 #14215)
+#14183 := (iff #14167 #14180)
+#14171 := (+ #14126 #14164)
+#14172 := (+ #1420 #14171)
+#14175 := (<= #14172 0::Int)
+#14181 := (iff #14175 #14180)
+#14182 := [rewrite]: #14181
+#14176 := (iff #14167 #14175)
+#14173 := (= #14166 #14172)
+#14174 := [rewrite]: #14173
+#14177 := [monotonicity #14174]: #14176
+#14184 := [trans #14177 #14182]: #14183
+#14217 := [monotonicity #14184]: #14216
+#14220 := [monotonicity #14217]: #14219
+#14213 := (iff #14210 #14212)
+#14214 := [rewrite]: #14213
+#14223 := [monotonicity #14214 #14220]: #14222
+#12858 := [monotonicity #14223]: #12857
+#12863 := [trans #12858 #12862]: #12775
+#12727 := [quant-inst #2313]: #12763
+#12864 := [mp #12727 #12863]: #12780
+#13258 := [unit-resolution #12864 #6477]: #14221
+#13294 := [unit-resolution #13258 #13336]: #14218
+#12872 := (or #14215 #12854)
+#12860 := [def-axiom]: #12872
+#13273 := [unit-resolution #12860 #13294]: #12854
+#12835 := (not #14180)
+#12877 := (or #14215 #12835)
+#12891 := [def-axiom]: #12877
+#13272 := [unit-resolution #12891 #13294]: #12835
+#19327 := (or #14180 #14169)
+#14991 := (f5 #6386 ?v0!20)
+#14992 := (f7 #14991)
+#15264 := (f13 f14 #14992)
+#19066 := (= #15264 #14126)
+#16058 := (= #14126 #15264)
+#14993 := (= ?v0!20 #14992)
+#16042 := (or #5129 #14993)
+#16038 := [quant-inst #6386 #2313]: #16042
+#19029 := [unit-resolution #16038 #4162]: #14993
+#19179 := [monotonicity #19029]: #16058
+#19067 := [symm #19179]: #19066
+#19145 := (= #2314 #15264)
+#19178 := (= #6404 #15264)
+#19180 := (= #15264 #6404)
+#16473 := (= #14992 #6386)
+#14038 := (= ?v0!20 #6386)
+#14999 := (f4 #14991)
+#15002 := (<= #14999 0::Int)
+#10978 := (* -1::Int #14999)
+#13192 := (+ #14160 #10978)
+#13179 := (>= #13192 0::Int)
+#13237 := (= #14160 #14999)
+#18958 := (= #14159 #14991)
+#18875 := (= #14991 #14159)
+#18876 := [monotonicity #7565]: #18875
+#18991 := [symm #18876]: #18958
+#18993 := [monotonicity #18991]: #13237
+#18880 := (not #13237)
+#18957 := (or #18880 #13179)
+#18990 := [th-lemma arith triangle-eq]: #18957
+#18998 := [unit-resolution #18990 #18993]: #13179
+#14076 := (+ #2314 #6522)
+#12830 := (<= #14076 0::Int)
+#11078 := (+ #6522 #10978)
+#10444 := (+ #2314 #11078)
+#10561 := (= #10444 0::Int)
+#11796 := (>= #10444 0::Int)
+#14185 := (+ #2315 #14160)
+#14186 := (+ #174 #14185)
+#12778 := (<= #14186 0::Int)
+#14189 := (= #14186 0::Int)
+#18954 := [hypothesis]: #12854
+#18947 := [hypothesis]: #12835
+#14192 := (or #14169 #14180 #14189)
+#12523 := (or #4376 #14169 #14180 #14189)
+#14161 := (+ #14160 #2315)
+#14162 := (+ #174 #14161)
+#14163 := (= #14162 0::Int)
+#14170 := (or #14169 #14167 #14163)
+#12797 := (or #4376 #14170)
+#12776 := (iff #12797 #12523)
+#12760 := (or #4376 #14192)
+#12800 := (iff #12760 #12523)
+#12753 := [rewrite]: #12800
+#12798 := (iff #12797 #12760)
+#14193 := (iff #14170 #14192)
+#14190 := (iff #14163 #14189)
+#14187 := (= #14162 #14186)
+#14188 := [rewrite]: #14187
+#14191 := [monotonicity #14188]: #14190
+#14194 := [monotonicity #14184 #14191]: #14193
+#12759 := [monotonicity #14194]: #12798
+#12756 := [trans #12759 #12753]: #12776
+#12799 := [quant-inst #2313]: #12797
+#12796 := [mp #12799 #12756]: #12523
+#23177 := [unit-resolution #12796 #6291]: #14192
+#18956 := [unit-resolution #23177 #18947 #18954]: #14189
+#22958 := (not #14189)
+#18988 := (or #22958 #12778)
+#18992 := [th-lemma arith triangle-eq]: #18988
+#18997 := [unit-resolution #18992 #18956]: #12778
+#18999 := (not #12778)
+#19032 := (or #18999 #11796)
+#6523 := (>= #6520 0::Int)
+#6589 := (or #4384 #6523)
+#6590 := [quant-inst #6386]: #6589
+#19000 := [unit-resolution #6590 #10275]: #6523
+#19026 := (not #13179)
+#19001 := (not #6523)
+#19024 := (or #18999 #11796 #19001 #10305 #19026)
+#19030 := [th-lemma arith assign-bounds 1 -1 -1 -1]: #19024
+#19027 := [unit-resolution #19030 #10273 #19000 #18998]: #19032
+#19028 := [unit-resolution #19027 #18997]: #11796
+#11809 := (<= #10444 0::Int)
+#8680 := (<= #13192 0::Int)
+#18881 := (or #18880 #8680)
+#18882 := [th-lemma arith triangle-eq]: #18881
+#18981 := [unit-resolution #18882 #18993]: #8680
+#19031 := [unit-resolution #14566 #8735]: #6512
+#12779 := (>= #14186 0::Int)
+#18970 := (or #22958 #12779)
+#18973 := [th-lemma arith triangle-eq]: #18970
+#18961 := [unit-resolution #18973 #18956]: #12779
+#18972 := (not #12779)
+#19094 := (not #8680)
+#19088 := (not #6512)
+#19092 := (not #6727)
+#19095 := (or #11809 #19092 #19088 #19094 #18972)
+#19087 := [th-lemma arith assign-bounds -1 -1 -1 1]: #19095
+#19089 := [unit-resolution #19087 #18961 #19093 #19031 #18981]: #11809
+#18910 := (not #11796)
+#18982 := (not #11809)
+#19068 := (or #10561 #18982 #18910)
+#19058 := [th-lemma arith triangle-eq]: #19068
+#19075 := [unit-resolution #19058 #19089 #19028]: #10561
+#11297 := (not #10561)
+#19074 := (or #11297 #12830)
+#11733 := (or #4427 #8999 #11297 #12830)
+#12945 := (+ #2315 #14999)
+#12890 := (+ #6521 #12945)
+#12946 := (= #12890 0::Int)
+#12947 := (not #12946)
+#12875 := (+ #6521 #2315)
+#12876 := (>= #12875 0::Int)
+#12882 := (or #8999 #12876 #12947)
+#11820 := (or #4427 #12882)
+#11805 := (iff #11820 #11733)
+#11818 := (or #8999 #11297 #12830)
+#11294 := (or #4427 #11818)
+#11785 := (iff #11294 #11733)
+#11800 := [rewrite]: #11785
+#11784 := (iff #11820 #11294)
+#11298 := (iff #12882 #11818)
+#11817 := (or #8999 #12830 #11297)
+#11821 := (iff #11817 #11818)
+#11633 := [rewrite]: #11821
+#11819 := (iff #12882 #11817)
+#12896 := (iff #12947 #11297)
+#11815 := (iff #12946 #10561)
+#12886 := (+ #6521 #14999)
+#12883 := (+ #2315 #12886)
+#10960 := (= #12883 0::Int)
+#12940 := (iff #10960 #10561)
+#11293 := [rewrite]: #12940
+#11240 := (iff #12946 #10960)
+#12884 := (= #12890 #12883)
+#12881 := [rewrite]: #12884
+#11241 := [monotonicity #12881]: #11240
+#11292 := [trans #11241 #11293]: #11815
+#11816 := [monotonicity #11292]: #12896
+#12887 := (iff #12876 #12830)
+#12892 := (+ #2315 #6521)
+#12871 := (>= #12892 0::Int)
+#12831 := (iff #12871 #12830)
+#12895 := [rewrite]: #12831
+#12894 := (iff #12876 #12871)
+#12893 := (= #12875 #12892)
+#12874 := [rewrite]: #12893
+#12879 := [monotonicity #12874]: #12894
+#12885 := [trans #12879 #12895]: #12887
+#11295 := [monotonicity #12885 #11816]: #11819
+#11734 := [trans #11295 #11633]: #11298
+#11797 := [monotonicity #11734]: #11784
+#11806 := [trans #11797 #11800]: #11805
+#11296 := [quant-inst #6386]: #11820
+#11803 := [mp #11296 #11806]: #11733
+#19077 := [unit-resolution #11803 #19076 #20484]: #19074
+#19078 := [unit-resolution #19077 #19075]: #12830
+#19097 := (not #12830)
+#19079 := (or #15002 #19001 #10305 #19026 #18999 #19097)
+#19103 := [th-lemma arith assign-bounds 1 1 1 -1 -1]: #19079
+#18980 := [unit-resolution #19103 #18997 #19000 #19078 #18998 #10273]: #15002
+#15003 := (not #15002)
+#15007 := (or #14038 #15003)
+#16051 := (or #6420 #14038 #15003)
+#14998 := (= #6386 ?v0!20)
+#15004 := (or #14998 #15003)
+#16105 := (or #6420 #15004)
+#16110 := (iff #16105 #16051)
+#16103 := (or #6420 #15007)
+#16107 := (iff #16103 #16051)
+#16108 := [rewrite]: #16107
+#16045 := (iff #16105 #16103)
+#15008 := (iff #15004 #15007)
+#15005 := (iff #14998 #14038)
+#15006 := [rewrite]: #15005
+#15009 := [monotonicity #15006]: #15008
+#16088 := [monotonicity #15009]: #16045
+#16053 := [trans #16088 #16108]: #16110
+#16106 := [quant-inst #6386 #2313]: #16105
+#16050 := [mp #16106 #16053]: #16051
+#19060 := [unit-resolution #16050 #4150]: #15007
+#19096 := [unit-resolution #19060 #18980]: #14038
+#19061 := (= #14992 ?v0!20)
+#19062 := [symm #19029]: #19061
+#19091 := [trans #19062 #19096]: #16473
+#19139 := [monotonicity #19091]: #19180
+#19170 := [symm #19139]: #19178
+#19141 := (= #2314 #6404)
+#19151 := (= #2314 #174)
+#19148 := (= #2314 #5955)
+#15523 := (f24 #14992)
+#19173 := (= #15523 #5955)
+#19063 := (= #14992 f22)
+#19176 := [trans #19091 #7565]: #19063
+#19174 := [monotonicity #19176]: #19173
+#16046 := (= #2314 #15523)
+#19172 := [monotonicity #19029]: #16046
+#19140 := [trans #19172 #19174]: #19148
+#19064 := [trans #19140 #8806]: #19151
+#19142 := [trans #19064 #8735]: #19141
+#19147 := [trans #19142 #19170]: #19145
+#19171 := [trans #19147 #19067]: #14212
+#18959 := (or #22448 #18972 #14180)
+#18984 := [th-lemma arith assign-bounds 1 -1]: #18959
+#18989 := [unit-resolution #18984 #18961 #18947]: #22448
+#18983 := [unit-resolution #22957 #18989]: #22951
+#19279 := [unit-resolution #18983 #19171]: false
+#19225 := [lemma #19279]: #19327
+[unit-resolution #19225 #13272 #13273]: false
 unsat

--- a/src/HOL/Boogie/Examples/Boogie_Max.certs	Tue May 31 19:27:19 2011 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Max.certs	Tue May 31 19:28:03 2011 +0200
@@ -1,2230 +1,2230 @@
-ebdcb1b84dec86e577085400a3a715ba51f95880 2229 0
+7200427fdf70f253d4fd5c12f16bd6805d130a31 2229 0
 #2 := false
-#42 := 0::Int
-decl f15 :: (-> Int Int)
-#46 := (f15 0::Int)
-#735 := -1::Int
-#2176 := (* -1::Int #46)
-decl f14 :: Int
-#45 := f14
-#2172 := (+ f14 #2176)
-#2173 := (>= #2172 0::Int)
-#47 := (= f14 #46)
+#35 := 0::Int
+decl f10 :: (-> Int Int)
+#39 := (f10 0::Int)
+#715 := -1::Int
+#2156 := (* -1::Int #39)
+decl f9 :: Int
+#38 := f9
+#2152 := (+ f9 #2156)
+#2153 := (>= #2152 0::Int)
+#40 := (= f9 #39)
+decl f8 :: Int
+#36 := f8
+#1033 := (<= f8 0::Int)
 decl f13 :: Int
-#43 := f13
-#1053 := (<= f13 0::Int)
+#63 := f13
+#990 := (* -1::Int f13)
+#47 := (:var 0 Int)
+#51 := (f10 #47)
+#991 := (+ #51 #990)
+#992 := (<= #991 0::Int)
+decl f12 :: Int
+#58 := f12
+#785 := (* -1::Int f12)
+#980 := (+ #47 #785)
+#979 := (>= #980 0::Int)
+#981 := (not #979)
+#704 := (>= #47 0::Int)
+#984 := (and #704 #981)
+#987 := (not #984)
+#995 := (or #987 #992)
+#998 := (forall (vars (?v0 Int)) #995)
+#1001 := (not #998)
+#95 := (f10 f12)
+#883 := (* -1::Int #95)
+#884 := (+ f13 #883)
+#882 := (>= #884 0::Int)
+#881 := (not #882)
 decl f18 :: Int
-#70 := f18
-#1010 := (* -1::Int f18)
-#54 := (:var 0 Int)
-#58 := (f15 #54)
-#1011 := (+ #58 #1010)
-#1012 := (<= #1011 0::Int)
+#100 := f18
+#817 := (>= f18 0::Int)
+#42 := 1::Int
+#734 := (>= f12 1::Int)
+#872 := (and #734 #817)
+#875 := (not #872)
+decl f20 :: Int
+#106 := f20
+#829 := (* -1::Int f20)
+#866 := (+ f12 #829)
+#865 := (= #866 -1::Int)
+#869 := (not #865)
+decl f19 :: Int
+#102 := f19
+#840 := (* -1::Int f19)
+#841 := (+ #51 #840)
+#842 := (<= #841 0::Int)
+#830 := (+ #47 #829)
+#828 := (>= #830 0::Int)
+#831 := (not #828)
+#834 := (and #704 #831)
+#837 := (not #834)
+#845 := (or #837 #842)
+#848 := (forall (vars (?v0 Int)) #845)
+#851 := (not #848)
+#117 := (f10 f18)
+#370 := (= f19 #117)
+#857 := (or #370 #851)
+#862 := (and #848 #857)
+#109 := 2::Int
+#820 := (>= f20 2::Int)
+#822 := (and #817 #820)
+#825 := (not #822)
+decl f11 :: Int
+#56 := f11
+#731 := (>= f11 0::Int)
+#736 := (and #731 #734)
+#739 := (not #736)
+#489 := (= f13 f19)
+#495 := (not #489)
+#486 := (= f11 f18)
+#504 := (not #486)
+#945 := (or #504 #495 #739 #825 #862 #869 #875 #881)
+#878 := (not #734)
 decl f17 :: Int
-#65 := f17
-#805 := (* -1::Int f17)
-#1000 := (+ #54 #805)
-#999 := (>= #1000 0::Int)
-#1001 := (not #999)
-#724 := (>= #54 0::Int)
-#1004 := (and #724 #1001)
-#1007 := (not #1004)
-#1015 := (or #1007 #1012)
-#1018 := (forall (vars (?v0 Int)) #1015)
-#1021 := (not #1018)
-#102 := (f15 f17)
-#903 := (* -1::Int #102)
-#904 := (+ f18 #903)
-#902 := (>= #904 0::Int)
-#901 := (not #902)
-decl f23 :: Int
-#107 := f23
-#837 := (>= f23 0::Int)
-#49 := 1::Int
-#754 := (>= f17 1::Int)
-#892 := (and #754 #837)
-#895 := (not #892)
-decl f25 :: Int
-#113 := f25
-#849 := (* -1::Int f25)
-#886 := (+ f17 #849)
-#885 := (= #886 -1::Int)
-#889 := (not #885)
-decl f24 :: Int
-#109 := f24
-#860 := (* -1::Int f24)
-#861 := (+ #58 #860)
-#862 := (<= #861 0::Int)
-#850 := (+ #54 #849)
-#848 := (>= #850 0::Int)
-#851 := (not #848)
-#854 := (and #724 #851)
-#857 := (not #854)
-#865 := (or #857 #862)
-#868 := (forall (vars (?v0 Int)) #865)
-#871 := (not #868)
-#124 := (f15 f23)
-#390 := (= f24 #124)
-#877 := (or #390 #871)
-#882 := (and #868 #877)
-#116 := 2::Int
-#840 := (>= f25 2::Int)
-#842 := (and #837 #840)
-#845 := (not #842)
+#97 := f17
+#351 := (= f17 f19)
+#429 := (not #351)
+#348 := (= f12 f18)
+#438 := (not #348)
+#343 := (= #95 f17)
+#456 := (not #343)
+#921 := (or #456 #438 #429 #878 #739 #825 #862 #869 #875 #882)
+#950 := (and #921 #945)
+#786 := (+ f8 #785)
+#787 := (<= #786 0::Int)
+#971 := (or #739 #787 #950)
+#790 := (not #787)
+decl f15 :: Int
+#72 := f15
+#768 := (* -1::Int f15)
+#769 := (+ #51 #768)
+#770 := (<= #769 0::Int)
+#742 := (* -1::Int #47)
+#743 := (+ f8 #742)
+#744 := (<= #743 0::Int)
+#745 := (not #744)
+#748 := (and #704 #745)
+#751 := (not #748)
+#773 := (or #751 #770)
+#776 := (forall (vars (?v0 Int)) #773)
+#78 := (= #51 f15)
+#757 := (or #78 #751)
+#762 := (exists (vars (?v0 Int)) #757)
+#765 := (not #762)
+#779 := (or #765 #776)
+#782 := (and #762 #779)
 decl f16 :: Int
-#63 := f16
-#751 := (>= f16 0::Int)
-#756 := (and #751 #754)
-#759 := (not #756)
-#509 := (= f18 f24)
-#515 := (not #509)
-#506 := (= f16 f23)
-#524 := (not #506)
-#965 := (or #524 #515 #759 #845 #882 #889 #895 #901)
-#898 := (not #754)
-decl f22 :: Int
-#104 := f22
-#371 := (= f22 f24)
-#449 := (not #371)
-#368 := (= f17 f23)
-#458 := (not #368)
-#363 := (= #102 f22)
-#476 := (not #363)
-#941 := (or #476 #458 #449 #898 #759 #845 #882 #889 #895 #902)
-#970 := (and #941 #965)
-#806 := (+ f13 #805)
-#807 := (<= #806 0::Int)
-#991 := (or #759 #807 #970)
-#810 := (not #807)
-decl f20 :: Int
-#79 := f20
-#788 := (* -1::Int f20)
-#789 := (+ #58 #788)
-#790 := (<= #789 0::Int)
-#762 := (* -1::Int #54)
-#763 := (+ f13 #762)
-#764 := (<= #763 0::Int)
-#765 := (not #764)
-#768 := (and #724 #765)
-#771 := (not #768)
-#793 := (or #771 #790)
-#796 := (forall (vars (?v0 Int)) #793)
-#85 := (= #58 f20)
-#777 := (or #85 #771)
-#782 := (exists (vars (?v0 Int)) #777)
-#785 := (not #782)
-#799 := (or #785 #796)
-#802 := (and #782 #799)
-decl f21 :: Int
-#81 := f21
-#268 := (= f17 f21)
-#306 := (not #268)
-#265 := (= f18 f20)
-#315 := (not #265)
-decl f19 :: Int
-#77 := f19
-#262 := (= f16 f19)
-#324 := (not #262)
-#831 := (or #324 #315 #306 #759 #802 #810)
-#996 := (and #831 #991)
-#74 := (f15 f16)
-#259 := (= f18 #74)
-#611 := (not #259)
-#644 := (not #47)
-#1039 := (or #644 #611 #759 #996 #1021)
-#1044 := (and #47 #1039)
-#738 := (* -1::Int #58)
-#739 := (+ f14 #738)
-#737 := (>= #739 0::Int)
-#727 := (>= #54 1::Int)
-#725 := (not #727)
-#729 := (and #724 #725)
-#732 := (not #729)
-#741 := (or #732 #737)
-#744 := (forall (vars (?v0 Int)) #741)
-#747 := (not #744)
-#1047 := (or #747 #1044)
-#1050 := (and #744 #1047)
-#1073 := (or #644 #1050 #1053)
-#1078 := (not #1073)
+#74 := f16
+#248 := (= f12 f16)
+#286 := (not #248)
+#245 := (= f13 f15)
+#295 := (not #245)
+decl f14 :: Int
+#70 := f14
+#242 := (= f11 f14)
+#304 := (not #242)
+#811 := (or #304 #295 #286 #739 #782 #790)
+#976 := (and #811 #971)
+#67 := (f10 f11)
+#239 := (= f13 #67)
+#591 := (not #239)
+#624 := (not #40)
+#1019 := (or #624 #591 #739 #976 #1001)
+#1024 := (and #40 #1019)
+#718 := (* -1::Int #51)
+#719 := (+ f9 #718)
+#717 := (>= #719 0::Int)
+#707 := (>= #47 1::Int)
+#705 := (not #707)
+#709 := (and #704 #705)
+#712 := (not #709)
+#721 := (or #712 #717)
+#724 := (forall (vars (?v0 Int)) #721)
+#727 := (not #724)
+#1027 := (or #727 #1024)
+#1030 := (and #724 #1027)
+#1053 := (or #624 #1030 #1033)
+#1058 := (not #1053)
 #1 := true
-#125 := (= #124 f24)
-#126 := (and #125 true)
-#121 := (<= #58 f24)
-#119 := (< #54 f25)
-#55 := (<= 0::Int #54)
-#120 := (and #55 #119)
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 #132 := (implies true #131)
-#142 := (= f24 f18)
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-#110 := (= f24 f22)
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-#108 := (= f23 f17)
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-#135 := (implies #106 #134)
-#105 := (= f22 #102)
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-#91 := (and #90 true)
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-#93 := (and #87 #92)
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-#80 := (= f20 f18)
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-#247 := (forall (vars (?v0 Int)) #244)
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-#686 := (or #685 #677)
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-#1070 := (or #1053 #1067)
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-#1068 := (iff #677 #1067)
-#1065 := (iff #669 #1064)
-#1051 := (iff #662 #1050)
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+#71 := (= f14 f11)
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+#156 := (and #54 #155)
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 #1048 := (iff #657 #1047)
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+#839 := [monotonicity #836]: #838
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+#850 := [quant-intro #847]: #849
+#853 := [monotonicity #850]: #852
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+#761 := [trans #756 #759]: #760
+#764 := [quant-intro #761]: #763
+#767 := [monotonicity #764]: #766
+#781 := [monotonicity #767 #778]: #780
+#784 := [monotonicity #764 #781]: #783
+#795 := [monotonicity #784]: #794
+#798 := [monotonicity #795]: #797
+#801 := [monotonicity #798]: #800
+#804 := [monotonicity #741 #801]: #803
+#791 := (iff #322 #790)
+#788 := (iff #69 #787)
+#789 := [rewrite]: #788
+#792 := [monotonicity #789]: #791
+#807 := [monotonicity #792 #804]: #806
+#810 := [monotonicity #741 #807]: #809
+#815 := [trans #810 #813]: #814
+#978 := [monotonicity #815 #975]: #977
+#1006 := [monotonicity #741 #978]: #1005
+#1009 := [monotonicity #1006]: #1008
+#1002 := (iff #600 #1001)
+#999 := (iff #236 #998)
+#996 := (iff #233 #995)
+#993 := (iff #64 #992)
+#994 := [rewrite]: #993
+#988 := (iff #232 #987)
+#985 := (iff #62 #984)
+#982 := (iff #61 #981)
+#983 := [rewrite]: #982
+#986 := [monotonicity #703 #983]: #985
+#989 := [monotonicity #986]: #988
+#997 := [monotonicity #989 #994]: #996
+#1000 := [quant-intro #997]: #999
+#1003 := [monotonicity #1000]: #1002
+#1012 := [monotonicity #1003 #1009]: #1011
+#1015 := [monotonicity #741 #1012]: #1014
+#1018 := [monotonicity #1015]: #1017
+#1023 := [trans #1018 #1021]: #1022
+#1026 := [monotonicity #1023]: #1025
+#728 := (iff #636 #727)
+#725 := (iff #227 #724)
+#722 := (iff #224 #721)
+#716 := (iff #52 #717)
+#720 := [rewrite]: #716
+#713 := (iff #223 #712)
+#710 := (iff #50 #709)
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+#711 := [monotonicity #703 #708]: #710
+#714 := [monotonicity #711]: #713
+#723 := [monotonicity #714 #720]: #722
+#726 := [quant-intro #723]: #725
+#729 := [monotonicity #726]: #728
+#1029 := [monotonicity #729 #1026]: #1028
+#1032 := [monotonicity #726 #1029]: #1031
+#700 := (iff #648 false)
+#695 := (not true)
+#698 := (iff #695 false)
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+#696 := (iff #648 #695)
+#693 := (iff #220 true)
+#685 := (and true true)
+#688 := (and true #685)
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+#683 := (iff #43 true)
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+#681 := (iff #41 true)
+#682 := [rewrite]: #681
+#687 := [monotonicity #682 #684]: #686
+#690 := [monotonicity #682 #687]: #689
+#694 := [trans #690 #692]: #693
+#697 := [monotonicity #694]: #696
+#701 := [trans #697 #699]: #700
+#1046 := [monotonicity #701 #1032]: #1045
+#1049 := [monotonicity #1046]: #1048
+#1042 := (iff #665 #1033)
+#1034 := (not #1033)
+#1037 := (not #1034)
+#1040 := (iff #1037 #1033)
 #1041 := [rewrite]: #1040
-#1037 := (iff #645 #1036)
-#1034 := (iff #629 #1033)
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-#985 := (or #807 #982)
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-#992 := (iff #988 #991)
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-#971 := (iff #562 #970)
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-#914 := (or #845 #882)
-#917 := (or #889 #914)
-#920 := (or #895 #917)
-#950 := (or #920 #515)
-#953 := (or #524 #950)
-#956 := (or #759 #953)
-#959 := (or #901 #956)
-#962 := (or #759 #959)
-#966 := (iff #962 #965)
-#967 := [rewrite]: #966
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-#883 := (iff #409 #882)
-#880 := (iff #404 #877)
-#874 := (or #871 #390)
-#878 := (iff #874 #877)
-#879 := [rewrite]: #878
-#875 := (iff #404 #874)
-#872 := (iff #403 #871)
-#869 := (iff #387 #868)
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-#863 := (iff #121 #862)
-#864 := [rewrite]: #863
-#858 := (iff #383 #857)
-#855 := (iff #120 #854)
-#852 := (iff #119 #851)
-#853 := [rewrite]: #852
-#722 := (iff #55 #724)
-#723 := [rewrite]: #722
-#856 := [monotonicity #723 #853]: #855
-#859 := [monotonicity #856]: #858
-#867 := [monotonicity #859 #864]: #866
-#870 := [quant-intro #867]: #869
-#873 := [monotonicity #870]: #872
-#876 := [monotonicity #873]: #875
-#881 := [trans #876 #879]: #880
-#884 := [monotonicity #870 #881]: #883
-#846 := (iff #415 #845)
-#843 := (iff #118 #842)
-#839 := (iff #117 #840)
-#841 := [rewrite]: #839
-#836 := (iff #111 #837)
-#838 := [rewrite]: #836
-#844 := [monotonicity #838 #841]: #843
-#847 := [monotonicity #844]: #846
-#916 := [monotonicity #847 #884]: #915
-#890 := (iff #424 #889)
-#887 := (iff #380 #885)
-#888 := [rewrite]: #887
-#891 := [monotonicity #888]: #890
-#919 := [monotonicity #891 #916]: #918
-#896 := (iff #433 #895)
-#893 := (iff #374 #892)
-#753 := (iff #66 #754)
-#755 := [rewrite]: #753
-#894 := [monotonicity #755 #838]: #893
-#897 := [monotonicity #894]: #896
-#922 := [monotonicity #897 #919]: #921
-#952 := [monotonicity #922]: #951
-#955 := [monotonicity #952]: #954
-#760 := (iff #333 #759)
-#757 := (iff #67 #756)
-#750 := (iff #64 #751)
-#752 := [rewrite]: #750
-#758 := [monotonicity #752 #755]: #757
-#761 := [monotonicity #758]: #760
-#958 := [monotonicity #761 #955]: #957
-#948 := (iff #541 #901)
-#946 := (iff #140 #902)
-#947 := [rewrite]: #946
-#949 := [monotonicity #947]: #948
-#961 := [monotonicity #949 #958]: #960
-#964 := [monotonicity #761 #961]: #963
-#969 := [trans #964 #967]: #968
-#944 := (iff #494 #941)
-#923 := (or #449 #920)
-#926 := (or #458 #923)
-#929 := (or #898 #926)
-#932 := (or #476 #929)
-#935 := (or #902 #932)
-#938 := (or #759 #935)
-#942 := (iff #938 #941)
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-#939 := (iff #494 #938)
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-#927 := (iff #459 #926)
-#924 := (iff #450 #923)
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-#928 := [monotonicity #925]: #927
-#899 := (iff #467 #898)
-#900 := [monotonicity #755]: #899
-#931 := [monotonicity #900 #928]: #930
-#934 := [monotonicity #931]: #933
-#912 := (iff #485 #902)
-#907 := (not #901)
-#910 := (iff #907 #902)
-#911 := [rewrite]: #910
-#908 := (iff #485 #907)
-#905 := (iff #103 #901)
-#906 := [rewrite]: #905
-#909 := [monotonicity #906]: #908
-#913 := [trans #909 #911]: #912
-#937 := [monotonicity #913 #934]: #936
-#940 := [monotonicity #761 #937]: #939
-#945 := [trans #940 #943]: #944
-#972 := [monotonicity #945 #969]: #971
-#984 := [monotonicity #761 #972]: #983
-#980 := (iff #576 #807)
-#975 := (not #810)
-#978 := (iff #975 #807)
-#979 := [rewrite]: #978
-#976 := (iff #576 #975)
-#973 := (iff #101 #810)
-#974 := [rewrite]: #973
-#977 := [monotonicity #974]: #976
-#981 := [trans #977 #979]: #980
-#987 := [monotonicity #981 #984]: #986
-#990 := [monotonicity #761 #987]: #989
-#995 := [trans #990 #993]: #994
-#834 := (iff #351 #831)
-#813 := (or #306 #802)
-#816 := (or #315 #813)
-#819 := (or #324 #816)
-#822 := (or #759 #819)
-#825 := (or #810 #822)
-#828 := (or #759 #825)
-#832 := (iff #828 #831)
-#833 := [rewrite]: #832
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-#817 := (iff #316 #816)
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-#794 := (iff #278 #793)
-#791 := (iff #88 #790)
-#792 := [rewrite]: #791
-#772 := (iff #271 #771)
-#769 := (iff #84 #768)
-#766 := (iff #83 #765)
-#767 := [rewrite]: #766
-#770 := [monotonicity #723 #767]: #769
-#773 := [monotonicity #770]: #772
-#795 := [monotonicity #773 #792]: #794
-#798 := [quant-intro #795]: #797
-#786 := (iff #294 #785)
-#783 := (iff #275 #782)
-#780 := (iff #272 #777)
-#774 := (or #771 #85)
-#778 := (iff #774 #777)
-#779 := [rewrite]: #778
-#775 := (iff #272 #774)
-#776 := [monotonicity #773]: #775
-#781 := [trans #776 #779]: #780
-#784 := [quant-intro #781]: #783
-#787 := [monotonicity #784]: #786
-#801 := [monotonicity #787 #798]: #800
-#804 := [monotonicity #784 #801]: #803
-#815 := [monotonicity #804]: #814
-#818 := [monotonicity #815]: #817
-#821 := [monotonicity #818]: #820
-#824 := [monotonicity #761 #821]: #823
-#811 := (iff #342 #810)
-#808 := (iff #76 #807)
-#809 := [rewrite]: #808
-#812 := [monotonicity #809]: #811
-#827 := [monotonicity #812 #824]: #826
-#830 := [monotonicity #761 #827]: #829
-#835 := [trans #830 #833]: #834
-#998 := [monotonicity #835 #995]: #997
-#1026 := [monotonicity #761 #998]: #1025
-#1029 := [monotonicity #1026]: #1028
-#1022 := (iff #620 #1021)
-#1019 := (iff #256 #1018)
-#1016 := (iff #253 #1015)
-#1013 := (iff #71 #1012)
-#1014 := [rewrite]: #1013
-#1008 := (iff #252 #1007)
-#1005 := (iff #69 #1004)
-#1002 := (iff #68 #1001)
-#1003 := [rewrite]: #1002
-#1006 := [monotonicity #723 #1003]: #1005
-#1009 := [monotonicity #1006]: #1008
-#1017 := [monotonicity #1009 #1014]: #1016
-#1020 := [quant-intro #1017]: #1019
-#1023 := [monotonicity #1020]: #1022
-#1032 := [monotonicity #1023 #1029]: #1031
-#1035 := [monotonicity #761 #1032]: #1034
-#1038 := [monotonicity #1035]: #1037
-#1043 := [trans #1038 #1041]: #1042
-#1046 := [monotonicity #1043]: #1045
-#748 := (iff #656 #747)
-#745 := (iff #247 #744)
-#742 := (iff #244 #741)
-#736 := (iff #59 #737)
-#740 := [rewrite]: #736
-#733 := (iff #243 #732)
-#730 := (iff #57 #729)
-#726 := (iff #56 #725)
-#728 := [rewrite]: #726
-#731 := [monotonicity #723 #728]: #730
-#734 := [monotonicity #731]: #733
-#743 := [monotonicity #734 #740]: #742
-#746 := [quant-intro #743]: #745
-#749 := [monotonicity #746]: #748
-#1049 := [monotonicity #749 #1046]: #1048
-#1052 := [monotonicity #746 #1049]: #1051
-#720 := (iff #668 false)
-#715 := (not true)
-#718 := (iff #715 false)
-#719 := [rewrite]: #718
-#716 := (iff #668 #715)
-#713 := (iff #240 true)
-#705 := (and true true)
-#708 := (and true #705)
-#711 := (iff #708 true)
-#712 := [rewrite]: #711
-#709 := (iff #240 #708)
-#706 := (iff #237 #705)
-#703 := (iff #50 true)
-#704 := [rewrite]: #703
-#701 := (iff #48 true)
-#702 := [rewrite]: #701
-#707 := [monotonicity #702 #704]: #706
-#710 := [monotonicity #702 #707]: #709
-#714 := [trans #710 #712]: #713
-#717 := [monotonicity #714]: #716
-#721 := [trans #717 #719]: #720
-#1066 := [monotonicity #721 #1052]: #1065
-#1069 := [monotonicity #1066]: #1068
-#1062 := (iff #685 #1053)
-#1054 := (not #1053)
-#1057 := (not #1054)
-#1060 := (iff #1057 #1053)
-#1061 := [rewrite]: #1060
-#1058 := (iff #685 #1057)
-#1055 := (iff #44 #1054)
-#1056 := [rewrite]: #1055
-#1059 := [monotonicity #1056]: #1058
-#1063 := [trans #1059 #1061]: #1062
-#1072 := [monotonicity #1063 #1069]: #1071
-#1077 := [trans #1072 #1075]: #1076
-#1080 := [monotonicity #1077]: #1079
-#699 := (iff #168 #698)
-#696 := (iff #167 #686)
-#691 := (implies true #686)
-#694 := (iff #691 #686)
-#695 := [rewrite]: #694
-#692 := (iff #167 #691)
-#689 := (iff #166 #686)
-#682 := (implies #44 #677)
-#687 := (iff #682 #686)
-#688 := [rewrite]: #687
-#683 := (iff #166 #682)
-#680 := (iff #165 #677)
-#674 := (implies #47 #669)
-#678 := (iff #674 #677)
-#679 := [rewrite]: #678
-#675 := (iff #165 #674)
-#672 := (iff #164 #669)
-#665 := (implies #240 #662)
-#670 := (iff #665 #669)
-#671 := [rewrite]: #670
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-#663 := (iff #163 #662)
-#660 := (iff #162 #657)
-#653 := (implies #247 #650)
-#658 := (iff #653 #657)
+#1038 := (iff #665 #1037)
+#1035 := (iff #37 #1034)
+#1036 := [rewrite]: #1035
+#1039 := [monotonicity #1036]: #1038
+#1043 := [trans #1039 #1041]: #1042
+#1052 := [monotonicity #1043 #1049]: #1051
+#1057 := [trans #1052 #1055]: #1056
+#1060 := [monotonicity #1057]: #1059
+#679 := (iff #161 #678)
+#676 := (iff #160 #666)
+#671 := (implies true #666)
+#674 := (iff #671 #666)
+#675 := [rewrite]: #674
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+#660 := (iff #158 #657)
+#654 := (implies #40 #649)
+#658 := (iff #654 #657)
 #659 := [rewrite]: #658
-#654 := (iff #162 #653)
-#651 := (iff #161 #650)
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-#638 := [rewrite]: #637
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-#631 := [rewrite]: #630
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+#634 := (iff #155 #633)
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+#610 := (iff #606 #609)
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+#607 := (iff #151 #606)
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+#597 := (implies #236 #592)
+#602 := (iff #597 #601)
+#603 := [rewrite]: #602
+#598 := (iff #150 #597)
+#595 := (iff #149 #592)
+#588 := (implies #239 #583)
+#593 := (iff #588 #592)
 #594 := [rewrite]: #593
-#591 := (iff #153 #590)
-#588 := (iff #152 #585)
-#582 := (implies #67 #577)
-#586 := (iff #582 #585)
-#587 := [rewrite]: #586
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-#573 := (implies #101 #568)
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-#579 := [rewrite]: #578
-#574 := (iff #151 #573)
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-#565 := (implies #67 #562)
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-#560 := (iff #148 #550)
-#555 := (implies true #550)
-#558 := (iff #555 #550)
+#589 := (iff #149 #588)
+#586 := (iff #148 #583)
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+#575 := (iff #146 #565)
+#570 := (implies true #565)
+#573 := (iff #570 #565)
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+#571 := (iff #146 #570)
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+#566 := (iff #562 #565)
+#567 := [rewrite]: #566
+#563 := (iff #145 #562)
+#560 := (iff #144 #557)
+#553 := (implies #94 #548)
+#558 := (iff #553 #557)
 #559 := [rewrite]: #558
-#556 := (iff #148 #555)
-#553 := (iff #147 #550)
-#547 := (implies #67 #542)
-#551 := (iff #547 #550)
-#552 := [rewrite]: #551
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-#545 := (iff #146 #542)
-#538 := (implies #140 #533)
-#543 := (iff #538 #542)
-#544 := [rewrite]: #543
-#539 := (iff #146 #538)
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-#530 := (implies #67 #525)
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-#535 := [rewrite]: #534
-#531 := (iff #145 #530)
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-#521 := (implies #506 #516)
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-#527 := [rewrite]: #526
-#522 := (iff #144 #521)
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-#512 := (implies #509 #434)
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-#436 := [rewrite]: #435
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-#421 := (implies #380 #416)
-#426 := (iff #421 #425)
-#427 := [rewrite]: #426
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-#419 := (iff #129 #416)
-#412 := (implies #118 #409)
-#417 := (iff #412 #416)
-#418 := [rewrite]: #417
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-#410 := (iff #128 #409)
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-#400 := (implies #387 #390)
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-#406 := [rewrite]: #405
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-#398 := (iff #126 #390)
-#393 := (and #390 true)
-#396 := (iff #393 #390)
-#397 := [rewrite]: #396
-#394 := (iff #126 #393)
-#391 := (iff #125 #390)
-#392 := [rewrite]: #391
-#395 := [monotonicity #392]: #394
-#399 := [trans #395 #397]: #398
-#388 := (iff #123 #387)
-#385 := (iff #122 #384)
+#554 := (iff #144 #553)
+#551 := (iff #143 #548)
+#545 := (implies #60 #542)
+#549 := (iff #545 #548)
+#550 := [rewrite]: #549
+#546 := (iff #143 #545)
+#543 := (iff #142 #542)
+#540 := (iff #141 #530)
+#535 := (implies true #530)
+#538 := (iff #535 #530)
+#539 := [rewrite]: #538
+#536 := (iff #141 #535)
+#533 := (iff #140 #530)
+#527 := (implies #60 #522)
+#531 := (iff #527 #530)
+#532 := [rewrite]: #531
+#528 := (iff #140 #527)
+#525 := (iff #139 #522)
+#518 := (implies #133 #513)
+#523 := (iff #518 #522)
+#524 := [rewrite]: #523
+#519 := (iff #139 #518)
+#516 := (iff #138 #513)
+#510 := (implies #60 #505)
+#514 := (iff #510 #513)
+#515 := [rewrite]: #514
+#511 := (iff #138 #510)
+#508 := (iff #137 #505)
+#501 := (implies #486 #496)
+#506 := (iff #501 #505)
+#507 := [rewrite]: #506
+#502 := (iff #137 #501)
+#499 := (iff #136 #496)
+#492 := (implies #489 #414)
+#497 := (iff #492 #496)
+#498 := [rewrite]: #497
+#493 := (iff #136 #492)
+#424 := (iff #125 #414)
+#419 := (implies true #414)
+#422 := (iff #419 #414)
+#423 := [rewrite]: #422
+#420 := (iff #125 #419)
+#417 := (iff #124 #414)
+#410 := (implies #354 #405)
+#415 := (iff #410 #414)
+#416 := [rewrite]: #415
+#411 := (iff #124 #410)
+#408 := (iff #123 #405)
+#401 := (implies #360 #396)
+#406 := (iff #401 #405)
+#407 := [rewrite]: #406
+#402 := (iff #123 #401)
+#399 := (iff #122 #396)
+#392 := (implies #111 #389)
+#397 := (iff #392 #396)
+#398 := [rewrite]: #397
+#393 := (iff #122 #392)
+#390 := (iff #121 #389)
+#387 := (iff #120 #384)
+#380 := (implies #367 #370)
+#385 := (iff #380 #384)
 #386 := [rewrite]: #385
-#389 := [quant-intro #386]: #388
-#402 := [monotonicity #389 #399]: #401
-#408 := [trans #402 #406]: #407
-#411 := [monotonicity #389 #408]: #410
-#414 := [monotonicity #411]: #413
-#420 := [trans #414 #418]: #419
-#381 := (iff #115 #380)
-#378 := (= #114 #377)
-#379 := [rewrite]: #378
-#382 := [monotonicity #379]: #381
-#423 := [monotonicity #382 #420]: #422
-#429 := [trans #423 #427]: #428
-#375 := (iff #112 #374)
-#376 := [rewrite]: #375
-#432 := [monotonicity #376 #429]: #431
-#438 := [trans #432 #436]: #437
-#441 := [monotonicity #438]: #440
-#445 := [trans #441 #443]: #444
-#510 := (iff #142 #509)
-#511 := [rewrite]: #510
-#514 := [monotonicity #511 #445]: #513
-#520 := [trans #514 #518]: #519
-#507 := (iff #141 #506)
-#508 := [rewrite]: #507
-#523 := [monotonicity #508 #520]: #522
-#529 := [trans #523 #527]: #528
-#532 := [monotonicity #529]: #531
-#537 := [trans #532 #535]: #536
-#540 := [monotonicity #537]: #539
-#546 := [trans #540 #544]: #545
-#549 := [monotonicity #546]: #548
-#554 := [trans #549 #552]: #553
-#557 := [monotonicity #554]: #556
-#561 := [trans #557 #559]: #560
-#504 := (iff #139 #494)
-#499 := (implies true #494)
-#502 := (iff #499 #494)
-#503 := [rewrite]: #502
-#500 := (iff #139 #499)
-#497 := (iff #138 #494)
-#491 := (implies #67 #486)
-#495 := (iff #491 #494)
-#496 := [rewrite]: #495
-#492 := (iff #138 #491)
-#489 := (iff #137 #486)
-#482 := (implies #103 #477)
-#487 := (iff #482 #486)
+#381 := (iff #120 #380)
+#378 := (iff #119 #370)
+#373 := (and #370 true)
+#376 := (iff #373 #370)
+#377 := [rewrite]: #376
+#374 := (iff #119 #373)
+#371 := (iff #118 #370)
+#372 := [rewrite]: #371
+#375 := [monotonicity #372]: #374
+#379 := [trans #375 #377]: #378
+#368 := (iff #116 #367)
+#365 := (iff #115 #364)
+#366 := [rewrite]: #365
+#369 := [quant-intro #366]: #368
+#382 := [monotonicity #369 #379]: #381
+#388 := [trans #382 #386]: #387
+#391 := [monotonicity #369 #388]: #390
+#394 := [monotonicity #391]: #393
+#400 := [trans #394 #398]: #399
+#361 := (iff #108 #360)
+#358 := (= #107 #357)
+#359 := [rewrite]: #358
+#362 := [monotonicity #359]: #361
+#403 := [monotonicity #362 #400]: #402
+#409 := [trans #403 #407]: #408
+#355 := (iff #105 #354)
+#356 := [rewrite]: #355
+#412 := [monotonicity #356 #409]: #411
+#418 := [trans #412 #416]: #417
+#421 := [monotonicity #418]: #420
+#425 := [trans #421 #423]: #424
+#490 := (iff #135 #489)
+#491 := [rewrite]: #490
+#494 := [monotonicity #491 #425]: #493
+#500 := [trans #494 #498]: #499
+#487 := (iff #134 #486)
 #488 := [rewrite]: #487
-#483 := (iff #137 #482)
-#480 := (iff #136 #477)
-#473 := (implies #363 #468)
-#478 := (iff #473 #477)
-#479 := [rewrite]: #478
-#474 := (iff #136 #473)
-#471 := (iff #135 #468)
-#464 := (implies #66 #459)
-#469 := (iff #464 #468)
-#470 := [rewrite]: #469
-#465 := (iff #135 #464)
-#462 := (iff #134 #459)
-#455 := (implies #368 #450)
-#460 := (iff #455 #459)
-#461 := [rewrite]: #460
-#456 := (iff #134 #455)
-#453 := (iff #133 #450)
-#446 := (implies #371 #434)
-#451 := (iff #446 #450)
-#452 := [rewrite]: #451
-#447 := (iff #133 #446)
-#372 := (iff #110 #371)
-#373 := [rewrite]: #372
-#448 := [monotonicity #373 #445]: #447
-#454 := [trans #448 #452]: #453
-#369 := (iff #108 #368)
-#370 := [rewrite]: #369
-#457 := [monotonicity #370 #454]: #456
-#463 := [trans #457 #461]: #462
-#366 := (iff #106 #66)
-#367 := [rewrite]: #366
-#466 := [monotonicity #367 #463]: #465
-#472 := [trans #466 #470]: #471
-#364 := (iff #105 #363)
-#365 := [rewrite]: #364
-#475 := [monotonicity #365 #472]: #474
-#481 := [trans #475 #479]: #480
-#484 := [monotonicity #481]: #483
-#490 := [trans #484 #488]: #489
-#493 := [monotonicity #490]: #492
-#498 := [trans #493 #496]: #497
-#501 := [monotonicity #498]: #500
-#505 := [trans #501 #503]: #504
-#564 := [monotonicity #505 #561]: #563
-#567 := [monotonicity #564]: #566
-#572 := [trans #567 #570]: #571
-#575 := [monotonicity #572]: #574
-#581 := [trans #575 #579]: #580
-#584 := [monotonicity #581]: #583
-#589 := [trans #584 #587]: #588
-#592 := [monotonicity #589]: #591
-#596 := [trans #592 #594]: #595
-#361 := (iff #100 #351)
-#356 := (implies true #351)
-#359 := (iff #356 #351)
-#360 := [rewrite]: #359
-#357 := (iff #100 #356)
-#354 := (iff #99 #351)
-#348 := (implies #67 #343)
-#352 := (iff #348 #351)
+#503 := [monotonicity #488 #500]: #502
+#509 := [trans #503 #507]: #508
+#512 := [monotonicity #509]: #511
+#517 := [trans #512 #515]: #516
+#520 := [monotonicity #517]: #519
+#526 := [trans #520 #524]: #525
+#529 := [monotonicity #526]: #528
+#534 := [trans #529 #532]: #533
+#537 := [monotonicity #534]: #536
+#541 := [trans #537 #539]: #540
+#484 := (iff #132 #474)
+#479 := (implies true #474)
+#482 := (iff #479 #474)
+#483 := [rewrite]: #482
+#480 := (iff #132 #479)
+#477 := (iff #131 #474)
+#471 := (implies #60 #466)
+#475 := (iff #471 #474)
+#476 := [rewrite]: #475
+#472 := (iff #131 #471)
+#469 := (iff #130 #466)
+#462 := (implies #96 #457)
+#467 := (iff #462 #466)
+#468 := [rewrite]: #467
+#463 := (iff #130 #462)
+#460 := (iff #129 #457)
+#453 := (implies #343 #448)
+#458 := (iff #453 #457)
+#459 := [rewrite]: #458
+#454 := (iff #129 #453)
+#451 := (iff #128 #448)
+#444 := (implies #59 #439)
+#449 := (iff #444 #448)
+#450 := [rewrite]: #449
+#445 := (iff #128 #444)
+#442 := (iff #127 #439)
+#435 := (implies #348 #430)
+#440 := (iff #435 #439)
+#441 := [rewrite]: #440
+#436 := (iff #127 #435)
+#433 := (iff #126 #430)
+#426 := (implies #351 #414)
+#431 := (iff #426 #430)
+#432 := [rewrite]: #431
+#427 := (iff #126 #426)
+#352 := (iff #103 #351)
 #353 := [rewrite]: #352
-#349 := (iff #99 #348)
-#346 := (iff #98 #343)
-#339 := (implies #76 #334)
-#344 := (iff #339 #343)
+#428 := [monotonicity #353 #425]: #427
+#434 := [trans #428 #432]: #433
+#349 := (iff #101 #348)
+#350 := [rewrite]: #349
+#437 := [monotonicity #350 #434]: #436
+#443 := [trans #437 #441]: #442
+#346 := (iff #99 #59)
+#347 := [rewrite]: #346
+#446 := [monotonicity #347 #443]: #445
+#452 := [trans #446 #450]: #451
+#344 := (iff #98 #343)
 #345 := [rewrite]: #344
-#340 := (iff #98 #339)
-#337 := (iff #97 #334)
-#330 := (implies #67 #325)
-#335 := (iff #330 #334)
-#336 := [rewrite]: #335
-#331 := (iff #97 #330)
-#328 := (iff #96 #325)
-#321 := (implies #262 #316)
-#326 := (iff #321 #325)
-#327 := [rewrite]: #326
-#322 := (iff #96 #321)
-#319 := (iff #95 #316)
-#312 := (implies #265 #307)
-#317 := (iff #312 #316)
-#318 := [rewrite]: #317
-#313 := (iff #95 #312)
-#310 := (iff #94 #307)
-#303 := (implies #268 #300)
-#308 := (iff #303 #307)
-#309 := [rewrite]: #308
-#304 := (iff #94 #303)
-#301 := (iff #93 #300)
-#298 := (iff #92 #295)
-#291 := (implies #275 #281)
-#296 := (iff #291 #295)
-#297 := [rewrite]: #296
-#292 := (iff #92 #291)
-#289 := (iff #91 #281)
-#284 := (and #281 true)
-#287 := (iff #284 #281)
-#288 := [rewrite]: #287
-#285 := (iff #91 #284)
-#282 := (iff #90 #281)
-#279 := (iff #89 #278)
-#280 := [rewrite]: #279
-#283 := [quant-intro #280]: #282
-#286 := [monotonicity #283]: #285
-#290 := [trans #286 #288]: #289
-#276 := (iff #87 #275)
-#273 := (iff #86 #272)
-#274 := [rewrite]: #273
-#277 := [quant-intro #274]: #276
-#293 := [monotonicity #277 #290]: #292
-#299 := [trans #293 #297]: #298
-#302 := [monotonicity #277 #299]: #301
-#269 := (iff #82 #268)
-#270 := [rewrite]: #269
-#305 := [monotonicity #270 #302]: #304
-#311 := [trans #305 #309]: #310
-#266 := (iff #80 #265)
-#267 := [rewrite]: #266
-#314 := [monotonicity #267 #311]: #313
-#320 := [trans #314 #318]: #319
-#263 := (iff #78 #262)
-#264 := [rewrite]: #263
-#323 := [monotonicity #264 #320]: #322
-#329 := [trans #323 #327]: #328
-#332 := [monotonicity #329]: #331
-#338 := [trans #332 #336]: #337
-#341 := [monotonicity #338]: #340
-#347 := [trans #341 #345]: #346
-#350 := [monotonicity #347]: #349
-#355 := [trans #350 #353]: #354
-#358 := [monotonicity #355]: #357
-#362 := [trans #358 #360]: #361
-#599 := [monotonicity #362 #596]: #598
-#602 := [monotonicity #599]: #601
-#607 := [trans #602 #605]: #606
-#260 := (iff #75 #259)
-#261 := [rewrite]: #260
-#610 := [monotonicity #261 #607]: #609
-#616 := [trans #610 #614]: #615
-#257 := (iff #73 #256)
-#254 := (iff #72 #253)
-#255 := [rewrite]: #254
-#258 := [quant-intro #255]: #257
-#619 := [monotonicity #258 #616]: #618
-#625 := [trans #619 #623]: #624
-#628 := [monotonicity #625]: #627
-#633 := [trans #628 #631]: #632
-#636 := [monotonicity #633]: #635
-#640 := [trans #636 #638]: #639
-#250 := (iff #62 #47)
-#251 := [rewrite]: #250
-#643 := [monotonicity #251 #640]: #642
-#649 := [trans #643 #647]: #648
-#652 := [monotonicity #251 #649]: #651
-#248 := (iff #61 #247)
-#245 := (iff #60 #244)
-#246 := [rewrite]: #245
-#249 := [quant-intro #246]: #248
-#655 := [monotonicity #249 #652]: #654
-#661 := [trans #655 #659]: #660
-#664 := [monotonicity #249 #661]: #663
-#241 := (iff #53 #240)
-#238 := (iff #52 #237)
-#234 := (iff #51 #50)
-#236 := [rewrite]: #234
-#239 := [monotonicity #236]: #238
-#242 := [monotonicity #239]: #241
-#667 := [monotonicity #242 #664]: #666
-#673 := [trans #667 #671]: #672
-#676 := [monotonicity #673]: #675
-#681 := [trans #676 #679]: #680
-#684 := [monotonicity #681]: #683
-#690 := [trans #684 #688]: #689
-#693 := [monotonicity #690]: #692
-#697 := [trans #693 #695]: #696
-#700 := [monotonicity #697]: #699
-#1082 := [trans #700 #1080]: #1081
-#233 := [asserted]: #168
-#1083 := [mp #233 #1082]: #1078
-#1084 := [not-or-elim #1083]: #47
-#2188 := (or #644 #2173)
-#2165 := [th-lemma arith triangle-eq]: #2188
-#2058 := [unit-resolution #2165 #1084]: #2173
+#455 := [monotonicity #345 #452]: #454
+#461 := [trans #455 #459]: #460
+#464 := [monotonicity #461]: #463
+#470 := [trans #464 #468]: #469
+#473 := [monotonicity #470]: #472
+#478 := [trans #473 #476]: #477
+#481 := [monotonicity #478]: #480
+#485 := [trans #481 #483]: #484
+#544 := [monotonicity #485 #541]: #543
+#547 := [monotonicity #544]: #546
+#552 := [trans #547 #550]: #551
+#555 := [monotonicity #552]: #554
+#561 := [trans #555 #559]: #560
+#564 := [monotonicity #561]: #563
+#569 := [trans #564 #567]: #568
+#572 := [monotonicity #569]: #571
+#576 := [trans #572 #574]: #575
+#341 := (iff #93 #331)
+#336 := (implies true #331)
+#339 := (iff #336 #331)
+#340 := [rewrite]: #339
+#337 := (iff #93 #336)
+#334 := (iff #92 #331)
+#328 := (implies #60 #323)
+#332 := (iff #328 #331)
+#333 := [rewrite]: #332
+#329 := (iff #92 #328)
+#326 := (iff #91 #323)
+#319 := (implies #69 #314)
+#324 := (iff #319 #323)
+#325 := [rewrite]: #324
+#320 := (iff #91 #319)
+#317 := (iff #90 #314)
+#310 := (implies #60 #305)
+#315 := (iff #310 #314)
+#316 := [rewrite]: #315
+#311 := (iff #90 #310)
+#308 := (iff #89 #305)
+#301 := (implies #242 #296)
+#306 := (iff #301 #305)
+#307 := [rewrite]: #306
+#302 := (iff #89 #301)
+#299 := (iff #88 #296)
+#292 := (implies #245 #287)
+#297 := (iff #292 #296)
+#298 := [rewrite]: #297
+#293 := (iff #88 #292)
+#290 := (iff #87 #287)
+#283 := (implies #248 #280)
+#288 := (iff #283 #287)
+#289 := [rewrite]: #288
+#284 := (iff #87 #283)
+#281 := (iff #86 #280)
+#278 := (iff #85 #275)
+#271 := (implies #255 #261)
+#276 := (iff #271 #275)
+#277 := [rewrite]: #276
+#272 := (iff #85 #271)
+#269 := (iff #84 #261)
+#264 := (and #261 true)
+#267 := (iff #264 #261)
+#268 := [rewrite]: #267
+#265 := (iff #84 #264)
+#262 := (iff #83 #261)
+#259 := (iff #82 #258)
+#260 := [rewrite]: #259
+#263 := [quant-intro #260]: #262
+#266 := [monotonicity #263]: #265
+#270 := [trans #266 #268]: #269
+#256 := (iff #80 #255)
+#253 := (iff #79 #252)
+#254 := [rewrite]: #253
+#257 := [quant-intro #254]: #256
+#273 := [monotonicity #257 #270]: #272
+#279 := [trans #273 #277]: #278
+#282 := [monotonicity #257 #279]: #281
+#249 := (iff #75 #248)
+#250 := [rewrite]: #249
+#285 := [monotonicity #250 #282]: #284
+#291 := [trans #285 #289]: #290
+#246 := (iff #73 #245)
+#247 := [rewrite]: #246
+#294 := [monotonicity #247 #291]: #293
+#300 := [trans #294 #298]: #299
+#243 := (iff #71 #242)
+#244 := [rewrite]: #243
+#303 := [monotonicity #244 #300]: #302
+#309 := [trans #303 #307]: #308
+#312 := [monotonicity #309]: #311
+#318 := [trans #312 #316]: #317
+#321 := [monotonicity #318]: #320
+#327 := [trans #321 #325]: #326
+#330 := [monotonicity #327]: #329
+#335 := [trans #330 #333]: #334
+#338 := [monotonicity #335]: #337
+#342 := [trans #338 #340]: #341
+#579 := [monotonicity #342 #576]: #578
+#582 := [monotonicity #579]: #581
+#587 := [trans #582 #585]: #586
+#240 := (iff #68 #239)
+#241 := [rewrite]: #240
+#590 := [monotonicity #241 #587]: #589
+#596 := [trans #590 #594]: #595
+#237 := (iff #66 #236)
+#234 := (iff #65 #233)
+#235 := [rewrite]: #234
+#238 := [quant-intro #235]: #237
+#599 := [monotonicity #238 #596]: #598
+#605 := [trans #599 #603]: #604
+#608 := [monotonicity #605]: #607
+#613 := [trans #608 #611]: #612
+#616 := [monotonicity #613]: #615
+#620 := [trans #616 #618]: #619
+#230 := (iff #55 #40)
+#231 := [rewrite]: #230
+#623 := [monotonicity #231 #620]: #622
+#629 := [trans #623 #627]: #628
+#632 := [monotonicity #231 #629]: #631
+#228 := (iff #54 #227)
+#225 := (iff #53 #224)
+#226 := [rewrite]: #225
+#229 := [quant-intro #226]: #228
+#635 := [monotonicity #229 #632]: #634
+#641 := [trans #635 #639]: #640
+#644 := [monotonicity #229 #641]: #643
+#221 := (iff #46 #220)
+#218 := (iff #45 #217)
+#215 := (iff #44 #43)
+#216 := [rewrite]: #215
+#219 := [monotonicity #216]: #218
+#222 := [monotonicity #219]: #221
+#647 := [monotonicity #222 #644]: #646
+#653 := [trans #647 #651]: #652
+#656 := [monotonicity #653]: #655
+#661 := [trans #656 #659]: #660
+#664 := [monotonicity #661]: #663
+#670 := [trans #664 #668]: #669
+#673 := [monotonicity #670]: #672
+#677 := [trans #673 #675]: #676
+#680 := [monotonicity #677]: #679
+#1062 := [trans #680 #1060]: #1061
+#213 := [asserted]: #161
+#1063 := [mp #213 #1062]: #1058
+#1064 := [not-or-elim #1063]: #40
+#2168 := (or #624 #2153)
+#2145 := [th-lemma arith triangle-eq]: #2168
+#2038 := [unit-resolution #2145 #1064]: #2153
 decl ?v0!0 :: Int
-#1150 := ?v0!0
-#1151 := (f15 ?v0!0)
-#1152 := (* -1::Int #1151)
-#1153 := (+ f14 #1152)
-#1154 := (>= #1153 0::Int)
-#1902 := (not #1154)
-#1157 := (>= ?v0!0 0::Int)
-#1228 := (not #1157)
-#1155 := (>= ?v0!0 1::Int)
-#1540 := (or #1154 #1155 #1228)
-#1545 := (not #1540)
+#1130 := ?v0!0
+#1131 := (f10 ?v0!0)
+#1132 := (* -1::Int #1131)
+#1133 := (+ f9 #1132)
+#1134 := (>= #1133 0::Int)
+#1882 := (not #1134)
+#1137 := (>= ?v0!0 0::Int)
+#1144 := (not #1137)
+#1135 := (>= ?v0!0 1::Int)
+#1520 := (or #1134 #1135 #1144)
+#1525 := (not #1520)
 decl ?v0!1 :: Int
-#1194 := ?v0!1
-#1202 := (f15 ?v0!1)
-#1375 := (= f20 #1202)
-#1199 := (>= ?v0!1 0::Int)
-#1618 := (not #1199)
-#1195 := (* -1::Int ?v0!1)
-#1196 := (+ f13 #1195)
-#1197 := (<= #1196 0::Int)
-#1633 := (or #1197 #1618 #1375)
-#1664 := (not #1633)
+#1174 := ?v0!1
+#1182 := (f10 ?v0!1)
+#1355 := (= f15 #1182)
+#1179 := (>= ?v0!1 0::Int)
+#1598 := (not #1179)
+#1175 := (* -1::Int ?v0!1)
+#1176 := (+ f8 #1175)
+#1177 := (<= #1176 0::Int)
+#1613 := (or #1177 #1598 #1355)
+#1644 := (not #1613)
 decl ?v0!2 :: Int
-#1212 := ?v0!2
-#1213 := (f15 ?v0!2)
-#1399 := (* -1::Int #1213)
-#1400 := (+ f20 #1399)
-#1401 := (>= #1400 0::Int)
-#1220 := (>= ?v0!2 0::Int)
-#1638 := (not #1220)
-#1216 := (* -1::Int ?v0!2)
-#1217 := (+ f13 #1216)
-#1218 := (<= #1217 0::Int)
-#1795 := (or #1218 #1638 #1401 #1664)
-#1798 := (not #1795)
-#2352 := (pattern #58)
-#1548 := (not #724)
-#1607 := (or #85 #1548 #764)
-#1612 := (not #1607)
-#2413 := (forall (vars (?v0 Int)) (:pat #2352) #1612)
-#2418 := (or #2413 #1798)
-#2421 := (not #2418)
-#1677 := (not #751)
-#2424 := (or #324 #315 #306 #1677 #898 #810 #2421)
-#2427 := (not #2424)
+#1192 := ?v0!2
+#1193 := (f10 ?v0!2)
+#1379 := (* -1::Int #1193)
+#1380 := (+ f15 #1379)
+#1381 := (>= #1380 0::Int)
+#1200 := (>= ?v0!2 0::Int)
+#1618 := (not #1200)
+#1196 := (* -1::Int ?v0!2)
+#1197 := (+ f8 #1196)
+#1198 := (<= #1197 0::Int)
+#1775 := (or #1198 #1618 #1381 #1644)
+#1778 := (not #1775)
+#2331 := (pattern #51)
+#1528 := (not #704)
+#1587 := (or #78 #1528 #744)
+#1592 := (not #1587)
+#2392 := (forall (vars (?v0 Int)) (:pat #2331) #1592)
+#2397 := (or #2392 #1778)
+#2400 := (not #2397)
+#1657 := (not #731)
+#2403 := (or #304 #295 #286 #1657 #878 #790 #2400)
+#2406 := (not #2403)
 decl ?v0!3 :: Int
-#1261 := ?v0!3
-#1262 := (f15 ?v0!3)
-#1464 := (* -1::Int #1262)
-#1465 := (+ f24 #1464)
-#1466 := (>= #1465 0::Int)
-#1442 := (* -1::Int ?v0!3)
-#1443 := (+ f25 #1442)
-#1444 := (<= #1443 0::Int)
-#1268 := (>= ?v0!3 0::Int)
-#1717 := (not #1268)
-#1732 := (or #1717 #1444 #1466)
-#1737 := (not #1732)
-#1699 := (or #1548 #848 #862)
-#2369 := (forall (vars (?v0 Int)) (:pat #2352) #1699)
-#2374 := (not #2369)
-#2377 := (or #390 #2374)
-#2380 := (not #2377)
-#2383 := (or #2380 #1737)
-#2386 := (not #2383)
-#1747 := (not #840)
-#1746 := (not #837)
-#2395 := (or #524 #515 #1677 #898 #1746 #1747 #889 #901 #2386)
-#2398 := (not #2395)
-#2389 := (or #476 #458 #449 #1677 #898 #1746 #1747 #889 #902 #2386)
-#2392 := (not #2389)
-#2401 := (or #2392 #2398)
-#2404 := (not #2401)
-#2407 := (or #1677 #898 #807 #2404)
-#2410 := (not #2407)
-#2430 := (or #2410 #2427)
-#2433 := (not #2430)
-#1585 := (or #1548 #999 #1012)
-#2361 := (forall (vars (?v0 Int)) (:pat #2352) #1585)
-#2366 := (not #2361)
-#1563 := (or #1548 #727 #737)
-#2353 := (forall (vars (?v0 Int)) (:pat #2352) #1563)
-#2358 := (not #2353)
-#2436 := (or #611 #1677 #898 #2358 #2366 #2433)
-#2766 := (+ #102 #1464)
-#2768 := (>= #2766 0::Int)
-#2765 := (= #102 #1262)
-#2644 := (= f17 ?v0!3)
-#2569 := (+ f17 #1442)
-#2570 := (<= #2569 0::Int)
-#2581 := (+ f18 #1464)
-#2582 := (>= #2581 0::Int)
-#2685 := (not #2582)
-#2313 := (not #1466)
-#2439 := (not #2436)
-#2769 := [hypothesis]: #2439
-#2215 := (or #2436 #2430)
-#2217 := [def-axiom]: #2215
-#2770 := [unit-resolution #2217 #2769]: #2430
-#2228 := (or #2436 #2361)
-#2214 := [def-axiom]: #2228
-#2771 := [unit-resolution #2214 #2769]: #2361
-#2237 := (or #2436 #259)
-#2221 := [def-axiom]: #2237
-#2772 := [unit-resolution #2221 #2769]: #259
-#2513 := (or #2424 #611 #2366)
-#2453 := (f15 f19)
-#2457 := (= f20 #2453)
-#2507 := (= #74 #2453)
-#2505 := (= #2453 #74)
-#2490 := [hypothesis]: #2427
-#2154 := (or #2424 #262)
-#2155 := [def-axiom]: #2154
-#2501 := [unit-resolution #2155 #2490]: #262
-#2502 := [symm #2501]: #78
-#2506 := [monotonicity #2502]: #2505
-#2508 := [symm #2506]: #2507
-#2509 := (= f20 #74)
-#2503 := [hypothesis]: #259
-#2156 := (or #2424 #265)
-#2157 := [def-axiom]: #2156
-#2493 := [unit-resolution #2157 #2490]: #265
-#2504 := [symm #2493]: #80
-#2510 := [trans #2504 #2503]: #2509
-#2511 := [trans #2510 #2508]: #2457
-#2485 := (not #2457)
-#2451 := (>= f19 0::Int)
-#2452 := (not #2451)
-#2448 := (* -1::Int f19)
-#2449 := (+ f13 #2448)
-#2450 := (<= #2449 0::Int)
-#2463 := (or #2450 #2452 #2457)
-#2468 := (not #2463)
-#2241 := (or #2424 #2418)
-#2242 := [def-axiom]: #2241
-#2491 := [unit-resolution #2242 #2490]: #2418
-#2229 := (or #2424 #807)
-#2231 := [def-axiom]: #2229
-#2492 := [unit-resolution #2231 #2490]: #807
-#1964 := [hypothesis]: #2361
-#2075 := (+ f18 #788)
-#2076 := (<= #2075 0::Int)
-#2494 := (or #315 #2076)
-#2495 := [th-lemma arith triangle-eq]: #2494
-#2496 := [unit-resolution #2495 #2493]: #2076
-#1971 := (not #2076)
-#1937 := (or #1795 #1971 #2366 #810)
-#1977 := [hypothesis]: #2076
-#2044 := (+ f18 #1399)
-#2045 := (>= #2044 0::Int)
-#2065 := (+ f17 #1216)
-#2066 := (<= #2065 0::Int)
-#1960 := (not #2066)
-#1953 := [hypothesis]: #807
-#1219 := (not #1218)
-#1958 := [hypothesis]: #1798
-#2256 := (or #1795 #1219)
-#2254 := [def-axiom]: #2256
-#1959 := [unit-resolution #2254 #1958]: #1219
-#1961 := (or #1960 #810 #1218)
-#1962 := [th-lemma arith assign-bounds 1 -1]: #1961
-#1963 := [unit-resolution #1962 #1959 #1953]: #1960
-#1945 := (or #2045 #2066)
-#2257 := (or #1795 #1220)
-#2139 := [def-axiom]: #2257
-#1952 := [unit-resolution #2139 #1958]: #1220
-#2034 := (or #2366 #1638 #2045 #2066)
-#2077 := (+ #1213 #1010)
-#2067 := (<= #2077 0::Int)
-#2057 := (+ ?v0!2 #805)
-#2059 := (>= #2057 0::Int)
-#2060 := (or #1638 #2059 #2067)
-#2035 := (or #2366 #2060)
-#2026 := (iff #2035 #2034)
-#2028 := (or #1638 #2045 #2066)
-#2029 := (or #2366 #2028)
-#2023 := (iff #2029 #2034)
-#2024 := [rewrite]: #2023
-#2037 := (iff #2035 #2029)
-#2032 := (iff #2060 #2028)
-#2050 := (or #1638 #2066 #2045)
-#2030 := (iff #2050 #2028)
-#2031 := [rewrite]: #2030
-#2039 := (iff #2060 #2050)
-#2048 := (iff #2067 #2045)
-#2056 := (+ #1010 #1213)
-#2041 := (<= #2056 0::Int)
-#2046 := (iff #2041 #2045)
-#2047 := [rewrite]: #2046
-#2042 := (iff #2067 #2041)
-#2038 := (= #2077 #2056)
-#2040 := [rewrite]: #2038
-#2043 := [monotonicity #2040]: #2042
-#2049 := [trans #2043 #2047]: #2048
-#2055 := (iff #2059 #2066)
-#2063 := (+ #805 ?v0!2)
-#2061 := (>= #2063 0::Int)
-#2052 := (iff #2061 #2066)
-#2054 := [rewrite]: #2052
-#2069 := (iff #2059 #2061)
-#2064 := (= #2057 #2063)
-#2068 := [rewrite]: #2064
-#2062 := [monotonicity #2068]: #2069
-#2053 := [trans #2062 #2054]: #2055
-#2051 := [monotonicity #2053 #2049]: #2039
-#2033 := [trans #2051 #2031]: #2032
-#2022 := [monotonicity #2033]: #2037
-#2025 := [trans #2022 #2024]: #2026
-#2036 := [quant-inst #1212]: #2035
-#2027 := [mp #2036 #2025]: #2034
-#1947 := [unit-resolution #2027 #1964 #1952]: #1945
-#1948 := [unit-resolution #1947 #1963]: #2045
-#2140 := (not #1401)
-#2141 := (or #1795 #2140)
-#2100 := [def-axiom]: #2141
-#1946 := [unit-resolution #2100 #1958]: #2140
-#1949 := [th-lemma arith farkas 1 -1 1 #1946 #1948 #1977]: false
-#1939 := [lemma #1949]: #1937
-#2497 := [unit-resolution #1939 #2496 #1964 #2492]: #1795
-#2145 := (or #2421 #2413 #1798)
-#2153 := [def-axiom]: #2145
-#2498 := [unit-resolution #2153 #2497 #2491]: #2413
-#2249 := (not #2413)
-#2471 := (or #2249 #2468)
-#2454 := (= #2453 f20)
-#2455 := (or #2454 #2452 #2450)
-#2456 := (not #2455)
-#2472 := (or #2249 #2456)
-#2474 := (iff #2472 #2471)
-#2476 := (iff #2471 #2471)
-#2477 := [rewrite]: #2476
-#2469 := (iff #2456 #2468)
-#2466 := (iff #2455 #2463)
-#2460 := (or #2457 #2452 #2450)
-#2464 := (iff #2460 #2463)
-#2465 := [rewrite]: #2464
-#2461 := (iff #2455 #2460)
-#2458 := (iff #2454 #2457)
-#2459 := [rewrite]: #2458
-#2462 := [monotonicity #2459]: #2461
-#2467 := [trans #2462 #2465]: #2466
-#2470 := [monotonicity #2467]: #2469
-#2475 := [monotonicity #2470]: #2474
-#2478 := [trans #2475 #2477]: #2474
-#2473 := [quant-inst #77]: #2472
-#2479 := [mp #2473 #2478]: #2471
-#2499 := [unit-resolution #2479 #2498]: #2468
-#2486 := (or #2463 #2485)
-#2487 := [def-axiom]: #2486
-#2500 := [unit-resolution #2487 #2499]: #2485
-#2512 := [unit-resolution #2500 #2511]: false
-#2514 := [lemma #2512]: #2513
-#2773 := [unit-resolution #2514 #2772 #2771]: #2424
-#2236 := (or #2433 #2410 #2427)
-#2230 := [def-axiom]: #2236
-#2774 := [unit-resolution #2230 #2773 #2770]: #2410
-#2264 := (or #2407 #2401)
-#2258 := [def-axiom]: #2264
-#2775 := [unit-resolution #2258 #2774]: #2401
-#2706 := (or #2389 #2366)
-#1449 := (not #1444)
-#2622 := [hypothesis]: #2392
-#2300 := (or #2389 #2383)
-#2303 := [def-axiom]: #2300
-#2640 := [unit-resolution #2303 #2622]: #2383
-#2664 := (= #102 #124)
-#2660 := (= #124 #102)
-#1955 := (or #2389 #368)
-#1956 := [def-axiom]: #1955
-#2643 := [unit-resolution #1956 #2622]: #368
-#2645 := [symm #2643]: #108
-#2661 := [monotonicity #2645]: #2660
-#2665 := [symm #2661]: #2664
-#2666 := (= f24 #102)
-#2291 := (or #2389 #363)
-#1954 := [def-axiom]: #2291
-#2642 := [unit-resolution #1954 #2622]: #363
-#2663 := [symm #2642]: #105
-#1957 := (or #2389 #371)
-#2293 := [def-axiom]: #1957
-#2641 := [unit-resolution #2293 #2622]: #371
-#2662 := [symm #2641]: #110
-#2667 := [trans #2662 #2663]: #2666
-#2668 := [trans #2667 #2665]: #390
-#1277 := (not #390)
-#1973 := (or #2377 #1277)
-#2308 := [def-axiom]: #1973
-#2669 := [unit-resolution #2308 #2668]: #2377
-#2307 := (or #2386 #2380 #1737)
-#1950 := [def-axiom]: #2307
-#2670 := [unit-resolution #1950 #2669 #2640]: #1737
-#2311 := (or #1732 #1449)
-#2312 := [def-axiom]: #2311
-#2671 := [unit-resolution #2312 #2670]: #1449
-#2620 := (>= #2569 0::Int)
-#2695 := (not #2620)
-#2657 := (not #2644)
-#2621 := (= #124 #1262)
-#2625 := (not #2621)
-#2628 := (+ #124 #1464)
-#2630 := (>= #2628 0::Int)
-#2635 := (not #2630)
-#2314 := (or #1732 #2313)
-#2309 := [def-axiom]: #2314
-#2672 := [unit-resolution #2309 #2670]: #2313
-#2516 := (* -1::Int #124)
-#2555 := (+ f24 #2516)
-#2557 := (>= #2555 0::Int)
-#2673 := (or #1277 #2557)
-#2674 := [th-lemma arith triangle-eq]: #2673
-#2675 := [unit-resolution #2674 #2668]: #2557
-#2636 := (not #2557)
-#2637 := (or #2635 #2636 #1466)
-#2631 := [hypothesis]: #2630
-#2632 := [hypothesis]: #2313
-#2633 := [hypothesis]: #2557
-#2634 := [th-lemma arith farkas 1 -1 1 #2633 #2632 #2631]: false
-#2638 := [lemma #2634]: #2637
-#2676 := [unit-resolution #2638 #2675 #2672]: #2635
-#2626 := (or #2625 #2630)
-#2627 := [th-lemma arith triangle-eq]: #2626
-#2677 := [unit-resolution #2627 #2676]: #2625
-#2658 := (or #2657 #2621 #458)
-#2653 := (= #1262 #124)
-#2651 := (= ?v0!3 f23)
-#2647 := [hypothesis]: #368
-#2649 := (= ?v0!3 f17)
-#2648 := [hypothesis]: #2644
-#2650 := [symm #2648]: #2649
-#2652 := [trans #2650 #2647]: #2651
-#2654 := [monotonicity #2652]: #2653
-#2655 := [symm #2654]: #2621
-#2646 := [hypothesis]: #2625
-#2656 := [unit-resolution #2646 #2655]: false
-#2659 := [lemma #2656]: #2658
-#2678 := [unit-resolution #2659 #2677 #2643]: #2657
-#2698 := (or #2644 #2695)
-#1942 := (or #2389 #901)
-#2302 := [def-axiom]: #1942
-#2679 := [unit-resolution #2302 #2622]: #901
-#1908 := (+ #102 #860)
-#2446 := (<= #1908 0::Int)
-#1905 := (= #102 f24)
-#2680 := [trans #2642 #2641]: #1905
-#2681 := (not #1905)
-#2682 := (or #2681 #2446)
-#2683 := [th-lemma arith triangle-eq]: #2682
-#2684 := [unit-resolution #2683 #2680]: #2446
-#2686 := (not #2446)
-#2687 := (or #2685 #1466 #2686 #902)
-#2688 := [th-lemma arith assign-bounds 1 1 1]: #2687
-#2689 := [unit-resolution #2688 #2672 #2684 #2679]: #2685
-#2691 := (or #2570 #2582)
-#1978 := (or #1732 #1268)
-#1979 := [def-axiom]: #1978
-#2690 := [unit-resolution #1979 #2670]: #1268
-#2590 := (or #2366 #1717 #2570 #2582)
-#2558 := (+ #1262 #1010)
-#2559 := (<= #2558 0::Int)
-#2560 := (+ ?v0!3 #805)
+#1241 := ?v0!3
+#1242 := (f10 ?v0!3)
+#1444 := (* -1::Int #1242)
+#1445 := (+ f19 #1444)
+#1446 := (>= #1445 0::Int)
+#1422 := (* -1::Int ?v0!3)
+#1423 := (+ f20 #1422)
+#1424 := (<= #1423 0::Int)
+#1248 := (>= ?v0!3 0::Int)
+#1697 := (not #1248)
+#1712 := (or #1697 #1424 #1446)
+#1717 := (not #1712)
+#1679 := (or #1528 #828 #842)
+#2348 := (forall (vars (?v0 Int)) (:pat #2331) #1679)
+#2353 := (not #2348)
+#2356 := (or #370 #2353)
+#2359 := (not #2356)
+#2362 := (or #2359 #1717)
+#2365 := (not #2362)
+#1727 := (not #820)
+#1726 := (not #817)
+#2374 := (or #504 #495 #1657 #878 #1726 #1727 #869 #881 #2365)
+#2377 := (not #2374)
+#2368 := (or #456 #438 #429 #1657 #878 #1726 #1727 #869 #882 #2365)
+#2371 := (not #2368)
+#2380 := (or #2371 #2377)
+#2383 := (not #2380)
+#2386 := (or #1657 #878 #787 #2383)
+#2389 := (not #2386)
+#2409 := (or #2389 #2406)
+#2412 := (not #2409)
+#1565 := (or #1528 #979 #992)
+#2340 := (forall (vars (?v0 Int)) (:pat #2331) #1565)
+#2345 := (not #2340)
+#1543 := (or #1528 #707 #717)
+#2332 := (forall (vars (?v0 Int)) (:pat #2331) #1543)
+#2337 := (not #2332)
+#2415 := (or #591 #1657 #878 #2337 #2345 #2412)
+#2745 := (+ #95 #1444)
+#2747 := (>= #2745 0::Int)
+#2744 := (= #95 #1242)
+#2623 := (= f12 ?v0!3)
+#2548 := (+ f12 #1422)
+#2549 := (<= #2548 0::Int)
+#2560 := (+ f13 #1444)
 #2561 := (>= #2560 0::Int)
-#2562 := (or #1717 #2561 #2559)
-#2591 := (or #2366 #2562)
-#2598 := (iff #2591 #2590)
-#2587 := (or #1717 #2570 #2582)
-#2593 := (or #2366 #2587)
-#2596 := (iff #2593 #2590)
-#2597 := [rewrite]: #2596
-#2594 := (iff #2591 #2593)
-#2588 := (iff #2562 #2587)
-#2585 := (iff #2559 #2582)
-#2575 := (+ #1010 #1262)
-#2578 := (<= #2575 0::Int)
-#2583 := (iff #2578 #2582)
-#2584 := [rewrite]: #2583
-#2579 := (iff #2559 #2578)
-#2576 := (= #2558 #2575)
-#2577 := [rewrite]: #2576
-#2580 := [monotonicity #2577]: #2579
-#2586 := [trans #2580 #2584]: #2585
-#2573 := (iff #2561 #2570)
-#2563 := (+ #805 ?v0!3)
-#2566 := (>= #2563 0::Int)
-#2571 := (iff #2566 #2570)
-#2572 := [rewrite]: #2571
-#2567 := (iff #2561 #2566)
-#2564 := (= #2560 #2563)
-#2565 := [rewrite]: #2564
-#2568 := [monotonicity #2565]: #2567
-#2574 := [trans #2568 #2572]: #2573
-#2589 := [monotonicity #2574 #2586]: #2588
-#2595 := [monotonicity #2589]: #2594
-#2599 := [trans #2595 #2597]: #2598
-#2592 := [quant-inst #1261]: #2591
-#2600 := [mp #2592 #2599]: #2590
-#2692 := [unit-resolution #2600 #1964 #2690]: #2691
-#2693 := [unit-resolution #2692 #2689]: #2570
-#2694 := (not #2570)
-#2696 := (or #2644 #2694 #2695)
-#2697 := [th-lemma arith triangle-eq]: #2696
-#2699 := [unit-resolution #2697 #2693]: #2698
-#2700 := [unit-resolution #2699 #2678]: #2695
-#1994 := (>= #886 -1::Int)
-#2301 := (or #2389 #885)
-#1941 := [def-axiom]: #2301
-#2701 := [unit-resolution #1941 #2622]: #885
-#2702 := (or #889 #1994)
-#2703 := [th-lemma arith triangle-eq]: #2702
-#2704 := [unit-resolution #2703 #2701]: #1994
-#2705 := [th-lemma arith farkas 1 -1 1 #2704 #2700 #2671]: false
-#2707 := [lemma #2705]: #2706
-#2776 := [unit-resolution #2707 #2771]: #2389
-#2270 := (or #2404 #2392 #2398)
-#2276 := [def-axiom]: #2270
-#2777 := [unit-resolution #2276 #2776 #2775]: #2398
-#2282 := (or #2395 #2383)
-#2271 := [def-axiom]: #2282
-#2778 := [unit-resolution #2271 #2777]: #2383
-#2528 := (= #74 #124)
-#2783 := (= #124 #74)
-#2008 := (or #2395 #506)
-#2009 := [def-axiom]: #2008
-#2779 := [unit-resolution #2009 #2777]: #506
-#2780 := [symm #2779]: #141
-#2784 := [monotonicity #2780]: #2783
-#2785 := [symm #2784]: #2528
-#2786 := (= f24 #74)
-#2283 := (or #2395 #509)
-#2287 := [def-axiom]: #2283
-#2781 := [unit-resolution #2287 #2777]: #509
-#2782 := [symm #2781]: #142
-#2787 := [trans #2782 #2772]: #2786
-#2788 := [trans #2787 #2785]: #390
-#2789 := [unit-resolution #2308 #2788]: #2377
-#2790 := [unit-resolution #1950 #2789 #2778]: #1737
-#2791 := [unit-resolution #2309 #2790]: #2313
-#1909 := (+ f18 #860)
-#2285 := (<= #1909 0::Int)
-#2792 := (or #515 #2285)
-#2793 := [th-lemma arith triangle-eq]: #2792
-#2794 := [unit-resolution #2793 #2781]: #2285
-#2795 := (not #2285)
-#2796 := (or #2685 #1466 #2795)
-#2797 := [th-lemma arith assign-bounds -1 -1]: #2796
-#2798 := [unit-resolution #2797 #2794 #2791]: #2685
-#2799 := [unit-resolution #1979 #2790]: #1268
-#2800 := [unit-resolution #2600 #2771 #2799 #2798]: #2570
-#2801 := [unit-resolution #2312 #2790]: #1449
-#1995 := (or #2395 #885)
-#2277 := [def-axiom]: #1995
-#2802 := [unit-resolution #2277 #2777]: #885
-#2803 := [unit-resolution #2703 #2802]: #1994
-#2762 := (not #1994)
-#2763 := (or #2620 #2762 #1444)
-#2758 := [hypothesis]: #1449
-#2759 := [hypothesis]: #2695
-#2760 := [hypothesis]: #1994
-#2761 := [th-lemma arith farkas 1 -1 1 #2760 #2759 #2758]: false
-#2764 := [lemma #2761]: #2763
-#2804 := [unit-resolution #2764 #2803 #2801]: #2620
-#2805 := [unit-resolution #2697 #2804 #2800]: #2644
-#2806 := [monotonicity #2805]: #2765
-#2807 := (not #2765)
-#2808 := (or #2807 #2768)
-#2809 := [th-lemma arith triangle-eq]: #2808
-#2810 := [unit-resolution #2809 #2806]: #2768
-#2281 := (or #2395 #902)
-#2278 := [def-axiom]: #2281
-#2811 := [unit-resolution #2278 #2777]: #902
-#2812 := [th-lemma arith farkas 1 -1 -1 1 #2811 #2791 #2794 #2810]: false
-#2813 := [lemma #2812]: #2436
-#2442 := (or #1545 #2439)
-#1615 := (forall (vars (?v0 Int)) #1612)
-#1801 := (or #1615 #1798)
-#1804 := (not #1801)
-#1807 := (or #324 #315 #306 #1677 #898 #810 #1804)
-#1810 := (not #1807)
-#1704 := (forall (vars (?v0 Int)) #1699)
-#1710 := (not #1704)
-#1711 := (or #390 #1710)
-#1712 := (not #1711)
-#1740 := (or #1712 #1737)
-#1748 := (not #1740)
-#1758 := (or #524 #515 #1677 #898 #1746 #1747 #889 #901 #1748)
-#1759 := (not #1758)
-#1749 := (or #476 #458 #449 #1677 #898 #1746 #1747 #889 #902 #1748)
-#1750 := (not #1749)
-#1764 := (or #1750 #1759)
-#1770 := (not #1764)
-#1771 := (or #1677 #898 #807 #1770)
-#1772 := (not #1771)
-#1816 := (or #1772 #1810)
-#1821 := (not #1816)
-#1590 := (forall (vars (?v0 Int)) #1585)
-#1784 := (not #1590)
-#1568 := (forall (vars (?v0 Int)) #1563)
-#1783 := (not #1568)
-#1824 := (or #611 #1677 #898 #1783 #1784 #1821)
-#1827 := (not #1824)
-#1830 := (or #1545 #1827)
-#2443 := (iff #1830 #2442)
-#2440 := (iff #1827 #2439)
-#2437 := (iff #1824 #2436)
-#2434 := (iff #1821 #2433)
-#2431 := (iff #1816 #2430)
-#2428 := (iff #1810 #2427)
-#2425 := (iff #1807 #2424)
-#2422 := (iff #1804 #2421)
-#2419 := (iff #1801 #2418)
-#2416 := (iff #1615 #2413)
-#2414 := (iff #1612 #1612)
-#2415 := [refl]: #2414
-#2417 := [quant-intro #2415]: #2416
+#2664 := (not #2561)
+#2293 := (not #1446)
+#2418 := (not #2415)
+#2748 := [hypothesis]: #2418
+#2195 := (or #2415 #2409)
+#2197 := [def-axiom]: #2195
+#2749 := [unit-resolution #2197 #2748]: #2409
+#2208 := (or #2415 #2340)
+#2194 := [def-axiom]: #2208
+#2750 := [unit-resolution #2194 #2748]: #2340
+#2217 := (or #2415 #239)
+#2201 := [def-axiom]: #2217
+#2751 := [unit-resolution #2201 #2748]: #239
+#2492 := (or #2403 #591 #2345)
+#2432 := (f10 f14)
+#2436 := (= f15 #2432)
+#2486 := (= #67 #2432)
+#2484 := (= #2432 #67)
+#2469 := [hypothesis]: #2406
+#2134 := (or #2403 #242)
+#2135 := [def-axiom]: #2134
+#2480 := [unit-resolution #2135 #2469]: #242
+#2481 := [symm #2480]: #71
+#2485 := [monotonicity #2481]: #2484
+#2487 := [symm #2485]: #2486
+#2488 := (= f15 #67)
+#2482 := [hypothesis]: #239
+#2136 := (or #2403 #245)
+#2137 := [def-axiom]: #2136
+#2472 := [unit-resolution #2137 #2469]: #245
+#2483 := [symm #2472]: #73
+#2489 := [trans #2483 #2482]: #2488
+#2490 := [trans #2489 #2487]: #2436
+#2464 := (not #2436)
+#2430 := (>= f14 0::Int)
+#2431 := (not #2430)
+#2427 := (* -1::Int f14)
+#2428 := (+ f8 #2427)
+#2429 := (<= #2428 0::Int)
+#2442 := (or #2429 #2431 #2436)
+#2447 := (not #2442)
+#2221 := (or #2403 #2397)
+#2222 := [def-axiom]: #2221
+#2470 := [unit-resolution #2222 #2469]: #2397
+#2209 := (or #2403 #787)
+#2211 := [def-axiom]: #2209
+#2471 := [unit-resolution #2211 #2469]: #787
+#1944 := [hypothesis]: #2340
+#2055 := (+ f13 #768)
+#2056 := (<= #2055 0::Int)
+#2473 := (or #295 #2056)
+#2474 := [th-lemma arith triangle-eq]: #2473
+#2475 := [unit-resolution #2474 #2472]: #2056
+#1951 := (not #2056)
+#1917 := (or #1775 #1951 #2345 #790)
+#1957 := [hypothesis]: #2056
+#2024 := (+ f13 #1379)
+#2025 := (>= #2024 0::Int)
+#2045 := (+ f12 #1196)
+#2046 := (<= #2045 0::Int)
+#1940 := (not #2046)
+#1933 := [hypothesis]: #787
+#1199 := (not #1198)
+#1938 := [hypothesis]: #1778
+#2236 := (or #1775 #1199)
+#2234 := [def-axiom]: #2236
+#1939 := [unit-resolution #2234 #1938]: #1199
+#1941 := (or #1940 #790 #1198)
+#1942 := [th-lemma arith assign-bounds 1 -1]: #1941
+#1943 := [unit-resolution #1942 #1939 #1933]: #1940
+#1925 := (or #2025 #2046)
+#2237 := (or #1775 #1200)
+#2119 := [def-axiom]: #2237
+#1932 := [unit-resolution #2119 #1938]: #1200
+#2014 := (or #2345 #1618 #2025 #2046)
+#2057 := (+ #1193 #990)
+#2047 := (<= #2057 0::Int)
+#2037 := (+ ?v0!2 #785)
+#2039 := (>= #2037 0::Int)
+#2040 := (or #1618 #2039 #2047)
+#2015 := (or #2345 #2040)
+#2006 := (iff #2015 #2014)
+#2008 := (or #1618 #2025 #2046)
+#2009 := (or #2345 #2008)
+#2003 := (iff #2009 #2014)
+#2004 := [rewrite]: #2003
+#2017 := (iff #2015 #2009)
+#2012 := (iff #2040 #2008)
+#2030 := (or #1618 #2046 #2025)
+#2010 := (iff #2030 #2008)
+#2011 := [rewrite]: #2010
+#2019 := (iff #2040 #2030)
+#2028 := (iff #2047 #2025)
+#2036 := (+ #990 #1193)
+#2021 := (<= #2036 0::Int)
+#2026 := (iff #2021 #2025)
+#2027 := [rewrite]: #2026
+#2022 := (iff #2047 #2021)
+#2018 := (= #2057 #2036)
+#2020 := [rewrite]: #2018
+#2023 := [monotonicity #2020]: #2022
+#2029 := [trans #2023 #2027]: #2028
+#2035 := (iff #2039 #2046)
+#2043 := (+ #785 ?v0!2)
+#2041 := (>= #2043 0::Int)
+#2032 := (iff #2041 #2046)
+#2034 := [rewrite]: #2032
+#2049 := (iff #2039 #2041)
+#2044 := (= #2037 #2043)
+#2048 := [rewrite]: #2044
+#2042 := [monotonicity #2048]: #2049
+#2033 := [trans #2042 #2034]: #2035
+#2031 := [monotonicity #2033 #2029]: #2019
+#2013 := [trans #2031 #2011]: #2012
+#2002 := [monotonicity #2013]: #2017
+#2005 := [trans #2002 #2004]: #2006
+#2016 := [quant-inst #1192]: #2015
+#2007 := [mp #2016 #2005]: #2014
+#1927 := [unit-resolution #2007 #1944 #1932]: #1925
+#1928 := [unit-resolution #1927 #1943]: #2025
+#2120 := (not #1381)
+#2121 := (or #1775 #2120)
+#2080 := [def-axiom]: #2121
+#1926 := [unit-resolution #2080 #1938]: #2120
+#1929 := [th-lemma arith farkas 1 -1 1 #1926 #1928 #1957]: false
+#1919 := [lemma #1929]: #1917
+#2476 := [unit-resolution #1919 #2475 #1944 #2471]: #1775
+#2125 := (or #2400 #2392 #1778)
+#2133 := [def-axiom]: #2125
+#2477 := [unit-resolution #2133 #2476 #2470]: #2392
+#2229 := (not #2392)
+#2450 := (or #2229 #2447)
+#2433 := (= #2432 f15)
+#2434 := (or #2433 #2431 #2429)
+#2435 := (not #2434)
+#2451 := (or #2229 #2435)
+#2453 := (iff #2451 #2450)
+#2455 := (iff #2450 #2450)
+#2456 := [rewrite]: #2455
+#2448 := (iff #2435 #2447)
+#2445 := (iff #2434 #2442)
+#2439 := (or #2436 #2431 #2429)
+#2443 := (iff #2439 #2442)
+#2444 := [rewrite]: #2443
+#2440 := (iff #2434 #2439)
+#2437 := (iff #2433 #2436)
+#2438 := [rewrite]: #2437
+#2441 := [monotonicity #2438]: #2440
+#2446 := [trans #2441 #2444]: #2445
+#2449 := [monotonicity #2446]: #2448
+#2454 := [monotonicity #2449]: #2453
+#2457 := [trans #2454 #2456]: #2453
+#2452 := [quant-inst #70]: #2451
+#2458 := [mp #2452 #2457]: #2450
+#2478 := [unit-resolution #2458 #2477]: #2447
+#2465 := (or #2442 #2464)
+#2466 := [def-axiom]: #2465
+#2479 := [unit-resolution #2466 #2478]: #2464
+#2491 := [unit-resolution #2479 #2490]: false
+#2493 := [lemma #2491]: #2492
+#2752 := [unit-resolution #2493 #2751 #2750]: #2403
+#2216 := (or #2412 #2389 #2406)
+#2210 := [def-axiom]: #2216
+#2753 := [unit-resolution #2210 #2752 #2749]: #2389
+#2244 := (or #2386 #2380)
+#2238 := [def-axiom]: #2244
+#2754 := [unit-resolution #2238 #2753]: #2380
+#2685 := (or #2368 #2345)
+#1429 := (not #1424)
+#2601 := [hypothesis]: #2371
+#2280 := (or #2368 #2362)
+#2283 := [def-axiom]: #2280
+#2619 := [unit-resolution #2283 #2601]: #2362
+#2643 := (= #95 #117)
+#2639 := (= #117 #95)
+#1935 := (or #2368 #348)
+#1936 := [def-axiom]: #1935
+#2622 := [unit-resolution #1936 #2601]: #348
+#2624 := [symm #2622]: #101
+#2640 := [monotonicity #2624]: #2639
+#2644 := [symm #2640]: #2643
+#2645 := (= f19 #95)
+#2271 := (or #2368 #343)
+#1934 := [def-axiom]: #2271
+#2621 := [unit-resolution #1934 #2601]: #343
+#2642 := [symm #2621]: #98
+#1937 := (or #2368 #351)
+#2273 := [def-axiom]: #1937
+#2620 := [unit-resolution #2273 #2601]: #351
+#2641 := [symm #2620]: #103
+#2646 := [trans #2641 #2642]: #2645
+#2647 := [trans #2646 #2644]: #370
+#1257 := (not #370)
+#1953 := (or #2356 #1257)
+#2288 := [def-axiom]: #1953
+#2648 := [unit-resolution #2288 #2647]: #2356
+#2287 := (or #2365 #2359 #1717)
+#1930 := [def-axiom]: #2287
+#2649 := [unit-resolution #1930 #2648 #2619]: #1717
+#2291 := (or #1712 #1429)
+#2292 := [def-axiom]: #2291
+#2650 := [unit-resolution #2292 #2649]: #1429
+#2599 := (>= #2548 0::Int)
+#2674 := (not #2599)
+#2636 := (not #2623)
+#2600 := (= #117 #1242)
+#2604 := (not #2600)
+#2607 := (+ #117 #1444)
+#2609 := (>= #2607 0::Int)
+#2614 := (not #2609)
+#2294 := (or #1712 #2293)
+#2289 := [def-axiom]: #2294
+#2651 := [unit-resolution #2289 #2649]: #2293
+#2495 := (* -1::Int #117)
+#2534 := (+ f19 #2495)
+#2536 := (>= #2534 0::Int)
+#2652 := (or #1257 #2536)
+#2653 := [th-lemma arith triangle-eq]: #2652
+#2654 := [unit-resolution #2653 #2647]: #2536
+#2615 := (not #2536)
+#2616 := (or #2614 #2615 #1446)
+#2610 := [hypothesis]: #2609
+#2611 := [hypothesis]: #2293
+#2612 := [hypothesis]: #2536
+#2613 := [th-lemma arith farkas 1 -1 1 #2612 #2611 #2610]: false
+#2617 := [lemma #2613]: #2616
+#2655 := [unit-resolution #2617 #2654 #2651]: #2614
+#2605 := (or #2604 #2609)
+#2606 := [th-lemma arith triangle-eq]: #2605
+#2656 := [unit-resolution #2606 #2655]: #2604
+#2637 := (or #2636 #2600 #438)
+#2632 := (= #1242 #117)
+#2630 := (= ?v0!3 f18)
+#2626 := [hypothesis]: #348
+#2628 := (= ?v0!3 f12)
+#2627 := [hypothesis]: #2623
+#2629 := [symm #2627]: #2628
+#2631 := [trans #2629 #2626]: #2630
+#2633 := [monotonicity #2631]: #2632
+#2634 := [symm #2633]: #2600
+#2625 := [hypothesis]: #2604
+#2635 := [unit-resolution #2625 #2634]: false
+#2638 := [lemma #2635]: #2637
+#2657 := [unit-resolution #2638 #2656 #2622]: #2636
+#2677 := (or #2623 #2674)
+#1922 := (or #2368 #881)
+#2282 := [def-axiom]: #1922
+#2658 := [unit-resolution #2282 #2601]: #881
+#1888 := (+ #95 #840)
+#2425 := (<= #1888 0::Int)
+#1885 := (= #95 f19)
+#2659 := [trans #2621 #2620]: #1885
+#2660 := (not #1885)
+#2661 := (or #2660 #2425)
+#2662 := [th-lemma arith triangle-eq]: #2661
+#2663 := [unit-resolution #2662 #2659]: #2425
+#2665 := (not #2425)
+#2666 := (or #2664 #1446 #2665 #882)
+#2667 := [th-lemma arith assign-bounds 1 1 1]: #2666
+#2668 := [unit-resolution #2667 #2651 #2663 #2658]: #2664
+#2670 := (or #2549 #2561)
+#1958 := (or #1712 #1248)
+#1959 := [def-axiom]: #1958
+#2669 := [unit-resolution #1959 #2649]: #1248
+#2569 := (or #2345 #1697 #2549 #2561)
+#2537 := (+ #1242 #990)
+#2538 := (<= #2537 0::Int)
+#2539 := (+ ?v0!3 #785)
+#2540 := (>= #2539 0::Int)
+#2541 := (or #1697 #2540 #2538)
+#2570 := (or #2345 #2541)
+#2577 := (iff #2570 #2569)
+#2566 := (or #1697 #2549 #2561)
+#2572 := (or #2345 #2566)
+#2575 := (iff #2572 #2569)
+#2576 := [rewrite]: #2575
+#2573 := (iff #2570 #2572)
+#2567 := (iff #2541 #2566)
+#2564 := (iff #2538 #2561)
+#2554 := (+ #990 #1242)
+#2557 := (<= #2554 0::Int)
+#2562 := (iff #2557 #2561)
+#2563 := [rewrite]: #2562
+#2558 := (iff #2538 #2557)
+#2555 := (= #2537 #2554)
+#2556 := [rewrite]: #2555
+#2559 := [monotonicity #2556]: #2558
+#2565 := [trans #2559 #2563]: #2564
+#2552 := (iff #2540 #2549)
+#2542 := (+ #785 ?v0!3)
+#2545 := (>= #2542 0::Int)
+#2550 := (iff #2545 #2549)
+#2551 := [rewrite]: #2550
+#2546 := (iff #2540 #2545)
+#2543 := (= #2539 #2542)
+#2544 := [rewrite]: #2543
+#2547 := [monotonicity #2544]: #2546
+#2553 := [trans #2547 #2551]: #2552
+#2568 := [monotonicity #2553 #2565]: #2567
+#2574 := [monotonicity #2568]: #2573
+#2578 := [trans #2574 #2576]: #2577
+#2571 := [quant-inst #1241]: #2570
+#2579 := [mp #2571 #2578]: #2569
+#2671 := [unit-resolution #2579 #1944 #2669]: #2670
+#2672 := [unit-resolution #2671 #2668]: #2549
+#2673 := (not #2549)
+#2675 := (or #2623 #2673 #2674)
+#2676 := [th-lemma arith triangle-eq]: #2675
+#2678 := [unit-resolution #2676 #2672]: #2677
+#2679 := [unit-resolution #2678 #2657]: #2674
+#1974 := (>= #866 -1::Int)
+#2281 := (or #2368 #865)
+#1921 := [def-axiom]: #2281
+#2680 := [unit-resolution #1921 #2601]: #865
+#2681 := (or #869 #1974)
+#2682 := [th-lemma arith triangle-eq]: #2681
+#2683 := [unit-resolution #2682 #2680]: #1974
+#2684 := [th-lemma arith farkas 1 -1 1 #2683 #2679 #2650]: false
+#2686 := [lemma #2684]: #2685
+#2755 := [unit-resolution #2686 #2750]: #2368
+#2250 := (or #2383 #2371 #2377)
+#2256 := [def-axiom]: #2250
+#2756 := [unit-resolution #2256 #2755 #2754]: #2377
+#2262 := (or #2374 #2362)
+#2251 := [def-axiom]: #2262
+#2757 := [unit-resolution #2251 #2756]: #2362
+#2507 := (= #67 #117)
+#2762 := (= #117 #67)
+#1988 := (or #2374 #486)
+#1989 := [def-axiom]: #1988
+#2758 := [unit-resolution #1989 #2756]: #486
+#2759 := [symm #2758]: #134
+#2763 := [monotonicity #2759]: #2762
+#2764 := [symm #2763]: #2507
+#2765 := (= f19 #67)
+#2263 := (or #2374 #489)
+#2267 := [def-axiom]: #2263
+#2760 := [unit-resolution #2267 #2756]: #489
+#2761 := [symm #2760]: #135
+#2766 := [trans #2761 #2751]: #2765
+#2767 := [trans #2766 #2764]: #370
+#2768 := [unit-resolution #2288 #2767]: #2356
+#2769 := [unit-resolution #1930 #2768 #2757]: #1717
+#2770 := [unit-resolution #2289 #2769]: #2293
+#1889 := (+ f13 #840)
+#2265 := (<= #1889 0::Int)
+#2771 := (or #495 #2265)
+#2772 := [th-lemma arith triangle-eq]: #2771
+#2773 := [unit-resolution #2772 #2760]: #2265
+#2774 := (not #2265)
+#2775 := (or #2664 #1446 #2774)
+#2776 := [th-lemma arith assign-bounds -1 -1]: #2775
+#2777 := [unit-resolution #2776 #2773 #2770]: #2664
+#2778 := [unit-resolution #1959 #2769]: #1248
+#2779 := [unit-resolution #2579 #2750 #2778 #2777]: #2549
+#2780 := [unit-resolution #2292 #2769]: #1429
+#1975 := (or #2374 #865)
+#2257 := [def-axiom]: #1975
+#2781 := [unit-resolution #2257 #2756]: #865
+#2782 := [unit-resolution #2682 #2781]: #1974
+#2741 := (not #1974)
+#2742 := (or #2599 #2741 #1424)
+#2737 := [hypothesis]: #1429
+#2738 := [hypothesis]: #2674
+#2739 := [hypothesis]: #1974
+#2740 := [th-lemma arith farkas 1 -1 1 #2739 #2738 #2737]: false
+#2743 := [lemma #2740]: #2742
+#2783 := [unit-resolution #2743 #2782 #2780]: #2599
+#2784 := [unit-resolution #2676 #2783 #2779]: #2623
+#2785 := [monotonicity #2784]: #2744
+#2786 := (not #2744)
+#2787 := (or #2786 #2747)
+#2788 := [th-lemma arith triangle-eq]: #2787
+#2789 := [unit-resolution #2788 #2785]: #2747
+#2261 := (or #2374 #882)
+#2258 := [def-axiom]: #2261
+#2790 := [unit-resolution #2258 #2756]: #882
+#2791 := [th-lemma arith farkas 1 -1 -1 1 #2790 #2770 #2773 #2789]: false
+#2792 := [lemma #2791]: #2415
+#2421 := (or #1525 #2418)
+#1595 := (forall (vars (?v0 Int)) #1592)
+#1781 := (or #1595 #1778)
+#1784 := (not #1781)
+#1787 := (or #304 #295 #286 #1657 #878 #790 #1784)
+#1790 := (not #1787)
+#1684 := (forall (vars (?v0 Int)) #1679)
+#1690 := (not #1684)
+#1691 := (or #370 #1690)
+#1692 := (not #1691)
+#1720 := (or #1692 #1717)
+#1728 := (not #1720)
+#1738 := (or #504 #495 #1657 #878 #1726 #1727 #869 #881 #1728)
+#1739 := (not #1738)
+#1729 := (or #456 #438 #429 #1657 #878 #1726 #1727 #869 #882 #1728)
+#1730 := (not #1729)
+#1744 := (or #1730 #1739)
+#1750 := (not #1744)
+#1751 := (or #1657 #878 #787 #1750)
+#1752 := (not #1751)
+#1796 := (or #1752 #1790)
+#1801 := (not #1796)
+#1570 := (forall (vars (?v0 Int)) #1565)
+#1764 := (not #1570)
+#1548 := (forall (vars (?v0 Int)) #1543)
+#1763 := (not #1548)
+#1804 := (or #591 #1657 #878 #1763 #1764 #1801)
+#1807 := (not #1804)
+#1810 := (or #1525 #1807)
+#2422 := (iff #1810 #2421)
+#2419 := (iff #1807 #2418)
+#2416 := (iff #1804 #2415)
+#2413 := (iff #1801 #2412)
+#2410 := (iff #1796 #2409)
+#2407 := (iff #1790 #2406)
+#2404 := (iff #1787 #2403)
+#2401 := (iff #1784 #2400)
+#2398 := (iff #1781 #2397)
+#2395 := (iff #1595 #2392)
+#2393 := (iff #1592 #1592)
+#2394 := [refl]: #2393
+#2396 := [quant-intro #2394]: #2395
+#2399 := [monotonicity #2396]: #2398
+#2402 := [monotonicity #2399]: #2401
+#2405 := [monotonicity #2402]: #2404
+#2408 := [monotonicity #2405]: #2407
+#2390 := (iff #1752 #2389)
+#2387 := (iff #1751 #2386)
+#2384 := (iff #1750 #2383)
+#2381 := (iff #1744 #2380)
+#2378 := (iff #1739 #2377)
+#2375 := (iff #1738 #2374)
+#2366 := (iff #1728 #2365)
+#2363 := (iff #1720 #2362)
+#2360 := (iff #1692 #2359)
+#2357 := (iff #1691 #2356)
+#2354 := (iff #1690 #2353)
+#2351 := (iff #1684 #2348)
+#2349 := (iff #1679 #1679)
+#2350 := [refl]: #2349
+#2352 := [quant-intro #2350]: #2351
+#2355 := [monotonicity #2352]: #2354
+#2358 := [monotonicity #2355]: #2357
+#2361 := [monotonicity #2358]: #2360
+#2364 := [monotonicity #2361]: #2363
+#2367 := [monotonicity #2364]: #2366
+#2376 := [monotonicity #2367]: #2375
+#2379 := [monotonicity #2376]: #2378
+#2372 := (iff #1730 #2371)
+#2369 := (iff #1729 #2368)
+#2370 := [monotonicity #2367]: #2369
+#2373 := [monotonicity #2370]: #2372
+#2382 := [monotonicity #2373 #2379]: #2381
+#2385 := [monotonicity #2382]: #2384
+#2388 := [monotonicity #2385]: #2387
+#2391 := [monotonicity #2388]: #2390
+#2411 := [monotonicity #2391 #2408]: #2410
+#2414 := [monotonicity #2411]: #2413
+#2346 := (iff #1764 #2345)
+#2343 := (iff #1570 #2340)
+#2341 := (iff #1565 #1565)
+#2342 := [refl]: #2341
+#2344 := [quant-intro #2342]: #2343
+#2347 := [monotonicity #2344]: #2346
+#2338 := (iff #1763 #2337)
+#2335 := (iff #1548 #2332)
+#2333 := (iff #1543 #1543)
+#2334 := [refl]: #2333
+#2336 := [quant-intro #2334]: #2335
+#2339 := [monotonicity #2336]: #2338
+#2417 := [monotonicity #2339 #2347 #2414]: #2416
 #2420 := [monotonicity #2417]: #2419
 #2423 := [monotonicity #2420]: #2422
-#2426 := [monotonicity #2423]: #2425
-#2429 := [monotonicity #2426]: #2428
-#2411 := (iff #1772 #2410)
-#2408 := (iff #1771 #2407)
-#2405 := (iff #1770 #2404)
-#2402 := (iff #1764 #2401)
-#2399 := (iff #1759 #2398)
-#2396 := (iff #1758 #2395)
-#2387 := (iff #1748 #2386)
-#2384 := (iff #1740 #2383)
-#2381 := (iff #1712 #2380)
-#2378 := (iff #1711 #2377)
-#2375 := (iff #1710 #2374)
-#2372 := (iff #1704 #2369)
-#2370 := (iff #1699 #1699)
-#2371 := [refl]: #2370
-#2373 := [quant-intro #2371]: #2372
-#2376 := [monotonicity #2373]: #2375
-#2379 := [monotonicity #2376]: #2378
-#2382 := [monotonicity #2379]: #2381
-#2385 := [monotonicity #2382]: #2384
-#2388 := [monotonicity #2385]: #2387
-#2397 := [monotonicity #2388]: #2396
-#2400 := [monotonicity #2397]: #2399
-#2393 := (iff #1750 #2392)
-#2390 := (iff #1749 #2389)
-#2391 := [monotonicity #2388]: #2390
-#2394 := [monotonicity #2391]: #2393
-#2403 := [monotonicity #2394 #2400]: #2402
-#2406 := [monotonicity #2403]: #2405
-#2409 := [monotonicity #2406]: #2408
-#2412 := [monotonicity #2409]: #2411
-#2432 := [monotonicity #2412 #2429]: #2431
-#2435 := [monotonicity #2432]: #2434
-#2367 := (iff #1784 #2366)
-#2364 := (iff #1590 #2361)
-#2362 := (iff #1585 #1585)
-#2363 := [refl]: #2362
-#2365 := [quant-intro #2363]: #2364
-#2368 := [monotonicity #2365]: #2367
-#2359 := (iff #1783 #2358)
-#2356 := (iff #1568 #2353)
-#2354 := (iff #1563 #1563)
-#2355 := [refl]: #2354
-#2357 := [quant-intro #2355]: #2356
-#2360 := [monotonicity #2357]: #2359
-#2438 := [monotonicity #2360 #2368 #2435]: #2437
-#2441 := [monotonicity #2438]: #2440
-#2444 := [monotonicity #2441]: #2443
-#1452 := (and #1268 #1449)
-#1455 := (not #1452)
-#1471 := (or #1455 #1466)
-#1474 := (not #1471)
-#1287 := (and #1277 #868)
-#1480 := (or #1287 #1474)
-#1504 := (and #506 #509 #751 #754 #837 #840 #885 #902 #1480)
-#1492 := (and #363 #368 #371 #751 #754 #837 #840 #885 #901 #1480)
-#1509 := (or #1492 #1504)
-#1515 := (and #751 #754 #810 #1509)
-#1387 := (and #1219 #1220)
-#1390 := (not #1387)
-#1406 := (or #1390 #1401)
-#1409 := (not #1406)
-#1198 := (not #1197)
-#1378 := (and #1198 #1199)
-#1381 := (not #1378)
-#1384 := (or #1375 #1381)
-#1412 := (and #1384 #1409)
-#1188 := (not #777)
-#1191 := (forall (vars (?v0 Int)) #1188)
-#1415 := (or #1191 #1412)
-#1421 := (and #262 #265 #268 #751 #754 #807 #1415)
-#1520 := (or #1421 #1515)
-#1526 := (and #259 #744 #751 #754 #1018 #1520)
-#1156 := (not #1155)
-#1348 := (and #1156 #1157)
-#1351 := (not #1348)
-#1357 := (or #1154 #1351)
-#1362 := (not #1357)
-#1531 := (or #1362 #1526)
-#1833 := (iff #1531 #1830)
-#1653 := (or #1218 #1638 #1401)
-#1665 := (or #1664 #1653)
-#1666 := (not #1665)
-#1671 := (or #1615 #1666)
-#1678 := (not #1671)
-#1679 := (or #324 #315 #306 #1677 #898 #810 #1678)
-#1680 := (not #1679)
-#1777 := (or #1680 #1772)
-#1785 := (not #1777)
-#1786 := (or #611 #1677 #898 #1783 #1784 #1785)
-#1787 := (not #1786)
-#1792 := (or #1545 #1787)
-#1831 := (iff #1792 #1830)
-#1828 := (iff #1787 #1827)
-#1825 := (iff #1786 #1824)
-#1822 := (iff #1785 #1821)
-#1819 := (iff #1777 #1816)
-#1813 := (or #1810 #1772)
-#1817 := (iff #1813 #1816)
-#1818 := [rewrite]: #1817
-#1814 := (iff #1777 #1813)
-#1811 := (iff #1680 #1810)
-#1808 := (iff #1679 #1807)
-#1805 := (iff #1678 #1804)
-#1802 := (iff #1671 #1801)
-#1799 := (iff #1666 #1798)
-#1796 := (iff #1665 #1795)
-#1797 := [rewrite]: #1796
-#1800 := [monotonicity #1797]: #1799
+#1432 := (and #1248 #1429)
+#1435 := (not #1432)
+#1451 := (or #1435 #1446)
+#1454 := (not #1451)
+#1267 := (and #1257 #848)
+#1460 := (or #1267 #1454)
+#1484 := (and #486 #489 #731 #734 #817 #820 #865 #882 #1460)
+#1472 := (and #343 #348 #351 #731 #734 #817 #820 #865 #881 #1460)
+#1489 := (or #1472 #1484)
+#1495 := (and #731 #734 #790 #1489)
+#1367 := (and #1199 #1200)
+#1370 := (not #1367)
+#1386 := (or #1370 #1381)
+#1389 := (not #1386)
+#1178 := (not #1177)
+#1358 := (and #1178 #1179)
+#1361 := (not #1358)
+#1364 := (or #1355 #1361)
+#1392 := (and #1364 #1389)
+#1168 := (not #757)
+#1171 := (forall (vars (?v0 Int)) #1168)
+#1395 := (or #1171 #1392)
+#1401 := (and #242 #245 #248 #731 #734 #787 #1395)
+#1500 := (or #1401 #1495)
+#1506 := (and #239 #724 #731 #734 #998 #1500)
+#1136 := (not #1135)
+#1328 := (and #1136 #1137)
+#1331 := (not #1328)
+#1337 := (or #1134 #1331)
+#1342 := (not #1337)
+#1511 := (or #1342 #1506)
+#1813 := (iff #1511 #1810)
+#1633 := (or #1198 #1618 #1381)
+#1645 := (or #1644 #1633)
+#1646 := (not #1645)
+#1651 := (or #1595 #1646)
+#1658 := (not #1651)
+#1659 := (or #304 #295 #286 #1657 #878 #790 #1658)
+#1660 := (not #1659)
+#1757 := (or #1660 #1752)
+#1765 := (not #1757)
+#1766 := (or #591 #1657 #878 #1763 #1764 #1765)
+#1767 := (not #1766)
+#1772 := (or #1525 #1767)
+#1811 := (iff #1772 #1810)
+#1808 := (iff #1767 #1807)
+#1805 := (iff #1766 #1804)
+#1802 := (iff #1765 #1801)
+#1799 := (iff #1757 #1796)
+#1793 := (or #1790 #1752)
+#1797 := (iff #1793 #1796)
+#1798 := [rewrite]: #1797
+#1794 := (iff #1757 #1793)
+#1791 := (iff #1660 #1790)
+#1788 := (iff #1659 #1787)
+#1785 := (iff #1658 #1784)
+#1782 := (iff #1651 #1781)
+#1779 := (iff #1646 #1778)
+#1776 := (iff #1645 #1775)
+#1777 := [rewrite]: #1776
+#1780 := [monotonicity #1777]: #1779
+#1783 := [monotonicity #1780]: #1782
+#1786 := [monotonicity #1783]: #1785
+#1789 := [monotonicity #1786]: #1788
+#1792 := [monotonicity #1789]: #1791
+#1795 := [monotonicity #1792]: #1794
+#1800 := [trans #1795 #1798]: #1799
 #1803 := [monotonicity #1800]: #1802
 #1806 := [monotonicity #1803]: #1805
 #1809 := [monotonicity #1806]: #1808
 #1812 := [monotonicity #1809]: #1811
-#1815 := [monotonicity #1812]: #1814
-#1820 := [trans #1815 #1818]: #1819
-#1823 := [monotonicity #1820]: #1822
-#1826 := [monotonicity #1823]: #1825
-#1829 := [monotonicity #1826]: #1828
-#1832 := [monotonicity #1829]: #1831
-#1793 := (iff #1531 #1792)
-#1790 := (iff #1526 #1787)
-#1780 := (and #259 #1568 #751 #754 #1590 #1777)
-#1788 := (iff #1780 #1787)
-#1789 := [rewrite]: #1788
-#1781 := (iff #1526 #1780)
-#1778 := (iff #1520 #1777)
-#1775 := (iff #1515 #1772)
-#1767 := (and #751 #754 #810 #1764)
-#1773 := (iff #1767 #1772)
-#1774 := [rewrite]: #1773
-#1768 := (iff #1515 #1767)
-#1765 := (iff #1509 #1764)
-#1762 := (iff #1504 #1759)
-#1755 := (and #506 #509 #751 #754 #837 #840 #885 #902 #1740)
-#1760 := (iff #1755 #1759)
-#1761 := [rewrite]: #1760
-#1756 := (iff #1504 #1755)
-#1741 := (iff #1480 #1740)
-#1738 := (iff #1474 #1737)
-#1735 := (iff #1471 #1732)
-#1718 := (or #1717 #1444)
-#1729 := (or #1718 #1466)
-#1733 := (iff #1729 #1732)
-#1734 := [rewrite]: #1733
-#1730 := (iff #1471 #1729)
-#1727 := (iff #1455 #1718)
-#1719 := (not #1718)
-#1722 := (not #1719)
-#1725 := (iff #1722 #1718)
-#1726 := [rewrite]: #1725
-#1723 := (iff #1455 #1722)
-#1720 := (iff #1452 #1719)
-#1721 := [rewrite]: #1720
-#1724 := [monotonicity #1721]: #1723
-#1728 := [trans #1724 #1726]: #1727
-#1731 := [monotonicity #1728]: #1730
-#1736 := [trans #1731 #1734]: #1735
-#1739 := [monotonicity #1736]: #1738
-#1715 := (iff #1287 #1712)
-#1707 := (and #1277 #1704)
-#1713 := (iff #1707 #1712)
+#1773 := (iff #1511 #1772)
+#1770 := (iff #1506 #1767)
+#1760 := (and #239 #1548 #731 #734 #1570 #1757)
+#1768 := (iff #1760 #1767)
+#1769 := [rewrite]: #1768
+#1761 := (iff #1506 #1760)
+#1758 := (iff #1500 #1757)
+#1755 := (iff #1495 #1752)
+#1747 := (and #731 #734 #790 #1744)
+#1753 := (iff #1747 #1752)
+#1754 := [rewrite]: #1753
+#1748 := (iff #1495 #1747)
+#1745 := (iff #1489 #1744)
+#1742 := (iff #1484 #1739)
+#1735 := (and #486 #489 #731 #734 #817 #820 #865 #882 #1720)
+#1740 := (iff #1735 #1739)
+#1741 := [rewrite]: #1740
+#1736 := (iff #1484 #1735)
+#1721 := (iff #1460 #1720)
+#1718 := (iff #1454 #1717)
+#1715 := (iff #1451 #1712)
+#1698 := (or #1697 #1424)
+#1709 := (or #1698 #1446)
+#1713 := (iff #1709 #1712)
 #1714 := [rewrite]: #1713
-#1708 := (iff #1287 #1707)
-#1705 := (iff #868 #1704)
-#1702 := (iff #865 #1699)
-#1685 := (or #1548 #848)
-#1696 := (or #1685 #862)
-#1700 := (iff #1696 #1699)
+#1710 := (iff #1451 #1709)
+#1707 := (iff #1435 #1698)
+#1699 := (not #1698)
+#1702 := (not #1699)
+#1705 := (iff #1702 #1698)
+#1706 := [rewrite]: #1705
+#1703 := (iff #1435 #1702)
+#1700 := (iff #1432 #1699)
 #1701 := [rewrite]: #1700
-#1697 := (iff #865 #1696)
-#1694 := (iff #857 #1685)
-#1686 := (not #1685)
-#1689 := (not #1686)
-#1692 := (iff #1689 #1685)
-#1693 := [rewrite]: #1692
-#1690 := (iff #857 #1689)
-#1687 := (iff #854 #1686)
-#1688 := [rewrite]: #1687
-#1691 := [monotonicity #1688]: #1690
-#1695 := [trans #1691 #1693]: #1694
-#1698 := [monotonicity #1695]: #1697
-#1703 := [trans #1698 #1701]: #1702
-#1706 := [quant-intro #1703]: #1705
-#1709 := [monotonicity #1706]: #1708
-#1716 := [trans #1709 #1714]: #1715
-#1742 := [monotonicity #1716 #1739]: #1741
-#1757 := [monotonicity #1742]: #1756
-#1763 := [trans #1757 #1761]: #1762
-#1753 := (iff #1492 #1750)
-#1743 := (and #363 #368 #371 #751 #754 #837 #840 #885 #901 #1740)
-#1751 := (iff #1743 #1750)
-#1752 := [rewrite]: #1751
-#1744 := (iff #1492 #1743)
-#1745 := [monotonicity #1742]: #1744
-#1754 := [trans #1745 #1752]: #1753
-#1766 := [monotonicity #1754 #1763]: #1765
-#1769 := [monotonicity #1766]: #1768
-#1776 := [trans #1769 #1774]: #1775
-#1683 := (iff #1421 #1680)
-#1674 := (and #262 #265 #268 #751 #754 #807 #1671)
-#1681 := (iff #1674 #1680)
-#1682 := [rewrite]: #1681
-#1675 := (iff #1421 #1674)
-#1672 := (iff #1415 #1671)
-#1669 := (iff #1412 #1666)
-#1658 := (not #1653)
-#1661 := (and #1633 #1658)
-#1667 := (iff #1661 #1666)
+#1704 := [monotonicity #1701]: #1703
+#1708 := [trans #1704 #1706]: #1707
+#1711 := [monotonicity #1708]: #1710
+#1716 := [trans #1711 #1714]: #1715
+#1719 := [monotonicity #1716]: #1718
+#1695 := (iff #1267 #1692)
+#1687 := (and #1257 #1684)
+#1693 := (iff #1687 #1692)
+#1694 := [rewrite]: #1693
+#1688 := (iff #1267 #1687)
+#1685 := (iff #848 #1684)
+#1682 := (iff #845 #1679)
+#1665 := (or #1528 #828)
+#1676 := (or #1665 #842)
+#1680 := (iff #1676 #1679)
+#1681 := [rewrite]: #1680
+#1677 := (iff #845 #1676)
+#1674 := (iff #837 #1665)
+#1666 := (not #1665)
+#1669 := (not #1666)
+#1672 := (iff #1669 #1665)
+#1673 := [rewrite]: #1672
+#1670 := (iff #837 #1669)
+#1667 := (iff #834 #1666)
 #1668 := [rewrite]: #1667
-#1662 := (iff #1412 #1661)
-#1659 := (iff #1409 #1658)
-#1656 := (iff #1406 #1653)
-#1639 := (or #1218 #1638)
-#1650 := (or #1639 #1401)
-#1654 := (iff #1650 #1653)
-#1655 := [rewrite]: #1654
-#1651 := (iff #1406 #1650)
-#1648 := (iff #1390 #1639)
-#1640 := (not #1639)
-#1643 := (not #1640)
-#1646 := (iff #1643 #1639)
-#1647 := [rewrite]: #1646
-#1644 := (iff #1390 #1643)
-#1641 := (iff #1387 #1640)
-#1642 := [rewrite]: #1641
-#1645 := [monotonicity #1642]: #1644
-#1649 := [trans #1645 #1647]: #1648
-#1652 := [monotonicity #1649]: #1651
-#1657 := [trans #1652 #1655]: #1656
-#1660 := [monotonicity #1657]: #1659
-#1636 := (iff #1384 #1633)
-#1619 := (or #1197 #1618)
-#1630 := (or #1375 #1619)
+#1671 := [monotonicity #1668]: #1670
+#1675 := [trans #1671 #1673]: #1674
+#1678 := [monotonicity #1675]: #1677
+#1683 := [trans #1678 #1681]: #1682
+#1686 := [quant-intro #1683]: #1685
+#1689 := [monotonicity #1686]: #1688
+#1696 := [trans #1689 #1694]: #1695
+#1722 := [monotonicity #1696 #1719]: #1721
+#1737 := [monotonicity #1722]: #1736
+#1743 := [trans #1737 #1741]: #1742
+#1733 := (iff #1472 #1730)
+#1723 := (and #343 #348 #351 #731 #734 #817 #820 #865 #881 #1720)
+#1731 := (iff #1723 #1730)
+#1732 := [rewrite]: #1731
+#1724 := (iff #1472 #1723)
+#1725 := [monotonicity #1722]: #1724
+#1734 := [trans #1725 #1732]: #1733
+#1746 := [monotonicity #1734 #1743]: #1745
+#1749 := [monotonicity #1746]: #1748
+#1756 := [trans #1749 #1754]: #1755
+#1663 := (iff #1401 #1660)
+#1654 := (and #242 #245 #248 #731 #734 #787 #1651)
+#1661 := (iff #1654 #1660)
+#1662 := [rewrite]: #1661
+#1655 := (iff #1401 #1654)
+#1652 := (iff #1395 #1651)
+#1649 := (iff #1392 #1646)
+#1638 := (not #1633)
+#1641 := (and #1613 #1638)
+#1647 := (iff #1641 #1646)
+#1648 := [rewrite]: #1647
+#1642 := (iff #1392 #1641)
+#1639 := (iff #1389 #1638)
+#1636 := (iff #1386 #1633)
+#1619 := (or #1198 #1618)
+#1630 := (or #1619 #1381)
 #1634 := (iff #1630 #1633)
 #1635 := [rewrite]: #1634
-#1631 := (iff #1384 #1630)
-#1628 := (iff #1381 #1619)
+#1631 := (iff #1386 #1630)
+#1628 := (iff #1370 #1619)
 #1620 := (not #1619)
 #1623 := (not #1620)
 #1626 := (iff #1623 #1619)
 #1627 := [rewrite]: #1626
-#1624 := (iff #1381 #1623)
-#1621 := (iff #1378 #1620)
+#1624 := (iff #1370 #1623)
+#1621 := (iff #1367 #1620)
 #1622 := [rewrite]: #1621
 #1625 := [monotonicity #1622]: #1624
 #1629 := [trans #1625 #1627]: #1628
 #1632 := [monotonicity #1629]: #1631
 #1637 := [trans #1632 #1635]: #1636
-#1663 := [monotonicity #1637 #1660]: #1662
-#1670 := [trans #1663 #1668]: #1669
-#1616 := (iff #1191 #1615)
-#1613 := (iff #1188 #1612)
-#1610 := (iff #777 #1607)
-#1593 := (or #1548 #764)
-#1604 := (or #85 #1593)
-#1608 := (iff #1604 #1607)
-#1609 := [rewrite]: #1608
-#1605 := (iff #777 #1604)
-#1602 := (iff #771 #1593)
-#1594 := (not #1593)
-#1597 := (not #1594)
-#1600 := (iff #1597 #1593)
-#1601 := [rewrite]: #1600
-#1598 := (iff #771 #1597)
-#1595 := (iff #768 #1594)
-#1596 := [rewrite]: #1595
-#1599 := [monotonicity #1596]: #1598
-#1603 := [trans #1599 #1601]: #1602
-#1606 := [monotonicity #1603]: #1605
-#1611 := [trans #1606 #1609]: #1610
-#1614 := [monotonicity #1611]: #1613
-#1617 := [quant-intro #1614]: #1616
-#1673 := [monotonicity #1617 #1670]: #1672
-#1676 := [monotonicity #1673]: #1675
-#1684 := [trans #1676 #1682]: #1683
-#1779 := [monotonicity #1684 #1776]: #1778
-#1591 := (iff #1018 #1590)
-#1588 := (iff #1015 #1585)
-#1571 := (or #1548 #999)
-#1582 := (or #1571 #1012)
-#1586 := (iff #1582 #1585)
-#1587 := [rewrite]: #1586
-#1583 := (iff #1015 #1582)
-#1580 := (iff #1007 #1571)
-#1572 := (not #1571)
-#1575 := (not #1572)
-#1578 := (iff #1575 #1571)
-#1579 := [rewrite]: #1578
-#1576 := (iff #1007 #1575)
-#1573 := (iff #1004 #1572)
-#1574 := [rewrite]: #1573
-#1577 := [monotonicity #1574]: #1576
-#1581 := [trans #1577 #1579]: #1580
-#1584 := [monotonicity #1581]: #1583
-#1589 := [trans #1584 #1587]: #1588
-#1592 := [quant-intro #1589]: #1591
-#1569 := (iff #744 #1568)
-#1566 := (iff #741 #1563)
-#1549 := (or #1548 #727)
-#1560 := (or #1549 #737)
-#1564 := (iff #1560 #1563)
-#1565 := [rewrite]: #1564
-#1561 := (iff #741 #1560)
-#1558 := (iff #732 #1549)
-#1550 := (not #1549)
-#1553 := (not #1550)
-#1556 := (iff #1553 #1549)
-#1557 := [rewrite]: #1556
-#1554 := (iff #732 #1553)
-#1551 := (iff #729 #1550)
-#1552 := [rewrite]: #1551
-#1555 := [monotonicity #1552]: #1554
-#1559 := [trans #1555 #1557]: #1558
-#1562 := [monotonicity #1559]: #1561
-#1567 := [trans #1562 #1565]: #1566
-#1570 := [quant-intro #1567]: #1569
-#1782 := [monotonicity #1570 #1592 #1779]: #1781
-#1791 := [trans #1782 #1789]: #1790
-#1546 := (iff #1362 #1545)
-#1543 := (iff #1357 #1540)
-#1229 := (or #1155 #1228)
-#1537 := (or #1154 #1229)
-#1541 := (iff #1537 #1540)
-#1542 := [rewrite]: #1541
-#1538 := (iff #1357 #1537)
-#1535 := (iff #1351 #1229)
-#1164 := (not #1229)
-#1276 := (not #1164)
-#1347 := (iff #1276 #1229)
-#1534 := [rewrite]: #1347
-#1207 := (iff #1351 #1276)
-#1165 := (iff #1348 #1164)
-#1275 := [rewrite]: #1165
-#1208 := [monotonicity #1275]: #1207
-#1536 := [trans #1208 #1534]: #1535
-#1539 := [monotonicity #1536]: #1538
-#1544 := [trans #1539 #1542]: #1543
-#1547 := [monotonicity #1544]: #1546
-#1794 := [monotonicity #1547 #1791]: #1793
-#1834 := [trans #1794 #1832]: #1833
-#1298 := (not #895)
-#1295 := (not #889)
-#1263 := (+ #1262 #860)
-#1264 := (<= #1263 0::Int)
-#1265 := (+ ?v0!3 #849)
-#1266 := (>= #1265 0::Int)
-#1267 := (not #1266)
-#1269 := (and #1268 #1267)
-#1270 := (not #1269)
-#1271 := (or #1270 #1264)
-#1272 := (not #1271)
-#1291 := (or #1272 #1287)
-#1258 := (not #845)
-#1176 := (not #759)
-#1310 := (not #515)
-#1307 := (not #524)
-#1315 := (and #1307 #1310 #1176 #1258 #1291 #1295 #1298 #907)
-#1255 := (not #898)
-#1252 := (not #449)
-#1249 := (not #458)
-#1246 := (not #476)
-#1303 := (and #1246 #1249 #1252 #1255 #1176 #1258 #1291 #1295 #1298 #901)
-#1319 := (or #1303 #1315)
-#1323 := (and #1176 #810 #1319)
-#1214 := (+ #1213 #788)
-#1215 := (<= #1214 0::Int)
-#1221 := (and #1220 #1219)
-#1222 := (not #1221)
-#1223 := (or #1222 #1215)
-#1224 := (not #1223)
-#1200 := (and #1199 #1198)
-#1201 := (not #1200)
-#1203 := (= #1202 f20)
-#1204 := (or #1203 #1201)
-#1230 := (and #1204 #1224)
-#1234 := (or #1191 #1230)
-#1185 := (not #306)
-#1182 := (not #315)
-#1179 := (not #324)
-#1240 := (and #1179 #1182 #1185 #1176 #1234 #975)
-#1327 := (or #1240 #1323)
-#1166 := (not #611)
-#1338 := (and #1166 #744 #1176 #1327 #1018)
-#1158 := (and #1157 #1156)
-#1159 := (not #1158)
-#1160 := (or #1159 #1154)
-#1161 := (not #1160)
-#1342 := (or #1161 #1338)
-#1532 := (iff #1342 #1531)
-#1529 := (iff #1338 #1526)
-#1523 := (and #259 #744 #756 #1520 #1018)
-#1527 := (iff #1523 #1526)
-#1528 := [rewrite]: #1527
-#1524 := (iff #1338 #1523)
-#1521 := (iff #1327 #1520)
-#1518 := (iff #1323 #1515)
-#1512 := (and #756 #810 #1509)
-#1516 := (iff #1512 #1515)
-#1517 := [rewrite]: #1516
-#1513 := (iff #1323 #1512)
-#1510 := (iff #1319 #1509)
-#1507 := (iff #1315 #1504)
-#1501 := (and #506 #509 #756 #842 #1480 #885 #892 #902)
-#1505 := (iff #1501 #1504)
-#1506 := [rewrite]: #1505
-#1502 := (iff #1315 #1501)
-#1487 := (iff #1298 #892)
-#1488 := [rewrite]: #1487
-#1485 := (iff #1295 #885)
+#1640 := [monotonicity #1637]: #1639
+#1616 := (iff #1364 #1613)
+#1599 := (or #1177 #1598)
+#1610 := (or #1355 #1599)
+#1614 := (iff #1610 #1613)
+#1615 := [rewrite]: #1614
+#1611 := (iff #1364 #1610)
+#1608 := (iff #1361 #1599)
+#1600 := (not #1599)
+#1603 := (not #1600)
+#1606 := (iff #1603 #1599)
+#1607 := [rewrite]: #1606
+#1604 := (iff #1361 #1603)
+#1601 := (iff #1358 #1600)
+#1602 := [rewrite]: #1601
+#1605 := [monotonicity #1602]: #1604
+#1609 := [trans #1605 #1607]: #1608
+#1612 := [monotonicity #1609]: #1611
+#1617 := [trans #1612 #1615]: #1616
+#1643 := [monotonicity #1617 #1640]: #1642
+#1650 := [trans #1643 #1648]: #1649
+#1596 := (iff #1171 #1595)
+#1593 := (iff #1168 #1592)
+#1590 := (iff #757 #1587)
+#1573 := (or #1528 #744)
+#1584 := (or #78 #1573)
+#1588 := (iff #1584 #1587)
+#1589 := [rewrite]: #1588
+#1585 := (iff #757 #1584)
+#1582 := (iff #751 #1573)
+#1574 := (not #1573)
+#1577 := (not #1574)
+#1580 := (iff #1577 #1573)
+#1581 := [rewrite]: #1580
+#1578 := (iff #751 #1577)
+#1575 := (iff #748 #1574)
+#1576 := [rewrite]: #1575
+#1579 := [monotonicity #1576]: #1578
+#1583 := [trans #1579 #1581]: #1582
+#1586 := [monotonicity #1583]: #1585
+#1591 := [trans #1586 #1589]: #1590
+#1594 := [monotonicity #1591]: #1593
+#1597 := [quant-intro #1594]: #1596
+#1653 := [monotonicity #1597 #1650]: #1652
+#1656 := [monotonicity #1653]: #1655
+#1664 := [trans #1656 #1662]: #1663
+#1759 := [monotonicity #1664 #1756]: #1758
+#1571 := (iff #998 #1570)
+#1568 := (iff #995 #1565)
+#1551 := (or #1528 #979)
+#1562 := (or #1551 #992)
+#1566 := (iff #1562 #1565)
+#1567 := [rewrite]: #1566
+#1563 := (iff #995 #1562)
+#1560 := (iff #987 #1551)
+#1552 := (not #1551)
+#1555 := (not #1552)
+#1558 := (iff #1555 #1551)
+#1559 := [rewrite]: #1558
+#1556 := (iff #987 #1555)
+#1553 := (iff #984 #1552)
+#1554 := [rewrite]: #1553
+#1557 := [monotonicity #1554]: #1556
+#1561 := [trans #1557 #1559]: #1560
+#1564 := [monotonicity #1561]: #1563
+#1569 := [trans #1564 #1567]: #1568
+#1572 := [quant-intro #1569]: #1571
+#1549 := (iff #724 #1548)
+#1546 := (iff #721 #1543)
+#1529 := (or #1528 #707)
+#1540 := (or #1529 #717)
+#1544 := (iff #1540 #1543)
+#1545 := [rewrite]: #1544
+#1541 := (iff #721 #1540)
+#1538 := (iff #712 #1529)
+#1530 := (not #1529)
+#1533 := (not #1530)
+#1536 := (iff #1533 #1529)
+#1537 := [rewrite]: #1536
+#1534 := (iff #712 #1533)
+#1531 := (iff #709 #1530)
+#1532 := [rewrite]: #1531
+#1535 := [monotonicity #1532]: #1534
+#1539 := [trans #1535 #1537]: #1538
+#1542 := [monotonicity #1539]: #1541
+#1547 := [trans #1542 #1545]: #1546
+#1550 := [quant-intro #1547]: #1549
+#1762 := [monotonicity #1550 #1572 #1759]: #1761
+#1771 := [trans #1762 #1769]: #1770
+#1526 := (iff #1342 #1525)
+#1523 := (iff #1337 #1520)
+#1145 := (or #1135 #1144)
+#1517 := (or #1134 #1145)
+#1521 := (iff #1517 #1520)
+#1522 := [rewrite]: #1521
+#1518 := (iff #1337 #1517)
+#1515 := (iff #1331 #1145)
+#1255 := (not #1145)
+#1188 := (not #1255)
+#1327 := (iff #1188 #1145)
+#1514 := [rewrite]: #1327
+#1208 := (iff #1331 #1188)
+#1256 := (iff #1328 #1255)
+#1187 := [rewrite]: #1256
+#1209 := [monotonicity #1187]: #1208
+#1516 := [trans #1209 #1514]: #1515
+#1519 := [monotonicity #1516]: #1518
+#1524 := [trans #1519 #1522]: #1523
+#1527 := [monotonicity #1524]: #1526
+#1774 := [monotonicity #1527 #1771]: #1773
+#1814 := [trans #1774 #1812]: #1813
+#1278 := (not #875)
+#1275 := (not #869)
+#1243 := (+ #1242 #840)
+#1244 := (<= #1243 0::Int)
+#1245 := (+ ?v0!3 #829)
+#1246 := (>= #1245 0::Int)
+#1247 := (not #1246)
+#1249 := (and #1248 #1247)
+#1250 := (not #1249)
+#1251 := (or #1250 #1244)
+#1252 := (not #1251)
+#1271 := (or #1252 #1267)
+#1238 := (not #825)
+#1156 := (not #739)
+#1290 := (not #495)
+#1287 := (not #504)
+#1295 := (and #1287 #1290 #1156 #1238 #1271 #1275 #1278 #887)
+#1235 := (not #878)
+#1232 := (not #429)
+#1229 := (not #438)
+#1226 := (not #456)
+#1283 := (and #1226 #1229 #1232 #1235 #1156 #1238 #1271 #1275 #1278 #881)
+#1299 := (or #1283 #1295)
+#1303 := (and #1156 #790 #1299)
+#1194 := (+ #1193 #768)
+#1195 := (<= #1194 0::Int)
+#1201 := (and #1200 #1199)
+#1202 := (not #1201)
+#1203 := (or #1202 #1195)
+#1204 := (not #1203)
+#1180 := (and #1179 #1178)
+#1181 := (not #1180)
+#1183 := (= #1182 f15)
+#1184 := (or #1183 #1181)
+#1210 := (and #1184 #1204)
+#1214 := (or #1171 #1210)
+#1165 := (not #286)
+#1162 := (not #295)
+#1159 := (not #304)
+#1220 := (and #1159 #1162 #1165 #1156 #1214 #955)
+#1307 := (or #1220 #1303)
+#1146 := (not #591)
+#1318 := (and #1146 #724 #1156 #1307 #998)
+#1138 := (and #1137 #1136)
+#1139 := (not #1138)
+#1140 := (or #1139 #1134)
+#1141 := (not #1140)
+#1322 := (or #1141 #1318)
+#1512 := (iff #1322 #1511)
+#1509 := (iff #1318 #1506)
+#1503 := (and #239 #724 #736 #1500 #998)
+#1507 := (iff #1503 #1506)
+#1508 := [rewrite]: #1507
+#1504 := (iff #1318 #1503)
+#1501 := (iff #1307 #1500)
+#1498 := (iff #1303 #1495)
+#1492 := (and #736 #790 #1489)
+#1496 := (iff #1492 #1495)
+#1497 := [rewrite]: #1496
+#1493 := (iff #1303 #1492)
+#1490 := (iff #1299 #1489)
+#1487 := (iff #1295 #1484)
+#1481 := (and #486 #489 #736 #822 #1460 #865 #872 #882)
+#1485 := (iff #1481 #1484)
 #1486 := [rewrite]: #1485
-#1483 := (iff #1291 #1480)
-#1477 := (or #1474 #1287)
-#1481 := (iff #1477 #1480)
-#1482 := [rewrite]: #1481
-#1478 := (iff #1291 #1477)
-#1475 := (iff #1272 #1474)
-#1472 := (iff #1271 #1471)
-#1469 := (iff #1264 #1466)
-#1458 := (+ #860 #1262)
-#1461 := (<= #1458 0::Int)
-#1467 := (iff #1461 #1466)
+#1482 := (iff #1295 #1481)
+#1467 := (iff #1278 #872)
 #1468 := [rewrite]: #1467
-#1462 := (iff #1264 #1461)
-#1459 := (= #1263 #1458)
-#1460 := [rewrite]: #1459
-#1463 := [monotonicity #1460]: #1462
-#1470 := [trans #1463 #1468]: #1469
-#1456 := (iff #1270 #1455)
-#1453 := (iff #1269 #1452)
-#1450 := (iff #1267 #1449)
-#1447 := (iff #1266 #1444)
-#1436 := (+ #849 ?v0!3)
-#1439 := (>= #1436 0::Int)
-#1445 := (iff #1439 #1444)
-#1446 := [rewrite]: #1445
-#1440 := (iff #1266 #1439)
-#1437 := (= #1265 #1436)
-#1438 := [rewrite]: #1437
-#1441 := [monotonicity #1438]: #1440
-#1448 := [trans #1441 #1446]: #1447
-#1451 := [monotonicity #1448]: #1450
-#1454 := [monotonicity #1451]: #1453
-#1457 := [monotonicity #1454]: #1456
-#1473 := [monotonicity #1457 #1470]: #1472
-#1476 := [monotonicity #1473]: #1475
-#1479 := [monotonicity #1476]: #1478
-#1484 := [trans #1479 #1482]: #1483
-#1434 := (iff #1258 #842)
-#1435 := [rewrite]: #1434
-#1367 := (iff #1176 #756)
-#1368 := [rewrite]: #1367
-#1499 := (iff #1310 #509)
-#1500 := [rewrite]: #1499
-#1497 := (iff #1307 #506)
-#1498 := [rewrite]: #1497
-#1503 := [monotonicity #1498 #1500 #1368 #1435 #1484 #1486 #1488 #911]: #1502
-#1508 := [trans #1503 #1506]: #1507
-#1495 := (iff #1303 #1492)
-#1489 := (and #363 #368 #371 #754 #756 #842 #1480 #885 #892 #901)
-#1493 := (iff #1489 #1492)
-#1494 := [rewrite]: #1493
-#1490 := (iff #1303 #1489)
-#1432 := (iff #1255 #754)
-#1433 := [rewrite]: #1432
-#1430 := (iff #1252 #371)
-#1431 := [rewrite]: #1430
-#1428 := (iff #1249 #368)
-#1429 := [rewrite]: #1428
-#1426 := (iff #1246 #363)
-#1427 := [rewrite]: #1426
-#1491 := [monotonicity #1427 #1429 #1431 #1433 #1368 #1435 #1484 #1486 #1488]: #1490
-#1496 := [trans #1491 #1494]: #1495
-#1511 := [monotonicity #1496 #1508]: #1510
-#1514 := [monotonicity #1368 #1511]: #1513
-#1519 := [trans #1514 #1517]: #1518
-#1424 := (iff #1240 #1421)
-#1418 := (and #262 #265 #268 #756 #1415 #807)
-#1422 := (iff #1418 #1421)
-#1423 := [rewrite]: #1422
-#1419 := (iff #1240 #1418)
-#1416 := (iff #1234 #1415)
-#1413 := (iff #1230 #1412)
-#1410 := (iff #1224 #1409)
-#1407 := (iff #1223 #1406)
-#1404 := (iff #1215 #1401)
-#1393 := (+ #788 #1213)
-#1396 := (<= #1393 0::Int)
-#1402 := (iff #1396 #1401)
+#1465 := (iff #1275 #865)
+#1466 := [rewrite]: #1465
+#1463 := (iff #1271 #1460)
+#1457 := (or #1454 #1267)
+#1461 := (iff #1457 #1460)
+#1462 := [rewrite]: #1461
+#1458 := (iff #1271 #1457)
+#1455 := (iff #1252 #1454)
+#1452 := (iff #1251 #1451)
+#1449 := (iff #1244 #1446)
+#1438 := (+ #840 #1242)
+#1441 := (<= #1438 0::Int)
+#1447 := (iff #1441 #1446)
+#1448 := [rewrite]: #1447
+#1442 := (iff #1244 #1441)
+#1439 := (= #1243 #1438)
+#1440 := [rewrite]: #1439
+#1443 := [monotonicity #1440]: #1442
+#1450 := [trans #1443 #1448]: #1449
+#1436 := (iff #1250 #1435)
+#1433 := (iff #1249 #1432)
+#1430 := (iff #1247 #1429)
+#1427 := (iff #1246 #1424)
+#1416 := (+ #829 ?v0!3)
+#1419 := (>= #1416 0::Int)
+#1425 := (iff #1419 #1424)
+#1426 := [rewrite]: #1425
+#1420 := (iff #1246 #1419)
+#1417 := (= #1245 #1416)
+#1418 := [rewrite]: #1417
+#1421 := [monotonicity #1418]: #1420
+#1428 := [trans #1421 #1426]: #1427
+#1431 := [monotonicity #1428]: #1430
+#1434 := [monotonicity #1431]: #1433
+#1437 := [monotonicity #1434]: #1436
+#1453 := [monotonicity #1437 #1450]: #1452
+#1456 := [monotonicity #1453]: #1455
+#1459 := [monotonicity #1456]: #1458
+#1464 := [trans #1459 #1462]: #1463
+#1414 := (iff #1238 #822)
+#1415 := [rewrite]: #1414
+#1347 := (iff #1156 #736)
+#1348 := [rewrite]: #1347
+#1479 := (iff #1290 #489)
+#1480 := [rewrite]: #1479
+#1477 := (iff #1287 #486)
+#1478 := [rewrite]: #1477
+#1483 := [monotonicity #1478 #1480 #1348 #1415 #1464 #1466 #1468 #891]: #1482
+#1488 := [trans #1483 #1486]: #1487
+#1475 := (iff #1283 #1472)
+#1469 := (and #343 #348 #351 #734 #736 #822 #1460 #865 #872 #881)
+#1473 := (iff #1469 #1472)
+#1474 := [rewrite]: #1473
+#1470 := (iff #1283 #1469)
+#1412 := (iff #1235 #734)
+#1413 := [rewrite]: #1412
+#1410 := (iff #1232 #351)
+#1411 := [rewrite]: #1410
+#1408 := (iff #1229 #348)
+#1409 := [rewrite]: #1408
+#1406 := (iff #1226 #343)
+#1407 := [rewrite]: #1406
+#1471 := [monotonicity #1407 #1409 #1411 #1413 #1348 #1415 #1464 #1466 #1468]: #1470
+#1476 := [trans #1471 #1474]: #1475
+#1491 := [monotonicity #1476 #1488]: #1490
+#1494 := [monotonicity #1348 #1491]: #1493
+#1499 := [trans #1494 #1497]: #1498
+#1404 := (iff #1220 #1401)
+#1398 := (and #242 #245 #248 #736 #1395 #787)
+#1402 := (iff #1398 #1401)
 #1403 := [rewrite]: #1402
-#1397 := (iff #1215 #1396)
-#1394 := (= #1214 #1393)
-#1395 := [rewrite]: #1394
-#1398 := [monotonicity #1395]: #1397
-#1405 := [trans #1398 #1403]: #1404
-#1391 := (iff #1222 #1390)
-#1388 := (iff #1221 #1387)
-#1389 := [rewrite]: #1388
-#1392 := [monotonicity #1389]: #1391
-#1408 := [monotonicity #1392 #1405]: #1407
-#1411 := [monotonicity #1408]: #1410
-#1385 := (iff #1204 #1384)
-#1382 := (iff #1201 #1381)
-#1379 := (iff #1200 #1378)
-#1380 := [rewrite]: #1379
-#1383 := [monotonicity #1380]: #1382
-#1376 := (iff #1203 #1375)
-#1377 := [rewrite]: #1376
-#1386 := [monotonicity #1377 #1383]: #1385
-#1414 := [monotonicity #1386 #1411]: #1413
-#1417 := [monotonicity #1414]: #1416
-#1373 := (iff #1185 #268)
-#1374 := [rewrite]: #1373
-#1371 := (iff #1182 #265)
-#1372 := [rewrite]: #1371
-#1369 := (iff #1179 #262)
-#1370 := [rewrite]: #1369
-#1420 := [monotonicity #1370 #1372 #1374 #1368 #1417 #979]: #1419
-#1425 := [trans #1420 #1423]: #1424
-#1522 := [monotonicity #1425 #1519]: #1521
-#1365 := (iff #1166 #259)
-#1366 := [rewrite]: #1365
-#1525 := [monotonicity #1366 #1368 #1522]: #1524
-#1530 := [trans #1525 #1528]: #1529
-#1363 := (iff #1161 #1362)
-#1360 := (iff #1160 #1357)
-#1354 := (or #1351 #1154)
-#1358 := (iff #1354 #1357)
-#1359 := [rewrite]: #1358
-#1355 := (iff #1160 #1354)
-#1352 := (iff #1159 #1351)
-#1349 := (iff #1158 #1348)
+#1399 := (iff #1220 #1398)
+#1396 := (iff #1214 #1395)
+#1393 := (iff #1210 #1392)
+#1390 := (iff #1204 #1389)
+#1387 := (iff #1203 #1386)
+#1384 := (iff #1195 #1381)
+#1373 := (+ #768 #1193)
+#1376 := (<= #1373 0::Int)
+#1382 := (iff #1376 #1381)
+#1383 := [rewrite]: #1382
+#1377 := (iff #1195 #1376)
+#1374 := (= #1194 #1373)
+#1375 := [rewrite]: #1374
+#1378 := [monotonicity #1375]: #1377
+#1385 := [trans #1378 #1383]: #1384
+#1371 := (iff #1202 #1370)
+#1368 := (iff #1201 #1367)
+#1369 := [rewrite]: #1368
+#1372 := [monotonicity #1369]: #1371
+#1388 := [monotonicity #1372 #1385]: #1387
+#1391 := [monotonicity #1388]: #1390
+#1365 := (iff #1184 #1364)
+#1362 := (iff #1181 #1361)
+#1359 := (iff #1180 #1358)
+#1360 := [rewrite]: #1359
+#1363 := [monotonicity #1360]: #1362
+#1356 := (iff #1183 #1355)
+#1357 := [rewrite]: #1356
+#1366 := [monotonicity #1357 #1363]: #1365
+#1394 := [monotonicity #1366 #1391]: #1393
+#1397 := [monotonicity #1394]: #1396
+#1353 := (iff #1165 #248)
+#1354 := [rewrite]: #1353
+#1351 := (iff #1162 #245)
+#1352 := [rewrite]: #1351
+#1349 := (iff #1159 #242)
 #1350 := [rewrite]: #1349
-#1353 := [monotonicity #1350]: #1352
-#1356 := [monotonicity #1353]: #1355
-#1361 := [trans #1356 #1359]: #1360
-#1364 := [monotonicity #1361]: #1363
-#1533 := [monotonicity #1364 #1530]: #1532
-#1125 := (or #611 #747 #759 #996 #1021)
-#1130 := (and #744 #1125)
-#1133 := (not #1130)
-#1343 := (~ #1133 #1342)
-#1339 := (not #1125)
-#1340 := (~ #1339 #1338)
-#1335 := (not #1021)
-#1336 := (~ #1335 #1018)
-#1333 := (~ #1018 #1018)
-#1331 := (~ #1015 #1015)
-#1332 := [refl]: #1331
-#1334 := [nnf-pos #1332]: #1333
-#1337 := [nnf-neg #1334]: #1336
-#1328 := (not #996)
-#1329 := (~ #1328 #1327)
-#1324 := (not #991)
-#1325 := (~ #1324 #1323)
-#1320 := (not #970)
-#1321 := (~ #1320 #1319)
-#1316 := (not #965)
-#1317 := (~ #1316 #1315)
-#1313 := (~ #907 #907)
-#1314 := [refl]: #1313
-#1299 := (~ #1298 #1298)
-#1300 := [refl]: #1299
-#1296 := (~ #1295 #1295)
-#1297 := [refl]: #1296
-#1292 := (not #882)
-#1293 := (~ #1292 #1291)
-#1288 := (not #877)
-#1289 := (~ #1288 #1287)
-#1284 := (not #871)
-#1285 := (~ #1284 #868)
-#1282 := (~ #868 #868)
-#1280 := (~ #865 #865)
-#1281 := [refl]: #1280
-#1283 := [nnf-pos #1281]: #1282
-#1286 := [nnf-neg #1283]: #1285
-#1278 := (~ #1277 #1277)
-#1279 := [refl]: #1278
-#1290 := [nnf-neg #1279 #1286]: #1289
-#1273 := (~ #871 #1272)
-#1274 := [sk]: #1273
-#1294 := [nnf-neg #1274 #1290]: #1293
-#1259 := (~ #1258 #1258)
-#1260 := [refl]: #1259
-#1177 := (~ #1176 #1176)
-#1178 := [refl]: #1177
-#1311 := (~ #1310 #1310)
+#1400 := [monotonicity #1350 #1352 #1354 #1348 #1397 #959]: #1399
+#1405 := [trans #1400 #1403]: #1404
+#1502 := [monotonicity #1405 #1499]: #1501
+#1345 := (iff #1146 #239)
+#1346 := [rewrite]: #1345
+#1505 := [monotonicity #1346 #1348 #1502]: #1504
+#1510 := [trans #1505 #1508]: #1509
+#1343 := (iff #1141 #1342)
+#1340 := (iff #1140 #1337)
+#1334 := (or #1331 #1134)
+#1338 := (iff #1334 #1337)
+#1339 := [rewrite]: #1338
+#1335 := (iff #1140 #1334)
+#1332 := (iff #1139 #1331)
+#1329 := (iff #1138 #1328)
+#1330 := [rewrite]: #1329
+#1333 := [monotonicity #1330]: #1332
+#1336 := [monotonicity #1333]: #1335
+#1341 := [trans #1336 #1339]: #1340
+#1344 := [monotonicity #1341]: #1343
+#1513 := [monotonicity #1344 #1510]: #1512
+#1105 := (or #591 #727 #739 #976 #1001)
+#1110 := (and #724 #1105)
+#1113 := (not #1110)
+#1323 := (~ #1113 #1322)
+#1319 := (not #1105)
+#1320 := (~ #1319 #1318)
+#1315 := (not #1001)
+#1316 := (~ #1315 #998)
+#1313 := (~ #998 #998)
+#1311 := (~ #995 #995)
 #1312 := [refl]: #1311
-#1308 := (~ #1307 #1307)
-#1309 := [refl]: #1308
-#1318 := [nnf-neg #1309 #1312 #1178 #1260 #1294 #1297 #1300 #1314]: #1317
-#1304 := (not #941)
+#1314 := [nnf-pos #1312]: #1313
+#1317 := [nnf-neg #1314]: #1316
+#1308 := (not #976)
+#1309 := (~ #1308 #1307)
+#1304 := (not #971)
 #1305 := (~ #1304 #1303)
-#1301 := (~ #901 #901)
-#1302 := [refl]: #1301
-#1256 := (~ #1255 #1255)
-#1257 := [refl]: #1256
-#1253 := (~ #1252 #1252)
-#1254 := [refl]: #1253
-#1250 := (~ #1249 #1249)
-#1251 := [refl]: #1250
-#1247 := (~ #1246 #1246)
-#1248 := [refl]: #1247
-#1306 := [nnf-neg #1248 #1251 #1254 #1257 #1178 #1260 #1294 #1297 #1300 #1302]: #1305
-#1322 := [nnf-neg #1306 #1318]: #1321
-#1244 := (~ #810 #810)
-#1245 := [refl]: #1244
-#1326 := [nnf-neg #1178 #1245 #1322]: #1325
-#1241 := (not #831)
-#1242 := (~ #1241 #1240)
-#1238 := (~ #975 #975)
-#1239 := [refl]: #1238
-#1235 := (not #802)
-#1236 := (~ #1235 #1234)
-#1231 := (not #799)
-#1232 := (~ #1231 #1230)
-#1225 := (not #796)
-#1226 := (~ #1225 #1224)
-#1227 := [sk]: #1226
-#1209 := (not #785)
-#1210 := (~ #1209 #1204)
-#1205 := (~ #782 #1204)
-#1206 := [sk]: #1205
-#1211 := [nnf-neg #1206]: #1210
-#1233 := [nnf-neg #1211 #1227]: #1232
-#1192 := (~ #785 #1191)
-#1189 := (~ #1188 #1188)
-#1190 := [refl]: #1189
-#1193 := [nnf-neg #1190]: #1192
-#1237 := [nnf-neg #1193 #1233]: #1236
-#1186 := (~ #1185 #1185)
-#1187 := [refl]: #1186
-#1183 := (~ #1182 #1182)
-#1184 := [refl]: #1183
-#1180 := (~ #1179 #1179)
-#1181 := [refl]: #1180
-#1243 := [nnf-neg #1181 #1184 #1187 #1178 #1237 #1239]: #1242
-#1330 := [nnf-neg #1243 #1326]: #1329
-#1173 := (not #747)
-#1174 := (~ #1173 #744)
-#1171 := (~ #744 #744)
-#1169 := (~ #741 #741)
+#1300 := (not #950)
+#1301 := (~ #1300 #1299)
+#1296 := (not #945)
+#1297 := (~ #1296 #1295)
+#1293 := (~ #887 #887)
+#1294 := [refl]: #1293
+#1279 := (~ #1278 #1278)
+#1280 := [refl]: #1279
+#1276 := (~ #1275 #1275)
+#1277 := [refl]: #1276
+#1272 := (not #862)
+#1273 := (~ #1272 #1271)
+#1268 := (not #857)
+#1269 := (~ #1268 #1267)
+#1264 := (not #851)
+#1265 := (~ #1264 #848)
+#1262 := (~ #848 #848)
+#1260 := (~ #845 #845)
+#1261 := [refl]: #1260
+#1263 := [nnf-pos #1261]: #1262
+#1266 := [nnf-neg #1263]: #1265
+#1258 := (~ #1257 #1257)
+#1259 := [refl]: #1258
+#1270 := [nnf-neg #1259 #1266]: #1269
+#1253 := (~ #851 #1252)
+#1254 := [sk]: #1253
+#1274 := [nnf-neg #1254 #1270]: #1273
+#1239 := (~ #1238 #1238)
+#1240 := [refl]: #1239
+#1157 := (~ #1156 #1156)
+#1158 := [refl]: #1157
+#1291 := (~ #1290 #1290)
+#1292 := [refl]: #1291
+#1288 := (~ #1287 #1287)
+#1289 := [refl]: #1288
+#1298 := [nnf-neg #1289 #1292 #1158 #1240 #1274 #1277 #1280 #1294]: #1297
+#1284 := (not #921)
+#1285 := (~ #1284 #1283)
+#1281 := (~ #881 #881)
+#1282 := [refl]: #1281
+#1236 := (~ #1235 #1235)
+#1237 := [refl]: #1236
+#1233 := (~ #1232 #1232)
+#1234 := [refl]: #1233
+#1230 := (~ #1229 #1229)
+#1231 := [refl]: #1230
+#1227 := (~ #1226 #1226)
+#1228 := [refl]: #1227
+#1286 := [nnf-neg #1228 #1231 #1234 #1237 #1158 #1240 #1274 #1277 #1280 #1282]: #1285
+#1302 := [nnf-neg #1286 #1298]: #1301
+#1224 := (~ #790 #790)
+#1225 := [refl]: #1224
+#1306 := [nnf-neg #1158 #1225 #1302]: #1305
+#1221 := (not #811)
+#1222 := (~ #1221 #1220)
+#1218 := (~ #955 #955)
+#1219 := [refl]: #1218
+#1215 := (not #782)
+#1216 := (~ #1215 #1214)
+#1211 := (not #779)
+#1212 := (~ #1211 #1210)
+#1205 := (not #776)
+#1206 := (~ #1205 #1204)
+#1207 := [sk]: #1206
+#1189 := (not #765)
+#1190 := (~ #1189 #1184)
+#1185 := (~ #762 #1184)
+#1186 := [sk]: #1185
+#1191 := [nnf-neg #1186]: #1190
+#1213 := [nnf-neg #1191 #1207]: #1212
+#1172 := (~ #765 #1171)
+#1169 := (~ #1168 #1168)
 #1170 := [refl]: #1169
-#1172 := [nnf-pos #1170]: #1171
-#1175 := [nnf-neg #1172]: #1174
-#1167 := (~ #1166 #1166)
-#1168 := [refl]: #1167
-#1341 := [nnf-neg #1168 #1175 #1178 #1330 #1337]: #1340
-#1162 := (~ #747 #1161)
-#1163 := [sk]: #1162
-#1344 := [nnf-neg #1163 #1341]: #1343
-#1085 := (not #1050)
-#1134 := (iff #1085 #1133)
-#1131 := (iff #1050 #1130)
-#1128 := (iff #1047 #1125)
-#1110 := (or #611 #759 #996 #1021)
-#1122 := (or #747 #1110)
-#1126 := (iff #1122 #1125)
-#1127 := [rewrite]: #1126
-#1123 := (iff #1047 #1122)
-#1120 := (iff #1044 #1110)
-#1115 := (and true #1110)
-#1118 := (iff #1115 #1110)
-#1119 := [rewrite]: #1118
-#1116 := (iff #1044 #1115)
-#1113 := (iff #1039 #1110)
-#1107 := (or false #611 #759 #996 #1021)
-#1111 := (iff #1107 #1110)
-#1112 := [rewrite]: #1111
-#1108 := (iff #1039 #1107)
-#1105 := (iff #644 false)
-#1103 := (iff #644 #715)
-#1101 := (iff #47 true)
-#1102 := [iff-true #1084]: #1101
-#1104 := [monotonicity #1102]: #1103
-#1106 := [trans #1104 #719]: #1105
-#1109 := [monotonicity #1106]: #1108
-#1114 := [trans #1109 #1112]: #1113
-#1117 := [monotonicity #1102 #1114]: #1116
-#1121 := [trans #1117 #1119]: #1120
-#1124 := [monotonicity #1121]: #1123
-#1129 := [trans #1124 #1127]: #1128
-#1132 := [monotonicity #1129]: #1131
-#1135 := [monotonicity #1132]: #1134
-#1086 := [not-or-elim #1083]: #1085
-#1136 := [mp #1086 #1135]: #1133
-#1345 := [mp~ #1136 #1344]: #1342
-#1346 := [mp #1345 #1533]: #1531
-#1835 := [mp #1346 #1834]: #1830
-#2445 := [mp #1835 #2444]: #2442
-#2169 := [unit-resolution #2445 #2813]: #1545
-#1987 := (or #1540 #1902)
-#1903 := [def-axiom]: #1987
-#2170 := [unit-resolution #1903 #2169]: #1902
-#2190 := (+ #46 #1152)
-#2164 := (>= #2190 0::Int)
-#2184 := (= #46 #1151)
-#2136 := (= #1151 #46)
-#2168 := (= ?v0!0 0::Int)
-#1988 := (or #1540 #1156)
-#1989 := [def-axiom]: #1988
-#2171 := [unit-resolution #1989 #2169]: #1156
-#1980 := (or #1540 #1157)
-#1991 := [def-axiom]: #1980
-#2162 := [unit-resolution #1991 #2169]: #1157
-#2167 := [th-lemma arith eq-propagate 0 0 #2162 #2171]: #2168
-#2143 := [monotonicity #2167]: #2136
-#2102 := [symm #2143]: #2184
-#2133 := (not #2184)
-#2135 := (or #2133 #2164)
-#2137 := [th-lemma arith triangle-eq]: #2135
-#2104 := [unit-resolution #2137 #2102]: #2164
-[th-lemma arith farkas 1 -1 1 #2104 #2170 #2058]: false
+#1173 := [nnf-neg #1170]: #1172
+#1217 := [nnf-neg #1173 #1213]: #1216
+#1166 := (~ #1165 #1165)
+#1167 := [refl]: #1166
+#1163 := (~ #1162 #1162)
+#1164 := [refl]: #1163
+#1160 := (~ #1159 #1159)
+#1161 := [refl]: #1160
+#1223 := [nnf-neg #1161 #1164 #1167 #1158 #1217 #1219]: #1222
+#1310 := [nnf-neg #1223 #1306]: #1309
+#1153 := (not #727)
+#1154 := (~ #1153 #724)
+#1151 := (~ #724 #724)
+#1149 := (~ #721 #721)
+#1150 := [refl]: #1149
+#1152 := [nnf-pos #1150]: #1151
+#1155 := [nnf-neg #1152]: #1154
+#1147 := (~ #1146 #1146)
+#1148 := [refl]: #1147
+#1321 := [nnf-neg #1148 #1155 #1158 #1310 #1317]: #1320
+#1142 := (~ #727 #1141)
+#1143 := [sk]: #1142
+#1324 := [nnf-neg #1143 #1321]: #1323
+#1065 := (not #1030)
+#1114 := (iff #1065 #1113)
+#1111 := (iff #1030 #1110)
+#1108 := (iff #1027 #1105)
+#1090 := (or #591 #739 #976 #1001)
+#1102 := (or #727 #1090)
+#1106 := (iff #1102 #1105)
+#1107 := [rewrite]: #1106
+#1103 := (iff #1027 #1102)
+#1100 := (iff #1024 #1090)
+#1095 := (and true #1090)
+#1098 := (iff #1095 #1090)
+#1099 := [rewrite]: #1098
+#1096 := (iff #1024 #1095)
+#1093 := (iff #1019 #1090)
+#1087 := (or false #591 #739 #976 #1001)
+#1091 := (iff #1087 #1090)
+#1092 := [rewrite]: #1091
+#1088 := (iff #1019 #1087)
+#1085 := (iff #624 false)
+#1083 := (iff #624 #695)
+#1081 := (iff #40 true)
+#1082 := [iff-true #1064]: #1081
+#1084 := [monotonicity #1082]: #1083
+#1086 := [trans #1084 #699]: #1085
+#1089 := [monotonicity #1086]: #1088
+#1094 := [trans #1089 #1092]: #1093
+#1097 := [monotonicity #1082 #1094]: #1096
+#1101 := [trans #1097 #1099]: #1100
+#1104 := [monotonicity #1101]: #1103
+#1109 := [trans #1104 #1107]: #1108
+#1112 := [monotonicity #1109]: #1111
+#1115 := [monotonicity #1112]: #1114
+#1066 := [not-or-elim #1063]: #1065
+#1116 := [mp #1066 #1115]: #1113
+#1325 := [mp~ #1116 #1324]: #1322
+#1326 := [mp #1325 #1513]: #1511
+#1815 := [mp #1326 #1814]: #1810
+#2424 := [mp #1815 #2423]: #2421
+#2149 := [unit-resolution #2424 #2792]: #1525
+#1967 := (or #1520 #1882)
+#1883 := [def-axiom]: #1967
+#2150 := [unit-resolution #1883 #2149]: #1882
+#2170 := (+ #39 #1132)
+#2144 := (>= #2170 0::Int)
+#2164 := (= #39 #1131)
+#2116 := (= #1131 #39)
+#2148 := (= ?v0!0 0::Int)
+#1968 := (or #1520 #1136)
+#1969 := [def-axiom]: #1968
+#2151 := [unit-resolution #1969 #2149]: #1136
+#1960 := (or #1520 #1137)
+#1971 := [def-axiom]: #1960
+#2142 := [unit-resolution #1971 #2149]: #1137
+#2147 := [th-lemma arith eq-propagate 0 0 #2142 #2151]: #2148
+#2123 := [monotonicity #2147]: #2116
+#2082 := [symm #2123]: #2164
+#2113 := (not #2164)
+#2115 := (or #2113 #2144)
+#2117 := [th-lemma arith triangle-eq]: #2115
+#2084 := [unit-resolution #2117 #2082]: #2144
+[th-lemma arith farkas 1 -1 1 #2084 #2150 #2038]: false
 unsat

--- a/src/HOL/Boogie/Examples/VCC_Max.certs	Tue May 31 19:27:19 2011 +0200
+++ b/src/HOL/Boogie/Examples/VCC_Max.certs	Tue May 31 19:28:03 2011 +0200
@@ -1,5134 +1,5153 @@
-d334e94512e2be06e90930c75ed763964895b7de 7803 0
+9b90a93b56d495f3526f4b091b0437d476f5976c 7803 0
 #2 := false
-decl f121 :: (-> S19 S20 Int)
-decl f77 :: (-> S20 Int S18 S20)
-decl f19 :: S18
-#50 := f19
+decl f111 :: (-> S4 S5 Int)
+decl f67 :: (-> S5 Int S3 S5)
+decl f9 :: S3
+#16 := f9
 decl ?v0!14 :: Int
-#18614 := ?v0!14
-decl f54 :: (-> S18 Int S20)
-decl f298 :: Int
-#3041 := f298
-#3042 := (f54 f19 f298)
-#18619 := (f77 #3042 ?v0!14 f19)
-decl f297 :: S19
-#3039 := f297
-#18620 := (f121 f297 #18619)
+#18594 := ?v0!14
+decl f44 :: (-> S3 Int S5)
+decl f293 :: Int
+#3034 := f293
+#3035 := (f44 f9 f293)
+#18599 := (f67 #3035 ?v0!14 f9)
+decl f292 :: S4
+#3032 := f292
+#18600 := (f111 f292 #18599)
+decl f304 :: Int
+#3132 := f304
+#3250 := (f67 #3035 f304 f9)
+#3259 := (f111 f292 #3250)
+#30570 := (= #3259 #18600)
+#30603 := (not #30570)
+#127 := 0::Int
+#4150 := -1::Int
+#18921 := (* -1::Int #18600)
+#30598 := (+ #3259 #18921)
+#30600 := (>= #30598 0::Int)
+#30610 := (not #30600)
+decl f310 :: Int
+#3268 := f310
+#13550 := (* -1::Int f310)
+#30323 := (+ #3259 #13550)
+#30151 := (<= #30323 0::Int)
+#30322 := (= #3259 f310)
 decl f309 :: Int
-#3139 := f309
-#3257 := (f77 #3042 f309 f19)
-#3266 := (f121 f297 #3257)
-#30591 := (= #3266 #18620)
-#30624 := (not #30591)
-#161 := 0::Int
-#4203 := -1::Int
-#18941 := (* -1::Int #18620)
-#30619 := (+ #3266 #18941)
-#30621 := (>= #30619 0::Int)
-#30631 := (not #30621)
-decl f315 :: Int
-#3275 := f315
-#13570 := (* -1::Int f315)
-#30344 := (+ #3266 #13570)
-#30172 := (<= #30344 0::Int)
-#30343 := (= #3266 f315)
-decl f314 :: Int
-#3268 := f314
-#12601 := (= f314 f315)
-#18942 := (+ f315 #18941)
-#18943 := (>= #18942 0::Int)
-#18928 := (* -1::Int ?v0!14)
-decl f317 :: Int
-#3285 := f317
-#18929 := (+ f317 #18928)
-#18930 := (<= #18929 0::Int)
-#18616 := (>= ?v0!14 0::Int)
-#22396 := (not #18616)
-#7632 := 4294967295::Int
-#18615 := (<= ?v0!14 4294967295::Int)
-#22395 := (not #18615)
-#22411 := (or #22395 #22396 #18930 #18943)
-#22416 := (not #22411)
-#202 := (:var 0 Int)
-#3123 := (f77 #3042 #202 f19)
-#23363 := (pattern #3123)
-#15219 := (<= #202 4294967295::Int)
-#19613 := (not #15219)
-#3124 := (f121 f297 #3123)
-#13571 := (+ #3124 #13570)
-#13572 := (<= #13571 0::Int)
-#13551 := (* -1::Int f317)
-#13559 := (+ #202 #13551)
-#13558 := (>= #13559 0::Int)
-#4202 := (>= #202 0::Int)
-#5124 := (not #4202)
-#22377 := (or #5124 #13558 #13572 #19613)
-#23380 := (forall (vars (?v0 Int)) (:pat #23363) #22377)
-#23385 := (not #23380)
-decl f316 :: Int
-#3277 := f316
-#13592 := (* -1::Int f316)
-decl f296 :: Int
-#3036 := f296
-#13593 := (+ f296 #13592)
-#13594 := (<= #13593 0::Int)
-#3298 := (f77 #3042 f316 f19)
-#3299 := (f121 f297 #3298)
-#12643 := (= f315 #3299)
-#22362 := (not #12643)
-#22363 := (or #22362 #13594)
-#22364 := (not #22363)
-#23388 := (or #22364 #23385)
-#23391 := (not #23388)
-#23394 := (or #23391 #22416)
-#23397 := (not #23394)
-#13552 := (+ f296 #13551)
-#13550 := (>= #13552 0::Int)
-#13555 := (not #13550)
-#23400 := (or #13555 #23397)
-#23403 := (not #23400)
-#23406 := (or #13555 #23403)
-#23409 := (not #23406)
-#15899 := 4294967294::Int
-#15900 := (<= f309 4294967294::Int)
-#18597 := (not #15900)
-#13619 := (+ f309 #13551)
-#13618 := (= #13619 -1::Int)
-#13622 := (not #13618)
-#935 := 2::Int
-#13542 := (>= f317 2::Int)
-#22439 := (not #13542)
-#13534 := (>= f309 -1::Int)
-#18594 := (not #13534)
-#13525 := (>= f316 0::Int)
-#22438 := (not #13525)
-decl f301 :: (-> S19 S17 S17 Int S18 S1)
-decl f16 :: S18
-#46 := f16
-decl f284 :: S17
-#3012 := f284
-decl f280 :: S17
-#3008 := f280
-#3287 := (f301 f297 f280 f284 f317 f16)
+#3261 := f309
+#12581 := (= f309 f310)
+#18922 := (+ f310 #18921)
+#18923 := (>= #18922 0::Int)
+#18908 := (* -1::Int ?v0!14)
+decl f312 :: Int
+#3278 := f312
+#18909 := (+ f312 #18908)
+#18910 := (<= #18909 0::Int)
+#18596 := (>= ?v0!14 0::Int)
+#22376 := (not #18596)
+#7579 := 4294967295::Int
+#18595 := (<= ?v0!14 4294967295::Int)
+#22375 := (not #18595)
+#22391 := (or #22375 #22376 #18910 #18923)
+#22396 := (not #22391)
+#168 := (:var 0 Int)
+#3116 := (f67 #3035 #168 f9)
+#23342 := (pattern #3116)
+#15199 := (<= #168 4294967295::Int)
+#19593 := (not #15199)
+#3117 := (f111 f292 #3116)
+#13551 := (+ #3117 #13550)
+#13552 := (<= #13551 0::Int)
+#13531 := (* -1::Int f312)
+#13539 := (+ #168 #13531)
+#13538 := (>= #13539 0::Int)
+#4149 := (>= #168 0::Int)
+#5071 := (not #4149)
+#22357 := (or #5071 #13538 #13552 #19593)
+#23359 := (forall (vars (?v0 Int)) (:pat #23342) #22357)
+#23364 := (not #23359)
+decl f311 :: Int
+#3270 := f311
+#13572 := (* -1::Int f311)
+decl f291 :: Int
+#3029 := f291
+#13573 := (+ f291 #13572)
+#13574 := (<= #13573 0::Int)
+#3291 := (f67 #3035 f311 f9)
+#3292 := (f111 f292 #3291)
+#12623 := (= f310 #3292)
+#22342 := (not #12623)
+#22343 := (or #22342 #13574)
+#22344 := (not #22343)
+#23367 := (or #22344 #23364)
+#23370 := (not #23367)
+#23373 := (or #23370 #22396)
+#23376 := (not #23373)
+#13532 := (+ f291 #13531)
+#13530 := (>= #13532 0::Int)
+#13535 := (not #13530)
+#23379 := (or #13535 #23376)
+#23382 := (not #23379)
+#23385 := (or #13535 #23382)
+#23388 := (not #23385)
+#15879 := 4294967294::Int
+#15880 := (<= f304 4294967294::Int)
+#18577 := (not #15880)
+#13599 := (+ f304 #13531)
+#13598 := (= #13599 -1::Int)
+#13602 := (not #13598)
+#901 := 2::Int
+#13522 := (>= f312 2::Int)
+#22419 := (not #13522)
+#13514 := (>= f304 -1::Int)
+#18574 := (not #13514)
+#13505 := (>= f311 0::Int)
+#22418 := (not #13505)
+decl f296 :: (-> S4 S2 S2 Int S3 S1)
+decl f6 :: S3
+#12 := f6
+decl f274 :: S2
+#2978 := f274
+decl f270 :: S2
+#2974 := f270
+#3280 := (f296 f292 f270 f274 f312 f6)
 decl f1 :: S1
 #4 := f1
-#12622 := (= f1 #3287)
-#12692 := (not #12622)
-#23412 := (or #12692 #22438 #18594 #22439 #13622 #18597 #23409)
-#23415 := (not #23412)
-#23418 := (or #18594 #18597 #23415)
-#23421 := (not #23418)
-#42 := 1::Int
-#13516 := (>= f309 1::Int)
-#13656 := (not #13516)
-#12604 := (= f309 f316)
-#12731 := (not #12604)
-#12740 := (not #12601)
-decl f286 :: S17
-#3014 := f286
-decl f281 :: S17
-#3009 := f281
-#3272 := (f301 f297 f281 f286 f309 f16)
-#12596 := (= f1 #3272)
-#12758 := (not #12596)
-decl f288 :: S17
-#3016 := f288
-decl f282 :: S17
-#3010 := f282
-#3270 := (f301 f297 f282 f288 f314 f19)
-#12593 := (= f1 #3270)
-#12767 := (not #12593)
-#12590 := (= #3266 f314)
-#12776 := (not #12590)
-decl f79 :: (-> S19 S20 S1)
-#3263 := (f79 f297 #3257)
-#12584 := (= f1 #3263)
-#18565 := (not #12584)
-decl f59 :: (-> S20 S18 S1)
-#3258 := (f59 #3257 f19)
-#12575 := (= f1 #3258)
-#18556 := (not #12575)
-#23424 := (or #18556 #18565 #12776 #12767 #12758 #12740 #12731 #13656 #22438 #23421)
-#23427 := (not #23424)
-decl f36 :: (-> S19 S20 S20)
-decl f146 :: (-> S29 S20)
-decl f69 :: (-> S28 S20 S29)
-decl f70 :: (-> S19 S28)
-#3220 := (f70 f297)
-#27834 := (f69 #3220 #3257)
-#28494 := (f146 #27834)
-#28497 := (f36 f297 #28494)
-decl f37 :: S20
-#116 := f37
-#28498 := (= f37 #28497)
-decl f221 :: (-> S19 S20 S1)
-#28495 := (f221 f297 #28494)
-#28496 := (= f1 #28495)
-#28554 := (or #28496 #28498)
-#28557 := (not #28554)
-decl f147 :: (-> S29 S1)
-#28507 := (f147 #27834)
-#28508 := (= f1 #28507)
-#28509 := (not #28508)
-decl f38 :: (-> S19 S20 S1)
-#28504 := (f38 f297 #28494)
-#28505 := (= f1 #28504)
-#28506 := (not #28505)
-#28548 := (or #28506 #28509)
-#28551 := (not #28548)
-decl f23 :: (-> S18 S23)
-decl f24 :: (-> S20 S18)
-#28202 := (f24 #3257)
-#28512 := (f23 #28202)
-decl f25 :: S23
-#67 := f25
-#28530 := (= f25 #28512)
-#28545 := (not #28530)
-#28501 := (f24 #28494)
-#28502 := (f23 #28501)
-#28503 := (= f25 #28502)
-#28563 := (or #28503 #28545 #28551 #28557)
-#28568 := (not #28563)
-#28519 := (f36 f297 #3257)
-#28520 := (= f37 #28519)
-#28517 := (f221 f297 #3257)
-#28518 := (= f1 #28517)
-#28533 := (or #28518 #28520)
+#12602 := (= f1 #3280)
+#12672 := (not #12602)
+#23391 := (or #12672 #22418 #18574 #22419 #13602 #18577 #23388)
+#23394 := (not #23391)
+#23397 := (or #18574 #18577 #23394)
+#23400 := (not #23397)
+#8 := 1::Int
+#13496 := (>= f304 1::Int)
+#13636 := (not #13496)
+#12584 := (= f304 f311)
+#12711 := (not #12584)
+#12720 := (not #12581)
+decl f276 :: S2
+#2980 := f276
+decl f271 :: S2
+#2975 := f271
+#3265 := (f296 f292 f271 f276 f304 f6)
+#12576 := (= f1 #3265)
+#12738 := (not #12576)
+decl f278 :: S2
+#2982 := f278
+decl f272 :: S2
+#2976 := f272
+#3263 := (f296 f292 f272 f278 f309 f9)
+#12573 := (= f1 #3263)
+#12747 := (not #12573)
+#12570 := (= #3259 f309)
+#12756 := (not #12570)
+decl f69 :: (-> S4 S5 S1)
+#3256 := (f69 f292 #3250)
+#12564 := (= f1 #3256)
+#18545 := (not #12564)
+decl f49 :: (-> S5 S3 S1)
+#3251 := (f49 #3250 f9)
+#12555 := (= f1 #3251)
+#18536 := (not #12555)
+#23403 := (or #18536 #18545 #12756 #12747 #12738 #12720 #12711 #13636 #22418 #23400)
+#23406 := (not #23403)
+decl f26 :: (-> S4 S5 S5)
+decl f136 :: (-> S14 S5)
+decl f59 :: (-> S13 S5 S14)
+decl f60 :: (-> S4 S13)
+#3213 := (f60 f292)
+#27813 := (f59 #3213 #3250)
+#28473 := (f136 #27813)
+#28476 := (f26 f292 #28473)
+decl f27 :: S5
+#82 := f27
+#28477 := (= f27 #28476)
+decl f211 :: (-> S4 S5 S1)
+#28474 := (f211 f292 #28473)
+#28475 := (= f1 #28474)
+#28533 := (or #28475 #28477)
 #28536 := (not #28533)
-#28539 := (or #28530 #28536)
-#28542 := (not #28539)
-#28571 := (or #28542 #28568)
-#28574 := (not #28571)
-decl f35 :: (-> S19 S20 S1)
-#3260 := (f35 f297 #3257)
-#12578 := (= f1 #3260)
-#18559 := (not #12578)
-#28577 := (or #18559 #28574)
-#28580 := (not #28577)
-#28583 := (iff #12584 #28580)
-#29899 := (not #28583)
-#30296 := [hypothesis]: #29899
-#62 := (:var 0 S20)
-#86 := (:var 1 S19)
-#2438 := (f79 #86 #62)
-#2439 := (pattern #2438)
-#324 := (f70 #86)
-#2441 := (f69 #324 #62)
-#2445 := (f146 #2441)
-#2456 := (f221 #86 #2445)
-#10696 := (= f1 #2456)
-#2454 := (f36 #86 #2445)
-#10693 := (= f37 #2454)
-#10699 := (or #10693 #10696)
-#22070 := (not #10699)
-#2450 := (f24 #2445)
-#2451 := (f23 #2450)
-#10687 := (= f25 #2451)
-#2446 := (f38 #86 #2445)
-#10678 := (= f1 #2446)
-#10681 := (not #10678)
-#2442 := (f147 #2441)
-#10672 := (= f1 #2442)
-#10675 := (not #10672)
-#10684 := (or #10675 #10681)
-#22069 := (not #10684)
-#65 := (f24 #62)
-#66 := (f23 #65)
-#68 := (= #66 f25)
-#91 := (not #68)
-#22071 := (or #91 #22069 #10687 #22070)
-#22072 := (not #22071)
-#2462 := (f221 #86 #62)
-#10711 := (= f1 #2462)
-#182 := (f36 #86 #62)
-#3761 := (= f37 #182)
-#10714 := (or #3761 #10711)
-#22064 := (not #10714)
-#22065 := (or #68 #22064)
-#22066 := (not #22065)
-#22075 := (or #22066 #22072)
-#22081 := (not #22075)
-#186 := (f35 #86 #62)
-#3767 := (= f1 #186)
-#11297 := (not #3767)
-#22082 := (or #11297 #22081)
-#22083 := (not #22082)
-#10668 := (= f1 #2438)
-#22088 := (iff #10668 #22083)
-#22091 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #22088)
-#10690 := (not #10687)
-#10732 := (and #68 #10684 #10690 #10699)
-#10717 := (and #91 #10714)
-#10738 := (or #10717 #10732)
-#10743 := (and #3767 #10738)
-#10746 := (iff #10668 #10743)
-#10749 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10746)
-#22092 := (iff #10749 #22091)
-#22089 := (iff #10746 #22088)
-#22086 := (iff #10743 #22083)
-#22078 := (and #3767 #22075)
-#22084 := (iff #22078 #22083)
-#22085 := [rewrite]: #22084
-#22079 := (iff #10743 #22078)
-#22076 := (iff #10738 #22075)
-#22073 := (iff #10732 #22072)
-#22074 := [rewrite]: #22073
-#22067 := (iff #10717 #22066)
-#22068 := [rewrite]: #22067
-#22077 := [monotonicity #22068 #22074]: #22076
-#22080 := [monotonicity #22077]: #22079
-#22087 := [trans #22080 #22085]: #22086
-#22090 := [monotonicity #22087]: #22089
-#22093 := [quant-intro #22090]: #22092
-#18014 := (~ #10749 #10749)
-#18012 := (~ #10746 #10746)
-#18013 := [refl]: #18012
-#18015 := [nnf-pos #18013]: #18014
-#2463 := (= #2462 f1)
-#183 := (= #182 f37)
-#2464 := (or #183 #2463)
-#2465 := (and #91 #2464)
-#2457 := (= #2456 f1)
-#2455 := (= #2454 f37)
-#2458 := (or #2455 #2457)
-#2452 := (= #2451 f25)
-#2453 := (not #2452)
-#2459 := (and #2453 #2458)
-#2447 := (= #2446 f1)
-#2448 := (not #2447)
-#2443 := (= #2442 f1)
-#2444 := (not #2443)
-#2449 := (or #2444 #2448)
-#2460 := (and #2449 #2459)
-#2461 := (and #68 #2460)
-#2466 := (or #2461 #2465)
-#187 := (= #186 f1)
-#2467 := (and #187 #2466)
-#2440 := (= #2438 f1)
-#2468 := (iff #2440 #2467)
-#2469 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #2468)
-#10752 := (iff #2469 #10749)
-#10702 := (and #10690 #10699)
-#10705 := (and #10684 #10702)
-#10708 := (and #68 #10705)
-#10720 := (or #10708 #10717)
-#10723 := (and #3767 #10720)
-#10726 := (iff #10668 #10723)
-#10729 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2439) #10726)
-#10750 := (iff #10729 #10749)
-#10747 := (iff #10726 #10746)
-#10744 := (iff #10723 #10743)
-#10741 := (iff #10720 #10738)
-#10735 := (or #10732 #10717)
-#10739 := (iff #10735 #10738)
-#10740 := [rewrite]: #10739
-#10736 := (iff #10720 #10735)
-#10733 := (iff #10708 #10732)
-#10734 := [rewrite]: #10733
-#10737 := [monotonicity #10734]: #10736
-#10742 := [trans #10737 #10740]: #10741
-#10745 := [monotonicity #10742]: #10744
-#10748 := [monotonicity #10745]: #10747
-#10751 := [quant-intro #10748]: #10750
-#10730 := (iff #2469 #10729)
-#10727 := (iff #2468 #10726)
-#10724 := (iff #2467 #10723)
-#10721 := (iff #2466 #10720)
-#10718 := (iff #2465 #10717)
-#10715 := (iff #2464 #10714)
-#10712 := (iff #2463 #10711)
-#10713 := [rewrite]: #10712
-#3762 := (iff #183 #3761)
-#3763 := [rewrite]: #3762
-#10716 := [monotonicity #3763 #10713]: #10715
-#10719 := [monotonicity #10716]: #10718
-#10709 := (iff #2461 #10708)
-#10706 := (iff #2460 #10705)
-#10703 := (iff #2459 #10702)
-#10700 := (iff #2458 #10699)
-#10697 := (iff #2457 #10696)
-#10698 := [rewrite]: #10697
-#10694 := (iff #2455 #10693)
-#10695 := [rewrite]: #10694
-#10701 := [monotonicity #10695 #10698]: #10700
-#10691 := (iff #2453 #10690)
-#10688 := (iff #2452 #10687)
-#10689 := [rewrite]: #10688
+decl f137 :: (-> S14 S1)
+#28486 := (f137 #27813)
+#28487 := (= f1 #28486)
+#28488 := (not #28487)
+decl f28 :: (-> S4 S5 S1)
+#28483 := (f28 f292 #28473)
+#28484 := (= f1 #28483)
+#28485 := (not #28484)
+#28527 := (or #28485 #28488)
+#28530 := (not #28527)
+decl f13 :: (-> S3 S8)
+decl f14 :: (-> S5 S3)
+#28181 := (f14 #3250)
+#28491 := (f13 #28181)
+decl f15 :: S8
+#33 := f15
+#28509 := (= f15 #28491)
+#28524 := (not #28509)
+#28480 := (f14 #28473)
+#28481 := (f13 #28480)
+#28482 := (= f15 #28481)
+#28542 := (or #28482 #28524 #28530 #28536)
+#28547 := (not #28542)
+#28498 := (f26 f292 #3250)
+#28499 := (= f27 #28498)
+#28496 := (f211 f292 #3250)
+#28497 := (= f1 #28496)
+#28512 := (or #28497 #28499)
+#28515 := (not #28512)
+#28518 := (or #28509 #28515)
+#28521 := (not #28518)
+#28550 := (or #28521 #28547)
+#28553 := (not #28550)
+decl f25 :: (-> S4 S5 S1)
+#3253 := (f25 f292 #3250)
+#12558 := (= f1 #3253)
+#18539 := (not #12558)
+#28556 := (or #18539 #28553)
+#28559 := (not #28556)
+#28562 := (iff #12564 #28559)
+#29878 := (not #28562)
+#30275 := [hypothesis]: #29878
+#28 := (:var 0 S5)
+#52 := (:var 1 S4)
+#2404 := (f69 #52 #28)
+#2405 := (pattern #2404)
+#290 := (f60 #52)
+#2407 := (f59 #290 #28)
+#2411 := (f136 #2407)
+#2422 := (f211 #52 #2411)
+#10643 := (= f1 #2422)
+#2420 := (f26 #52 #2411)
+#10640 := (= f27 #2420)
+#10646 := (or #10640 #10643)
+#22050 := (not #10646)
+#2416 := (f14 #2411)
+#2417 := (f13 #2416)
+#10634 := (= f15 #2417)
+#2412 := (f28 #52 #2411)
+#10625 := (= f1 #2412)
+#10628 := (not #10625)
+#2408 := (f137 #2407)
+#10619 := (= f1 #2408)
+#10622 := (not #10619)
+#10631 := (or #10622 #10628)
+#22049 := (not #10631)
+#31 := (f14 #28)
+#32 := (f13 #31)
+#34 := (= #32 f15)
+#57 := (not #34)
+#22051 := (or #57 #22049 #10634 #22050)
+#22052 := (not #22051)
+#2428 := (f211 #52 #28)
+#10658 := (= f1 #2428)
+#148 := (f26 #52 #28)
+#3708 := (= f27 #148)
+#10661 := (or #3708 #10658)
+#22044 := (not #10661)
+#22045 := (or #34 #22044)
+#22046 := (not #22045)
+#22055 := (or #22046 #22052)
+#22061 := (not #22055)
+#152 := (f25 #52 #28)
+#3714 := (= f1 #152)
+#11244 := (not #3714)
+#22062 := (or #11244 #22061)
+#22063 := (not #22062)
+#10615 := (= f1 #2404)
+#22068 := (iff #10615 #22063)
+#22071 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2405) #22068)
+#10637 := (not #10634)
+#10679 := (and #34 #10631 #10637 #10646)
+#10664 := (and #57 #10661)
+#10685 := (or #10664 #10679)
+#10690 := (and #3714 #10685)
+#10693 := (iff #10615 #10690)
+#10696 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2405) #10693)
+#22072 := (iff #10696 #22071)
+#22069 := (iff #10693 #22068)
+#22066 := (iff #10690 #22063)
+#22058 := (and #3714 #22055)
+#22064 := (iff #22058 #22063)
+#22065 := [rewrite]: #22064
+#22059 := (iff #10690 #22058)
+#22056 := (iff #10685 #22055)
+#22053 := (iff #10679 #22052)
+#22054 := [rewrite]: #22053
+#22047 := (iff #10664 #22046)
+#22048 := [rewrite]: #22047
+#22057 := [monotonicity #22048 #22054]: #22056
+#22060 := [monotonicity #22057]: #22059
+#22067 := [trans #22060 #22065]: #22066
+#22070 := [monotonicity #22067]: #22069
+#22073 := [quant-intro #22070]: #22072
+#17969 := (~ #10696 #10696)
+#17967 := (~ #10693 #10693)
+#17968 := [refl]: #17967
+#17970 := [nnf-pos #17968]: #17969
+#2429 := (= #2428 f1)
+#149 := (= #148 f27)
+#2430 := (or #149 #2429)
+#2431 := (and #57 #2430)
+#2423 := (= #2422 f1)
+#2421 := (= #2420 f27)
+#2424 := (or #2421 #2423)
+#2418 := (= #2417 f15)
+#2419 := (not #2418)
+#2425 := (and #2419 #2424)
+#2413 := (= #2412 f1)
+#2414 := (not #2413)
+#2409 := (= #2408 f1)
+#2410 := (not #2409)
+#2415 := (or #2410 #2414)
+#2426 := (and #2415 #2425)
+#2427 := (and #34 #2426)
+#2432 := (or #2427 #2431)
+#153 := (= #152 f1)
+#2433 := (and #153 #2432)
+#2406 := (= #2404 f1)
+#2434 := (iff #2406 #2433)
+#2435 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2405) #2434)
+#10699 := (iff #2435 #10696)
+#10649 := (and #10637 #10646)
+#10652 := (and #10631 #10649)
+#10655 := (and #34 #10652)
+#10667 := (or #10655 #10664)
+#10670 := (and #3714 #10667)
+#10673 := (iff #10615 #10670)
+#10676 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2405) #10673)
+#10697 := (iff #10676 #10696)
+#10694 := (iff #10673 #10693)
+#10691 := (iff #10670 #10690)
+#10688 := (iff #10667 #10685)
+#10682 := (or #10679 #10664)
+#10686 := (iff #10682 #10685)
+#10687 := [rewrite]: #10686
+#10683 := (iff #10667 #10682)
+#10680 := (iff #10655 #10679)
+#10681 := [rewrite]: #10680
+#10684 := [monotonicity #10681]: #10683
+#10689 := [trans #10684 #10687]: #10688
 #10692 := [monotonicity #10689]: #10691
-#10704 := [monotonicity #10692 #10701]: #10703
-#10685 := (iff #2449 #10684)
-#10682 := (iff #2448 #10681)
-#10679 := (iff #2447 #10678)
-#10680 := [rewrite]: #10679
-#10683 := [monotonicity #10680]: #10682
-#10676 := (iff #2444 #10675)
-#10673 := (iff #2443 #10672)
-#10674 := [rewrite]: #10673
-#10677 := [monotonicity #10674]: #10676
-#10686 := [monotonicity #10677 #10683]: #10685
-#10707 := [monotonicity #10686 #10704]: #10706
-#10710 := [monotonicity #10707]: #10709
-#10722 := [monotonicity #10710 #10719]: #10721
-#3768 := (iff #187 #3767)
-#3769 := [rewrite]: #3768
-#10725 := [monotonicity #3769 #10722]: #10724
-#10670 := (iff #2440 #10668)
-#10671 := [rewrite]: #10670
-#10728 := [monotonicity #10671 #10725]: #10727
-#10731 := [quant-intro #10728]: #10730
-#10753 := [trans #10731 #10751]: #10752
-#10667 := [asserted]: #2469
-#10754 := [mp #10667 #10753]: #10749
-#18016 := [mp~ #10754 #18015]: #10749
-#22094 := [mp #18016 #22093]: #22091
-#28423 := (not #22091)
-#29896 := (or #28423 #28583)
-#28499 := (or #28498 #28496)
-#28500 := (not #28499)
-#28510 := (or #28509 #28506)
-#28511 := (not #28510)
-#28513 := (= #28512 f25)
-#28514 := (not #28513)
-#28515 := (or #28514 #28511 #28503 #28500)
-#28516 := (not #28515)
-#28521 := (or #28520 #28518)
-#28522 := (not #28521)
-#28523 := (or #28513 #28522)
-#28524 := (not #28523)
-#28525 := (or #28524 #28516)
-#28526 := (not #28525)
-#28527 := (or #18559 #28526)
-#28528 := (not #28527)
-#28529 := (iff #12584 #28528)
-#29897 := (or #28423 #28529)
-#29946 := (iff #29897 #29896)
-#29888 := (iff #29896 #29896)
-#29891 := [rewrite]: #29888
-#28584 := (iff #28529 #28583)
-#28581 := (iff #28528 #28580)
-#28578 := (iff #28527 #28577)
-#28575 := (iff #28526 #28574)
-#28572 := (iff #28525 #28571)
-#28569 := (iff #28516 #28568)
-#28566 := (iff #28515 #28563)
-#28560 := (or #28545 #28551 #28503 #28557)
-#28564 := (iff #28560 #28563)
-#28565 := [rewrite]: #28564
-#28561 := (iff #28515 #28560)
-#28558 := (iff #28500 #28557)
-#28555 := (iff #28499 #28554)
-#28556 := [rewrite]: #28555
-#28559 := [monotonicity #28556]: #28558
-#28552 := (iff #28511 #28551)
-#28549 := (iff #28510 #28548)
-#28550 := [rewrite]: #28549
-#28553 := [monotonicity #28550]: #28552
-#28546 := (iff #28514 #28545)
-#28531 := (iff #28513 #28530)
-#28532 := [rewrite]: #28531
-#28547 := [monotonicity #28532]: #28546
-#28562 := [monotonicity #28547 #28553 #28559]: #28561
-#28567 := [trans #28562 #28565]: #28566
-#28570 := [monotonicity #28567]: #28569
-#28543 := (iff #28524 #28542)
-#28540 := (iff #28523 #28539)
-#28537 := (iff #28522 #28536)
-#28534 := (iff #28521 #28533)
+#10695 := [monotonicity #10692]: #10694
+#10698 := [quant-intro #10695]: #10697
+#10677 := (iff #2435 #10676)
+#10674 := (iff #2434 #10673)
+#10671 := (iff #2433 #10670)
+#10668 := (iff #2432 #10667)
+#10665 := (iff #2431 #10664)
+#10662 := (iff #2430 #10661)
+#10659 := (iff #2429 #10658)
+#10660 := [rewrite]: #10659
+#3709 := (iff #149 #3708)
+#3710 := [rewrite]: #3709
+#10663 := [monotonicity #3710 #10660]: #10662
+#10666 := [monotonicity #10663]: #10665
+#10656 := (iff #2427 #10655)
+#10653 := (iff #2426 #10652)
+#10650 := (iff #2425 #10649)
+#10647 := (iff #2424 #10646)
+#10644 := (iff #2423 #10643)
+#10645 := [rewrite]: #10644
+#10641 := (iff #2421 #10640)
+#10642 := [rewrite]: #10641
+#10648 := [monotonicity #10642 #10645]: #10647
+#10638 := (iff #2419 #10637)
+#10635 := (iff #2418 #10634)
+#10636 := [rewrite]: #10635
+#10639 := [monotonicity #10636]: #10638
+#10651 := [monotonicity #10639 #10648]: #10650
+#10632 := (iff #2415 #10631)
+#10629 := (iff #2414 #10628)
+#10626 := (iff #2413 #10625)
+#10627 := [rewrite]: #10626
+#10630 := [monotonicity #10627]: #10629
+#10623 := (iff #2410 #10622)
+#10620 := (iff #2409 #10619)
+#10621 := [rewrite]: #10620
+#10624 := [monotonicity #10621]: #10623
+#10633 := [monotonicity #10624 #10630]: #10632
+#10654 := [monotonicity #10633 #10651]: #10653
+#10657 := [monotonicity #10654]: #10656
+#10669 := [monotonicity #10657 #10666]: #10668
+#3715 := (iff #153 #3714)
+#3716 := [rewrite]: #3715
+#10672 := [monotonicity #3716 #10669]: #10671
+#10617 := (iff #2406 #10615)
+#10618 := [rewrite]: #10617
+#10675 := [monotonicity #10618 #10672]: #10674
+#10678 := [quant-intro #10675]: #10677
+#10700 := [trans #10678 #10698]: #10699
+#10614 := [asserted]: #2435
+#10701 := [mp #10614 #10700]: #10696
+#17971 := [mp~ #10701 #17970]: #10696
+#22074 := [mp #17971 #22073]: #22071
+#28402 := (not #22071)
+#29875 := (or #28402 #28562)
+#28478 := (or #28477 #28475)
+#28479 := (not #28478)
+#28489 := (or #28488 #28485)
+#28490 := (not #28489)
+#28492 := (= #28491 f15)
+#28493 := (not #28492)
+#28494 := (or #28493 #28490 #28482 #28479)
+#28495 := (not #28494)
+#28500 := (or #28499 #28497)
+#28501 := (not #28500)
+#28502 := (or #28492 #28501)
+#28503 := (not #28502)
+#28504 := (or #28503 #28495)
+#28505 := (not #28504)
+#28506 := (or #18539 #28505)
+#28507 := (not #28506)
+#28508 := (iff #12564 #28507)
+#29876 := (or #28402 #28508)
+#29925 := (iff #29876 #29875)
+#29867 := (iff #29875 #29875)
+#29870 := [rewrite]: #29867
+#28563 := (iff #28508 #28562)
+#28560 := (iff #28507 #28559)
+#28557 := (iff #28506 #28556)
+#28554 := (iff #28505 #28553)
+#28551 := (iff #28504 #28550)
+#28548 := (iff #28495 #28547)
+#28545 := (iff #28494 #28542)
+#28539 := (or #28524 #28530 #28482 #28536)
+#28543 := (iff #28539 #28542)
+#28544 := [rewrite]: #28543
+#28540 := (iff #28494 #28539)
+#28537 := (iff #28479 #28536)
+#28534 := (iff #28478 #28533)
 #28535 := [rewrite]: #28534
 #28538 := [monotonicity #28535]: #28537
-#28541 := [monotonicity #28532 #28538]: #28540
-#28544 := [monotonicity #28541]: #28543
-#28573 := [monotonicity #28544 #28570]: #28572
-#28576 := [monotonicity #28573]: #28575
-#28579 := [monotonicity #28576]: #28578
-#28582 := [monotonicity #28579]: #28581
-#28585 := [monotonicity #28582]: #28584
-#29935 := [monotonicity #28585]: #29946
-#29933 := [trans #29935 #29891]: #29946
-#29945 := [quant-inst #3039 #3257]: #29897
-#29889 := [mp #29945 #29933]: #29896
-#30214 := [unit-resolution #29889 #22094 #30296]: false
-#30215 := [lemma #30214]: #28583
-#30322 := (or #29899 #12584)
-#30167 := [hypothesis]: #28563
-decl f127 :: (-> S20 Int)
-#3043 := (f127 #3042)
-decl f135 :: (-> S18 Int S18)
-#3040 := (f135 f19 f296)
-#3044 := (f54 #3040 #3043)
-#3047 := (f36 f297 #3044)
-#30199 := (= #3047 #28497)
-#30193 := (= #28497 #3047)
-#30284 := (= #28494 #3044)
-decl f154 :: (-> S18 Int)
-#24998 := (f154 #3040)
-decl f155 :: (-> S18 S18)
-#24996 := (f155 #3040)
-#27144 := (f135 #24996 #24998)
-#27145 := (f54 #27144 #3043)
-#28787 := (= #27145 #3044)
-#28807 := (= #27144 #3040)
-#28805 := (= #24998 f296)
-#24999 := (= f296 #24998)
-#369 := (:var 1 S18)
-#1401 := (f135 #369 #202)
-#1638 := (pattern #1401)
-#1649 := (f154 #1401)
-#8444 := (= #202 #1649)
-#8447 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8444)
-#17390 := (~ #8447 #8447)
-#17388 := (~ #8444 #8444)
-#17389 := [refl]: #17388
-#17391 := [nnf-pos #17389]: #17390
-#1650 := (= #1649 #202)
-#1651 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1650)
-#8448 := (iff #1651 #8447)
-#8445 := (iff #1650 #8444)
-#8446 := [rewrite]: #8445
-#8449 := [quant-intro #8446]: #8448
-#8443 := [asserted]: #1651
-#8452 := [mp #8443 #8449]: #8447
-#17392 := [mp~ #8452 #17391]: #8447
-#25005 := (not #8447)
-#25006 := (or #25005 #24999)
-#25007 := [quant-inst #50 #3036]: #25006
-#28406 := [unit-resolution #25007 #17392]: #24999
-#28806 := [symm #28406]: #28805
-#28385 := (= #24996 f19)
-#24997 := (= f19 #24996)
-#1652 := (f155 #1401)
-#8451 := (= #369 #1652)
-#8455 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #8451)
-#17395 := (~ #8455 #8455)
-#17393 := (~ #8451 #8451)
-#17394 := [refl]: #17393
-#17396 := [nnf-pos #17394]: #17395
-#1653 := (= #1652 #369)
-#1654 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #1638) #1653)
-#8456 := (iff #1654 #8455)
-#8453 := (iff #1653 #8451)
-#8454 := [rewrite]: #8453
-#8457 := [quant-intro #8454]: #8456
-#8450 := [asserted]: #1654
-#8460 := [mp #8450 #8457]: #8455
-#17397 := [mp~ #8460 #17396]: #8455
-#25000 := (not #8455)
-#25001 := (or #25000 #24997)
-#25002 := [quant-inst #50 #3036]: #25001
-#28384 := [unit-resolution #25002 #17397]: #24997
-#28386 := [symm #28384]: #28385
-#28808 := [monotonicity #28386 #28806]: #28807
-#28789 := [monotonicity #28808]: #28787
-#30282 := (= #28494 #27145)
-decl f136 :: (-> S20 S20 Int)
-decl f39 :: (-> Int S20)
-decl f40 :: (-> S20 Int)
-#3076 := (f40 #3042)
-#24833 := (f39 #3076)
-#27122 := (f24 #24833)
-#29367 := (f77 #24833 f309 #27122)
-#29368 := (f136 #29367 #24833)
-#29431 := (f77 #27145 #29368 #24996)
-#29452 := (f69 #3220 #29431)
-#29458 := (f146 #29452)
-#30280 := (= #29458 #27145)
-#29459 := (= #27145 #29458)
-#29460 := (not #29459)
-#29456 := (f147 #29452)
-#29457 := (= f1 #29456)
-decl f78 :: (-> S29 S1)
-#29453 := (f78 #29452)
-#29454 := (= f1 #29453)
-#29455 := (not #29454)
-#29449 := (f35 f297 #29431)
-#29450 := (= f1 #29449)
-#29451 := (not #29450)
-#29481 := (or #29451 #29455 #29457 #29460)
-#29484 := (not #29481)
-#29474 := (* -1::Int #29368)
-#29475 := (+ #24998 #29474)
-#29476 := (<= #29475 0::Int)
-#30241 := (not #29476)
-#29583 := (+ f309 #29474)
-#29585 := (>= #29583 0::Int)
-#29369 := (= f309 #29368)
-#55 := (:var 1 S20)
-#1433 := (f24 #55)
-#1434 := (f77 #55 #202 #1433)
-#1435 := (pattern #1434)
-#1436 := (f136 #1434 #55)
-#7824 := (= #202 #1436)
-#7828 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #7824)
-#17105 := (~ #7828 #7828)
-#17103 := (~ #7824 #7824)
-#17104 := [refl]: #17103
-#17106 := [nnf-pos #17104]: #17105
-#1437 := (= #1436 #202)
-#1438 := (forall (vars (?v0 S20) (?v1 Int)) (:pat #1435) #1437)
-#7829 := (iff #1438 #7828)
-#7826 := (iff #1437 #7824)
-#7827 := [rewrite]: #7826
-#7830 := [quant-intro #7827]: #7829
-#7823 := [asserted]: #1438
-#7833 := [mp #7823 #7830]: #7828
-#17107 := [mp~ #7833 #17106]: #7828
-#27129 := (not #7828)
-#29432 := (or #27129 #29369)
-#29448 := [quant-inst #24833 #3139]: #29432
-#29674 := [unit-resolution #29448 #17107]: #29369
-#29675 := (not #29369)
-#30235 := (or #29675 #29585)
-#30236 := [th-lemma arith triangle-eq]: #30235
-#30237 := [unit-resolution #30236 #29674]: #29585
-#13537 := (* -1::Int f309)
-#13800 := (+ f296 #13537)
-#13801 := (<= #13800 0::Int)
-#13802 := (not #13801)
-#13709 := (* -1::Int #3266)
-decl f307 :: Int
-#3131 := f307
-#13710 := (+ f307 #13709)
-#13708 := (>= #13710 0::Int)
-#13707 := (not #13708)
+#28531 := (iff #28490 #28530)
+#28528 := (iff #28489 #28527)
+#28529 := [rewrite]: #28528
+#28532 := [monotonicity #28529]: #28531
+#28525 := (iff #28493 #28524)
+#28510 := (iff #28492 #28509)
+#28511 := [rewrite]: #28510
+#28526 := [monotonicity #28511]: #28525
+#28541 := [monotonicity #28526 #28532 #28538]: #28540
+#28546 := [trans #28541 #28544]: #28545
+#28549 := [monotonicity #28546]: #28548
+#28522 := (iff #28503 #28521)
+#28519 := (iff #28502 #28518)
+#28516 := (iff #28501 #28515)
+#28513 := (iff #28500 #28512)
+#28514 := [rewrite]: #28513
+#28517 := [monotonicity #28514]: #28516
+#28520 := [monotonicity #28511 #28517]: #28519
+#28523 := [monotonicity #28520]: #28522
+#28552 := [monotonicity #28523 #28549]: #28551
+#28555 := [monotonicity #28552]: #28554
+#28558 := [monotonicity #28555]: #28557
+#28561 := [monotonicity #28558]: #28560
+#28564 := [monotonicity #28561]: #28563
+#29914 := [monotonicity #28564]: #29925
+#29912 := [trans #29914 #29870]: #29925
+#29924 := [quant-inst #3032 #3250]: #29876
+#29868 := [mp #29924 #29912]: #29875
+#30193 := [unit-resolution #29868 #22074 #30275]: false
+#30194 := [lemma #30193]: #28562
+#30301 := (or #29878 #12564)
+#30146 := [hypothesis]: #28542
+decl f117 :: (-> S5 Int)
+#3036 := (f117 #3035)
+decl f125 :: (-> S3 Int S3)
+#3033 := (f125 f9 f291)
+#3037 := (f44 #3033 #3036)
+#3040 := (f26 f292 #3037)
+#30178 := (= #3040 #28476)
+#30172 := (= #28476 #3040)
+#30263 := (= #28473 #3037)
+decl f144 :: (-> S3 Int)
+#24977 := (f144 #3033)
+decl f145 :: (-> S3 S3)
+#24975 := (f145 #3033)
+#27123 := (f125 #24975 #24977)
+#27124 := (f44 #27123 #3036)
+#28766 := (= #27124 #3037)
+#28786 := (= #27123 #3033)
+#28784 := (= #24977 f291)
+#24978 := (= f291 #24977)
+#335 := (:var 1 S3)
+#1367 := (f125 #335 #168)
+#1604 := (pattern #1367)
+#1615 := (f144 #1367)
+#8391 := (= #168 #1615)
+#8394 := (forall (vars (?v0 S3) (?v1 Int)) (:pat #1604) #8391)
+#17345 := (~ #8394 #8394)
+#17343 := (~ #8391 #8391)
+#17344 := [refl]: #17343
+#17346 := [nnf-pos #17344]: #17345
+#1616 := (= #1615 #168)
+#1617 := (forall (vars (?v0 S3) (?v1 Int)) (:pat #1604) #1616)
+#8395 := (iff #1617 #8394)
+#8392 := (iff #1616 #8391)
+#8393 := [rewrite]: #8392
+#8396 := [quant-intro #8393]: #8395
+#8390 := [asserted]: #1617
+#8399 := [mp #8390 #8396]: #8394
+#17347 := [mp~ #8399 #17346]: #8394
+#24984 := (not #8394)
+#24985 := (or #24984 #24978)
+#24986 := [quant-inst #16 #3029]: #24985
+#28385 := [unit-resolution #24986 #17347]: #24978
+#28785 := [symm #28385]: #28784
+#28364 := (= #24975 f9)
+#24976 := (= f9 #24975)
+#1618 := (f145 #1367)
+#8398 := (= #335 #1618)
+#8402 := (forall (vars (?v0 S3) (?v1 Int)) (:pat #1604) #8398)
+#17350 := (~ #8402 #8402)
+#17348 := (~ #8398 #8398)
+#17349 := [refl]: #17348
+#17351 := [nnf-pos #17349]: #17350
+#1619 := (= #1618 #335)
+#1620 := (forall (vars (?v0 S3) (?v1 Int)) (:pat #1604) #1619)
+#8403 := (iff #1620 #8402)
+#8400 := (iff #1619 #8398)
+#8401 := [rewrite]: #8400
+#8404 := [quant-intro #8401]: #8403
+#8397 := [asserted]: #1620
+#8407 := [mp #8397 #8404]: #8402
+#17352 := [mp~ #8407 #17351]: #8402
+#24979 := (not #8402)
+#24980 := (or #24979 #24976)
+#24981 := [quant-inst #16 #3029]: #24980
+#28363 := [unit-resolution #24981 #17352]: #24976
+#28365 := [symm #28363]: #28364
+#28787 := [monotonicity #28365 #28785]: #28786
+#28768 := [monotonicity #28787]: #28766
+#30261 := (= #28473 #27124)
+decl f126 :: (-> S5 S5 Int)
+decl f29 :: (-> Int S5)
+decl f30 :: (-> S5 Int)
+#3069 := (f30 #3035)
+#24812 := (f29 #3069)
+#27101 := (f14 #24812)
+#29346 := (f67 #24812 f304 #27101)
+#29347 := (f126 #29346 #24812)
+#29410 := (f67 #27124 #29347 #24975)
+#29431 := (f59 #3213 #29410)
+#29437 := (f136 #29431)
+#30259 := (= #29437 #27124)
+#29438 := (= #27124 #29437)
+#29439 := (not #29438)
+#29435 := (f137 #29431)
+#29436 := (= f1 #29435)
+decl f68 :: (-> S14 S1)
+#29432 := (f68 #29431)
+#29433 := (= f1 #29432)
+#29434 := (not #29433)
+#29428 := (f25 f292 #29410)
+#29429 := (= f1 #29428)
+#29430 := (not #29429)
+#29460 := (or #29430 #29434 #29436 #29439)
+#29463 := (not #29460)
+#29453 := (* -1::Int #29347)
+#29454 := (+ #24977 #29453)
+#29455 := (<= #29454 0::Int)
+#30220 := (not #29455)
+#29562 := (+ f304 #29453)
+#29564 := (>= #29562 0::Int)
+#29348 := (= f304 #29347)
+#21 := (:var 1 S5)
+#1399 := (f14 #21)
+#1400 := (f67 #21 #168 #1399)
+#1401 := (pattern #1400)
+#1402 := (f126 #1400 #21)
+#7771 := (= #168 #1402)
+#7775 := (forall (vars (?v0 S5) (?v1 Int)) (:pat #1401) #7771)
+#17060 := (~ #7775 #7775)
+#17058 := (~ #7771 #7771)
+#17059 := [refl]: #17058
+#17061 := [nnf-pos #17059]: #17060
+#1403 := (= #1402 #168)
+#1404 := (forall (vars (?v0 S5) (?v1 Int)) (:pat #1401) #1403)
+#7776 := (iff #1404 #7775)
+#7773 := (iff #1403 #7771)
+#7774 := [rewrite]: #7773
+#7777 := [quant-intro #7774]: #7776
+#7770 := [asserted]: #1404
+#7780 := [mp #7770 #7777]: #7775
+#17062 := [mp~ #7780 #17061]: #7775
+#27108 := (not #7775)
+#29411 := (or #27108 #29348)
+#29427 := [quant-inst #24812 #3132]: #29411
+#29653 := [unit-resolution #29427 #17062]: #29348
+#29654 := (not #29348)
+#30214 := (or #29654 #29564)
+#30215 := [th-lemma arith triangle-eq]: #30214
+#30216 := [unit-resolution #30215 #29653]: #29564
+#13517 := (* -1::Int f304)
+#13780 := (+ f291 #13517)
+#13781 := (<= #13780 0::Int)
+#13782 := (not #13781)
+#13689 := (* -1::Int #3259)
+decl f302 :: Int
+#3124 := f302
+#13690 := (+ f302 #13689)
+#13688 := (>= #13690 0::Int)
+#13687 := (not #13688)
+decl f303 :: Int
+#3128 := f303
+#13493 := (>= f303 0::Int)
+#22459 := (not #13493)
+#12822 := (= f303 f311)
+#12828 := (not #12822)
+#12819 := (= f302 f310)
+#12837 := (not #12819)
+#23433 := (or #12837 #12828 #22459 #13636 #22418 #13687 #23400)
+#23436 := (not #23433)
+#23409 := (or #18536 #18545 #23406)
+#23412 := (not #23409)
+#23415 := (or #18536 #18539 #23412)
+#23418 := (not #23415)
+#23421 := (or #18536 #18539 #23418)
+#23424 := (not #23421)
+#23427 := (or #22459 #13636 #13688 #23424)
+#23430 := (not #23427)
+#23439 := (or #23430 #23436)
+#23442 := (not #23439)
+#23445 := (or #18536 #18545 #22459 #13636 #23442)
+#23448 := (not #23445)
+#23451 := (or #18536 #18545 #23448)
+#23454 := (not #23451)
+#23457 := (or #18536 #18539 #23454)
+#23460 := (not #23457)
+#23463 := (or #18536 #18539 #23460)
+#23466 := (not #23463)
+#23469 := (or #22459 #13636 #13781 #23466)
+#23472 := (not #23469)
+decl ?v0!15 :: Int
+#18718 := ?v0!15
+#18723 := (f67 #3035 ?v0!15 f9)
+#18724 := (f111 f292 #18723)
+#19069 := (* -1::Int #18724)
 decl f308 :: Int
-#3135 := f308
-#13513 := (>= f308 0::Int)
-#22479 := (not #13513)
-#12842 := (= f308 f316)
-#12848 := (not #12842)
-#12839 := (= f307 f315)
-#12857 := (not #12839)
-#23454 := (or #12857 #12848 #22479 #13656 #22438 #13707 #23421)
-#23457 := (not #23454)
-#23430 := (or #18556 #18565 #23427)
-#23433 := (not #23430)
-#23436 := (or #18556 #18559 #23433)
-#23439 := (not #23436)
-#23442 := (or #18556 #18559 #23439)
-#23445 := (not #23442)
-#23448 := (or #22479 #13656 #13708 #23445)
-#23451 := (not #23448)
-#23460 := (or #23451 #23457)
-#23463 := (not #23460)
-#23466 := (or #18556 #18565 #22479 #13656 #23463)
-#23469 := (not #23466)
-#23472 := (or #18556 #18565 #23469)
-#23475 := (not #23472)
-#23478 := (or #18556 #18559 #23475)
-#23481 := (not #23478)
-#23484 := (or #18556 #18559 #23481)
-#23487 := (not #23484)
-#23490 := (or #22479 #13656 #13801 #23487)
-#23493 := (not #23490)
-decl ?v0!15 :: Int
-#18738 := ?v0!15
-#18743 := (f77 #3042 ?v0!15 f19)
-#18744 := (f121 f297 #18743)
-#19089 := (* -1::Int #18744)
-decl f313 :: Int
-#3166 := f313
-#19090 := (+ f313 #19089)
-#19091 := (>= #19090 0::Int)
-#19076 := (* -1::Int ?v0!15)
-#19077 := (+ f296 #19076)
-#19078 := (<= #19077 0::Int)
-#18740 := (>= ?v0!15 0::Int)
-#22573 := (not #18740)
-#18739 := (<= ?v0!15 4294967295::Int)
-#22572 := (not #18739)
-#22588 := (or #22572 #22573 #19078 #19091)
-#22593 := (not #22588)
-#13442 := (* -1::Int f296)
-#13830 := (+ #202 #13442)
-#13829 := (>= #13830 0::Int)
-#3173 := (= #3124 f313)
-#22546 := (not #3173)
-#22547 := (or #22546 #5124 #13829 #19613)
-#23504 := (forall (vars (?v0 Int)) (:pat #23363) #22547)
-#23509 := (not #23504)
-#13841 := (* -1::Int f313)
-#13842 := (+ #3124 #13841)
-#13843 := (<= #13842 0::Int)
-#22538 := (or #5124 #13829 #13843 #19613)
-#23496 := (forall (vars (?v0 Int)) (:pat #23363) #22538)
-#23501 := (not #23496)
-#23512 := (or #23501 #23509)
-#23515 := (not #23512)
-#23518 := (or #23515 #22593)
-#23521 := (not #23518)
-#12278 := (= f307 f313)
-#12313 := (not #12278)
-decl f312 :: Int
-#3164 := f312
-#12275 := (= f308 f312)
-#12322 := (not #12275)
-decl f311 :: Int
-#3162 := f311
-#12272 := (= f309 f311)
-#12331 := (not #12272)
-decl f310 :: Int
-#3160 := f310
-#12269 := (= f307 f310)
-#12340 := (not #12269)
-#23524 := (or #12340 #12331 #12322 #12313 #22479 #13656 #13802 #23521)
-#23527 := (not #23524)
-#23530 := (or #23493 #23527)
-#23533 := (not #23530)
-#14006 := (* -1::Int f307)
-#14007 := (+ #3124 #14006)
-#14008 := (<= #14007 0::Int)
-#13995 := (+ #202 #13537)
-#13994 := (>= #13995 0::Int)
-#22354 := (or #5124 #13994 #14008 #19613)
-#23372 := (forall (vars (?v0 Int)) (:pat #23363) #22354)
-#23377 := (not #23372)
-#1374 := 255::Int
-#15885 := (<= f307 255::Int)
-#22623 := (not #15885)
-#15868 := (<= f308 4294967295::Int)
-#22622 := (not #15868)
-#15851 := (<= f309 4294967295::Int)
-#22621 := (not #15851)
-#14056 := (>= f307 0::Int)
-#22619 := (not #14056)
-#14034 := (>= f309 0::Int)
-#22618 := (not #14034)
-#14028 := (>= #13800 0::Int)
-#14031 := (not #14028)
-#13977 := (* -1::Int f308)
-#13978 := (+ f296 #13977)
-#13979 := (<= #13978 0::Int)
-#13508 := (<= f296 0::Int)
-decl f302 :: (-> S19 S17 S17 S20 S18 S1)
-decl f18 :: (-> S18 S18)
-#51 := (f18 f19)
-decl f291 :: S17
-#3019 := f291
-decl f283 :: S17
-#3011 := f283
-#3250 := (f302 f297 f283 f291 #3042 #51)
-#12558 := (= f1 #3250)
-#22617 := (not #12558)
-#3248 := (f301 f297 f283 f291 #3076 #51)
-#12555 := (= f1 #3248)
-#22616 := (not #12555)
-decl f290 :: S17
-#3018 := f290
-#3246 := (f301 f297 f283 f290 f296 f16)
-#12552 := (= f1 #3246)
-#13033 := (not #12552)
-#3244 := (f301 f297 f283 f288 f307 f19)
-#12549 := (= f1 #3244)
-#13042 := (not #12549)
-#3242 := (f301 f297 f283 f286 f308 f16)
-#12546 := (= f1 #3242)
-#13051 := (not #12546)
-#3240 := (f301 f297 f283 f284 f309 f16)
-#12543 := (= f1 #3240)
-#13060 := (not #12543)
-decl f189 :: (-> S19 S19 S1)
-#3232 := (f189 f297 f297)
-#12515 := (= f1 #3232)
-#13974 := (not #12515)
-decl f213 :: (-> S17 S19 S1)
-#3157 := (f213 f283 f297)
-#12258 := (= f1 #3157)
-#15299 := (not #12258)
-#3152 := (f77 #3042 f308 f19)
-#3153 := (f121 f297 #3152)
-#12250 := (= f307 #3153)
-#22615 := (not #12250)
-#3098 := (f77 #3042 0::Int f19)
-#3108 := (f121 f297 #3098)
+#3159 := f308
+#19070 := (+ f308 #19069)
+#19071 := (>= #19070 0::Int)
+#19056 := (* -1::Int ?v0!15)
+#19057 := (+ f291 #19056)
+#19058 := (<= #19057 0::Int)
+#18720 := (>= ?v0!15 0::Int)
+#22553 := (not #18720)
+#18719 := (<= ?v0!15 4294967295::Int)
+#22552 := (not #18719)
+#22568 := (or #22552 #22553 #19058 #19071)
+#22573 := (not #22568)
+#13422 := (* -1::Int f291)
+#13810 := (+ #168 #13422)
+#13809 := (>= #13810 0::Int)
+#3166 := (= #3117 f308)
+#22526 := (not #3166)
+#22527 := (or #22526 #5071 #13809 #19593)
+#23483 := (forall (vars (?v0 Int)) (:pat #23342) #22527)
+#23488 := (not #23483)
+#13821 := (* -1::Int f308)
+#13822 := (+ #3117 #13821)
+#13823 := (<= #13822 0::Int)
+#22518 := (or #5071 #13809 #13823 #19593)
+#23475 := (forall (vars (?v0 Int)) (:pat #23342) #22518)
+#23480 := (not #23475)
+#23491 := (or #23480 #23488)
+#23494 := (not #23491)
+#23497 := (or #23494 #22573)
+#23500 := (not #23497)
+#12258 := (= f302 f308)
+#12293 := (not #12258)
+decl f307 :: Int
+#3157 := f307
+#12255 := (= f303 f307)
+#12302 := (not #12255)
 decl f306 :: Int
-#3107 := f306
-#3109 := (= f306 #3108)
-#13267 := (not #3109)
-#23536 := (or #13267 #22615 #15299 #13974 #13060 #13051 #13042 #13033 #22616 #22617 #13508 #22479 #13656 #13979 #14031 #22618 #22619 #22621 #22622 #22623 #23377 #23533)
-#23539 := (not #23536)
-#23542 := (or #13267 #13508 #23539)
-#23545 := (not #23542)
-#13488 := (* -1::Int #3124)
-#13489 := (+ f306 #13488)
-#13487 := (>= #13489 0::Int)
-#13475 := (>= #202 1::Int)
-#22343 := (or #5124 #13475 #13487 #19613)
-#23364 := (forall (vars (?v0 Int)) (:pat #23363) #22343)
-#23369 := (not #23364)
-#23548 := (or #23369 #23545)
-#23551 := (not #23548)
+#3155 := f306
+#12252 := (= f304 f306)
+#12311 := (not #12252)
+decl f305 :: Int
+#3153 := f305
+#12249 := (= f302 f305)
+#12320 := (not #12249)
+#23503 := (or #12320 #12311 #12302 #12293 #22459 #13636 #13782 #23500)
+#23506 := (not #23503)
+#23509 := (or #23472 #23506)
+#23512 := (not #23509)
+#13986 := (* -1::Int f302)
+#13987 := (+ #3117 #13986)
+#13988 := (<= #13987 0::Int)
+#13975 := (+ #168 #13517)
+#13974 := (>= #13975 0::Int)
+#22334 := (or #5071 #13974 #13988 #19593)
+#23351 := (forall (vars (?v0 Int)) (:pat #23342) #22334)
+#23356 := (not #23351)
+#1340 := 255::Int
+#15865 := (<= f302 255::Int)
+#22603 := (not #15865)
+#15848 := (<= f303 4294967295::Int)
+#22602 := (not #15848)
+#15831 := (<= f304 4294967295::Int)
+#22601 := (not #15831)
+#14036 := (>= f302 0::Int)
+#22599 := (not #14036)
+#14014 := (>= f304 0::Int)
+#22598 := (not #14014)
+#14008 := (>= #13780 0::Int)
+#14011 := (not #14008)
+#13957 := (* -1::Int f303)
+#13958 := (+ f291 #13957)
+#13959 := (<= #13958 0::Int)
+#13488 := (<= f291 0::Int)
+decl f297 :: (-> S4 S2 S2 S5 S3 S1)
+decl f8 :: (-> S3 S3)
+#17 := (f8 f9)
+decl f281 :: S2
+#2985 := f281
+decl f273 :: S2
+#2977 := f273
+#3243 := (f297 f292 f273 f281 #3035 #17)
+#12538 := (= f1 #3243)
+#22597 := (not #12538)
+#3241 := (f296 f292 f273 f281 #3069 #17)
+#12535 := (= f1 #3241)
+#22596 := (not #12535)
+decl f280 :: S2
+#2984 := f280
+#3239 := (f296 f292 f273 f280 f291 f6)
+#12532 := (= f1 #3239)
+#13013 := (not #12532)
+#3237 := (f296 f292 f273 f278 f302 f9)
+#12529 := (= f1 #3237)
+#13022 := (not #12529)
+#3235 := (f296 f292 f273 f276 f303 f6)
+#12526 := (= f1 #3235)
+#13031 := (not #12526)
+#3233 := (f296 f292 f273 f274 f304 f6)
+#12523 := (= f1 #3233)
+#13040 := (not #12523)
+decl f179 :: (-> S4 S4 S1)
+#3225 := (f179 f292 f292)
+#12495 := (= f1 #3225)
+#13954 := (not #12495)
+decl f203 :: (-> S2 S4 S1)
+#3150 := (f203 f273 f292)
+#12238 := (= f1 #3150)
+#15279 := (not #12238)
+#3145 := (f67 #3035 f303 f9)
+#3146 := (f111 f292 #3145)
+#12230 := (= f302 #3146)
+#22595 := (not #12230)
+#3091 := (f67 #3035 0::Int f9)
+#3101 := (f111 f292 #3091)
+decl f301 :: Int
+#3100 := f301
+#3102 := (= f301 #3101)
+#13247 := (not #3102)
+#23515 := (or #13247 #22595 #15279 #13954 #13040 #13031 #13022 #13013 #22596 #22597 #13488 #22459 #13636 #13959 #14011 #22598 #22599 #22601 #22602 #22603 #23356 #23512)
+#23518 := (not #23515)
+#23521 := (or #13247 #13488 #23518)
+#23524 := (not #23521)
+#13468 := (* -1::Int #3117)
+#13469 := (+ f301 #13468)
+#13467 := (>= #13469 0::Int)
+#13455 := (>= #168 1::Int)
+#22323 := (or #5071 #13455 #13467 #19593)
+#23343 := (forall (vars (?v0 Int)) (:pat #23342) #22323)
+#23348 := (not #23343)
+#23527 := (or #23348 #23524)
+#23530 := (not #23527)
 decl ?v0!13 :: Int
-#18477 := ?v0!13
-#18487 := (>= ?v0!13 1::Int)
-#18482 := (f77 #3042 ?v0!13 f19)
-#18483 := (f121 f297 #18482)
-#18484 := (* -1::Int #18483)
-#18485 := (+ f306 #18484)
-#18486 := (>= #18485 0::Int)
-#18479 := (>= ?v0!13 0::Int)
-#22317 := (not #18479)
-#18478 := (<= ?v0!13 4294967295::Int)
-#22316 := (not #18478)
-#22332 := (or #22316 #22317 #18486 #18487)
-#22337 := (not #22332)
-#23554 := (or #22337 #23551)
-#23557 := (not #23554)
-#13469 := (>= f296 1::Int)
-#13472 := (not #13469)
-#23560 := (or #13472 #23557)
-#23563 := (not #23560)
-#23566 := (or #13472 #23563)
-#23569 := (not #23566)
-decl f285 :: S17
-#3013 := f285
-#3114 := (f301 f297 f285 f284 1::Int f16)
-#12201 := (= f1 #3114)
-#13240 := (not #12201)
-decl f287 :: S17
-#3015 := f287
-#3112 := (f301 f297 f287 f286 0::Int f16)
-#12198 := (= f1 #3112)
-#13249 := (not #12198)
-decl f289 :: S17
-#3017 := f289
-#3110 := (f301 f297 f289 f288 f306 f19)
-#12195 := (= f1 #3110)
-#13258 := (not #12195)
-#3104 := (f79 f297 #3098)
-#12189 := (= f1 #3104)
-#18454 := (not #12189)
-#3099 := (f59 #3098 f19)
-#12180 := (= f1 #3099)
-#18445 := (not #12180)
-#23572 := (or #13267 #18445 #18454 #13258 #13249 #13240 #23569)
-#23575 := (not #23572)
-#27039 := (f24 #3098)
-#27040 := (= #24996 #27039)
-#27013 := (f59 #3098 #24996)
-#27014 := (= f1 #27013)
-#27042 := (iff #27014 #27040)
-#275 := (:var 0 S18)
-#2729 := (f59 #55 #275)
-#2730 := (pattern #2729)
-#11369 := (= f1 #2729)
-#9220 := (= #275 #1433)
-#11390 := (iff #9220 #11369)
-#23294 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11390)
-#11395 := (forall (vars (?v0 S20) (?v1 S18)) #11390)
-#23297 := (iff #11395 #23294)
-#23295 := (iff #11390 #11390)
-#23296 := [refl]: #23295
-#23298 := [quant-intro #23296]: #23297
-#18287 := (~ #11395 #11395)
-#18285 := (~ #11390 #11390)
-#18286 := [refl]: #18285
-#18288 := [nnf-pos #18286]: #18287
-#1939 := (= #1433 #275)
-#2731 := (= #2729 f1)
-#2736 := (iff #2731 #1939)
-#2737 := (forall (vars (?v0 S20) (?v1 S18)) #2736)
-#11396 := (iff #2737 #11395)
-#11393 := (iff #2736 #11390)
-#11386 := (iff #11369 #9220)
-#11391 := (iff #11386 #11390)
-#11392 := [rewrite]: #11391
-#11388 := (iff #2736 #11386)
-#9221 := (iff #1939 #9220)
-#9222 := [rewrite]: #9221
-#11371 := (iff #2731 #11369)
-#11372 := [rewrite]: #11371
-#11389 := [monotonicity #11372 #9222]: #11388
-#11394 := [trans #11389 #11392]: #11393
-#11397 := [quant-intro #11394]: #11396
-#11385 := [asserted]: #2737
-#11400 := [mp #11385 #11397]: #11395
-#18289 := [mp~ #11400 #18288]: #11395
-#23299 := [mp #18289 #23298]: #23294
-#26210 := (not #23294)
-#27513 := (or #26210 #27042)
-#27041 := (iff #27040 #27014)
-#27551 := (or #26210 #27041)
-#27552 := (iff #27551 #27513)
-#27592 := (iff #27513 #27513)
-#27593 := [rewrite]: #27592
-#27043 := (iff #27041 #27042)
-#27044 := [rewrite]: #27043
-#27594 := [monotonicity #27044]: #27552
-#27595 := [trans #27594 #27593]: #27552
-#27546 := [quant-inst #3098 #24996]: #27551
-#27596 := [mp #27546 #27595]: #27513
-#27640 := [unit-resolution #27596 #23299]: #27042
-#25112 := (f24 #3042)
-#27668 := (= #25112 #27039)
-#27682 := (= #27039 #25112)
-#27680 := (= #3098 #3042)
-#27070 := (f127 #24833)
-#27086 := (f54 #24996 #27070)
-#27410 := (= #27086 #3042)
-#27367 := (= #27070 f298)
-#28390 := (= #3043 f298)
-#25116 := (= f298 #3043)
-#2761 := (f54 #369 #202)
-#23300 := (pattern #2761)
-#2762 := (f127 #2761)
-#11445 := (= #202 #2762)
-#23301 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23300) #11445)
-#11449 := (forall (vars (?v0 S18) (?v1 Int)) #11445)
-#23304 := (iff #11449 #23301)
-#23302 := (iff #11445 #11445)
-#23303 := [refl]: #23302
-#23305 := [quant-intro #23303]: #23304
-#18302 := (~ #11449 #11449)
-#18300 := (~ #11445 #11445)
-#18301 := [refl]: #18300
-#18303 := [nnf-pos #18301]: #18302
-#2763 := (= #2762 #202)
-#2764 := (forall (vars (?v0 S18) (?v1 Int)) #2763)
-#11450 := (iff #2764 #11449)
-#11447 := (iff #2763 #11445)
-#11448 := [rewrite]: #11447
-#11451 := [quant-intro #11448]: #11450
-#11444 := [asserted]: #2764
-#11454 := [mp #11444 #11451]: #11449
-#18304 := [mp~ #11454 #18303]: #11449
-#23306 := [mp #18304 #23305]: #23301
-#25070 := (not #23301)
-#25121 := (or #25070 #25116)
-#25122 := [quant-inst #50 #3041]: #25121
-#28389 := [unit-resolution #25122 #23306]: #25116
-#28391 := [symm #28389]: #28390
-#27143 := (= #27070 #3043)
-#27141 := (= #24833 #3042)
-#24834 := (= #3042 #24833)
-#132 := (f40 #62)
-#23211 := (pattern #132)
-#133 := (f39 #132)
-#3682 := (= #62 #133)
-#23212 := (forall (vars (?v0 S20)) (:pat #23211) #3682)
-#3685 := (forall (vars (?v0 S20)) #3682)
-#23213 := (iff #3685 #23212)
-#23215 := (iff #23212 #23212)
-#23216 := [rewrite]: #23215
-#23214 := [rewrite]: #23213
-#23217 := [trans #23214 #23216]: #23213
-#16342 := (~ #3685 #3685)
-#16332 := (~ #3682 #3682)
-#16333 := [refl]: #16332
-#16398 := [nnf-pos #16333]: #16342
-#134 := (= #133 #62)
-#135 := (forall (vars (?v0 S20)) #134)
-#3686 := (iff #135 #3685)
-#3683 := (iff #134 #3682)
-#3684 := [rewrite]: #3683
-#3687 := [quant-intro #3684]: #3686
-#3681 := [asserted]: #135
-#3690 := [mp #3681 #3687]: #3685
-#16399 := [mp~ #3690 #16398]: #3685
-#23218 := [mp #16399 #23217]: #23212
-#24837 := (not #23212)
-#24838 := (or #24837 #24834)
-#24839 := [quant-inst #3042]: #24838
-#27140 := [unit-resolution #24839 #23218]: #24834
-#27142 := [symm #27140]: #27141
-#27275 := [monotonicity #27142]: #27143
-#27368 := [trans #27275 #28391]: #27367
-#27414 := [monotonicity #28386 #27368]: #27410
-#27415 := (= #3098 #27086)
-#27064 := (f77 #24833 0::Int #24996)
-#27089 := (= #27064 #27086)
-#27092 := (not #27089)
-decl f149 :: (-> S20 S20 S1)
-#27065 := (f149 #27064 #24833)
-#27066 := (= f1 #27065)
-#27067 := (not #27066)
-#27098 := (or #27067 #27092)
-#27103 := (not #27098)
-#28651 := [hypothesis]: #27098
-#289 := (:var 1 Int)
-#60 := (:var 2 S20)
-#1622 := (f77 #60 #289 #275)
-#1623 := (pattern #1622)
-#1624 := (f149 #1622 #60)
-#8390 := (= f1 #1624)
-#21232 := (not #8390)
-decl f150 :: (-> S18 Int)
-#1627 := (f150 #275)
-#1628 := (* #289 #1627)
-#1626 := (f127 #60)
-#1629 := (+ #1626 #1628)
-#1630 := (f54 #275 #1629)
-#1631 := (= #1622 #1630)
-#21231 := (not #1631)
-#21233 := (or #21231 #21232)
-#21234 := (not #21233)
-#21237 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #21234)
-#8396 := (and #1631 #8390)
-#8401 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #8396)
-#21238 := (iff #8401 #21237)
-#21235 := (iff #8396 #21234)
-#21236 := [rewrite]: #21235
-#21239 := [quant-intro #21236]: #21238
-#17365 := (~ #8401 #8401)
-#17363 := (~ #8396 #8396)
-#17364 := [refl]: #17363
-#17366 := [nnf-pos #17364]: #17365
-#1625 := (= #1624 f1)
-#1632 := (and #1625 #1631)
-#1633 := (forall (vars (?v0 S20) (?v1 Int) (?v2 S18)) (:pat #1623) #1632)
-#8402 := (iff #1633 #8401)
-#8399 := (iff #1632 #8396)
-#8393 := (and #8390 #1631)
-#8397 := (iff #8393 #8396)
-#8398 := [rewrite]: #8397
-#8394 := (iff #1632 #8393)
-#8391 := (iff #1625 #8390)
-#8392 := [rewrite]: #8391
-#8395 := [monotonicity #8392]: #8394
-#8400 := [trans #8395 #8398]: #8399
-#8403 := [quant-intro #8400]: #8402
-#8389 := [asserted]: #1633
-#8406 := [mp #8389 #8403]: #8401
-#17367 := [mp~ #8406 #17366]: #8401
-#21240 := [mp #17367 #21239]: #21237
-#27721 := (not #21237)
-#27728 := (or #27721 #27103)
-#27068 := (f150 #24996)
-#27069 := (* 0::Int #27068)
-#27071 := (+ #27070 #27069)
-#27072 := (f54 #24996 #27071)
-#27073 := (= #27064 #27072)
-#27074 := (not #27073)
-#27075 := (or #27074 #27067)
-#27076 := (not #27075)
-#27729 := (or #27721 #27076)
-#27730 := (iff #27729 #27728)
-#27736 := (iff #27728 #27728)
-#27737 := [rewrite]: #27736
-#27104 := (iff #27076 #27103)
-#27101 := (iff #27075 #27098)
-#27095 := (or #27092 #27067)
-#27099 := (iff #27095 #27098)
-#27100 := [rewrite]: #27099
-#27096 := (iff #27075 #27095)
-#27093 := (iff #27074 #27092)
-#27090 := (iff #27073 #27089)
-#27087 := (= #27072 #27086)
-#27084 := (= #27071 #27070)
-#27079 := (+ #27070 0::Int)
-#27082 := (= #27079 #27070)
-#27083 := [rewrite]: #27082
-#27080 := (= #27071 #27079)
-#27077 := (= #27069 0::Int)
-#27078 := [rewrite]: #27077
-#27081 := [monotonicity #27078]: #27080
-#27085 := [trans #27081 #27083]: #27084
-#27088 := [monotonicity #27085]: #27087
-#27091 := [monotonicity #27088]: #27090
-#27094 := [monotonicity #27091]: #27093
-#27097 := [monotonicity #27094]: #27096
-#27102 := [trans #27097 #27100]: #27101
-#27105 := [monotonicity #27102]: #27104
-#27731 := [monotonicity #27105]: #27730
-#27745 := [trans #27731 #27737]: #27730
-#27727 := [quant-inst #24833 #161 #24996]: #27729
-#27746 := [mp #27727 #27745]: #27728
-#28652 := [unit-resolution #27746 #21240 #28651]: false
-#28653 := [lemma #28652]: #27103
-#27748 := (or #27098 #27089)
-#27749 := [def-axiom]: #27748
-#27673 := [unit-resolution #27749 #28653]: #27089
-#27371 := (= #3098 #27064)
-#27409 := [monotonicity #27140 #28384]: #27371
-#27674 := [trans #27409 #27673]: #27415
-#27675 := [trans #27674 #27414]: #27680
-#27676 := [monotonicity #27675]: #27682
-#27669 := [symm #27676]: #27668
-#27670 := (= #24996 #25112)
-#25113 := (= f19 #25112)
-#2765 := (f24 #2761)
-#11453 := (= #369 #2765)
-#23307 := (forall (vars (?v0 S18) (?v1 Int)) (:pat #23300) #11453)
-#11457 := (forall (vars (?v0 S18) (?v1 Int)) #11453)
-#23310 := (iff #11457 #23307)
-#23308 := (iff #11453 #11453)
-#23309 := [refl]: #23308
-#23311 := [quant-intro #23309]: #23310
-#18307 := (~ #11457 #11457)
-#18305 := (~ #11453 #11453)
-#18306 := [refl]: #18305
-#18308 := [nnf-pos #18306]: #18307
-#2766 := (= #2765 #369)
-#2767 := (forall (vars (?v0 S18) (?v1 Int)) #2766)
-#11458 := (iff #2767 #11457)
-#11455 := (iff #2766 #11453)
-#11456 := [rewrite]: #11455
-#11459 := [quant-intro #11456]: #11458
-#11452 := [asserted]: #2767
-#11462 := [mp #11452 #11459]: #11457
-#18309 := [mp~ #11462 #18308]: #11457
-#23312 := [mp #18309 #23311]: #23307
-#25064 := (not #23307)
-#25118 := (or #25064 #25113)
-#25119 := [quant-inst #50 #3041]: #25118
-#27139 := [unit-resolution #25119 #23312]: #25113
-#27671 := [trans #28386 #27139]: #27670
-#27672 := [trans #27671 #27669]: #27040
-#27021 := (not #27014)
-#27677 := (iff #18445 #27021)
-#27722 := (iff #12180 #27014)
-#27750 := (iff #27014 #12180)
-#27744 := (= #27013 #3099)
-#27747 := [monotonicity #28386]: #27744
-#27751 := [monotonicity #27747]: #27750
-#27723 := [symm #27751]: #27722
-#27724 := [monotonicity #27723]: #27677
-#27667 := [hypothesis]: #18445
-#27725 := [mp #27667 #27724]: #27021
-#27604 := (not #27040)
-#27597 := (not #27042)
-#27605 := (or #27597 #27014 #27604)
-#27603 := [def-axiom]: #27605
-#27726 := [unit-resolution #27603 #27725 #27672 #27640]: false
-#27642 := [lemma #27726]: #12180
-#28945 := (or #27098 #12189)
-#26985 := (f69 #3220 #3098)
-#27775 := (f146 #26985)
-#27778 := (f36 f297 #27775)
-#27786 := (= f37 #27778)
-#27776 := (f221 f297 #27775)
-#27777 := (= f1 #27776)
-#28363 := (or #27777 #27786)
-#28365 := (not #28363)
-#28146 := (f147 #26985)
-#28147 := (= f1 #28146)
-#28148 := (not #28147)
-#28100 := (f38 f297 #27775)
-#28093 := (= f1 #28100)
-#28145 := (not #28093)
-#28326 := (or #28145 #28148)
-#28340 := (not #28326)
-#27920 := (f23 #27039)
-#28266 := (= f25 #27920)
-#28322 := (not #28266)
-#28095 := (f24 #27775)
-#28096 := (f23 #28095)
-#28097 := (= f25 #28096)
-#28345 := (or #28097 #28322 #28340 #28365)
-#28437 := (not #28345)
-#28209 := (f221 f297 #3098)
-#28207 := (= f1 #28209)
-#28196 := (f36 f297 #3098)
-#28197 := (= f37 #28196)
-#28195 := (or #28197 #28207)
-#28275 := (not #28195)
-#28271 := (or #28275 #28266)
-#28273 := (not #28271)
-#28440 := (or #28273 #28437)
-#28443 := (not #28440)
-#3101 := (f35 f297 #3098)
-#12183 := (= f1 #3101)
-#18448 := (not #12183)
-#28446 := (or #18448 #28443)
-#28377 := (not #28446)
-#28367 := (iff #12189 #28377)
-#28434 := (or #28423 #28367)
-#27787 := (or #27786 #27777)
-#28094 := (not #27787)
-#27921 := (or #28148 #28145)
-#27919 := (not #27921)
-#27931 := (= #27920 f25)
-#27965 := (not #27931)
-#27966 := (or #27965 #27919 #28097 #28094)
-#28208 := (not #27966)
-#28276 := (or #27931 #28275)
-#28274 := (not #28276)
-#28277 := (or #28274 #28208)
-#28278 := (not #28277)
-#28279 := (or #18448 #28278)
-#28264 := (not #28279)
-#28265 := (iff #12189 #28264)
-#28435 := (or #28423 #28265)
-#28448 := (iff #28435 #28434)
-#28450 := (iff #28434 #28434)
-#28451 := [rewrite]: #28450
-#28348 := (iff #28265 #28367)
-#28378 := (iff #28264 #28377)
-#28368 := (iff #28279 #28446)
-#28444 := (iff #28278 #28443)
-#28441 := (iff #28277 #28440)
-#28438 := (iff #28208 #28437)
-#28360 := (iff #27966 #28345)
-#28341 := (or #28322 #28340 #28097 #28365)
-#28346 := (iff #28341 #28345)
-#28347 := [rewrite]: #28346
-#28343 := (iff #27966 #28341)
-#28339 := (iff #28094 #28365)
-#28364 := (iff #27787 #28363)
-#28359 := [rewrite]: #28364
-#28342 := [monotonicity #28359]: #28339
-#28361 := (iff #27919 #28340)
-#28331 := (iff #27921 #28326)
-#28332 := [rewrite]: #28331
-#28362 := [monotonicity #28332]: #28361
-#28281 := (iff #27965 #28322)
-#28267 := (iff #27931 #28266)
-#28268 := [rewrite]: #28267
-#28325 := [monotonicity #28268]: #28281
-#28344 := [monotonicity #28325 #28362 #28342]: #28343
-#28436 := [trans #28344 #28347]: #28360
-#28439 := [monotonicity #28436]: #28438
-#28320 := (iff #28274 #28273)
-#28284 := (iff #28276 #28271)
-#28263 := (or #28266 #28275)
-#28272 := (iff #28263 #28271)
-#28283 := [rewrite]: #28272
-#28269 := (iff #28276 #28263)
-#28270 := [monotonicity #28268]: #28269
-#28282 := [trans #28270 #28283]: #28284
-#28321 := [monotonicity #28282]: #28320
-#28442 := [monotonicity #28321 #28439]: #28441
-#28445 := [monotonicity #28442]: #28444
-#28369 := [monotonicity #28445]: #28368
-#28213 := [monotonicity #28369]: #28378
-#28349 := [monotonicity #28213]: #28348
-#28449 := [monotonicity #28349]: #28448
-#28456 := [trans #28449 #28451]: #28448
-#28447 := [quant-inst #3039 #3098]: #28435
-#28457 := [mp #28447 #28456]: #28434
-#28776 := [unit-resolution #28457 #22094]: #28367
-#28625 := (not #28367)
-#28779 := (or #28625 #28446)
-#28778 := [hypothesis]: #18454
-#28626 := (or #28625 #12189 #28446)
-#28627 := [def-axiom]: #28626
-#28777 := [unit-resolution #28627 #28778]: #28779
-#28780 := [unit-resolution #28777 #28776]: #28446
-#28816 := (or #28377 #28443)
-decl f26 :: (-> S20 S21 S1)
-decl f27 :: (-> S19 S20 S21)
-#24880 := (f127 #3044)
-#26182 := (f54 #3040 #24880)
-#26775 := (f27 f297 #26182)
-#27233 := (f26 #27145 #26775)
-#27234 := (= f1 #27233)
-#26776 := (f26 #26182 #26775)
-#28795 := (= #26776 #27233)
-#28792 := (= #27233 #26776)
-#28790 := (= #27145 #26182)
-#26189 := (= #3044 #26182)
-#3049 := (f59 #3044 #3040)
-#12109 := (= f1 #3049)
-decl f34 :: (-> S18 S1)
-#3056 := (f34 #3040)
-#12121 := (= f1 #3056)
-#3053 := (f23 #3040)
-#12115 := (= f25 #3053)
-#12118 := (not #12115)
-#3051 := (f35 f297 #3044)
-#12112 := (= f1 #3051)
-#12106 := (= f37 #3047)
-#3045 := (f38 f297 #3044)
-#12102 := (= f1 #3045)
-#14228 := (and #12102 #12106 #12109 #12112 #12118 #12121)
-decl f293 :: Int
-#3024 := f293
-#14284 := (* -1::Int f293)
-decl f89 :: Int
-#472 := f89
-#14285 := (+ f89 #14284)
-#14283 := (>= #14285 0::Int)
-#14281 := (>= f293 0::Int)
-#14288 := (and #14281 #14283)
-#14291 := (not #14288)
-decl f294 :: Int
-#3028 := f294
-#14270 := (* -1::Int f294)
-decl f87 :: Int
-#452 := f87
-#14271 := (+ f87 #14270)
-#14269 := (>= #14271 0::Int)
-#14267 := (>= f294 0::Int)
-#14274 := (and #14267 #14269)
-#14277 := (not #14274)
+#18457 := ?v0!13
+#18467 := (>= ?v0!13 1::Int)
+#18462 := (f67 #3035 ?v0!13 f9)
+#18463 := (f111 f292 #18462)
+#18464 := (* -1::Int #18463)
+#18465 := (+ f301 #18464)
+#18466 := (>= #18465 0::Int)
+#18459 := (>= ?v0!13 0::Int)
+#22297 := (not #18459)
+#18458 := (<= ?v0!13 4294967295::Int)
+#22296 := (not #18458)
+#22312 := (or #22296 #22297 #18466 #18467)
+#22317 := (not #22312)
+#23533 := (or #22317 #23530)
+#23536 := (not #23533)
+#13449 := (>= f291 1::Int)
+#13452 := (not #13449)
+#23539 := (or #13452 #23536)
+#23542 := (not #23539)
+#23545 := (or #13452 #23542)
+#23548 := (not #23545)
+decl f275 :: S2
+#2979 := f275
+#3107 := (f296 f292 f275 f274 1::Int f6)
+#12181 := (= f1 #3107)
+#13220 := (not #12181)
+decl f277 :: S2
+#2981 := f277
+#3105 := (f296 f292 f277 f276 0::Int f6)
+#12178 := (= f1 #3105)
+#13229 := (not #12178)
+decl f279 :: S2
+#2983 := f279
+#3103 := (f296 f292 f279 f278 f301 f9)
+#12175 := (= f1 #3103)
+#13238 := (not #12175)
+#3097 := (f69 f292 #3091)
+#12169 := (= f1 #3097)
+#18434 := (not #12169)
+#3092 := (f49 #3091 f9)
+#12160 := (= f1 #3092)
+#18425 := (not #12160)
+#23551 := (or #13247 #18425 #18434 #13238 #13229 #13220 #23548)
+#23554 := (not #23551)
+#27018 := (f14 #3091)
+#27019 := (= #24975 #27018)
+#26992 := (f49 #3091 #24975)
+#26993 := (= f1 #26992)
+#27021 := (iff #26993 #27019)
+#241 := (:var 0 S3)
+#2695 := (f49 #21 #241)
+#2696 := (pattern #2695)
+#11316 := (= f1 #2695)
+#9167 := (= #241 #1399)
+#11337 := (iff #9167 #11316)
+#23238 := (forall (vars (?v0 S5) (?v1 S3)) (:pat #2696) #11337)
+#11342 := (forall (vars (?v0 S5) (?v1 S3)) #11337)
+#23241 := (iff #11342 #23238)
+#23239 := (iff #11337 #11337)
+#23240 := [refl]: #23239
+#23242 := [quant-intro #23240]: #23241
+#18242 := (~ #11342 #11342)
+#18240 := (~ #11337 #11337)
+#18241 := [refl]: #18240
+#18243 := [nnf-pos #18241]: #18242
+#1905 := (= #1399 #241)
+#2697 := (= #2695 f1)
+#2702 := (iff #2697 #1905)
+#2703 := (forall (vars (?v0 S5) (?v1 S3)) #2702)
+#11343 := (iff #2703 #11342)
+#11340 := (iff #2702 #11337)
+#11333 := (iff #11316 #9167)
+#11338 := (iff #11333 #11337)
+#11339 := [rewrite]: #11338
+#11335 := (iff #2702 #11333)
+#9168 := (iff #1905 #9167)
+#9169 := [rewrite]: #9168
+#11318 := (iff #2697 #11316)
+#11319 := [rewrite]: #11318
+#11336 := [monotonicity #11319 #9169]: #11335
+#11341 := [trans #11336 #11339]: #11340
+#11344 := [quant-intro #11341]: #11343
+#11332 := [asserted]: #2703
+#11347 := [mp #11332 #11344]: #11342
+#18244 := [mp~ #11347 #18243]: #11342
+#23243 := [mp #18244 #23242]: #23238
+#26189 := (not #23238)
+#27492 := (or #26189 #27021)
+#27020 := (iff #27019 #26993)
+#27530 := (or #26189 #27020)
+#27531 := (iff #27530 #27492)
+#27571 := (iff #27492 #27492)
+#27572 := [rewrite]: #27571
+#27022 := (iff #27020 #27021)
+#27023 := [rewrite]: #27022
+#27573 := [monotonicity #27023]: #27531
+#27574 := [trans #27573 #27572]: #27531
+#27525 := [quant-inst #3091 #24975]: #27530
+#27575 := [mp #27525 #27574]: #27492
+#27619 := [unit-resolution #27575 #23243]: #27021
+#25091 := (f14 #3035)
+#27647 := (= #25091 #27018)
+#27661 := (= #27018 #25091)
+#27659 := (= #3091 #3035)
+#27049 := (f117 #24812)
+#27065 := (f44 #24975 #27049)
+#27389 := (= #27065 #3035)
+#27346 := (= #27049 f293)
+#28369 := (= #3036 f293)
+#25095 := (= f293 #3036)
+#2727 := (f44 #335 #168)
+#23244 := (pattern #2727)
+#2728 := (f117 #2727)
+#11392 := (= #168 #2728)
+#23245 := (forall (vars (?v0 S3) (?v1 Int)) (:pat #23244) #11392)
+#11396 := (forall (vars (?v0 S3) (?v1 Int)) #11392)
+#23248 := (iff #11396 #23245)
+#23246 := (iff #11392 #11392)
+#23247 := [refl]: #23246
+#23249 := [quant-intro #23247]: #23248
+#18257 := (~ #11396 #11396)
+#18255 := (~ #11392 #11392)
+#18256 := [refl]: #18255
+#18258 := [nnf-pos #18256]: #18257
+#2729 := (= #2728 #168)
+#2730 := (forall (vars (?v0 S3) (?v1 Int)) #2729)
+#11397 := (iff #2730 #11396)
+#11394 := (iff #2729 #11392)
+#11395 := [rewrite]: #11394
+#11398 := [quant-intro #11395]: #11397
+#11391 := [asserted]: #2730
+#11401 := [mp #11391 #11398]: #11396
+#18259 := [mp~ #11401 #18258]: #11396
+#23250 := [mp #18259 #23249]: #23245
+#25049 := (not #23245)
+#25100 := (or #25049 #25095)
+#25101 := [quant-inst #16 #3034]: #25100
+#28368 := [unit-resolution #25101 #23250]: #25095
+#28370 := [symm #28368]: #28369
+#27122 := (= #27049 #3036)
+#27120 := (= #24812 #3035)
+#24813 := (= #3035 #24812)
+#98 := (f30 #28)
+#23155 := (pattern #98)
+#99 := (f29 #98)
+#3629 := (= #28 #99)
+#23156 := (forall (vars (?v0 S5)) (:pat #23155) #3629)
+#3632 := (forall (vars (?v0 S5)) #3629)
+#23157 := (iff #3632 #23156)
+#23159 := (iff #23156 #23156)
+#23160 := [rewrite]: #23159
+#23158 := [rewrite]: #23157
+#23161 := [trans #23158 #23160]: #23157
+#16297 := (~ #3632 #3632)
+#16287 := (~ #3629 #3629)
+#16288 := [refl]: #16287
+#16353 := [nnf-pos #16288]: #16297
+#100 := (= #99 #28)
+#101 := (forall (vars (?v0 S5)) #100)
+#3633 := (iff #101 #3632)
+#3630 := (iff #100 #3629)
+#3631 := [rewrite]: #3630
+#3634 := [quant-intro #3631]: #3633
+#3628 := [asserted]: #101
+#3637 := [mp #3628 #3634]: #3632
+#16354 := [mp~ #3637 #16353]: #3632
+#23162 := [mp #16354 #23161]: #23156
+#24816 := (not #23156)
+#24817 := (or #24816 #24813)
+#24818 := [quant-inst #3035]: #24817
+#27119 := [unit-resolution #24818 #23162]: #24813
+#27121 := [symm #27119]: #27120
+#27254 := [monotonicity #27121]: #27122
+#27347 := [trans #27254 #28370]: #27346
+#27393 := [monotonicity #28365 #27347]: #27389
+#27394 := (= #3091 #27065)
+#27043 := (f67 #24812 0::Int #24975)
+#27068 := (= #27043 #27065)
+#27071 := (not #27068)
+decl f139 :: (-> S5 S5 S1)
+#27044 := (f139 #27043 #24812)
+#27045 := (= f1 #27044)
+#27046 := (not #27045)
+#27077 := (or #27046 #27071)
+#27082 := (not #27077)
+#28630 := [hypothesis]: #27077
+#255 := (:var 1 Int)
+#26 := (:var 2 S5)
+#1588 := (f67 #26 #255 #241)
+#1589 := (pattern #1588)
+#1590 := (f139 #1588 #26)
+#8337 := (= f1 #1590)
+#21212 := (not #8337)
+decl f140 :: (-> S3 Int)
+#1593 := (f140 #241)
+#1594 := (* #255 #1593)
+#1592 := (f117 #26)
+#1595 := (+ #1592 #1594)
+#1596 := (f44 #241 #1595)
+#1597 := (= #1588 #1596)
+#21211 := (not #1597)
+#21213 := (or #21211 #21212)
+#21214 := (not #21213)
+#21217 := (forall (vars (?v0 S5) (?v1 Int) (?v2 S3)) (:pat #1589) #21214)
+#8343 := (and #1597 #8337)
+#8348 := (forall (vars (?v0 S5) (?v1 Int) (?v2 S3)) (:pat #1589) #8343)
+#21218 := (iff #8348 #21217)
+#21215 := (iff #8343 #21214)
+#21216 := [rewrite]: #21215
+#21219 := [quant-intro #21216]: #21218
+#17320 := (~ #8348 #8348)
+#17318 := (~ #8343 #8343)
+#17319 := [refl]: #17318
+#17321 := [nnf-pos #17319]: #17320
+#1591 := (= #1590 f1)
+#1598 := (and #1591 #1597)
+#1599 := (forall (vars (?v0 S5) (?v1 Int) (?v2 S3)) (:pat #1589) #1598)
+#8349 := (iff #1599 #8348)
+#8346 := (iff #1598 #8343)
+#8340 := (and #8337 #1597)
+#8344 := (iff #8340 #8343)
+#8345 := [rewrite]: #8344
+#8341 := (iff #1598 #8340)
+#8338 := (iff #1591 #8337)
+#8339 := [rewrite]: #8338
+#8342 := [monotonicity #8339]: #8341
+#8347 := [trans #8342 #8345]: #8346
+#8350 := [quant-intro #8347]: #8349
+#8336 := [asserted]: #1599
+#8353 := [mp #8336 #8350]: #8348
+#17322 := [mp~ #8353 #17321]: #8348
+#21220 := [mp #17322 #21219]: #21217
+#27700 := (not #21217)
+#27707 := (or #27700 #27082)
+#27047 := (f140 #24975)
+#27048 := (* 0::Int #27047)
+#27050 := (+ #27049 #27048)
+#27051 := (f44 #24975 #27050)
+#27052 := (= #27043 #27051)
+#27053 := (not #27052)
+#27054 := (or #27053 #27046)
+#27055 := (not #27054)
+#27708 := (or #27700 #27055)
+#27709 := (iff #27708 #27707)
+#27715 := (iff #27707 #27707)
+#27716 := [rewrite]: #27715
+#27083 := (iff #27055 #27082)
+#27080 := (iff #27054 #27077)
+#27074 := (or #27071 #27046)
+#27078 := (iff #27074 #27077)
+#27079 := [rewrite]: #27078
+#27075 := (iff #27054 #27074)
+#27072 := (iff #27053 #27071)
+#27069 := (iff #27052 #27068)
+#27066 := (= #27051 #27065)
+#27063 := (= #27050 #27049)
+#27058 := (+ #27049 0::Int)
+#27061 := (= #27058 #27049)
+#27062 := [rewrite]: #27061
+#27059 := (= #27050 #27058)
+#27056 := (= #27048 0::Int)
+#27057 := [rewrite]: #27056
+#27060 := [monotonicity #27057]: #27059
+#27064 := [trans #27060 #27062]: #27063
+#27067 := [monotonicity #27064]: #27066
+#27070 := [monotonicity #27067]: #27069
+#27073 := [monotonicity #27070]: #27072
+#27076 := [monotonicity #27073]: #27075
+#27081 := [trans #27076 #27079]: #27080
+#27084 := [monotonicity #27081]: #27083
+#27710 := [monotonicity #27084]: #27709
+#27724 := [trans #27710 #27716]: #27709
+#27706 := [quant-inst #24812 #127 #24975]: #27708
+#27725 := [mp #27706 #27724]: #27707
+#28631 := [unit-resolution #27725 #21220 #28630]: false
+#28632 := [lemma #28631]: #27082
+#27727 := (or #27077 #27068)
+#27728 := [def-axiom]: #27727
+#27652 := [unit-resolution #27728 #28632]: #27068
+#27350 := (= #3091 #27043)
+#27388 := [monotonicity #27119 #28363]: #27350
+#27653 := [trans #27388 #27652]: #27394
+#27654 := [trans #27653 #27393]: #27659
+#27655 := [monotonicity #27654]: #27661
+#27648 := [symm #27655]: #27647
+#27649 := (= #24975 #25091)
+#25092 := (= f9 #25091)
+#2731 := (f14 #2727)
+#11400 := (= #335 #2731)
+#23251 := (forall (vars (?v0 S3) (?v1 Int)) (:pat #23244) #11400)
+#11404 := (forall (vars (?v0 S3) (?v1 Int)) #11400)
+#23254 := (iff #11404 #23251)
+#23252 := (iff #11400 #11400)
+#23253 := [refl]: #23252
+#23255 := [quant-intro #23253]: #23254
+#18262 := (~ #11404 #11404)
+#18260 := (~ #11400 #11400)
+#18261 := [refl]: #18260
+#18263 := [nnf-pos #18261]: #18262
+#2732 := (= #2731 #335)
+#2733 := (forall (vars (?v0 S3) (?v1 Int)) #2732)
+#11405 := (iff #2733 #11404)
+#11402 := (iff #2732 #11400)
+#11403 := [rewrite]: #11402
+#11406 := [quant-intro #11403]: #11405
+#11399 := [asserted]: #2733
+#11409 := [mp #11399 #11406]: #11404
+#18264 := [mp~ #11409 #18263]: #11404
+#23256 := [mp #18264 #23255]: #23251
+#25043 := (not #23251)
+#25097 := (or #25043 #25092)
+#25098 := [quant-inst #16 #3034]: #25097
+#27118 := [unit-resolution #25098 #23256]: #25092
+#27650 := [trans #28365 #27118]: #27649
+#27651 := [trans #27650 #27648]: #27019
+#27000 := (not #26993)
+#27656 := (iff #18425 #27000)
+#27701 := (iff #12160 #26993)
+#27729 := (iff #26993 #12160)
+#27723 := (= #26992 #3092)
+#27726 := [monotonicity #28365]: #27723
+#27730 := [monotonicity #27726]: #27729
+#27702 := [symm #27730]: #27701
+#27703 := [monotonicity #27702]: #27656
+#27646 := [hypothesis]: #18425
+#27704 := [mp #27646 #27703]: #27000
+#27583 := (not #27019)
+#27576 := (not #27021)
+#27584 := (or #27576 #26993 #27583)
+#27582 := [def-axiom]: #27584
+#27705 := [unit-resolution #27582 #27704 #27651 #27619]: false
+#27621 := [lemma #27705]: #12160
+#28924 := (or #27077 #12169)
+#26964 := (f59 #3213 #3091)
+#27754 := (f136 #26964)
+#27757 := (f26 f292 #27754)
+#27765 := (= f27 #27757)
+#27755 := (f211 f292 #27754)
+#27756 := (= f1 #27755)
+#28342 := (or #27756 #27765)
+#28344 := (not #28342)
+#28125 := (f137 #26964)
+#28126 := (= f1 #28125)
+#28127 := (not #28126)
+#28079 := (f28 f292 #27754)
+#28072 := (= f1 #28079)
+#28124 := (not #28072)
+#28305 := (or #28124 #28127)
+#28319 := (not #28305)
+#27899 := (f13 #27018)
+#28245 := (= f15 #27899)
+#28301 := (not #28245)
+#28074 := (f14 #27754)
+#28075 := (f13 #28074)
+#28076 := (= f15 #28075)
+#28324 := (or #28076 #28301 #28319 #28344)
+#28416 := (not #28324)
+#28188 := (f211 f292 #3091)
+#28186 := (= f1 #28188)
+#28175 := (f26 f292 #3091)
+#28176 := (= f27 #28175)
+#28174 := (or #28176 #28186)
+#28254 := (not #28174)
+#28250 := (or #28254 #28245)
+#28252 := (not #28250)
+#28419 := (or #28252 #28416)
+#28422 := (not #28419)
+#3094 := (f25 f292 #3091)
+#12163 := (= f1 #3094)
+#18428 := (not #12163)
+#28425 := (or #18428 #28422)
+#28356 := (not #28425)
+#28346 := (iff #12169 #28356)
+#28413 := (or #28402 #28346)
+#27766 := (or #27765 #27756)
+#28073 := (not #27766)
+#27900 := (or #28127 #28124)
+#27898 := (not #27900)
+#27910 := (= #27899 f15)
+#27944 := (not #27910)
+#27945 := (or #27944 #27898 #28076 #28073)
+#28187 := (not #27945)
+#28255 := (or #27910 #28254)
+#28253 := (not #28255)
+#28256 := (or #28253 #28187)
+#28257 := (not #28256)
+#28258 := (or #18428 #28257)
+#28243 := (not #28258)
+#28244 := (iff #12169 #28243)
+#28414 := (or #28402 #28244)
+#28427 := (iff #28414 #28413)
+#28429 := (iff #28413 #28413)
+#28430 := [rewrite]: #28429
+#28327 := (iff #28244 #28346)
+#28357 := (iff #28243 #28356)
+#28347 := (iff #28258 #28425)
+#28423 := (iff #28257 #28422)
+#28420 := (iff #28256 #28419)
+#28417 := (iff #28187 #28416)
+#28339 := (iff #27945 #28324)
+#28320 := (or #28301 #28319 #28076 #28344)
+#28325 := (iff #28320 #28324)
+#28326 := [rewrite]: #28325
+#28322 := (iff #27945 #28320)
+#28318 := (iff #28073 #28344)
+#28343 := (iff #27766 #28342)
+#28338 := [rewrite]: #28343
+#28321 := [monotonicity #28338]: #28318
+#28340 := (iff #27898 #28319)
+#28310 := (iff #27900 #28305)
+#28311 := [rewrite]: #28310
+#28341 := [monotonicity #28311]: #28340
+#28260 := (iff #27944 #28301)
+#28246 := (iff #27910 #28245)
+#28247 := [rewrite]: #28246
+#28304 := [monotonicity #28247]: #28260
+#28323 := [monotonicity #28304 #28341 #28321]: #28322
+#28415 := [trans #28323 #28326]: #28339
+#28418 := [monotonicity #28415]: #28417
+#28299 := (iff #28253 #28252)
+#28263 := (iff #28255 #28250)
+#28242 := (or #28245 #28254)
+#28251 := (iff #28242 #28250)
+#28262 := [rewrite]: #28251
+#28248 := (iff #28255 #28242)
+#28249 := [monotonicity #28247]: #28248
+#28261 := [trans #28249 #28262]: #28263
+#28300 := [monotonicity #28261]: #28299
+#28421 := [monotonicity #28300 #28418]: #28420
+#28424 := [monotonicity #28421]: #28423
+#28348 := [monotonicity #28424]: #28347
+#28192 := [monotonicity #28348]: #28357
+#28328 := [monotonicity #28192]: #28327
+#28428 := [monotonicity #28328]: #28427
+#28435 := [trans #28428 #28430]: #28427
+#28426 := [quant-inst #3032 #3091]: #28414
+#28436 := [mp #28426 #28435]: #28413
+#28755 := [unit-resolution #28436 #22074]: #28346
+#28604 := (not #28346)
+#28758 := (or #28604 #28425)
+#28757 := [hypothesis]: #18434
+#28605 := (or #28604 #12169 #28425)
+#28606 := [def-axiom]: #28605
+#28756 := [unit-resolution #28606 #28757]: #28758
+#28759 := [unit-resolution #28756 #28755]: #28425
+#28795 := (or #28356 #28422)
+decl f16 :: (-> S5 S6 S1)
+decl f17 :: (-> S4 S5 S6)
+#24859 := (f117 #3037)
+#26161 := (f44 #3033 #24859)
+#26754 := (f17 f292 #26161)
+#27212 := (f16 #27124 #26754)
+#27213 := (= f1 #27212)
+#26755 := (f16 #26161 #26754)
+#28774 := (= #26755 #27212)
+#28771 := (= #27212 #26755)
+#28769 := (= #27124 #26161)
+#26168 := (= #3037 #26161)
+#3042 := (f49 #3037 #3033)
+#12089 := (= f1 #3042)
+decl f24 :: (-> S3 S1)
+#3049 := (f24 #3033)
+#12101 := (= f1 #3049)
+#3046 := (f13 #3033)
+#12095 := (= f15 #3046)
+#12098 := (not #12095)
+#3044 := (f25 f292 #3037)
+#12092 := (= f1 #3044)
+#12086 := (= f27 #3040)
+#3038 := (f28 f292 #3037)
+#12083 := (= f1 #3038)
+#14208 := (and #12083 #12086 #12089 #12092 #12098 #12101)
+decl f288 :: Int
+#3017 := f288
+#14264 := (* -1::Int f288)
+decl f79 :: Int
+#438 := f79
+#14265 := (+ f79 #14264)
+#14263 := (>= #14265 0::Int)
+#14261 := (>= f288 0::Int)
+#14268 := (and #14261 #14263)
+#14271 := (not #14268)
+decl f289 :: Int
+#3021 := f289
+#14250 := (* -1::Int f289)
+decl f77 :: Int
+#418 := f77
+#14251 := (+ f77 #14250)
+#14249 := (>= #14251 0::Int)
+#14247 := (>= f289 0::Int)
+#14254 := (and #14247 #14249)
+#14257 := (not #14254)
+decl f290 :: Int
+#3025 := f290
+#14236 := (* -1::Int f290)
+#14237 := (+ f77 #14236)
+#14235 := (>= #14237 0::Int)
+#14233 := (>= f290 0::Int)
+#14240 := (and #14233 #14235)
+#14243 := (not #14240)
+#1051 := 1099511627776::Int
+#14221 := (>= f291 1099511627776::Int)
+#14211 := (not #14208)
+decl f294 :: (-> S22 Int)
+#3063 := (:var 0 S22)
+#3064 := (f294 #3063)
+#3065 := (pattern #3064)
 decl f295 :: Int
-#3032 := f295
-#14256 := (* -1::Int f295)
-#14257 := (+ f87 #14256)
-#14255 := (>= #14257 0::Int)
-#14253 := (>= f295 0::Int)
-#14260 := (and #14253 #14255)
-#14263 := (not #14260)
-#1085 := 1099511627776::Int
-#14241 := (>= f296 1099511627776::Int)
-#14231 := (not #14228)
-decl f299 :: (-> S34 Int)
-#3070 := (:var 0 S34)
-#3071 := (f299 #3070)
-#3072 := (pattern #3071)
-decl f300 :: Int
-#3073 := f300
-#14218 := (* -1::Int f300)
-#14219 := (+ #3071 #14218)
-#14217 := (>= #14219 0::Int)
-#14216 := (not #14217)
-#14222 := (forall (vars (?v0 S34)) (:pat #3072) #14216)
-#14225 := (not #14222)
-#13509 := (not #13508)
-#14072 := (and #3109 #13509)
-#14077 := (not #14072)
-#14060 := (+ f89 #14006)
-#14059 := (>= #14060 0::Int)
-#14063 := (and #14056 #14059)
-#14066 := (not #14063)
-#14047 := (+ f87 #13977)
-#14046 := (>= #14047 0::Int)
-#14050 := (and #13513 #14046)
-#14053 := (not #14050)
-#13538 := (+ f87 #13537)
-#14037 := (>= #13538 0::Int)
-#14040 := (and #14034 #14037)
-#14043 := (not #14040)
-#4514 := (* -1::Int f87)
-#4515 := (+ #202 #4514)
-#4516 := (<= #4515 0::Int)
-#4523 := (and #4202 #4516)
-#5738 := (not #4523)
-#14017 := (or #5738 #13994 #14008)
-#14022 := (forall (vars (?v0 Int)) #14017)
-#14025 := (not #14022)
-#13980 := (not #13979)
-#13986 := (and #12250 #13980)
-#13991 := (not #13986)
-#13831 := (not #13829)
-#13869 := (and #3173 #4202 #4516 #13831)
-#13874 := (exists (vars (?v0 Int)) #13869)
-#13852 := (or #5738 #13829 #13843)
-#13857 := (forall (vars (?v0 Int)) #13852)
-#13877 := (not #13857)
-#13883 := (or #13877 #13874)
-#13888 := (and #13857 #13883)
-#13518 := (and #13513 #13516)
-#13521 := (not #13518)
-decl f227 :: S1
-#2541 := f227
-#10960 := (= f1 f227)
-#12374 := (not #10960)
-#13915 := (or #12374 #12340 #12331 #12322 #12313 #13521 #13888)
-#13920 := (and #10960 #13915)
-#13945 := (or #13521 #13802 #13920)
-#13536 := (>= #13538 1::Int)
-#13625 := (and #13534 #13536)
-#13628 := (not #13625)
-#13595 := (not #13594)
-#13601 := (and #12643 #13595)
-#13581 := (or #5738 #13558 #13572)
-#13586 := (forall (vars (?v0 Int)) #13581)
-#13589 := (not #13586)
-#13606 := (or #13589 #13601)
-#13609 := (and #13586 #13606)
-#13612 := (or #13555 #13609)
-#13615 := (and #13550 #13612)
-#13544 := (and #13525 #13542)
-#13547 := (not #13544)
-#13643 := (or #12692 #13547 #13615 #13622 #13628)
-#13651 := (and #13534 #13536 #13643)
-#13527 := (and #13516 #13525)
-#13530 := (not #13527)
-#13762 := (or #12857 #12848 #13521 #13530 #13651 #13707)
-#12587 := (and #12575 #12584)
-#12785 := (not #12587)
-#13683 := (or #12785 #12776 #12767 #12758 #12740 #12731 #13656 #13530 #13651)
-#13691 := (and #12575 #12584 #13683)
-#12581 := (and #12575 #12578)
-#12797 := (not #12581)
-#13696 := (or #12797 #13691)
-#13702 := (and #12575 #12578 #13696)
-#13732 := (or #13521 #13702 #13708)
-#13767 := (and #13732 #13762)
-#13776 := (or #12785 #13521 #13767)
-#13784 := (and #12575 #12584 #13776)
-#13789 := (or #12797 #13784)
-#13795 := (and #12575 #12578 #13789)
-#13824 := (or #13521 #13795 #13801)
-#13950 := (and #13824 #13945)
+#3066 := f295
+#14198 := (* -1::Int f295)
+#14199 := (+ #3064 #14198)
+#14197 := (>= #14199 0::Int)
+#14196 := (not #14197)
+#14202 := (forall (vars (?v0 S22)) (:pat #3065) #14196)
+#14205 := (not #14202)
+#13489 := (not #13488)
+#14052 := (and #3102 #13489)
+#14057 := (not #14052)
+#14040 := (+ f79 #13986)
+#14039 := (>= #14040 0::Int)
+#14043 := (and #14036 #14039)
+#14046 := (not #14043)
+#14027 := (+ f77 #13957)
+#14026 := (>= #14027 0::Int)
+#14030 := (and #13493 #14026)
+#14033 := (not #14030)
+#13518 := (+ f77 #13517)
+#14017 := (>= #13518 0::Int)
+#14020 := (and #14014 #14017)
+#14023 := (not #14020)
+#4461 := (* -1::Int f77)
+#4462 := (+ #168 #4461)
+#4463 := (<= #4462 0::Int)
+#4470 := (and #4149 #4463)
+#5685 := (not #4470)
+#13997 := (or #5685 #13974 #13988)
+#14002 := (forall (vars (?v0 Int)) #13997)
+#14005 := (not #14002)
+#13960 := (not #13959)
+#13966 := (and #12230 #13960)
+#13971 := (not #13966)
+#13811 := (not #13809)
+#13849 := (and #3166 #4149 #4463 #13811)
+#13854 := (exists (vars (?v0 Int)) #13849)
+#13832 := (or #5685 #13809 #13823)
+#13837 := (forall (vars (?v0 Int)) #13832)
+#13857 := (not #13837)
+#13863 := (or #13857 #13854)
+#13868 := (and #13837 #13863)
+#13498 := (and #13493 #13496)
+#13501 := (not #13498)
+decl f217 :: S1
+#2507 := f217
+#10907 := (= f1 f217)
+#12354 := (not #10907)
+#13895 := (or #12354 #12320 #12311 #12302 #12293 #13501 #13868)
+#13900 := (and #10907 #13895)
+#13925 := (or #13501 #13782 #13900)
+#13516 := (>= #13518 1::Int)
+#13605 := (and #13514 #13516)
+#13608 := (not #13605)
+#13575 := (not #13574)
+#13581 := (and #12623 #13575)
+#13561 := (or #5685 #13538 #13552)
+#13566 := (forall (vars (?v0 Int)) #13561)
+#13569 := (not #13566)
+#13586 := (or #13569 #13581)
+#13589 := (and #13566 #13586)
+#13592 := (or #13535 #13589)
+#13595 := (and #13530 #13592)
+#13524 := (and #13505 #13522)
+#13527 := (not #13524)
+#13623 := (or #12672 #13527 #13595 #13602 #13608)
+#13631 := (and #13514 #13516 #13623)
+#13507 := (and #13496 #13505)
+#13510 := (not #13507)
+#13742 := (or #12837 #12828 #13501 #13510 #13631 #13687)
+#12567 := (and #12555 #12564)
+#12765 := (not #12567)
+#13663 := (or #12765 #12756 #12747 #12738 #12720 #12711 #13636 #13510 #13631)
+#13671 := (and #12555 #12564 #13663)
 #12561 := (and #12555 #12558)
-#13024 := (not #12561)
-decl f66 :: (-> S19 S1)
-#3067 := (f66 f297)
-#12145 := (= f1 #3067)
-#12264 := (and #12145 #12258)
-#12402 := (not #12264)
-#14143 := (or #12402 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13950 #13991 #14025 #14031 #14043 #14053 #14066 #14077)
-#14151 := (and #3109 #13509 #14143)
-#13497 := (or #5738 #13475 #13487)
-#13502 := (forall (vars (?v0 Int)) #13497)
-#13505 := (not #13502)
-#14156 := (or #13505 #14151)
-#14159 := (and #13502 #14156)
-#14162 := (or #13472 #14159)
-#14165 := (and #13469 #14162)
-#12192 := (and #12180 #12189)
-#13276 := (not #12192)
-#14186 := (or #13267 #13276 #13258 #13249 #13240 #14165)
-#14194 := (and #12180 #12189 #14186)
-#12186 := (and #12180 #12183)
-#13288 := (not #12186)
-#14199 := (or #13288 #14194)
-#14205 := (and #12180 #12183 #14199)
-decl f211 :: (-> S19 S20 S20 S31 S1)
-decl f305 :: S31
-#3095 := f305
-#3096 := (f211 f297 #3044 #3044 f305)
-#12177 := (= f1 #3096)
-#13300 := (not #12177)
-#14210 := (or #13300 #14205)
-#14213 := (and #12177 #14210)
-#13443 := (+ f87 #13442)
-#13441 := (>= #13443 0::Int)
-#13439 := (>= f296 0::Int)
-#13446 := (and #13439 #13441)
-#13449 := (not #13446)
-decl f304 :: (-> Int S20 S1)
-decl f303 :: Int
-#3084 := f303
-#3087 := (f304 f303 #62)
-#3088 := (pattern #3087)
-#12163 := (= f1 #3087)
-#12169 := (not #12163)
-#12174 := (forall (vars (?v0 S20)) (:pat #3088) #12169)
-#13321 := (not #12174)
-decl f292 :: S17
-#3020 := f292
-#3082 := (f301 f297 f292 f290 f296 f16)
-#12160 := (= f1 #3082)
-#13339 := (not #12160)
-#3079 := (f302 f297 f292 f291 #3042 #51)
-#12154 := (= f1 #3079)
-#3077 := (f301 f297 f292 f291 #3076 #51)
-#12151 := (= f1 #3077)
-#12157 := (and #12151 #12154)
-#13348 := (not #12157)
-#3065 := (f213 f292 f297)
-#12142 := (= f1 #3065)
-#12148 := (and #12142 #12145)
-#13366 := (not #12148)
-decl f214 :: (-> S19 S1)
-#3063 := (f214 f297)
-#12139 := (= f1 #3063)
-#13375 := (not #12139)
-decl f184 :: (-> S19 Int)
-#3085 := (f184 f297)
-#3086 := (= f303 #3085)
-#13330 := (not #3086)
-#14336 := (or #13330 #13375 #13366 #13348 #13339 #13321 #13449 #13508 #14213 #14225 #14231 #14241 #14263 #14277 #14291)
-#14341 := (not #14336)
+#12777 := (not #12561)
+#13676 := (or #12777 #13671)
+#13682 := (and #12555 #12558 #13676)
+#13712 := (or #13501 #13682 #13688)
+#13747 := (and #13712 #13742)
+#13756 := (or #12765 #13501 #13747)
+#13764 := (and #12555 #12564 #13756)
+#13769 := (or #12777 #13764)
+#13775 := (and #12555 #12558 #13769)
+#13804 := (or #13501 #13775 #13781)
+#13930 := (and #13804 #13925)
+#12541 := (and #12535 #12538)
+#13004 := (not #12541)
+decl f56 :: (-> S4 S1)
+#3060 := (f56 f292)
+#12125 := (= f1 #3060)
+#12244 := (and #12125 #12238)
+#12382 := (not #12244)
+#14123 := (or #12382 #13954 #13040 #13031 #13022 #13013 #13004 #13501 #13930 #13971 #14005 #14011 #14023 #14033 #14046 #14057)
+#14131 := (and #3102 #13489 #14123)
+#13477 := (or #5685 #13455 #13467)
+#13482 := (forall (vars (?v0 Int)) #13477)
+#13485 := (not #13482)
+#14136 := (or #13485 #14131)
+#14139 := (and #13482 #14136)
+#14142 := (or #13452 #14139)
+#14145 := (and #13449 #14142)
+#12172 := (and #12160 #12169)
+#13256 := (not #12172)
+#14166 := (or #13247 #13256 #13238 #13229 #13220 #14145)
+#14174 := (and #12160 #12169 #14166)
+#12166 := (and #12160 #12163)
+#13268 := (not #12166)
+#14179 := (or #13268 #14174)
+#14185 := (and #12160 #12163 #14179)
+decl f201 :: (-> S4 S5 S5 S16 S1)
+decl f300 :: S16
+#3088 := f300
+#3089 := (f201 f292 #3037 #3037 f300)
+#12157 := (= f1 #3089)
+#13280 := (not #12157)
+#14190 := (or #13280 #14185)
+#14193 := (and #12157 #14190)
+#13423 := (+ f77 #13422)
+#13421 := (>= #13423 0::Int)
+#13419 := (>= f291 0::Int)
+#13426 := (and #13419 #13421)
+#13429 := (not #13426)
+decl f299 :: (-> Int S5 S1)
+decl f298 :: Int
+#3077 := f298
+#3080 := (f299 f298 #28)
+#3081 := (pattern #3080)
+#12143 := (= f1 #3080)
+#12149 := (not #12143)
+#12154 := (forall (vars (?v0 S5)) (:pat #3081) #12149)
+#13301 := (not #12154)
+decl f282 :: S2
+#2986 := f282
+#3075 := (f296 f292 f282 f280 f291 f6)
+#12140 := (= f1 #3075)
+#13319 := (not #12140)
+#3072 := (f297 f292 f282 f281 #3035 #17)
+#12134 := (= f1 #3072)
+#3070 := (f296 f292 f282 f281 #3069 #17)
+#12131 := (= f1 #3070)
+#12137 := (and #12131 #12134)
+#13328 := (not #12137)
+#3058 := (f203 f282 f292)
+#12122 := (= f1 #3058)
+#12128 := (and #12122 #12125)
+#13346 := (not #12128)
+decl f204 :: (-> S4 S1)
+#3056 := (f204 f292)
+#12119 := (= f1 #3056)
+#13355 := (not #12119)
+decl f174 :: (-> S4 Int)
+#3078 := (f174 f292)
+#3079 := (= f298 #3078)
+#13310 := (not #3079)
+#14316 := (or #13310 #13355 #13346 #13328 #13319 #13301 #13429 #13488 #14193 #14205 #14211 #14221 #14243 #14257 #14271)
+#14321 := (not #14316)
 #1 := true
-#3168 := (< #202 f296)
-#3174 := (and #3168 #3173)
-#454 := (<= #202 f87)
-#3175 := (and #454 #3174)
-#327 := (<= 0::Int #202)
-#3176 := (and #327 #3175)
-#3177 := (exists (vars (?v0 Int)) #3176)
-#3178 := (and #3177 true)
-#3169 := (<= #3124 f313)
-#3170 := (implies #3168 #3169)
-#455 := (and #327 #454)
-#3171 := (implies #455 #3170)
-#3172 := (forall (vars (?v0 Int)) #3171)
-#3179 := (implies #3172 #3178)
-#3180 := (and #3172 #3179)
-#3167 := (= f313 f307)
-#3181 := (implies #3167 #3180)
-#3165 := (= f312 f308)
-#3182 := (implies #3165 #3181)
-#3163 := (= f311 f309)
-#3183 := (implies #3163 #3182)
-#3161 := (= f310 f307)
-#3184 := (implies #3161 #3183)
-#3136 := (<= 0::Int f308)
-#3143 := (<= 1::Int f309)
-#3144 := (and #3143 #3136)
-#3185 := (implies #3144 #3184)
-#3186 := (implies #3144 #3185)
-#3187 := (implies #3144 #3186)
-#2542 := (= f227 f1)
-#3188 := (implies #2542 #3187)
-#3189 := (and #2542 #3188)
-#3190 := (implies #3144 #3189)
-#3191 := (implies #3144 #3190)
-#3348 := (implies #3144 #3191)
-#3349 := (implies #3144 #3348)
-#3347 := (<= f296 f309)
-#3350 := (implies #3347 #3349)
-#3351 := (implies #3144 #3350)
-#3300 := (= #3299 f315)
-#3297 := (< f316 f296)
-#3301 := (and #3297 #3300)
-#3302 := (and #3301 true)
-#3293 := (<= #3124 f315)
-#3292 := (< #202 f317)
-#3294 := (implies #3292 #3293)
-#3295 := (implies #455 #3294)
-#3296 := (forall (vars (?v0 Int)) #3295)
-#3303 := (implies #3296 #3302)
-#3304 := (and #3296 #3303)
-#3291 := (<= f317 f296)
-#3305 := (implies #3291 #3304)
-#3306 := (and #3291 #3305)
-#3279 := (<= 0::Int f316)
-#3289 := (<= 2::Int f317)
-#3290 := (and #3289 #3279)
-#3307 := (implies #3290 #3306)
-#3288 := (= #3287 f1)
-#3308 := (implies #3288 #3307)
-#3281 := (+ f309 1::Int)
-#3286 := (= f317 #3281)
-#3309 := (implies #3286 #3308)
-#3283 := (<= #3281 f87)
-#3282 := (<= 0::Int #3281)
-#3284 := (and #3282 #3283)
-#3310 := (implies #3284 #3309)
-#3311 := (and #3284 #3310)
-#3280 := (and #3143 #3279)
-#3312 := (implies #3280 #3311)
-#3329 := (= f316 f308)
-#3330 := (implies #3329 #3312)
-#3328 := (= f315 f307)
-#3331 := (implies #3328 #3330)
-#3332 := (implies #3144 #3331)
-#3333 := (implies #3144 #3332)
-#3334 := (implies #3144 #3333)
-#3327 := (<= #3266 f307)
-#3335 := (implies #3327 #3334)
-#3336 := (implies #3144 #3335)
-#3278 := (= f316 f309)
-#3313 := (implies #3278 #3312)
-#3276 := (= f315 f314)
-#3314 := (implies #3276 #3313)
-#3274 := (and #3143 #3143)
-#3315 := (implies #3274 #3314)
-#3273 := (= #3272 f1)
-#3316 := (implies #3273 #3315)
-#3271 := (= #3270 f1)
-#3317 := (implies #3271 #3316)
-#3269 := (= f314 #3266)
-#3318 := (implies #3269 #3317)
+#3161 := (< #168 f291)
+#3167 := (and #3161 #3166)
+#420 := (<= #168 f77)
+#3168 := (and #420 #3167)
+#293 := (<= 0::Int #168)
+#3169 := (and #293 #3168)
+#3170 := (exists (vars (?v0 Int)) #3169)
+#3171 := (and #3170 true)
+#3162 := (<= #3117 f308)
+#3163 := (implies #3161 #3162)
+#421 := (and #293 #420)
+#3164 := (implies #421 #3163)
+#3165 := (forall (vars (?v0 Int)) #3164)
+#3172 := (implies #3165 #3171)
+#3173 := (and #3165 #3172)
+#3160 := (= f308 f302)
+#3174 := (implies #3160 #3173)
+#3158 := (= f307 f303)
+#3175 := (implies #3158 #3174)
+#3156 := (= f306 f304)
+#3176 := (implies #3156 #3175)
+#3154 := (= f305 f302)
+#3177 := (implies #3154 #3176)
+#3129 := (<= 0::Int f303)
+#3136 := (<= 1::Int f304)
+#3137 := (and #3136 #3129)
+#3178 := (implies #3137 #3177)
+#3179 := (implies #3137 #3178)
+#3180 := (implies #3137 #3179)
+#2508 := (= f217 f1)
+#3181 := (implies #2508 #3180)
+#3182 := (and #2508 #3181)
+#3183 := (implies #3137 #3182)
+#3184 := (implies #3137 #3183)
+#3341 := (implies #3137 #3184)
+#3342 := (implies #3137 #3341)
+#3340 := (<= f291 f304)
+#3343 := (implies #3340 #3342)
+#3344 := (implies #3137 #3343)
+#3293 := (= #3292 f310)
+#3290 := (< f311 f291)
+#3294 := (and #3290 #3293)
+#3295 := (and #3294 true)
+#3286 := (<= #3117 f310)
+#3285 := (< #168 f312)
+#3287 := (implies #3285 #3286)
+#3288 := (implies #421 #3287)
+#3289 := (forall (vars (?v0 Int)) #3288)
+#3296 := (implies #3289 #3295)
+#3297 := (and #3289 #3296)
+#3284 := (<= f312 f291)
+#3298 := (implies #3284 #3297)
+#3299 := (and #3284 #3298)
+#3272 := (<= 0::Int f311)
+#3282 := (<= 2::Int f312)
+#3283 := (and #3282 #3272)
+#3300 := (implies #3283 #3299)
+#3281 := (= #3280 f1)
+#3301 := (implies #3281 #3300)
+#3274 := (+ f304 1::Int)
+#3279 := (= f312 #3274)
+#3302 := (implies #3279 #3301)
+#3276 := (<= #3274 f77)
+#3275 := (<= 0::Int #3274)
+#3277 := (and #3275 #3276)
+#3303 := (implies #3277 #3302)
+#3304 := (and #3277 #3303)
+#3273 := (and #3136 #3272)
+#3305 := (implies #3273 #3304)
+#3322 := (= f311 f303)
+#3323 := (implies #3322 #3305)
+#3321 := (= f310 f302)
+#3324 := (implies #3321 #3323)
+#3325 := (implies #3137 #3324)
+#3326 := (implies #3137 #3325)
+#3327 := (implies #3137 #3326)
+#3320 := (<= #3259 f302)
+#3328 := (implies #3320 #3327)
+#3329 := (implies #3137 #3328)
+#3271 := (= f311 f304)
+#3306 := (implies #3271 #3305)
+#3269 := (= f310 f309)
+#3307 := (implies #3269 #3306)
+#3267 := (and #3136 #3136)
+#3308 := (implies #3267 #3307)
+#3266 := (= #3265 f1)
+#3309 := (implies #3266 #3308)
 #3264 := (= #3263 f1)
-#3259 := (= #3258 f1)
-#3265 := (and #3259 #3264)
-#3319 := (implies #3265 #3318)
-#3320 := (and #3265 #3319)
-#3261 := (= #3260 f1)
-#3262 := (and #3259 #3261)
-#3321 := (implies #3262 #3320)
-#3322 := (and #3262 #3321)
-#3323 := (implies #3144 #3322)
-#3324 := (implies #3144 #3323)
-#3267 := (< f307 #3266)
-#3325 := (implies #3267 #3324)
-#3326 := (implies #3144 #3325)
-#3337 := (and #3326 #3336)
-#3338 := (implies #3144 #3337)
-#3339 := (implies #3265 #3338)
-#3340 := (and #3265 #3339)
-#3341 := (implies #3262 #3340)
-#3342 := (and #3262 #3341)
-#3343 := (implies #3144 #3342)
-#3344 := (implies #3144 #3343)
-#3256 := (< f309 f296)
-#3345 := (implies #3256 #3344)
-#3346 := (implies #3144 #3345)
-#3352 := (and #3346 #3351)
-#3353 := (implies #3144 #3352)
-decl f52 :: (-> S19 S27)
-#3197 := (f52 f297)
-#3254 := (= #3197 #3197)
-#3253 := (= #3220 #3220)
-#3255 := (and #3253 #3254)
-#3354 := (implies #3255 #3353)
-#3251 := (= #3250 f1)
-#3249 := (= #3248 f1)
-#3252 := (and #3249 #3251)
-#3355 := (implies #3252 #3354)
-#3247 := (= #3246 f1)
-#3356 := (implies #3247 #3355)
-#3245 := (= #3244 f1)
-#3357 := (implies #3245 #3356)
-#3243 := (= #3242 f1)
-#3358 := (implies #3243 #3357)
-#3241 := (= #3240 f1)
-#3359 := (implies #3241 #3358)
-#3068 := (= #3067 f1)
-#3158 := (= #3157 f1)
-#3159 := (and #3158 #3068)
-#3360 := (implies #3159 #3359)
-#3233 := (= #3232 f1)
-decl f183 :: (-> S19 S20 Int)
-#3228 := (f183 f297 #62)
-#3229 := (pattern #3228)
-#3230 := (<= #3228 #3228)
-#3231 := (forall (vars (?v0 S20)) (:pat #3229) #3230)
-#3234 := (and #3231 #3233)
-#3227 := (<= #3085 #3085)
-#3235 := (and #3227 #3234)
-#3361 := (implies #3235 #3360)
-#3221 := (f69 #3220 #62)
+#3310 := (implies #3264 #3309)
+#3262 := (= f309 #3259)
+#3311 := (implies #3262 #3310)
+#3257 := (= #3256 f1)
+#3252 := (= #3251 f1)
+#3258 := (and #3252 #3257)
+#3312 := (implies #3258 #3311)
+#3313 := (and #3258 #3312)
+#3254 := (= #3253 f1)
+#3255 := (and #3252 #3254)
+#3314 := (implies #3255 #3313)
+#3315 := (and #3255 #3314)
+#3316 := (implies #3137 #3315)
+#3317 := (implies #3137 #3316)
+#3260 := (< f302 #3259)
+#3318 := (implies #3260 #3317)
+#3319 := (implies #3137 #3318)
+#3330 := (and #3319 #3329)
+#3331 := (implies #3137 #3330)
+#3332 := (implies #3258 #3331)
+#3333 := (and #3258 #3332)
+#3334 := (implies #3255 #3333)
+#3335 := (and #3255 #3334)
+#3336 := (implies #3137 #3335)
+#3337 := (implies #3137 #3336)
+#3249 := (< f304 f291)
+#3338 := (implies #3249 #3337)
+#3339 := (implies #3137 #3338)
+#3345 := (and #3339 #3344)
+#3346 := (implies #3137 #3345)
+decl f42 :: (-> S4 S12)
+#3190 := (f42 f292)
+#3247 := (= #3190 #3190)
+#3246 := (= #3213 #3213)
+#3248 := (and #3246 #3247)
+#3347 := (implies #3248 #3346)
+#3244 := (= #3243 f1)
+#3242 := (= #3241 f1)
+#3245 := (and #3242 #3244)
+#3348 := (implies #3245 #3347)
+#3240 := (= #3239 f1)
+#3349 := (implies #3240 #3348)
+#3238 := (= #3237 f1)
+#3350 := (implies #3238 #3349)
+#3236 := (= #3235 f1)
+#3351 := (implies #3236 #3350)
+#3234 := (= #3233 f1)
+#3352 := (implies #3234 #3351)
+#3061 := (= #3060 f1)
+#3151 := (= #3150 f1)
+#3152 := (and #3151 #3061)
+#3353 := (implies #3152 #3352)
+#3226 := (= #3225 f1)
+decl f173 :: (-> S4 S5 Int)
+#3221 := (f173 f292 #28)
 #3222 := (pattern #3221)
-#3210 := (f79 f297 #62)
-#3211 := (= #3210 f1)
-#3223 := (= #3221 #3221)
-#3224 := (and #3223 #3211)
-#3225 := (implies #3211 #3224)
-#3226 := (forall (vars (?v0 S20)) (:pat #3222) #3225)
-#3236 := (and #3226 #3235)
-decl f51 :: (-> S27 S20 S26)
-#3198 := (f51 #3197 #62)
-#3199 := (pattern #3198)
-#3216 := (= #3198 #3198)
-#3217 := (and #3216 #3211)
-#3218 := (implies #3211 #3217)
-#3219 := (forall (vars (?v0 S20)) (:pat #3199) #3218)
-#3237 := (and #3219 #3236)
-decl f30 :: (-> S24 S20 Int)
-decl f31 :: (-> S19 S24)
-#3207 := (f31 f297)
-#3208 := (f30 #3207 #62)
-#3209 := (pattern #3208)
-#3212 := (= #3208 #3208)
-#3213 := (and #3212 #3211)
-#3214 := (implies #3211 #3213)
-#3215 := (forall (vars (?v0 S20)) (:pat #3209) #3214)
-#3238 := (and #3215 #3237)
-decl f272 :: S23
-#2903 := f272
-#3200 := (f36 f297 #62)
-#3201 := (f24 #3200)
-#3202 := (f23 #3201)
-#3203 := (= #3202 f272)
-#3204 := (not #3203)
-#3205 := (implies #3204 #3204)
-#3206 := (forall (vars (?v0 S20)) (:pat #3199) #3205)
-#3239 := (and #3206 #3238)
-#3362 := (implies #3239 #3361)
-#3363 := (implies #3144 #3362)
-#3364 := (implies #3144 #3363)
-#3365 := (implies #3144 #3364)
-#3192 := (implies #3159 #3191)
-#3193 := (implies #3144 #3192)
-#3194 := (implies #3144 #3193)
-#3156 := (not true)
-#3195 := (implies #3156 #3194)
-#3196 := (implies #3144 #3195)
-#3366 := (and #3196 #3365)
-#3367 := (implies #3144 #3366)
-#3154 := (= #3153 f307)
-#3151 := (< f308 f296)
-#3155 := (and #3151 #3154)
-#3368 := (implies #3155 #3367)
-#3147 := (<= #3124 f307)
-#3146 := (< #202 f309)
-#3148 := (implies #3146 #3147)
-#3149 := (implies #455 #3148)
-#3150 := (forall (vars (?v0 Int)) #3149)
-#3369 := (implies #3150 #3368)
-#3145 := (<= f309 f296)
-#3370 := (implies #3145 #3369)
-#3371 := (implies #3144 #3370)
-#3141 := (<= f309 f87)
-#3140 := (<= 0::Int f309)
-#3142 := (and #3140 #3141)
-#3372 := (implies #3142 #3371)
-#3137 := (<= f308 f87)
-#3138 := (and #3136 #3137)
-#3373 := (implies #3138 #3372)
-#3133 := (<= f307 f89)
-#3132 := (<= 0::Int f307)
-#3134 := (and #3132 #3133)
-#3374 := (implies #3134 #3373)
-#3129 := (= #3108 f306)
-#3038 := (< 0::Int f296)
-#3130 := (and #3038 #3129)
-#3375 := (implies #3130 #3374)
-#3376 := (and #3130 #3375)
-#3125 := (<= #3124 f306)
-#3122 := (< #202 1::Int)
-#3126 := (implies #3122 #3125)
-#3127 := (implies #455 #3126)
-#3128 := (forall (vars (?v0 Int)) #3127)
-#3377 := (implies #3128 #3376)
-#3378 := (and #3128 #3377)
-#3121 := (<= 1::Int f296)
-#3379 := (implies #3121 #3378)
-#3380 := (and #3121 #3379)
-#3117 := (<= 0::Int 0::Int)
-#3118 := (and #3117 #3117)
-#3116 := (<= 1::Int 1::Int)
-#3119 := (and #3116 #3118)
-#3120 := (and #3116 #3119)
-#3381 := (implies #3120 #3380)
-#3115 := (= #3114 f1)
-#3382 := (implies #3115 #3381)
-#3113 := (= #3112 f1)
-#3383 := (implies #3113 #3382)
-#3111 := (= #3110 f1)
-#3384 := (implies #3111 #3383)
-#3385 := (implies #3109 #3384)
-#3105 := (= #3104 f1)
-#3100 := (= #3099 f1)
-#3106 := (and #3100 #3105)
-#3386 := (implies #3106 #3385)
-#3387 := (and #3106 #3386)
-#3102 := (= #3101 f1)
-#3103 := (and #3100 #3102)
-#3388 := (implies #3103 #3387)
-#3389 := (and #3103 #3388)
-#3097 := (= #3096 f1)
-#3390 := (implies #3097 #3389)
-#3391 := (and #3097 #3390)
-#3093 := (<= f296 f87)
-#3092 := (<= 0::Int f296)
-#3094 := (and #3092 #3093)
-#3392 := (implies #3094 #3391)
-#3089 := (= #3087 f1)
-#3090 := (iff #3089 false)
-#3091 := (forall (vars (?v0 S20)) (:pat #3088) #3090)
-#3393 := (implies #3091 #3392)
-#3394 := (implies #3086 #3393)
-#3083 := (= #3082 f1)
-#3395 := (implies #3083 #3394)
-#3080 := (= #3079 f1)
-#3078 := (= #3077 f1)
-#3081 := (and #3078 #3080)
-#3396 := (implies #3081 #3395)
-#3074 := (< #3071 f300)
-#3075 := (forall (vars (?v0 S34)) (:pat #3072) #3074)
-#3397 := (implies #3075 #3396)
-#3066 := (= #3065 f1)
-#3069 := (and #3066 #3068)
-#3398 := (implies #3069 #3397)
-#3064 := (= #3063 f1)
-#3399 := (implies #3064 #3398)
+#3223 := (<= #3221 #3221)
+#3224 := (forall (vars (?v0 S5)) (:pat #3222) #3223)
+#3227 := (and #3224 #3226)
+#3220 := (<= #3078 #3078)
+#3228 := (and #3220 #3227)
+#3354 := (implies #3228 #3353)
+#3214 := (f59 #3213 #28)
+#3215 := (pattern #3214)
+#3203 := (f69 f292 #28)
+#3204 := (= #3203 f1)
+#3216 := (= #3214 #3214)
+#3217 := (and #3216 #3204)
+#3218 := (implies #3204 #3217)
+#3219 := (forall (vars (?v0 S5)) (:pat #3215) #3218)
+#3229 := (and #3219 #3228)
+decl f41 :: (-> S12 S5 S11)
+#3191 := (f41 #3190 #28)
+#3192 := (pattern #3191)
+#3209 := (= #3191 #3191)
+#3210 := (and #3209 #3204)
+#3211 := (implies #3204 #3210)
+#3212 := (forall (vars (?v0 S5)) (:pat #3192) #3211)
+#3230 := (and #3212 #3229)
+decl f20 :: (-> S9 S5 Int)
+decl f21 :: (-> S4 S9)
+#3200 := (f21 f292)
+#3201 := (f20 #3200 #28)
+#3202 := (pattern #3201)
+#3205 := (= #3201 #3201)
+#3206 := (and #3205 #3204)
+#3207 := (implies #3204 #3206)
+#3208 := (forall (vars (?v0 S5)) (:pat #3202) #3207)
+#3231 := (and #3208 #3230)
+decl f262 :: S8
+#2869 := f262
+#3193 := (f26 f292 #28)
+#3194 := (f14 #3193)
+#3195 := (f13 #3194)
+#3196 := (= #3195 f262)
+#3197 := (not #3196)
+#3198 := (implies #3197 #3197)
+#3199 := (forall (vars (?v0 S5)) (:pat #3192) #3198)
+#3232 := (and #3199 #3231)
+#3355 := (implies #3232 #3354)
+#3356 := (implies #3137 #3355)
+#3357 := (implies #3137 #3356)
+#3358 := (implies #3137 #3357)
+#3185 := (implies #3152 #3184)
+#3186 := (implies #3137 #3185)
+#3187 := (implies #3137 #3186)
+#3149 := (not true)
+#3188 := (implies #3149 #3187)
+#3189 := (implies #3137 #3188)
+#3359 := (and #3189 #3358)
+#3360 := (implies #3137 #3359)
+#3147 := (= #3146 f302)
+#3144 := (< f303 f291)
+#3148 := (and #3144 #3147)
+#3361 := (implies #3148 #3360)
+#3140 := (<= #3117 f302)
+#3139 := (< #168 f304)
+#3141 := (implies #3139 #3140)
+#3142 := (implies #421 #3141)
+#3143 := (forall (vars (?v0 Int)) #3142)
+#3362 := (implies #3143 #3361)
+#3138 := (<= f304 f291)
+#3363 := (implies #3138 #3362)
+#3364 := (implies #3137 #3363)
+#3134 := (<= f304 f77)
+#3133 := (<= 0::Int f304)
+#3135 := (and #3133 #3134)
+#3365 := (implies #3135 #3364)
+#3130 := (<= f303 f77)
+#3131 := (and #3129 #3130)
+#3366 := (implies #3131 #3365)
+#3126 := (<= f302 f79)
+#3125 := (<= 0::Int f302)
+#3127 := (and #3125 #3126)
+#3367 := (implies #3127 #3366)
+#3122 := (= #3101 f301)
+#3031 := (< 0::Int f291)
+#3123 := (and #3031 #3122)
+#3368 := (implies #3123 #3367)
+#3369 := (and #3123 #3368)
+#3118 := (<= #3117 f301)
+#3115 := (< #168 1::Int)
+#3119 := (implies #3115 #3118)
+#3120 := (implies #421 #3119)
+#3121 := (forall (vars (?v0 Int)) #3120)
+#3370 := (implies #3121 #3369)
+#3371 := (and #3121 #3370)
+#3114 := (<= 1::Int f291)
+#3372 := (implies #3114 #3371)
+#3373 := (and #3114 #3372)
+#3110 := (<= 0::Int 0::Int)
+#3111 := (and #3110 #3110)
+#3109 := (<= 1::Int 1::Int)
+#3112 := (and #3109 #3111)
+#3113 := (and #3109 #3112)
+#3374 := (implies #3113 #3373)
+#3108 := (= #3107 f1)
+#3375 := (implies #3108 #3374)
+#3106 := (= #3105 f1)
+#3376 := (implies #3106 #3375)
+#3104 := (= #3103 f1)
+#3377 := (implies #3104 #3376)
+#3378 := (implies #3102 #3377)
+#3098 := (= #3097 f1)
+#3093 := (= #3092 f1)
+#3099 := (and #3093 #3098)
+#3379 := (implies #3099 #3378)
+#3380 := (and #3099 #3379)
+#3095 := (= #3094 f1)
+#3096 := (and #3093 #3095)
+#3381 := (implies #3096 #3380)
+#3382 := (and #3096 #3381)
+#3090 := (= #3089 f1)
+#3383 := (implies #3090 #3382)
+#3384 := (and #3090 #3383)
+#3086 := (<= f291 f77)
+#3085 := (<= 0::Int f291)
+#3087 := (and #3085 #3086)
+#3385 := (implies #3087 #3384)
+#3082 := (= #3080 f1)
+#3083 := (iff #3082 false)
+#3084 := (forall (vars (?v0 S5)) (:pat #3081) #3083)
+#3386 := (implies #3084 #3385)
+#3387 := (implies #3079 #3386)
+#3076 := (= #3075 f1)
+#3388 := (implies #3076 #3387)
+#3073 := (= #3072 f1)
+#3071 := (= #3070 f1)
+#3074 := (and #3071 #3073)
+#3389 := (implies #3074 #3388)
+#3067 := (< #3064 f295)
+#3068 := (forall (vars (?v0 S22)) (:pat #3065) #3067)
+#3390 := (implies #3068 #3389)
+#3059 := (= #3058 f1)
+#3062 := (and #3059 #3061)
+#3391 := (implies #3062 #3390)
 #3057 := (= #3056 f1)
-#3054 := (= #3053 f25)
-#3055 := (not #3054)
-#3058 := (and #3055 #3057)
-#3052 := (= #3051 f1)
-#3059 := (and #3052 #3058)
+#3392 := (implies #3057 #3391)
 #3050 := (= #3049 f1)
-#3060 := (and #3050 #3059)
-#3048 := (= #3047 f37)
-#3061 := (and #3048 #3060)
-#3046 := (= #3045 f1)
-#3062 := (and #3046 #3061)
-#3400 := (implies #3062 #3399)
-#3401 := (implies #3038 #3400)
-#3037 := (< f296 1099511627776::Int)
-#3402 := (implies #3037 #3401)
-#3034 := (<= f295 f87)
-#3033 := (<= 0::Int f295)
-#3035 := (and #3033 #3034)
-#3403 := (implies #3035 #3402)
-#3030 := (<= f294 f87)
-#3029 := (<= 0::Int f294)
-#3031 := (and #3029 #3030)
-#3404 := (implies #3031 #3403)
-#3026 := (<= f293 f89)
-#3025 := (<= 0::Int f293)
-#3027 := (and #3025 #3026)
-#3405 := (implies #3027 #3404)
-#3406 := (not #3405)
-#14344 := (iff #3406 #14341)
-#12281 := (not #3168)
-#12282 := (or #12281 #3169)
-#5729 := (not #455)
-#12288 := (or #5729 #12282)
-#12293 := (forall (vars (?v0 Int)) #12288)
-#12301 := (not #12293)
-#12302 := (or #3177 #12301)
-#12307 := (and #12293 #12302)
-#12314 := (or #12313 #12307)
-#12323 := (or #12322 #12314)
-#12332 := (or #12331 #12323)
-#12341 := (or #12340 #12332)
-#12232 := (and #3136 #3143)
-#12349 := (not #12232)
-#12350 := (or #12349 #12341)
-#12358 := (or #12349 #12350)
-#12366 := (or #12349 #12358)
-#12375 := (or #12374 #12366)
-#12380 := (and #10960 #12375)
-#12386 := (or #12349 #12380)
-#12394 := (or #12349 #12386)
-#12973 := (or #12349 #12394)
-#12981 := (or #12349 #12973)
-#12989 := (not #3347)
-#12990 := (or #12989 #12981)
-#12998 := (or #12349 #12990)
-#12646 := (and #3297 #12643)
-#12628 := (not #3292)
-#12629 := (or #12628 #3293)
-#12635 := (or #5729 #12629)
-#12640 := (forall (vars (?v0 Int)) #12635)
-#12659 := (not #12640)
-#12660 := (or #12659 #12646)
-#12665 := (and #12640 #12660)
-#12671 := (not #3291)
-#12672 := (or #12671 #12665)
-#12677 := (and #3291 #12672)
-#12625 := (and #3279 #3289)
-#12683 := (not #12625)
-#12684 := (or #12683 #12677)
-#12693 := (or #12692 #12684)
-#12607 := (+ 1::Int f309)
-#12619 := (= f317 #12607)
-#12701 := (not #12619)
-#12702 := (or #12701 #12693)
-#12613 := (<= #12607 f87)
-#12610 := (<= 0::Int #12607)
-#12616 := (and #12610 #12613)
-#12710 := (not #12616)
-#12711 := (or #12710 #12702)
-#12716 := (and #12616 #12711)
-#12722 := (not #3280)
-#12723 := (or #12722 #12716)
-#12849 := (or #12723 #12848)
-#12858 := (or #12857 #12849)
-#12866 := (or #12349 #12858)
-#12874 := (or #12349 #12866)
-#12882 := (or #12349 #12874)
-#12890 := (not #3327)
-#12891 := (or #12890 #12882)
-#12899 := (or #12349 #12891)
-#12732 := (or #12731 #12723)
-#12741 := (or #12740 #12732)
-#12749 := (not #3143)
-#12750 := (or #12749 #12741)
-#12759 := (or #12758 #12750)
-#12768 := (or #12767 #12759)
-#12777 := (or #12776 #12768)
-#12786 := (or #12785 #12777)
-#12791 := (and #12587 #12786)
-#12798 := (or #12797 #12791)
-#12803 := (and #12581 #12798)
-#12809 := (or #12349 #12803)
-#12817 := (or #12349 #12809)
-#12825 := (not #3267)
-#12826 := (or #12825 #12817)
-#12834 := (or #12349 #12826)
-#12904 := (and #12834 #12899)
-#12910 := (or #12349 #12904)
-#12918 := (or #12785 #12910)
-#12923 := (and #12587 #12918)
-#12929 := (or #12797 #12923)
-#12934 := (and #12581 #12929)
-#12940 := (or #12349 #12934)
-#12948 := (or #12349 #12940)
-#12956 := (not #3256)
-#12957 := (or #12956 #12948)
-#12965 := (or #12349 #12957)
-#13003 := (and #12965 #12998)
-#13009 := (or #12349 #13003)
-#13025 := (or #13024 #13009)
-#13034 := (or #13033 #13025)
-#13043 := (or #13042 #13034)
-#13052 := (or #13051 #13043)
-#13061 := (or #13060 #13052)
-#13069 := (or #12402 #13061)
-#12518 := (and #3231 #12515)
-#12521 := (and #3227 #12518)
-#13077 := (not #12521)
-#13078 := (or #13077 #13069)
-#13086 := (or #13077 #13078)
-#13094 := (or #12349 #13086)
-#13102 := (or #12349 #13094)
-#13110 := (or #12349 #13102)
-#13125 := (or #12349 #13110)
-#12253 := (and #3151 #12250)
-#13133 := (not #12253)
-#13134 := (or #13133 #13125)
-#12235 := (not #3146)
-#12236 := (or #12235 #3147)
-#12242 := (or #5729 #12236)
-#12247 := (forall (vars (?v0 Int)) #12242)
-#13142 := (not #12247)
-#13143 := (or #13142 #13134)
-#13151 := (not #3145)
-#13152 := (or #13151 #13143)
-#13160 := (or #12349 #13152)
-#13168 := (not #3142)
-#13169 := (or #13168 #13160)
-#13177 := (not #3138)
-#13178 := (or #13177 #13169)
-#13186 := (not #3134)
-#13187 := (or #13186 #13178)
-#12229 := (and #3038 #3109)
-#13195 := (not #12229)
-#13196 := (or #13195 #13187)
-#13201 := (and #12229 #13196)
-#12212 := (not #3122)
-#12213 := (or #12212 #3125)
-#12219 := (or #5729 #12213)
-#12224 := (forall (vars (?v0 Int)) #12219)
-#13207 := (not #12224)
-#13208 := (or #13207 #13201)
-#13213 := (and #12224 #13208)
-#13219 := (not #3121)
-#13220 := (or #13219 #13213)
-#13225 := (and #3121 #13220)
-#12206 := (and #3116 #3117)
-#12209 := (and #3116 #12206)
-#13231 := (not #12209)
-#13232 := (or #13231 #13225)
-#13241 := (or #13240 #13232)
-#13250 := (or #13249 #13241)
-#13259 := (or #13258 #13250)
-#13268 := (or #13267 #13259)
-#13277 := (or #13276 #13268)
-#13282 := (and #12192 #13277)
-#13289 := (or #13288 #13282)
-#13294 := (and #12186 #13289)
-#13301 := (or #13300 #13294)
-#13306 := (and #12177 #13301)
-#13312 := (not #3094)
-#13313 := (or #13312 #13306)
-#13322 := (or #13321 #13313)
-#13331 := (or #13330 #13322)
-#13340 := (or #13339 #13331)
-#13349 := (or #13348 #13340)
-#13357 := (not #3075)
-#13358 := (or #13357 #13349)
-#13367 := (or #13366 #13358)
-#13376 := (or #13375 #13367)
-#12124 := (and #12118 #12121)
-#12127 := (and #12112 #12124)
-#12130 := (and #12109 #12127)
-#12133 := (and #12106 #12130)
-#12136 := (and #12102 #12133)
-#13384 := (not #12136)
-#13385 := (or #13384 #13376)
-#13393 := (not #3038)
-#13394 := (or #13393 #13385)
-#13402 := (not #3037)
-#13403 := (or #13402 #13394)
-#13411 := (not #3035)
-#13412 := (or #13411 #13403)
-#13420 := (not #3031)
-#13421 := (or #13420 #13412)
-#13429 := (not #3027)
-#13430 := (or #13429 #13421)
-#13435 := (not #13430)
-#14342 := (iff #13435 #14341)
-#14339 := (iff #13430 #14336)
-#14294 := (or #13449 #14213)
-#14297 := (or #13321 #14294)
-#14300 := (or #13330 #14297)
-#14303 := (or #13339 #14300)
-#14306 := (or #13348 #14303)
-#14309 := (or #14225 #14306)
-#14312 := (or #13366 #14309)
-#14315 := (or #13375 #14312)
-#14318 := (or #14231 #14315)
-#14321 := (or #13508 #14318)
-#14324 := (or #14241 #14321)
-#14327 := (or #14263 #14324)
-#14330 := (or #14277 #14327)
-#14333 := (or #14291 #14330)
-#14337 := (iff #14333 #14336)
-#14338 := [rewrite]: #14337
-#14334 := (iff #13430 #14333)
-#14331 := (iff #13421 #14330)
-#14328 := (iff #13412 #14327)
-#14325 := (iff #13403 #14324)
-#14322 := (iff #13394 #14321)
-#14319 := (iff #13385 #14318)
-#14316 := (iff #13376 #14315)
-#14313 := (iff #13367 #14312)
-#14310 := (iff #13358 #14309)
-#14307 := (iff #13349 #14306)
-#14304 := (iff #13340 #14303)
-#14301 := (iff #13331 #14300)
-#14298 := (iff #13322 #14297)
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+#13917 := (iff #12961 #13916)
+#13914 := (iff #12953 #13913)
+#13911 := (iff #12374 #13910)
+#13908 := (iff #12366 #13907)
+#13901 := (iff #12360 #13900)
+#13898 := (iff #12355 #13895)
+#13871 := (or #12293 #13868)
+#13874 := (or #12302 #13871)
+#13877 := (or #12311 #13874)
+#13880 := (or #12320 #13877)
+#13883 := (or #13501 #13880)
+#13886 := (or #13501 #13883)
+#13889 := (or #13501 #13886)
+#13892 := (or #12354 #13889)
+#13896 := (iff #13892 #13895)
+#13897 := [rewrite]: #13896
+#13893 := (iff #12355 #13892)
+#13890 := (iff #12346 #13889)
+#13887 := (iff #12338 #13886)
+#13884 := (iff #12330 #13883)
+#13881 := (iff #12321 #13880)
+#13878 := (iff #12312 #13877)
+#13875 := (iff #12303 #13874)
+#13872 := (iff #12294 #13871)
+#13869 := (iff #12287 #13868)
+#13866 := (iff #12282 #13863)
+#13860 := (or #13854 #13857)
+#13864 := (iff #13860 #13863)
+#13865 := [rewrite]: #13864
+#13861 := (iff #12282 #13860)
+#13858 := (iff #12281 #13857)
+#13838 := (iff #12273 #13837)
+#13835 := (iff #12268 #13832)
+#13826 := (or #13809 #13823)
+#13829 := (or #5685 #13826)
+#13833 := (iff #13829 #13832)
+#13834 := [rewrite]: #13833
+#13830 := (iff #12268 #13829)
+#13827 := (iff #12262 #13826)
+#13824 := (iff #3162 #13823)
+#13825 := [rewrite]: #13824
+#13819 := (iff #12261 #13809)
+#13814 := (not #13811)
+#13817 := (iff #13814 #13809)
+#13818 := [rewrite]: #13817
+#13815 := (iff #12261 #13814)
+#13812 := (iff #3161 #13811)
+#13813 := [rewrite]: #13812
+#13816 := [monotonicity #13813]: #13815
+#13820 := [trans #13816 #13818]: #13819
+#13828 := [monotonicity #13820 #13825]: #13827
+#5686 := (iff #5676 #5685)
+#4471 := (iff #421 #4470)
+#4464 := (iff #420 #4463)
+#4465 := [rewrite]: #4464
+#4147 := (iff #293 #4149)
+#4148 := [rewrite]: #4147
+#4472 := [monotonicity #4148 #4465]: #4471
+#5687 := [monotonicity #4472]: #5686
+#13831 := [monotonicity #5687 #13828]: #13830
+#13836 := [trans #13831 #13834]: #13835
+#13839 := [quant-intro #13836]: #13838
+#13859 := [monotonicity #13839]: #13858
+#13855 := (iff #3170 #13854)
+#13852 := (iff #3169 #13849)
+#13840 := (and #13811 #3166)
+#13843 := (and #4463 #13840)
+#13846 := (and #4149 #13843)
+#13850 := (iff #13846 #13849)
+#13851 := [rewrite]: #13850
+#13847 := (iff #3169 #13846)
+#13844 := (iff #3168 #13843)
+#13841 := (iff #3167 #13840)
+#13842 := [monotonicity #13813]: #13841
+#13845 := [monotonicity #4465 #13842]: #13844
+#13848 := [monotonicity #4148 #13845]: #13847
+#13853 := [trans #13848 #13851]: #13852
+#13856 := [quant-intro #13853]: #13855
+#13862 := [monotonicity #13856 #13859]: #13861
+#13867 := [trans #13862 #13865]: #13866
+#13870 := [monotonicity #13839 #13867]: #13869
+#13873 := [monotonicity #13870]: #13872
+#13876 := [monotonicity #13873]: #13875
+#13879 := [monotonicity #13876]: #13878
+#13882 := [monotonicity #13879]: #13881
+#13502 := (iff #12329 #13501)
+#13499 := (iff #12212 #13498)
+#13495 := (iff #3136 #13496)
+#13497 := [rewrite]: #13495
+#13492 := (iff #3129 #13493)
+#13494 := [rewrite]: #13492
+#13500 := [monotonicity #13494 #13497]: #13499
+#13503 := [monotonicity #13500]: #13502
+#13885 := [monotonicity #13503 #13882]: #13884
+#13888 := [monotonicity #13503 #13885]: #13887
+#13891 := [monotonicity #13503 #13888]: #13890
+#13894 := [monotonicity #13891]: #13893
+#13899 := [trans #13894 #13897]: #13898
 #13902 := [monotonicity #13899]: #13901
-#13522 := (iff #12349 #13521)
-#13519 := (iff #12232 #13518)
-#13515 := (iff #3143 #13516)
-#13517 := [rewrite]: #13515
-#13512 := (iff #3136 #13513)
-#13514 := [rewrite]: #13512
-#13520 := [monotonicity #13514 #13517]: #13519
-#13523 := [monotonicity #13520]: #13522
-#13905 := [monotonicity #13523 #13902]: #13904
-#13908 := [monotonicity #13523 #13905]: #13907
-#13911 := [monotonicity #13523 #13908]: #13910
-#13914 := [monotonicity #13911]: #13913
-#13919 := [trans #13914 #13917]: #13918
-#13922 := [monotonicity #13919]: #13921
-#13929 := [monotonicity #13523 #13922]: #13928
-#13932 := [monotonicity #13523 #13929]: #13931
-#13935 := [monotonicity #13523 #13932]: #13934
-#13938 := [monotonicity #13523 #13935]: #13937
-#13925 := (iff #12989 #13802)
-#13923 := (iff #3347 #13801)
-#13924 := [rewrite]: #13923
-#13926 := [monotonicity #13924]: #13925
-#13941 := [monotonicity #13926 #13938]: #13940
-#13944 := [monotonicity #13523 #13941]: #13943
-#13949 := [trans #13944 #13947]: #13948
-#13827 := (iff #12965 #13824)
-#13812 := (or #13521 #13795)
-#13815 := (or #13521 #13812)
-#13818 := (or #13801 #13815)
-#13821 := (or #13521 #13818)
-#13825 := (iff #13821 #13824)
-#13826 := [rewrite]: #13825
-#13822 := (iff #12965 #13821)
-#13819 := (iff #12957 #13818)
-#13816 := (iff #12948 #13815)
-#13813 := (iff #12940 #13812)
-#13798 := (iff #12934 #13795)
-#13792 := (and #12581 #13789)
-#13796 := (iff #13792 #13795)
-#13797 := [rewrite]: #13796
-#13793 := (iff #12934 #13792)
-#13790 := (iff #12929 #13789)
-#13787 := (iff #12923 #13784)
-#13781 := (and #12587 #13776)
-#13785 := (iff #13781 #13784)
-#13786 := [rewrite]: #13785
-#13782 := (iff #12923 #13781)
-#13779 := (iff #12918 #13776)
-#13770 := (or #13521 #13767)
-#13773 := (or #12785 #13770)
-#13777 := (iff #13773 #13776)
-#13778 := [rewrite]: #13777
-#13774 := (iff #12918 #13773)
-#13771 := (iff #12910 #13770)
-#13768 := (iff #12904 #13767)
-#13765 := (iff #12899 #13762)
-#13659 := (or #13530 #13651)
-#13741 := (or #13659 #12848)
-#13744 := (or #12857 #13741)
-#13747 := (or #13521 #13744)
-#13750 := (or #13521 #13747)
-#13753 := (or #13521 #13750)
-#13756 := (or #13707 #13753)
-#13759 := (or #13521 #13756)
-#13763 := (iff #13759 #13762)
-#13764 := [rewrite]: #13763
-#13760 := (iff #12899 #13759)
-#13757 := (iff #12891 #13756)
-#13754 := (iff #12882 #13753)
-#13751 := (iff #12874 #13750)
-#13748 := (iff #12866 #13747)
-#13745 := (iff #12858 #13744)
-#13742 := (iff #12849 #13741)
-#13660 := (iff #12723 #13659)
-#13654 := (iff #12716 #13651)
-#13648 := (and #13625 #13643)
-#13652 := (iff #13648 #13651)
-#13653 := [rewrite]: #13652
-#13649 := (iff #12716 #13648)
-#13646 := (iff #12711 #13643)
-#13631 := (or #13547 #13615)
-#13634 := (or #12692 #13631)
-#13637 := (or #13622 #13634)
-#13640 := (or #13628 #13637)
-#13644 := (iff #13640 #13643)
-#13645 := [rewrite]: #13644
-#13641 := (iff #12711 #13640)
-#13638 := (iff #12702 #13637)
-#13635 := (iff #12693 #13634)
-#13632 := (iff #12684 #13631)
-#13616 := (iff #12677 #13615)
-#13613 := (iff #12672 #13612)
-#13610 := (iff #12665 #13609)
-#13607 := (iff #12660 #13606)
-#13604 := (iff #12646 #13601)
-#13598 := (and #13595 #12643)
-#13602 := (iff #13598 #13601)
-#13603 := [rewrite]: #13602
-#13599 := (iff #12646 #13598)
-#13596 := (iff #3297 #13595)
-#13597 := [rewrite]: #13596
-#13600 := [monotonicity #13597]: #13599
-#13605 := [trans #13600 #13603]: #13604
-#13590 := (iff #12659 #13589)
+#13909 := [monotonicity #13503 #13902]: #13908
+#13912 := [monotonicity #13503 #13909]: #13911
+#13915 := [monotonicity #13503 #13912]: #13914
+#13918 := [monotonicity #13503 #13915]: #13917
+#13905 := (iff #12969 #13782)
+#13903 := (iff #3340 #13781)
+#13904 := [rewrite]: #13903
+#13906 := [monotonicity #13904]: #13905
+#13921 := [monotonicity #13906 #13918]: #13920
+#13924 := [monotonicity #13503 #13921]: #13923
+#13929 := [trans #13924 #13927]: #13928
+#13807 := (iff #12945 #13804)
+#13792 := (or #13501 #13775)
+#13795 := (or #13501 #13792)
+#13798 := (or #13781 #13795)
+#13801 := (or #13501 #13798)
+#13805 := (iff #13801 #13804)
+#13806 := [rewrite]: #13805
+#13802 := (iff #12945 #13801)
+#13799 := (iff #12937 #13798)
+#13796 := (iff #12928 #13795)
+#13793 := (iff #12920 #13792)
+#13778 := (iff #12914 #13775)
+#13772 := (and #12561 #13769)
+#13776 := (iff #13772 #13775)
+#13777 := [rewrite]: #13776
+#13773 := (iff #12914 #13772)
+#13770 := (iff #12909 #13769)
+#13767 := (iff #12903 #13764)
+#13761 := (and #12567 #13756)
+#13765 := (iff #13761 #13764)
+#13766 := [rewrite]: #13765
+#13762 := (iff #12903 #13761)
+#13759 := (iff #12898 #13756)
+#13750 := (or #13501 #13747)
+#13753 := (or #12765 #13750)
+#13757 := (iff #13753 #13756)
+#13758 := [rewrite]: #13757
+#13754 := (iff #12898 #13753)
+#13751 := (iff #12890 #13750)
+#13748 := (iff #12884 #13747)
+#13745 := (iff #12879 #13742)
+#13639 := (or #13510 #13631)
+#13721 := (or #13639 #12828)
+#13724 := (or #12837 #13721)
+#13727 := (or #13501 #13724)
+#13730 := (or #13501 #13727)
+#13733 := (or #13501 #13730)
+#13736 := (or #13687 #13733)
+#13739 := (or #13501 #13736)
+#13743 := (iff #13739 #13742)
+#13744 := [rewrite]: #13743
+#13740 := (iff #12879 #13739)
+#13737 := (iff #12871 #13736)
+#13734 := (iff #12862 #13733)
+#13731 := (iff #12854 #13730)
+#13728 := (iff #12846 #13727)
+#13725 := (iff #12838 #13724)
+#13722 := (iff #12829 #13721)
+#13640 := (iff #12703 #13639)
+#13634 := (iff #12696 #13631)
+#13628 := (and #13605 #13623)
+#13632 := (iff #13628 #13631)
+#13633 := [rewrite]: #13632
+#13629 := (iff #12696 #13628)
+#13626 := (iff #12691 #13623)
+#13611 := (or #13527 #13595)
+#13614 := (or #12672 #13611)
+#13617 := (or #13602 #13614)
+#13620 := (or #13608 #13617)
+#13624 := (iff #13620 #13623)
+#13625 := [rewrite]: #13624
+#13621 := (iff #12691 #13620)
+#13618 := (iff #12682 #13617)
+#13615 := (iff #12673 #13614)
+#13612 := (iff #12664 #13611)
+#13596 := (iff #12657 #13595)
+#13593 := (iff #12652 #13592)
+#13590 := (iff #12645 #13589)
 #13587 := (iff #12640 #13586)
-#13584 := (iff #12635 #13581)
-#13575 := (or #13558 #13572)
-#13578 := (or #5738 #13575)
+#13584 := (iff #12626 #13581)
+#13578 := (and #13575 #12623)
 #13582 := (iff #13578 #13581)
 #13583 := [rewrite]: #13582
-#13579 := (iff #12635 #13578)
-#13576 := (iff #12629 #13575)
-#13573 := (iff #3293 #13572)
-#13574 := [rewrite]: #13573
-#13568 := (iff #12628 #13558)
-#13560 := (not #13558)
-#13563 := (not #13560)
-#13566 := (iff #13563 #13558)
-#13567 := [rewrite]: #13566
-#13564 := (iff #12628 #13563)
-#13561 := (iff #3292 #13560)
-#13562 := [rewrite]: #13561
-#13565 := [monotonicity #13562]: #13564
-#13569 := [trans #13565 #13567]: #13568
-#13577 := [monotonicity #13569 #13574]: #13576
-#13580 := [monotonicity #5740 #13577]: #13579
+#13579 := (iff #12626 #13578)
+#13576 := (iff #3290 #13575)
+#13577 := [rewrite]: #13576
+#13580 := [monotonicity #13577]: #13579
 #13585 := [trans #13580 #13583]: #13584
-#13588 := [quant-intro #13585]: #13587
-#13591 := [monotonicity #13588]: #13590
-#13608 := [monotonicity #13591 #13605]: #13607
-#13611 := [monotonicity #13588 #13608]: #13610
-#13556 := (iff #12671 #13555)
-#13553 := (iff #3291 #13550)
+#13570 := (iff #12639 #13569)
+#13567 := (iff #12620 #13566)
+#13564 := (iff #12615 #13561)
+#13555 := (or #13538 #13552)
+#13558 := (or #5685 #13555)
+#13562 := (iff #13558 #13561)
+#13563 := [rewrite]: #13562
+#13559 := (iff #12615 #13558)
+#13556 := (iff #12609 #13555)
+#13553 := (iff #3286 #13552)
 #13554 := [rewrite]: #13553
-#13557 := [monotonicity #13554]: #13556
-#13614 := [monotonicity #13557 #13611]: #13613
-#13617 := [monotonicity #13554 #13614]: #13616
-#13548 := (iff #12683 #13547)
-#13545 := (iff #12625 #13544)
-#13541 := (iff #3289 #13542)
-#13543 := [rewrite]: #13541
-#13524 := (iff #3279 #13525)
-#13526 := [rewrite]: #13524
-#13546 := [monotonicity #13526 #13543]: #13545
-#13549 := [monotonicity #13546]: #13548
-#13633 := [monotonicity #13549 #13617]: #13632
-#13636 := [monotonicity #13633]: #13635
-#13623 := (iff #12701 #13622)
-#13620 := (iff #12619 #13618)
-#13621 := [rewrite]: #13620
-#13624 := [monotonicity #13621]: #13623
-#13639 := [monotonicity #13624 #13636]: #13638
-#13629 := (iff #12710 #13628)
-#13626 := (iff #12616 #13625)
-#13539 := (iff #12613 #13536)
-#13540 := [rewrite]: #13539
-#13533 := (iff #12610 #13534)
-#13535 := [rewrite]: #13533
-#13627 := [monotonicity #13535 #13540]: #13626
-#13630 := [monotonicity #13627]: #13629
-#13642 := [monotonicity #13630 #13639]: #13641
-#13647 := [trans #13642 #13645]: #13646
-#13650 := [monotonicity #13627 #13647]: #13649
-#13655 := [trans #13650 #13653]: #13654
-#13531 := (iff #12722 #13530)
-#13528 := (iff #3280 #13527)
-#13529 := [monotonicity #13517 #13526]: #13528
-#13532 := [monotonicity #13529]: #13531
-#13661 := [monotonicity #13532 #13655]: #13660
-#13743 := [monotonicity #13661]: #13742
-#13746 := [monotonicity #13743]: #13745
-#13749 := [monotonicity #13523 #13746]: #13748
-#13752 := [monotonicity #13523 #13749]: #13751
-#13755 := [monotonicity #13523 #13752]: #13754
-#13739 := (iff #12890 #13707)
-#13737 := (iff #3327 #13708)
-#13738 := [rewrite]: #13737
-#13740 := [monotonicity #13738]: #13739
-#13758 := [monotonicity #13740 #13755]: #13757
-#13761 := [monotonicity #13523 #13758]: #13760
-#13766 := [trans #13761 #13764]: #13765
-#13735 := (iff #12834 #13732)
-#13720 := (or #13521 #13702)
-#13723 := (or #13521 #13720)
-#13726 := (or #13708 #13723)
-#13729 := (or #13521 #13726)
-#13733 := (iff #13729 #13732)
-#13734 := [rewrite]: #13733
-#13730 := (iff #12834 #13729)
-#13727 := (iff #12826 #13726)
-#13724 := (iff #12817 #13723)
-#13721 := (iff #12809 #13720)
-#13705 := (iff #12803 #13702)
-#13699 := (and #12581 #13696)
-#13703 := (iff #13699 #13702)
-#13704 := [rewrite]: #13703
-#13700 := (iff #12803 #13699)
-#13697 := (iff #12798 #13696)
-#13694 := (iff #12791 #13691)
-#13688 := (and #12587 #13683)
-#13692 := (iff #13688 #13691)
-#13693 := [rewrite]: #13692
-#13689 := (iff #12791 #13688)
-#13686 := (iff #12786 #13683)
-#13662 := (or #12731 #13659)
-#13665 := (or #12740 #13662)
-#13668 := (or #13656 #13665)
-#13671 := (or #12758 #13668)
-#13674 := (or #12767 #13671)
-#13677 := (or #12776 #13674)
-#13680 := (or #12785 #13677)
-#13684 := (iff #13680 #13683)
-#13685 := [rewrite]: #13684
-#13681 := (iff #12786 #13680)
-#13678 := (iff #12777 #13677)
-#13675 := (iff #12768 #13674)
-#13672 := (iff #12759 #13671)
-#13669 := (iff #12750 #13668)
-#13666 := (iff #12741 #13665)
-#13663 := (iff #12732 #13662)
-#13664 := [monotonicity #13661]: #13663
-#13667 := [monotonicity #13664]: #13666
-#13657 := (iff #12749 #13656)
-#13658 := [monotonicity #13517]: #13657
-#13670 := [monotonicity #13658 #13667]: #13669
-#13673 := [monotonicity #13670]: #13672
-#13676 := [monotonicity #13673]: #13675
-#13679 := [monotonicity #13676]: #13678
-#13682 := [monotonicity #13679]: #13681
-#13687 := [trans #13682 #13685]: #13686
-#13690 := [monotonicity #13687]: #13689
-#13695 := [trans #13690 #13693]: #13694
-#13698 := [monotonicity #13695]: #13697
-#13701 := [monotonicity #13698]: #13700
-#13706 := [trans #13701 #13704]: #13705
-#13722 := [monotonicity #13523 #13706]: #13721
-#13725 := [monotonicity #13523 #13722]: #13724
-#13718 := (iff #12825 #13708)
-#13713 := (not #13707)
-#13716 := (iff #13713 #13708)
-#13717 := [rewrite]: #13716
-#13714 := (iff #12825 #13713)
-#13711 := (iff #3267 #13707)
-#13712 := [rewrite]: #13711
-#13715 := [monotonicity #13712]: #13714
-#13719 := [trans #13715 #13717]: #13718
-#13728 := [monotonicity #13719 #13725]: #13727
-#13731 := [monotonicity #13523 #13728]: #13730
-#13736 := [trans #13731 #13734]: #13735
-#13769 := [monotonicity #13736 #13766]: #13768
-#13772 := [monotonicity #13523 #13769]: #13771
-#13775 := [monotonicity #13772]: #13774
-#13780 := [trans #13775 #13778]: #13779
-#13783 := [monotonicity #13780]: #13782
-#13788 := [trans #13783 #13786]: #13787
-#13791 := [monotonicity #13788]: #13790
-#13794 := [monotonicity #13791]: #13793
-#13799 := [trans #13794 #13797]: #13798
-#13814 := [monotonicity #13523 #13799]: #13813
-#13817 := [monotonicity #13523 #13814]: #13816
-#13810 := (iff #12956 #13801)
-#13805 := (not #13802)
-#13808 := (iff #13805 #13801)
-#13809 := [rewrite]: #13808
-#13806 := (iff #12956 #13805)
-#13803 := (iff #3256 #13802)
-#13804 := [rewrite]: #13803
-#13807 := [monotonicity #13804]: #13806
-#13811 := [trans #13807 #13809]: #13810
-#13820 := [monotonicity #13811 #13817]: #13819
-#13823 := [monotonicity #13523 #13820]: #13822
-#13828 := [trans #13823 #13826]: #13827
-#13952 := [monotonicity #13828 #13949]: #13951
-#14082 := [monotonicity #13523 #13952]: #14081
-#14085 := [monotonicity #14082]: #14084
-#14088 := [monotonicity #14085]: #14087
-#14091 := [monotonicity #14088]: #14090
-#14094 := [monotonicity #14091]: #14093
-#14097 := [monotonicity #14094]: #14096
-#14100 := [monotonicity #14097]: #14099
-#13975 := (iff #13077 #13974)
-#13972 := (iff #12521 #12515)
-#13964 := (and true #12515)
-#13967 := (and true #13964)
-#13970 := (iff #13967 #12515)
-#13971 := [rewrite]: #13970
-#13968 := (iff #12521 #13967)
-#13965 := (iff #12518 #13964)
-#13960 := (iff #3231 true)
-#13955 := (forall (vars (?v0 S20)) (:pat #3229) true)
-#13958 := (iff #13955 true)
-#13959 := [elim-unused]: #13958
-#13956 := (iff #3231 #13955)
-#13953 := (iff #3230 true)
-#13954 := [rewrite]: #13953
-#13957 := [quant-intro #13954]: #13956
-#13961 := [trans #13957 #13959]: #13960
-#13966 := [monotonicity #13961]: #13965
-#13962 := (iff #3227 true)
-#13963 := [rewrite]: #13962
-#13969 := [monotonicity #13963 #13966]: #13968
-#13973 := [trans #13969 #13971]: #13972
-#13976 := [monotonicity #13973]: #13975
-#14103 := [monotonicity #13976 #14100]: #14102
-#14106 := [monotonicity #13976 #14103]: #14105
-#14109 := [monotonicity #13523 #14106]: #14108
-#14112 := [monotonicity #13523 #14109]: #14111
-#14115 := [monotonicity #13523 #14112]: #14114
-#14118 := [monotonicity #13523 #14115]: #14117
-#13992 := (iff #13133 #13991)
-#13989 := (iff #12253 #13986)
-#13983 := (and #13980 #12250)
-#13987 := (iff #13983 #13986)
-#13988 := [rewrite]: #13987
-#13984 := (iff #12253 #13983)
-#13981 := (iff #3151 #13980)
-#13982 := [rewrite]: #13981
-#13985 := [monotonicity #13982]: #13984
-#13990 := [trans #13985 #13988]: #13989
-#13993 := [monotonicity #13990]: #13992
-#14121 := [monotonicity #13993 #14118]: #14120
-#14026 := (iff #13142 #14025)
-#14023 := (iff #12247 #14022)
-#14020 := (iff #12242 #14017)
-#14011 := (or #13994 #14008)
-#14014 := (or #5738 #14011)
-#14018 := (iff #14014 #14017)
+#13548 := (iff #12608 #13538)
+#13540 := (not #13538)
+#13543 := (not #13540)
+#13546 := (iff #13543 #13538)
+#13547 := [rewrite]: #13546
+#13544 := (iff #12608 #13543)
+#13541 := (iff #3285 #13540)
+#13542 := [rewrite]: #13541
+#13545 := [monotonicity #13542]: #13544
+#13549 := [trans #13545 #13547]: #13548
+#13557 := [monotonicity #13549 #13554]: #13556
+#13560 := [monotonicity #5687 #13557]: #13559
+#13565 := [trans #13560 #13563]: #13564
+#13568 := [quant-intro #13565]: #13567
+#13571 := [monotonicity #13568]: #13570
+#13588 := [monotonicity #13571 #13585]: #13587
+#13591 := [monotonicity #13568 #13588]: #13590
+#13536 := (iff #12651 #13535)
+#13533 := (iff #3284 #13530)
+#13534 := [rewrite]: #13533
+#13537 := [monotonicity #13534]: #13536
+#13594 := [monotonicity #13537 #13591]: #13593
+#13597 := [monotonicity #13534 #13594]: #13596
+#13528 := (iff #12663 #13527)
+#13525 := (iff #12605 #13524)
+#13521 := (iff #3282 #13522)
+#13523 := [rewrite]: #13521
+#13504 := (iff #3272 #13505)
+#13506 := [rewrite]: #13504
+#13526 := [monotonicity #13506 #13523]: #13525
+#13529 := [monotonicity #13526]: #13528
+#13613 := [monotonicity #13529 #13597]: #13612
+#13616 := [monotonicity #13613]: #13615
+#13603 := (iff #12681 #13602)
+#13600 := (iff #12599 #13598)
+#13601 := [rewrite]: #13600
+#13604 := [monotonicity #13601]: #13603
+#13619 := [monotonicity #13604 #13616]: #13618
+#13609 := (iff #12690 #13608)
+#13606 := (iff #12596 #13605)
+#13519 := (iff #12593 #13516)
+#13520 := [rewrite]: #13519
+#13513 := (iff #12590 #13514)
+#13515 := [rewrite]: #13513
+#13607 := [monotonicity #13515 #13520]: #13606
+#13610 := [monotonicity #13607]: #13609
+#13622 := [monotonicity #13610 #13619]: #13621
+#13627 := [trans #13622 #13625]: #13626
+#13630 := [monotonicity #13607 #13627]: #13629
+#13635 := [trans #13630 #13633]: #13634
+#13511 := (iff #12702 #13510)
+#13508 := (iff #3273 #13507)
+#13509 := [monotonicity #13497 #13506]: #13508
+#13512 := [monotonicity #13509]: #13511
+#13641 := [monotonicity #13512 #13635]: #13640
+#13723 := [monotonicity #13641]: #13722
+#13726 := [monotonicity #13723]: #13725
+#13729 := [monotonicity #13503 #13726]: #13728
+#13732 := [monotonicity #13503 #13729]: #13731
+#13735 := [monotonicity #13503 #13732]: #13734
+#13719 := (iff #12870 #13687)
+#13717 := (iff #3320 #13688)
+#13718 := [rewrite]: #13717
+#13720 := [monotonicity #13718]: #13719
+#13738 := [monotonicity #13720 #13735]: #13737
+#13741 := [monotonicity #13503 #13738]: #13740
+#13746 := [trans #13741 #13744]: #13745
+#13715 := (iff #12814 #13712)
+#13700 := (or #13501 #13682)
+#13703 := (or #13501 #13700)
+#13706 := (or #13688 #13703)
+#13709 := (or #13501 #13706)
+#13713 := (iff #13709 #13712)
+#13714 := [rewrite]: #13713
+#13710 := (iff #12814 #13709)
+#13707 := (iff #12806 #13706)
+#13704 := (iff #12797 #13703)
+#13701 := (iff #12789 #13700)
+#13685 := (iff #12783 #13682)
+#13679 := (and #12561 #13676)
+#13683 := (iff #13679 #13682)
+#13684 := [rewrite]: #13683
+#13680 := (iff #12783 #13679)
+#13677 := (iff #12778 #13676)
+#13674 := (iff #12771 #13671)
+#13668 := (and #12567 #13663)
+#13672 := (iff #13668 #13671)
+#13673 := [rewrite]: #13672
+#13669 := (iff #12771 #13668)
+#13666 := (iff #12766 #13663)
+#13642 := (or #12711 #13639)
+#13645 := (or #12720 #13642)
+#13648 := (or #13636 #13645)
+#13651 := (or #12738 #13648)
+#13654 := (or #12747 #13651)
+#13657 := (or #12756 #13654)
+#13660 := (or #12765 #13657)
+#13664 := (iff #13660 #13663)
+#13665 := [rewrite]: #13664
+#13661 := (iff #12766 #13660)
+#13658 := (iff #12757 #13657)
+#13655 := (iff #12748 #13654)
+#13652 := (iff #12739 #13651)
+#13649 := (iff #12730 #13648)
+#13646 := (iff #12721 #13645)
+#13643 := (iff #12712 #13642)
+#13644 := [monotonicity #13641]: #13643
+#13647 := [monotonicity #13644]: #13646
+#13637 := (iff #12729 #13636)
+#13638 := [monotonicity #13497]: #13637
+#13650 := [monotonicity #13638 #13647]: #13649
+#13653 := [monotonicity #13650]: #13652
+#13656 := [monotonicity #13653]: #13655
+#13659 := [monotonicity #13656]: #13658
+#13662 := [monotonicity #13659]: #13661
+#13667 := [trans #13662 #13665]: #13666
+#13670 := [monotonicity #13667]: #13669
+#13675 := [trans #13670 #13673]: #13674
+#13678 := [monotonicity #13675]: #13677
+#13681 := [monotonicity #13678]: #13680
+#13686 := [trans #13681 #13684]: #13685
+#13702 := [monotonicity #13503 #13686]: #13701
+#13705 := [monotonicity #13503 #13702]: #13704
+#13698 := (iff #12805 #13688)
+#13693 := (not #13687)
+#13696 := (iff #13693 #13688)
+#13697 := [rewrite]: #13696
+#13694 := (iff #12805 #13693)
+#13691 := (iff #3260 #13687)
+#13692 := [rewrite]: #13691
+#13695 := [monotonicity #13692]: #13694
+#13699 := [trans #13695 #13697]: #13698
+#13708 := [monotonicity #13699 #13705]: #13707
+#13711 := [monotonicity #13503 #13708]: #13710
+#13716 := [trans #13711 #13714]: #13715
+#13749 := [monotonicity #13716 #13746]: #13748
+#13752 := [monotonicity #13503 #13749]: #13751
+#13755 := [monotonicity #13752]: #13754
+#13760 := [trans #13755 #13758]: #13759
+#13763 := [monotonicity #13760]: #13762
+#13768 := [trans #13763 #13766]: #13767
+#13771 := [monotonicity #13768]: #13770
+#13774 := [monotonicity #13771]: #13773
+#13779 := [trans #13774 #13777]: #13778
+#13794 := [monotonicity #13503 #13779]: #13793
+#13797 := [monotonicity #13503 #13794]: #13796
+#13790 := (iff #12936 #13781)
+#13785 := (not #13782)
+#13788 := (iff #13785 #13781)
+#13789 := [rewrite]: #13788
+#13786 := (iff #12936 #13785)
+#13783 := (iff #3249 #13782)
+#13784 := [rewrite]: #13783
+#13787 := [monotonicity #13784]: #13786
+#13791 := [trans #13787 #13789]: #13790
+#13800 := [monotonicity #13791 #13797]: #13799
+#13803 := [monotonicity #13503 #13800]: #13802
+#13808 := [trans #13803 #13806]: #13807
+#13932 := [monotonicity #13808 #13929]: #13931
+#14062 := [monotonicity #13503 #13932]: #14061
+#14065 := [monotonicity #14062]: #14064
+#14068 := [monotonicity #14065]: #14067
+#14071 := [monotonicity #14068]: #14070
+#14074 := [monotonicity #14071]: #14073
+#14077 := [monotonicity #14074]: #14076
+#14080 := [monotonicity #14077]: #14079
+#13955 := (iff #13057 #13954)
+#13952 := (iff #12501 #12495)
+#13944 := (and true #12495)
+#13947 := (and true #13944)
+#13950 := (iff #13947 #12495)
+#13951 := [rewrite]: #13950
+#13948 := (iff #12501 #13947)
+#13945 := (iff #12498 #13944)
+#13940 := (iff #3224 true)
+#13935 := (forall (vars (?v0 S5)) (:pat #3222) true)
+#13938 := (iff #13935 true)
+#13939 := [elim-unused]: #13938
+#13936 := (iff #3224 #13935)
+#13933 := (iff #3223 true)
+#13934 := [rewrite]: #13933
+#13937 := [quant-intro #13934]: #13936
+#13941 := [trans #13937 #13939]: #13940
+#13946 := [monotonicity #13941]: #13945
+#13942 := (iff #3220 true)
+#13943 := [rewrite]: #13942
+#13949 := [monotonicity #13943 #13946]: #13948
+#13953 := [trans #13949 #13951]: #13952
+#13956 := [monotonicity #13953]: #13955
+#14083 := [monotonicity #13956 #14080]: #14082
+#14086 := [monotonicity #13956 #14083]: #14085
+#14089 := [monotonicity #13503 #14086]: #14088
+#14092 := [monotonicity #13503 #14089]: #14091
+#14095 := [monotonicity #13503 #14092]: #14094
+#14098 := [monotonicity #13503 #14095]: #14097
+#13972 := (iff #13113 #13971)
+#13969 := (iff #12233 #13966)
+#13963 := (and #13960 #12230)
+#13967 := (iff #13963 #13966)
+#13968 := [rewrite]: #13967
+#13964 := (iff #12233 #13963)
+#13961 := (iff #3144 #13960)
+#13962 := [rewrite]: #13961
+#13965 := [monotonicity #13962]: #13964
+#13970 := [trans #13965 #13968]: #13969
+#13973 := [monotonicity #13970]: #13972
+#14101 := [monotonicity #13973 #14098]: #14100
+#14006 := (iff #13122 #14005)
+#14003 := (iff #12227 #14002)
+#14000 := (iff #12222 #13997)
+#13991 := (or #13974 #13988)
+#13994 := (or #5685 #13991)
+#13998 := (iff #13994 #13997)
+#13999 := [rewrite]: #13998
+#13995 := (iff #12222 #13994)
+#13992 := (iff #12216 #13991)
+#13989 := (iff #3140 #13988)
+#13990 := [rewrite]: #13989
+#13984 := (iff #12215 #13974)
+#13976 := (not #13974)
+#13979 := (not #13976)
+#13982 := (iff #13979 #13974)
+#13983 := [rewrite]: #13982
+#13980 := (iff #12215 #13979)
+#13977 := (iff #3139 #13976)
+#13978 := [rewrite]: #13977
+#13981 := [monotonicity #13978]: #13980
+#13985 := [trans #13981 #13983]: #13984
+#13993 := [monotonicity #13985 #13990]: #13992
+#13996 := [monotonicity #5687 #13993]: #13995
+#14001 := [trans #13996 #13999]: #14000
+#14004 := [quant-intro #14001]: #14003
+#14007 := [monotonicity #14004]: #14006
+#14104 := [monotonicity #14007 #14101]: #14103
+#14012 := (iff #13131 #14011)
+#14009 := (iff #3138 #14008)
+#14010 := [rewrite]: #14009
+#14013 := [monotonicity #14010]: #14012
+#14107 := [monotonicity #14013 #14104]: #14106
+#14110 := [monotonicity #13503 #14107]: #14109
+#14024 := (iff #13148 #14023)
+#14021 := (iff #3135 #14020)
+#14018 := (iff #3134 #14017)
 #14019 := [rewrite]: #14018
-#14015 := (iff #12242 #14014)
-#14012 := (iff #12236 #14011)
-#14009 := (iff #3147 #14008)
-#14010 := [rewrite]: #14009
-#14004 := (iff #12235 #13994)
-#13996 := (not #13994)
-#13999 := (not #13996)
-#14002 := (iff #13999 #13994)
-#14003 := [rewrite]: #14002
-#14000 := (iff #12235 #13999)
-#13997 := (iff #3146 #13996)
-#13998 := [rewrite]: #13997
-#14001 := [monotonicity #13998]: #14000
-#14005 := [trans #14001 #14003]: #14004
-#14013 := [monotonicity #14005 #14010]: #14012
-#14016 := [monotonicity #5740 #14013]: #14015
-#14021 := [trans #14016 #14019]: #14020
-#14024 := [quant-intro #14021]: #14023
-#14027 := [monotonicity #14024]: #14026
-#14124 := [monotonicity #14027 #14121]: #14123
-#14032 := (iff #13151 #14031)
-#14029 := (iff #3145 #14028)
-#14030 := [rewrite]: #14029
-#14033 := [monotonicity #14030]: #14032
-#14127 := [monotonicity #14033 #14124]: #14126
-#14130 := [monotonicity #13523 #14127]: #14129
-#14044 := (iff #13168 #14043)
-#14041 := (iff #3142 #14040)
-#14038 := (iff #3141 #14037)
-#14039 := [rewrite]: #14038
-#14035 := (iff #3140 #14034)
-#14036 := [rewrite]: #14035
-#14042 := [monotonicity #14036 #14039]: #14041
-#14045 := [monotonicity #14042]: #14044
-#14133 := [monotonicity #14045 #14130]: #14132
-#14054 := (iff #13177 #14053)
-#14051 := (iff #3138 #14050)
-#14048 := (iff #3137 #14046)
-#14049 := [rewrite]: #14048
-#14052 := [monotonicity #13514 #14049]: #14051
-#14055 := [monotonicity #14052]: #14054
-#14136 := [monotonicity #14055 #14133]: #14135
-#14067 := (iff #13186 #14066)
-#14064 := (iff #3134 #14063)
-#14061 := (iff #3133 #14059)
-#14062 := [rewrite]: #14061
-#14057 := (iff #3132 #14056)
-#14058 := [rewrite]: #14057
-#14065 := [monotonicity #14058 #14062]: #14064
-#14068 := [monotonicity #14065]: #14067
-#14139 := [monotonicity #14068 #14136]: #14138
-#14078 := (iff #13195 #14077)
-#14075 := (iff #12229 #14072)
-#14073 := (iff #14069 #14072)
-#14074 := [rewrite]: #14073
-#14070 := (iff #12229 #14069)
-#13510 := (iff #3038 #13509)
-#13511 := [rewrite]: #13510
-#14071 := [monotonicity #13511]: #14070
-#14076 := [trans #14071 #14074]: #14075
-#14079 := [monotonicity #14076]: #14078
-#14142 := [monotonicity #14079 #14139]: #14141
-#14147 := [trans #14142 #14145]: #14146
-#14150 := [monotonicity #14071 #14147]: #14149
-#14155 := [trans #14150 #14153]: #14154
-#13506 := (iff #13207 #13505)
-#13503 := (iff #12224 #13502)
-#13500 := (iff #12219 #13497)
-#13491 := (or #13475 #13487)
-#13494 := (or #5738 #13491)
-#13498 := (iff #13494 #13497)
-#13499 := [rewrite]: #13498
-#13495 := (iff #12219 #13494)
-#13492 := (iff #12213 #13491)
-#13486 := (iff #3125 #13487)
-#13490 := [rewrite]: #13486
-#13484 := (iff #12212 #13475)
-#13476 := (not #13475)
-#13479 := (not #13476)
-#13482 := (iff #13479 #13475)
-#13483 := [rewrite]: #13482
-#13480 := (iff #12212 #13479)
-#13477 := (iff #3122 #13476)
-#13478 := [rewrite]: #13477
-#13481 := [monotonicity #13478]: #13480
-#13485 := [trans #13481 #13483]: #13484
-#13493 := [monotonicity #13485 #13490]: #13492
-#13496 := [monotonicity #5740 #13493]: #13495
-#13501 := [trans #13496 #13499]: #13500
-#13504 := [quant-intro #13501]: #13503
-#13507 := [monotonicity #13504]: #13506
-#14158 := [monotonicity #13507 #14155]: #14157
-#14161 := [monotonicity #13504 #14158]: #14160
-#13473 := (iff #13219 #13472)
-#13470 := (iff #3121 #13469)
-#13471 := [rewrite]: #13470
-#13474 := [monotonicity #13471]: #13473
-#14164 := [monotonicity #13474 #14161]: #14163
-#14167 := [monotonicity #13471 #14164]: #14166
-#13467 := (iff #13231 false)
-#12256 := (iff #3156 false)
-#12257 := [rewrite]: #12256
-#13465 := (iff #13231 #3156)
-#13463 := (iff #12209 true)
-#12568 := (and true true)
-#13458 := (and true #12568)
-#13461 := (iff #13458 true)
-#13462 := [rewrite]: #13461
-#13459 := (iff #12209 #13458)
-#13456 := (iff #12206 #12568)
-#13454 := (iff #3117 true)
-#13455 := [rewrite]: #13454
-#13452 := (iff #3116 true)
-#13453 := [rewrite]: #13452
-#13457 := [monotonicity #13453 #13455]: #13456
-#13460 := [monotonicity #13453 #13457]: #13459
-#13464 := [trans #13460 #13462]: #13463
-#13466 := [monotonicity #13464]: #13465
-#13468 := [trans #13466 #12257]: #13467
-#14170 := [monotonicity #13468 #14167]: #14169
+#14015 := (iff #3133 #14014)
+#14016 := [rewrite]: #14015
+#14022 := [monotonicity #14016 #14019]: #14021
+#14025 := [monotonicity #14022]: #14024
+#14113 := [monotonicity #14025 #14110]: #14112
+#14034 := (iff #13157 #14033)
+#14031 := (iff #3131 #14030)
+#14028 := (iff #3130 #14026)
+#14029 := [rewrite]: #14028
+#14032 := [monotonicity #13494 #14029]: #14031
+#14035 := [monotonicity #14032]: #14034
+#14116 := [monotonicity #14035 #14113]: #14115
+#14047 := (iff #13166 #14046)
+#14044 := (iff #3127 #14043)
+#14041 := (iff #3126 #14039)
+#14042 := [rewrite]: #14041
+#14037 := (iff #3125 #14036)
+#14038 := [rewrite]: #14037
+#14045 := [monotonicity #14038 #14042]: #14044
+#14048 := [monotonicity #14045]: #14047
+#14119 := [monotonicity #14048 #14116]: #14118
+#14058 := (iff #13175 #14057)
+#14055 := (iff #12209 #14052)
+#14053 := (iff #14049 #14052)
+#14054 := [rewrite]: #14053
+#14050 := (iff #12209 #14049)
+#13490 := (iff #3031 #13489)
+#13491 := [rewrite]: #13490
+#14051 := [monotonicity #13491]: #14050
+#14056 := [trans #14051 #14054]: #14055
+#14059 := [monotonicity #14056]: #14058
+#14122 := [monotonicity #14059 #14119]: #14121
+#14127 := [trans #14122 #14125]: #14126
+#14130 := [monotonicity #14051 #14127]: #14129
+#14135 := [trans #14130 #14133]: #14134
+#13486 := (iff #13187 #13485)
+#13483 := (iff #12204 #13482)
+#13480 := (iff #12199 #13477)
+#13471 := (or #13455 #13467)
+#13474 := (or #5685 #13471)
+#13478 := (iff #13474 #13477)
+#13479 := [rewrite]: #13478
+#13475 := (iff #12199 #13474)
+#13472 := (iff #12193 #13471)
+#13466 := (iff #3118 #13467)
+#13470 := [rewrite]: #13466
+#13464 := (iff #12192 #13455)
+#13456 := (not #13455)
+#13459 := (not #13456)
+#13462 := (iff #13459 #13455)
+#13463 := [rewrite]: #13462
+#13460 := (iff #12192 #13459)
+#13457 := (iff #3115 #13456)
+#13458 := [rewrite]: #13457
+#13461 := [monotonicity #13458]: #13460
+#13465 := [trans #13461 #13463]: #13464
+#13473 := [monotonicity #13465 #13470]: #13472
+#13476 := [monotonicity #5687 #13473]: #13475
+#13481 := [trans #13476 #13479]: #13480
+#13484 := [quant-intro #13481]: #13483
+#13487 := [monotonicity #13484]: #13486
+#14138 := [monotonicity #13487 #14135]: #14137
+#14141 := [monotonicity #13484 #14138]: #14140
+#13453 := (iff #13199 #13452)
+#13450 := (iff #3114 #13449)
+#13451 := [rewrite]: #13450
+#13454 := [monotonicity #13451]: #13453
+#14144 := [monotonicity #13454 #14141]: #14143
+#14147 := [monotonicity #13451 #14144]: #14146
+#13447 := (iff #13211 false)
+#12236 := (iff #3149 false)
+#12237 := [rewrite]: #12236
+#13445 := (iff #13211 #3149)
+#13443 := (iff #12189 true)
+#12548 := (and true true)
+#13438 := (and true #12548)
+#13441 := (iff #13438 true)
+#13442 := [rewrite]: #13441
+#13439 := (iff #12189 #13438)
+#13436 := (iff #12186 #12548)
+#13434 := (iff #3110 true)
+#13435 := [rewrite]: #13434
+#13432 := (iff #3109 true)
+#13433 := [rewrite]: #13432
+#13437 := [monotonicity #13433 #13435]: #13436
+#13440 := [monotonicity #13433 #13437]: #13439
+#13444 := [trans #13440 #13442]: #13443
+#13446 := [monotonicity #13444]: #13445
+#13448 := [trans #13446 #12237]: #13447
+#14150 := [monotonicity #13448 #14147]: #14149
+#14153 := [monotonicity #14150]: #14152
+#14156 := [monotonicity #14153]: #14155
+#14159 := [monotonicity #14156]: #14158
+#14162 := [monotonicity #14159]: #14161
+#14165 := [monotonicity #14162]: #14164
+#14170 := [trans #14165 #14168]: #14169
 #14173 := [monotonicity #14170]: #14172
-#14176 := [monotonicity #14173]: #14175
-#14179 := [monotonicity #14176]: #14178
-#14182 := [monotonicity #14179]: #14181
-#14185 := [monotonicity #14182]: #14184
-#14190 := [trans #14185 #14188]: #14189
-#14193 := [monotonicity #14190]: #14192
-#14198 := [trans #14193 #14196]: #14197
-#14201 := [monotonicity #14198]: #14200
-#14204 := [monotonicity #14201]: #14203
-#14209 := [trans #14204 #14207]: #14208
-#14212 := [monotonicity #14209]: #14211
-#14215 := [monotonicity #14212]: #14214
-#13450 := (iff #13312 #13449)
-#13447 := (iff #3094 #13446)
-#13444 := (iff #3093 #13441)
-#13445 := [rewrite]: #13444
-#13438 := (iff #3092 #13439)
-#13440 := [rewrite]: #13438
-#13448 := [monotonicity #13440 #13445]: #13447
-#13451 := [monotonicity #13448]: #13450
-#14296 := [monotonicity #13451 #14215]: #14295
-#14299 := [monotonicity #14296]: #14298
-#14302 := [monotonicity #14299]: #14301
-#14305 := [monotonicity #14302]: #14304
-#14308 := [monotonicity #14305]: #14307
-#14226 := (iff #13357 #14225)
-#14223 := (iff #3075 #14222)
-#14220 := (iff #3074 #14216)
-#14221 := [rewrite]: #14220
-#14224 := [quant-intro #14221]: #14223
-#14227 := [monotonicity #14224]: #14226
-#14311 := [monotonicity #14227 #14308]: #14310
-#14314 := [monotonicity #14311]: #14313
-#14317 := [monotonicity #14314]: #14316
-#14232 := (iff #13384 #14231)
-#14229 := (iff #12136 #14228)
-#14230 := [rewrite]: #14229
-#14233 := [monotonicity #14230]: #14232
-#14320 := [monotonicity #14233 #14317]: #14319
-#14239 := (iff #13393 #13508)
-#14234 := (not #13509)
-#14237 := (iff #14234 #13508)
-#14238 := [rewrite]: #14237
-#14235 := (iff #13393 #14234)
-#14236 := [monotonicity #13511]: #14235
-#14240 := [trans #14236 #14238]: #14239
-#14323 := [monotonicity #14240 #14320]: #14322
-#14250 := (iff #13402 #14241)
-#14242 := (not #14241)
-#14245 := (not #14242)
-#14248 := (iff #14245 #14241)
-#14249 := [rewrite]: #14248
-#14246 := (iff #13402 #14245)
-#14243 := (iff #3037 #14242)
-#14244 := [rewrite]: #14243
-#14247 := [monotonicity #14244]: #14246
-#14251 := [trans #14247 #14249]: #14250
-#14326 := [monotonicity #14251 #14323]: #14325
-#14264 := (iff #13411 #14263)
-#14261 := (iff #3035 #14260)
-#14258 := (iff #3034 #14255)
-#14259 := [rewrite]: #14258
-#14252 := (iff #3033 #14253)
-#14254 := [rewrite]: #14252
-#14262 := [monotonicity #14254 #14259]: #14261
-#14265 := [monotonicity #14262]: #14264
-#14329 := [monotonicity #14265 #14326]: #14328
-#14278 := (iff #13420 #14277)
-#14275 := (iff #3031 #14274)
-#14272 := (iff #3030 #14269)
-#14273 := [rewrite]: #14272
-#14266 := (iff #3029 #14267)
-#14268 := [rewrite]: #14266
-#14276 := [monotonicity #14268 #14273]: #14275
+#14178 := [trans #14173 #14176]: #14177
+#14181 := [monotonicity #14178]: #14180
+#14184 := [monotonicity #14181]: #14183
+#14189 := [trans #14184 #14187]: #14188
+#14192 := [monotonicity #14189]: #14191
+#14195 := [monotonicity #14192]: #14194
+#13430 := (iff #13292 #13429)
+#13427 := (iff #3087 #13426)
+#13424 := (iff #3086 #13421)
+#13425 := [rewrite]: #13424
+#13418 := (iff #3085 #13419)
+#13420 := [rewrite]: #13418
+#13428 := [monotonicity #13420 #13425]: #13427
+#13431 := [monotonicity #13428]: #13430
+#14276 := [monotonicity #13431 #14195]: #14275
 #14279 := [monotonicity #14276]: #14278
-#14332 := [monotonicity #14279 #14329]: #14331
-#14292 := (iff #13429 #14291)
-#14289 := (iff #3027 #14288)
-#14286 := (iff #3026 #14283)
-#14287 := [rewrite]: #14286
-#14280 := (iff #3025 #14281)
-#14282 := [rewrite]: #14280
-#14290 := [monotonicity #14282 #14287]: #14289
-#14293 := [monotonicity #14290]: #14292
-#14335 := [monotonicity #14293 #14332]: #14334
-#14340 := [trans #14335 #14338]: #14339
-#14343 := [monotonicity #14340]: #14342
-#13436 := (iff #3406 #13435)
-#13433 := (iff #3405 #13430)
-#13426 := (implies #3027 #13421)
-#13431 := (iff #13426 #13430)
-#13432 := [rewrite]: #13431
-#13427 := (iff #3405 #13426)
-#13424 := (iff #3404 #13421)
-#13417 := (implies #3031 #13412)
-#13422 := (iff #13417 #13421)
-#13423 := [rewrite]: #13422
-#13418 := (iff #3404 #13417)
-#13415 := (iff #3403 #13412)
-#13408 := (implies #3035 #13403)
-#13413 := (iff #13408 #13412)
-#13414 := [rewrite]: #13413
-#13409 := (iff #3403 #13408)
-#13406 := (iff #3402 #13403)
-#13399 := (implies #3037 #13394)
-#13404 := (iff #13399 #13403)
-#13405 := [rewrite]: #13404
-#13400 := (iff #3402 #13399)
-#13397 := (iff #3401 #13394)
-#13390 := (implies #3038 #13385)
-#13395 := (iff #13390 #13394)
-#13396 := [rewrite]: #13395
-#13391 := (iff #3401 #13390)
-#13388 := (iff #3400 #13385)
-#13381 := (implies #12136 #13376)
-#13386 := (iff #13381 #13385)
-#13387 := [rewrite]: #13386
-#13382 := (iff #3400 #13381)
-#13379 := (iff #3399 #13376)
-#13372 := (implies #12139 #13367)
-#13377 := (iff #13372 #13376)
-#13378 := [rewrite]: #13377
-#13373 := (iff #3399 #13372)
-#13370 := (iff #3398 #13367)
-#13363 := (implies #12148 #13358)
-#13368 := (iff #13363 #13367)
-#13369 := [rewrite]: #13368
-#13364 := (iff #3398 #13363)
-#13361 := (iff #3397 #13358)
-#13354 := (implies #3075 #13349)
-#13359 := (iff #13354 #13358)
-#13360 := [rewrite]: #13359
-#13355 := (iff #3397 #13354)
-#13352 := (iff #3396 #13349)
-#13345 := (implies #12157 #13340)
-#13350 := (iff #13345 #13349)
-#13351 := [rewrite]: #13350
-#13346 := (iff #3396 #13345)
-#13343 := (iff #3395 #13340)
-#13336 := (implies #12160 #13331)
-#13341 := (iff #13336 #13340)
-#13342 := [rewrite]: #13341
-#13337 := (iff #3395 #13336)
-#13334 := (iff #3394 #13331)
-#13327 := (implies #3086 #13322)
-#13332 := (iff #13327 #13331)
-#13333 := [rewrite]: #13332
-#13328 := (iff #3394 #13327)
-#13325 := (iff #3393 #13322)
-#13318 := (implies #12174 #13313)
-#13323 := (iff #13318 #13322)
-#13324 := [rewrite]: #13323
-#13319 := (iff #3393 #13318)
-#13316 := (iff #3392 #13313)
-#13309 := (implies #3094 #13306)
-#13314 := (iff #13309 #13313)
-#13315 := [rewrite]: #13314
-#13310 := (iff #3392 #13309)
-#13307 := (iff #3391 #13306)
-#13304 := (iff #3390 #13301)
-#13297 := (implies #12177 #13294)
-#13302 := (iff #13297 #13301)
-#13303 := [rewrite]: #13302
-#13298 := (iff #3390 #13297)
-#13295 := (iff #3389 #13294)
-#13292 := (iff #3388 #13289)
-#13285 := (implies #12186 #13282)
-#13290 := (iff #13285 #13289)
-#13291 := [rewrite]: #13290
-#13286 := (iff #3388 #13285)
-#13283 := (iff #3387 #13282)
-#13280 := (iff #3386 #13277)
-#13273 := (implies #12192 #13268)
-#13278 := (iff #13273 #13277)
-#13279 := [rewrite]: #13278
-#13274 := (iff #3386 #13273)
-#13271 := (iff #3385 #13268)
-#13264 := (implies #3109 #13259)
-#13269 := (iff #13264 #13268)
-#13270 := [rewrite]: #13269
-#13265 := (iff #3385 #13264)
-#13262 := (iff #3384 #13259)
-#13255 := (implies #12195 #13250)
-#13260 := (iff #13255 #13259)
-#13261 := [rewrite]: #13260
-#13256 := (iff #3384 #13255)
-#13253 := (iff #3383 #13250)
-#13246 := (implies #12198 #13241)
-#13251 := (iff #13246 #13250)
-#13252 := [rewrite]: #13251
-#13247 := (iff #3383 #13246)
-#13244 := (iff #3382 #13241)
-#13237 := (implies #12201 #13232)
-#13242 := (iff #13237 #13241)
-#13243 := [rewrite]: #13242
-#13238 := (iff #3382 #13237)
-#13235 := (iff #3381 #13232)
-#13228 := (implies #12209 #13225)
-#13233 := (iff #13228 #13232)
-#13234 := [rewrite]: #13233
-#13229 := (iff #3381 #13228)
-#13226 := (iff #3380 #13225)
-#13223 := (iff #3379 #13220)
-#13216 := (implies #3121 #13213)
-#13221 := (iff #13216 #13220)
-#13222 := [rewrite]: #13221
-#13217 := (iff #3379 #13216)
-#13214 := (iff #3378 #13213)
-#13211 := (iff #3377 #13208)
-#13204 := (implies #12224 #13201)
-#13209 := (iff #13204 #13208)
-#13210 := [rewrite]: #13209
-#13205 := (iff #3377 #13204)
-#13202 := (iff #3376 #13201)
-#13199 := (iff #3375 #13196)
-#13192 := (implies #12229 #13187)
-#13197 := (iff #13192 #13196)
-#13198 := [rewrite]: #13197
-#13193 := (iff #3375 #13192)
-#13190 := (iff #3374 #13187)
-#13183 := (implies #3134 #13178)
-#13188 := (iff #13183 #13187)
-#13189 := [rewrite]: #13188
-#13184 := (iff #3374 #13183)
-#13181 := (iff #3373 #13178)
-#13174 := (implies #3138 #13169)
-#13179 := (iff #13174 #13178)
-#13180 := [rewrite]: #13179
-#13175 := (iff #3373 #13174)
-#13172 := (iff #3372 #13169)
-#13165 := (implies #3142 #13160)
-#13170 := (iff #13165 #13169)
-#13171 := [rewrite]: #13170
-#13166 := (iff #3372 #13165)
-#13163 := (iff #3371 #13160)
-#13157 := (implies #12232 #13152)
-#13161 := (iff #13157 #13160)
-#13162 := [rewrite]: #13161
-#13158 := (iff #3371 #13157)
-#13155 := (iff #3370 #13152)
-#13148 := (implies #3145 #13143)
-#13153 := (iff #13148 #13152)
-#13154 := [rewrite]: #13153
-#13149 := (iff #3370 #13148)
-#13146 := (iff #3369 #13143)
-#13139 := (implies #12247 #13134)
-#13144 := (iff #13139 #13143)
-#13145 := [rewrite]: #13144
-#13140 := (iff #3369 #13139)
-#13137 := (iff #3368 #13134)
-#13130 := (implies #12253 #13125)
-#13135 := (iff #13130 #13134)
-#13136 := [rewrite]: #13135
-#13131 := (iff #3368 #13130)
-#13128 := (iff #3367 #13125)
-#13122 := (implies #12232 #13110)
-#13126 := (iff #13122 #13125)
-#13127 := [rewrite]: #13126
-#13123 := (iff #3367 #13122)
-#13120 := (iff #3366 #13110)
-#13115 := (and true #13110)
-#13118 := (iff #13115 #13110)
-#13119 := [rewrite]: #13118
-#13116 := (iff #3366 #13115)
-#13113 := (iff #3365 #13110)
-#13107 := (implies #12232 #13102)
-#13111 := (iff #13107 #13110)
-#13112 := [rewrite]: #13111
-#13108 := (iff #3365 #13107)
-#13105 := (iff #3364 #13102)
-#13099 := (implies #12232 #13094)
-#13103 := (iff #13099 #13102)
-#13104 := [rewrite]: #13103
-#13100 := (iff #3364 #13099)
-#13097 := (iff #3363 #13094)
-#13091 := (implies #12232 #13086)
-#13095 := (iff #13091 #13094)
-#13096 := [rewrite]: #13095
-#13092 := (iff #3363 #13091)
-#13089 := (iff #3362 #13086)
-#13083 := (implies #12521 #13078)
-#13087 := (iff #13083 #13086)
-#13088 := [rewrite]: #13087
-#13084 := (iff #3362 #13083)
-#13081 := (iff #3361 #13078)
-#13074 := (implies #12521 #13069)
-#13079 := (iff #13074 #13078)
-#13080 := [rewrite]: #13079
-#13075 := (iff #3361 #13074)
-#13072 := (iff #3360 #13069)
-#13066 := (implies #12264 #13061)
-#13070 := (iff #13066 #13069)
-#13071 := [rewrite]: #13070
-#13067 := (iff #3360 #13066)
-#13064 := (iff #3359 #13061)
-#13057 := (implies #12543 #13052)
-#13062 := (iff #13057 #13061)
-#13063 := [rewrite]: #13062
-#13058 := (iff #3359 #13057)
-#13055 := (iff #3358 #13052)
-#13048 := (implies #12546 #13043)
-#13053 := (iff #13048 #13052)
-#13054 := [rewrite]: #13053
-#13049 := (iff #3358 #13048)
-#13046 := (iff #3357 #13043)
-#13039 := (implies #12549 #13034)
-#13044 := (iff #13039 #13043)
-#13045 := [rewrite]: #13044
-#13040 := (iff #3357 #13039)
-#13037 := (iff #3356 #13034)
-#13030 := (implies #12552 #13025)
-#13035 := (iff #13030 #13034)
-#13036 := [rewrite]: #13035
-#13031 := (iff #3356 #13030)
-#13028 := (iff #3355 #13025)
-#13021 := (implies #12561 #13009)
-#13026 := (iff #13021 #13025)
-#13027 := [rewrite]: #13026
-#13022 := (iff #3355 #13021)
-#13019 := (iff #3354 #13009)
-#13014 := (implies true #13009)
-#13017 := (iff #13014 #13009)
-#13018 := [rewrite]: #13017
-#13015 := (iff #3354 #13014)
-#13012 := (iff #3353 #13009)
-#13006 := (implies #12232 #13003)
-#13010 := (iff #13006 #13009)
-#13011 := [rewrite]: #13010
-#13007 := (iff #3353 #13006)
-#13004 := (iff #3352 #13003)
-#13001 := (iff #3351 #12998)
-#12995 := (implies #12232 #12990)
-#12999 := (iff #12995 #12998)
-#13000 := [rewrite]: #12999
-#12996 := (iff #3351 #12995)
-#12993 := (iff #3350 #12990)
-#12986 := (implies #3347 #12981)
-#12991 := (iff #12986 #12990)
-#12992 := [rewrite]: #12991
-#12987 := (iff #3350 #12986)
-#12984 := (iff #3349 #12981)
-#12978 := (implies #12232 #12973)
-#12982 := (iff #12978 #12981)
-#12983 := [rewrite]: #12982
-#12979 := (iff #3349 #12978)
-#12976 := (iff #3348 #12973)
-#12970 := (implies #12232 #12394)
-#12974 := (iff #12970 #12973)
-#12975 := [rewrite]: #12974
-#12971 := (iff #3348 #12970)
-#12397 := (iff #3191 #12394)
-#12391 := (implies #12232 #12386)
-#12395 := (iff #12391 #12394)
-#12396 := [rewrite]: #12395
-#12392 := (iff #3191 #12391)
-#12389 := (iff #3190 #12386)
-#12383 := (implies #12232 #12380)
-#12387 := (iff #12383 #12386)
-#12388 := [rewrite]: #12387
-#12384 := (iff #3190 #12383)
-#12381 := (iff #3189 #12380)
-#12378 := (iff #3188 #12375)
-#12371 := (implies #10960 #12366)
-#12376 := (iff #12371 #12375)
-#12377 := [rewrite]: #12376
-#12372 := (iff #3188 #12371)
-#12369 := (iff #3187 #12366)
-#12363 := (implies #12232 #12358)
+#14282 := [monotonicity #14279]: #14281
+#14285 := [monotonicity #14282]: #14284
+#14288 := [monotonicity #14285]: #14287
+#14206 := (iff #13337 #14205)
+#14203 := (iff #3068 #14202)
+#14200 := (iff #3067 #14196)
+#14201 := [rewrite]: #14200
+#14204 := [quant-intro #14201]: #14203
+#14207 := [monotonicity #14204]: #14206
+#14291 := [monotonicity #14207 #14288]: #14290
+#14294 := [monotonicity #14291]: #14293
+#14297 := [monotonicity #14294]: #14296
+#14212 := (iff #13364 #14211)
+#14209 := (iff #12116 #14208)
+#14210 := [rewrite]: #14209
+#14213 := [monotonicity #14210]: #14212
+#14300 := [monotonicity #14213 #14297]: #14299
+#14219 := (iff #13373 #13488)
+#14214 := (not #13489)
+#14217 := (iff #14214 #13488)
+#14218 := [rewrite]: #14217
+#14215 := (iff #13373 #14214)
+#14216 := [monotonicity #13491]: #14215
+#14220 := [trans #14216 #14218]: #14219
+#14303 := [monotonicity #14220 #14300]: #14302
+#14230 := (iff #13382 #14221)
+#14222 := (not #14221)
+#14225 := (not #14222)
+#14228 := (iff #14225 #14221)
+#14229 := [rewrite]: #14228
+#14226 := (iff #13382 #14225)
+#14223 := (iff #3030 #14222)
+#14224 := [rewrite]: #14223
+#14227 := [monotonicity #14224]: #14226
+#14231 := [trans #14227 #14229]: #14230
+#14306 := [monotonicity #14231 #14303]: #14305
+#14244 := (iff #13391 #14243)
+#14241 := (iff #3028 #14240)
+#14238 := (iff #3027 #14235)
+#14239 := [rewrite]: #14238
+#14232 := (iff #3026 #14233)
+#14234 := [rewrite]: #14232
+#14242 := [monotonicity #14234 #14239]: #14241
+#14245 := [monotonicity #14242]: #14244
+#14309 := [monotonicity #14245 #14306]: #14308
+#14258 := (iff #13400 #14257)
+#14255 := (iff #3024 #14254)
+#14252 := (iff #3023 #14249)
+#14253 := [rewrite]: #14252
+#14246 := (iff #3022 #14247)
+#14248 := [rewrite]: #14246
+#14256 := [monotonicity #14248 #14253]: #14255
+#14259 := [monotonicity #14256]: #14258
+#14312 := [monotonicity #14259 #14309]: #14311
+#14272 := (iff #13409 #14271)
+#14269 := (iff #3020 #14268)
+#14266 := (iff #3019 #14263)
+#14267 := [rewrite]: #14266
+#14260 := (iff #3018 #14261)
+#14262 := [rewrite]: #14260
+#14270 := [monotonicity #14262 #14267]: #14269
+#14273 := [monotonicity #14270]: #14272
+#14315 := [monotonicity #14273 #14312]: #14314
+#14320 := [trans #14315 #14318]: #14319
+#14323 := [monotonicity #14320]: #14322
+#13416 := (iff #3399 #13415)
+#13413 := (iff #3398 #13410)
+#13406 := (implies #3020 #13401)
+#13411 := (iff #13406 #13410)
+#13412 := [rewrite]: #13411
+#13407 := (iff #3398 #13406)
+#13404 := (iff #3397 #13401)
+#13397 := (implies #3024 #13392)
+#13402 := (iff #13397 #13401)
+#13403 := [rewrite]: #13402
+#13398 := (iff #3397 #13397)
+#13395 := (iff #3396 #13392)
+#13388 := (implies #3028 #13383)
+#13393 := (iff #13388 #13392)
+#13394 := [rewrite]: #13393
+#13389 := (iff #3396 #13388)
+#13386 := (iff #3395 #13383)
+#13379 := (implies #3030 #13374)
+#13384 := (iff #13379 #13383)
+#13385 := [rewrite]: #13384
+#13380 := (iff #3395 #13379)
+#13377 := (iff #3394 #13374)
+#13370 := (implies #3031 #13365)
+#13375 := (iff #13370 #13374)
+#13376 := [rewrite]: #13375
+#13371 := (iff #3394 #13370)
+#13368 := (iff #3393 #13365)
+#13361 := (implies #12116 #13356)
+#13366 := (iff #13361 #13365)
+#13367 := [rewrite]: #13366
+#13362 := (iff #3393 #13361)
+#13359 := (iff #3392 #13356)
+#13352 := (implies #12119 #13347)
+#13357 := (iff #13352 #13356)
+#13358 := [rewrite]: #13357
+#13353 := (iff #3392 #13352)
+#13350 := (iff #3391 #13347)
+#13343 := (implies #12128 #13338)
+#13348 := (iff #13343 #13347)
+#13349 := [rewrite]: #13348
+#13344 := (iff #3391 #13343)
+#13341 := (iff #3390 #13338)
+#13334 := (implies #3068 #13329)
+#13339 := (iff #13334 #13338)
+#13340 := [rewrite]: #13339
+#13335 := (iff #3390 #13334)
+#13332 := (iff #3389 #13329)
+#13325 := (implies #12137 #13320)
+#13330 := (iff #13325 #13329)
+#13331 := [rewrite]: #13330
+#13326 := (iff #3389 #13325)
+#13323 := (iff #3388 #13320)
+#13316 := (implies #12140 #13311)
+#13321 := (iff #13316 #13320)
+#13322 := [rewrite]: #13321
+#13317 := (iff #3388 #13316)
+#13314 := (iff #3387 #13311)
+#13307 := (implies #3079 #13302)
+#13312 := (iff #13307 #13311)
+#13313 := [rewrite]: #13312
+#13308 := (iff #3387 #13307)
+#13305 := (iff #3386 #13302)
+#13298 := (implies #12154 #13293)
+#13303 := (iff #13298 #13302)
+#13304 := [rewrite]: #13303
+#13299 := (iff #3386 #13298)
+#13296 := (iff #3385 #13293)
+#13289 := (implies #3087 #13286)
+#13294 := (iff #13289 #13293)
+#13295 := [rewrite]: #13294
+#13290 := (iff #3385 #13289)
+#13287 := (iff #3384 #13286)
+#13284 := (iff #3383 #13281)
+#13277 := (implies #12157 #13274)
+#13282 := (iff #13277 #13281)
+#13283 := [rewrite]: #13282
+#13278 := (iff #3383 #13277)
+#13275 := (iff #3382 #13274)
+#13272 := (iff #3381 #13269)
+#13265 := (implies #12166 #13262)
+#13270 := (iff #13265 #13269)
+#13271 := [rewrite]: #13270
+#13266 := (iff #3381 #13265)
+#13263 := (iff #3380 #13262)
+#13260 := (iff #3379 #13257)
+#13253 := (implies #12172 #13248)
+#13258 := (iff #13253 #13257)
+#13259 := [rewrite]: #13258
+#13254 := (iff #3379 #13253)
+#13251 := (iff #3378 #13248)
+#13244 := (implies #3102 #13239)
+#13249 := (iff #13244 #13248)
+#13250 := [rewrite]: #13249
+#13245 := (iff #3378 #13244)
+#13242 := (iff #3377 #13239)
+#13235 := (implies #12175 #13230)
+#13240 := (iff #13235 #13239)
+#13241 := [rewrite]: #13240
+#13236 := (iff #3377 #13235)
+#13233 := (iff #3376 #13230)
+#13226 := (implies #12178 #13221)
+#13231 := (iff #13226 #13230)
+#13232 := [rewrite]: #13231
+#13227 := (iff #3376 #13226)
+#13224 := (iff #3375 #13221)
+#13217 := (implies #12181 #13212)
+#13222 := (iff #13217 #13221)
+#13223 := [rewrite]: #13222
+#13218 := (iff #3375 #13217)
+#13215 := (iff #3374 #13212)
+#13208 := (implies #12189 #13205)
+#13213 := (iff #13208 #13212)
+#13214 := [rewrite]: #13213
+#13209 := (iff #3374 #13208)
+#13206 := (iff #3373 #13205)
+#13203 := (iff #3372 #13200)
+#13196 := (implies #3114 #13193)
+#13201 := (iff #13196 #13200)
+#13202 := [rewrite]: #13201
+#13197 := (iff #3372 #13196)
+#13194 := (iff #3371 #13193)
+#13191 := (iff #3370 #13188)
+#13184 := (implies #12204 #13181)
+#13189 := (iff #13184 #13188)
+#13190 := [rewrite]: #13189
+#13185 := (iff #3370 #13184)
+#13182 := (iff #3369 #13181)
+#13179 := (iff #3368 #13176)
+#13172 := (implies #12209 #13167)
+#13177 := (iff #13172 #13176)
+#13178 := [rewrite]: #13177
+#13173 := (iff #3368 #13172)
+#13170 := (iff #3367 #13167)
+#13163 := (implies #3127 #13158)
+#13168 := (iff #13163 #13167)
+#13169 := [rewrite]: #13168
+#13164 := (iff #3367 #13163)
+#13161 := (iff #3366 #13158)
+#13154 := (implies #3131 #13149)
+#13159 := (iff #13154 #13158)
+#13160 := [rewrite]: #13159
+#13155 := (iff #3366 #13154)
+#13152 := (iff #3365 #13149)
+#13145 := (implies #3135 #13140)
+#13150 := (iff #13145 #13149)
+#13151 := [rewrite]: #13150
+#13146 := (iff #3365 #13145)
+#13143 := (iff #3364 #13140)
+#13137 := (implies #12212 #13132)
+#13141 := (iff #13137 #13140)
+#13142 := [rewrite]: #13141
+#13138 := (iff #3364 #13137)
+#13135 := (iff #3363 #13132)
+#13128 := (implies #3138 #13123)
+#13133 := (iff #13128 #13132)
+#13134 := [rewrite]: #13133
+#13129 := (iff #3363 #13128)
+#13126 := (iff #3362 #13123)
+#13119 := (implies #12227 #13114)
+#13124 := (iff #13119 #13123)
+#13125 := [rewrite]: #13124
+#13120 := (iff #3362 #13119)
+#13117 := (iff #3361 #13114)
+#13110 := (implies #12233 #13105)
+#13115 := (iff #13110 #13114)
+#13116 := [rewrite]: #13115
+#13111 := (iff #3361 #13110)
+#13108 := (iff #3360 #13105)
+#13102 := (implies #12212 #13090)
+#13106 := (iff #13102 #13105)
+#13107 := [rewrite]: #13106
+#13103 := (iff #3360 #13102)
+#13100 := (iff #3359 #13090)
+#13095 := (and true #13090)
+#13098 := (iff #13095 #13090)
+#13099 := [rewrite]: #13098
+#13096 := (iff #3359 #13095)
+#13093 := (iff #3358 #13090)
+#13087 := (implies #12212 #13082)
+#13091 := (iff #13087 #13090)
+#13092 := [rewrite]: #13091
+#13088 := (iff #3358 #13087)
+#13085 := (iff #3357 #13082)
+#13079 := (implies #12212 #13074)
+#13083 := (iff #13079 #13082)
+#13084 := [rewrite]: #13083
+#13080 := (iff #3357 #13079)
+#13077 := (iff #3356 #13074)
+#13071 := (implies #12212 #13066)
+#13075 := (iff #13071 #13074)
+#13076 := [rewrite]: #13075
+#13072 := (iff #3356 #13071)
+#13069 := (iff #3355 #13066)
+#13063 := (implies #12501 #13058)
+#13067 := (iff #13063 #13066)
+#13068 := [rewrite]: #13067
+#13064 := (iff #3355 #13063)
+#13061 := (iff #3354 #13058)
+#13054 := (implies #12501 #13049)
+#13059 := (iff #13054 #13058)
+#13060 := [rewrite]: #13059
+#13055 := (iff #3354 #13054)
+#13052 := (iff #3353 #13049)
+#13046 := (implies #12244 #13041)
+#13050 := (iff #13046 #13049)
+#13051 := [rewrite]: #13050
+#13047 := (iff #3353 #13046)
+#13044 := (iff #3352 #13041)
+#13037 := (implies #12523 #13032)
+#13042 := (iff #13037 #13041)
+#13043 := [rewrite]: #13042
+#13038 := (iff #3352 #13037)
+#13035 := (iff #3351 #13032)
+#13028 := (implies #12526 #13023)
+#13033 := (iff #13028 #13032)
+#13034 := [rewrite]: #13033
+#13029 := (iff #3351 #13028)
+#13026 := (iff #3350 #13023)
+#13019 := (implies #12529 #13014)
+#13024 := (iff #13019 #13023)
+#13025 := [rewrite]: #13024
+#13020 := (iff #3350 #13019)
+#13017 := (iff #3349 #13014)
+#13010 := (implies #12532 #13005)
+#13015 := (iff #13010 #13014)
+#13016 := [rewrite]: #13015
+#13011 := (iff #3349 #13010)
+#13008 := (iff #3348 #13005)
+#13001 := (implies #12541 #12989)
+#13006 := (iff #13001 #13005)
+#13007 := [rewrite]: #13006
+#13002 := (iff #3348 #13001)
+#12999 := (iff #3347 #12989)
+#12994 := (implies true #12989)
+#12997 := (iff #12994 #12989)
+#12998 := [rewrite]: #12997
+#12995 := (iff #3347 #12994)
+#12992 := (iff #3346 #12989)
+#12986 := (implies #12212 #12983)
+#12990 := (iff #12986 #12989)
+#12991 := [rewrite]: #12990
+#12987 := (iff #3346 #12986)
+#12984 := (iff #3345 #12983)
+#12981 := (iff #3344 #12978)
+#12975 := (implies #12212 #12970)
+#12979 := (iff #12975 #12978)
+#12980 := [rewrite]: #12979
+#12976 := (iff #3344 #12975)
+#12973 := (iff #3343 #12970)
+#12966 := (implies #3340 #12961)
+#12971 := (iff #12966 #12970)
+#12972 := [rewrite]: #12971
+#12967 := (iff #3343 #12966)
+#12964 := (iff #3342 #12961)
+#12958 := (implies #12212 #12953)
+#12962 := (iff #12958 #12961)
+#12963 := [rewrite]: #12962
+#12959 := (iff #3342 #12958)
+#12956 := (iff #3341 #12953)
+#12950 := (implies #12212 #12374)
+#12954 := (iff #12950 #12953)
+#12955 := [rewrite]: #12954
+#12951 := (iff #3341 #12950)
+#12377 := (iff #3184 #12374)
+#12371 := (implies #12212 #12366)
+#12375 := (iff #12371 #12374)
+#12376 := [rewrite]: #12375
+#12372 := (iff #3184 #12371)
+#12369 := (iff #3183 #12366)
+#12363 := (implies #12212 #12360)
 #12367 := (iff #12363 #12366)
 #12368 := [rewrite]: #12367
-#12364 := (iff #3187 #12363)
-#12361 := (iff #3186 #12358)
-#12355 := (implies #12232 #12350)
-#12359 := (iff #12355 #12358)
-#12360 := [rewrite]: #12359
-#12356 := (iff #3186 #12355)
-#12353 := (iff #3185 #12350)
-#12346 := (implies #12232 #12341)
-#12351 := (iff #12346 #12350)
-#12352 := [rewrite]: #12351
-#12347 := (iff #3185 #12346)
-#12344 := (iff #3184 #12341)
-#12337 := (implies #12269 #12332)
-#12342 := (iff #12337 #12341)
-#12343 := [rewrite]: #12342
-#12338 := (iff #3184 #12337)
-#12335 := (iff #3183 #12332)
-#12328 := (implies #12272 #12323)
-#12333 := (iff #12328 #12332)
-#12334 := [rewrite]: #12333
-#12329 := (iff #3183 #12328)
-#12326 := (iff #3182 #12323)
-#12319 := (implies #12275 #12314)
-#12324 := (iff #12319 #12323)
-#12325 := [rewrite]: #12324
-#12320 := (iff #3182 #12319)
-#12317 := (iff #3181 #12314)
-#12310 := (implies #12278 #12307)
-#12315 := (iff #12310 #12314)
-#12316 := [rewrite]: #12315
-#12311 := (iff #3181 #12310)
-#12308 := (iff #3180 #12307)
-#12305 := (iff #3179 #12302)
-#12298 := (implies #12293 #3177)
-#12303 := (iff #12298 #12302)
-#12304 := [rewrite]: #12303
-#12299 := (iff #3179 #12298)
-#12296 := (iff #3178 #3177)
-#12297 := [rewrite]: #12296
-#12294 := (iff #3172 #12293)
-#12291 := (iff #3171 #12288)
-#12285 := (implies #455 #12282)
-#12289 := (iff #12285 #12288)
-#12290 := [rewrite]: #12289
-#12286 := (iff #3171 #12285)
-#12283 := (iff #3170 #12282)
+#12364 := (iff #3183 #12363)
+#12361 := (iff #3182 #12360)
+#12358 := (iff #3181 #12355)
+#12351 := (implies #10907 #12346)
+#12356 := (iff #12351 #12355)
+#12357 := [rewrite]: #12356
+#12352 := (iff #3181 #12351)
+#12349 := (iff #3180 #12346)
+#12343 := (implies #12212 #12338)
+#12347 := (iff #12343 #12346)
+#12348 := [rewrite]: #12347
+#12344 := (iff #3180 #12343)
+#12341 := (iff #3179 #12338)
+#12335 := (implies #12212 #12330)
+#12339 := (iff #12335 #12338)
+#12340 := [rewrite]: #12339
+#12336 := (iff #3179 #12335)
+#12333 := (iff #3178 #12330)
+#12326 := (implies #12212 #12321)
+#12331 := (iff #12326 #12330)
+#12332 := [rewrite]: #12331
+#12327 := (iff #3178 #12326)
+#12324 := (iff #3177 #12321)
+#12317 := (implies #12249 #12312)
+#12322 := (iff #12317 #12321)
+#12323 := [rewrite]: #12322
+#12318 := (iff #3177 #12317)
+#12315 := (iff #3176 #12312)
+#12308 := (implies #12252 #12303)
+#12313 := (iff #12308 #12312)
+#12314 := [rewrite]: #12313
+#12309 := (iff #3176 #12308)
+#12306 := (iff #3175 #12303)
+#12299 := (implies #12255 #12294)
+#12304 := (iff #12299 #12303)
+#12305 := [rewrite]: #12304
+#12300 := (iff #3175 #12299)
+#12297 := (iff #3174 #12294)
+#12290 := (implies #12258 #12287)
+#12295 := (iff #12290 #12294)
+#12296 := [rewrite]: #12295
+#12291 := (iff #3174 #12290)
+#12288 := (iff #3173 #12287)
+#12285 := (iff #3172 #12282)
+#12278 := (implies #12273 #3170)
+#12283 := (iff #12278 #12282)
 #12284 := [rewrite]: #12283
-#12287 := [monotonicity #12284]: #12286
-#12292 := [trans #12287 #12290]: #12291
-#12295 := [quant-intro #12292]: #12294
-#12300 := [monotonicity #12295 #12297]: #12299
-#12306 := [trans #12300 #12304]: #12305
-#12309 := [monotonicity #12295 #12306]: #12308
-#12279 := (iff #3167 #12278)
-#12280 := [rewrite]: #12279
-#12312 := [monotonicity #12280 #12309]: #12311
-#12318 := [trans #12312 #12316]: #12317
-#12276 := (iff #3165 #12275)
+#12279 := (iff #3172 #12278)
+#12276 := (iff #3171 #3170)
 #12277 := [rewrite]: #12276
-#12321 := [monotonicity #12277 #12318]: #12320
-#12327 := [trans #12321 #12325]: #12326
-#12273 := (iff #3163 #12272)
-#12274 := [rewrite]: #12273
-#12330 := [monotonicity #12274 #12327]: #12329
-#12336 := [trans #12330 #12334]: #12335
-#12270 := (iff #3161 #12269)
-#12271 := [rewrite]: #12270
-#12339 := [monotonicity #12271 #12336]: #12338
-#12345 := [trans #12339 #12343]: #12344
-#12233 := (iff #3144 #12232)
-#12234 := [rewrite]: #12233
-#12348 := [monotonicity #12234 #12345]: #12347
-#12354 := [trans #12348 #12352]: #12353
-#12357 := [monotonicity #12234 #12354]: #12356
-#12362 := [trans #12357 #12360]: #12361
-#12365 := [monotonicity #12234 #12362]: #12364
+#12274 := (iff #3165 #12273)
+#12271 := (iff #3164 #12268)
+#12265 := (implies #421 #12262)
+#12269 := (iff #12265 #12268)
+#12270 := [rewrite]: #12269
+#12266 := (iff #3164 #12265)
+#12263 := (iff #3163 #12262)
+#12264 := [rewrite]: #12263
+#12267 := [monotonicity #12264]: #12266
+#12272 := [trans #12267 #12270]: #12271
+#12275 := [quant-intro #12272]: #12274
+#12280 := [monotonicity #12275 #12277]: #12279
+#12286 := [trans #12280 #12284]: #12285
+#12289 := [monotonicity #12275 #12286]: #12288
+#12259 := (iff #3160 #12258)
+#12260 := [rewrite]: #12259
+#12292 := [monotonicity #12260 #12289]: #12291
+#12298 := [trans #12292 #12296]: #12297
+#12256 := (iff #3158 #12255)
+#12257 := [rewrite]: #12256
+#12301 := [monotonicity #12257 #12298]: #12300
+#12307 := [trans #12301 #12305]: #12306
+#12253 := (iff #3156 #12252)
+#12254 := [rewrite]: #12253
+#12310 := [monotonicity #12254 #12307]: #12309
+#12316 := [trans #12310 #12314]: #12315
+#12250 := (iff #3154 #12249)
+#12251 := [rewrite]: #12250
+#12319 := [monotonicity #12251 #12316]: #12318
+#12325 := [trans #12319 #12323]: #12324
+#12213 := (iff #3137 #12212)
+#12214 := [rewrite]: #12213
+#12328 := [monotonicity #12214 #12325]: #12327
+#12334 := [trans #12328 #12332]: #12333
+#12337 := [monotonicity #12214 #12334]: #12336
+#12342 := [trans #12337 #12340]: #12341
+#12345 := [monotonicity #12214 #12342]: #12344
+#12350 := [trans #12345 #12348]: #12349
+#10909 := (iff #2508 #10907)
+#10910 := [rewrite]: #10909
+#12353 := [monotonicity #10910 #12350]: #12352
+#12359 := [trans #12353 #12357]: #12358
+#12362 := [monotonicity #10910 #12359]: #12361
+#12365 := [monotonicity #12214 #12362]: #12364
 #12370 := [trans #12365 #12368]: #12369
-#10962 := (iff #2542 #10960)
-#10963 := [rewrite]: #10962
-#12373 := [monotonicity #10963 #12370]: #12372
-#12379 := [trans #12373 #12377]: #12378
-#12382 := [monotonicity #10963 #12379]: #12381
-#12385 := [monotonicity #12234 #12382]: #12384
-#12390 := [trans #12385 #12388]: #12389
-#12393 := [monotonicity #12234 #12390]: #12392
-#12398 := [trans #12393 #12396]: #12397
-#12972 := [monotonicity #12234 #12398]: #12971
-#12977 := [trans #12972 #12975]: #12976
-#12980 := [monotonicity #12234 #12977]: #12979
-#12985 := [trans #12980 #12983]: #12984
-#12988 := [monotonicity #12985]: #12987
-#12994 := [trans #12988 #12992]: #12993
-#12997 := [monotonicity #12234 #12994]: #12996
-#13002 := [trans #12997 #13000]: #13001
-#12968 := (iff #3346 #12965)
-#12962 := (implies #12232 #12957)
-#12966 := (iff #12962 #12965)
-#12967 := [rewrite]: #12966
-#12963 := (iff #3346 #12962)
-#12960 := (iff #3345 #12957)
-#12953 := (implies #3256 #12948)
-#12958 := (iff #12953 #12957)
-#12959 := [rewrite]: #12958
-#12954 := (iff #3345 #12953)
-#12951 := (iff #3344 #12948)
-#12945 := (implies #12232 #12940)
-#12949 := (iff #12945 #12948)
-#12950 := [rewrite]: #12949
-#12946 := (iff #3344 #12945)
-#12943 := (iff #3343 #12940)
-#12937 := (implies #12232 #12934)
-#12941 := (iff #12937 #12940)
-#12942 := [rewrite]: #12941
-#12938 := (iff #3343 #12937)
-#12935 := (iff #3342 #12934)
-#12932 := (iff #3341 #12929)
-#12926 := (implies #12581 #12923)
-#12930 := (iff #12926 #12929)
-#12931 := [rewrite]: #12930
-#12927 := (iff #3341 #12926)
-#12924 := (iff #3340 #12923)
-#12921 := (iff #3339 #12918)
-#12915 := (implies #12587 #12910)
-#12919 := (iff #12915 #12918)
-#12920 := [rewrite]: #12919
-#12916 := (iff #3339 #12915)
-#12913 := (iff #3338 #12910)
-#12907 := (implies #12232 #12904)
-#12911 := (iff #12907 #12910)
-#12912 := [rewrite]: #12911
-#12908 := (iff #3338 #12907)
-#12905 := (iff #3337 #12904)
-#12902 := (iff #3336 #12899)
-#12896 := (implies #12232 #12891)
-#12900 := (iff #12896 #12899)
-#12901 := [rewrite]: #12900
-#12897 := (iff #3336 #12896)
-#12894 := (iff #3335 #12891)
-#12887 := (implies #3327 #12882)
-#12892 := (iff #12887 #12891)
-#12893 := [rewrite]: #12892
-#12888 := (iff #3335 #12887)
-#12885 := (iff #3334 #12882)
-#12879 := (implies #12232 #12874)
-#12883 := (iff #12879 #12882)
-#12884 := [rewrite]: #12883
-#12880 := (iff #3334 #12879)
-#12877 := (iff #3333 #12874)
-#12871 := (implies #12232 #12866)
-#12875 := (iff #12871 #12874)
-#12876 := [rewrite]: #12875
-#12872 := (iff #3333 #12871)
-#12869 := (iff #3332 #12866)
-#12863 := (implies #12232 #12858)
-#12867 := (iff #12863 #12866)
-#12868 := [rewrite]: #12867
-#12864 := (iff #3332 #12863)
-#12861 := (iff #3331 #12858)
-#12854 := (implies #12839 #12849)
-#12859 := (iff #12854 #12858)
-#12860 := [rewrite]: #12859
-#12855 := (iff #3331 #12854)
-#12852 := (iff #3330 #12849)
-#12845 := (implies #12842 #12723)
-#12850 := (iff #12845 #12849)
-#12851 := [rewrite]: #12850
-#12846 := (iff #3330 #12845)
-#12726 := (iff #3312 #12723)
-#12719 := (implies #3280 #12716)
-#12724 := (iff #12719 #12723)
-#12725 := [rewrite]: #12724
-#12720 := (iff #3312 #12719)
-#12717 := (iff #3311 #12716)
-#12714 := (iff #3310 #12711)
-#12707 := (implies #12616 #12702)
-#12712 := (iff #12707 #12711)
-#12713 := [rewrite]: #12712
-#12708 := (iff #3310 #12707)
-#12705 := (iff #3309 #12702)
-#12698 := (implies #12619 #12693)
-#12703 := (iff #12698 #12702)
-#12704 := [rewrite]: #12703
-#12699 := (iff #3309 #12698)
-#12696 := (iff #3308 #12693)
-#12689 := (implies #12622 #12684)
-#12694 := (iff #12689 #12693)
-#12695 := [rewrite]: #12694
-#12690 := (iff #3308 #12689)
-#12687 := (iff #3307 #12684)
-#12680 := (implies #12625 #12677)
-#12685 := (iff #12680 #12684)
-#12686 := [rewrite]: #12685
-#12681 := (iff #3307 #12680)
-#12678 := (iff #3306 #12677)
-#12675 := (iff #3305 #12672)
-#12668 := (implies #3291 #12665)
-#12673 := (iff #12668 #12672)
-#12674 := [rewrite]: #12673
-#12669 := (iff #3305 #12668)
-#12666 := (iff #3304 #12665)
-#12663 := (iff #3303 #12660)
-#12656 := (implies #12640 #12646)
-#12661 := (iff #12656 #12660)
-#12662 := [rewrite]: #12661
-#12657 := (iff #3303 #12656)
-#12654 := (iff #3302 #12646)
-#12649 := (and #12646 true)
-#12652 := (iff #12649 #12646)
-#12653 := [rewrite]: #12652
-#12650 := (iff #3302 #12649)
-#12647 := (iff #3301 #12646)
-#12644 := (iff #3300 #12643)
-#12645 := [rewrite]: #12644
-#12648 := [monotonicity #12645]: #12647
-#12651 := [monotonicity #12648]: #12650
-#12655 := [trans #12651 #12653]: #12654
-#12641 := (iff #3296 #12640)
-#12638 := (iff #3295 #12635)
-#12632 := (implies #455 #12629)
-#12636 := (iff #12632 #12635)
-#12637 := [rewrite]: #12636
-#12633 := (iff #3295 #12632)
-#12630 := (iff #3294 #12629)
-#12631 := [rewrite]: #12630
-#12634 := [monotonicity #12631]: #12633
-#12639 := [trans #12634 #12637]: #12638
-#12642 := [quant-intro #12639]: #12641
-#12658 := [monotonicity #12642 #12655]: #12657
-#12664 := [trans #12658 #12662]: #12663
-#12667 := [monotonicity #12642 #12664]: #12666
-#12670 := [monotonicity #12667]: #12669
-#12676 := [trans #12670 #12674]: #12675
-#12679 := [monotonicity #12676]: #12678
-#12626 := (iff #3290 #12625)
-#12627 := [rewrite]: #12626
-#12682 := [monotonicity #12627 #12679]: #12681
-#12688 := [trans #12682 #12686]: #12687
-#12623 := (iff #3288 #12622)
-#12624 := [rewrite]: #12623
-#12691 := [monotonicity #12624 #12688]: #12690
-#12697 := [trans #12691 #12695]: #12696
-#12620 := (iff #3286 #12619)
-#12608 := (= #3281 #12607)
-#12609 := [rewrite]: #12608
-#12621 := [monotonicity #12609]: #12620
-#12700 := [monotonicity #12621 #12697]: #12699
-#12706 := [trans #12700 #12704]: #12705
-#12617 := (iff #3284 #12616)
-#12614 := (iff #3283 #12613)
-#12615 := [monotonicity #12609]: #12614
-#12611 := (iff #3282 #12610)
-#12612 := [monotonicity #12609]: #12611
-#12618 := [monotonicity #12612 #12615]: #12617
-#12709 := [monotonicity #12618 #12706]: #12708
-#12715 := [trans #12709 #12713]: #12714
-#12718 := [monotonicity #12618 #12715]: #12717
-#12721 := [monotonicity #12718]: #12720
-#12727 := [trans #12721 #12725]: #12726
-#12843 := (iff #3329 #12842)
-#12844 := [rewrite]: #12843
-#12847 := [monotonicity #12844 #12727]: #12846
-#12853 := [trans #12847 #12851]: #12852
-#12840 := (iff #3328 #12839)
-#12841 := [rewrite]: #12840
-#12856 := [monotonicity #12841 #12853]: #12855
-#12862 := [trans #12856 #12860]: #12861
-#12865 := [monotonicity #12234 #12862]: #12864
-#12870 := [trans #12865 #12868]: #12869
-#12873 := [monotonicity #12234 #12870]: #12872
-#12878 := [trans #12873 #12876]: #12877
-#12881 := [monotonicity #12234 #12878]: #12880
-#12886 := [trans #12881 #12884]: #12885
-#12889 := [monotonicity #12886]: #12888
-#12895 := [trans #12889 #12893]: #12894
-#12898 := [monotonicity #12234 #12895]: #12897
-#12903 := [trans #12898 #12901]: #12902
-#12837 := (iff #3326 #12834)
-#12831 := (implies #12232 #12826)
-#12835 := (iff #12831 #12834)
-#12836 := [rewrite]: #12835
-#12832 := (iff #3326 #12831)
-#12829 := (iff #3325 #12826)
-#12822 := (implies #3267 #12817)
-#12827 := (iff #12822 #12826)
-#12828 := [rewrite]: #12827
-#12823 := (iff #3325 #12822)
-#12820 := (iff #3324 #12817)
-#12814 := (implies #12232 #12809)
-#12818 := (iff #12814 #12817)
-#12819 := [rewrite]: #12818
-#12815 := (iff #3324 #12814)
-#12812 := (iff #3323 #12809)
-#12806 := (implies #12232 #12803)
-#12810 := (iff #12806 #12809)
-#12811 := [rewrite]: #12810
-#12807 := (iff #3323 #12806)
-#12804 := (iff #3322 #12803)
-#12801 := (iff #3321 #12798)
-#12794 := (implies #12581 #12791)
-#12799 := (iff #12794 #12798)
-#12800 := [rewrite]: #12799
-#12795 := (iff #3321 #12794)
-#12792 := (iff #3320 #12791)
-#12789 := (iff #3319 #12786)
-#12782 := (implies #12587 #12777)
-#12787 := (iff #12782 #12786)
-#12788 := [rewrite]: #12787
-#12783 := (iff #3319 #12782)
-#12780 := (iff #3318 #12777)
-#12773 := (implies #12590 #12768)
-#12778 := (iff #12773 #12777)
-#12779 := [rewrite]: #12778
-#12774 := (iff #3318 #12773)
-#12771 := (iff #3317 #12768)
-#12764 := (implies #12593 #12759)
-#12769 := (iff #12764 #12768)
-#12770 := [rewrite]: #12769
-#12765 := (iff #3317 #12764)
-#12762 := (iff #3316 #12759)
-#12755 := (implies #12596 #12750)
-#12760 := (iff #12755 #12759)
-#12761 := [rewrite]: #12760
-#12756 := (iff #3316 #12755)
-#12753 := (iff #3315 #12750)
-#12746 := (implies #3143 #12741)
-#12751 := (iff #12746 #12750)
-#12752 := [rewrite]: #12751
-#12747 := (iff #3315 #12746)
-#12744 := (iff #3314 #12741)
-#12737 := (implies #12601 #12732)
-#12742 := (iff #12737 #12741)
-#12743 := [rewrite]: #12742
-#12738 := (iff #3314 #12737)
-#12735 := (iff #3313 #12732)
-#12728 := (implies #12604 #12723)
-#12733 := (iff #12728 #12732)
-#12734 := [rewrite]: #12733
-#12729 := (iff #3313 #12728)
-#12605 := (iff #3278 #12604)
-#12606 := [rewrite]: #12605
-#12730 := [monotonicity #12606 #12727]: #12729
-#12736 := [trans #12730 #12734]: #12735
-#12602 := (iff #3276 #12601)
-#12603 := [rewrite]: #12602
-#12739 := [monotonicity #12603 #12736]: #12738
-#12745 := [trans #12739 #12743]: #12744
-#12599 := (iff #3274 #3143)
-#12600 := [rewrite]: #12599
-#12748 := [monotonicity #12600 #12745]: #12747
-#12754 := [trans #12748 #12752]: #12753
-#12597 := (iff #3273 #12596)
-#12598 := [rewrite]: #12597
-#12757 := [monotonicity #12598 #12754]: #12756
-#12763 := [trans #12757 #12761]: #12762
-#12594 := (iff #3271 #12593)
-#12595 := [rewrite]: #12594
-#12766 := [monotonicity #12595 #12763]: #12765
-#12772 := [trans #12766 #12770]: #12771
-#12591 := (iff #3269 #12590)
-#12592 := [rewrite]: #12591
-#12775 := [monotonicity #12592 #12772]: #12774
-#12781 := [trans #12775 #12779]: #12780
-#12588 := (iff #3265 #12587)
-#12585 := (iff #3264 #12584)
+#12373 := [monotonicity #12214 #12370]: #12372
+#12378 := [trans #12373 #12376]: #12377
+#12952 := [monotonicity #12214 #12378]: #12951
+#12957 := [trans #12952 #12955]: #12956
+#12960 := [monotonicity #12214 #12957]: #12959
+#12965 := [trans #12960 #12963]: #12964
+#12968 := [monotonicity #12965]: #12967
+#12974 := [trans #12968 #12972]: #12973
+#12977 := [monotonicity #12214 #12974]: #12976
+#12982 := [trans #12977 #12980]: #12981
+#12948 := (iff #3339 #12945)
+#12942 := (implies #12212 #12937)
+#12946 := (iff #12942 #12945)
+#12947 := [rewrite]: #12946
+#12943 := (iff #3339 #12942)
+#12940 := (iff #3338 #12937)
+#12933 := (implies #3249 #12928)
+#12938 := (iff #12933 #12937)
+#12939 := [rewrite]: #12938
+#12934 := (iff #3338 #12933)
+#12931 := (iff #3337 #12928)
+#12925 := (implies #12212 #12920)
+#12929 := (iff #12925 #12928)
+#12930 := [rewrite]: #12929
+#12926 := (iff #3337 #12925)
+#12923 := (iff #3336 #12920)
+#12917 := (implies #12212 #12914)
+#12921 := (iff #12917 #12920)
+#12922 := [rewrite]: #12921
+#12918 := (iff #3336 #12917)
+#12915 := (iff #3335 #12914)
+#12912 := (iff #3334 #12909)
+#12906 := (implies #12561 #12903)
+#12910 := (iff #12906 #12909)
+#12911 := [rewrite]: #12910
+#12907 := (iff #3334 #12906)
+#12904 := (iff #3333 #12903)
+#12901 := (iff #3332 #12898)
+#12895 := (implies #12567 #12890)
+#12899 := (iff #12895 #12898)
+#12900 := [rewrite]: #12899
+#12896 := (iff #3332 #12895)
+#12893 := (iff #3331 #12890)
+#12887 := (implies #12212 #12884)
+#12891 := (iff #12887 #12890)
+#12892 := [rewrite]: #12891
+#12888 := (iff #3331 #12887)
+#12885 := (iff #3330 #12884)
+#12882 := (iff #3329 #12879)
+#12876 := (implies #12212 #12871)
+#12880 := (iff #12876 #12879)
+#12881 := [rewrite]: #12880
+#12877 := (iff #3329 #12876)
+#12874 := (iff #3328 #12871)
+#12867 := (implies #3320 #12862)
+#12872 := (iff #12867 #12871)
+#12873 := [rewrite]: #12872
+#12868 := (iff #3328 #12867)
+#12865 := (iff #3327 #12862)
+#12859 := (implies #12212 #12854)
+#12863 := (iff #12859 #12862)
+#12864 := [rewrite]: #12863
+#12860 := (iff #3327 #12859)
+#12857 := (iff #3326 #12854)
+#12851 := (implies #12212 #12846)
+#12855 := (iff #12851 #12854)
+#12856 := [rewrite]: #12855
+#12852 := (iff #3326 #12851)
+#12849 := (iff #3325 #12846)
+#12843 := (implies #12212 #12838)
+#12847 := (iff #12843 #12846)
+#12848 := [rewrite]: #12847
+#12844 := (iff #3325 #12843)
+#12841 := (iff #3324 #12838)
+#12834 := (implies #12819 #12829)
+#12839 := (iff #12834 #12838)
+#12840 := [rewrite]: #12839
+#12835 := (iff #3324 #12834)
+#12832 := (iff #3323 #12829)
+#12825 := (implies #12822 #12703)
+#12830 := (iff #12825 #12829)
+#12831 := [rewrite]: #12830
+#12826 := (iff #3323 #12825)
+#12706 := (iff #3305 #12703)
+#12699 := (implies #3273 #12696)
+#12704 := (iff #12699 #12703)
+#12705 := [rewrite]: #12704
+#12700 := (iff #3305 #12699)
+#12697 := (iff #3304 #12696)
+#12694 := (iff #3303 #12691)
+#12687 := (implies #12596 #12682)
+#12692 := (iff #12687 #12691)
+#12693 := [rewrite]: #12692
+#12688 := (iff #3303 #12687)
+#12685 := (iff #3302 #12682)
+#12678 := (implies #12599 #12673)
+#12683 := (iff #12678 #12682)
+#12684 := [rewrite]: #12683
+#12679 := (iff #3302 #12678)
+#12676 := (iff #3301 #12673)
+#12669 := (implies #12602 #12664)
+#12674 := (iff #12669 #12673)
+#12675 := [rewrite]: #12674
+#12670 := (iff #3301 #12669)
+#12667 := (iff #3300 #12664)
+#12660 := (implies #12605 #12657)
+#12665 := (iff #12660 #12664)
+#12666 := [rewrite]: #12665
+#12661 := (iff #3300 #12660)
+#12658 := (iff #3299 #12657)
+#12655 := (iff #3298 #12652)
+#12648 := (implies #3284 #12645)
+#12653 := (iff #12648 #12652)
+#12654 := [rewrite]: #12653
+#12649 := (iff #3298 #12648)
+#12646 := (iff #3297 #12645)
+#12643 := (iff #3296 #12640)
+#12636 := (implies #12620 #12626)
+#12641 := (iff #12636 #12640)
+#12642 := [rewrite]: #12641
+#12637 := (iff #3296 #12636)
+#12634 := (iff #3295 #12626)
+#12629 := (and #12626 true)
+#12632 := (iff #12629 #12626)
+#12633 := [rewrite]: #12632
+#12630 := (iff #3295 #12629)
+#12627 := (iff #3294 #12626)
+#12624 := (iff #3293 #12623)
+#12625 := [rewrite]: #12624
+#12628 := [monotonicity #12625]: #12627
+#12631 := [monotonicity #12628]: #12630
+#12635 := [trans #12631 #12633]: #12634
+#12621 := (iff #3289 #12620)
+#12618 := (iff #3288 #12615)
+#12612 := (implies #421 #12609)
+#12616 := (iff #12612 #12615)
+#12617 := [rewrite]: #12616
+#12613 := (iff #3288 #12612)
+#12610 := (iff #3287 #12609)
+#12611 := [rewrite]: #12610
+#12614 := [monotonicity #12611]: #12613
+#12619 := [trans #12614 #12617]: #12618
+#12622 := [quant-intro #12619]: #12621
+#12638 := [monotonicity #12622 #12635]: #12637
+#12644 := [trans #12638 #12642]: #12643
+#12647 := [monotonicity #12622 #12644]: #12646
+#12650 := [monotonicity #12647]: #12649
+#12656 := [trans #12650 #12654]: #12655
+#12659 := [monotonicity #12656]: #12658
+#12606 := (iff #3283 #12605)
+#12607 := [rewrite]: #12606
+#12662 := [monotonicity #12607 #12659]: #12661
+#12668 := [trans #12662 #12666]: #12667
+#12603 := (iff #3281 #12602)
+#12604 := [rewrite]: #12603
+#12671 := [monotonicity #12604 #12668]: #12670
+#12677 := [trans #12671 #12675]: #12676
+#12600 := (iff #3279 #12599)
+#12588 := (= #3274 #12587)
+#12589 := [rewrite]: #12588
+#12601 := [monotonicity #12589]: #12600
+#12680 := [monotonicity #12601 #12677]: #12679
+#12686 := [trans #12680 #12684]: #12685
+#12597 := (iff #3277 #12596)
+#12594 := (iff #3276 #12593)
+#12595 := [monotonicity #12589]: #12594
+#12591 := (iff #3275 #12590)
+#12592 := [monotonicity #12589]: #12591
+#12598 := [monotonicity #12592 #12595]: #12597
+#12689 := [monotonicity #12598 #12686]: #12688
+#12695 := [trans #12689 #12693]: #12694
+#12698 := [monotonicity #12598 #12695]: #12697
+#12701 := [monotonicity #12698]: #12700
+#12707 := [trans #12701 #12705]: #12706
+#12823 := (iff #3322 #12822)
+#12824 := [rewrite]: #12823
+#12827 := [monotonicity #12824 #12707]: #12826
+#12833 := [trans #12827 #12831]: #12832
+#12820 := (iff #3321 #12819)
+#12821 := [rewrite]: #12820
+#12836 := [monotonicity #12821 #12833]: #12835
+#12842 := [trans #12836 #12840]: #12841
+#12845 := [monotonicity #12214 #12842]: #12844
+#12850 := [trans #12845 #12848]: #12849
+#12853 := [monotonicity #12214 #12850]: #12852
+#12858 := [trans #12853 #12856]: #12857
+#12861 := [monotonicity #12214 #12858]: #12860
+#12866 := [trans #12861 #12864]: #12865
+#12869 := [monotonicity #12866]: #12868
+#12875 := [trans #12869 #12873]: #12874
+#12878 := [monotonicity #12214 #12875]: #12877
+#12883 := [trans #12878 #12881]: #12882
+#12817 := (iff #3319 #12814)
+#12811 := (implies #12212 #12806)
+#12815 := (iff #12811 #12814)
+#12816 := [rewrite]: #12815
+#12812 := (iff #3319 #12811)
+#12809 := (iff #3318 #12806)
+#12802 := (implies #3260 #12797)
+#12807 := (iff #12802 #12806)
+#12808 := [rewrite]: #12807
+#12803 := (iff #3318 #12802)
+#12800 := (iff #3317 #12797)
+#12794 := (implies #12212 #12789)
+#12798 := (iff #12794 #12797)
+#12799 := [rewrite]: #12798
+#12795 := (iff #3317 #12794)
+#12792 := (iff #3316 #12789)
+#12786 := (implies #12212 #12783)
+#12790 := (iff #12786 #12789)
+#12791 := [rewrite]: #12790
+#12787 := (iff #3316 #12786)
+#12784 := (iff #3315 #12783)
+#12781 := (iff #3314 #12778)
+#12774 := (implies #12561 #12771)
+#12779 := (iff #12774 #12778)
+#12780 := [rewrite]: #12779
+#12775 := (iff #3314 #12774)
+#12772 := (iff #3313 #12771)
+#12769 := (iff #3312 #12766)
+#12762 := (implies #12567 #12757)
+#12767 := (iff #12762 #12766)
+#12768 := [rewrite]: #12767
+#12763 := (iff #3312 #12762)
+#12760 := (iff #3311 #12757)
+#12753 := (implies #12570 #12748)
+#12758 := (iff #12753 #12757)
+#12759 := [rewrite]: #12758
+#12754 := (iff #3311 #12753)
+#12751 := (iff #3310 #12748)
+#12744 := (implies #12573 #12739)
+#12749 := (iff #12744 #12748)
+#12750 := [rewrite]: #12749
+#12745 := (iff #3310 #12744)
+#12742 := (iff #3309 #12739)
+#12735 := (implies #12576 #12730)
+#12740 := (iff #12735 #12739)
+#12741 := [rewrite]: #12740
+#12736 := (iff #3309 #12735)
+#12733 := (iff #3308 #12730)
+#12726 := (implies #3136 #12721)
+#12731 := (iff #12726 #12730)
+#12732 := [rewrite]: #12731
+#12727 := (iff #3308 #12726)
+#12724 := (iff #3307 #12721)
+#12717 := (implies #12581 #12712)
+#12722 := (iff #12717 #12721)
+#12723 := [rewrite]: #12722
+#12718 := (iff #3307 #12717)
+#12715 := (iff #3306 #12712)
+#12708 := (implies #12584 #12703)
+#12713 := (iff #12708 #12712)
+#12714 := [rewrite]: #12713
+#12709 := (iff #3306 #12708)
+#12585 := (iff #3271 #12584)
 #12586 := [rewrite]: #12585
-#12576 := (iff #3259 #12575)
-#12577 := [rewrite]: #12576
-#12589 := [monotonicity #12577 #12586]: #12588
-#12784 := [monotonicity #12589 #12781]: #12783
-#12790 := [trans #12784 #12788]: #12789
-#12793 := [monotonicity #12589 #12790]: #12792
-#12582 := (iff #3262 #12581)
-#12579 := (iff #3261 #12578)
+#12710 := [monotonicity #12586 #12707]: #12709
+#12716 := [trans #12710 #12714]: #12715
+#12582 := (iff #3269 #12581)
+#12583 := [rewrite]: #12582
+#12719 := [monotonicity #12583 #12716]: #12718
+#12725 := [trans #12719 #12723]: #12724
+#12579 := (iff #3267 #3136)
 #12580 := [rewrite]: #12579
-#12583 := [monotonicity #12577 #12580]: #12582
-#12796 := [monotonicity #12583 #12793]: #12795
-#12802 := [trans #12796 #12800]: #12801
-#12805 := [monotonicity #12583 #12802]: #12804
-#12808 := [monotonicity #12234 #12805]: #12807
-#12813 := [trans #12808 #12811]: #12812
-#12816 := [monotonicity #12234 #12813]: #12815
-#12821 := [trans #12816 #12819]: #12820
-#12824 := [monotonicity #12821]: #12823
-#12830 := [trans #12824 #12828]: #12829
-#12833 := [monotonicity #12234 #12830]: #12832
-#12838 := [trans #12833 #12836]: #12837
-#12906 := [monotonicity #12838 #12903]: #12905
-#12909 := [monotonicity #12234 #12906]: #12908
-#12914 := [trans #12909 #12912]: #12913
-#12917 := [monotonicity #12589 #12914]: #12916
-#12922 := [trans #12917 #12920]: #12921
-#12925 := [monotonicity #12589 #12922]: #12924
-#12928 := [monotonicity #12583 #12925]: #12927
-#12933 := [trans #12928 #12931]: #12932
-#12936 := [monotonicity #12583 #12933]: #12935
-#12939 := [monotonicity #12234 #12936]: #12938
-#12944 := [trans #12939 #12942]: #12943
-#12947 := [monotonicity #12234 #12944]: #12946
-#12952 := [trans #12947 #12950]: #12951
-#12955 := [monotonicity #12952]: #12954
-#12961 := [trans #12955 #12959]: #12960
-#12964 := [monotonicity #12234 #12961]: #12963
-#12969 := [trans #12964 #12967]: #12968
-#13005 := [monotonicity #12969 #13002]: #13004
-#13008 := [monotonicity #12234 #13005]: #13007
-#13013 := [trans #13008 #13011]: #13012
-#12573 := (iff #3255 true)
-#12571 := (iff #12568 true)
+#12728 := [monotonicity #12580 #12725]: #12727
+#12734 := [trans #12728 #12732]: #12733
+#12577 := (iff #3266 #12576)
+#12578 := [rewrite]: #12577
+#12737 := [monotonicity #12578 #12734]: #12736
+#12743 := [trans #12737 #12741]: #12742
+#12574 := (iff #3264 #12573)
+#12575 := [rewrite]: #12574
+#12746 := [monotonicity #12575 #12743]: #12745
+#12752 := [trans #12746 #12750]: #12751
+#12571 := (iff #3262 #12570)
 #12572 := [rewrite]: #12571
-#12569 := (iff #3255 #12568)
-#12566 := (iff #3254 true)
-#12567 := [rewrite]: #12566
-#12564 := (iff #3253 true)
-#12565 := [rewrite]: #12564
-#12570 := [monotonicity #12565 #12567]: #12569
-#12574 := [trans #12570 #12572]: #12573
-#13016 := [monotonicity #12574 #13013]: #13015
-#13020 := [trans #13016 #13018]: #13019
-#12562 := (iff #3252 #12561)
-#12559 := (iff #3251 #12558)
+#12755 := [monotonicity #12572 #12752]: #12754
+#12761 := [trans #12755 #12759]: #12760
+#12568 := (iff #3258 #12567)
+#12565 := (iff #3257 #12564)
+#12566 := [rewrite]: #12565
+#12556 := (iff #3252 #12555)
+#12557 := [rewrite]: #12556
+#12569 := [monotonicity #12557 #12566]: #12568
+#12764 := [monotonicity #12569 #12761]: #12763
+#12770 := [trans #12764 #12768]: #12769
+#12773 := [monotonicity #12569 #12770]: #12772
+#12562 := (iff #3255 #12561)
+#12559 := (iff #3254 #12558)
 #12560 := [rewrite]: #12559
-#12556 := (iff #3249 #12555)
-#12557 := [rewrite]: #12556
 #12563 := [monotonicity #12557 #12560]: #12562
-#13023 := [monotonicity #12563 #13020]: #13022
-#13029 := [trans #13023 #13027]: #13028
-#12553 := (iff #3247 #12552)
-#12554 := [rewrite]: #12553
-#13032 := [monotonicity #12554 #13029]: #13031
-#13038 := [trans #13032 #13036]: #13037
-#12550 := (iff #3245 #12549)
-#12551 := [rewrite]: #12550
-#13041 := [monotonicity #12551 #13038]: #13040
-#13047 := [trans #13041 #13045]: #13046
-#12547 := (iff #3243 #12546)
-#12548 := [rewrite]: #12547
-#13050 := [monotonicity #12548 #13047]: #13049
-#13056 := [trans #13050 #13054]: #13055
-#12544 := (iff #3241 #12543)
+#12776 := [monotonicity #12563 #12773]: #12775
+#12782 := [trans #12776 #12780]: #12781
+#12785 := [monotonicity #12563 #12782]: #12784
+#12788 := [monotonicity #12214 #12785]: #12787
+#12793 := [trans #12788 #12791]: #12792
+#12796 := [monotonicity #12214 #12793]: #12795
+#12801 := [trans #12796 #12799]: #12800
+#12804 := [monotonicity #12801]: #12803
+#12810 := [trans #12804 #12808]: #12809
+#12813 := [monotonicity #12214 #12810]: #12812
+#12818 := [trans #12813 #12816]: #12817
+#12886 := [monotonicity #12818 #12883]: #12885
+#12889 := [monotonicity #12214 #12886]: #12888
+#12894 := [trans #12889 #12892]: #12893
+#12897 := [monotonicity #12569 #12894]: #12896
+#12902 := [trans #12897 #12900]: #12901
+#12905 := [monotonicity #12569 #12902]: #12904
+#12908 := [monotonicity #12563 #12905]: #12907
+#12913 := [trans #12908 #12911]: #12912
+#12916 := [monotonicity #12563 #12913]: #12915
+#12919 := [monotonicity #12214 #12916]: #12918
+#12924 := [trans #12919 #12922]: #12923
+#12927 := [monotonicity #12214 #12924]: #12926
+#12932 := [trans #12927 #12930]: #12931
+#12935 := [monotonicity #12932]: #12934
+#12941 := [trans #12935 #12939]: #12940
+#12944 := [monotonicity #12214 #12941]: #12943
+#12949 := [trans #12944 #12947]: #12948
+#12985 := [monotonicity #12949 #12982]: #12984
+#12988 := [monotonicity #12214 #12985]: #12987
+#12993 := [trans #12988 #12991]: #12992
+#12553 := (iff #3248 true)
+#12551 := (iff #12548 true)
+#12552 := [rewrite]: #12551
+#12549 := (iff #3248 #12548)
+#12546 := (iff #3247 true)
+#12547 := [rewrite]: #12546
+#12544 := (iff #3246 true)
 #12545 := [rewrite]: #12544
-#13059 := [monotonicity #12545 #13056]: #13058
-#13065 := [trans #13059 #13063]: #13064
-#12267 := (iff #3159 #12264)
-#12261 := (and #12258 #12145)
-#12265 := (iff #12261 #12264)
-#12266 := [rewrite]: #12265
-#12262 := (iff #3159 #12261)
-#12146 := (iff #3068 #12145)
-#12147 := [rewrite]: #12146
-#12259 := (iff #3158 #12258)
-#12260 := [rewrite]: #12259
-#12263 := [monotonicity #12260 #12147]: #12262
-#12268 := [trans #12263 #12266]: #12267
-#13068 := [monotonicity #12268 #13065]: #13067
-#13073 := [trans #13068 #13071]: #13072
-#12522 := (iff #3235 #12521)
-#12519 := (iff #3234 #12518)
-#12516 := (iff #3233 #12515)
-#12517 := [rewrite]: #12516
-#12520 := [monotonicity #12517]: #12519
-#12523 := [monotonicity #12520]: #12522
-#13076 := [monotonicity #12523 #13073]: #13075
-#13082 := [trans #13076 #13080]: #13081
-#12541 := (iff #3239 #12521)
-#12524 := (and true #12521)
-#12527 := (iff #12524 #12521)
+#12550 := [monotonicity #12545 #12547]: #12549
+#12554 := [trans #12550 #12552]: #12553
+#12996 := [monotonicity #12554 #12993]: #12995
+#13000 := [trans #12996 #12998]: #12999
+#12542 := (iff #3245 #12541)
+#12539 := (iff #3244 #12538)
+#12540 := [rewrite]: #12539
+#12536 := (iff #3242 #12535)
+#12537 := [rewrite]: #12536
+#12543 := [monotonicity #12537 #12540]: #12542
+#13003 := [monotonicity #12543 #13000]: #13002
+#13009 := [trans #13003 #13007]: #13008
+#12533 := (iff #3240 #12532)
+#12534 := [rewrite]: #12533
+#13012 := [monotonicity #12534 #13009]: #13011
+#13018 := [trans #13012 #13016]: #13017
+#12530 := (iff #3238 #12529)
+#12531 := [rewrite]: #12530
+#13021 := [monotonicity #12531 #13018]: #13020
+#13027 := [trans #13021 #13025]: #13026
+#12527 := (iff #3236 #12526)
 #12528 := [rewrite]: #12527
-#12539 := (iff #3239 #12524)
-#12537 := (iff #3238 #12521)
-#12535 := (iff #3238 #12524)
-#12533 := (iff #3237 #12521)
-#12531 := (iff #3237 #12524)
-#12529 := (iff #3236 #12521)
-#12525 := (iff #3236 #12524)
-#12513 := (iff #3226 true)
-#12508 := (forall (vars (?v0 S20)) (:pat #3222) true)
-#12511 := (iff #12508 true)
-#12512 := [elim-unused]: #12511
-#12509 := (iff #3226 #12508)
-#12506 := (iff #3225 true)
-#12458 := (= f1 #3210)
-#12470 := (implies #12458 #12458)
-#12473 := (iff #12470 true)
-#12474 := [rewrite]: #12473
-#12504 := (iff #3225 #12470)
-#12502 := (iff #3224 #12458)
-#12463 := (and true #12458)
-#12466 := (iff #12463 #12458)
-#12467 := [rewrite]: #12466
-#12500 := (iff #3224 #12463)
-#12459 := (iff #3211 #12458)
-#12460 := [rewrite]: #12459
-#12498 := (iff #3223 true)
-#12499 := [rewrite]: #12498
-#12501 := [monotonicity #12499 #12460]: #12500
-#12503 := [trans #12501 #12467]: #12502
-#12505 := [monotonicity #12460 #12503]: #12504
-#12507 := [trans #12505 #12474]: #12506
-#12510 := [quant-intro #12507]: #12509
-#12514 := [trans #12510 #12512]: #12513
-#12526 := [monotonicity #12514 #12523]: #12525
-#12530 := [trans #12526 #12528]: #12529
-#12496 := (iff #3219 true)
-#12451 := (forall (vars (?v0 S20)) (:pat #3199) true)
-#12454 := (iff #12451 true)
-#12455 := [elim-unused]: #12454
-#12494 := (iff #3219 #12451)
-#12492 := (iff #3218 true)
-#12490 := (iff #3218 #12470)
-#12488 := (iff #3217 #12458)
-#12486 := (iff #3217 #12463)
-#12484 := (iff #3216 true)
-#12485 := [rewrite]: #12484
-#12487 := [monotonicity #12485 #12460]: #12486
-#12489 := [trans #12487 #12467]: #12488
-#12491 := [monotonicity #12460 #12489]: #12490
-#12493 := [trans #12491 #12474]: #12492
-#12495 := [quant-intro #12493]: #12494
-#12497 := [trans #12495 #12455]: #12496
-#12532 := [monotonicity #12497 #12530]: #12531
-#12534 := [trans #12532 #12528]: #12533
-#12482 := (iff #3215 true)
-#12477 := (forall (vars (?v0 S20)) (:pat #3209) true)
-#12480 := (iff #12477 true)
-#12481 := [elim-unused]: #12480
-#12478 := (iff #3215 #12477)
-#12475 := (iff #3214 true)
-#12471 := (iff #3214 #12470)
-#12468 := (iff #3213 #12458)
-#12464 := (iff #3213 #12463)
-#12461 := (iff #3212 true)
-#12462 := [rewrite]: #12461
-#12465 := [monotonicity #12462 #12460]: #12464
-#12469 := [trans #12465 #12467]: #12468
-#12472 := [monotonicity #12460 #12469]: #12471
-#12476 := [trans #12472 #12474]: #12475
-#12479 := [quant-intro #12476]: #12478
-#12483 := [trans #12479 #12481]: #12482
-#12536 := [monotonicity #12483 #12534]: #12535
-#12538 := [trans #12536 #12528]: #12537
-#12456 := (iff #3206 true)
-#12452 := (iff #3206 #12451)
-#12449 := (iff #3205 true)
-#12438 := (= f272 #3202)
-#12441 := (not #12438)
-#12444 := (implies #12441 #12441)
-#12447 := (iff #12444 true)
-#12448 := [rewrite]: #12447
-#12445 := (iff #3205 #12444)
-#12442 := (iff #3204 #12441)
-#12439 := (iff #3203 #12438)
+#13030 := [monotonicity #12528 #13027]: #13029
+#13036 := [trans #13030 #13034]: #13035
+#12524 := (iff #3234 #12523)
+#12525 := [rewrite]: #12524
+#13039 := [monotonicity #12525 #13036]: #13038
+#13045 := [trans #13039 #13043]: #13044
+#12247 := (iff #3152 #12244)
+#12241 := (and #12238 #12125)
+#12245 := (iff #12241 #12244)
+#12246 := [rewrite]: #12245
+#12242 := (iff #3152 #12241)
+#12126 := (iff #3061 #12125)
+#12127 := [rewrite]: #12126
+#12239 := (iff #3151 #12238)
+#12240 := [rewrite]: #12239
+#12243 := [monotonicity #12240 #12127]: #12242
+#12248 := [trans #12243 #12246]: #12247
+#13048 := [monotonicity #12248 #13045]: #13047
+#13053 := [trans #13048 #13051]: #13052
+#12502 := (iff #3228 #12501)
+#12499 := (iff #3227 #12498)
+#12496 := (iff #3226 #12495)
+#12497 := [rewrite]: #12496
+#12500 := [monotonicity #12497]: #12499
+#12503 := [monotonicity #12500]: #12502
+#13056 := [monotonicity #12503 #13053]: #13055
+#13062 := [trans #13056 #13060]: #13061
+#12521 := (iff #3232 #12501)
+#12504 := (and true #12501)
+#12507 := (iff #12504 #12501)
+#12508 := [rewrite]: #12507
+#12519 := (iff #3232 #12504)
+#12517 := (iff #3231 #12501)
+#12515 := (iff #3231 #12504)
+#12513 := (iff #3230 #12501)
+#12511 := (iff #3230 #12504)
+#12509 := (iff #3229 #12501)
+#12505 := (iff #3229 #12504)
+#12493 := (iff #3219 true)
+#12488 := (forall (vars (?v0 S5)) (:pat #3215) true)
+#12491 := (iff #12488 true)
+#12492 := [elim-unused]: #12491
+#12489 := (iff #3219 #12488)
+#12486 := (iff #3218 true)
+#12438 := (= f1 #3203)
+#12450 := (implies #12438 #12438)
+#12453 := (iff #12450 true)
+#12454 := [rewrite]: #12453
+#12484 := (iff #3218 #12450)
+#12482 := (iff #3217 #12438)
+#12443 := (and true #12438)
+#12446 := (iff #12443 #12438)
+#12447 := [rewrite]: #12446
+#12480 := (iff #3217 #12443)
+#12439 := (iff #3204 #12438)
 #12440 := [rewrite]: #12439
-#12443 := [monotonicity #12440]: #12442
-#12446 := [monotonicity #12443 #12443]: #12445
-#12450 := [trans #12446 #12448]: #12449
-#12453 := [quant-intro #12450]: #12452
-#12457 := [trans #12453 #12455]: #12456
-#12540 := [monotonicity #12457 #12538]: #12539
-#12542 := [trans #12540 #12528]: #12541
-#13085 := [monotonicity #12542 #13082]: #13084
-#13090 := [trans #13085 #13088]: #13089
-#13093 := [monotonicity #12234 #13090]: #13092
-#13098 := [trans #13093 #13096]: #13097
-#13101 := [monotonicity #12234 #13098]: #13100
-#13106 := [trans #13101 #13104]: #13105
-#13109 := [monotonicity #12234 #13106]: #13108
-#13114 := [trans #13109 #13112]: #13113
-#12436 := (iff #3196 true)
-#12431 := (implies #12232 true)
+#12478 := (iff #3216 true)
+#12479 := [rewrite]: #12478
+#12481 := [monotonicity #12479 #12440]: #12480
+#12483 := [trans #12481 #12447]: #12482
+#12485 := [monotonicity #12440 #12483]: #12484
+#12487 := [trans #12485 #12454]: #12486
+#12490 := [quant-intro #12487]: #12489
+#12494 := [trans #12490 #12492]: #12493
+#12506 := [monotonicity #12494 #12503]: #12505
+#12510 := [trans #12506 #12508]: #12509
+#12476 := (iff #3212 true)
+#12431 := (forall (vars (?v0 S5)) (:pat #3192) true)
 #12434 := (iff #12431 true)
-#12435 := [rewrite]: #12434
-#12432 := (iff #3196 #12431)
-#12429 := (iff #3195 true)
-#12403 := (or #12402 #12394)
-#12411 := (or #12349 #12403)
-#12419 := (or #12349 #12411)
-#12424 := (implies false #12419)
+#12435 := [elim-unused]: #12434
+#12474 := (iff #3212 #12431)
+#12472 := (iff #3211 true)
+#12470 := (iff #3211 #12450)
+#12468 := (iff #3210 #12438)
+#12466 := (iff #3210 #12443)
+#12464 := (iff #3209 true)
+#12465 := [rewrite]: #12464
+#12467 := [monotonicity #12465 #12440]: #12466
+#12469 := [trans #12467 #12447]: #12468
+#12471 := [monotonicity #12440 #12469]: #12470
+#12473 := [trans #12471 #12454]: #12472
+#12475 := [quant-intro #12473]: #12474
+#12477 := [trans #12475 #12435]: #12476
+#12512 := [monotonicity #12477 #12510]: #12511
+#12514 := [trans #12512 #12508]: #12513
+#12462 := (iff #3208 true)
+#12457 := (forall (vars (?v0 S5)) (:pat #3202) true)
+#12460 := (iff #12457 true)
+#12461 := [elim-unused]: #12460
+#12458 := (iff #3208 #12457)
+#12455 := (iff #3207 true)
+#12451 := (iff #3207 #12450)
+#12448 := (iff #3206 #12438)
+#12444 := (iff #3206 #12443)
+#12441 := (iff #3205 true)
+#12442 := [rewrite]: #12441
+#12445 := [monotonicity #12442 #12440]: #12444
+#12449 := [trans #12445 #12447]: #12448
+#12452 := [monotonicity #12440 #12449]: #12451
+#12456 := [trans #12452 #12454]: #12455
+#12459 := [quant-intro #12456]: #12458
+#12463 := [trans #12459 #12461]: #12462
+#12516 := [monotonicity #12463 #12514]: #12515
+#12518 := [trans #12516 #12508]: #12517
+#12436 := (iff #3199 true)
+#12432 := (iff #3199 #12431)
+#12429 := (iff #3198 true)
+#12418 := (= f262 #3195)
+#12421 := (not #12418)
+#12424 := (implies #12421 #12421)
 #12427 := (iff #12424 true)
 #12428 := [rewrite]: #12427
-#12425 := (iff #3195 #12424)
-#12422 := (iff #3194 #12419)
-#12416 := (implies #12232 #12411)
-#12420 := (iff #12416 #12419)
-#12421 := [rewrite]: #12420
-#12417 := (iff #3194 #12416)
-#12414 := (iff #3193 #12411)
-#12408 := (implies #12232 #12403)
-#12412 := (iff #12408 #12411)
-#12413 := [rewrite]: #12412
-#12409 := (iff #3193 #12408)
-#12406 := (iff #3192 #12403)
-#12399 := (implies #12264 #12394)
-#12404 := (iff #12399 #12403)
-#12405 := [rewrite]: #12404
-#12400 := (iff #3192 #12399)
-#12401 := [monotonicity #12268 #12398]: #12400
-#12407 := [trans #12401 #12405]: #12406
-#12410 := [monotonicity #12234 #12407]: #12409
-#12415 := [trans #12410 #12413]: #12414
-#12418 := [monotonicity #12234 #12415]: #12417
-#12423 := [trans #12418 #12421]: #12422
-#12426 := [monotonicity #12257 #12423]: #12425
+#12425 := (iff #3198 #12424)
+#12422 := (iff #3197 #12421)
+#12419 := (iff #3196 #12418)
+#12420 := [rewrite]: #12419
+#12423 := [monotonicity #12420]: #12422
+#12426 := [monotonicity #12423 #12423]: #12425
 #12430 := [trans #12426 #12428]: #12429
-#12433 := [monotonicity #12234 #12430]: #12432
+#12433 := [quant-intro #12430]: #12432
 #12437 := [trans #12433 #12435]: #12436
-#13117 := [monotonicity #12437 #13114]: #13116
-#13121 := [trans #13117 #13119]: #13120
-#13124 := [monotonicity #12234 #13121]: #13123
-#13129 := [trans #13124 #13127]: #13128
-#12254 := (iff #3155 #12253)
-#12251 := (iff #3154 #12250)
-#12252 := [rewrite]: #12251
-#12255 := [monotonicity #12252]: #12254
-#13132 := [monotonicity #12255 #13129]: #13131
-#13138 := [trans #13132 #13136]: #13137
-#12248 := (iff #3150 #12247)
-#12245 := (iff #3149 #12242)
-#12239 := (implies #455 #12236)
-#12243 := (iff #12239 #12242)
-#12244 := [rewrite]: #12243
-#12240 := (iff #3149 #12239)
-#12237 := (iff #3148 #12236)
-#12238 := [rewrite]: #12237
-#12241 := [monotonicity #12238]: #12240
-#12246 := [trans #12241 #12244]: #12245
-#12249 := [quant-intro #12246]: #12248
-#13141 := [monotonicity #12249 #13138]: #13140
-#13147 := [trans #13141 #13145]: #13146
-#13150 := [monotonicity #13147]: #13149
-#13156 := [trans #13150 #13154]: #13155
-#13159 := [monotonicity #12234 #13156]: #13158
-#13164 := [trans #13159 #13162]: #13163
-#13167 := [monotonicity #13164]: #13166
-#13173 := [trans #13167 #13171]: #13172
-#13176 := [monotonicity #13173]: #13175
-#13182 := [trans #13176 #13180]: #13181
-#13185 := [monotonicity #13182]: #13184
-#13191 := [trans #13185 #13189]: #13190
-#12230 := (iff #3130 #12229)
-#12227 := (iff #3129 #3109)
-#12228 := [rewrite]: #12227
-#12231 := [monotonicity #12228]: #12230
-#13194 := [monotonicity #12231 #13191]: #13193
-#13200 := [trans #13194 #13198]: #13199
-#13203 := [monotonicity #12231 #13200]: #13202
-#12225 := (iff #3128 #12224)
-#12222 := (iff #3127 #12219)
-#12216 := (implies #455 #12213)
-#12220 := (iff #12216 #12219)
-#12221 := [rewrite]: #12220
-#12217 := (iff #3127 #12216)
-#12214 := (iff #3126 #12213)
-#12215 := [rewrite]: #12214
-#12218 := [monotonicity #12215]: #12217
-#12223 := [trans #12218 #12221]: #12222
-#12226 := [quant-intro #12223]: #12225
-#13206 := [monotonicity #12226 #13203]: #13205
-#13212 := [trans #13206 #13210]: #13211
-#13215 := [monotonicity #12226 #13212]: #13214
-#13218 := [monotonicity #13215]: #13217
-#13224 := [trans #13218 #13222]: #13223
-#13227 := [monotonicity #13224]: #13226
-#12210 := (iff #3120 #12209)
-#12207 := (iff #3119 #12206)
-#12204 := (iff #3118 #3117)
-#12205 := [rewrite]: #12204
-#12208 := [monotonicity #12205]: #12207
+#12520 := [monotonicity #12437 #12518]: #12519
+#12522 := [trans #12520 #12508]: #12521
+#13065 := [monotonicity #12522 #13062]: #13064
+#13070 := [trans #13065 #13068]: #13069
+#13073 := [monotonicity #12214 #13070]: #13072
+#13078 := [trans #13073 #13076]: #13077
+#13081 := [monotonicity #12214 #13078]: #13080
+#13086 := [trans #13081 #13084]: #13085
+#13089 := [monotonicity #12214 #13086]: #13088
+#13094 := [trans #13089 #13092]: #13093
+#12416 := (iff #3189 true)
+#12411 := (implies #12212 true)
+#12414 := (iff #12411 true)
+#12415 := [rewrite]: #12414
+#12412 := (iff #3189 #12411)
+#12409 := (iff #3188 true)
+#12383 := (or #12382 #12374)
+#12391 := (or #12329 #12383)
+#12399 := (or #12329 #12391)
+#12404 := (implies false #12399)
+#12407 := (iff #12404 true)
+#12408 := [rewrite]: #12407
+#12405 := (iff #3188 #12404)
+#12402 := (iff #3187 #12399)
+#12396 := (implies #12212 #12391)
+#12400 := (iff #12396 #12399)
+#12401 := [rewrite]: #12400
+#12397 := (iff #3187 #12396)
+#12394 := (iff #3186 #12391)
+#12388 := (implies #12212 #12383)
+#12392 := (iff #12388 #12391)
+#12393 := [rewrite]: #12392
+#12389 := (iff #3186 #12388)
+#12386 := (iff #3185 #12383)
+#12379 := (implies #12244 #12374)
+#12384 := (iff #12379 #12383)
+#12385 := [rewrite]: #12384
+#12380 := (iff #3185 #12379)
+#12381 := [monotonicity #12248 #12378]: #12380
+#12387 := [trans #12381 #12385]: #12386
+#12390 := [monotonicity #12214 #12387]: #12389
+#12395 := [trans #12390 #12393]: #12394
+#12398 := [monotonicity #12214 #12395]: #12397
+#12403 := [trans #12398 #12401]: #12402
+#12406 := [monotonicity #12237 #12403]: #12405
+#12410 := [trans #12406 #12408]: #12409
+#12413 := [monotonicity #12214 #12410]: #12412
+#12417 := [trans #12413 #12415]: #12416
+#13097 := [monotonicity #12417 #13094]: #13096
+#13101 := [trans #13097 #13099]: #13100
+#13104 := [monotonicity #12214 #13101]: #13103
+#13109 := [trans #13104 #13107]: #13108
+#12234 := (iff #3148 #12233)
+#12231 := (iff #3147 #12230)
+#12232 := [rewrite]: #12231
+#12235 := [monotonicity #12232]: #12234
+#13112 := [monotonicity #12235 #13109]: #13111
+#13118 := [trans #13112 #13116]: #13117
+#12228 := (iff #3143 #12227)
+#12225 := (iff #3142 #12222)
+#12219 := (implies #421 #12216)
+#12223 := (iff #12219 #12222)
+#12224 := [rewrite]: #12223
+#12220 := (iff #3142 #12219)
+#12217 := (iff #3141 #12216)
+#12218 := [rewrite]: #12217
+#12221 := [monotonicity #12218]: #12220
+#12226 := [trans #12221 #12224]: #12225
+#12229 := [quant-intro #12226]: #12228
+#13121 := [monotonicity #12229 #13118]: #13120
+#13127 := [trans #13121 #13125]: #13126
+#13130 := [monotonicity #13127]: #13129
+#13136 := [trans #13130 #13134]: #13135
+#13139 := [monotonicity #12214 #13136]: #13138
+#13144 := [trans #13139 #13142]: #13143
+#13147 := [monotonicity #13144]: #13146
+#13153 := [trans #13147 #13151]: #13152
+#13156 := [monotonicity #13153]: #13155
+#13162 := [trans #13156 #13160]: #13161
+#13165 := [monotonicity #13162]: #13164
+#13171 := [trans #13165 #13169]: #13170
+#12210 := (iff #3123 #12209)
+#12207 := (iff #3122 #3102)
+#12208 := [rewrite]: #12207
 #12211 := [monotonicity #12208]: #12210
-#13230 := [monotonicity #12211 #13227]: #13229
-#13236 := [trans #13230 #13234]: #13235
-#12202 := (iff #3115 #12201)
-#12203 := [rewrite]: #12202
-#13239 := [monotonicity #12203 #13236]: #13238
-#13245 := [trans #13239 #13243]: #13244
-#12199 := (iff #3113 #12198)
-#12200 := [rewrite]: #12199
-#13248 := [monotonicity #12200 #13245]: #13247
-#13254 := [trans #13248 #13252]: #13253
-#12196 := (iff #3111 #12195)
-#12197 := [rewrite]: #12196
-#13257 := [monotonicity #12197 #13254]: #13256
-#13263 := [trans #13257 #13261]: #13262
-#13266 := [monotonicity #13263]: #13265
-#13272 := [trans #13266 #13270]: #13271
-#12193 := (iff #3106 #12192)
-#12190 := (iff #3105 #12189)
-#12191 := [rewrite]: #12190
-#12181 := (iff #3100 #12180)
-#12182 := [rewrite]: #12181
-#12194 := [monotonicity #12182 #12191]: #12193
-#13275 := [monotonicity #12194 #13272]: #13274
-#13281 := [trans #13275 #13279]: #13280
-#13284 := [monotonicity #12194 #13281]: #13283
-#12187 := (iff #3103 #12186)
-#12184 := (iff #3102 #12183)
+#13174 := [monotonicity #12211 #13171]: #13173
+#13180 := [trans #13174 #13178]: #13179
+#13183 := [monotonicity #12211 #13180]: #13182
+#12205 := (iff #3121 #12204)
+#12202 := (iff #3120 #12199)
+#12196 := (implies #421 #12193)
+#12200 := (iff #12196 #12199)
+#12201 := [rewrite]: #12200
+#12197 := (iff #3120 #12196)
+#12194 := (iff #3119 #12193)
+#12195 := [rewrite]: #12194
+#12198 := [monotonicity #12195]: #12197
+#12203 := [trans #12198 #12201]: #12202
+#12206 := [quant-intro #12203]: #12205
+#13186 := [monotonicity #12206 #13183]: #13185
+#13192 := [trans #13186 #13190]: #13191
+#13195 := [monotonicity #12206 #13192]: #13194
+#13198 := [monotonicity #13195]: #13197
+#13204 := [trans #13198 #13202]: #13203
+#13207 := [monotonicity #13204]: #13206
+#12190 := (iff #3113 #12189)
+#12187 := (iff #3112 #12186)
+#12184 := (iff #3111 #3110)
 #12185 := [rewrite]: #12184
-#12188 := [monotonicity #12182 #12185]: #12187
-#13287 := [monotonicity #12188 #13284]: #13286
-#13293 := [trans #13287 #13291]: #13292
-#13296 := [monotonicity #12188 #13293]: #13295
-#12178 := (iff #3097 #12177)
-#12179 := [rewrite]: #12178
-#13299 := [monotonicity #12179 #13296]: #13298
-#13305 := [trans #13299 #13303]: #13304
-#13308 := [monotonicity #12179 #13305]: #13307
-#13311 := [monotonicity #13308]: #13310
-#13317 := [trans #13311 #13315]: #13316
-#12175 := (iff #3091 #12174)
-#12172 := (iff #3090 #12169)
-#12166 := (iff #12163 false)
-#12170 := (iff #12166 #12169)
+#12188 := [monotonicity #12185]: #12187
+#12191 := [monotonicity #12188]: #12190
+#13210 := [monotonicity #12191 #13207]: #13209
+#13216 := [trans #13210 #13214]: #13215
+#12182 := (iff #3108 #12181)
+#12183 := [rewrite]: #12182
+#13219 := [monotonicity #12183 #13216]: #13218
+#13225 := [trans #13219 #13223]: #13224
+#12179 := (iff #3106 #12178)
+#12180 := [rewrite]: #12179
+#13228 := [monotonicity #12180 #13225]: #13227
+#13234 := [trans #13228 #13232]: #13233
+#12176 := (iff #3104 #12175)
+#12177 := [rewrite]: #12176
+#13237 := [monotonicity #12177 #13234]: #13236
+#13243 := [trans #13237 #13241]: #13242
+#13246 := [monotonicity #13243]: #13245
+#13252 := [trans #13246 #13250]: #13251
+#12173 := (iff #3099 #12172)
+#12170 := (iff #3098 #12169)
 #12171 := [rewrite]: #12170
-#12167 := (iff #3090 #12166)
-#12164 := (iff #3089 #12163)
-#12165 := [rewrite]: #12164
-#12168 := [monotonicity #12165]: #12167
-#12173 := [trans #12168 #12171]: #12172
-#12176 := [quant-intro #12173]: #12175
-#13320 := [monotonicity #12176 #13317]: #13319
-#13326 := [trans #13320 #13324]: #13325
-#13329 := [monotonicity #13326]: #13328
-#13335 := [trans #13329 #13333]: #13334
-#12161 := (iff #3083 #12160)
+#12161 := (iff #3093 #12160)
 #12162 := [rewrite]: #12161
-#13338 := [monotonicity #12162 #13335]: #13337
-#13344 := [trans #13338 #13342]: #13343
-#12158 := (iff #3081 #12157)
-#12155 := (iff #3080 #12154)
-#12156 := [rewrite]: #12155
-#12152 := (iff #3078 #12151)
-#12153 := [rewrite]: #12152
-#12159 := [monotonicity #12153 #12156]: #12158
-#13347 := [monotonicity #12159 #13344]: #13346
-#13353 := [trans #13347 #13351]: #13352
-#13356 := [monotonicity #13353]: #13355
-#13362 := [trans #13356 #13360]: #13361
-#12149 := (iff #3069 #12148)
-#12143 := (iff #3066 #12142)
-#12144 := [rewrite]: #12143
-#12150 := [monotonicity #12144 #12147]: #12149
-#13365 := [monotonicity #12150 #13362]: #13364
-#13371 := [trans #13365 #13369]: #13370
-#12140 := (iff #3064 #12139)
-#12141 := [rewrite]: #12140
-#13374 := [monotonicity #12141 #13371]: #13373
-#13380 := [trans #13374 #13378]: #13379
-#12137 := (iff #3062 #12136)
-#12134 := (iff #3061 #12133)
-#12131 := (iff #3060 #12130)
-#12128 := (iff #3059 #12127)
-#12125 := (iff #3058 #12124)
-#12122 := (iff #3057 #12121)
-#12123 := [rewrite]: #12122
-#12119 := (iff #3055 #12118)
-#12116 := (iff #3054 #12115)
-#12117 := [rewrite]: #12116
-#12120 := [monotonicity #12117]: #12119
-#12126 := [monotonicity #12120 #12123]: #12125
-#12113 := (iff #3052 #12112)
-#12114 := [rewrite]: #12113
-#12129 := [monotonicity #12114 #12126]: #12128
-#12110 := (iff #3050 #12109)
-#12111 := [rewrite]: #12110
-#12132 := [monotonicity #12111 #12129]: #12131
-#12107 := (iff #3048 #12106)
-#12108 := [rewrite]: #12107
-#12135 := [monotonicity #12108 #12132]: #12134
-#12104 := (iff #3046 #12102)
-#12105 := [rewrite]: #12104
-#12138 := [monotonicity #12105 #12135]: #12137
-#13383 := [monotonicity #12138 #13380]: #13382
-#13389 := [trans #13383 #13387]: #13388
-#13392 := [monotonicity #13389]: #13391
-#13398 := [trans #13392 #13396]: #13397
-#13401 := [monotonicity #13398]: #13400
-#13407 := [trans #13401 #13405]: #13406
-#13410 := [monotonicity #13407]: #13409
-#13416 := [trans #13410 #13414]: #13415
-#13419 := [monotonicity #13416]: #13418
-#13425 := [trans #13419 #13423]: #13424
-#13428 := [monotonicity #13425]: #13427
-#13434 := [trans #13428 #13432]: #13433
-#13437 := [monotonicity #13434]: #13436
-#14345 := [trans #13437 #14343]: #14344
-#12101 := [asserted]: #3406
-#14346 := [mp #12101 #14345]: #14341
-#14364 := [not-or-elim #14346]: #14228
-#14367 := [and-elim #14364]: #12109
-#11376 := (not #11369)
-#1302 := (f127 #55)
-#2732 := (f54 #275 #1302)
-#2733 := (= #55 #2732)
-#11377 := (or #2733 #11376)
-#11382 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #11377)
-#18282 := (~ #11382 #11382)
-#18280 := (~ #11377 #11377)
-#18281 := [refl]: #18280
-#18283 := [nnf-pos #18281]: #18282
-#2734 := (implies #2731 #2733)
-#2735 := (forall (vars (?v0 S20) (?v1 S18)) (:pat #2730) #2734)
-#11383 := (iff #2735 #11382)
-#11380 := (iff #2734 #11377)
-#11373 := (implies #11369 #2733)
-#11378 := (iff #11373 #11377)
-#11379 := [rewrite]: #11378
-#11374 := (iff #2734 #11373)
-#11375 := [monotonicity #11372]: #11374
-#11381 := [trans #11375 #11379]: #11380
-#11384 := [quant-intro #11381]: #11383
-#11368 := [asserted]: #2735
-#11387 := [mp #11368 #11384]: #11382
-#18284 := [mp~ #11387 #18283]: #11382
-#26181 := (not #12109)
-#26194 := (not #11382)
-#26195 := (or #26194 #26181 #26189)
-#26190 := (or #26189 #26181)
-#26196 := (or #26194 #26190)
-#26203 := (iff #26196 #26195)
-#26191 := (or #26181 #26189)
-#26198 := (or #26194 #26191)
-#26201 := (iff #26198 #26195)
-#26202 := [rewrite]: #26201
-#26199 := (iff #26196 #26198)
-#26192 := (iff #26190 #26191)
-#26193 := [rewrite]: #26192
-#26200 := [monotonicity #26193]: #26199
-#26204 := [trans #26200 #26202]: #26203
-#26197 := [quant-inst #3044 #3040]: #26196
-#26205 := [mp #26197 #26204]: #26195
-#28848 := [unit-resolution #26205 #18284 #14367]: #26189
-#28791 := [trans #28789 #28848]: #28790
-#28793 := [monotonicity #28791]: #28792
-#28796 := [symm #28793]: #28795
-#26777 := (= f1 #26776)
-decl f64 :: (-> S19 S20 S21)
-#26765 := (f64 f297 #26182)
-#26766 := (f26 #62 #26765)
-#26772 := (pattern #26766)
-decl f208 :: (-> S18 S1)
-#26586 := (f24 #26182)
-#26769 := (f208 #26586)
-#26770 := (= f1 #26769)
-#26767 := (= f1 #26766)
-#26768 := (not #26767)
-decl f158 :: (-> S20 S21 S1)
-decl f203 :: (-> S22 S21)
-decl f22 :: (-> S19 S20 S22)
-#26761 := (f22 f297 #26182)
-#26762 := (f203 #26761)
-#26763 := (f158 #62 #26762)
-#26764 := (= f1 #26763)
-#26782 := (or #26764 #26768 #26770)
-#26785 := (forall (vars (?v3 S20)) (:pat #26772) #26782)
-#26788 := (not #26785)
-#26778 := (not #26777)
-#26626 := (f38 f297 #26182)
-#26627 := (= f1 #26626)
-#26649 := (not #26627)
-#26791 := (or #26649 #26778 #26788)
-#26794 := (not #26791)
-decl f207 :: (-> S19 S20 S20 S1)
-#26714 := (f207 f297 #26182 #26182)
-#26715 := (= f1 #26714)
-#26716 := (f211 f297 #26182 #26182 f305)
-#26717 := (= f1 #26716)
-#26719 := (iff #26715 #26717)
-#2299 := (:var 0 S31)
-#53 := (:var 3 S19)
-#2311 := (f211 #53 #60 #55 #2299)
-#2312 := (pattern #2311)
-#2314 := (f207 #53 #60 #55)
-#10318 := (= f1 #2314)
-#10314 := (= f1 #2311)
-#10321 := (iff #10314 #10318)
-#10324 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #10321)
-#17924 := (~ #10324 #10324)
-#17922 := (~ #10321 #10321)
-#17923 := [refl]: #17922
-#17925 := [nnf-pos #17923]: #17924
-#2315 := (= #2314 f1)
-#2313 := (= #2311 f1)
-#2316 := (iff #2313 #2315)
-#2317 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20) (?v3 S31)) (:pat #2312) #2316)
-#10325 := (iff #2317 #10324)
-#10322 := (iff #2316 #10321)
-#10319 := (iff #2315 #10318)
-#10320 := [rewrite]: #10319
-#10316 := (iff #2313 #10314)
-#10317 := [rewrite]: #10316
-#10323 := [monotonicity #10317 #10320]: #10322
-#10326 := [quant-intro #10323]: #10325
-#10313 := [asserted]: #2317
-#10329 := [mp #10313 #10326]: #10324
-#17926 := [mp~ #10329 #17925]: #10324
-#26731 := (not #10324)
-#26749 := (or #26731 #26719)
-#26718 := (iff #26717 #26715)
-#26734 := (or #26731 #26718)
-#26738 := (iff #26734 #26749)
-#26739 := (iff #26749 #26749)
-#26740 := [rewrite]: #26739
-#26720 := (iff #26718 #26719)
-#26721 := [rewrite]: #26720
-#26735 := [monotonicity #26721]: #26738
-#26741 := [trans #26735 #26740]: #26738
-#26737 := [quant-inst #3039 #26182 #26182 #3095]: #26734
-#26742 := [mp #26737 #26741]: #26749
-#26937 := [unit-resolution #26742 #17926]: #26719
-#28782 := (= #3096 #26716)
-#26939 := (= #26716 #3096)
-#26934 := (= #26182 #3044)
-#26940 := [symm #28848]: #26934
-#26966 := [monotonicity #26940 #26940]: #26939
-#28799 := [symm #26966]: #28782
-#26828 := (f23 #26586)
-#26831 := (= f25 #26828)
-#26933 := (not #26831)
-#26947 := (iff #12118 #26933)
-#26950 := (iff #12115 #26831)
-#26948 := (iff #26831 #12115)
-#26960 := (= #26828 #3053)
-#26943 := (= #26586 #3040)
-#25117 := (f24 #3044)
-#28850 := (= #25117 #3040)
-#25120 := (= #3040 #25117)
-#25125 := (or #25064 #25120)
-#25126 := [quant-inst #3040 #3043]: #25125
-#28849 := [unit-resolution #25126 #23312]: #25120
-#28851 := [symm #28849]: #28850
-#26941 := (= #26586 #25117)
-#26942 := [monotonicity #26940]: #26941
-#26944 := [trans #26942 #28851]: #26943
-#26946 := [monotonicity #26944]: #26960
-#26949 := [monotonicity #26946]: #26948
-#26951 := [symm #26949]: #26950
-#26935 := [monotonicity #26951]: #26947
-#14369 := [and-elim #14364]: #12118
-#26936 := [mp #14369 #26935]: #26933
-#26736 := (not #26715)
-#26733 := (not #26717)
-#26958 := (iff #13300 #26733)
-#26969 := (iff #12177 #26717)
-#26967 := (iff #26717 #12177)
-#26968 := [monotonicity #26966]: #26967
-#26957 := [symm #26968]: #26969
-#26959 := [monotonicity #26957]: #26958
-#26938 := [hypothesis]: #13300
-#26972 := [mp #26938 #26959]: #26733
-#26722 := (not #26719)
-#26753 := (or #26722 #26736 #26717)
-#26754 := [def-axiom]: #26753
-#26974 := [unit-resolution #26754 #26972 #26937]: #26736
-#26820 := (f35 f297 #26182)
-#26821 := (= f1 #26820)
-#26965 := (= #3051 #26820)
-#26975 := (= #26820 #3051)
-#26963 := [monotonicity #26940]: #26975
-#26961 := [symm #26963]: #26965
-#14368 := [and-elim #14364]: #12112
-#26973 := [trans #14368 #26961]: #26821
-#26823 := (f59 #26182 #26586)
-#26824 := (= f1 #26823)
-#26978 := (= #3049 #26823)
-#26976 := (= #26823 #3049)
-#26962 := [monotonicity #26940 #26944]: #26976
-#26979 := [symm #26962]: #26978
-#26980 := [trans #14367 #26979]: #26824
-#26825 := (not #26824)
-#26822 := (not #26821)
-#27030 := (or #26715 #26822 #26825 #26831)
-#26598 := (f36 f297 #26182)
-#26826 := (= f37 #26598)
-#26989 := (= #3047 #26598)
-#26981 := (= #26598 #3047)
-#26987 := [monotonicity #26940]: #26981
-#27001 := [symm #26987]: #26989
-#14366 := [and-elim #14364]: #12106
-#27002 := [trans #14366 #27001]: #26826
-#27008 := (= #3045 #26626)
-#27003 := (= #26626 #3045)
-#27004 := [monotonicity #26940]: #27003
-#27009 := [symm #27004]: #27008
-#14365 := [and-elim #14364]: #12102
-#27010 := [trans #14365 #27009]: #26627
-#26587 := (f34 #26586)
-#26594 := (= f1 #26587)
-#27019 := (= #3056 #26587)
-#26996 := (= #26587 #3056)
-#26997 := [monotonicity #26944]: #26996
-#27020 := [symm #26997]: #27019
-#14370 := [and-elim #14364]: #12121
-#27029 := [trans #14370 #27020]: #26594
-#14349 := [not-or-elim #14346]: #12148
-#14351 := [and-elim #14349]: #12145
-#2270 := (f207 #86 #62 #62)
-#2271 := (pattern #2270)
-#10190 := (= f1 #2270)
-#269 := (f66 #86)
-#4055 := (= f1 #269)
-#19481 := (not #4055)
-#184 := (f59 #62 #65)
-#3764 := (= f1 #184)
-#19355 := (not #3764)
-#19354 := (not #3761)
-#175 := (f38 #86 #62)
-#3746 := (= f1 #175)
-#10910 := (not #3746)
-#110 := (f34 #65)
-#3595 := (= f1 #110)
-#10969 := (not #3595)
-#21914 := (or #68 #10969 #10910 #19354 #19355 #11297 #19481 #10190)
-#21919 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #21914)
-#10205 := (and #91 #3595 #3746 #3761 #3764 #3767 #4055)
-#10208 := (not #10205)
-#10214 := (or #10190 #10208)
-#10219 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10214)
-#21920 := (iff #10219 #21919)
-#21917 := (iff #10214 #21914)
-#21900 := (or #68 #10969 #10910 #19354 #19355 #11297 #19481)
-#21911 := (or #10190 #21900)
-#21915 := (iff #21911 #21914)
-#21916 := [rewrite]: #21915
-#21912 := (iff #10214 #21911)
-#21909 := (iff #10208 #21900)
-#21901 := (not #21900)
-#21904 := (not #21901)
-#21907 := (iff #21904 #21900)
-#21908 := [rewrite]: #21907
-#21905 := (iff #10208 #21904)
-#21902 := (iff #10205 #21901)
-#21903 := [rewrite]: #21902
-#21906 := [monotonicity #21903]: #21905
-#21910 := [trans #21906 #21908]: #21909
-#21913 := [monotonicity #21910]: #21912
-#21918 := [trans #21913 #21916]: #21917
-#21921 := [quant-intro #21918]: #21920
-#17892 := (~ #10219 #10219)
-#17890 := (~ #10214 #10214)
-#17891 := [refl]: #17890
-#17893 := [nnf-pos #17891]: #17892
-#2278 := (= #2270 f1)
-#111 := (= #110 f1)
-#2272 := (and #91 #111)
-#2273 := (and #187 #2272)
-#185 := (= #184 f1)
-#2274 := (and #185 #2273)
-#2275 := (and #183 #2274)
-#176 := (= #175 f1)
-#2276 := (and #176 #2275)
-#271 := (= #269 f1)
-#2277 := (and #271 #2276)
-#2279 := (implies #2277 #2278)
-#2280 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #2279)
-#10222 := (iff #2280 #10219)
-#10171 := (and #91 #3595)
-#10175 := (and #3767 #10171)
-#10178 := (and #3764 #10175)
-#10181 := (and #3761 #10178)
-#10184 := (and #3746 #10181)
-#10187 := (and #4055 #10184)
-#10196 := (not #10187)
-#10197 := (or #10196 #10190)
-#10202 := (forall (vars (?v0 S19) (?v1 S20)) (:pat #2271) #10197)
-#10220 := (iff #10202 #10219)
-#10217 := (iff #10197 #10214)
-#10211 := (or #10208 #10190)
-#10215 := (iff #10211 #10214)
-#10216 := [rewrite]: #10215
-#10212 := (iff #10197 #10211)
-#10209 := (iff #10196 #10208)
-#10206 := (iff #10187 #10205)
-#10207 := [rewrite]: #10206
-#10210 := [monotonicity #10207]: #10209
-#10213 := [monotonicity #10210]: #10212
-#10218 := [trans #10213 #10216]: #10217
-#10221 := [quant-intro #10218]: #10220
-#10203 := (iff #2280 #10202)
-#10200 := (iff #2279 #10197)
-#10193 := (implies #10187 #10190)
-#10198 := (iff #10193 #10197)
-#10199 := [rewrite]: #10198
-#10194 := (iff #2279 #10193)
-#10191 := (iff #2278 #10190)
-#10192 := [rewrite]: #10191
-#10188 := (iff #2277 #10187)
-#10185 := (iff #2276 #10184)
-#10182 := (iff #2275 #10181)
-#10179 := (iff #2274 #10178)
-#10176 := (iff #2273 #10175)
-#10173 := (iff #2272 #10171)
-#3596 := (iff #111 #3595)
-#3597 := [rewrite]: #3596
-#10174 := [monotonicity #3597]: #10173
-#10177 := [monotonicity #3769 #10174]: #10176
-#3765 := (iff #185 #3764)
-#3766 := [rewrite]: #3765
-#10180 := [monotonicity #3766 #10177]: #10179
-#10183 := [monotonicity #3763 #10180]: #10182
-#3748 := (iff #176 #3746)
-#3749 := [rewrite]: #3748
-#10186 := [monotonicity #3749 #10183]: #10185
-#4057 := (iff #271 #4055)
-#4058 := [rewrite]: #4057
-#10189 := [monotonicity #4058 #10186]: #10188
-#10195 := [monotonicity #10189 #10192]: #10194
-#10201 := [trans #10195 #10199]: #10200
-#10204 := [quant-intro #10201]: #10203
-#10223 := [trans #10204 #10221]: #10222
-#10170 := [asserted]: #2280
-#10224 := [mp #10170 #10223]: #10219
-#17894 := [mp~ #10224 #17893]: #10219
-#21922 := [mp #17894 #21921]: #21919
-#26827 := (not #26826)
-#26595 := (not #26594)
-#24846 := (not #12145)
-#26800 := (not #21919)
-#26802 := (or #26800 #24846 #26595 #26649 #26715 #26822 #26825 #26827 #26831)
-#26829 := (= #26828 f25)
-#26830 := (or #26829 #26595 #26649 #26827 #26825 #26822 #24846 #26715)
-#26803 := (or #26800 #26830)
-#26843 := (iff #26803 #26802)
-#26837 := (or #24846 #26595 #26649 #26715 #26822 #26825 #26827 #26831)
-#26805 := (or #26800 #26837)
-#26847 := (iff #26805 #26802)
-#26848 := [rewrite]: #26847
-#26844 := (iff #26803 #26805)
-#26840 := (iff #26830 #26837)
-#26834 := (or #26831 #26595 #26649 #26827 #26825 #26822 #24846 #26715)
-#26838 := (iff #26834 #26837)
-#26839 := [rewrite]: #26838
-#26835 := (iff #26830 #26834)
-#26832 := (iff #26829 #26831)
-#26833 := [rewrite]: #26832
-#26836 := [monotonicity #26833]: #26835
-#26841 := [trans #26836 #26839]: #26840
-#26846 := [monotonicity #26841]: #26844
-#26849 := [trans #26846 #26848]: #26843
-#26804 := [quant-inst #3039 #26182]: #26803
-#26845 := [mp #26804 #26849]: #26802
-#27031 := [unit-resolution #26845 #21922 #14351 #27029 #27010 #27002]: #27030
-#27032 := [unit-resolution #27031 #26980 #26973 #26974 #26936]: false
-#27033 := [lemma #27032]: #12177
-#28800 := [trans #27033 #28799]: #26717
-#26724 := (or #26722 #26715 #26733)
-#26751 := [def-axiom]: #26724
-#28801 := [unit-resolution #26751 #28800 #26937]: #26715
-#26797 := (or #26736 #26794)
-#54 := (:var 2 S19)
-#2218 := (f207 #54 #55 #62)
-#2281 := (pattern #2218)
-#2282 := (f64 #53 #60)
-#2283 := (f26 #62 #2282)
-#2284 := (pattern #2283)
-#2210 := (f22 #53 #55)
-#2290 := (f203 #2210)
-#2291 := (f158 #62 #2290)
-#10238 := (= f1 #2291)
-#10232 := (= f1 #2283)
-#21923 := (not #10232)
-#1425 := (f24 #60)
-#2285 := (f208 #1425)
-#10226 := (= f1 #2285)
-#21938 := (or #10226 #21923 #10238)
-#21943 := (forall (vars (?v3 S20)) (:pat #2284) #21938)
-#21949 := (not #21943)
-#2197 := (f27 #54 #62)
-#2198 := (f26 #55 #2197)
-#9926 := (= f1 #2198)
-#21758 := (not #9926)
-#221 := (f38 #54 #55)
-#3873 := (= f1 #221)
-#10576 := (not #3873)
-#21950 := (or #10576 #21758 #21949)
-#21951 := (not #21950)
-#9974 := (= f1 #2218)
-#10262 := (not #9974)
-#21956 := (or #10262 #21951)
-#21959 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #21956)
-#10229 := (not #10226)
-#10235 := (and #10229 #10232)
-#10244 := (not #10235)
-#10245 := (or #10244 #10238)
-#10250 := (forall (vars (?v3 S20)) (:pat #2284) #10245)
-#10271 := (and #3873 #9926 #10250)
-#10274 := (or #10262 #10271)
-#10277 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10274)
-#21960 := (iff #10277 #21959)
-#21957 := (iff #10274 #21956)
-#21954 := (iff #10271 #21951)
-#21946 := (and #3873 #9926 #21943)
-#21952 := (iff #21946 #21951)
-#21953 := [rewrite]: #21952
-#21947 := (iff #10271 #21946)
-#21944 := (iff #10250 #21943)
-#21941 := (iff #10245 #21938)
-#21924 := (or #10226 #21923)
-#21935 := (or #21924 #10238)
-#21939 := (iff #21935 #21938)
-#21940 := [rewrite]: #21939
-#21936 := (iff #10245 #21935)
-#21933 := (iff #10244 #21924)
-#21925 := (not #21924)
-#21928 := (not #21925)
-#21931 := (iff #21928 #21924)
-#21932 := [rewrite]: #21931
-#21929 := (iff #10244 #21928)
-#21926 := (iff #10235 #21925)
-#21927 := [rewrite]: #21926
-#21930 := [monotonicity #21927]: #21929
-#21934 := [trans #21930 #21932]: #21933
-#21937 := [monotonicity #21934]: #21936
-#21942 := [trans #21937 #21940]: #21941
-#21945 := [quant-intro #21942]: #21944
-#21948 := [monotonicity #21945]: #21947
-#21955 := [trans #21948 #21953]: #21954
-#21958 := [monotonicity #21955]: #21957
-#21961 := [quant-intro #21958]: #21960
-#17909 := (~ #10277 #10277)
-#17907 := (~ #10274 #10274)
-#17905 := (~ #10271 #10271)
-#17903 := (~ #10250 #10250)
-#17901 := (~ #10245 #10245)
-#17902 := [refl]: #17901
-#17904 := [nnf-pos #17902]: #17903
-#17899 := (~ #9926 #9926)
-#17900 := [refl]: #17899
-#17897 := (~ #3873 #3873)
-#17898 := [refl]: #17897
-#17906 := [monotonicity #17898 #17900 #17904]: #17905
-#17895 := (~ #10262 #10262)
-#17896 := [refl]: #17895
-#17908 := [monotonicity #17896 #17906]: #17907
-#17910 := [nnf-pos #17908]: #17909
-#2292 := (= #2291 f1)
-#2288 := (= #2283 f1)
-#2286 := (= #2285 f1)
-#2287 := (not #2286)
-#2289 := (and #2287 #2288)
-#2293 := (implies #2289 #2292)
-#2294 := (forall (vars (?v3 S20)) (:pat #2284) #2293)
-#225 := (= #221 f1)
-#2295 := (and #225 #2294)
-#2203 := (= #2198 f1)
-#2296 := (and #2203 #2295)
-#2219 := (= #2218 f1)
-#2297 := (implies #2219 #2296)
-#2298 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #2297)
-#10280 := (iff #2298 #10277)
-#10253 := (and #3873 #10250)
-#10256 := (and #9926 #10253)
-#10263 := (or #10262 #10256)
-#10268 := (forall (vars (?v0 S19) (?v1 S20) (?v2 S20)) (:pat #2281) #10263)
-#10278 := (iff #10268 #10277)
-#10275 := (iff #10263 #10274)
-#10272 := (iff #10256 #10271)
-#10273 := [rewrite]: #10272
-#10276 := [monotonicity #10273]: #10275
-#10279 := [quant-intro #10276]: #10278
-#10269 := (iff #2298 #10268)
-#10266 := (iff #2297 #10263)
-#10259 := (implies #9974 #10256)
-#10264 := (iff #10259 #10263)
-#10265 := [rewrite]: #10264
-#10260 := (iff #2297 #10259)
-#10257 := (iff #2296 #10256)
-#10254 := (iff #2295 #10253)
-#10251 := (iff #2294 #10250)
-#10248 := (iff #2293 #10245)
-#10241 := (implies #10235 #10238)
-#10246 := (iff #10241 #10245)
-#10247 := [rewrite]: #10246
-#10242 := (iff #2293 #10241)
-#10239 := (iff #2292 #10238)
-#10240 := [rewrite]: #10239
-#10236 := (iff #2289 #10235)
-#10233 := (iff #2288 #10232)
-#10234 := [rewrite]: #10233
-#10230 := (iff #2287 #10229)
-#10227 := (iff #2286 #10226)
-#10228 := [rewrite]: #10227
-#10231 := [monotonicity #10228]: #10230
-#10237 := [monotonicity #10231 #10234]: #10236
-#10243 := [monotonicity #10237 #10240]: #10242
-#10249 := [trans #10243 #10247]: #10248
-#10252 := [quant-intro #10249]: #10251
-#3874 := (iff #225 #3873)
-#3875 := [rewrite]: #3874
-#10255 := [monotonicity #3875 #10252]: #10254
-#9927 := (iff #2203 #9926)
-#9928 := [rewrite]: #9927
-#10258 := [monotonicity #9928 #10255]: #10257
-#9975 := (iff #2219 #9974)
-#9976 := [rewrite]: #9975
-#10261 := [monotonicity #9976 #10258]: #10260
-#10267 := [trans #10261 #10265]: #10266
-#10270 := [quant-intro #10267]: #10269
-#10281 := [trans #10270 #10279]: #10280
-#10225 := [asserted]: #2298
-#10282 := [mp #10225 #10281]: #10277
-#17911 := [mp~ #10282 #17910]: #10277
-#21962 := [mp #17911 #21961]: #21959
-#26806 := (not #21959)
-#26801 := (or #26806 #26736 #26794)
-#26771 := (or #26770 #26768 #26764)
-#26773 := (forall (vars (?v3 S20)) (:pat #26772) #26771)
-#26774 := (not #26773)
-#26779 := (or #26649 #26778 #26774)
-#26780 := (not #26779)
-#26781 := (or #26736 #26780)
-#26758 := (or #26806 #26781)
-#26852 := (iff #26758 #26801)
-#26808 := (or #26806 #26797)
-#26811 := (iff #26808 #26801)
-#26850 := [rewrite]: #26811
-#26809 := (iff #26758 #26808)
-#26798 := (iff #26781 #26797)
-#26795 := (iff #26780 #26794)
-#26792 := (iff #26779 #26791)
-#26789 := (iff #26774 #26788)
-#26786 := (iff #26773 #26785)
-#26783 := (iff #26771 #26782)
-#26784 := [rewrite]: #26783
-#26787 := [quant-intro #26784]: #26786
-#26790 := [monotonicity #26787]: #26789
-#26793 := [monotonicity #26790]: #26792
-#26796 := [monotonicity #26793]: #26795
-#26799 := [monotonicity #26796]: #26798
-#26810 := [monotonicity #26799]: #26809
-#26853 := [trans #26810 #26850]: #26852
-#26807 := [quant-inst #3039 #26182 #26182]: #26758
-#26858 := [mp #26807 #26853]: #26801
-#28802 := [unit-resolution #26858 #21962]: #26797
-#28803 := [unit-resolution #28802 #28801]: #26794
-#26851 := (or #26791 #26777)
-#26863 := [def-axiom]: #26851
-#28804 := [unit-resolution #26863 #28803]: #26777
-#28797 := [trans #28804 #28796]: #27234
-#27235 := (not #27234)
-#27547 := (or #12183 #27235)
-#27223 := (f54 #24996 #3043)
-#27224 := (f77 #27223 0::Int #24996)
-#27228 := (f35 f297 #27224)
-#27229 := (= f1 #27228)
-#27230 := (not #27229)
-#27503 := (iff #18448 #27230)
-#27491 := (iff #12183 #27229)
-#27489 := (iff #27229 #12183)
-#27487 := (= #27228 #3101)
-#27486 := (= #27224 #3098)
-#28392 := (= #27223 #3042)
-#28393 := [monotonicity #28386 #28391]: #28392
-#27481 := [monotonicity #28393 #28386]: #27486
-#27488 := [monotonicity #27481]: #27487
-#27490 := [monotonicity #27488]: #27489
-#27502 := [symm #27490]: #27491
-#27511 := [monotonicity #27502]: #27503
-#27485 := [hypothesis]: #18448
-#27512 := [mp #27485 #27511]: #27230
-#27225 := (f69 #3220 #27224)
-#27226 := (f147 #27225)
-#27227 := (= f1 #27226)
-#27240 := (or #27227 #27230)
-#27243 := (not #27240)
-decl f33 :: (-> S18 S1)
-#27236 := (f33 #24996)
-#27237 := (= f1 #27236)
-#2848 := (f33 f19)
-#28424 := (= #2848 #27236)
-#28421 := (= #27236 #2848)
-#28422 := [monotonicity #28386]: #28421
-#28425 := [symm #28422]: #28424
-#11624 := (= f1 #2848)
-#2849 := (= #2848 f1)
-#11626 := (iff #2849 #11624)
-#11627 := [rewrite]: #11626
-#11623 := [asserted]: #2849
-#11630 := [mp #11623 #11627]: #11624
-#28426 := [trans #11630 #28425]: #27237
-#27238 := (not #27237)
-#27517 := (or #27238 #27243)
-#28427 := [hypothesis]: #27234
-#27181 := (<= #24998 0::Int)
-#27514 := (not #27181)
-#14360 := [not-or-elim #14346]: #13509
-#27164 := (* -1::Int #24998)
-#27273 := (+ f296 #27164)
-#27274 := (<= #27273 0::Int)
-#28407 := (not #24999)
-#28408 := (or #28407 #27274)
-#28409 := [th-lemma arith triangle-eq]: #28408
-#28410 := [unit-resolution #28409 #28406]: #27274
-#28416 := (not #27274)
-#27515 := (or #27514 #13508 #28416)
-#27510 := [th-lemma arith assign-bounds -1 1]: #27515
-#27516 := [unit-resolution #27510 #28410 #14360]: #27514
-#279 := (f33 #275)
-#805 := (:var 4 Int)
-#2121 := (f54 #275 #805)
-#2122 := (f77 #2121 #289 #275)
-#1416 := (:var 5 S19)
-#2138 := (f36 #1416 #2122)
-#1408 := (:var 3 S20)
-#2119 := (f27 #1416 #1408)
-#310 := (:var 2 Int)
-#2117 := (f135 #275 #310)
-#2118 := (f54 #2117 #805)
-#2120 := (f26 #2118 #2119)
-#2139 := (pattern #2120 #2138 #279)
-#1590 := (f70 #1416)
-#2136 := (f69 #1590 #2122)
-#2137 := (pattern #2120 #2136 #279)
-#2142 := (f147 #2136)
-#9734 := (= f1 #2142)
-#2140 := (f35 #1416 #2122)
-#9731 := (= f1 #2140)
-#21668 := (not #9731)
-#21669 := (or #21668 #9734)
-#21670 := (not #21669)
-#9675 := (= f1 #2120)
-#21644 := (not #9675)
-#2125 := (f66 #1416)
-#9672 := (= f1 #2125)
-#21643 := (not #9672)
-#4206 := (* -1::Int #310)
-#6270 := (+ #289 #4206)
-#6867 := (>= #6270 0::Int)
-#4468 := (>= #289 0::Int)
-#19581 := (not #4468)
-#4084 := (= f1 #279)
-#10461 := (not #4084)
-#21676 := (or #10461 #19581 #6867 #21643 #21644 #21670)
-#21681 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #21676)
-#9737 := (not #9734)
-#9740 := (and #9731 #9737)
-#7934 := (not #6867)
-#9713 := (and #4084 #4468 #7934 #9672 #9675)
-#9718 := (not #9713)
-#9754 := (or #9718 #9740)
-#9757 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9754)
-#21682 := (iff #9757 #21681)
-#21679 := (iff #9754 #21676)
-#21645 := (or #10461 #19581 #6867 #21643 #21644)
-#21673 := (or #21645 #21670)
-#21677 := (iff #21673 #21676)
-#21678 := [rewrite]: #21677
-#21674 := (iff #9754 #21673)
-#21671 := (iff #9740 #21670)
-#21672 := [rewrite]: #21671
-#21654 := (iff #9718 #21645)
-#21646 := (not #21645)
-#21649 := (not #21646)
-#21652 := (iff #21649 #21645)
-#21653 := [rewrite]: #21652
-#21650 := (iff #9718 #21649)
-#21647 := (iff #9713 #21646)
-#21648 := [rewrite]: #21647
-#21651 := [monotonicity #21648]: #21650
-#21655 := [trans #21651 #21653]: #21654
-#21675 := [monotonicity #21655 #21672]: #21674
-#21680 := [trans #21675 #21678]: #21679
-#21683 := [quant-intro #21680]: #21682
-#17775 := (~ #9757 #9757)
-#17773 := (~ #9754 #9754)
-#17774 := [refl]: #17773
-#17776 := [nnf-pos #17774]: #17775
-#2143 := (= #2142 f1)
-#2144 := (not #2143)
-#2141 := (= #2140 f1)
-#2145 := (and #2141 #2144)
-#1477 := (< #289 #310)
-#440 := (<= 0::Int #289)
-#1478 := (and #440 #1477)
-#2127 := (= #2120 f1)
-#2128 := (and #2127 #1478)
-#280 := (= #279 f1)
-#2129 := (and #280 #2128)
-#2126 := (= #2125 f1)
-#2130 := (and #2126 #2129)
-#2146 := (implies #2130 #2145)
-#2147 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #2146)
-#9760 := (iff #2147 #9757)
-#9681 := (and #1478 #9675)
-#9686 := (and #4084 #9681)
-#9689 := (and #9672 #9686)
-#9695 := (not #9689)
-#9746 := (or #9695 #9740)
-#9751 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S20) (?v3 Int) (?v4 Int) (?v5 S18)) (:pat #2137 #2139) #9746)
-#9758 := (iff #9751 #9757)
-#9755 := (iff #9746 #9754)
-#9719 := (iff #9695 #9718)
-#9716 := (iff #9689 #9713)
-#7937 := (and #4468 #7934)
-#9704 := (and #7937 #9675)
-#9707 := (and #4084 #9704)
-#9710 := (and #9672 #9707)
-#9714 := (iff #9710 #9713)
-#9715 := [rewrite]: #9714
-#9711 := (iff #9689 #9710)
-#9708 := (iff #9686 #9707)
-#9705 := (iff #9681 #9704)
-#7938 := (iff #1478 #7937)
-#7935 := (iff #1477 #7934)
-#7936 := [rewrite]: #7935
-#4467 := (iff #440 #4468)
-#4469 := [rewrite]: #4467
-#7939 := [monotonicity #4469 #7936]: #7938
-#9706 := [monotonicity #7939]: #9705
-#9709 := [monotonicity #9706]: #9708
-#9712 := [monotonicity #9709]: #9711
-#9717 := [trans #9712 #9715]: #9716
-#9720 := [monotonicity #9717]: #9719
-#9756 := [monotonicity #9720]: #9755
-#9759 := [quant-intro #9756]: #9758
-#9752 := (iff #2147 #9751)
-#9749 := (iff #2146 #9746)
-#9743 := (implies #9689 #9740)
-#9747 := (iff #9743 #9746)
-#9748 := [rewrite]: #9747
-#9744 := (iff #2146 #9743)
-#9741 := (iff #2145 #9740)
-#9738 := (iff #2144 #9737)
-#9735 := (iff #2143 #9734)
-#9736 := [rewrite]: #9735
-#9739 := [monotonicity #9736]: #9738
-#9732 := (iff #2141 #9731)
-#9733 := [rewrite]: #9732
-#9742 := [monotonicity #9733 #9739]: #9741
-#9690 := (iff #2130 #9689)
-#9687 := (iff #2129 #9686)
-#9684 := (iff #2128 #9681)
-#9678 := (and #9675 #1478)
-#9682 := (iff #9678 #9681)
+#12174 := [monotonicity #12162 #12171]: #12173
+#13255 := [monotonicity #12174 #13252]: #13254
+#13261 := [trans #13255 #13259]: #13260
+#13264 := [monotonicity #12174 #13261]: #13263
+#12167 := (iff #3096 #12166)
+#12164 := (iff #3095 #12163)
+#12165 := [rewrite]: #12164
+#12168 := [monotonicity #12162 #12165]: #12167
+#13267 := [monotonicity #12168 #13264]: #13266
+#13273 := [trans #13267 #13271]: #13272
+#13276 := [monotonicity #12168 #13273]: #13275
+#12158 := (iff #3090 #12157)
+#12159 := [rewrite]: #12158
+#13279 := [monotonicity #12159 #13276]: #13278
+#13285 := [trans #13279 #13283]: #13284
+#13288 := [monotonicity #12159 #13285]: #13287
+#13291 := [monotonicity #13288]: #13290
+#13297 := [trans #13291 #13295]: #13296
+#12155 := (iff #3084 #12154)
+#12152 := (iff #3083 #12149)
+#12146 := (iff #12143 false)
+#12150 := (iff #12146 #12149)
+#12151 := [rewrite]: #12150
+#12147 := (iff #3083 #12146)
+#12144 := (iff #3082 #12143)
+#12145 := [rewrite]: #12144
+#12148 := [monotonicity #12145]: #12147
+#12153 := [trans #12148 #12151]: #12152
+#12156 := [quant-intro #12153]: #12155
+#13300 := [monotonicity #12156 #13297]: #13299
+#13306 := [trans #13300 #13304]: #13305
+#13309 := [monotonicity #13306]: #13308
+#13315 := [trans #13309 #13313]: #13314
+#12141 := (iff #3076 #12140)
+#12142 := [rewrite]: #12141
+#13318 := [monotonicity #12142 #13315]: #13317
+#13324 := [trans #13318 #13322]: #13323
+#12138 := (iff #3074 #12137)
+#12135 := (iff #3073 #12134)
+#12136 := [rewrite]: #12135
+#12132 := (iff #3071 #12131)
+#12133 := [rewrite]: #12132
+#12139 := [monotonicity #12133 #12136]: #12138
+#13327 := [monotonicity #12139 #13324]: #13326
+#13333 := [trans #13327 #13331]: #13332
+#13336 := [monotonicity #13333]: #13335
+#13342 := [trans #13336 #13340]: #13341
+#12129 := (iff #3062 #12128)
+#12123 := (iff #3059 #12122)
+#12124 := [rewrite]: #12123
+#12130 := [monotonicity #12124 #12127]: #12129
+#13345 := [monotonicity #12130 #13342]: #13344
+#13351 := [trans #13345 #13349]: #13350
+#12120 := (iff #3057 #12119)
+#12121 := [rewrite]: #12120
+#13354 := [monotonicity #12121 #13351]: #13353
+#13360 := [trans #13354 #13358]: #13359
+#12117 := (iff #3055 #12116)
+#12114 := (iff #3054 #12113)
+#12111 := (iff #3053 #12110)
+#12108 := (iff #3052 #12107)
+#12105 := (iff #3051 #12104)
+#12102 := (iff #3050 #12101)
+#12103 := [rewrite]: #12102
+#12099 := (iff #3048 #12098)
+#12096 := (iff #3047 #12095)
+#12097 := [rewrite]: #12096
+#12100 := [monotonicity #12097]: #12099
+#12106 := [monotonicity #12100 #12103]: #12105
+#12093 := (iff #3045 #12092)
+#12094 := [rewrite]: #12093
+#12109 := [monotonicity #12094 #12106]: #12108
+#12090 := (iff #3043 #12089)
+#12091 := [rewrite]: #12090
+#12112 := [monotonicity #12091 #12109]: #12111
+#12087 := (iff #3041 #12086)
+#12088 := [rewrite]: #12087
+#12115 := [monotonicity #12088 #12112]: #12114
+#12084 := (iff #3039 #12083)
+#12085 := [rewrite]: #12084
+#12118 := [monotonicity #12085 #12115]: #12117
+#13363 := [monotonicity #12118 #13360]: #13362
+#13369 := [trans #13363 #13367]: #13368
+#13372 := [monotonicity #13369]: #13371
+#13378 := [trans #13372 #13376]: #13377
+#13381 := [monotonicity #13378]: #13380
+#13387 := [trans #13381 #13385]: #13386
+#13390 := [monotonicity #13387]: #13389
+#13396 := [trans #13390 #13394]: #13395
+#13399 := [monotonicity #13396]: #13398
+#13405 := [trans #13399 #13403]: #13404
+#13408 := [monotonicity #13405]: #13407
+#13414 := [trans #13408 #13412]: #13413
+#13417 := [monotonicity #13414]: #13416
+#14325 := [trans #13417 #14323]: #14324
+#12081 := [asserted]: #3399
+#14326 := [mp #12081 #14325]: #14321
+#14344 := [not-or-elim #14326]: #14208
+#14347 := [and-elim #14344]: #12089
+#11323 := (not #11316)
+#1268 := (f117 #21)
+#2698 := (f44 #241 #1268)
+#2699 := (= #21 #2698)
+#11324 := (or #2699 #11323)
+#11329 := (forall (vars (?v0 S5) (?v1 S3)) (:pat #2696) #11324)
+#18237 := (~ #11329 #11329)
+#18235 := (~ #11324 #11324)
+#18236 := [refl]: #18235
+#18238 := [nnf-pos #18236]: #18237
+#2700 := (implies #2697 #2699)
+#2701 := (forall (vars (?v0 S5) (?v1 S3)) (:pat #2696) #2700)
+#11330 := (iff #2701 #11329)
+#11327 := (iff #2700 #11324)
+#11320 := (implies #11316 #2699)
+#11325 := (iff #11320 #11324)
+#11326 := [rewrite]: #11325
+#11321 := (iff #2700 #11320)
+#11322 := [monotonicity #11319]: #11321
+#11328 := [trans #11322 #11326]: #11327
+#11331 := [quant-intro #11328]: #11330
+#11315 := [asserted]: #2701
+#11334 := [mp #11315 #11331]: #11329
+#18239 := [mp~ #11334 #18238]: #11329
+#26160 := (not #12089)
+#26173 := (not #11329)
+#26174 := (or #26173 #26160 #26168)
+#26169 := (or #26168 #26160)
+#26175 := (or #26173 #26169)
+#26182 := (iff #26175 #26174)
+#26170 := (or #26160 #26168)
+#26177 := (or #26173 #26170)
+#26180 := (iff #26177 #26174)
+#26181 := [rewrite]: #26180
+#26178 := (iff #26175 #26177)
+#26171 := (iff #26169 #26170)
+#26172 := [rewrite]: #26171
+#26179 := [monotonicity #26172]: #26178
+#26183 := [trans #26179 #26181]: #26182
+#26176 := [quant-inst #3037 #3033]: #26175
+#26184 := [mp #26176 #26183]: #26174
+#28827 := [unit-resolution #26184 #18239 #14347]: #26168
+#28770 := [trans #28768 #28827]: #28769
+#28772 := [monotonicity #28770]: #28771
+#28775 := [symm #28772]: #28774
+#26756 := (= f1 #26755)
+decl f54 :: (-> S4 S5 S6)
+#26744 := (f54 f292 #26161)
+#26745 := (f16 #28 #26744)
+#26751 := (pattern #26745)
+decl f198 :: (-> S3 S1)
+#26565 := (f14 #26161)
+#26748 := (f198 #26565)
+#26749 := (= f1 #26748)
+#26746 := (= f1 #26745)
+#26747 := (not #26746)
+decl f148 :: (-> S5 S6 S1)
+decl f193 :: (-> S7 S6)
+decl f12 :: (-> S4 S5 S7)
+#26740 := (f12 f292 #26161)
+#26741 := (f193 #26740)
+#26742 := (f148 #28 #26741)
+#26743 := (= f1 #26742)
+#26761 := (or #26743 #26747 #26749)
+#26764 := (forall (vars (?v3 S5)) (:pat #26751) #26761)
+#26767 := (not #26764)
+#26757 := (not #26756)
+#26605 := (f28 f292 #26161)
+#26606 := (= f1 #26605)
+#26628 := (not #26606)
+#26770 := (or #26628 #26757 #26767)
+#26773 := (not #26770)
+decl f197 :: (-> S4 S5 S5 S1)
+#26693 := (f197 f292 #26161 #26161)
+#26694 := (= f1 #26693)
+#26695 := (f201 f292 #26161 #26161 f300)
+#26696 := (= f1 #26695)
+#26698 := (iff #26694 #26696)
+#2265 := (:var 0 S16)
+#19 := (:var 3 S4)
+#2277 := (f201 #19 #26 #21 #2265)
+#2278 := (pattern #2277)
+#2280 := (f197 #19 #26 #21)
+#10265 := (= f1 #2280)
+#10261 := (= f1 #2277)
+#10268 := (iff #10261 #10265)
+#10271 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5) (?v3 S16)) (:pat #2278) #10268)
+#17879 := (~ #10271 #10271)
+#17877 := (~ #10268 #10268)
+#17878 := [refl]: #17877
+#17880 := [nnf-pos #17878]: #17879
+#2281 := (= #2280 f1)
+#2279 := (= #2277 f1)
+#2282 := (iff #2279 #2281)
+#2283 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5) (?v3 S16)) (:pat #2278) #2282)
+#10272 := (iff #2283 #10271)
+#10269 := (iff #2282 #10268)
+#10266 := (iff #2281 #10265)
+#10267 := [rewrite]: #10266
+#10263 := (iff #2279 #10261)
+#10264 := [rewrite]: #10263
+#10270 := [monotonicity #10264 #10267]: #10269
+#10273 := [quant-intro #10270]: #10272
+#10260 := [asserted]: #2283
+#10276 := [mp #10260 #10273]: #10271
+#17881 := [mp~ #10276 #17880]: #10271
+#26710 := (not #10271)
+#26728 := (or #26710 #26698)
+#26697 := (iff #26696 #26694)
+#26713 := (or #26710 #26697)
+#26717 := (iff #26713 #26728)
+#26718 := (iff #26728 #26728)
+#26719 := [rewrite]: #26718
+#26699 := (iff #26697 #26698)
+#26700 := [rewrite]: #26699
+#26714 := [monotonicity #26700]: #26717
+#26720 := [trans #26714 #26719]: #26717
+#26716 := [quant-inst #3032 #26161 #26161 #3088]: #26713
+#26721 := [mp #26716 #26720]: #26728
+#26916 := [unit-resolution #26721 #17881]: #26698
+#28761 := (= #3089 #26695)
+#26918 := (= #26695 #3089)
+#26913 := (= #26161 #3037)
+#26919 := [symm #28827]: #26913
+#26945 := [monotonicity #26919 #26919]: #26918
+#28778 := [symm #26945]: #28761
+#26807 := (f13 #26565)
+#26810 := (= f15 #26807)
+#26912 := (not #26810)
+#26926 := (iff #12098 #26912)
+#26929 := (iff #12095 #26810)
+#26927 := (iff #26810 #12095)
+#26939 := (= #26807 #3046)
+#26922 := (= #26565 #3033)
+#25096 := (f14 #3037)
+#28829 := (= #25096 #3033)
+#25099 := (= #3033 #25096)
+#25104 := (or #25043 #25099)
+#25105 := [quant-inst #3033 #3036]: #25104
+#28828 := [unit-resolution #25105 #23256]: #25099
+#28830 := [symm #28828]: #28829
+#26920 := (= #26565 #25096)
+#26921 := [monotonicity #26919]: #26920
+#26923 := [trans #26921 #28830]: #26922
+#26925 := [monotonicity #26923]: #26939
+#26928 := [monotonicity #26925]: #26927
+#26930 := [symm #26928]: #26929
+#26914 := [monotonicity #26930]: #26926
+#14349 := [and-elim #14344]: #12098
+#26915 := [mp #14349 #26914]: #26912
+#26715 := (not #26694)
+#26712 := (not #26696)
+#26937 := (iff #13280 #26712)
+#26948 := (iff #12157 #26696)
+#26946 := (iff #26696 #12157)
+#26947 := [monotonicity #26945]: #26946
+#26936 := [symm #26947]: #26948
+#26938 := [monotonicity #26936]: #26937
+#26917 := [hypothesis]: #13280
+#26951 := [mp #26917 #26938]: #26712
+#26701 := (not #26698)
+#26732 := (or #26701 #26715 #26696)
+#26733 := [def-axiom]: #26732
+#26953 := [unit-resolution #26733 #26951 #26916]: #26715
+#26799 := (f25 f292 #26161)
+#26800 := (= f1 #26799)
+#26944 := (= #3044 #26799)
+#26954 := (= #26799 #3044)
+#26942 := [monotonicity #26919]: #26954
+#26940 := [symm #26942]: #26944
+#14348 := [and-elim #14344]: #12092
+#26952 := [trans #14348 #26940]: #26800
+#26802 := (f49 #26161 #26565)
+#26803 := (= f1 #26802)
+#26957 := (= #3042 #26802)
+#26955 := (= #26802 #3042)
+#26941 := [monotonicity #26919 #26923]: #26955
+#26958 := [symm #26941]: #26957
+#26959 := [trans #14347 #26958]: #26803
+#26804 := (not #26803)
+#26801 := (not #26800)
+#27009 := (or #26694 #26801 #26804 #26810)
+#26577 := (f26 f292 #26161)
+#26805 := (= f27 #26577)
+#26968 := (= #3040 #26577)
+#26960 := (= #26577 #3040)
+#26966 := [monotonicity #26919]: #26960
+#26980 := [symm #26966]: #26968
+#14346 := [and-elim #14344]: #12086
+#26981 := [trans #14346 #26980]: #26805
+#26987 := (= #3038 #26605)
+#26982 := (= #26605 #3038)
+#26983 := [monotonicity #26919]: #26982
+#26988 := [symm #26983]: #26987
+#14345 := [and-elim #14344]: #12083
+#26989 := [trans #14345 #26988]: #26606
+#26566 := (f24 #26565)
+#26573 := (= f1 #26566)
+#26998 := (= #3049 #26566)
+#26975 := (= #26566 #3049)
+#26976 := [monotonicity #26923]: #26975
+#26999 := [symm #26976]: #26998
+#14350 := [and-elim #14344]: #12101
+#27008 := [trans #14350 #26999]: #26573
+#14329 := [not-or-elim #14326]: #12128
+#14331 := [and-elim #14329]: #12125
+#2236 := (f197 #52 #28 #28)
+#2237 := (pattern #2236)
+#10137 := (= f1 #2236)
+#235 := (f56 #52)
+#4002 := (= f1 #235)
+#19461 := (not #4002)
+#150 := (f49 #28 #31)
+#3711 := (= f1 #150)
+#19335 := (not #3711)
+#19334 := (not #3708)
+#141 := (f28 #52 #28)
+#3693 := (= f1 #141)
+#10857 := (not #3693)
+#76 := (f24 #31)
+#3542 := (= f1 #76)
+#10916 := (not #3542)
+#21894 := (or #34 #10916 #10857 #19334 #19335 #11244 #19461 #10137)
+#21899 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2237) #21894)
+#10152 := (and #57 #3542 #3693 #3708 #3711 #3714 #4002)
+#10155 := (not #10152)
+#10161 := (or #10137 #10155)
+#10166 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2237) #10161)
+#21900 := (iff #10166 #21899)
+#21897 := (iff #10161 #21894)
+#21880 := (or #34 #10916 #10857 #19334 #19335 #11244 #19461)
+#21891 := (or #10137 #21880)
+#21895 := (iff #21891 #21894)
+#21896 := [rewrite]: #21895
+#21892 := (iff #10161 #21891)
+#21889 := (iff #10155 #21880)
+#21881 := (not #21880)
+#21884 := (not #21881)
+#21887 := (iff #21884 #21880)
+#21888 := [rewrite]: #21887
+#21885 := (iff #10155 #21884)
+#21882 := (iff #10152 #21881)
+#21883 := [rewrite]: #21882
+#21886 := [monotonicity #21883]: #21885
+#21890 := [trans #21886 #21888]: #21889
+#21893 := [monotonicity #21890]: #21892
+#21898 := [trans #21893 #21896]: #21897
+#21901 := [quant-intro #21898]: #21900
+#17847 := (~ #10166 #10166)
+#17845 := (~ #10161 #10161)
+#17846 := [refl]: #17845
+#17848 := [nnf-pos #17846]: #17847
+#2244 := (= #2236 f1)
+#77 := (= #76 f1)
+#2238 := (and #57 #77)
+#2239 := (and #153 #2238)
+#151 := (= #150 f1)
+#2240 := (and #151 #2239)
+#2241 := (and #149 #2240)
+#142 := (= #141 f1)
+#2242 := (and #142 #2241)
+#237 := (= #235 f1)
+#2243 := (and #237 #2242)
+#2245 := (implies #2243 #2244)
+#2246 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2237) #2245)
+#10169 := (iff #2246 #10166)
+#10118 := (and #57 #3542)
+#10122 := (and #3714 #10118)
+#10125 := (and #3711 #10122)
+#10128 := (and #3708 #10125)
+#10131 := (and #3693 #10128)
+#10134 := (and #4002 #10131)
+#10143 := (not #10134)
+#10144 := (or #10143 #10137)
+#10149 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #2237) #10144)
+#10167 := (iff #10149 #10166)
+#10164 := (iff #10144 #10161)
+#10158 := (or #10155 #10137)
+#10162 := (iff #10158 #10161)
+#10163 := [rewrite]: #10162
+#10159 := (iff #10144 #10158)
+#10156 := (iff #10143 #10155)
+#10153 := (iff #10134 #10152)
+#10154 := [rewrite]: #10153
+#10157 := [monotonicity #10154]: #10156
+#10160 := [monotonicity #10157]: #10159
+#10165 := [trans #10160 #10163]: #10164
+#10168 := [quant-intro #10165]: #10167
+#10150 := (iff #2246 #10149)
+#10147 := (iff #2245 #10144)
+#10140 := (implies #10134 #10137)
+#10145 := (iff #10140 #10144)
+#10146 := [rewrite]: #10145
+#10141 := (iff #2245 #10140)
+#10138 := (iff #2244 #10137)
+#10139 := [rewrite]: #10138
+#10135 := (iff #2243 #10134)
+#10132 := (iff #2242 #10131)
+#10129 := (iff #2241 #10128)
+#10126 := (iff #2240 #10125)
+#10123 := (iff #2239 #10122)
+#10120 := (iff #2238 #10118)
+#3543 := (iff #77 #3542)
+#3544 := [rewrite]: #3543
+#10121 := [monotonicity #3544]: #10120
+#10124 := [monotonicity #3716 #10121]: #10123
+#3712 := (iff #151 #3711)
+#3713 := [rewrite]: #3712
+#10127 := [monotonicity #3713 #10124]: #10126
+#10130 := [monotonicity #3710 #10127]: #10129
+#3695 := (iff #142 #3693)
+#3696 := [rewrite]: #3695
+#10133 := [monotonicity #3696 #10130]: #10132
+#4004 := (iff #237 #4002)
+#4005 := [rewrite]: #4004
+#10136 := [monotonicity #4005 #10133]: #10135
+#10142 := [monotonicity #10136 #10139]: #10141
+#10148 := [trans #10142 #10146]: #10147
+#10151 := [quant-intro #10148]: #10150
+#10170 := [trans #10151 #10168]: #10169
+#10117 := [asserted]: #2246
+#10171 := [mp #10117 #10170]: #10166
+#17849 := [mp~ #10171 #17848]: #10166
+#21902 := [mp #17849 #21901]: #21899
+#26806 := (not #26805)
+#26574 := (not #26573)
+#24825 := (not #12125)
+#26779 := (not #21899)
+#26781 := (or #26779 #24825 #26574 #26628 #26694 #26801 #26804 #26806 #26810)
+#26808 := (= #26807 f15)
+#26809 := (or #26808 #26574 #26628 #26806 #26804 #26801 #24825 #26694)
+#26782 := (or #26779 #26809)
+#26822 := (iff #26782 #26781)
+#26816 := (or #24825 #26574 #26628 #26694 #26801 #26804 #26806 #26810)
+#26784 := (or #26779 #26816)
+#26826 := (iff #26784 #26781)
+#26827 := [rewrite]: #26826
+#26823 := (iff #26782 #26784)
+#26819 := (iff #26809 #26816)
+#26813 := (or #26810 #26574 #26628 #26806 #26804 #26801 #24825 #26694)
+#26817 := (iff #26813 #26816)
+#26818 := [rewrite]: #26817
+#26814 := (iff #26809 #26813)
+#26811 := (iff #26808 #26810)
+#26812 := [rewrite]: #26811
+#26815 := [monotonicity #26812]: #26814
+#26820 := [trans #26815 #26818]: #26819
+#26825 := [monotonicity #26820]: #26823
+#26828 := [trans #26825 #26827]: #26822
+#26783 := [quant-inst #3032 #26161]: #26782
+#26824 := [mp #26783 #26828]: #26781
+#27010 := [unit-resolution #26824 #21902 #14331 #27008 #26989 #26981]: #27009
+#27011 := [unit-resolution #27010 #26959 #26952 #26953 #26915]: false
+#27012 := [lemma #27011]: #12157
+#28779 := [trans #27012 #28778]: #26696
+#26703 := (or #26701 #26694 #26712)
+#26730 := [def-axiom]: #26703
+#28780 := [unit-resolution #26730 #28779 #26916]: #26694
+#26776 := (or #26715 #26773)
+#20 := (:var 2 S4)
+#2184 := (f197 #20 #21 #28)
+#2247 := (pattern #2184)
+#2248 := (f54 #19 #26)
+#2249 := (f16 #28 #2248)
+#2250 := (pattern #2249)
+#2176 := (f12 #19 #21)
+#2256 := (f193 #2176)
+#2257 := (f148 #28 #2256)
+#10185 := (= f1 #2257)
+#10179 := (= f1 #2249)
+#21903 := (not #10179)
+#1391 := (f14 #26)
+#2251 := (f198 #1391)
+#10173 := (= f1 #2251)
+#21918 := (or #10173 #21903 #10185)
+#21923 := (forall (vars (?v3 S5)) (:pat #2250) #21918)
+#21929 := (not #21923)
+#2163 := (f17 #20 #28)
+#2164 := (f16 #21 #2163)
+#9873 := (= f1 #2164)
+#21738 := (not #9873)
+#187 := (f28 #20 #21)
+#3820 := (= f1 #187)
+#10523 := (not #3820)
+#21930 := (or #10523 #21738 #21929)
+#21931 := (not #21930)
+#9921 := (= f1 #2184)
+#10209 := (not #9921)
+#21936 := (or #10209 #21931)
+#21939 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5)) (:pat #2247) #21936)
+#10176 := (not #10173)
+#10182 := (and #10176 #10179)
+#10191 := (not #10182)
+#10192 := (or #10191 #10185)
+#10197 := (forall (vars (?v3 S5)) (:pat #2250) #10192)
+#10218 := (and #3820 #9873 #10197)
+#10221 := (or #10209 #10218)
+#10224 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5)) (:pat #2247) #10221)
+#21940 := (iff #10224 #21939)
+#21937 := (iff #10221 #21936)
+#21934 := (iff #10218 #21931)
+#21926 := (and #3820 #9873 #21923)
+#21932 := (iff #21926 #21931)
+#21933 := [rewrite]: #21932
+#21927 := (iff #10218 #21926)
+#21924 := (iff #10197 #21923)
+#21921 := (iff #10192 #21918)
+#21904 := (or #10173 #21903)
+#21915 := (or #21904 #10185)
+#21919 := (iff #21915 #21918)
+#21920 := [rewrite]: #21919
+#21916 := (iff #10192 #21915)
+#21913 := (iff #10191 #21904)
+#21905 := (not #21904)
+#21908 := (not #21905)
+#21911 := (iff #21908 #21904)
+#21912 := [rewrite]: #21911
+#21909 := (iff #10191 #21908)
+#21906 := (iff #10182 #21905)
+#21907 := [rewrite]: #21906
+#21910 := [monotonicity #21907]: #21909
+#21914 := [trans #21910 #21912]: #21913
+#21917 := [monotonicity #21914]: #21916
+#21922 := [trans #21917 #21920]: #21921
+#21925 := [quant-intro #21922]: #21924
+#21928 := [monotonicity #21925]: #21927
+#21935 := [trans #21928 #21933]: #21934
+#21938 := [monotonicity #21935]: #21937
+#21941 := [quant-intro #21938]: #21940
+#17864 := (~ #10224 #10224)
+#17862 := (~ #10221 #10221)
+#17860 := (~ #10218 #10218)
+#17858 := (~ #10197 #10197)
+#17856 := (~ #10192 #10192)
+#17857 := [refl]: #17856
+#17859 := [nnf-pos #17857]: #17858
+#17854 := (~ #9873 #9873)
+#17855 := [refl]: #17854
+#17852 := (~ #3820 #3820)
+#17853 := [refl]: #17852
+#17861 := [monotonicity #17853 #17855 #17859]: #17860
+#17850 := (~ #10209 #10209)
+#17851 := [refl]: #17850
+#17863 := [monotonicity #17851 #17861]: #17862
+#17865 := [nnf-pos #17863]: #17864
+#2258 := (= #2257 f1)
+#2254 := (= #2249 f1)
+#2252 := (= #2251 f1)
+#2253 := (not #2252)
+#2255 := (and #2253 #2254)
+#2259 := (implies #2255 #2258)
+#2260 := (forall (vars (?v3 S5)) (:pat #2250) #2259)
+#191 := (= #187 f1)
+#2261 := (and #191 #2260)
+#2169 := (= #2164 f1)
+#2262 := (and #2169 #2261)
+#2185 := (= #2184 f1)
+#2263 := (implies #2185 #2262)
+#2264 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5)) (:pat #2247) #2263)
+#10227 := (iff #2264 #10224)
+#10200 := (and #3820 #10197)
+#10203 := (and #9873 #10200)
+#10210 := (or #10209 #10203)
+#10215 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S5)) (:pat #2247) #10210)
+#10225 := (iff #10215 #10224)
+#10222 := (iff #10210 #10221)
+#10219 := (iff #10203 #10218)
+#10220 := [rewrite]: #10219
+#10223 := [monotonicity #10220]: #10222
+#10226 := [quant-intro #10223]: #10225
+#10216 := (iff #2264 #10215)
+#10213 := (iff #2263 #10210)
+#10206 := (implies #9921 #10203)
+#10211 := (iff #10206 #10210)
+#10212 := [rewrite]: #10211
+#10207 := (iff #2263 #10206)
+#10204 := (iff #2262 #10203)
+#10201 := (iff #2261 #10200)
+#10198 := (iff #2260 #10197)
+#10195 := (iff #2259 #10192)
+#10188 := (implies #10182 #10185)
+#10193 := (iff #10188 #10192)
+#10194 := [rewrite]: #10193
+#10189 := (iff #2259 #10188)
+#10186 := (iff #2258 #10185)
+#10187 := [rewrite]: #10186
+#10183 := (iff #2255 #10182)
+#10180 := (iff #2254 #10179)
+#10181 := [rewrite]: #10180
+#10177 := (iff #2253 #10176)
+#10174 := (iff #2252 #10173)
+#10175 := [rewrite]: #10174
+#10178 := [monotonicity #10175]: #10177
+#10184 := [monotonicity #10178 #10181]: #10183
+#10190 := [monotonicity #10184 #10187]: #10189
+#10196 := [trans #10190 #10194]: #10195
+#10199 := [quant-intro #10196]: #10198
+#3821 := (iff #191 #3820)
+#3822 := [rewrite]: #3821
+#10202 := [monotonicity #3822 #10199]: #10201
+#9874 := (iff #2169 #9873)
+#9875 := [rewrite]: #9874
+#10205 := [monotonicity #9875 #10202]: #10204
+#9922 := (iff #2185 #9921)
+#9923 := [rewrite]: #9922
+#10208 := [monotonicity #9923 #10205]: #10207
+#10214 := [trans #10208 #10212]: #10213
+#10217 := [quant-intro #10214]: #10216
+#10228 := [trans #10217 #10226]: #10227
+#10172 := [asserted]: #2264
+#10229 := [mp #10172 #10228]: #10224
+#17866 := [mp~ #10229 #17865]: #10224
+#21942 := [mp #17866 #21941]: #21939
+#26785 := (not #21939)
+#26780 := (or #26785 #26715 #26773)
+#26750 := (or #26749 #26747 #26743)
+#26752 := (forall (vars (?v3 S5)) (:pat #26751) #26750)
+#26753 := (not #26752)
+#26758 := (or #26628 #26757 #26753)
+#26759 := (not #26758)
+#26760 := (or #26715 #26759)
+#26737 := (or #26785 #26760)
+#26831 := (iff #26737 #26780)
+#26787 := (or #26785 #26776)
+#26790 := (iff #26787 #26780)
+#26829 := [rewrite]: #26790
+#26788 := (iff #26737 #26787)
+#26777 := (iff #26760 #26776)
+#26774 := (iff #26759 #26773)
+#26771 := (iff #26758 #26770)
+#26768 := (iff #26753 #26767)
+#26765 := (iff #26752 #26764)
+#26762 := (iff #26750 #26761)
+#26763 := [rewrite]: #26762
+#26766 := [quant-intro #26763]: #26765
+#26769 := [monotonicity #26766]: #26768
+#26772 := [monotonicity #26769]: #26771
+#26775 := [monotonicity #26772]: #26774
+#26778 := [monotonicity #26775]: #26777
+#26789 := [monotonicity #26778]: #26788
+#26832 := [trans #26789 #26829]: #26831
+#26786 := [quant-inst #3032 #26161 #26161]: #26737
+#26837 := [mp #26786 #26832]: #26780
+#28781 := [unit-resolution #26837 #21942]: #26776
+#28782 := [unit-resolution #28781 #28780]: #26773
+#26830 := (or #26770 #26756)
+#26842 := [def-axiom]: #26830
+#28783 := [unit-resolution #26842 #28782]: #26756
+#28776 := [trans #28783 #28775]: #27213
+#27214 := (not #27213)
+#27526 := (or #12163 #27214)
+#27202 := (f44 #24975 #3036)
+#27203 := (f67 #27202 0::Int #24975)
+#27207 := (f25 f292 #27203)
+#27208 := (= f1 #27207)
+#27209 := (not #27208)
+#27482 := (iff #18428 #27209)
+#27470 := (iff #12163 #27208)
+#27468 := (iff #27208 #12163)
+#27466 := (= #27207 #3094)
+#27465 := (= #27203 #3091)
+#28371 := (= #27202 #3035)
+#28372 := [monotonicity #28365 #28370]: #28371
+#27460 := [monotonicity #28372 #28365]: #27465
+#27467 := [monotonicity #27460]: #27466
+#27469 := [monotonicity #27467]: #27468
+#27481 := [symm #27469]: #27470
+#27490 := [monotonicity #27481]: #27482
+#27464 := [hypothesis]: #18428
+#27491 := [mp #27464 #27490]: #27209
+#27204 := (f59 #3213 #27203)
+#27205 := (f137 #27204)
+#27206 := (= f1 #27205)
+#27219 := (or #27206 #27209)
+#27222 := (not #27219)
+decl f23 :: (-> S3 S1)
+#27215 := (f23 #24975)
+#27216 := (= f1 #27215)
+#2814 := (f23 f9)
+#28403 := (= #2814 #27215)
+#28400 := (= #27215 #2814)
+#28401 := [monotonicity #28365]: #28400
+#28404 := [symm #28401]: #28403
+#11571 := (= f1 #2814)
+#2815 := (= #2814 f1)
+#11573 := (iff #2815 #11571)
+#11574 := [rewrite]: #11573
+#11570 := [asserted]: #2815
+#11577 := [mp #11570 #11574]: #11571
+#28405 := [trans #11577 #28404]: #27216
+#27217 := (not #27216)
+#27496 := (or #27217 #27222)
+#28406 := [hypothesis]: #27213
+#27160 := (<= #24977 0::Int)
+#27493 := (not #27160)
+#14340 := [not-or-elim #14326]: #13489
+#27143 := (* -1::Int #24977)
+#27252 := (+ f291 #27143)
+#27253 := (<= #27252 0::Int)
+#28386 := (not #24978)
+#28387 := (or #28386 #27253)
+#28388 := [th-lemma arith triangle-eq]: #28387
+#28389 := [unit-resolution #28388 #28385]: #27253
+#28395 := (not #27253)
+#27494 := (or #27493 #13488 #28395)
+#27489 := [th-lemma arith assign-bounds -1 1]: #27494
+#27495 := [unit-resolution #27489 #28389 #14340]: #27493
+#245 := (f23 #241)
+#771 := (:var 4 Int)
+#2087 := (f44 #241 #771)
+#2088 := (f67 #2087 #255 #241)
+#1382 := (:var 5 S4)
+#2104 := (f26 #1382 #2088)
+#1374 := (:var 3 S5)
+#2085 := (f17 #1382 #1374)
+#276 := (:var 2 Int)
+#2083 := (f125 #241 #276)
+#2084 := (f44 #2083 #771)
+#2086 := (f16 #2084 #2085)
+#2105 := (pattern #2086 #2104 #245)
+#1556 := (f60 #1382)
+#2102 := (f59 #1556 #2088)
+#2103 := (pattern #2086 #2102 #245)
+#2108 := (f137 #2102)
+#9681 := (= f1 #2108)
+#2106 := (f25 #1382 #2088)
+#9678 := (= f1 #2106)
+#21648 := (not #9678)
+#21649 := (or #21648 #9681)
+#21650 := (not #21649)
+#9622 := (= f1 #2086)
+#21624 := (not #9622)
+#2091 := (f56 #1382)
+#9619 := (= f1 #2091)
+#21623 := (not #9619)
+#4153 := (* -1::Int #276)
+#6217 := (+ #255 #4153)
+#6814 := (>= #6217 0::Int)
+#4415 := (>= #255 0::Int)
+#19561 := (not #4415)
+#4031 := (= f1 #245)
+#10408 := (not #4031)
+#21656 := (or #10408 #19561 #6814 #21623 #21624 #21650)
+#21661 := (forall (vars (?v0 S4) (?v1 Int) (?v2 S5) (?v3 Int) (?v4 Int) (?v5 S3)) (:pat #2103 #2105) #21656)
+#9684 := (not #9681)
+#9687 := (and #9678 #9684)
+#7881 := (not #6814)
+#9660 := (and #4031 #4415 #7881 #9619 #9622)
+#9665 := (not #9660)
+#9701 := (or #9665 #9687)
+#9704 := (forall (vars (?v0 S4) (?v1 Int) (?v2 S5) (?v3 Int) (?v4 Int) (?v5 S3)) (:pat #2103 #2105) #9701)
+#21662 := (iff #9704 #21661)
+#21659 := (iff #9701 #21656)
+#21625 := (or #10408 #19561 #6814 #21623 #21624)
+#21653 := (or #21625 #21650)
+#21657 := (iff #21653 #21656)
+#21658 := [rewrite]: #21657
+#21654 := (iff #9701 #21653)
+#21651 := (iff #9687 #21650)
+#21652 := [rewrite]: #21651
+#21634 := (iff #9665 #21625)
+#21626 := (not #21625)
+#21629 := (not #21626)
+#21632 := (iff #21629 #21625)
+#21633 := [rewrite]: #21632
+#21630 := (iff #9665 #21629)
+#21627 := (iff #9660 #21626)
+#21628 := [rewrite]: #21627
+#21631 := [monotonicity #21628]: #21630
+#21635 := [trans #21631 #21633]: #21634
+#21655 := [monotonicity #21635 #21652]: #21654
+#21660 := [trans #21655 #21658]: #21659
+#21663 := [quant-intro #21660]: #21662
+#17730 := (~ #9704 #9704)
+#17728 := (~ #9701 #9701)
+#17729 := [refl]: #17728
+#17731 := [nnf-pos #17729]: #17730
+#2109 := (= #2108 f1)
+#2110 := (not #2109)
+#2107 := (= #2106 f1)
+#2111 := (and #2107 #2110)
+#1443 := (< #255 #276)
+#406 := (<= 0::Int #255)
+#1444 := (and #406 #1443)
+#2093 := (= #2086 f1)
+#2094 := (and #2093 #1444)
+#246 := (= #245 f1)
+#2095 := (and #246 #2094)
+#2092 := (= #2091 f1)
+#2096 := (and #2092 #2095)
+#2112 := (implies #2096 #2111)
+#2113 := (forall (vars (?v0 S4) (?v1 Int) (?v2 S5) (?v3 Int) (?v4 Int) (?v5 S3)) (:pat #2103 #2105) #2112)
+#9707 := (iff #2113 #9704)
+#9628 := (and #1444 #9622)
+#9633 := (and #4031 #9628)
+#9636 := (and #9619 #9633)
+#9642 := (not #9636)
+#9693 := (or #9642 #9687)
+#9698 := (forall (vars (?v0 S4) (?v1 Int) (?v2 S5) (?v3 Int) (?v4 Int) (?v5 S3)) (:pat #2103 #2105) #9693)
+#9705 := (iff #9698 #9704)
+#9702 := (iff #9693 #9701)
+#9666 := (iff #9642 #9665)
+#9663 := (iff #9636 #9660)
+#7884 := (and #4415 #7881)
+#9651 := (and #7884 #9622)
+#9654 := (and #4031 #9651)
+#9657 := (and #9619 #9654)
+#9661 := (iff #9657 #9660)
+#9662 := [rewrite]: #9661
+#9658 := (iff #9636 #9657)
+#9655 := (iff #9633 #9654)
+#9652 := (iff #9628 #9651)
+#7885 := (iff #1444 #7884)
+#7882 := (iff #1443 #7881)
+#7883 := [rewrite]: #7882
+#4414 := (iff #406 #4415)
+#4416 := [rewrite]: #4414
+#7886 := [monotonicity #4416 #7883]: #7885
+#9653 := [monotonicity #7886]: #9652
+#9656 := [monotonicity #9653]: #9655
+#9659 := [monotonicity #9656]: #9658
+#9664 := [trans #9659 #9662]: #9663
+#9667 := [monotonicity #9664]: #9666
+#9703 := [monotonicity #9667]: #9702
+#9706 := [quant-intro #9703]: #9705
+#9699 := (iff #2113 #9698)
+#9696 := (iff #2112 #9693)
+#9690 := (implies #9636 #9687)
+#9694 := (iff #9690 #9693)
+#9695 := [rewrite]: #9694
+#9691 := (iff #2112 #9690)
+#9688 := (iff #2111 #9687)
+#9685 := (iff #2110 #9684)
+#9682 := (iff #2109 #9681)
 #9683 := [rewrite]: #9682
-#9679 := (iff #2128 #9678)
-#9676 := (iff #2127 #9675)
-#9677 := [rewrite]: #9676
-#9680 := [monotonicity #9677]: #9679
-#9685 := [trans #9680 #9683]: #9684
-#4085 := (iff #280 #4084)
-#4086 := [rewrite]: #4085
-#9688 := [monotonicity #4086 #9685]: #9687
-#9673 := (iff #2126 #9672)
-#9674 := [rewrite]: #9673
-#9691 := [monotonicity #9674 #9688]: #9690
-#9745 := [monotonicity #9691 #9742]: #9744
-#9750 := [trans #9745 #9748]: #9749
-#9753 := [quant-intro #9750]: #9752
-#9761 := [trans #9753 #9759]: #9760
-#9730 := [asserted]: #2147
-#9762 := [mp #9730 #9761]: #9757
-#17777 := [mp~ #9762 #17776]: #9757
-#21684 := [mp #17777 #21683]: #21681
-#27254 := (not #21681)
-#27453 := (or #27254 #24846 #27181 #27235 #27238 #27243)
-#27231 := (or #27230 #27227)
-#27232 := (not #27231)
-#27165 := (+ 0::Int #27164)
-#27166 := (>= #27165 0::Int)
-#27167 := (>= 0::Int 0::Int)
-#27168 := (not #27167)
-#27239 := (or #27238 #27168 #27166 #24846 #27235 #27232)
-#27454 := (or #27254 #27239)
-#27466 := (iff #27454 #27453)
-#27249 := (or #24846 #27181 #27235 #27238 #27243)
-#27459 := (or #27254 #27249)
-#27464 := (iff #27459 #27453)
-#27465 := [rewrite]: #27464
-#27460 := (iff #27454 #27459)
-#27252 := (iff #27239 #27249)
-#27246 := (or #27238 false #27181 #24846 #27235 #27243)
-#27250 := (iff #27246 #27249)
-#27251 := [rewrite]: #27250
-#27247 := (iff #27239 #27246)
-#27244 := (iff #27232 #27243)
-#27241 := (iff #27231 #27240)
-#27242 := [rewrite]: #27241
-#27245 := [monotonicity #27242]: #27244
-#27184 := (iff #27166 #27181)
-#27178 := (>= #27164 0::Int)
-#27182 := (iff #27178 #27181)
-#27183 := [rewrite]: #27182
-#27179 := (iff #27166 #27178)
-#27176 := (= #27165 #27164)
-#27177 := [rewrite]: #27176
-#27180 := [monotonicity #27177]: #27179
-#27185 := [trans #27180 #27183]: #27184
-#27174 := (iff #27168 false)
-#27172 := (iff #27168 #3156)
-#27170 := (iff #27167 true)
-#27171 := [rewrite]: #27170
-#27173 := [monotonicity #27171]: #27172
-#27175 := [trans #27173 #12257]: #27174
-#27248 := [monotonicity #27175 #27185 #27245]: #27247
-#27253 := [trans #27248 #27251]: #27252
-#27461 := [monotonicity #27253]: #27460
-#27492 := [trans #27461 #27465]: #27466
-#27455 := [quant-inst #3039 #3043 #26182 #24998 #161 #24996]: #27454
-#27493 := [mp #27455 #27492]: #27453
-#27518 := [unit-resolution #27493 #21684 #14351 #27516 #28427]: #27517
-#27519 := [unit-resolution #27518 #28426]: #27243
-#27497 := (or #27240 #27229)
-#27482 := [def-axiom]: #27497
-#27520 := [unit-resolution #27482 #27519 #27512]: false
-#27548 := [lemma #27520]: #27547
-#28798 := [unit-resolution #27548 #28797]: #12183
-#28623 := (or #28377 #18448 #28443)
-#28624 := [def-axiom]: #28623
-#28817 := [unit-resolution #28624 #28798]: #28816
-#28818 := [unit-resolution #28817 #28780]: #28443
-#28615 := (or #28440 #28345)
-#28616 := [def-axiom]: #28615
-#28819 := [unit-resolution #28616 #28818]: #28345
-#28592 := (not #27227)
-#28835 := (iff #28592 #28148)
-#28832 := (iff #27227 #28147)
-#28814 := (= #27226 #28146)
-#28824 := (= #27225 #26985)
-#28825 := [monotonicity #27481]: #28824
-#28815 := [monotonicity #28825]: #28814
-#28834 := [monotonicity #28815]: #28832
-#28833 := [monotonicity #28834]: #28835
-#28821 := [unit-resolution #27493 #21684 #14351 #27516 #28797]: #27517
-#28822 := [unit-resolution #28821 #28426]: #27243
-#28593 := (or #27240 #28592)
-#28594 := [def-axiom]: #28593
-#28823 := [unit-resolution #28594 #28822]: #28592
-#28836 := [mp #28823 #28833]: #28148
-#28478 := (or #28326 #28147)
-#28484 := [def-axiom]: #28478
-#28837 := [unit-resolution #28484 #28836]: #28326
-#25501 := (f23 f19)
-#28366 := (= #25501 #27920)
-#27753 := (= #27920 #25501)
-#27686 := (= #27039 f19)
-#27684 := (= #25112 f19)
-#27685 := [symm #27139]: #27684
-#27369 := [hypothesis]: #27103
-#27370 := [unit-resolution #27749 #27369]: #27089
-#27416 := [trans #27409 #27370]: #27415
-#27681 := [trans #27416 #27414]: #27680
-#27683 := [monotonicity #27681]: #27682
-#27687 := [trans #27683 #27685]: #27686
-#27754 := [monotonicity #27687]: #27753
-#28467 := [symm #27754]: #28366
-#25502 := (= f25 #25501)
-#25509 := (iff #11624 #25502)
-#2363 := (pattern #279)
-#2902 := (f23 #275)
-#11803 := (= f25 #2902)
-#11807 := (iff #4084 #11803)
-#11810 := (forall (vars (?v0 S18)) (:pat #2363) #11807)
-#18402 := (~ #11810 #11810)
-#18400 := (~ #11807 #11807)
-#18401 := [refl]: #18400
-#18403 := [nnf-pos #18401]: #18402
-#2915 := (= #2902 f25)
-#2916 := (iff #280 #2915)
-#2917 := (forall (vars (?v0 S18)) (:pat #2363) #2916)
-#11811 := (iff #2917 #11810)
-#11808 := (iff #2916 #11807)
-#11805 := (iff #2915 #11803)
-#11806 := [rewrite]: #11805
-#11809 := [monotonicity #4086 #11806]: #11808
-#11812 := [quant-intro #11809]: #11811
-#11802 := [asserted]: #2917
-#11815 := [mp #11802 #11812]: #11810
-#18404 := [mp~ #11815 #18403]: #11810
-#25168 := (not #11810)
-#25512 := (or #25168 #25509)
-#25513 := [quant-inst #50]: #25512
-#28838 := [unit-resolution #25513 #18404]: #25509
-#25514 := (not #25509)
-#28839 := (or #25514 #25502)
-#25518 := (not #11624)
-#25519 := (or #25514 #25518 #25502)
-#25520 := [def-axiom]: #25519
-#28840 := [unit-resolution #25520 #11630]: #28839
-#28841 := [unit-resolution #28840 #28838]: #25502
-#28468 := [trans #28841 #28467]: #28266
-#28602 := (not #28097)
-#28934 := (iff #12118 #28602)
-#28932 := (iff #12115 #28097)
-#28930 := (iff #28097 #12115)
-#28928 := (= #28096 #3053)
-#28926 := (= #28095 #3040)
-#28924 := (= #28095 #25117)
-#28922 := (= #27775 #3044)
-#28920 := (= #27775 #27145)
-#27146 := (f77 #27145 0::Int #24996)
-#27150 := (f69 #3220 #27146)
-#27156 := (f146 #27150)
-#28918 := (= #27156 #27145)
-#27157 := (= #27145 #27156)
-#27158 := (not #27157)
-#27154 := (f147 #27150)
-#27155 := (= f1 #27154)
-#27151 := (f78 #27150)
-#27152 := (= f1 #27151)
-#27153 := (not #27152)
-#27147 := (f35 f297 #27146)
-#27148 := (= f1 #27147)
-#27149 := (not #27148)
-#27186 := (or #27149 #27153 #27155 #27158)
-#27189 := (not #27186)
-#27161 := (f35 f297 #27145)
-#27162 := (= f1 #27161)
-#28492 := (= #3051 #27161)
-#28489 := (= #27161 #3051)
-#28490 := [monotonicity #28789]: #28489
-#28872 := [symm #28490]: #28492
-#28873 := [trans #14368 #28872]: #27162
-#27163 := (not #27162)
-#28859 := (or #27163 #27189)
-#319 := (:var 3 Int)
-#353 := (:var 2 S18)
-#1513 := (f135 #353 #289)
-#1514 := (f54 #1513 #319)
-#1510 := (f54 #353 #319)
-#1511 := (f77 #1510 #202 #353)
-#74 := (:var 4 S19)
-#1516 := (f70 #74)
-#1517 := (f69 #1516 #1511)
-#1518 := (pattern #1517 #1514)
-#1509 := (f52 #74)
-#1512 := (f51 #1509 #1511)
-#1515 := (pattern #1512 #1514)
-#1521 := (f77 #1514 #202 #353)
-#1530 := (f35 #74 #1521)
-#8095 := (= f1 #1530)
-#21008 := (not #8095)
-#1522 := (f69 #1516 #1521)
-#1528 := (f78 #1522)
-#8092 := (= f1 #1528)
-#21007 := (not #8092)
-#1525 := (f147 #1522)
-#8086 := (= f1 #1525)
-#1523 := (f146 #1522)
-#8083 := (= #1514 #1523)
-#21006 := (not #8083)
-#21009 := (or #21006 #8086 #21007 #21008)
-#21010 := (not #21009)
-#1519 := (f35 #74 #1514)
-#8080 := (= f1 #1519)
-#8118 := (not #8080)
-#5395 := (* -1::Int #289)
-#6275 := (+ #202 #5395)
-#6276 := (>= #6275 0::Int)
-#21016 := (or #5124 #6276 #8118 #21010)
-#21021 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #21016)
-#8089 := (not #8086)
-#8127 := (and #8083 #8089 #8092 #8095)
-#7779 := (not #6276)
-#7782 := (and #4202 #7779)
-#7785 := (not #7782)
-#8136 := (or #7785 #8118 #8127)
-#8141 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8136)
-#21022 := (iff #8141 #21021)
-#21019 := (iff #8136 #21016)
-#20891 := (or #5124 #6276)
-#21013 := (or #20891 #8118 #21010)
-#21017 := (iff #21013 #21016)
-#21018 := [rewrite]: #21017
-#21014 := (iff #8136 #21013)
-#21011 := (iff #8127 #21010)
-#21012 := [rewrite]: #21011
-#20900 := (iff #7785 #20891)
-#20892 := (not #20891)
-#20895 := (not #20892)
-#20898 := (iff #20895 #20891)
-#20899 := [rewrite]: #20898
-#20896 := (iff #7785 #20895)
-#20893 := (iff #7782 #20892)
-#20894 := [rewrite]: #20893
-#20897 := [monotonicity #20894]: #20896
-#20901 := [trans #20897 #20899]: #20900
-#21015 := [monotonicity #20901 #21012]: #21014
-#21020 := [trans #21015 #21018]: #21019
-#21023 := [quant-intro #21020]: #21022
-#17140 := (~ #8141 #8141)
-#17138 := (~ #8136 #8136)
-#17139 := [refl]: #17138
-#17141 := [nnf-pos #17139]: #17140
-#1531 := (= #1530 f1)
-#1529 := (= #1528 f1)
-#1532 := (and #1529 #1531)
-#1526 := (= #1525 f1)
-#1527 := (not #1526)
-#1533 := (and #1527 #1532)
-#1524 := (= #1523 #1514)
-#1534 := (and #1524 #1533)
-#1414 := (< #202 #289)
-#1415 := (and #327 #1414)
-#1535 := (implies #1415 #1534)
-#1520 := (= #1519 f1)
-#1536 := (implies #1520 #1535)
-#1537 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #1536)
-#8144 := (iff #1537 #8141)
-#8098 := (and #8092 #8095)
-#8101 := (and #8089 #8098)
-#8104 := (and #8083 #8101)
-#7749 := (not #1415)
-#8110 := (or #7749 #8104)
-#8119 := (or #8118 #8110)
-#8124 := (forall (vars (?v0 S19) (?v1 Int) (?v2 S18) (?v3 Int) (?v4 Int)) (:pat #1515 #1518) #8119)
-#8142 := (iff #8124 #8141)
-#8139 := (iff #8119 #8136)
-#8130 := (or #7785 #8127)
-#8133 := (or #8118 #8130)
-#8137 := (iff #8133 #8136)
-#8138 := [rewrite]: #8137
-#8134 := (iff #8119 #8133)
-#8131 := (iff #8110 #8130)
-#8128 := (iff #8104 #8127)
-#8129 := [rewrite]: #8128
-#7786 := (iff #7749 #7785)
-#7783 := (iff #1415 #7782)
-#7780 := (iff #1414 #7779)
-#7781 := [rewrite]: #7780
-#7784 := [monotonicity #4201 #7781]: #7783
-#7787 := [monotonicity #7784]: #7786
-#8132 := [monotonicity #7787 #8129]: #8131
-#8135 := [monotonicity #8132]: #8134
-#8140 := [trans #8135 #8138]: #8139
-#8143 := [quant-intro #8140]: #8142
-#8125 := (iff #1537 #8124)
-#8122 := (iff #1536 #8119)
-#8115 := (implies #8080 #8110)
-#8120 := (iff #8115 #8119)
-#8121 := [rewrite]: #8120
-#8116 := (iff #1536 #8115)
-#8113 := (iff #1535 #8110)
-#8107 := (implies #1415 #8104)
-#8111 := (iff #8107 #8110)
-#8112 := [rewrite]: #8111
-#8108 := (iff #1535 #8107)
-#8105 := (iff #1534 #8104)
-#8102 := (iff #1533 #8101)
-#8099 := (iff #1532 #8098)
-#8096 := (iff #1531 #8095)
-#8097 := [rewrite]: #8096
-#8093 := (iff #1529 #8092)
-#8094 := [rewrite]: #8093
-#8100 := [monotonicity #8094 #8097]: #8099
-#8090 := (iff #1527 #8089)
-#8087 := (iff #1526 #8086)
-#8088 := [rewrite]: #8087
-#8091 := [monotonicity #8088]: #8090
-#8103 := [monotonicity #8091 #8100]: #8102
-#8084 := (iff #1524 #8083)
+#9686 := [monotonicity #9683]: #9685
+#9679 := (iff #2107 #9678)
+#9680 := [rewrite]: #9679
+#9689 := [monotonicity #9680 #9686]: #9688
+#9637 := (iff #2096 #9636)
+#9634 := (iff #2095 #9633)
+#9631 := (iff #2094 #9628)
+#9625 := (and #9622 #1444)
+#9629 := (iff #9625 #9628)
+#9630 := [rewrite]: #9629
+#9626 := (iff #2094 #9625)
+#9623 := (iff #2093 #9622)
+#9624 := [rewrite]: #9623
+#9627 := [monotonicity #9624]: #9626
+#9632 := [trans #9627 #9630]: #9631
+#4032 := (iff #246 #4031)
+#4033 := [rewrite]: #4032
+#9635 := [monotonicity #4033 #9632]: #9634
+#9620 := (iff #2092 #9619)
+#9621 := [rewrite]: #9620
+#9638 := [monotonicity #9621 #9635]: #9637
+#9692 := [monotonicity #9638 #9689]: #9691
+#9697 := [trans #9692 #9695]: #9696
+#9700 := [quant-intro #9697]: #9699
+#9708 := [trans #9700 #9706]: #9707
+#9677 := [asserted]: #2113
+#9709 := [mp #9677 #9708]: #9704
+#17732 := [mp~ #9709 #17731]: #9704
+#21664 := [mp #17732 #21663]: #21661
+#27233 := (not #21661)
+#27432 := (or #27233 #24825 #27160 #27214 #27217 #27222)
+#27210 := (or #27209 #27206)
+#27211 := (not #27210)
+#27144 := (+ 0::Int #27143)
+#27145 := (>= #27144 0::Int)
+#27146 := (>= 0::Int 0::Int)
+#27147 := (not #27146)
+#27218 := (or #27217 #27147 #27145 #24825 #27214 #27211)
+#27433 := (or #27233 #27218)
+#27445 := (iff #27433 #27432)
+#27228 := (or #24825 #27160 #27214 #27217 #27222)
+#27438 := (or #27233 #27228)
+#27443 := (iff #27438 #27432)
+#27444 := [rewrite]: #27443
+#27439 := (iff #27433 #27438)
+#27231 := (iff #27218 #27228)
+#27225 := (or #27217 false #27160 #24825 #27214 #27222)
+#27229 := (iff #27225 #27228)
+#27230 := [rewrite]: #27229
+#27226 := (iff #27218 #27225)
+#27223 := (iff #27211 #27222)
+#27220 := (iff #27210 #27219)
+#27221 := [rewrite]: #27220
+#27224 := [monotonicity #27221]: #27223
+#27163 := (iff #27145 #27160)
+#27157 := (>= #27143 0::Int)
+#27161 := (iff #27157 #27160)
+#27162 := [rewrite]: #27161
+#27158 := (iff #27145 #27157)
+#27155 := (= #27144 #27143)
+#27156 := [rewrite]: #27155
+#27159 := [monotonicity #27156]: #27158
+#27164 := [trans #27159 #27162]: #27163
+#27153 := (iff #27147 false)
+#27151 := (iff #27147 #3149)
+#27149 := (iff #27146 true)
+#27150 := [rewrite]: #27149
+#27152 := [monotonicity #27150]: #27151
+#27154 := [trans #27152 #12237]: #27153
+#27227 := [monotonicity #27154 #27164 #27224]: #27226
+#27232 := [trans #27227 #27230]: #27231
+#27440 := [monotonicity #27232]: #27439
+#27471 := [trans #27440 #27444]: #27445
+#27434 := [quant-inst #3032 #3036 #26161 #24977 #127 #24975]: #27433
+#27472 := [mp #27434 #27471]: #27432
+#27497 := [unit-resolution #27472 #21664 #14331 #27495 #28406]: #27496
+#27498 := [unit-resolution #27497 #28405]: #27222
+#27476 := (or #27219 #27208)
+#27461 := [def-axiom]: #27476
+#27499 := [unit-resolution #27461 #27498 #27491]: false
+#27527 := [lemma #27499]: #27526
+#28777 := [unit-resolution #27527 #28776]: #12163
+#28602 := (or #28356 #18428 #28422)
+#28603 := [def-axiom]: #28602
+#28796 := [unit-resolution #28603 #28777]: #28795
+#28797 := [unit-resolution #28796 #28759]: #28422
+#28594 := (or #28419 #28324)
+#28595 := [def-axiom]: #28594
+#28798 := [unit-resolution #28595 #28797]: #28324
+#28571 := (not #27206)
+#28814 := (iff #28571 #28127)
+#28811 := (iff #27206 #28126)
+#28793 := (= #27205 #28125)
+#28803 := (= #27204 #26964)
+#28804 := [monotonicity #27460]: #28803
+#28794 := [monotonicity #28804]: #28793
+#28813 := [monotonicity #28794]: #28811
+#28812 := [monotonicity #28813]: #28814
+#28800 := [unit-resolution #27472 #21664 #14331 #27495 #28776]: #27496
+#28801 := [unit-resolution #28800 #28405]: #27222
+#28572 := (or #27219 #28571)
+#28573 := [def-axiom]: #28572
+#28802 := [unit-resolution #28573 #28801]: #28571
+#28815 := [mp #28802 #28812]: #28127
+#28457 := (or #28305 #28126)
+#28463 := [def-axiom]: #28457
+#28816 := [unit-resolution #28463 #28815]: #28305
+#25480 := (f13 f9)
+#28345 := (= #25480 #27899)
+#27732 := (= #27899 #25480)
+#27665 := (= #27018 f9)
+#27663 := (= #25091 f9)
+#27664 := [symm #27118]: #27663
+#27348 := [hypothesis]: #27082
+#27349 := [unit-resolution #27728 #27348]: #27068
+#27395 := [trans #27388 #27349]: #27394
+#27660 := [trans #27395 #27393]: #27659
+#27662 := [monotonicity #27660]: #27661
+#27666 := [trans #27662 #27664]: #27665
+#27733 := [monotonicity #27666]: #27732
+#28446 := [symm #27733]: #28345
+#25481 := (= f15 #25480)
+#25488 := (iff #11571 #25481)
+#2329 := (pattern #245)
+#2868 := (f13 #241)
+#11750 := (= f15 #2868)
+#11754 := (iff #4031 #11750)
+#11757 := (forall (vars (?v0 S3)) (:pat #2329) #11754)
+#18357 := (~ #11757 #11757)
+#18355 := (~ #11754 #11754)
+#18356 := [refl]: #18355
+#18358 := [nnf-pos #18356]: #18357
+#2881 := (= #2868 f15)
+#2882 := (iff #246 #2881)
+#2883 := (forall (vars (?v0 S3)) (:pat #2329) #2882)
+#11758 := (iff #2883 #11757)
+#11755 := (iff #2882 #11754)
+#11752 := (iff #2881 #11750)
+#11753 := [rewrite]: #11752
+#11756 := [monotonicity #4033 #11753]: #11755
+#11759 := [quant-intro #11756]: #11758
+#11749 := [asserted]: #2883
+#11762 := [mp #11749 #11759]: #11757
+#18359 := [mp~ #11762 #18358]: #11757
+#25147 := (not #11757)
+#25491 := (or #25147 #25488)
+#25492 := [quant-inst #16]: #25491
+#28817 := [unit-resolution #25492 #18359]: #25488
+#25493 := (not #25488)
+#28818 := (or #25493 #25481)
+#25497 := (not #11571)
+#25498 := (or #25493 #25497 #25481)
+#25499 := [def-axiom]: #25498
+#28819 := [unit-resolution #25499 #11577]: #28818
+#28820 := [unit-resolution #28819 #28817]: #25481
+#28447 := [trans #28820 #28446]: #28245
+#28581 := (not #28076)
+#28913 := (iff #12098 #28581)
+#28911 := (iff #12095 #28076)
+#28909 := (iff #28076 #12095)
+#28907 := (= #28075 #3046)
+#28905 := (= #28074 #3033)
+#28903 := (= #28074 #25096)
+#28901 := (= #27754 #3037)
+#28899 := (= #27754 #27124)
+#27125 := (f67 #27124 0::Int #24975)
+#27129 := (f59 #3213 #27125)
+#27135 := (f136 #27129)
+#28897 := (= #27135 #27124)
+#27136 := (= #27124 #27135)
+#27137 := (not #27136)
+#27133 := (f137 #27129)
+#27134 := (= f1 #27133)
+#27130 := (f68 #27129)
+#27131 := (= f1 #27130)
+#27132 := (not #27131)
+#27126 := (f25 f292 #27125)
+#27127 := (= f1 #27126)
+#27128 := (not #27127)
+#27165 := (or #27128 #27132 #27134 #27137)
+#27168 := (not #27165)
+#27140 := (f25 f292 #27124)
+#27141 := (= f1 #27140)
+#28471 := (= #3044 #27140)
+#28468 := (= #27140 #3044)
+#28469 := [monotonicity #28768]: #28468
+#28851 := [symm #28469]: #28471
+#28852 := [trans #14348 #28851]: #27141
+#27142 := (not #27141)
+#28838 := (or #27142 #27168)
+#285 := (:var 3 Int)
+#319 := (:var 2 S3)
+#1479 := (f125 #319 #255)
+#1480 := (f44 #1479 #285)
+#1476 := (f44 #319 #285)
+#1477 := (f67 #1476 #168 #319)
+#40 := (:var 4 S4)
+#1482 := (f60 #40)
+#1483 := (f59 #1482 #1477)
+#1484 := (pattern #1483 #1480)
+#1475 := (f42 #40)
+#1478 := (f41 #1475 #1477)
+#1481 := (pattern #1478 #1480)
+#1487 := (f67 #1480 #168 #319)
+#1496 := (f25 #40 #1487)
+#8042 := (= f1 #1496)
+#20988 := (not #8042)
+#1488 := (f59 #1482 #1487)
+#1494 := (f68 #1488)
+#8039 := (= f1 #1494)
+#20987 := (not #8039)
+#1491 := (f137 #1488)
+#8033 := (= f1 #1491)
+#1489 := (f136 #1488)
+#8030 := (= #1480 #1489)
+#20986 := (not #8030)
+#20989 := (or #20986 #8033 #20987 #20988)
+#20990 := (not #20989)
+#1485 := (f25 #40 #1480)
+#8027 := (= f1 #1485)
+#8065 := (not #8027)
+#5342 := (* -1::Int #255)
+#6222 := (+ #168 #5342)
+#6223 := (>= #6222 0::Int)
+#20996 := (or #5071 #6223 #8065 #20990)
+#21001 := (forall (vars (?v0 S4) (?v1 Int) (?v2 S3) (?v3 Int) (?v4 Int)) (:pat #1481 #1484) #20996)
+#8036 := (not #8033)
+#8074 := (and #8030 #8036 #8039 #8042)
+#7726 := (not #6223)
+#7729 := (and #4149 #7726)
+#7732 := (not #7729)
+#8083 := (or #7732 #8065 #8074)
+#8088 := (forall (vars (?v0 S4) (?v1 Int) (?v2 S3) (?v3 Int) (?v4 Int)) (:pat #1481 #1484) #8083)
+#21002 := (iff #8088 #21001)
+#20999 := (iff #8083 #20996)
+#20871 := (or #5071 #6223)
+#20993 := (or #20871 #8065 #20990)
+#20997 := (iff #20993 #20996)
+#20998 := [rewrite]: #20997
+#20994 := (iff #8083 #20993)
+#20991 := (iff #8074 #20990)
+#20992 := [rewrite]: #20991
+#20880 := (iff #7732 #20871)
+#20872 := (not #20871)
+#20875 := (not #20872)
+#20878 := (iff #20875 #20871)
+#20879 := [rewrite]: #20878
+#20876 := (iff #7732 #20875)
+#20873 := (iff #7729 #20872)
+#20874 := [rewrite]: #20873
+#20877 := [monotonicity #20874]: #20876
+#20881 := [trans #20877 #20879]: #20880
+#20995 := [monotonicity #20881 #20992]: #20994
+#21000 := [trans #20995 #20998]: #20999
+#21003 := [quant-intro #21000]: #21002
+#17095 := (~ #8088 #8088)
+#17093 := (~ #8083 #8083)
+#17094 := [refl]: #17093
+#17096 := [nnf-pos #17094]: #17095
+#1497 := (= #1496 f1)
+#1495 := (= #1494 f1)
+#1498 := (and #1495 #1497)
+#1492 := (= #1491 f1)
+#1493 := (not #1492)
+#1499 := (and #1493 #1498)
+#1490 := (= #1489 #1480)
+#1500 := (and #1490 #1499)
+#1380 := (< #168 #255)
+#1381 := (and #293 #1380)
+#1501 := (implies #1381 #1500)
+#1486 := (= #1485 f1)
+#1502 := (implies #1486 #1501)
+#1503 := (forall (vars (?v0 S4) (?v1 Int) (?v2 S3) (?v3 Int) (?v4 Int)) (:pat #1481 #1484) #1502)
+#8091 := (iff #1503 #8088)
+#8045 := (and #8039 #8042)
+#8048 := (and #8036 #8045)
+#8051 := (and #8030 #8048)
+#7696 := (not #1381)
+#8057 := (or #7696 #8051)
+#8066 := (or #8065 #8057)
+#8071 := (forall (vars (?v0 S4) (?v1 Int) (?v2 S3) (?v3 Int) (?v4 Int)) (:pat #1481 #1484) #8066)
+#8089 := (iff #8071 #8088)
+#8086 := (iff #8066 #8083)
+#8077 := (or #7732 #8074)
+#8080 := (or #8065 #8077)
+#8084 := (iff #8080 #8083)
 #8085 := [rewrite]: #8084
-#8106 := [monotonicity #8085 #8103]: #8105
-#8109 := [monotonicity #8106]: #8108
-#8114 := [trans #8109 #8112]: #8113
-#8081 := (iff #1520 #8080)
-#8082 := [rewrite]: #8081
-#8117 := [monotonicity #8082 #8114]: #8116
-#8123 := [trans #8117 #8121]: #8122
-#8126 := [quant-intro #8123]: #8125
-#8145 := [trans #8126 #8143]: #8144
-#8079 := [asserted]: #1537
-#8146 := [mp #8079 #8145]: #8141
-#17142 := [mp~ #8146 #17141]: #8141
-#21024 := [mp #17142 #21023]: #21021
-#28639 := (not #21021)
-#28640 := (or #28639 #27163 #27181 #27189)
-#27159 := (or #27158 #27155 #27153 #27149)
-#27160 := (not #27159)
-#27169 := (or #27168 #27166 #27163 #27160)
-#28641 := (or #28639 #27169)
-#28648 := (iff #28641 #28640)
-#27195 := (or #27163 #27181 #27189)
-#28643 := (or #28639 #27195)
-#28646 := (iff #28643 #28640)
-#28647 := [rewrite]: #28646
-#28644 := (iff #28641 #28643)
-#27198 := (iff #27169 #27195)
-#27192 := (or false #27181 #27163 #27189)
-#27196 := (iff #27192 #27195)
-#27197 := [rewrite]: #27196
-#27193 := (iff #27169 #27192)
-#27190 := (iff #27160 #27189)
-#27187 := (iff #27159 #27186)
-#27188 := [rewrite]: #27187
-#27191 := [monotonicity #27188]: #27190
-#27194 := [monotonicity #27175 #27185 #27191]: #27193
-#27199 := [trans #27194 #27197]: #27198
-#28645 := [monotonicity #27199]: #28644
-#28649 := [trans #28645 #28647]: #28648
-#28642 := [quant-inst #3039 #3043 #24996 #24998 #161]: #28641
-#28650 := [mp #28642 #28649]: #28640
-#28860 := [unit-resolution #28650 #21024 #27516]: #28859
-#28879 := [unit-resolution #28860 #28873]: #27189
-#28589 := (or #27186 #27157)
-#28587 := [def-axiom]: #28589
-#28880 := [unit-resolution #28587 #28879]: #27157
-#28919 := [symm #28880]: #28918
-#28916 := (= #27775 #27156)
-#28914 := (= #26985 #27150)
-#28912 := (= #27150 #26985)
-#28910 := (= #27146 #3098)
-#28900 := (= #27064 #3098)
-#28901 := [symm #27409]: #28900
-#28908 := (= #27146 #27064)
-#28898 := (= #27086 #27064)
-#28899 := [symm #27370]: #28898
-#28906 := (= #27146 #27086)
-#28896 := (= #3042 #27086)
-#28897 := [symm #27414]: #28896
-#28904 := (= #27146 #3042)
-#27318 := (f127 #26182)
-#27332 := (f54 #24996 #27318)
-#28894 := (= #27332 #3042)
-#28888 := (= #27318 f298)
-#28886 := (= #27318 #3043)
-#28884 := (= #24880 #3043)
-#25123 := (= #3043 #24880)
-#25128 := (or #25070 #25123)
-#25129 := [quant-inst #3040 #3043]: #25128
-#28881 := [unit-resolution #25129 #23306]: #25123
-#28885 := [symm #28881]: #28884
-#28882 := (= #27318 #24880)
-#28883 := [monotonicity #26940]: #28882
-#28887 := [trans #28883 #28885]: #28886
-#28889 := [trans #28887 #28391]: #28888
-#28895 := [monotonicity #28386 #28889]: #28894
-#28902 := (= #27146 #27332)
-#27314 := (f77 #26182 0::Int #24996)
-#27335 := (= #27314 #27332)
-#27338 := (not #27335)
-#27315 := (f149 #27314 #26182)
-#27316 := (= f1 #27315)
-#27317 := (not #27316)
-#27344 := (or #27317 #27338)
-#27349 := (not #27344)
-#28722 := (or #27721 #27349)
-#27319 := (+ #27318 #27069)
-#27320 := (f54 #24996 #27319)
-#27321 := (= #27314 #27320)
-#27322 := (not #27321)
-#27323 := (or #27322 #27317)
-#27324 := (not #27323)
-#28764 := (or #27721 #27324)
-#28766 := (iff #28764 #28722)
-#28768 := (iff #28722 #28722)
-#28769 := [rewrite]: #28768
-#27350 := (iff #27324 #27349)
-#27347 := (iff #27323 #27344)
-#27341 := (or #27338 #27317)
-#27345 := (iff #27341 #27344)
-#27346 := [rewrite]: #27345
-#27342 := (iff #27323 #27341)
-#27339 := (iff #27322 #27338)
-#27336 := (iff #27321 #27335)
-#27333 := (= #27320 #27332)
-#27330 := (= #27319 #27318)
-#27325 := (+ #27318 0::Int)
-#27328 := (= #27325 #27318)
-#27329 := [rewrite]: #27328
-#27326 := (= #27319 #27325)
-#27327 := [monotonicity #27078]: #27326
-#27331 := [trans #27327 #27329]: #27330
-#27334 := [monotonicity #27331]: #27333
-#27337 := [monotonicity #27334]: #27336
-#27340 := [monotonicity #27337]: #27339
-#27343 := [monotonicity #27340]: #27342
-#27348 := [trans #27343 #27346]: #27347
-#27351 := [monotonicity #27348]: #27350
-#28767 := [monotonicity #27351]: #28766
-#28770 := [trans #28767 #28769]: #28766
-#28765 := [quant-inst #26182 #161 #24996]: #28764
-#28752 := [mp #28765 #28770]: #28722
-#28890 := [unit-resolution #28752 #21240]: #27349
-#28756 := (or #27344 #27335)
-#28757 := [def-axiom]: #28756
-#28891 := [unit-resolution #28757 #28890]: #27335
-#28892 := (= #27146 #27314)
-#28893 := [monotonicity #28791]: #28892
-#28903 := [trans #28893 #28891]: #28902
-#28905 := [trans #28903 #28895]: #28904
-#28907 := [trans #28905 #28897]: #28906
-#28909 := [trans #28907 #28899]: #28908
-#28911 := [trans #28909 #28901]: #28910
-#28913 := [monotonicity #28911]: #28912
-#28915 := [symm #28913]: #28914
-#28917 := [monotonicity #28915]: #28916
-#28921 := [trans #28917 #28919]: #28920
-#28923 := [trans #28921 #28789]: #28922
-#28925 := [monotonicity #28923]: #28924
-#28927 := [trans #28925 #28851]: #28926
-#28929 := [monotonicity #28927]: #28928
-#28931 := [monotonicity #28929]: #28930
-#28933 := [symm #28931]: #28932
-#28935 := [monotonicity #28933]: #28934
-#28936 := [mp #14369 #28935]: #28602
-#28940 := (= #3047 #27778)
-#28937 := (= #27778 #3047)
-#28938 := [monotonicity #28923]: #28937
-#28941 := [symm #28938]: #28940
-#28942 := [trans #14366 #28941]: #27786
-#28597 := (not #27786)
-#28598 := (or #28363 #28597)
-#28599 := [def-axiom]: #28598
-#28943 := [unit-resolution #28599 #28942]: #28363
-#28611 := (or #28437 #28097 #28322 #28340 #28365)
-#28612 := [def-axiom]: #28611
-#28944 := [unit-resolution #28612 #28943 #28936 #28468 #28837 #28819]: false
-#28946 := [lemma #28944]: #28945
-#29128 := [unit-resolution #28946 #28653]: #12189
-#23578 := (or #18445 #18454 #23575)
-#23581 := (not #23578)
-#23584 := (or #18445 #18448 #23581)
-#23587 := (not #23584)
-#23590 := (or #18445 #18448 #23587)
-#23593 := (not #23590)
-#23596 := (or #13300 #23593)
-#23599 := (not #23596)
-#23602 := (or #13300 #23599)
-#22558 := (forall (vars (?v0 Int)) #22547)
-#22565 := (not #22558)
-#22543 := (forall (vars (?v0 Int)) #22538)
-#22564 := (not #22543)
-#22566 := (or #22564 #22565)
-#22567 := (not #22566)
-#22596 := (or #22567 #22593)
-#22602 := (not #22596)
-#22603 := (or #12340 #12331 #12322 #12313 #22479 #13656 #13802 #22602)
-#22604 := (not #22603)
-#22382 := (forall (vars (?v0 Int)) #22377)
-#22388 := (not #22382)
-#22389 := (or #22364 #22388)
-#22390 := (not #22389)
-#22419 := (or #22390 #22416)
-#22425 := (not #22419)
-#22426 := (or #13555 #22425)
-#22427 := (not #22426)
-#22432 := (or #13555 #22427)
-#22440 := (not #22432)
-#22441 := (or #12692 #22438 #18594 #22439 #13622 #18597 #22440)
-#22442 := (not #22441)
-#22447 := (or #18594 #18597 #22442)
-#22453 := (not #22447)
-#22490 := (or #12857 #12848 #22479 #13656 #22438 #13707 #22453)
-#22491 := (not #22490)
-#22454 := (or #18556 #18565 #12776 #12767 #12758 #12740 #12731 #13656 #22438 #22453)
-#22455 := (not #22454)
-#22460 := (or #18556 #18565 #22455)
-#22466 := (not #22460)
-#22467 := (or #18556 #18559 #22466)
-#22468 := (not #22467)
-#22473 := (or #18556 #18559 #22468)
-#22480 := (not #22473)
-#22481 := (or #22479 #13656 #13708 #22480)
-#22482 := (not #22481)
-#22496 := (or #22482 #22491)
-#22502 := (not #22496)
-#22503 := (or #18556 #18565 #22479 #13656 #22502)
-#22504 := (not #22503)
-#22509 := (or #18556 #18565 #22504)
-#22515 := (not #22509)
-#22516 := (or #18556 #18559 #22515)
-#22517 := (not #22516)
-#22522 := (or #18556 #18559 #22517)
-#22528 := (not #22522)
-#22529 := (or #22479 #13656 #13801 #22528)
-#22530 := (not #22529)
-#22609 := (or #22530 #22604)
-#22624 := (not #22609)
-#22359 := (forall (vars (?v0 Int)) #22354)
-#22620 := (not #22359)
-#22625 := (or #13267 #22615 #15299 #13974 #13060 #13051 #13042 #13033 #22616 #22617 #13508 #22479 #13656 #13979 #14031 #22618 #22619 #22621 #22622 #22623 #22620 #22624)
-#22626 := (not #22625)
-#22631 := (or #13267 #13508 #22626)
-#22638 := (not #22631)
-#22348 := (forall (vars (?v0 Int)) #22343)
-#22637 := (not #22348)
-#22639 := (or #22637 #22638)
-#22640 := (not #22639)
-#22645 := (or #22337 #22640)
-#22651 := (not #22645)
-#22652 := (or #13472 #22651)
-#22653 := (not #22652)
-#22658 := (or #13472 #22653)
-#22664 := (not #22658)
-#22665 := (or #13267 #18445 #18454 #13258 #13249 #13240 #22664)
-#22666 := (not #22665)
-#22671 := (or #18445 #18454 #22666)
-#22677 := (not #22671)
-#22678 := (or #18445 #18448 #22677)
-#22679 := (not #22678)
-#22684 := (or #18445 #18448 #22679)
-#22690 := (not #22684)
-#22691 := (or #13300 #22690)
-#22692 := (not #22691)
-#22697 := (or #13300 #22692)
-#23603 := (iff #22697 #23602)
-#23600 := (iff #22692 #23599)
-#23597 := (iff #22691 #23596)
-#23594 := (iff #22690 #23593)
-#23591 := (iff #22684 #23590)
-#23588 := (iff #22679 #23587)
-#23585 := (iff #22678 #23584)
+#8081 := (iff #8066 #8080)
+#8078 := (iff #8057 #8077)
+#8075 := (iff #8051 #8074)
+#8076 := [rewrite]: #8075
+#7733 := (iff #7696 #7732)
+#7730 := (iff #1381 #7729)
+#7727 := (iff #1380 #7726)
+#7728 := [rewrite]: #7727
+#7731 := [monotonicity #4148 #7728]: #7730
+#7734 := [monotonicity #7731]: #7733
+#8079 := [monotonicity #7734 #8076]: #8078
+#8082 := [monotonicity #8079]: #8081
+#8087 := [trans #8082 #8085]: #8086
+#8090 := [quant-intro #8087]: #8089
+#8072 := (iff #1503 #8071)
+#8069 := (iff #1502 #8066)
+#8062 := (implies #8027 #8057)
+#8067 := (iff #8062 #8066)
+#8068 := [rewrite]: #8067
+#8063 := (iff #1502 #8062)
+#8060 := (iff #1501 #8057)
+#8054 := (implies #1381 #8051)
+#8058 := (iff #8054 #8057)
+#8059 := [rewrite]: #8058
+#8055 := (iff #1501 #8054)
+#8052 := (iff #1500 #8051)
+#8049 := (iff #1499 #8048)
+#8046 := (iff #1498 #8045)
+#8043 := (iff #1497 #8042)
+#8044 := [rewrite]: #8043
+#8040 := (iff #1495 #8039)
+#8041 := [rewrite]: #8040
+#8047 := [monotonicity #8041 #8044]: #8046
+#8037 := (iff #1493 #8036)
+#8034 := (iff #1492 #8033)
+#8035 := [rewrite]: #8034
+#8038 := [monotonicity #8035]: #8037
+#8050 := [monotonicity #8038 #8047]: #8049
+#8031 := (iff #1490 #8030)
+#8032 := [rewrite]: #8031
+#8053 := [monotonicity #8032 #8050]: #8052
+#8056 := [monotonicity #8053]: #8055
+#8061 := [trans #8056 #8059]: #8060
+#8028 := (iff #1486 #8027)
+#8029 := [rewrite]: #8028
+#8064 := [monotonicity #8029 #8061]: #8063
+#8070 := [trans #8064 #8068]: #8069
+#8073 := [quant-intro #8070]: #8072
+#8092 := [trans #8073 #8090]: #8091
+#8026 := [asserted]: #1503
+#8093 := [mp #8026 #8092]: #8088
+#17097 := [mp~ #8093 #17096]: #8088
+#21004 := [mp #17097 #21003]: #21001
+#28618 := (not #21001)
+#28619 := (or #28618 #27142 #27160 #27168)
+#27138 := (or #27137 #27134 #27132 #27128)
+#27139 := (not #27138)
+#27148 := (or #27147 #27145 #27142 #27139)
+#28620 := (or #28618 #27148)
+#28627 := (iff #28620 #28619)
+#27174 := (or #27142 #27160 #27168)
+#28622 := (or #28618 #27174)
+#28625 := (iff #28622 #28619)
+#28626 := [rewrite]: #28625
+#28623 := (iff #28620 #28622)
+#27177 := (iff #27148 #27174)
+#27171 := (or false #27160 #27142 #27168)
+#27175 := (iff #27171 #27174)
+#27176 := [rewrite]: #27175
+#27172 := (iff #27148 #27171)
+#27169 := (iff #27139 #27168)
+#27166 := (iff #27138 #27165)
+#27167 := [rewrite]: #27166
+#27170 := [monotonicity #27167]: #27169
+#27173 := [monotonicity #27154 #27164 #27170]: #27172
+#27178 := [trans #27173 #27176]: #27177
+#28624 := [monotonicity #27178]: #28623
+#28628 := [trans #28624 #28626]: #28627
+#28621 := [quant-inst #3032 #3036 #24975 #24977 #127]: #28620
+#28629 := [mp #28621 #28628]: #28619
+#28839 := [unit-resolution #28629 #21004 #27495]: #28838
+#28858 := [unit-resolution #28839 #28852]: #27168
+#28568 := (or #27165 #27136)
+#28566 := [def-axiom]: #28568
+#28859 := [unit-resolution #28566 #28858]: #27136
+#28898 := [symm #28859]: #28897
+#28895 := (= #27754 #27135)
+#28893 := (= #26964 #27129)
+#28891 := (= #27129 #26964)
+#28889 := (= #27125 #3091)
+#28879 := (= #27043 #3091)
+#28880 := [symm #27388]: #28879
+#28887 := (= #27125 #27043)
+#28877 := (= #27065 #27043)
+#28878 := [symm #27349]: #28877
+#28885 := (= #27125 #27065)
+#28875 := (= #3035 #27065)
+#28876 := [symm #27393]: #28875
+#28883 := (= #27125 #3035)
+#27297 := (f117 #26161)
+#27311 := (f44 #24975 #27297)
+#28873 := (= #27311 #3035)
+#28867 := (= #27297 f293)
+#28865 := (= #27297 #3036)
+#28863 := (= #24859 #3036)
+#25102 := (= #3036 #24859)
+#25107 := (or #25049 #25102)
+#25108 := [quant-inst #3033 #3036]: #25107
+#28860 := [unit-resolution #25108 #23250]: #25102
+#28864 := [symm #28860]: #28863
+#28861 := (= #27297 #24859)
+#28862 := [monotonicity #26919]: #28861
+#28866 := [trans #28862 #28864]: #28865
+#28868 := [trans #28866 #28370]: #28867
+#28874 := [monotonicity #28365 #28868]: #28873
+#28881 := (= #27125 #27311)
+#27293 := (f67 #26161 0::Int #24975)
+#27314 := (= #27293 #27311)
+#27317 := (not #27314)
+#27294 := (f139 #27293 #26161)
+#27295 := (= f1 #27294)
+#27296 := (not #27295)
+#27323 := (or #27296 #27317)
+#27328 := (not #27323)
+#28701 := (or #27700 #27328)
+#27298 := (+ #27297 #27048)
+#27299 := (f44 #24975 #27298)
+#27300 := (= #27293 #27299)
+#27301 := (not #27300)
+#27302 := (or #27301 #27296)
+#27303 := (not #27302)
+#28743 := (or #27700 #27303)
+#28745 := (iff #28743 #28701)
+#28747 := (iff #28701 #28701)
+#28748 := [rewrite]: #28747
+#27329 := (iff #27303 #27328)
+#27326 := (iff #27302 #27323)
+#27320 := (or #27317 #27296)
+#27324 := (iff #27320 #27323)
+#27325 := [rewrite]: #27324
+#27321 := (iff #27302 #27320)
+#27318 := (iff #27301 #27317)
+#27315 := (iff #27300 #27314)
+#27312 := (= #27299 #27311)
+#27309 := (= #27298 #27297)
+#27304 := (+ #27297 0::Int)
+#27307 := (= #27304 #27297)
+#27308 := [rewrite]: #27307
+#27305 := (= #27298 #27304)
+#27306 := [monotonicity #27057]: #27305
+#27310 := [trans #27306 #27308]: #27309
+#27313 := [monotonicity #27310]: #27312
+#27316 := [monotonicity #27313]: #27315
+#27319 := [monotonicity #27316]: #27318
+#27322 := [monotonicity #27319]: #27321
+#27327 := [trans #27322 #27325]: #27326
+#27330 := [monotonicity #27327]: #27329
+#28746 := [monotonicity #27330]: #28745
+#28749 := [trans #28746 #28748]: #28745
+#28744 := [quant-inst #26161 #127 #24975]: #28743
+#28731 := [mp #28744 #28749]: #28701
+#28869 := [unit-resolution #28731 #21220]: #27328
+#28735 := (or #27323 #27314)
+#28736 := [def-axiom]: #28735
+#28870 := [unit-resolution #28736 #28869]: #27314
+#28871 := (= #27125 #27293)
+#28872 := [monotonicity #28770]: #28871
+#28882 := [trans #28872 #28870]: #28881
+#28884 := [trans #28882 #28874]: #28883
+#28886 := [trans #28884 #28876]: #28885
+#28888 := [trans #28886 #28878]: #28887
+#28890 := [trans #28888 #28880]: #28889
+#28892 := [monotonicity #28890]: #28891
+#28894 := [symm #28892]: #28893
+#28896 := [monotonicity #28894]: #28895
+#28900 := [trans #28896 #28898]: #28899
+#28902 := [trans #28900 #28768]: #28901
+#28904 := [monotonicity #28902]: #28903
+#28906 := [trans #28904 #28830]: #28905
+#28908 := [monotonicity #28906]: #28907
+#28910 := [monotonicity #28908]: #28909
+#28912 := [symm #28910]: #28911
+#28914 := [monotonicity #28912]: #28913
+#28915 := [mp #14349 #28914]: #28581
+#28919 := (= #3040 #27757)
+#28916 := (= #27757 #3040)
+#28917 := [monotonicity #28902]: #28916
+#28920 := [symm #28917]: #28919
+#28921 := [trans #14346 #28920]: #27765
+#28576 := (not #27765)
+#28577 := (or #28342 #28576)
+#28578 := [def-axiom]: #28577
+#28922 := [unit-resolution #28578 #28921]: #28342
+#28590 := (or #28416 #28076 #28301 #28319 #28344)
+#28591 := [def-axiom]: #28590
+#28923 := [unit-resolution #28591 #28922 #28915 #28447 #28816 #28798]: false
+#28925 := [lemma #28923]: #28924
+#29107 := [unit-resolution #28925 #28632]: #12169
+#23557 := (or #18425 #18434 #23554)
+#23560 := (not #23557)
+#23563 := (or #18425 #18428 #23560)
+#23566 := (not #23563)
+#23569 := (or #18425 #18428 #23566)
+#23572 := (not #23569)
+#23575 := (or #13280 #23572)
+#23578 := (not #23575)
+#23581 := (or #13280 #23578)
+#22538 := (forall (vars (?v0 Int)) #22527)
+#22545 := (not #22538)
+#22523 := (forall (vars (?v0 Int)) #22518)
+#22544 := (not #22523)
+#22546 := (or #22544 #22545)
+#22547 := (not #22546)
+#22576 := (or #22547 #22573)
+#22582 := (not #22576)
+#22583 := (or #12320 #12311 #12302 #12293 #22459 #13636 #13782 #22582)
+#22584 := (not #22583)
+#22362 := (forall (vars (?v0 Int)) #22357)
+#22368 := (not #22362)
+#22369 := (or #22344 #22368)
+#22370 := (not #22369)
+#22399 := (or #22370 #22396)
+#22405 := (not #22399)
+#22406 := (or #13535 #22405)
+#22407 := (not #22406)
+#22412 := (or #13535 #22407)
+#22420 := (not #22412)
+#22421 := (or #12672 #22418 #18574 #22419 #13602 #18577 #22420)
+#22422 := (not #22421)
+#22427 := (or #18574 #18577 #22422)
+#22433 := (not #22427)
+#22470 := (or #12837 #12828 #22459 #13636 #22418 #13687 #22433)
+#22471 := (not #22470)
+#22434 := (or #18536 #18545 #12756 #12747 #12738 #12720 #12711 #13636 #22418 #22433)
+#22435 := (not #22434)
+#22440 := (or #18536 #18545 #22435)
+#22446 := (not #22440)
+#22447 := (or #18536 #18539 #22446)
+#22448 := (not #22447)
+#22453 := (or #18536 #18539 #22448)
+#22460 := (not #22453)
+#22461 := (or #22459 #13636 #13688 #22460)
+#22462 := (not #22461)
+#22476 := (or #22462 #22471)
+#22482 := (not #22476)
+#22483 := (or #18536 #18545 #22459 #13636 #22482)
+#22484 := (not #22483)
+#22489 := (or #18536 #18545 #22484)
+#22495 := (not #22489)
+#22496 := (or #18536 #18539 #22495)
+#22497 := (not #22496)
+#22502 := (or #18536 #18539 #22497)
+#22508 := (not #22502)
+#22509 := (or #22459 #13636 #13781 #22508)
+#22510 := (not #22509)
+#22589 := (or #22510 #22584)
+#22604 := (not #22589)
+#22339 := (forall (vars (?v0 Int)) #22334)
+#22600 := (not #22339)
+#22605 := (or #13247 #22595 #15279 #13954 #13040 #13031 #13022 #13013 #22596 #22597 #13488 #22459 #13636 #13959 #14011 #22598 #22599 #22601 #22602 #22603 #22600 #22604)
+#22606 := (not #22605)
+#22611 := (or #13247 #13488 #22606)
+#22618 := (not #22611)
+#22328 := (forall (vars (?v0 Int)) #22323)
+#22617 := (not #22328)
+#22619 := (or #22617 #22618)
+#22620 := (not #22619)
+#22625 := (or #22317 #22620)
+#22631 := (not #22625)
+#22632 := (or #13452 #22631)
+#22633 := (not #22632)
+#22638 := (or #13452 #22633)
+#22644 := (not #22638)
+#22645 := (or #13247 #18425 #18434 #13238 #13229 #13220 #22644)
+#22646 := (not #22645)
+#22651 := (or #18425 #18434 #22646)
+#22657 := (not #22651)
+#22658 := (or #18425 #18428 #22657)
+#22659 := (not #22658)
+#22664 := (or #18425 #18428 #22659)
+#22670 := (not #22664)
+#22671 := (or #13280 #22670)
+#22672 := (not #22671)
+#22677 := (or #13280 #22672)
 #23582 := (iff #22677 #23581)
-#23579 := (iff #22671 #23578)
-#23576 := (iff #22666 #23575)
-#23573 := (iff #22665 #23572)
+#23579 := (iff #22672 #23578)
+#23576 := (iff #22671 #23575)
+#23573 := (iff #22670 #23572)
 #23570 := (iff #22664 #23569)
-#23567 := (iff #22658 #23566)
-#23564 := (iff #22653 #23563)
-#23561 := (iff #22652 #23560)
+#23567 := (iff #22659 #23566)
+#23564 := (iff #22658 #23563)
+#23561 := (iff #22657 #23560)
 #23558 := (iff #22651 #23557)
-#23555 := (iff #22645 #23554)
-#23552 := (iff #22640 #23551)
-#23549 := (iff #22639 #23548)
+#23555 := (iff #22646 #23554)
+#23552 := (iff #22645 #23551)
+#23549 := (iff #22644 #23548)
 #23546 := (iff #22638 #23545)
-#23543 := (iff #22631 #23542)
-#23540 := (iff #22626 #23539)
-#23537 := (iff #22625 #23536)
-#23534 := (iff #22624 #23533)
-#23531 := (iff #22609 #23530)
-#23528 := (iff #22604 #23527)
-#23525 := (iff #22603 #23524)
-#23522 := (iff #22602 #23521)
-#23519 := (iff #22596 #23518)
-#23516 := (iff #22567 #23515)
-#23513 := (iff #22566 #23512)
-#23510 := (iff #22565 #23509)
-#23507 := (iff #22558 #23504)
-#23505 := (iff #22547 #22547)
-#23506 := [refl]: #23505
-#23508 := [quant-intro #23506]: #23507
-#23511 := [monotonicity #23508]: #23510
-#23502 := (iff #22564 #23501)
-#23499 := (iff #22543 #23496)
-#23497 := (iff #22538 #22538)
-#23498 := [refl]: #23497
-#23500 := [quant-intro #23498]: #23499
-#23503 := [monotonicity #23500]: #23502
-#23514 := [monotonicity #23503 #23511]: #23513
-#23517 := [monotonicity #23514]: #23516
-#23520 := [monotonicity #23517]: #23519
-#23523 := [monotonicity #23520]: #23522
-#23526 := [monotonicity #23523]: #23525
-#23529 := [monotonicity #23526]: #23528
-#23494 := (iff #22530 #23493)
-#23491 := (iff #22529 #23490)
-#23488 := (iff #22528 #23487)
-#23485 := (iff #22522 #23484)
-#23482 := (iff #22517 #23481)
-#23479 := (iff #22516 #23478)
-#23476 := (iff #22515 #23475)
-#23473 := (iff #22509 #23472)
-#23470 := (iff #22504 #23469)
-#23467 := (iff #22503 #23466)
+#23543 := (iff #22633 #23542)
+#23540 := (iff #22632 #23539)
+#23537 := (iff #22631 #23536)
+#23534 := (iff #22625 #23533)
+#23531 := (iff #22620 #23530)
+#23528 := (iff #22619 #23527)
+#23525 := (iff #22618 #23524)
+#23522 := (iff #22611 #23521)
+#23519 := (iff #22606 #23518)
+#23516 := (iff #22605 #23515)
+#23513 := (iff #22604 #23512)
+#23510 := (iff #22589 #23509)
+#23507 := (iff #22584 #23506)
+#23504 := (iff #22583 #23503)
+#23501 := (iff #22582 #23500)
+#23498 := (iff #22576 #23497)
+#23495 := (iff #22547 #23494)
+#23492 := (iff #22546 #23491)
+#23489 := (iff #22545 #23488)
+#23486 := (iff #22538 #23483)
+#23484 := (iff #22527 #22527)
+#23485 := [refl]: #23484
+#23487 := [quant-intro #23485]: #23486
+#23490 := [monotonicity #23487]: #23489
+#23481 := (iff #22544 #23480)
+#23478 := (iff #22523 #23475)
+#23476 := (iff #22518 #22518)
+#23477 := [refl]: #23476
+#23479 := [quant-intro #23477]: #23478
+#23482 := [monotonicity #23479]: #23481
+#23493 := [monotonicity #23482 #23490]: #23492
+#23496 := [monotonicity #23493]: #23495
+#23499 := [monotonicity #23496]: #23498
+#23502 := [monotonicity #23499]: #23501
+#23505 := [monotonicity #23502]: #23504
+#23508 := [monotonicity #23505]: #23507
+#23473 := (iff #22510 #23472)
+#23470 := (iff #22509 #23469)
+#23467 := (iff #22508 #23466)
 #23464 := (iff #22502 #23463)
-#23461 := (iff #22496 #23460)
-#23458 := (iff #22491 #23457)
-#23455 := (iff #22490 #23454)
-#23422 := (iff #22453 #23421)
-#23419 := (iff #22447 #23418)
-#23416 := (iff #22442 #23415)
-#23413 := (iff #22441 #23412)
-#23410 := (iff #22440 #23409)
-#23407 := (iff #22432 #23406)
-#23404 := (iff #22427 #23403)
-#23401 := (iff #22426 #23400)
-#23398 := (iff #22425 #23397)
-#23395 := (iff #22419 #23394)
-#23392 := (iff #22390 #23391)
-#23389 := (iff #22389 #23388)
-#23386 := (iff #22388 #23385)
-#23383 := (iff #22382 #23380)
-#23381 := (iff #22377 #22377)
-#23382 := [refl]: #23381
-#23384 := [quant-intro #23382]: #23383
+#23461 := (iff #22497 #23460)
+#23458 := (iff #22496 #23457)
+#23455 := (iff #22495 #23454)
+#23452 := (iff #22489 #23451)
+#23449 := (iff #22484 #23448)
+#23446 := (iff #22483 #23445)
+#23443 := (iff #22482 #23442)
+#23440 := (iff #22476 #23439)
+#23437 := (iff #22471 #23436)
+#23434 := (iff #22470 #23433)
+#23401 := (iff #22433 #23400)
+#23398 := (iff #22427 #23397)
+#23395 := (iff #22422 #23394)
+#23392 := (iff #22421 #23391)
+#23389 := (iff #22420 #23388)
+#23386 := (iff #22412 #23385)
+#23383 := (iff #22407 #23382)
+#23380 := (iff #22406 #23379)
+#23377 := (iff #22405 #23376)
+#23374 := (iff #22399 #23373)
+#23371 := (iff #22370 #23370)
+#23368 := (iff #22369 #23367)
+#23365 := (iff #22368 #23364)
+#23362 := (iff #22362 #23359)
+#23360 := (iff #22357 #22357)
+#23361 := [refl]: #23360
+#23363 := [quant-intro #23361]: #23362
+#23366 := [monotonicity #23363]: #23365
+#23369 := [monotonicity #23366]: #23368
+#23372 := [monotonicity #23369]: #23371
+#23375 := [monotonicity #23372]: #23374
+#23378 := [monotonicity #23375]: #23377
+#23381 := [monotonicity #23378]: #23380
+#23384 := [monotonicity #23381]: #23383
 #23387 := [monotonicity #23384]: #23386
 #23390 := [monotonicity #23387]: #23389
 #23393 := [monotonicity #23390]: #23392
 #23396 := [monotonicity #23393]: #23395
 #23399 := [monotonicity #23396]: #23398
 #23402 := [monotonicity #23399]: #23401
+#23435 := [monotonicity #23402]: #23434
+#23438 := [monotonicity #23435]: #23437
+#23431 := (iff #22462 #23430)
+#23428 := (iff #22461 #23427)
+#23425 := (iff #22460 #23424)
+#23422 := (iff #22453 #23421)
+#23419 := (iff #22448 #23418)
+#23416 := (iff #22447 #23415)
+#23413 := (iff #22446 #23412)
+#23410 := (iff #22440 #23409)
+#23407 := (iff #22435 #23406)
+#23404 := (iff #22434 #23403)
 #23405 := [monotonicity #23402]: #23404
 #23408 := [monotonicity #23405]: #23407
 #23411 := [monotonicity #23408]: #23410
@@ -5136,59 +5155,47 @@
 #23417 := [monotonicity #23414]: #23416
 #23420 := [monotonicity #23417]: #23419
 #23423 := [monotonicity #23420]: #23422
-#23456 := [monotonicity #23423]: #23455
-#23459 := [monotonicity #23456]: #23458
-#23452 := (iff #22482 #23451)
-#23449 := (iff #22481 #23448)
-#23446 := (iff #22480 #23445)
-#23443 := (iff #22473 #23442)
-#23440 := (iff #22468 #23439)
-#23437 := (iff #22467 #23436)
-#23434 := (iff #22466 #23433)
-#23431 := (iff #22460 #23430)
-#23428 := (iff #22455 #23427)
-#23425 := (iff #22454 #23424)
 #23426 := [monotonicity #23423]: #23425
 #23429 := [monotonicity #23426]: #23428
 #23432 := [monotonicity #23429]: #23431
-#23435 := [monotonicity #23432]: #23434
-#23438 := [monotonicity #23435]: #23437
-#23441 := [monotonicity #23438]: #23440
+#23441 := [monotonicity #23432 #23438]: #23440
 #23444 := [monotonicity #23441]: #23443
 #23447 := [monotonicity #23444]: #23446
 #23450 := [monotonicity #23447]: #23449
 #23453 := [monotonicity #23450]: #23452
-#23462 := [monotonicity #23453 #23459]: #23461
+#23456 := [monotonicity #23453]: #23455
+#23459 := [monotonicity #23456]: #23458
+#23462 := [monotonicity #23459]: #23461
 #23465 := [monotonicity #23462]: #23464
 #23468 := [monotonicity #23465]: #23467
 #23471 := [monotonicity #23468]: #23470
 #23474 := [monotonicity #23471]: #23473
-#23477 := [monotonicity #23474]: #23476
-#23480 := [monotonicity #23477]: #23479
-#23483 := [monotonicity #23480]: #23482
-#23486 := [monotonicity #23483]: #23485
-#23489 := [monotonicity #23486]: #23488
-#23492 := [monotonicity #23489]: #23491
-#23495 := [monotonicity #23492]: #23494
-#23532 := [monotonicity #23495 #23529]: #23531
+#23511 := [monotonicity #23474 #23508]: #23510
+#23514 := [monotonicity #23511]: #23513
+#23357 := (iff #22600 #23356)
+#23354 := (iff #22339 #23351)
+#23352 := (iff #22334 #22334)
+#23353 := [refl]: #23352
+#23355 := [quant-intro #23353]: #23354
+#23358 := [monotonicity #23355]: #23357
+#23517 := [monotonicity #23358 #23514]: #23516
+#23520 := [monotonicity #23517]: #23519
+#23523 := [monotonicity #23520]: #23522
+#23526 := [monotonicity #23523]: #23525
+#23349 := (iff #22617 #23348)
+#23346 := (iff #22328 #23343)
+#23344 := (iff #22323 #22323)
+#23345 := [refl]: #23344
+#23347 := [quant-intro #23345]: #23346
+#23350 := [monotonicity #23347]: #23349
+#23529 := [monotonicity #23350 #23526]: #23528
+#23532 := [monotonicity #23529]: #23531
 #23535 := [monotonicity #23532]: #23534
-#23378 := (iff #22620 #23377)
-#23375 := (iff #22359 #23372)
-#23373 := (iff #22354 #22354)
-#23374 := [refl]: #23373
-#23376 := [quant-intro #23374]: #23375
-#23379 := [monotonicity #23376]: #23378
-#23538 := [monotonicity #23379 #23535]: #23537
+#23538 := [monotonicity #23535]: #23537
 #23541 := [monotonicity #23538]: #23540
 #23544 := [monotonicity #23541]: #23543
 #23547 := [monotonicity #23544]: #23546
-#23370 := (iff #22637 #23369)
-#23367 := (iff #22348 #23364)
-#23365 := (iff #22343 #22343)
-#23366 := [refl]: #23365
-#23368 := [quant-intro #23366]: #23367
-#23371 := [monotonicity #23368]: #23370
-#23550 := [monotonicity #23371 #23547]: #23549
+#23550 := [monotonicity #23547]: #23549
 #23553 := [monotonicity #23550]: #23552
 #23556 := [monotonicity #23553]: #23555
 #23559 := [monotonicity #23556]: #23558
@@ -5200,810 +5207,793 @@
 #23577 := [monotonicity #23574]: #23576
 #23580 := [monotonicity #23577]: #23579
 #23583 := [monotonicity #23580]: #23582
-#23586 := [monotonicity #23583]: #23585
-#23589 := [monotonicity #23586]: #23588
-#23592 := [monotonicity #23589]: #23591
-#23595 := [monotonicity #23592]: #23594
-#23598 := [monotonicity #23595]: #23597
-#23601 := [monotonicity #23598]: #23600
-#23604 := [monotonicity #23601]: #23603
-#19096 := (and #18739 #18740)
-#19099 := (not #19096)
-#19102 := (or #19078 #19091 #19099)
-#19105 := (not #19102)
-#16021 := (and #3173 #4202 #13831 #15219)
-#18762 := (not #16021)
-#18765 := (forall (vars (?v0 Int)) #18762)
-#14462 := (and #4202 #15219)
-#14461 := (not #14462)
-#16007 := (or #13829 #13843 #14461)
-#16012 := (forall (vars (?v0 Int)) #16007)
-#18769 := (and #16012 #18765)
-#19111 := (or #18769 #19105)
-#19119 := (and #12269 #12272 #12275 #12278 #13513 #13516 #13801 #19111)
-#18948 := (and #18615 #18616)
-#18951 := (not #18948)
-#18954 := (or #18930 #18943 #18951)
-#18957 := (not #18954)
-#15908 := (or #13558 #13572 #14461)
-#15913 := (forall (vars (?v0 Int)) #15908)
-#18631 := (not #13601)
-#18641 := (and #18631 #15913)
-#18963 := (or #18641 #18957)
-#18968 := (and #13550 #18963)
-#18971 := (or #13555 #18968)
-#18979 := (and #12622 #13525 #13534 #13542 #13618 #15900 #18971)
-#18984 := (or #18594 #18597 #18979)
-#19024 := (and #12839 #12842 #13513 #13516 #13525 #13708 #18984)
-#18990 := (and #12575 #12584 #12590 #12593 #12596 #12601 #12604 #13516 #13525 #18984)
-#18995 := (or #18556 #18565 #18990)
-#19001 := (and #12575 #12578 #18995)
-#19006 := (or #18556 #18559 #19001)
-#19012 := (and #13513 #13516 #13707 #19006)
-#19029 := (or #19012 #19024)
-#19035 := (and #12575 #12584 #13513 #13516 #19029)
-#19040 := (or #18556 #18565 #19035)
-#19046 := (and #12575 #12578 #19040)
-#19051 := (or #18556 #18559 #19046)
-#19057 := (and #13513 #13516 #13802 #19051)
-#19124 := (or #19057 #19119)
-#15834 := (or #13994 #14008 #14461)
-#15839 := (forall (vars (?v0 Int)) #15834)
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 #19142 := (iff #18797 #19141)
 #19139 := (iff #18793 #19138)
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-#19133 := (iff #18785 #19130)
-#19127 := (and #12258 #12515 #12543 #12546 #12549 #12552 #12561 #13518 #13986 #14028 #14072 #15839 #15856 #15873 #15890 #19124)
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 #19128 := (iff #18785 #19127)
 #19125 := (iff #18781 #19124)
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-#19112 := (iff #19108 #19111)
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-#19100 := (iff #18742 #19099)
-#19097 := (iff #18741 #19096)
-#19098 := [rewrite]: #19097
-#19101 := [monotonicity #19098]: #19100
-#19094 := (iff #18746 #19091)
-#19083 := (+ #13841 #18744)
-#19086 := (<= #19083 0::Int)
-#19092 := (iff #19086 #19091)
+#19122 := (iff #18777 #19121)
+#19119 := (iff #18773 #19118)
+#19116 := (iff #18769 #19115)
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+#19111 := (iff #19107 #19110)
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+#19108 := (iff #18765 #19107)
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+#19097 := (iff #18757 #19096)
+#19094 := (iff #18753 #19091)
+#19088 := (or #19085 #18749)
+#19092 := (iff #19088 #19091)
 #19093 := [rewrite]: #19092
-#19087 := (iff #18746 #19086)
-#19084 := (= #18745 #19083)
-#19085 := [rewrite]: #19084
-#19088 := [monotonicity #19085]: #19087
-#19095 := [trans #19088 #19093]: #19094
-#19081 := (iff #18748 #19078)
-#19070 := (+ #13442 ?v0!15)
-#19073 := (>= #19070 0::Int)
-#19079 := (iff #19073 #19078)
-#19080 := [rewrite]: #19079
-#19074 := (iff #18748 #19073)
-#19071 := (= #18747 #19070)
-#19072 := [rewrite]: #19071
-#19075 := [monotonicity #19072]: #19074
-#19082 := [trans #19075 #19080]: #19081
-#19104 := [monotonicity #19082 #19095 #19101]: #19103
-#19107 := [monotonicity #19104]: #19106
-#19110 := [monotonicity #19107]: #19109
-#19115 := [trans #19110 #19113]: #19114
-#18882 := (iff #18526 #13518)
-#18883 := [rewrite]: #18882
-#19068 := (iff #18733 #12278)
-#19069 := [rewrite]: #19068
-#19066 := (iff #18730 #12275)
-#19067 := [rewrite]: #19066
-#19064 := (iff #18727 #12272)
+#19089 := (iff #18753 #19088)
+#19086 := (iff #18730 #19085)
+#19083 := (iff #18729 #19082)
+#19080 := (iff #18722 #19079)
+#19077 := (iff #18721 #19076)
+#19078 := [rewrite]: #19077
+#19081 := [monotonicity #19078]: #19080
+#19074 := (iff #18726 #19071)
+#19063 := (+ #13821 #18724)
+#19066 := (<= #19063 0::Int)
+#19072 := (iff #19066 #19071)
+#19073 := [rewrite]: #19072
+#19067 := (iff #18726 #19066)
+#19064 := (= #18725 #19063)
 #19065 := [rewrite]: #19064
-#19062 := (iff #18724 #12269)
-#19063 := [rewrite]: #19062
-#19118 := [monotonicity #19063 #19065 #19067 #19069 #18883 #13809 #19115]: #19117
-#19123 := [trans #19118 #19121]: #19122
-#19060 := (iff #18720 #19057)
-#19054 := (and #13518 #13802 #19051)
-#19058 := (iff #19054 #19057)
-#19059 := [rewrite]: #19058
-#19055 := (iff #18720 #19054)
-#19052 := (iff #18716 #19051)
-#19049 := (iff #18712 #19046)
-#19043 := (and #12581 #19040)
-#19047 := (iff #19043 #19046)
-#19048 := [rewrite]: #19047
-#19044 := (iff #18712 #19043)
-#19041 := (iff #18708 #19040)
-#19038 := (iff #18704 #19035)
-#19032 := (and #12587 #13518 #19029)
-#19036 := (iff #19032 #19035)
-#19037 := [rewrite]: #19036
-#19033 := (iff #18704 #19032)
-#19030 := (iff #18700 #19029)
-#19027 := (iff #18696 #19024)
-#19021 := (and #12839 #12842 #13518 #13527 #13708 #18984)
-#19025 := (iff #19021 #19024)
-#19026 := [rewrite]: #19025
-#19022 := (iff #18696 #19021)
-#18985 := (iff #18664 #18984)
-#18982 := (iff #18660 #18979)
-#18976 := (and #12622 #13544 #13618 #18971 #15936)
-#18980 := (iff #18976 #18979)
-#18981 := [rewrite]: #18980
-#18977 := (iff #18660 #18976)
-#18974 := (iff #18657 #15936)
-#18975 := [rewrite]: #18974
-#18972 := (iff #18653 #18971)
-#18969 := (iff #18649 #18968)
-#18966 := (iff #18645 #18963)
-#18960 := (or #18957 #18641)
-#18964 := (iff #18960 #18963)
-#18965 := [rewrite]: #18964
-#18961 := (iff #18645 #18960)
-#18958 := (iff #18626 #18957)
-#18955 := (iff #18625 #18954)
-#18952 := (iff #18618 #18951)
-#18949 := (iff #18617 #18948)
-#18950 := [rewrite]: #18949
-#18953 := [monotonicity #18950]: #18952
-#18946 := (iff #18622 #18943)
-#18935 := (+ #13570 #18620)
-#18938 := (<= #18935 0::Int)
-#18944 := (iff #18938 #18943)
+#19068 := [monotonicity #19065]: #19067
+#19075 := [trans #19068 #19073]: #19074
+#19061 := (iff #18728 #19058)
+#19050 := (+ #13422 ?v0!15)
+#19053 := (>= #19050 0::Int)
+#19059 := (iff #19053 #19058)
+#19060 := [rewrite]: #19059
+#19054 := (iff #18728 #19053)
+#19051 := (= #18727 #19050)
+#19052 := [rewrite]: #19051
+#19055 := [monotonicity #19052]: #19054
+#19062 := [trans #19055 #19060]: #19061
+#19084 := [monotonicity #19062 #19075 #19081]: #19083
+#19087 := [monotonicity #19084]: #19086
+#19090 := [monotonicity #19087]: #19089
+#19095 := [trans #19090 #19093]: #19094
+#18862 := (iff #18506 #13498)
+#18863 := [rewrite]: #18862
+#19048 := (iff #18713 #12258)
+#19049 := [rewrite]: #19048
+#19046 := (iff #18710 #12255)
+#19047 := [rewrite]: #19046
+#19044 := (iff #18707 #12252)
+#19045 := [rewrite]: #19044
+#19042 := (iff #18704 #12249)
+#19043 := [rewrite]: #19042
+#19098 := [monotonicity #19043 #19045 #19047 #19049 #18863 #13789 #19095]: #19097
+#19103 := [trans #19098 #19101]: #19102
+#19040 := (iff #18700 #19037)
+#19034 := (and #13498 #13782 #19031)
+#19038 := (iff #19034 #19037)
+#19039 := [rewrite]: #19038
+#19035 := (iff #18700 #19034)
+#19032 := (iff #18696 #19031)
+#19029 := (iff #18692 #19026)
+#19023 := (and #12561 #19020)
+#19027 := (iff #19023 #19026)
+#19028 := [rewrite]: #19027
+#19024 := (iff #18692 #19023)
+#19021 := (iff #18688 #19020)
+#19018 := (iff #18684 #19015)
+#19012 := (and #12567 #13498 #19009)
+#19016 := (iff #19012 #19015)
+#19017 := [rewrite]: #19016
+#19013 := (iff #18684 #19012)
+#19010 := (iff #18680 #19009)
+#19007 := (iff #18676 #19004)
+#19001 := (and #12819 #12822 #13498 #13507 #13688 #18964)
+#19005 := (iff #19001 #19004)
+#19006 := [rewrite]: #19005
+#19002 := (iff #18676 #19001)
+#18965 := (iff #18644 #18964)
+#18962 := (iff #18640 #18959)
+#18956 := (and #12602 #13524 #13598 #18951 #15916)
+#18960 := (iff #18956 #18959)
+#18961 := [rewrite]: #18960
+#18957 := (iff #18640 #18956)
+#18954 := (iff #18637 #15916)
+#18955 := [rewrite]: #18954
+#18952 := (iff #18633 #18951)
+#18949 := (iff #18629 #18948)
+#18946 := (iff #18625 #18943)
+#18940 := (or #18937 #18621)
+#18944 := (iff #18940 #18943)
 #18945 := [rewrite]: #18944
-#18939 := (iff #18622 #18938)
-#18936 := (= #18621 #18935)
-#18937 := [rewrite]: #18936
-#18940 := [monotonicity #18937]: #18939
-#18947 := [trans #18940 #18945]: #18946
-#18933 := (iff #18624 #18930)
-#18922 := (+ #13551 ?v0!14)
-#18925 := (>= #18922 0::Int)
-#18931 := (iff #18925 #18930)
-#18932 := [rewrite]: #18931
-#18926 := (iff #18624 #18925)
-#18923 := (= #18623 #18922)
-#18924 := [rewrite]: #18923
-#18927 := [monotonicity #18924]: #18926
-#18934 := [trans #18927 #18932]: #18933
-#18956 := [monotonicity #18934 #18947 #18953]: #18955
-#18959 := [monotonicity #18956]: #18958
-#18962 := [monotonicity #18959]: #18961
-#18967 := [trans #18962 #18965]: #18966
-#18920 := (iff #18611 #13550)
-#18921 := [rewrite]: #18920
-#18970 := [monotonicity #18921 #18967]: #18969
-#18973 := [monotonicity #18970]: #18972
-#18918 := (iff #18606 #13618)
-#18919 := [rewrite]: #18918
-#18916 := (iff #18603 #13544)
+#18941 := (iff #18625 #18940)
+#18938 := (iff #18606 #18937)
+#18935 := (iff #18605 #18934)
+#18932 := (iff #18598 #18931)
+#18929 := (iff #18597 #18928)
+#18930 := [rewrite]: #18929
+#18933 := [monotonicity #18930]: #18932
+#18926 := (iff #18602 #18923)
+#18915 := (+ #13550 #18600)
+#18918 := (<= #18915 0::Int)
+#18924 := (iff #18918 #18923)
+#18925 := [rewrite]: #18924
+#18919 := (iff #18602 #18918)
+#18916 := (= #18601 #18915)
 #18917 := [rewrite]: #18916
-#18914 := (iff #18600 #12622)
-#18915 := [rewrite]: #18914
-#18978 := [monotonicity #18915 #18917 #18919 #18973 #18975]: #18977
-#18983 := [trans #18978 #18981]: #18982
-#18986 := [monotonicity #18983]: #18985
-#18912 := (iff #18591 #13527)
-#18913 := [rewrite]: #18912
-#19019 := (iff #18691 #12842)
-#19020 := [rewrite]: #19019
-#19017 := (iff #18688 #12839)
-#19018 := [rewrite]: #19017
-#19023 := [monotonicity #19018 #19020 #18883 #18913 #13717 #18986]: #19022
-#19028 := [trans #19023 #19026]: #19027
-#19015 := (iff #18684 #19012)
-#19009 := (and #13518 #13707 #19006)
-#19013 := (iff #19009 #19012)
-#19014 := [rewrite]: #19013
-#19010 := (iff #18684 #19009)
-#19007 := (iff #18680 #19006)
-#19004 := (iff #18676 #19001)
-#18998 := (and #12581 #18995)
-#19002 := (iff #18998 #19001)
-#19003 := [rewrite]: #19002
-#18999 := (iff #18676 #18998)
-#18996 := (iff #18672 #18995)
-#18993 := (iff #18668 #18990)
-#18987 := (and #12587 #12590 #12593 #12596 #12601 #12604 #13516 #13527 #18984)
-#18991 := (iff #18987 #18990)
-#18992 := [rewrite]: #18991
-#18988 := (iff #18668 #18987)
-#18910 := (iff #18588 #13516)
-#18911 := [rewrite]: #18910
-#18908 := (iff #18585 #12604)
-#18909 := [rewrite]: #18908
-#18906 := (iff #18582 #12601)
-#18907 := [rewrite]: #18906
-#18904 := (iff #18579 #12596)
-#18905 := [rewrite]: #18904
-#18902 := (iff #18576 #12593)
-#18903 := [rewrite]: #18902
-#18900 := (iff #18573 #12590)
+#18920 := [monotonicity #18917]: #18919
+#18927 := [trans #18920 #18925]: #18926
+#18913 := (iff #18604 #18910)
+#18902 := (+ #13531 ?v0!14)
+#18905 := (>= #18902 0::Int)
+#18911 := (iff #18905 #18910)
+#18912 := [rewrite]: #18911
+#18906 := (iff #18604 #18905)
+#18903 := (= #18603 #18902)
+#18904 := [rewrite]: #18903
+#18907 := [monotonicity #18904]: #18906
+#18914 := [trans #18907 #18912]: #18913
+#18936 := [monotonicity #18914 #18927 #18933]: #18935
+#18939 := [monotonicity #18936]: #18938
+#18942 := [monotonicity #18939]: #18941
+#18947 := [trans #18942 #18945]: #18946
+#18900 := (iff #18591 #13530)
 #18901 := [rewrite]: #18900
-#18898 := (iff #18568 #12587)
+#18950 := [monotonicity #18901 #18947]: #18949
+#18953 := [monotonicity #18950]: #18952
+#18898 := (iff #18586 #13598)
 #18899 := [rewrite]: #18898
-#18989 := [monotonicity #18899 #18901 #18903 #18905 #18907 #18909 #18911 #18913 #18986]: #18988
-#18994 := [trans #18989 #18992]: #18993
-#18997 := [monotonicity #18994]: #18996
-#18896 := (iff #18562 #12581)
+#18896 := (iff #18583 #13524)
 #18897 := [rewrite]: #18896
-#19000 := [monotonicity #18897 #18997]: #18999
-#19005 := [trans #19000 #19003]: #19004
-#19008 := [monotonicity #19005]: #19007
-#19011 := [monotonicity #18883 #19008]: #19010
-#19016 := [trans #19011 #19014]: #19015
-#19031 := [monotonicity #19016 #19028]: #19030
-#19034 := [monotonicity #18899 #18883 #19031]: #19033
-#19039 := [trans #19034 #19037]: #19038
-#19042 := [monotonicity #19039]: #19041
-#19045 := [monotonicity #18897 #19042]: #19044
-#19050 := [trans #19045 #19048]: #19049
-#19053 := [monotonicity #19050]: #19052
-#19056 := [monotonicity #18883 #19053]: #19055
-#19061 := [trans #19056 #19059]: #19060
-#19126 := [monotonicity #19061 #19123]: #19125
-#18894 := (iff #18551 #15890)
+#18894 := (iff #18580 #12602)
 #18895 := [rewrite]: #18894
-#18892 := (iff #18548 #15873)
+#18958 := [monotonicity #18895 #18897 #18899 #18953 #18955]: #18957
+#18963 := [trans #18958 #18961]: #18962
+#18966 := [monotonicity #18963]: #18965
+#18892 := (iff #18571 #13507)
 #18893 := [rewrite]: #18892
-#18890 := (iff #18545 #15856)
+#18999 := (iff #18671 #12822)
+#19000 := [rewrite]: #18999
+#18997 := (iff #18668 #12819)
+#18998 := [rewrite]: #18997
+#19003 := [monotonicity #18998 #19000 #18863 #18893 #13697 #18966]: #19002
+#19008 := [trans #19003 #19006]: #19007
+#18995 := (iff #18664 #18992)
+#18989 := (and #13498 #13687 #18986)
+#18993 := (iff #18989 #18992)
+#18994 := [rewrite]: #18993
+#18990 := (iff #18664 #18989)
+#18987 := (iff #18660 #18986)
+#18984 := (iff #18656 #18981)
+#18978 := (and #12561 #18975)
+#18982 := (iff #18978 #18981)
+#18983 := [rewrite]: #18982
+#18979 := (iff #18656 #18978)
+#18976 := (iff #18652 #18975)
+#18973 := (iff #18648 #18970)
+#18967 := (and #12567 #12570 #12573 #12576 #12581 #12584 #13496 #13507 #18964)
+#18971 := (iff #18967 #18970)
+#18972 := [rewrite]: #18971
+#18968 := (iff #18648 #18967)
+#18890 := (iff #18568 #13496)
 #18891 := [rewrite]: #18890
-#18888 := (iff #18535 #14072)
+#18888 := (iff #18565 #12584)
 #18889 := [rewrite]: #18888
-#18886 := (iff #18532 #14028)
+#18886 := (iff #18562 #12581)
 #18887 := [rewrite]: #18886
-#18884 := (iff #18529 #13986)
+#18884 := (iff #18559 #12576)
 #18885 := [rewrite]: #18884
-#18880 := (iff #18523 #12561)
+#18882 := (iff #18556 #12573)
+#18883 := [rewrite]: #18882
+#18880 := (iff #18553 #12570)
 #18881 := [rewrite]: #18880
-#18878 := (iff #18520 #12552)
+#18878 := (iff #18548 #12567)
 #18879 := [rewrite]: #18878
-#18876 := (iff #18517 #12549)
+#18969 := [monotonicity #18879 #18881 #18883 #18885 #18887 #18889 #18891 #18893 #18966]: #18968
+#18974 := [trans #18969 #18972]: #18973
+#18977 := [monotonicity #18974]: #18976
+#18876 := (iff #18542 #12561)
 #18877 := [rewrite]: #18876
-#18874 := (iff #18514 #12546)
+#18980 := [monotonicity #18877 #18977]: #18979
+#18985 := [trans #18980 #18983]: #18984
+#18988 := [monotonicity #18985]: #18987
+#18991 := [monotonicity #18863 #18988]: #18990
+#18996 := [trans #18991 #18994]: #18995
+#19011 := [monotonicity #18996 #19008]: #19010
+#19014 := [monotonicity #18879 #18863 #19011]: #19013
+#19019 := [trans #19014 #19017]: #19018
+#19022 := [monotonicity #19019]: #19021
+#19025 := [monotonicity #18877 #19022]: #19024
+#19030 := [trans #19025 #19028]: #19029
+#19033 := [monotonicity #19030]: #19032
+#19036 := [monotonicity #18863 #19033]: #19035
+#19041 := [trans #19036 #19039]: #19040
+#19106 := [monotonicity #19041 #19103]: #19105
+#18874 := (iff #18531 #15870)
 #18875 := [rewrite]: #18874
-#18872 := (iff #18511 #12543)
+#18872 := (iff #18528 #15853)
 #18873 := [rewrite]: #18872
-#18870 := (iff #18508 #12515)
+#18870 := (iff #18525 #15836)
 #18871 := [rewrite]: #18870
-#18868 := (iff #18505 #12258)
+#18868 := (iff #18515 #14052)
 #18869 := [rewrite]: #18868
-#19129 := [monotonicity #18869 #18871 #18873 #18875 #18877 #18879 #18881 #18883 #18885 #18887 #18889 #18891 #18893 #18895 #19126]: #19128
-#19134 := [trans #19129 #19132]: #19133
-#19137 := [monotonicity #14238 #19134]: #19136
+#18866 := (iff #18512 #14008)
+#18867 := [rewrite]: #18866
+#18864 := (iff #18509 #13966)
+#18865 := [rewrite]: #18864
+#18860 := (iff #18503 #12541)
+#18861 := [rewrite]: #18860
+#18858 := (iff #18500 #12532)
+#18859 := [rewrite]: #18858
+#18856 := (iff #18497 #12529)
+#18857 := [rewrite]: #18856
+#18854 := (iff #18494 #12526)
+#18855 := [rewrite]: #18854
+#18852 := (iff #18491 #12523)
+#18853 := [rewrite]: #18852
+#18850 := (iff #18488 #12495)
+#18851 := [rewrite]: #18850
+#18848 := (iff #18485 #12238)
+#18849 := [rewrite]: #18848
+#19109 := [monotonicity #18849 #18851 #18853 #18855 #18857 #18859 #18861 #18863 #18865 #18867 #18869 #18871 #18873 #18875 #19106]: #19108
+#19114 := [trans #19109 #19112]: #19113
+#19117 := [monotonicity #14218 #19114]: #19116
+#19120 := [monotonicity #19117]: #19119
+#18846 := (iff #18469 #18845)
+#18843 := (iff #18468 #18840)
+#18837 := (or #18467 #18466 #18834)
+#18841 := (iff #18837 #18840)
+#18842 := [rewrite]: #18841
+#18838 := (iff #18468 #18837)
+#18835 := (iff #18461 #18834)
+#18832 := (iff #18460 #18831)
+#18833 := [rewrite]: #18832
+#18836 := [monotonicity #18833]: #18835
+#18839 := [monotonicity #18836]: #18838
+#18844 := [trans #18839 #18842]: #18843
+#18847 := [monotonicity #18844]: #18846
+#19123 := [monotonicity #18847 #19120]: #19122
+#18829 := (iff #18454 #13449)
+#18830 := [rewrite]: #18829
+#19126 := [monotonicity #18830 #19123]: #19125
+#19129 := [monotonicity #19126]: #19128
+#18827 := (iff #18449 #12181)
+#18828 := [rewrite]: #18827
+#18825 := (iff #18446 #12178)
+#18826 := [rewrite]: #18825
+#18823 := (iff #18443 #12175)
+#18824 := [rewrite]: #18823
+#18821 := (iff #18440 #12172)
+#18822 := [rewrite]: #18821
+#18819 := (iff #18437 #3102)
+#18820 := [rewrite]: #18819
+#19132 := [monotonicity #18820 #18822 #18824 #18826 #18828 #19129]: #19131
+#19137 := [trans #19132 #19135]: #19136
 #19140 := [monotonicity #19137]: #19139
-#18866 := (iff #18489 #18865)
-#18863 := (iff #18488 #18860)
-#18857 := (or #18487 #18486 #18854)
-#18861 := (iff #18857 #18860)
-#18862 := [rewrite]: #18861
-#18858 := (iff #18488 #18857)
-#18855 := (iff #18481 #18854)
-#18852 := (iff #18480 #18851)
-#18853 := [rewrite]: #18852
-#18856 := [monotonicity #18853]: #18855
-#18859 := [monotonicity #18856]: #18858
-#18864 := [trans #18859 #18862]: #18863
-#18867 := [monotonicity #18864]: #18866
-#19143 := [monotonicity #18867 #19140]: #19142
-#18849 := (iff #18474 #13469)
-#18850 := [rewrite]: #18849
-#19146 := [monotonicity #18850 #19143]: #19145
-#19149 := [monotonicity #19146]: #19148
-#18847 := (iff #18469 #12201)
-#18848 := [rewrite]: #18847
-#18845 := (iff #18466 #12198)
-#18846 := [rewrite]: #18845
-#18843 := (iff #18463 #12195)
-#18844 := [rewrite]: #18843
-#18841 := (iff #18460 #12192)
-#18842 := [rewrite]: #18841
-#18839 := (iff #18457 #3109)
-#18840 := [rewrite]: #18839
-#19152 := [monotonicity #18840 #18842 #18844 #18846 #18848 #19149]: #19151
-#19157 := [trans #19152 #19155]: #19156
-#19160 := [monotonicity #19157]: #19159
-#18837 := (iff #18451 #12186)
-#18838 := [rewrite]: #18837
-#19163 := [monotonicity #18838 #19160]: #19162
-#19168 := [trans #19163 #19166]: #19167
-#19171 := [monotonicity #19168]: #19170
-#18835 := (iff #18442 #12177)
-#18836 := [rewrite]: #18835
-#19174 := [monotonicity #18836 #19171]: #19173
-#19177 := [monotonicity #19174]: #19176
-#16026 := (exists (vars (?v0 Int)) #16021)
-#16015 := (not #16012)
-#16029 := (or #16015 #16026)
-#16032 := (and #16012 #16029)
-#16035 := (or #12340 #12331 #12322 #12313 #13521 #13802 #16032)
-#15916 := (not #15913)
-#15922 := (or #13601 #15916)
-#15927 := (and #15913 #15922)
-#15930 := (or #13555 #15927)
-#15933 := (and #13550 #15930)
-#15945 := (or #12692 #13547 #13622 #15933 #15939)
-#15950 := (and #13534 #15900 #15945)
-#15976 := (or #12857 #12848 #13521 #13530 #13707 #15950)
-#15953 := (or #12785 #12776 #12767 #12758 #12740 #12731 #13656 #13530 #15950)
-#15956 := (and #12575 #12584 #15953)
-#15959 := (or #12797 #15956)
-#15962 := (and #12575 #12578 #15959)
-#15968 := (or #13521 #13708 #15962)
-#15981 := (and #15968 #15976)
-#15984 := (or #12785 #13521 #15981)
-#15987 := (and #12575 #12584 #15984)
-#15990 := (or #12797 #15987)
-#15993 := (and #12575 #12578 #15990)
-#15999 := (or #13521 #13801 #15993)
-#16038 := (and #15999 #16035)
-#15842 := (not #15839)
-#16044 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #14031 #14077 #15842 #15859 #15876 #15893 #16038)
-#16049 := (and #3109 #13509 #16044)
-#15828 := (not #15825)
-#16052 := (or #15828 #16049)
-#16055 := (and #15825 #16052)
-#16058 := (or #13472 #16055)
-#16061 := (and #13469 #16058)
-#16064 := (or #13267 #13276 #13258 #13249 #13240 #16061)
-#16067 := (and #12180 #12189 #16064)
-#16070 := (or #13288 #16067)
-#16073 := (and #12180 #12183 #16070)
-#16076 := (or #13300 #16073)
-#16079 := (and #12177 #16076)
-#16082 := (not #16079)
-#18830 := (~ #16082 #18829)
-#18826 := (not #16076)
-#18827 := (~ #18826 #18825)
-#18822 := (not #16073)
-#18823 := (~ #18822 #18821)
-#18818 := (not #16070)
-#18819 := (~ #18818 #18817)
-#18814 := (not #16067)
-#18815 := (~ #18814 #18813)
-#18810 := (not #16064)
-#18811 := (~ #18810 #18809)
-#18806 := (not #16061)
+#18817 := (iff #18431 #12166)
+#18818 := [rewrite]: #18817
+#19143 := [monotonicity #18818 #19140]: #19142
+#19148 := [trans #19143 #19146]: #19147
+#19151 := [monotonicity #19148]: #19150
+#18815 := (iff #18422 #12157)
+#18816 := [rewrite]: #18815
+#19154 := [monotonicity #18816 #19151]: #19153
+#19157 := [monotonicity #19154]: #19156
+#16006 := (exists (vars (?v0 Int)) #16001)
+#15995 := (not #15992)
+#16009 := (or #15995 #16006)
+#16012 := (and #15992 #16009)
+#16015 := (or #12320 #12311 #12302 #12293 #13501 #13782 #16012)
+#15896 := (not #15893)
+#15902 := (or #13581 #15896)
+#15907 := (and #15893 #15902)
+#15910 := (or #13535 #15907)
+#15913 := (and #13530 #15910)
+#15925 := (or #12672 #13527 #13602 #15913 #15919)
+#15930 := (and #13514 #15880 #15925)
+#15956 := (or #12837 #12828 #13501 #13510 #13687 #15930)
+#15933 := (or #12765 #12756 #12747 #12738 #12720 #12711 #13636 #13510 #15930)
+#15936 := (and #12555 #12564 #15933)
+#15939 := (or #12777 #15936)
+#15942 := (and #12555 #12558 #15939)
+#15948 := (or #13501 #13688 #15942)
+#15961 := (and #15948 #15956)
+#15964 := (or #12765 #13501 #15961)
+#15967 := (and #12555 #12564 #15964)
+#15970 := (or #12777 #15967)
+#15973 := (and #12555 #12558 #15970)
+#15979 := (or #13501 #13781 #15973)
+#16018 := (and #15979 #16015)
+#15822 := (not #15819)
+#16024 := (or #15279 #13954 #13040 #13031 #13022 #13013 #13004 #13501 #13971 #14011 #14057 #15822 #15839 #15856 #15873 #16018)
+#16029 := (and #3102 #13489 #16024)
+#15808 := (not #15805)
+#16032 := (or #15808 #16029)
+#16035 := (and #15805 #16032)
+#16038 := (or #13452 #16035)
+#16041 := (and #13449 #16038)
+#16044 := (or #13247 #13256 #13238 #13229 #13220 #16041)
+#16047 := (and #12160 #12169 #16044)
+#16050 := (or #13268 #16047)
+#16053 := (and #12160 #12163 #16050)
+#16056 := (or #13280 #16053)
+#16059 := (and #12157 #16056)
+#16062 := (not #16059)
+#18810 := (~ #16062 #18809)
+#18806 := (not #16056)
 #18807 := (~ #18806 #18805)
-#18802 := (not #16058)
+#18802 := (not #16053)
 #18803 := (~ #18802 #18801)
-#18798 := (not #16055)
+#18798 := (not #16050)
 #18799 := (~ #18798 #18797)
-#18794 := (not #16052)
+#18794 := (not #16047)
 #18795 := (~ #18794 #18793)
-#18790 := (not #16049)
+#18790 := (not #16044)
 #18791 := (~ #18790 #18789)
-#18786 := (not #16044)
+#18786 := (not #16041)
 #18787 := (~ #18786 #18785)
 #18782 := (not #16038)
 #18783 := (~ #18782 #18781)
@@ -6013,1792 +6003,1802 @@
 #18775 := (~ #18774 #18773)
 #18770 := (not #16029)
 #18771 := (~ #18770 #18769)
-#18766 := (not #16026)
+#18766 := (not #16024)
 #18767 := (~ #18766 #18765)
-#18763 := (~ #18762 #18762)
-#18764 := [refl]: #18763
-#18768 := [nnf-neg #18764]: #18767
-#18759 := (not #16015)
-#18760 := (~ #18759 #16012)
-#18757 := (~ #16012 #16012)
-#18755 := (~ #16007 #16007)
-#18756 := [refl]: #18755
-#18758 := [nnf-pos #18756]: #18757
-#18761 := [nnf-neg #18758]: #18760
-#18772 := [nnf-neg #18761 #18768]: #18771
-#18751 := (~ #16015 #18750)
-#18752 := [sk]: #18751
-#18776 := [nnf-neg #18752 #18772]: #18775
-#18736 := (~ #13805 #13805)
-#18737 := [refl]: #18736
-#18527 := (~ #18526 #18526)
-#18528 := [refl]: #18527
-#18734 := (~ #18733 #18733)
-#18735 := [refl]: #18734
-#18731 := (~ #18730 #18730)
-#18732 := [refl]: #18731
-#18728 := (~ #18727 #18727)
-#18729 := [refl]: #18728
-#18725 := (~ #18724 #18724)
-#18726 := [refl]: #18725
-#18780 := [nnf-neg #18726 #18729 #18732 #18735 #18528 #18737 #18776]: #18779
-#18721 := (not #15999)
-#18722 := (~ #18721 #18720)
-#18717 := (not #15993)
-#18718 := (~ #18717 #18716)
-#18713 := (not #15990)
-#18714 := (~ #18713 #18712)
-#18709 := (not #15987)
-#18710 := (~ #18709 #18708)
-#18705 := (not #15984)
-#18706 := (~ #18705 #18704)
-#18701 := (not #15981)
+#18762 := (not #16018)
+#18763 := (~ #18762 #18761)
+#18758 := (not #16015)
+#18759 := (~ #18758 #18757)
+#18754 := (not #16012)
+#18755 := (~ #18754 #18753)
+#18750 := (not #16009)
+#18751 := (~ #18750 #18749)
+#18746 := (not #16006)
+#18747 := (~ #18746 #18745)
+#18743 := (~ #18742 #18742)
+#18744 := [refl]: #18743
+#18748 := [nnf-neg #18744]: #18747
+#18739 := (not #15995)
+#18740 := (~ #18739 #15992)
+#18737 := (~ #15992 #15992)
+#18735 := (~ #15987 #15987)
+#18736 := [refl]: #18735
+#18738 := [nnf-pos #18736]: #18737
+#18741 := [nnf-neg #18738]: #18740
+#18752 := [nnf-neg #18741 #18748]: #18751
+#18731 := (~ #15995 #18730)
+#18732 := [sk]: #18731
+#18756 := [nnf-neg #18732 #18752]: #18755
+#18716 := (~ #13785 #13785)
+#18717 := [refl]: #18716
+#18507 := (~ #18506 #18506)
+#18508 := [refl]: #18507
+#18714 := (~ #18713 #18713)
+#18715 := [refl]: #18714
+#18711 := (~ #18710 #18710)
+#18712 := [refl]: #18711
+#18708 := (~ #18707 #18707)
+#18709 := [refl]: #18708
+#18705 := (~ #18704 #18704)
+#18706 := [refl]: #18705
+#18760 := [nnf-neg #18706 #18709 #18712 #18715 #18508 #18717 #18756]: #18759
+#18701 := (not #15979)
 #18702 := (~ #18701 #18700)
-#18697 := (not #15976)
+#18697 := (not #15973)
 #18698 := (~ #18697 #18696)
-#18665 := (not #15950)
-#18666 := (~ #18665 #18664)
-#18661 := (not #15945)
-#18662 := (~ #18661 #18660)
-#18658 := (~ #18657 #18657)
-#18659 := [refl]: #18658
-#18654 := (not #15933)
-#18655 := (~ #18654 #18653)
-#18650 := (not #15930)
-#18651 := (~ #18650 #18649)
-#18646 := (not #15927)
-#18647 := (~ #18646 #18645)
-#18642 := (not #15922)
-#18643 := (~ #18642 #18641)
-#18638 := (not #15916)
-#18639 := (~ #18638 #15913)
-#18636 := (~ #15913 #15913)
-#18634 := (~ #15908 #15908)
-#18635 := [refl]: #18634
-#18637 := [nnf-pos #18635]: #18636
-#18640 := [nnf-neg #18637]: #18639
-#18632 := (~ #18631 #18631)
-#18633 := [refl]: #18632
-#18644 := [nnf-neg #18633 #18640]: #18643
-#18627 := (~ #15916 #18626)
-#18628 := [sk]: #18627
-#18648 := [nnf-neg #18628 #18644]: #18647
+#18693 := (not #15970)
+#18694 := (~ #18693 #18692)
+#18689 := (not #15967)
+#18690 := (~ #18689 #18688)
+#18685 := (not #15964)
+#18686 := (~ #18685 #18684)
+#18681 := (not #15961)
+#18682 := (~ #18681 #18680)
+#18677 := (not #15956)
+#18678 := (~ #18677 #18676)
+#18645 := (not #15930)
+#18646 := (~ #18645 #18644)
+#18641 := (not #15925)
+#18642 := (~ #18641 #18640)
+#18638 := (~ #18637 #18637)
+#18639 := [refl]: #18638
+#18634 := (not #15913)
+#18635 := (~ #18634 #18633)
+#18630 := (not #15910)
+#18631 := (~ #18630 #18629)
+#18626 := (not #15907)
+#18627 := (~ #18626 #18625)
+#18622 := (not #15902)
+#18623 := (~ #18622 #18621)
+#18618 := (not #15896)
+#18619 := (~ #18618 #15893)
+#18616 := (~ #15893 #15893)
+#18614 := (~ #15888 #15888)
+#18615 := [refl]: #18614
+#18617 := [nnf-pos #18615]: #18616
+#18620 := [nnf-neg #18617]: #18619
 #18612 := (~ #18611 #18611)
 #18613 := [refl]: #18612
-#18652 := [nnf-neg #18613 #18648]: #18651
-#18609 := (~ #13555 #13555)
-#18610 := [refl]: #18609
-#18656 := [nnf-neg #18610 #18652]: #18655
-#18607 := (~ #18606 #18606)
-#18608 := [refl]: #18607
-#18604 := (~ #18603 #18603)
-#18605 := [refl]: #18604
-#18601 := (~ #18600 #18600)
-#18602 := [refl]: #18601
-#18663 := [nnf-neg #18602 #18605 #18608 #18656 #18659]: #18662
-#18598 := (~ #18597 #18597)
-#18599 := [refl]: #18598
-#18595 := (~ #18594 #18594)
-#18596 := [refl]: #18595
-#18667 := [nnf-neg #18596 #18599 #18663]: #18666
-#18694 := (~ #13713 #13713)
-#18695 := [refl]: #18694
+#18624 := [nnf-neg #18613 #18620]: #18623
+#18607 := (~ #15896 #18606)
+#18608 := [sk]: #18607
+#18628 := [nnf-neg #18608 #18624]: #18627
 #18592 := (~ #18591 #18591)
 #18593 := [refl]: #18592
-#18692 := (~ #18691 #18691)
-#18693 := [refl]: #18692
-#18689 := (~ #18688 #18688)
-#18690 := [refl]: #18689
-#18699 := [nnf-neg #18690 #18693 #18528 #18593 #18695 #18667]: #18698
-#18685 := (not #15968)
-#18686 := (~ #18685 #18684)
-#18681 := (not #15962)
-#18682 := (~ #18681 #18680)
-#18677 := (not #15959)
-#18678 := (~ #18677 #18676)
-#18673 := (not #15956)
-#18674 := (~ #18673 #18672)
-#18669 := (not #15953)
-#18670 := (~ #18669 #18668)
-#18589 := (~ #18588 #18588)
+#18632 := [nnf-neg #18593 #18628]: #18631
+#18589 := (~ #13535 #13535)
 #18590 := [refl]: #18589
-#18586 := (~ #18585 #18585)
-#18587 := [refl]: #18586
-#18583 := (~ #18582 #18582)
-#18584 := [refl]: #18583
-#18580 := (~ #18579 #18579)
-#18581 := [refl]: #18580
-#18577 := (~ #18576 #18576)
-#18578 := [refl]: #18577
-#18574 := (~ #18573 #18573)
-#18575 := [refl]: #18574
+#18636 := [nnf-neg #18590 #18632]: #18635
+#18587 := (~ #18586 #18586)
+#18588 := [refl]: #18587
+#18584 := (~ #18583 #18583)
+#18585 := [refl]: #18584
+#18581 := (~ #18580 #18580)
+#18582 := [refl]: #18581
+#18643 := [nnf-neg #18582 #18585 #18588 #18636 #18639]: #18642
+#18578 := (~ #18577 #18577)
+#18579 := [refl]: #18578
+#18575 := (~ #18574 #18574)
+#18576 := [refl]: #18575
+#18647 := [nnf-neg #18576 #18579 #18643]: #18646
+#18674 := (~ #13693 #13693)
+#18675 := [refl]: #18674
+#18572 := (~ #18571 #18571)
+#18573 := [refl]: #18572
+#18672 := (~ #18671 #18671)
+#18673 := [refl]: #18672
+#18669 := (~ #18668 #18668)
+#18670 := [refl]: #18669
+#18679 := [nnf-neg #18670 #18673 #18508 #18573 #18675 #18647]: #18678
+#18665 := (not #15948)
+#18666 := (~ #18665 #18664)
+#18661 := (not #15942)
+#18662 := (~ #18661 #18660)
+#18657 := (not #15939)
+#18658 := (~ #18657 #18656)
+#18653 := (not #15936)
+#18654 := (~ #18653 #18652)
+#18649 := (not #15933)
+#18650 := (~ #18649 #18648)
 #18569 := (~ #18568 #18568)
 #18570 := [refl]: #18569
-#18671 := [nnf-neg #18570 #18575 #18578 #18581 #18584 #18587 #18590 #18593 #18667]: #18670
 #18566 := (~ #18565 #18565)
 #18567 := [refl]: #18566
-#18557 := (~ #18556 #18556)
-#18558 := [refl]: #18557
-#18675 := [nnf-neg #18558 #18567 #18671]: #18674
 #18563 := (~ #18562 #18562)
 #18564 := [refl]: #18563
-#18679 := [nnf-neg #18564 #18675]: #18678
 #18560 := (~ #18559 #18559)
 #18561 := [refl]: #18560
-#18683 := [nnf-neg #18558 #18561 #18679]: #18682
-#18571 := (~ #13707 #13707)
-#18572 := [refl]: #18571
-#18687 := [nnf-neg #18528 #18572 #18683]: #18686
-#18703 := [nnf-neg #18687 #18699]: #18702
-#18707 := [nnf-neg #18570 #18528 #18703]: #18706
-#18711 := [nnf-neg #18558 #18567 #18707]: #18710
-#18715 := [nnf-neg #18564 #18711]: #18714
-#18719 := [nnf-neg #18558 #18561 #18715]: #18718
-#18554 := (~ #13802 #13802)
+#18557 := (~ #18556 #18556)
+#18558 := [refl]: #18557
+#18554 := (~ #18553 #18553)
 #18555 := [refl]: #18554
-#18723 := [nnf-neg #18528 #18555 #18719]: #18722
-#18784 := [nnf-neg #18723 #18780]: #18783
-#18552 := (~ #18551 #18551)
-#18553 := [refl]: #18552
 #18549 := (~ #18548 #18548)
 #18550 := [refl]: #18549
+#18651 := [nnf-neg #18550 #18555 #18558 #18561 #18564 #18567 #18570 #18573 #18647]: #18650
 #18546 := (~ #18545 #18545)
 #18547 := [refl]: #18546
-#18542 := (not #15842)
-#18543 := (~ #18542 #15839)
-#18540 := (~ #15839 #15839)
-#18538 := (~ #15834 #15834)
-#18539 := [refl]: #18538
-#18541 := [nnf-pos #18539]: #18540
-#18544 := [nnf-neg #18541]: #18543
-#18536 := (~ #18535 #18535)
-#18537 := [refl]: #18536
-#18533 := (~ #18532 #18532)
-#18534 := [refl]: #18533
-#18530 := (~ #18529 #18529)
-#18531 := [refl]: #18530
-#18524 := (~ #18523 #18523)
-#18525 := [refl]: #18524
-#18521 := (~ #18520 #18520)
-#18522 := [refl]: #18521
-#18518 := (~ #18517 #18517)
+#18537 := (~ #18536 #18536)
+#18538 := [refl]: #18537
+#18655 := [nnf-neg #18538 #18547 #18651]: #18654
+#18543 := (~ #18542 #18542)
+#18544 := [refl]: #18543
+#18659 := [nnf-neg #18544 #18655]: #18658
+#18540 := (~ #18539 #18539)
+#18541 := [refl]: #18540
+#18663 := [nnf-neg #18538 #18541 #18659]: #18662
+#18551 := (~ #13687 #13687)
+#18552 := [refl]: #18551
+#18667 := [nnf-neg #18508 #18552 #18663]: #18666
+#18683 := [nnf-neg #18667 #18679]: #18682
+#18687 := [nnf-neg #18550 #18508 #18683]: #18686
+#18691 := [nnf-neg #18538 #18547 #18687]: #18690
+#18695 := [nnf-neg #18544 #18691]: #18694
+#18699 := [nnf-neg #18538 #18541 #18695]: #18698
+#18534 := (~ #13782 #13782)
+#18535 := [refl]: #18534
+#18703 := [nnf-neg #18508 #18535 #18699]: #18702
+#18764 := [nnf-neg #18703 #18760]: #18763
+#18532 := (~ #18531 #18531)
+#18533 := [refl]: #18532
+#18529 := (~ #18528 #18528)
+#18530 := [refl]: #18529
+#18526 := (~ #18525 #18525)
+#18527 := [refl]: #18526
+#18522 := (not #15822)
+#18523 := (~ #18522 #15819)
+#18520 := (~ #15819 #15819)
+#18518 := (~ #15814 #15814)
 #18519 := [refl]: #18518
-#18515 := (~ #18514 #18514)
-#18516 := [refl]: #18515
-#18512 := (~ #18511 #18511)
-#18513 := [refl]: #18512
-#18509 := (~ #18508 #18508)
-#18510 := [refl]: #18509
-#18506 := (~ #18505 #18505)
-#18507 := [refl]: #18506
-#18788 := [nnf-neg #18507 #18510 #18513 #18516 #18519 #18522 #18525 #18528 #18531 #18534 #18537 #18544 #18547 #18550 #18553 #18784]: #18787
-#18503 := (~ #14234 #14234)
-#18504 := [refl]: #18503
-#18501 := (~ #13267 #13267)
+#18521 := [nnf-pos #18519]: #18520
+#18524 := [nnf-neg #18521]: #18523
+#18516 := (~ #18515 #18515)
+#18517 := [refl]: #18516
+#18513 := (~ #18512 #18512)
+#18514 := [refl]: #18513
+#18510 := (~ #18509 #18509)
+#18511 := [refl]: #18510
+#18504 := (~ #18503 #18503)
+#18505 := [refl]: #18504
+#18501 := (~ #18500 #18500)
 #18502 := [refl]: #18501
-#18792 := [nnf-neg #18502 #18504 #18788]: #18791
-#18498 := (not #15828)
-#18499 := (~ #18498 #15825)
-#18496 := (~ #15825 #15825)
-#18494 := (~ #15820 #15820)
-#18495 := [refl]: #18494
-#18497 := [nnf-pos #18495]: #18496
-#18500 := [nnf-neg #18497]: #18499
-#18796 := [nnf-neg #18500 #18792]: #18795
-#18490 := (~ #15828 #18489)
-#18491 := [sk]: #18490
-#18800 := [nnf-neg #18491 #18796]: #18799
-#18475 := (~ #18474 #18474)
-#18476 := [refl]: #18475
-#18804 := [nnf-neg #18476 #18800]: #18803
-#18472 := (~ #13472 #13472)
-#18473 := [refl]: #18472
-#18808 := [nnf-neg #18473 #18804]: #18807
-#18470 := (~ #18469 #18469)
-#18471 := [refl]: #18470
-#18467 := (~ #18466 #18466)
-#18468 := [refl]: #18467
-#18464 := (~ #18463 #18463)
-#18465 := [refl]: #18464
-#18461 := (~ #18460 #18460)
-#18462 := [refl]: #18461
-#18458 := (~ #18457 #18457)
-#18459 := [refl]: #18458
-#18812 := [nnf-neg #18459 #18462 #18465 #18468 #18471 #18808]: #18811
+#18498 := (~ #18497 #18497)
+#18499 := [refl]: #18498
+#18495 := (~ #18494 #18494)
+#18496 := [refl]: #18495
+#18492 := (~ #18491 #18491)
+#18493 := [refl]: #18492
+#18489 := (~ #18488 #18488)
+#18490 := [refl]: #18489
+#18486 := (~ #18485 #18485)
+#18487 := [refl]: #18486
+#18768 := [nnf-neg #18487 #18490 #18493 #18496 #18499 #18502 #18505 #18508 #18511 #18514 #18517 #18524 #18527 #18530 #18533 #18764]: #18767
+#18483 := (~ #14214 #14214)
+#18484 := [refl]: #18483
+#18481 := (~ #13247 #13247)
+#18482 := [refl]: #18481
+#18772 := [nnf-neg #18482 #18484 #18768]: #18771
+#18478 := (not #15808)
+#18479 := (~ #18478 #15805)
+#18476 := (~ #15805 #15805)
+#18474 := (~ #15800 #15800)
+#18475 := [refl]: #18474
+#18477 := [nnf-pos #18475]: #18476
+#18480 := [nnf-neg #18477]: #18479
+#18776 := [nnf-neg #18480 #18772]: #18775
+#18470 := (~ #15808 #18469)
+#18471 := [sk]: #18470
+#18780 := [nnf-neg #18471 #18776]: #18779
 #18455 := (~ #18454 #18454)
 #18456 := [refl]: #18455
-#18446 := (~ #18445 #18445)
-#18447 := [refl]: #18446
-#18816 := [nnf-neg #18447 #18456 #18812]: #18815
-#18452 := (~ #18451 #18451)
+#18784 := [nnf-neg #18456 #18780]: #18783
+#18452 := (~ #13452 #13452)
 #18453 := [refl]: #18452
-#18820 := [nnf-neg #18453 #18816]: #18819
-#18449 := (~ #18448 #18448)
-#18450 := [refl]: #18449
-#18824 := [nnf-neg #18447 #18450 #18820]: #18823
-#18443 := (~ #18442 #18442)
-#18444 := [refl]: #18443
-#18828 := [nnf-neg #18444 #18824]: #18827
-#18440 := (~ #13300 #13300)
-#18441 := [refl]: #18440
-#18831 := [nnf-neg #18441 #18828]: #18830
-#15324 := (or #12340 #12331 #12322 #12313 #13521 #13802 #13888)
-#15329 := (and #13824 #15324)
-#15335 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #14025 #14031 #14043 #14053 #14066 #14077 #15329)
-#15340 := (and #3109 #13509 #15335)
-#15343 := (or #13505 #15340)
-#15346 := (and #13502 #15343)
-#15349 := (or #13472 #15346)
-#15352 := (and #13469 #15349)
-#15355 := (or #13267 #13276 #13258 #13249 #13240 #15352)
-#15358 := (and #12180 #12189 #15355)
-#15361 := (or #13288 #15358)
-#15364 := (and #12180 #12183 #15361)
-#15367 := (or #13300 #15364)
-#15370 := (and #12177 #15367)
-#15373 := (not #15370)
-#16083 := (iff #15373 #16082)
-#16080 := (iff #15370 #16079)
-#16077 := (iff #15367 #16076)
-#16074 := (iff #15364 #16073)
-#16071 := (iff #15361 #16070)
-#16068 := (iff #15358 #16067)
-#16065 := (iff #15355 #16064)
-#16062 := (iff #15352 #16061)
-#16059 := (iff #15349 #16058)
-#16056 := (iff #15346 #16055)
-#16053 := (iff #15343 #16052)
-#16050 := (iff #15340 #16049)
-#16047 := (iff #15335 #16044)
-#16041 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #13991 #15842 #14031 #15859 #15876 #15893 #14077 #16038)
-#16045 := (iff #16041 #16044)
-#16046 := [rewrite]: #16045
-#16042 := (iff #15335 #16041)
+#18788 := [nnf-neg #18453 #18784]: #18787
+#18450 := (~ #18449 #18449)
+#18451 := [refl]: #18450
+#18447 := (~ #18446 #18446)
+#18448 := [refl]: #18447
+#18444 := (~ #18443 #18443)
+#18445 := [refl]: #18444
+#18441 := (~ #18440 #18440)
+#18442 := [refl]: #18441
+#18438 := (~ #18437 #18437)
+#18439 := [refl]: #18438
+#18792 := [nnf-neg #18439 #18442 #18445 #18448 #18451 #18788]: #18791
+#18435 := (~ #18434 #18434)
+#18436 := [refl]: #18435
+#18426 := (~ #18425 #18425)
+#18427 := [refl]: #18426
+#18796 := [nnf-neg #18427 #18436 #18792]: #18795
+#18432 := (~ #18431 #18431)
+#18433 := [refl]: #18432
+#18800 := [nnf-neg #18433 #18796]: #18799
+#18429 := (~ #18428 #18428)
+#18430 := [refl]: #18429
+#18804 := [nnf-neg #18427 #18430 #18800]: #18803
+#18423 := (~ #18422 #18422)
+#18424 := [refl]: #18423
+#18808 := [nnf-neg #18424 #18804]: #18807
+#18420 := (~ #13280 #13280)
+#18421 := [refl]: #18420
+#18811 := [nnf-neg #18421 #18808]: #18810
+#15304 := (or #12320 #12311 #12302 #12293 #13501 #13782 #13868)
+#15309 := (and #13804 #15304)
+#15315 := (or #15279 #13954 #13040 #13031 #13022 #13013 #13004 #13501 #13971 #14005 #14011 #14023 #14033 #14046 #14057 #15309)
+#15320 := (and #3102 #13489 #15315)
+#15323 := (or #13485 #15320)
+#15326 := (and #13482 #15323)
+#15329 := (or #13452 #15326)
+#15332 := (and #13449 #15329)
+#15335 := (or #13247 #13256 #13238 #13229 #13220 #15332)
+#15338 := (and #12160 #12169 #15335)
+#15341 := (or #13268 #15338)
+#15344 := (and #12160 #12163 #15341)
+#15347 := (or #13280 #15344)
+#15350 := (and #12157 #15347)
+#15353 := (not #15350)
+#16063 := (iff #15353 #16062)
+#16060 := (iff #15350 #16059)
+#16057 := (iff #15347 #16056)
+#16054 := (iff #15344 #16053)
+#16051 := (iff #15341 #16050)
+#16048 := (iff #15338 #16047)
+#16045 := (iff #15335 #16044)
+#16042 := (iff #15332 #16041)
 #16039 := (iff #15329 #16038)
-#16036 := (iff #15324 #16035)
-#16033 := (iff #13888 #16032)
-#16030 := (iff #13883 #16029)
-#16027 := (iff #13874 #16026)
-#16024 := (iff #13869 #16021)
-#16018 := (and #3173 #4202 #15219 #13831)
-#16022 := (iff #16018 #16021)
-#16023 := [rewrite]: #16022
-#16019 := (iff #13869 #16018)
-#15214 := (iff #4516 #15219)
-#15235 := -4294967295::Int
-#15227 := (+ -4294967295::Int #202)
-#15220 := (<= #15227 0::Int)
-#15216 := (iff #15220 #15219)
-#15217 := [rewrite]: #15216
-#15221 := (iff #4516 #15220)
-#15222 := (= #4515 #15227)
-#15228 := (+ #202 -4294967295::Int)
-#15224 := (= #15228 #15227)
-#15225 := [rewrite]: #15224
-#15229 := (= #4515 #15228)
-#15230 := (= #4514 -4294967295::Int)
-#15236 := (* -1::Int 4294967295::Int)
-#15232 := (= #15236 -4294967295::Int)
-#15233 := [rewrite]: #15232
-#15237 := (= #4514 #15236)
-#7637 := (= f87 4294967295::Int)
-#990 := 65536::Int
-#1365 := (* 65536::Int 65536::Int)
-#1370 := (- #1365 1::Int)
-#1371 := (= f87 #1370)
-#7638 := (iff #1371 #7637)
-#7635 := (= #1370 4294967295::Int)
-#1053 := 4294967296::Int
-#7628 := (- 4294967296::Int 1::Int)
-#7633 := (= #7628 4294967295::Int)
-#7634 := [rewrite]: #7633
-#7630 := (= #1370 #7628)
-#7599 := (= #1365 4294967296::Int)
-#7600 := [rewrite]: #7599
-#7631 := [monotonicity #7600]: #7630
-#7636 := [trans #7631 #7634]: #7635
-#7639 := [monotonicity #7636]: #7638
-#7627 := [asserted]: #1371
-#7642 := [mp #7627 #7639]: #7637
-#15234 := [monotonicity #7642]: #15237
-#15231 := [trans #15234 #15233]: #15230
-#15226 := [monotonicity #15231]: #15229
-#15223 := [trans #15226 #15225]: #15222
-#15218 := [monotonicity #15223]: #15221
-#15215 := [trans #15218 #15217]: #15214
-#16020 := [monotonicity #15215]: #16019
-#16025 := [trans #16020 #16023]: #16024
-#16028 := [quant-intro #16025]: #16027
-#16016 := (iff #13877 #16015)
-#16013 := (iff #13857 #16012)
-#16010 := (iff #13852 #16007)
-#16004 := (or #14461 #13829 #13843)
-#16008 := (iff #16004 #16007)
-#16009 := [rewrite]: #16008
-#16005 := (iff #13852 #16004)
-#14458 := (iff #5738 #14461)
-#14463 := (iff #4523 #14462)
-#14460 := [monotonicity #15215]: #14463
-#14459 := [monotonicity #14460]: #14458
-#16006 := [monotonicity #14459]: #16005
-#16011 := [trans #16006 #16009]: #16010
-#16014 := [quant-intro #16011]: #16013
+#16036 := (iff #15326 #16035)
+#16033 := (iff #15323 #16032)
+#16030 := (iff #15320 #16029)
+#16027 := (iff #15315 #16024)
+#16021 := (or #15279 #13954 #13040 #13031 #13022 #13013 #13004 #13501 #13971 #15822 #14011 #15839 #15856 #15873 #14057 #16018)
+#16025 := (iff #16021 #16024)
+#16026 := [rewrite]: #16025
+#16022 := (iff #15315 #16021)
+#16019 := (iff #15309 #16018)
+#16016 := (iff #15304 #16015)
+#16013 := (iff #13868 #16012)
+#16010 := (iff #13863 #16009)
+#16007 := (iff #13854 #16006)
+#16004 := (iff #13849 #16001)
+#15998 := (and #3166 #4149 #15199 #13811)
+#16002 := (iff #15998 #16001)
+#16003 := [rewrite]: #16002
+#15999 := (iff #13849 #15998)
+#15194 := (iff #4463 #15199)
+#15215 := -4294967295::Int
+#15207 := (+ -4294967295::Int #168)
+#15200 := (<= #15207 0::Int)
+#15196 := (iff #15200 #15199)
+#15197 := [rewrite]: #15196
+#15201 := (iff #4463 #15200)
+#15202 := (= #4462 #15207)
+#15208 := (+ #168 -4294967295::Int)
+#15204 := (= #15208 #15207)
+#15205 := [rewrite]: #15204
+#15209 := (= #4462 #15208)
+#15210 := (= #4461 -4294967295::Int)
+#15216 := (* -1::Int 4294967295::Int)
+#15212 := (= #15216 -4294967295::Int)
+#15213 := [rewrite]: #15212
+#15217 := (= #4461 #15216)
+#7584 := (= f77 4294967295::Int)
+#956 := 65536::Int
+#1331 := (* 65536::Int 65536::Int)
+#1336 := (- #1331 1::Int)
+#1337 := (= f77 #1336)
+#7585 := (iff #1337 #7584)
+#7582 := (= #1336 4294967295::Int)
+#1019 := 4294967296::Int
+#7575 := (- 4294967296::Int 1::Int)
+#7580 := (= #7575 4294967295::Int)
+#7581 := [rewrite]: #7580
+#7577 := (= #1336 #7575)
+#7546 := (= #1331 4294967296::Int)
+#7547 := [rewrite]: #7546
+#7578 := [monotonicity #7547]: #7577
+#7583 := [trans #7578 #7581]: #7582
+#7586 := [monotonicity #7583]: #7585
+#7574 := [asserted]: #1337
+#7589 := [mp #7574 #7586]: #7584
+#15214 := [monotonicity #7589]: #15217
+#15211 := [trans #15214 #15213]: #15210
+#15206 := [monotonicity #15211]: #15209
+#15203 := [trans #15206 #15205]: #15202
+#15198 := [monotonicity #15203]: #15201
+#15195 := [trans #15198 #15197]: #15194
+#16000 := [monotonicity #15195]: #15999
+#16005 := [trans #16000 #16003]: #16004
+#16008 := [quant-intro #16005]: #16007
+#15996 := (iff #13857 #15995)
+#15993 := (iff #13837 #15992)
+#15990 := (iff #13832 #15987)
+#15984 := (or #14441 #13809 #13823)
+#15988 := (iff #15984 #15987)
+#15989 := [rewrite]: #15988
+#15985 := (iff #13832 #15984)
+#14438 := (iff #5685 #14441)
+#14443 := (iff #4470 #14442)
+#14440 := [monotonicity #15195]: #14443
+#14439 := [monotonicity #14440]: #14438
+#15986 := [monotonicity #14439]: #15985
+#15991 := [trans #15986 #15989]: #15990
+#15994 := [quant-intro #15991]: #15993
+#15997 := [monotonicity #15994]: #15996
+#16011 := [monotonicity #15997 #16008]: #16010
+#16014 := [monotonicity #15994 #16011]: #16013
 #16017 := [monotonicity #16014]: #16016
-#16031 := [monotonicity #16017 #16028]: #16030
-#16034 := [monotonicity #16014 #16031]: #16033
-#16037 := [monotonicity #16034]: #16036
-#16002 := (iff #13824 #15999)
-#15996 := (or #13521 #15993 #13801)
-#16000 := (iff #15996 #15999)
-#16001 := [rewrite]: #16000
-#15997 := (iff #13824 #15996)
-#15994 := (iff #13795 #15993)
-#15991 := (iff #13789 #15990)
-#15988 := (iff #13784 #15987)
-#15985 := (iff #13776 #15984)
-#15982 := (iff #13767 #15981)
-#15979 := (iff #13762 #15976)
-#15973 := (or #12857 #12848 #13521 #13530 #15950 #13707)
-#15977 := (iff #15973 #15976)
-#15978 := [rewrite]: #15977
-#15974 := (iff #13762 #15973)
-#15951 := (iff #13651 #15950)
-#15948 := (iff #13643 #15945)
-#15942 := (or #12692 #13547 #15933 #13622 #15939)
-#15946 := (iff #15942 #15945)
-#15947 := [rewrite]: #15946
-#15943 := (iff #13643 #15942)
-#15940 := (iff #13628 #15939)
-#15937 := (iff #13625 #15936)
-#15903 := (iff #13536 #15900)
-#15845 := (+ 4294967295::Int #13537)
-#15896 := (>= #15845 1::Int)
-#15901 := (iff #15896 #15900)
-#15902 := [rewrite]: #15901
-#15897 := (iff #13536 #15896)
-#15846 := (= #13538 #15845)
-#15847 := [monotonicity #7642]: #15846
-#15898 := [monotonicity #15847]: #15897
-#15904 := [trans #15898 #15902]: #15903
-#15938 := [monotonicity #15904]: #15937
-#15941 := [monotonicity #15938]: #15940
-#15934 := (iff #13615 #15933)
-#15931 := (iff #13612 #15930)
-#15928 := (iff #13609 #15927)
-#15925 := (iff #13606 #15922)
-#15919 := (or #15916 #13601)
-#15923 := (iff #15919 #15922)
-#15924 := [rewrite]: #15923
-#15920 := (iff #13606 #15919)
-#15917 := (iff #13589 #15916)
-#15914 := (iff #13586 #15913)
-#15911 := (iff #13581 #15908)
-#15905 := (or #14461 #13558 #13572)
-#15909 := (iff #15905 #15908)
-#15910 := [rewrite]: #15909
-#15906 := (iff #13581 #15905)
-#15907 := [monotonicity #14459]: #15906
-#15912 := [trans #15907 #15910]: #15911
-#15915 := [quant-intro #15912]: #15914
-#15918 := [monotonicity #15915]: #15917
+#15982 := (iff #13804 #15979)
+#15976 := (or #13501 #15973 #13781)
+#15980 := (iff #15976 #15979)
+#15981 := [rewrite]: #15980
+#15977 := (iff #13804 #15976)
+#15974 := (iff #13775 #15973)
+#15971 := (iff #13769 #15970)
+#15968 := (iff #13764 #15967)
+#15965 := (iff #13756 #15964)
+#15962 := (iff #13747 #15961)
+#15959 := (iff #13742 #15956)
+#15953 := (or #12837 #12828 #13501 #13510 #15930 #13687)
+#15957 := (iff #15953 #15956)
+#15958 := [rewrite]: #15957
+#15954 := (iff #13742 #15953)
+#15931 := (iff #13631 #15930)
+#15928 := (iff #13623 #15925)
+#15922 := (or #12672 #13527 #15913 #13602 #15919)
+#15926 := (iff #15922 #15925)
+#15927 := [rewrite]: #15926
+#15923 := (iff #13623 #15922)
+#15920 := (iff #13608 #15919)
+#15917 := (iff #13605 #15916)
+#15883 := (iff #13516 #15880)
+#15825 := (+ 4294967295::Int #13517)
+#15876 := (>= #15825 1::Int)
+#15881 := (iff #15876 #15880)
+#15882 := [rewrite]: #15881
+#15877 := (iff #13516 #15876)
+#15826 := (= #13518 #15825)
+#15827 := [monotonicity #7589]: #15826
+#15878 := [monotonicity #15827]: #15877
+#15884 := [trans #15878 #15882]: #15883
+#15918 := [monotonicity #15884]: #15917
 #15921 := [monotonicity #15918]: #15920
-#15926 := [trans #15921 #15924]: #15925
-#15929 := [monotonicity #15915 #15926]: #15928
-#15932 := [monotonicity #15929]: #15931
+#15914 := (iff #13595 #15913)
+#15911 := (iff #13592 #15910)
+#15908 := (iff #13589 #15907)
+#15905 := (iff #13586 #15902)
+#15899 := (or #15896 #13581)
+#15903 := (iff #15899 #15902)
+#15904 := [rewrite]: #15903
+#15900 := (iff #13586 #15899)
+#15897 := (iff #13569 #15896)
+#15894 := (iff #13566 #15893)
+#15891 := (iff #13561 #15888)
+#15885 := (or #14441 #13538 #13552)
+#15889 := (iff #15885 #15888)
+#15890 := [rewrite]: #15889
+#15886 := (iff #13561 #15885)
+#15887 := [monotonicity #14439]: #15886
+#15892 := [trans #15887 #15890]: #15891
+#15895 := [quant-intro #15892]: #15894
+#15898 := [monotonicity #15895]: #15897
+#15901 := [monotonicity #15898]: #15900
+#15906 := [trans #15901 #15904]: #15905
+#15909 := [monotonicity #15895 #15906]: #15908
+#15912 := [monotonicity #15909]: #15911
+#15915 := [monotonicity #15912]: #15914
+#15924 := [monotonicity #15915 #15921]: #15923
+#15929 := [trans #15924 #15927]: #15928
+#15932 := [monotonicity #15884 #15929]: #15931
+#15955 := [monotonicity #15932]: #15954
+#15960 := [trans #15955 #15958]: #15959
+#15951 := (iff #13712 #15948)
+#15945 := (or #13501 #15942 #13688)
+#15949 := (iff #15945 #15948)
+#15950 := [rewrite]: #15949
+#15946 := (iff #13712 #15945)
+#15943 := (iff #13682 #15942)
+#15940 := (iff #13676 #15939)
+#15937 := (iff #13671 #15936)
+#15934 := (iff #13663 #15933)
 #15935 := [monotonicity #15932]: #15934
-#15944 := [monotonicity #15935 #15941]: #15943
-#15949 := [trans #15944 #15947]: #15948
-#15952 := [monotonicity #15904 #15949]: #15951
-#15975 := [monotonicity #15952]: #15974
-#15980 := [trans #15975 #15978]: #15979
-#15971 := (iff #13732 #15968)
-#15965 := (or #13521 #15962 #13708)
-#15969 := (iff #15965 #15968)
-#15970 := [rewrite]: #15969
-#15966 := (iff #13732 #15965)
-#15963 := (iff #13702 #15962)
-#15960 := (iff #13696 #15959)
-#15957 := (iff #13691 #15956)
-#15954 := (iff #13683 #15953)
-#15955 := [monotonicity #15952]: #15954
-#15958 := [monotonicity #15955]: #15957
-#15961 := [monotonicity #15958]: #15960
-#15964 := [monotonicity #15961]: #15963
-#15967 := [monotonicity #15964]: #15966
-#15972 := [trans #15967 #15970]: #15971
-#15983 := [monotonicity #15972 #15980]: #15982
-#15986 := [monotonicity #15983]: #15985
-#15989 := [monotonicity #15986]: #15988
-#15992 := [monotonicity #15989]: #15991
-#15995 := [monotonicity #15992]: #15994
-#15998 := [monotonicity #15995]: #15997
-#16003 := [trans #15998 #16001]: #16002
-#16040 := [monotonicity #16003 #16037]: #16039
-#15894 := (iff #14066 #15893)
-#15891 := (iff #14063 #15890)
-#15888 := (iff #14059 #15885)
-#15879 := (+ 255::Int #14006)
-#15882 := (>= #15879 0::Int)
-#15886 := (iff #15882 #15885)
-#15887 := [rewrite]: #15886
-#15883 := (iff #14059 #15882)
-#15880 := (= #14060 #15879)
-#1375 := (= f89 255::Int)
-#7641 := [asserted]: #1375
-#15881 := [monotonicity #7641]: #15880
-#15884 := [monotonicity #15881]: #15883
-#15889 := [trans #15884 #15887]: #15888
-#15892 := [monotonicity #15889]: #15891
-#15895 := [monotonicity #15892]: #15894
-#15877 := (iff #14053 #15876)
-#15874 := (iff #14050 #15873)
-#15871 := (iff #14046 #15868)
-#15862 := (+ 4294967295::Int #13977)
-#15865 := (>= #15862 0::Int)
-#15869 := (iff #15865 #15868)
-#15870 := [rewrite]: #15869
-#15866 := (iff #14046 #15865)
-#15863 := (= #14047 #15862)
-#15864 := [monotonicity #7642]: #15863
-#15867 := [monotonicity #15864]: #15866
-#15872 := [trans #15867 #15870]: #15871
+#15938 := [monotonicity #15935]: #15937
+#15941 := [monotonicity #15938]: #15940
+#15944 := [monotonicity #15941]: #15943
+#15947 := [monotonicity #15944]: #15946
+#15952 := [trans #15947 #15950]: #15951
+#15963 := [monotonicity #15952 #15960]: #15962
+#15966 := [monotonicity #15963]: #15965
+#15969 := [monotonicity #15966]: #15968
+#15972 := [monotonicity #15969]: #15971
+#15975 := [monotonicity #15972]: #15974
+#15978 := [monotonicity #15975]: #15977
+#15983 := [trans #15978 #15981]: #15982
+#16020 := [monotonicity #15983 #16017]: #16019
+#15874 := (iff #14046 #15873)
+#15871 := (iff #14043 #15870)
+#15868 := (iff #14039 #15865)
+#15859 := (+ 255::Int #13986)
+#15862 := (>= #15859 0::Int)
+#15866 := (iff #15862 #15865)
+#15867 := [rewrite]: #15866
+#15863 := (iff #14039 #15862)
+#15860 := (= #14040 #15859)
+#1341 := (= f79 255::Int)
+#7588 := [asserted]: #1341
+#15861 := [monotonicity #7588]: #15860
+#15864 := [monotonicity #15861]: #15863
+#15869 := [trans #15864 #15867]: #15868
+#15872 := [monotonicity #15869]: #15871
 #15875 := [monotonicity #15872]: #15874
-#15878 := [monotonicity #15875]: #15877
-#15860 := (iff #14043 #15859)
-#15857 := (iff #14040 #15856)
-#15854 := (iff #14037 #15851)
-#15848 := (>= #15845 0::Int)
-#15852 := (iff #15848 #15851)
-#15853 := [rewrite]: #15852
-#15849 := (iff #14037 #15848)
-#15850 := [monotonicity #15847]: #15849
-#15855 := [trans #15850 #15853]: #15854
+#15857 := (iff #14033 #15856)
+#15854 := (iff #14030 #15853)
+#15851 := (iff #14026 #15848)
+#15842 := (+ 4294967295::Int #13957)
+#15845 := (>= #15842 0::Int)
+#15849 := (iff #15845 #15848)
+#15850 := [rewrite]: #15849
+#15846 := (iff #14026 #15845)
+#15843 := (= #14027 #15842)
+#15844 := [monotonicity #7589]: #15843
+#15847 := [monotonicity #15844]: #15846
+#15852 := [trans #15847 #15850]: #15851
+#15855 := [monotonicity #15852]: #15854
 #15858 := [monotonicity #15855]: #15857
-#15861 := [monotonicity #15858]: #15860
-#15843 := (iff #14025 #15842)
-#15840 := (iff #14022 #15839)
-#15837 := (iff #14017 #15834)
-#15831 := (or #14461 #13994 #14008)
-#15835 := (iff #15831 #15834)
-#15836 := [rewrite]: #15835
-#15832 := (iff #14017 #15831)
-#15833 := [monotonicity #14459]: #15832
-#15838 := [trans #15833 #15836]: #15837
-#15841 := [quant-intro #15838]: #15840
-#15844 := [monotonicity #15841]: #15843
-#16043 := [monotonicity #15844 #15861 #15878 #15895 #16040]: #16042
-#16048 := [trans #16043 #16046]: #16047
-#16051 := [monotonicity #16048]: #16050
-#15829 := (iff #13505 #15828)
-#15826 := (iff #13502 #15825)
-#15823 := (iff #13497 #15820)
-#15817 := (or #14461 #13475 #13487)
-#15821 := (iff #15817 #15820)
-#15822 := [rewrite]: #15821
-#15818 := (iff #13497 #15817)
-#15819 := [monotonicity #14459]: #15818
-#15824 := [trans #15819 #15822]: #15823
-#15827 := [quant-intro #15824]: #15826
+#15840 := (iff #14023 #15839)
+#15837 := (iff #14020 #15836)
+#15834 := (iff #14017 #15831)
+#15828 := (>= #15825 0::Int)
+#15832 := (iff #15828 #15831)
+#15833 := [rewrite]: #15832
+#15829 := (iff #14017 #15828)
 #15830 := [monotonicity #15827]: #15829
-#16054 := [monotonicity #15830 #16051]: #16053
-#16057 := [monotonicity #15827 #16054]: #16056
-#16060 := [monotonicity #16057]: #16059
-#16063 := [monotonicity #16060]: #16062
-#16066 := [monotonicity #16063]: #16065
-#16069 := [monotonicity #16066]: #16068
-#16072 := [monotonicity #16069]: #16071
-#16075 := [monotonicity #16072]: #16074
-#16078 := [monotonicity #16075]: #16077
-#16081 := [monotonicity #16078]: #16080
-#16084 := [monotonicity #16081]: #16083
-#14361 := (not #14213)
-#15374 := (iff #14361 #15373)
-#15371 := (iff #14213 #15370)
-#15368 := (iff #14210 #15367)
-#15365 := (iff #14205 #15364)
-#15362 := (iff #14199 #15361)
-#15359 := (iff #14194 #15358)
-#15356 := (iff #14186 #15355)
-#15353 := (iff #14165 #15352)
-#15350 := (iff #14162 #15349)
-#15347 := (iff #14159 #15346)
-#15344 := (iff #14156 #15343)
-#15341 := (iff #14151 #15340)
-#15338 := (iff #14143 #15335)
-#15332 := (or #15299 #13974 #13060 #13051 #13042 #13033 #13024 #13521 #15329 #13991 #14025 #14031 #14043 #14053 #14066 #14077)
-#15336 := (iff #15332 #15335)
-#15337 := [rewrite]: #15336
-#15333 := (iff #14143 #15332)
-#15330 := (iff #13950 #15329)
-#15327 := (iff #13945 #15324)
-#15309 := (or #12340 #12331 #12322 #12313 #13521 #13888)
-#15321 := (or #13521 #13802 #15309)
-#15325 := (iff #15321 #15324)
-#15326 := [rewrite]: #15325
-#15322 := (iff #13945 #15321)
-#15319 := (iff #13920 #15309)
-#15314 := (and true #15309)
-#15317 := (iff #15314 #15309)
-#15318 := [rewrite]: #15317
-#15315 := (iff #13920 #15314)
-#15312 := (iff #13915 #15309)
-#15306 := (or false #12340 #12331 #12322 #12313 #13521 #13888)
-#15310 := (iff #15306 #15309)
-#15311 := [rewrite]: #15310
-#15307 := (iff #13915 #15306)
-#15304 := (iff #12374 false)
-#15302 := (iff #12374 #3156)
-#15040 := (iff #10960 true)
-#10959 := [asserted]: #2542
-#10966 := [mp #10959 #10963]: #10960
-#15041 := [iff-true #10966]: #15040
-#15303 := [monotonicity #15041]: #15302
-#15305 := [trans #15303 #12257]: #15304
-#15308 := [monotonicity #15305]: #15307
-#15313 := [trans #15308 #15311]: #15312
-#15316 := [monotonicity #15041 #15313]: #15315
-#15320 := [trans #15316 #15318]: #15319
-#15323 := [monotonicity #15320]: #15322
-#15328 := [trans #15323 #15326]: #15327
+#15835 := [trans #15830 #15833]: #15834
+#15838 := [monotonicity #15835]: #15837
+#15841 := [monotonicity #15838]: #15840
+#15823 := (iff #14005 #15822)
+#15820 := (iff #14002 #15819)
+#15817 := (iff #13997 #15814)
+#15811 := (or #14441 #13974 #13988)
+#15815 := (iff #15811 #15814)
+#15816 := [rewrite]: #15815
+#15812 := (iff #13997 #15811)
+#15813 := [monotonicity #14439]: #15812
+#15818 := [trans #15813 #15816]: #15817
+#15821 := [quant-intro #15818]: #15820
+#15824 := [monotonicity #15821]: #15823
+#16023 := [monotonicity #15824 #15841 #15858 #15875 #16020]: #16022
+#16028 := [trans #16023 #16026]: #16027
+#16031 := [monotonicity #16028]: #16030
+#15809 := (iff #13485 #15808)
+#15806 := (iff #13482 #15805)
+#15803 := (iff #13477 #15800)
+#15797 := (or #14441 #13455 #13467)
+#15801 := (iff #15797 #15800)
+#15802 := [rewrite]: #15801
+#15798 := (iff #13477 #15797)
+#15799 := [monotonicity #14439]: #15798
+#15804 := [trans #15799 #15802]: #15803
+#15807 := [quant-intro #15804]: #15806
+#15810 := [monotonicity #15807]: #15809
+#16034 := [monotonicity #15810 #16031]: #16033
+#16037 := [monotonicity #15807 #16034]: #16036
+#16040 := [monotonicity #16037]: #16039
+#16043 := [monotonicity #16040]: #16042
+#16046 := [monotonicity #16043]: #16045
+#16049 := [monotonicity #16046]: #16048
+#16052 := [monotonicity #16049]: #16051
+#16055 := [monotonicity #16052]: #16054
+#16058 := [monotonicity #16055]: #16057
+#16061 := [monotonicity #16058]: #16060
+#16064 := [monotonicity #16061]: #16063
+#14341 := (not #14193)
+#15354 := (iff #14341 #15353)
+#15351 := (iff #14193 #15350)
+#15348 := (iff #14190 #15347)
+#15345 := (iff #14185 #15344)
+#15342 := (iff #14179 #15341)
+#15339 := (iff #14174 #15338)
+#15336 := (iff #14166 #15335)
+#15333 := (iff #14145 #15332)
+#15330 := (iff #14142 #15329)
+#15327 := (iff #14139 #15326)
+#15324 := (iff #14136 #15323)
+#15321 := (iff #14131 #15320)
+#15318 := (iff #14123 #15315)
+#15312 := (or #15279 #13954 #13040 #13031 #13022 #13013 #13004 #13501 #15309 #13971 #14005 #14011 #14023 #14033 #14046 #14057)
+#15316 := (iff #15312 #15315)
+#15317 := [rewrite]: #15316
+#15313 := (iff #14123 #15312)
+#15310 := (iff #13930 #15309)
+#15307 := (iff #13925 #15304)
+#15289 := (or #12320 #12311 #12302 #12293 #13501 #13868)
+#15301 := (or #13501 #13782 #15289)
+#15305 := (iff #15301 #15304)
+#15306 := [rewrite]: #15305
+#15302 := (iff #13925 #15301)
+#15299 := (iff #13900 #15289)
+#15294 := (and true #15289)
+#15297 := (iff #15294 #15289)
+#15298 := [rewrite]: #15297
+#15295 := (iff #13900 #15294)
+#15292 := (iff #13895 #15289)
+#15286 := (or false #12320 #12311 #12302 #12293 #13501 #13868)
+#15290 := (iff #15286 #15289)
+#15291 := [rewrite]: #15290
+#15287 := (iff #13895 #15286)
+#15284 := (iff #12354 false)
+#15282 := (iff #12354 #3149)
+#15010 := (iff #10907 true)
+#10906 := [asserted]: #2508
+#10913 := [mp #10906 #10910]: #10907
+#15011 := [iff-true #10913]: #15010
+#15283 := [monotonicity #15011]: #15282
+#15285 := [trans #15283 #12237]: #15284
+#15288 := [monotonicity #15285]: #15287
+#15293 := [trans #15288 #15291]: #15292
+#15296 := [monotonicity #15011 #15293]: #15295
+#15300 := [trans #15296 #15298]: #15299
+#15303 := [monotonicity #15300]: #15302
+#15308 := [trans #15303 #15306]: #15307
+#15311 := [monotonicity #15308]: #15310
+#15280 := (iff #12382 #15279)
+#15277 := (iff #12244 #12238)
+#15272 := (and true #12238)
+#15275 := (iff #15272 #12238)
+#15276 := [rewrite]: #15275
+#15273 := (iff #12244 #15272)
+#15256 := (iff #12125 true)
+#15257 := [iff-true #14331]: #15256
+#15274 := [monotonicity #15257]: #15273
+#15278 := [trans #15274 #15276]: #15277
+#15281 := [monotonicity #15278]: #15280
+#15314 := [monotonicity #15281 #15311]: #15313
+#15319 := [trans #15314 #15317]: #15318
+#15322 := [monotonicity #15319]: #15321
+#15325 := [monotonicity #15322]: #15324
+#15328 := [monotonicity #15325]: #15327
 #15331 := [monotonicity #15328]: #15330
-#15300 := (iff #12402 #15299)
-#15297 := (iff #12264 #12258)
-#15292 := (and true #12258)
-#15295 := (iff #15292 #12258)
-#15296 := [rewrite]: #15295
-#15293 := (iff #12264 #15292)
-#15276 := (iff #12145 true)
-#15277 := [iff-true #14351]: #15276
-#15294 := [monotonicity #15277]: #15293
-#15298 := [trans #15294 #15296]: #15297
-#15301 := [monotonicity #15298]: #15300
-#15334 := [monotonicity #15301 #15331]: #15333
-#15339 := [trans #15334 #15337]: #15338
-#15342 := [monotonicity #15339]: #15341
-#15345 := [monotonicity #15342]: #15344
-#15348 := [monotonicity #15345]: #15347
-#15351 := [monotonicity #15348]: #15350
-#15354 := [monotonicity #15351]: #15353
-#15357 := [monotonicity #15354]: #15356
-#15360 := [monotonicity #15357]: #15359
-#15363 := [monotonicity #15360]: #15362
-#15366 := [monotonicity #15363]: #15365
-#15369 := [monotonicity #15366]: #15368
-#15372 := [monotonicity #15369]: #15371
-#15375 := [monotonicity #15372]: #15374
-#14362 := [not-or-elim #14346]: #14361
-#15376 := [mp #14362 #15375]: #15373
-#16085 := [mp #15376 #16084]: #16082
-#18832 := [mp~ #16085 #18831]: #18829
-#18833 := [mp #18832 #19177]: #19175
-#22700 := [mp #18833 #22699]: #22697
-#23605 := [mp #22700 #23604]: #23602
-#29129 := [unit-resolution #23605 #27033]: #23599
-#24829 := (or #23596 #23590)
-#24830 := [def-axiom]: #24829
-#29130 := [unit-resolution #24830 #29129]: #23590
-#24825 := (or #23593 #18445 #18448 #23587)
-#24826 := [def-axiom]: #24825
-#29134 := [unit-resolution #24826 #27642 #28798 #29130]: #23587
-#24815 := (or #23584 #23578)
-#24816 := [def-axiom]: #24815
-#29135 := [unit-resolution #24816 #29134]: #23578
-#24809 := (or #23581 #18445 #18454 #23575)
-#24810 := [def-axiom]: #24809
-#29136 := [unit-resolution #24810 #29135 #29128 #27642]: #23575
-#24787 := (or #23572 #3109)
-#24788 := [def-axiom]: #24787
-#29137 := [unit-resolution #24788 #29136]: #3109
-#24799 := (or #23572 #23566)
-#24800 := [def-axiom]: #24799
-#29663 := [unit-resolution #24800 #29136]: #23566
-#29664 := (or #23569 #23563)
-#27310 := [hypothesis]: #13472
-#27311 := [th-lemma arith farkas 1 1 #14360 #27310]: false
-#27312 := [lemma #27311]: #13469
-#24785 := (or #23569 #13472 #23563)
-#24786 := [def-axiom]: #24785
-#29665 := [unit-resolution #24786 #27312]: #29664
-#29666 := [unit-resolution #29665 #29663]: #23563
-#24777 := (or #23560 #23554)
-#24778 := [def-axiom]: #24777
-#29667 := [unit-resolution #24778 #29666]: #23554
-#27615 := (* -1::Int #3108)
-#27616 := (+ f306 #27615)
-#27617 := (>= #27616 0::Int)
-#29138 := (or #13267 #27617)
-#29139 := [th-lemma arith triangle-eq]: #29138
-#29140 := [unit-resolution #29139 #29137]: #27617
-#24455 := (not #18486)
-#29141 := [hypothesis]: #22337
-#24456 := (or #22332 #24455)
-#24457 := [def-axiom]: #24456
-#29142 := [unit-resolution #24457 #29141]: #24455
-#29102 := (+ #3108 #18484)
-#29104 := (>= #29102 0::Int)
-#29101 := (= #3108 #18483)
-#29149 := (= #18483 #3108)
-#29147 := (= #18482 #3098)
-#29145 := (= ?v0!13 0::Int)
-#24458 := (not #18487)
-#24459 := (or #22332 #24458)
-#24460 := [def-axiom]: #24459
-#29143 := [unit-resolution #24460 #29141]: #24458
-#24453 := (or #22332 #18479)
-#24454 := [def-axiom]: #24453
-#29144 := [unit-resolution #24454 #29141]: #18479
-#29146 := [th-lemma arith eq-propagate 0 0 #29144 #29143]: #29145
-#29148 := [monotonicity #29146]: #29147
-#29150 := [monotonicity #29148]: #29149
-#29151 := [symm #29150]: #29101
-#29152 := (not #29101)
-#29153 := (or #29152 #29104)
-#29154 := [th-lemma arith triangle-eq]: #29153
-#29155 := [unit-resolution #29154 #29151]: #29104
-#29156 := [th-lemma arith farkas 1 -1 1 #29155 #29142 #29140]: false
-#29157 := [lemma #29156]: #22332
-#24773 := (or #23557 #22337 #23551)
-#24774 := [def-axiom]: #24773
-#29668 := [unit-resolution #24774 #29157 #29667]: #23551
-#24765 := (or #23548 #23542)
-#24766 := [def-axiom]: #24765
-#29669 := [unit-resolution #24766 #29668]: #23542
-#29670 := (or #23545 #13267 #23539)
-#24761 := (or #23545 #13267 #13508 #23539)
-#24762 := [def-axiom]: #24761
-#29671 := [unit-resolution #24762 #14360]: #29670
-#29672 := [unit-resolution #29671 #29669 #29137]: #23539
-#24751 := (or #23536 #23530)
-#24752 := [def-axiom]: #24751
-#30100 := [unit-resolution #24752 #29672]: #23530
-#24749 := (or #23536 #23372)
-#24750 := [def-axiom]: #24749
-#30095 := [unit-resolution #24750 #29672]: #23372
-#24711 := (or #23536 #12250)
-#24712 := [def-axiom]: #24711
-#30101 := [unit-resolution #24712 #29672]: #12250
-#24745 := (or #23536 #15868)
-#24746 := [def-axiom]: #24745
-#30102 := [unit-resolution #24746 #29672]: #15868
-#24735 := (or #23536 #13980)
-#24736 := [def-axiom]: #24735
-#30103 := [unit-resolution #24736 #29672]: #13980
-#27607 := (f24 #27086)
-#27608 := (f77 #27086 f308 #27607)
-#27609 := (f136 #27608 #27086)
-#27690 := (>= #27609 0::Int)
-#24731 := (or #23536 #13513)
-#24732 := [def-axiom]: #24731
-#30104 := [unit-resolution #24732 #29672]: #13513
-#27706 := (* -1::Int #27609)
-#27779 := (+ f308 #27706)
-#27780 := (<= #27779 0::Int)
-#27610 := (= f308 #27609)
-#29180 := (f77 #24833 f308 #27122)
-#29181 := (f136 #29180 #24833)
-#30129 := (= #29181 #27609)
-#30127 := (= #27609 #29181)
-#30105 := (= #27086 #24833)
-#30109 := [trans #27414 #27140]: #30105
-#30124 := (= #27608 #29180)
-#30122 := (= #3152 #29180)
-#30120 := (= #29180 #3152)
-#30112 := (= #27122 f19)
-#30110 := (= #27122 #25112)
-#30111 := [monotonicity #27142]: #30110
-#30113 := [trans #30111 #27685]: #30112
-#30121 := [monotonicity #27142 #30113]: #30120
-#30123 := [symm #30121]: #30122
-#30118 := (= #27608 #3152)
-#30116 := (= #27607 f19)
-#30114 := (= #27607 #25112)
-#30115 := [monotonicity #27414]: #30114
-#30117 := [trans #30115 #27685]: #30116
-#30119 := [monotonicity #27414 #30117]: #30118
-#30125 := [trans #30119 #30123]: #30124
-#30128 := [monotonicity #30125 #30109]: #30127
-#30130 := [symm #30128]: #30129
-#29182 := (= f308 #29181)
-#29185 := (or #27129 #29182)
-#29186 := [quant-inst #24833 #3135]: #29185
-#30126 := [unit-resolution #29186 #17107]: #29182
-#30131 := [trans #30126 #30130]: #27610
-#28118 := (not #27610)
-#30132 := (or #28118 #27780)
-#30133 := [th-lemma arith triangle-eq]: #30132
-#30134 := [unit-resolution #30133 #30131]: #27780
-#30135 := (not #27780)
-#30136 := (or #27690 #22479 #30135)
-#30137 := [th-lemma arith assign-bounds -1 1]: #30136
-#30138 := [unit-resolution #30137 #30134 #30104]: #27690
-#27691 := (not #27690)
-#28143 := (or #23524 #27691 #13979 #22622 #22615 #23377)
-#27988 := (f77 #3042 #27609 f19)
-#27989 := (f121 f297 #27988)
-#27992 := (= f313 #27989)
-#28098 := (= #3153 #27989)
-#28111 := (= #27989 #3153)
-#28105 := (= #27988 #3152)
-#28103 := (= #27609 f308)
-#27613 := (or #27129 #27610)
-#27614 := [quant-inst #27086 #3135]: #27613
-#28102 := [unit-resolution #27614 #17107]: #27610
-#28104 := [symm #28102]: #28103
-#28106 := [monotonicity #28104]: #28105
-#28112 := [monotonicity #28106]: #28111
-#28113 := [symm #28112]: #28098
-#28114 := (= f313 #3153)
-#28107 := [hypothesis]: #12250
-#28108 := [hypothesis]: #23527
-#24691 := (or #23524 #12278)
-#24692 := [def-axiom]: #24691
-#28109 := [unit-resolution #24692 #28108]: #12278
-#28110 := [symm #28109]: #3167
-#28115 := [trans #28110 #28107]: #28114
-#28116 := [trans #28115 #28113]: #27992
-#27973 := (<= #27609 4294967295::Int)
-#28117 := [hypothesis]: #15868
-#27781 := (>= #27779 0::Int)
-#28119 := (or #28118 #27781)
-#28120 := [th-lemma arith triangle-eq]: #28119
-#28121 := [unit-resolution #28120 #28102]: #27781
-#28122 := (not #27781)
-#28123 := (or #27973 #22622 #28122)
-#28124 := [th-lemma arith assign-bounds -1 1]: #28123
-#28125 := [unit-resolution #28124 #28121 #28117]: #27973
-#28015 := (+ f296 #27706)
-#28016 := (<= #28015 0::Int)
-#28127 := (not #28016)
-#28126 := [hypothesis]: #13980
-#28128 := (or #28127 #13979 #28122)
-#28129 := [th-lemma arith assign-bounds -1 -1]: #28128
-#28130 := [unit-resolution #28129 #28121 #28126]: #28127
-#27995 := (not #27992)
-#27974 := (not #27973)
-#28140 := (or #27974 #27995 #28016)
-#28131 := [hypothesis]: #27690
-#24699 := (or #23524 #23518)
-#24700 := [def-axiom]: #24699
-#28132 := [unit-resolution #24700 #28108]: #23518
-#24697 := (or #23524 #13801)
-#24698 := [def-axiom]: #24697
-#28133 := [unit-resolution #24698 #28108]: #13801
-#28039 := [hypothesis]: #23372
-#27785 := (+ f307 #13841)
-#27788 := (<= #27785 0::Int)
-#28134 := (or #12313 #27788)
-#28135 := [th-lemma arith triangle-eq]: #28134
-#28136 := [unit-resolution #28135 #28109]: #27788
-#28044 := (not #27788)
-#28045 := (or #22588 #28044 #23377 #13802)
-#28032 := [hypothesis]: #27788
-#24674 := (not #19091)
-#28033 := [hypothesis]: #22593
-#24675 := (or #22588 #24674)
-#24676 := [def-axiom]: #24675
-#28034 := [unit-resolution #24676 #28033]: #24674
-#27868 := (+ f307 #19089)
-#27869 := (>= #27868 0::Int)
-#27856 := (+ f309 #19076)
-#27857 := (<= #27856 0::Int)
-#28029 := (not #27857)
-#28023 := [hypothesis]: #13801
-#24671 := (not #19078)
-#24672 := (or #22588 #24671)
-#24673 := [def-axiom]: #24672
-#28035 := [unit-resolution #24673 #28033]: #24671
-#28030 := (or #28029 #19078 #13802)
-#28024 := [hypothesis]: #27857
-#28027 := [hypothesis]: #24671
-#28028 := [th-lemma arith farkas -1 1 1 #28027 #28024 #28023]: false
-#28031 := [lemma #28028]: #28030
-#28036 := [unit-resolution #28031 #28035 #28023]: #28029
-#28040 := (or #27857 #27869)
-#24669 := (or #22588 #18740)
-#24670 := [def-axiom]: #24669
-#28037 := [unit-resolution #24670 #28033]: #18740
-#24667 := (or #22588 #18739)
-#24668 := [def-axiom]: #24667
-#28038 := [unit-resolution #24668 #28033]: #18739
-#27882 := (or #23377 #22572 #22573 #27857 #27869)
-#27845 := (+ #18744 #14006)
-#27846 := (<= #27845 0::Int)
-#27847 := (+ ?v0!15 #13537)
+#15334 := [monotonicity #15331]: #15333
+#15337 := [monotonicity #15334]: #15336
+#15340 := [monotonicity #15337]: #15339
+#15343 := [monotonicity #15340]: #15342
+#15346 := [monotonicity #15343]: #15345
+#15349 := [monotonicity #15346]: #15348
+#15352 := [monotonicity #15349]: #15351
+#15355 := [monotonicity #15352]: #15354
+#14342 := [not-or-elim #14326]: #14341
+#15356 := [mp #14342 #15355]: #15353
+#16065 := [mp #15356 #16064]: #16062
+#18812 := [mp~ #16065 #18811]: #18809
+#18813 := [mp #18812 #19157]: #19155
+#22680 := [mp #18813 #22679]: #22677
+#23584 := [mp #22680 #23583]: #23581
+#29108 := [unit-resolution #23584 #27012]: #23578
+#24808 := (or #23575 #23569)
+#24809 := [def-axiom]: #24808
+#29109 := [unit-resolution #24809 #29108]: #23569
+#24804 := (or #23572 #18425 #18428 #23566)
+#24805 := [def-axiom]: #24804
+#29113 := [unit-resolution #24805 #27621 #28777 #29109]: #23566
+#24794 := (or #23563 #23557)
+#24795 := [def-axiom]: #24794
+#29114 := [unit-resolution #24795 #29113]: #23557
+#24788 := (or #23560 #18425 #18434 #23554)
+#24789 := [def-axiom]: #24788
+#29115 := [unit-resolution #24789 #29114 #29107 #27621]: #23554
+#24766 := (or #23551 #3102)
+#24767 := [def-axiom]: #24766
+#29116 := [unit-resolution #24767 #29115]: #3102
+#24778 := (or #23551 #23545)
+#24779 := [def-axiom]: #24778
+#29642 := [unit-resolution #24779 #29115]: #23545
+#29643 := (or #23548 #23542)
+#27289 := [hypothesis]: #13452
+#27290 := [th-lemma arith farkas 1 1 #14340 #27289]: false
+#27291 := [lemma #27290]: #13449
+#24764 := (or #23548 #13452 #23542)
+#24765 := [def-axiom]: #24764
+#29644 := [unit-resolution #24765 #27291]: #29643
+#29645 := [unit-resolution #29644 #29642]: #23542
+#24756 := (or #23539 #23533)
+#24757 := [def-axiom]: #24756
+#29646 := [unit-resolution #24757 #29645]: #23533
+#27594 := (* -1::Int #3101)
+#27595 := (+ f301 #27594)
+#27596 := (>= #27595 0::Int)
+#29117 := (or #13247 #27596)
+#29118 := [th-lemma arith triangle-eq]: #29117
+#29119 := [unit-resolution #29118 #29116]: #27596
+#24434 := (not #18466)
+#29120 := [hypothesis]: #22317
+#24435 := (or #22312 #24434)
+#24436 := [def-axiom]: #24435
+#29121 := [unit-resolution #24436 #29120]: #24434
+#29081 := (+ #3101 #18464)
+#29083 := (>= #29081 0::Int)
+#29080 := (= #3101 #18463)
+#29128 := (= #18463 #3101)
+#29126 := (= #18462 #3091)
+#29124 := (= ?v0!13 0::Int)
+#24437 := (not #18467)
+#24438 := (or #22312 #24437)
+#24439 := [def-axiom]: #24438
+#29122 := [unit-resolution #24439 #29120]: #24437
+#24432 := (or #22312 #18459)
+#24433 := [def-axiom]: #24432
+#29123 := [unit-resolution #24433 #29120]: #18459
+#29125 := [th-lemma arith eq-propagate 0 0 #29123 #29122]: #29124
+#29127 := [monotonicity #29125]: #29126
+#29129 := [monotonicity #29127]: #29128
+#29130 := [symm #29129]: #29080
+#29131 := (not #29080)
+#29132 := (or #29131 #29083)
+#29133 := [th-lemma arith triangle-eq]: #29132
+#29134 := [unit-resolution #29133 #29130]: #29083
+#29135 := [th-lemma arith farkas 1 -1 1 #29134 #29121 #29119]: false
+#29136 := [lemma #29135]: #22312
+#24752 := (or #23536 #22317 #23530)
+#24753 := [def-axiom]: #24752
+#29647 := [unit-resolution #24753 #29136 #29646]: #23530
+#24744 := (or #23527 #23521)
+#24745 := [def-axiom]: #24744
+#29648 := [unit-resolution #24745 #29647]: #23521
+#29649 := (or #23524 #13247 #23518)
+#24740 := (or #23524 #13247 #13488 #23518)
+#24741 := [def-axiom]: #24740
+#29650 := [unit-resolution #24741 #14340]: #29649
+#29651 := [unit-resolution #29650 #29648 #29116]: #23518
+#24730 := (or #23515 #23509)
+#24731 := [def-axiom]: #24730
+#30079 := [unit-resolution #24731 #29651]: #23509
+#24728 := (or #23515 #23351)
+#24729 := [def-axiom]: #24728
+#30074 := [unit-resolution #24729 #29651]: #23351
+#24690 := (or #23515 #12230)
+#24691 := [def-axiom]: #24690
+#30080 := [unit-resolution #24691 #29651]: #12230
+#24724 := (or #23515 #15848)
+#24725 := [def-axiom]: #24724
+#30081 := [unit-resolution #24725 #29651]: #15848
+#24714 := (or #23515 #13960)
+#24715 := [def-axiom]: #24714
+#30082 := [unit-resolution #24715 #29651]: #13960
+#27586 := (f14 #27065)
+#27587 := (f67 #27065 f303 #27586)
+#27588 := (f126 #27587 #27065)
+#27669 := (>= #27588 0::Int)
+#24710 := (or #23515 #13493)
+#24711 := [def-axiom]: #24710
+#30083 := [unit-resolution #24711 #29651]: #13493
+#27685 := (* -1::Int #27588)
+#27758 := (+ f303 #27685)
+#27759 := (<= #27758 0::Int)
+#27589 := (= f303 #27588)
+#29159 := (f67 #24812 f303 #27101)
+#29160 := (f126 #29159 #24812)
+#30108 := (= #29160 #27588)
+#30106 := (= #27588 #29160)
+#30084 := (= #27065 #24812)
+#30088 := [trans #27393 #27119]: #30084
+#30103 := (= #27587 #29159)
+#30101 := (= #3145 #29159)
+#30099 := (= #29159 #3145)
+#30091 := (= #27101 f9)
+#30089 := (= #27101 #25091)
+#30090 := [monotonicity #27121]: #30089
+#30092 := [trans #30090 #27664]: #30091
+#30100 := [monotonicity #27121 #30092]: #30099
+#30102 := [symm #30100]: #30101
+#30097 := (= #27587 #3145)
+#30095 := (= #27586 f9)
+#30093 := (= #27586 #25091)
+#30094 := [monotonicity #27393]: #30093
+#30096 := [trans #30094 #27664]: #30095
+#30098 := [monotonicity #27393 #30096]: #30097
+#30104 := [trans #30098 #30102]: #30103
+#30107 := [monotonicity #30104 #30088]: #30106
+#30109 := [symm #30107]: #30108
+#29161 := (= f303 #29160)
+#29164 := (or #27108 #29161)
+#29165 := [quant-inst #24812 #3128]: #29164
+#30105 := [unit-resolution #29165 #17062]: #29161
+#30110 := [trans #30105 #30109]: #27589
+#28097 := (not #27589)
+#30111 := (or #28097 #27759)
+#30112 := [th-lemma arith triangle-eq]: #30111
+#30113 := [unit-resolution #30112 #30110]: #27759
+#30114 := (not #27759)
+#30115 := (or #27669 #22459 #30114)
+#30116 := [th-lemma arith assign-bounds -1 1]: #30115
+#30117 := [unit-resolution #30116 #30113 #30083]: #27669
+#27670 := (not #27669)
+#28122 := (or #23503 #27670 #13959 #22602 #22595 #23356)
+#27967 := (f67 #3035 #27588 f9)
+#27968 := (f111 f292 #27967)
+#27971 := (= f308 #27968)
+#28077 := (= #3146 #27968)
+#28090 := (= #27968 #3146)
+#28084 := (= #27967 #3145)
+#28082 := (= #27588 f303)
+#27592 := (or #27108 #27589)
+#27593 := [quant-inst #27065 #3128]: #27592
+#28081 := [unit-resolution #27593 #17062]: #27589
+#28083 := [symm #28081]: #28082
+#28085 := [monotonicity #28083]: #28084
+#28091 := [monotonicity #28085]: #28090
+#28092 := [symm #28091]: #28077
+#28093 := (= f308 #3146)
+#28086 := [hypothesis]: #12230
+#28087 := [hypothesis]: #23506
+#24670 := (or #23503 #12258)
+#24671 := [def-axiom]: #24670
+#28088 := [unit-resolution #24671 #28087]: #12258
+#28089 := [symm #28088]: #3160
+#28094 := [trans #28089 #28086]: #28093
+#28095 := [trans #28094 #28092]: #27971
+#27952 := (<= #27588 4294967295::Int)
+#28096 := [hypothesis]: #15848
+#27760 := (>= #27758 0::Int)
+#28098 := (or #28097 #27760)
+#28099 := [th-lemma arith triangle-eq]: #28098
+#28100 := [unit-resolution #28099 #28081]: #27760
+#28101 := (not #27760)
+#28102 := (or #27952 #22602 #28101)
+#28103 := [th-lemma arith assign-bounds -1 1]: #28102
+#28104 := [unit-resolution #28103 #28100 #28096]: #27952
+#27994 := (+ f291 #27685)
+#27995 := (<= #27994 0::Int)
+#28106 := (not #27995)
+#28105 := [hypothesis]: #13960
+#28107 := (or #28106 #13959 #28101)
+#28108 := [th-lemma arith assign-bounds -1 -1]: #28107
+#28109 := [unit-resolution #28108 #28100 #28105]: #28106
+#27974 := (not #27971)
+#27953 := (not #27952)
+#28119 := (or #27953 #27974 #27995)
+#28110 := [hypothesis]: #27669
+#24678 := (or #23503 #23497)
+#24679 := [def-axiom]: #24678
+#28111 := [unit-resolution #24679 #28087]: #23497
+#24676 := (or #23503 #13781)
+#24677 := [def-axiom]: #24676
+#28112 := [unit-resolution #24677 #28087]: #13781
+#28018 := [hypothesis]: #23351
+#27764 := (+ f302 #13821)
+#27767 := (<= #27764 0::Int)
+#28113 := (or #12293 #27767)
+#28114 := [th-lemma arith triangle-eq]: #28113
+#28115 := [unit-resolution #28114 #28088]: #27767
+#28023 := (not #27767)
+#28024 := (or #22568 #28023 #23356 #13782)
+#28011 := [hypothesis]: #27767
+#24653 := (not #19071)
+#28012 := [hypothesis]: #22573
+#24654 := (or #22568 #24653)
+#24655 := [def-axiom]: #24654
+#28013 := [unit-resolution #24655 #28012]: #24653
+#27847 := (+ f302 #19069)
 #27848 := (>= #27847 0::Int)
-#27849 := (or #22573 #27848 #27846 #22572)
-#27883 := (or #23377 #27849)
-#27890 := (iff #27883 #27882)
-#27877 := (or #22572 #22573 #27857 #27869)
-#27885 := (or #23377 #27877)
-#27888 := (iff #27885 #27882)
-#27889 := [rewrite]: #27888
-#27886 := (iff #27883 #27885)
-#27880 := (iff #27849 #27877)
-#27874 := (or #22573 #27857 #27869 #22572)
-#27878 := (iff #27874 #27877)
-#27879 := [rewrite]: #27878
-#27875 := (iff #27849 #27874)
-#27872 := (iff #27846 #27869)
-#27862 := (+ #14006 #18744)
-#27865 := (<= #27862 0::Int)
-#27870 := (iff #27865 #27869)
-#27871 := [rewrite]: #27870
-#27866 := (iff #27846 #27865)
-#27863 := (= #27845 #27862)
-#27864 := [rewrite]: #27863
-#27867 := [monotonicity #27864]: #27866
-#27873 := [trans #27867 #27871]: #27872
-#27860 := (iff #27848 #27857)
-#27850 := (+ #13537 ?v0!15)
-#27853 := (>= #27850 0::Int)
-#27858 := (iff #27853 #27857)
-#27859 := [rewrite]: #27858
-#27854 := (iff #27848 #27853)
-#27851 := (= #27847 #27850)
-#27852 := [rewrite]: #27851
-#27855 := [monotonicity #27852]: #27854
-#27861 := [trans #27855 #27859]: #27860
-#27876 := [monotonicity #27861 #27873]: #27875
-#27881 := [trans #27876 #27879]: #27880
-#27887 := [monotonicity #27881]: #27886
-#27891 := [trans #27887 #27889]: #27890
-#27884 := [quant-inst #18738]: #27883
-#27892 := [mp #27884 #27891]: #27882
-#28041 := [unit-resolution #27892 #28039 #28038 #28037]: #28040
-#28042 := [unit-resolution #28041 #28036]: #27869
-#28043 := [th-lemma arith farkas -1 1 1 #28042 #28034 #28032]: false
-#28046 := [lemma #28043]: #28045
-#28137 := [unit-resolution #28046 #28136 #28039 #28133]: #22588
-#24683 := (or #23521 #23515 #22593)
-#24684 := [def-axiom]: #24683
-#28138 := [unit-resolution #24684 #28137 #28132]: #23515
-#24663 := (or #23512 #23504)
-#24664 := [def-axiom]: #24663
-#28139 := [unit-resolution #24664 #28138]: #23504
-#28052 := (or #23509 #27691 #27974 #27995 #28016)
-#27979 := (+ #27609 #13442)
-#27980 := (>= #27979 0::Int)
-#27987 := (= #27989 f313)
-#27990 := (not #27987)
-#27991 := (or #27990 #27691 #27980 #27974)
-#28053 := (or #23509 #27991)
-#28060 := (iff #28053 #28052)
-#28047 := (or #27691 #27974 #27995 #28016)
-#28055 := (or #23509 #28047)
-#28058 := (iff #28055 #28052)
-#28059 := [rewrite]: #28058
-#28056 := (iff #28053 #28055)
-#28050 := (iff #27991 #28047)
-#27996 := (or #27995 #27691 #28016 #27974)
-#28048 := (iff #27996 #28047)
-#28049 := [rewrite]: #28048
-#27997 := (iff #27991 #27996)
-#28026 := (iff #27980 #28016)
-#28010 := (+ #13442 #27609)
-#28007 := (>= #28010 0::Int)
-#28017 := (iff #28007 #28016)
-#28025 := [rewrite]: #28017
-#28013 := (iff #27980 #28007)
-#28011 := (= #27979 #28010)
-#28012 := [rewrite]: #28011
-#28014 := [monotonicity #28012]: #28013
-#27928 := [trans #28014 #28025]: #28026
-#28008 := (iff #27990 #27995)
-#27993 := (iff #27987 #27992)
-#27994 := [rewrite]: #27993
-#28009 := [monotonicity #27994]: #28008
-#28020 := [monotonicity #28009 #27928]: #27997
-#28051 := [trans #28020 #28049]: #28050
-#28057 := [monotonicity #28051]: #28056
-#28061 := [trans #28057 #28059]: #28060
-#28054 := [quant-inst #27609]: #28053
-#28062 := [mp #28054 #28061]: #28052
-#28141 := [unit-resolution #28062 #28139 #28131]: #28140
-#28142 := [unit-resolution #28141 #28130 #28125 #28116]: false
-#28144 := [lemma #28142]: #28143
-#30139 := [unit-resolution #28144 #30138 #30103 #30102 #30101 #30095]: #23524
-#24707 := (or #23533 #23493 #23527)
-#24708 := [def-axiom]: #24707
-#30140 := [unit-resolution #24708 #30139 #30100]: #23493
-#24655 := (or #23490 #13802)
-#24656 := [def-axiom]: #24655
-#30141 := [unit-resolution #24656 #30140]: #13802
-#30242 := (not #29585)
-#30243 := (or #30241 #28416 #30242 #13801)
-#30244 := [th-lemma arith assign-bounds 1 -1 -1]: #30243
-#30245 := [unit-resolution #30244 #28410 #30141 #30237]: #30241
-#29465 := (>= #29368 0::Int)
-#24733 := (or #23536 #13516)
-#24734 := [def-axiom]: #24733
-#29673 := [unit-resolution #24734 #29672]: #13516
-#29584 := (<= #29583 0::Int)
-#29676 := (or #29675 #29584)
-#29677 := [th-lemma arith triangle-eq]: #29676
-#29678 := [unit-resolution #29677 #29674]: #29584
-#29466 := (not #29465)
-#29679 := [hypothesis]: #29466
-#29680 := [th-lemma arith farkas 1 1 1 #29679 #29678 #29673]: false
-#29681 := [lemma #29680]: #29465
-#30247 := (or #29466 #29476 #29484)
-#29495 := (or #28639 #27163 #29466 #29476 #29484)
-#29461 := (or #29460 #29457 #29455 #29451)
-#29462 := (not #29461)
-#29463 := (+ #29368 #27164)
-#29464 := (>= #29463 0::Int)
-#29467 := (or #29466 #29464 #27163 #29462)
-#29496 := (or #28639 #29467)
-#29503 := (iff #29496 #29495)
-#29490 := (or #27163 #29466 #29476 #29484)
-#29498 := (or #28639 #29490)
-#29501 := (iff #29498 #29495)
-#29502 := [rewrite]: #29501
-#29499 := (iff #29496 #29498)
-#29493 := (iff #29467 #29490)
-#29487 := (or #29466 #29476 #27163 #29484)
-#29491 := (iff #29487 #29490)
-#29492 := [rewrite]: #29491
-#29488 := (iff #29467 #29487)
-#29485 := (iff #29462 #29484)
-#29482 := (iff #29461 #29481)
-#29483 := [rewrite]: #29482
-#29486 := [monotonicity #29483]: #29485
-#29479 := (iff #29464 #29476)
-#29468 := (+ #27164 #29368)
-#29471 := (>= #29468 0::Int)
-#29477 := (iff #29471 #29476)
-#29478 := [rewrite]: #29477
-#29472 := (iff #29464 #29471)
-#29469 := (= #29463 #29468)
-#29470 := [rewrite]: #29469
-#29473 := [monotonicity #29470]: #29472
-#29480 := [trans #29473 #29478]: #29479
-#29489 := [monotonicity #29480 #29486]: #29488
-#29494 := [trans #29489 #29492]: #29493
-#29500 := [monotonicity #29494]: #29499
-#29504 := [trans #29500 #29502]: #29503
-#29497 := [quant-inst #3039 #3043 #24996 #24998 #29368]: #29496
-#29505 := [mp #29497 #29504]: #29495
-#30248 := [unit-resolution #29505 #21024 #28873]: #30247
-#30249 := [unit-resolution #30248 #29681 #30245]: #29484
-#29513 := (or #29481 #29459)
-#29514 := [def-axiom]: #29513
-#30250 := [unit-resolution #29514 #30249]: #29459
-#30281 := [symm #30250]: #30280
-#30278 := (= #28494 #29458)
-#30276 := (= #27834 #29452)
-#30274 := (= #29452 #27834)
-#30272 := (= #29431 #3257)
-#28088 := (f127 #3257)
-#28199 := (f54 #24996 #28088)
-#30266 := (= #28199 #3257)
-#28200 := (= #3257 #28199)
-#28205 := (f59 #3257 #24996)
-#28206 := (= f1 #28205)
-#30252 := (= #3258 #28205)
-#29418 := (= #28205 #3258)
-#29419 := [monotonicity #28386]: #29418
-#30253 := [symm #29419]: #30252
-#28203 := (= #24996 #28202)
-#28182 := (* f309 #27068)
-#29340 := (+ #27070 #28182)
-#29341 := (f54 #24996 #29340)
-#29371 := (f24 #29341)
-#29443 := (= #29371 #28202)
-#29439 := (= #28202 #29371)
-#29437 := (= #3257 #29341)
-#29336 := (f77 #24833 f309 #24996)
-#29342 := (= #29336 #29341)
-#29343 := (not #29342)
-#29337 := (f149 #29336 #24833)
-#29338 := (= f1 #29337)
-#29339 := (not #29338)
-#29346 := (or #29339 #29343)
-#29349 := (not #29346)
-#29352 := (or #27721 #29349)
-#29344 := (or #29343 #29339)
-#29345 := (not #29344)
-#29353 := (or #27721 #29345)
-#29355 := (iff #29353 #29352)
-#29357 := (iff #29352 #29352)
-#29358 := [rewrite]: #29357
-#29350 := (iff #29345 #29349)
-#29347 := (iff #29344 #29346)
-#29348 := [rewrite]: #29347
-#29351 := [monotonicity #29348]: #29350
-#29356 := [monotonicity #29351]: #29355
-#29359 := [trans #29356 #29358]: #29355
-#29354 := [quant-inst #24833 #3139 #24996]: #29353
-#29360 := [mp #29354 #29359]: #29352
-#29429 := [unit-resolution #29360 #21240]: #29349
-#29363 := (or #29346 #29342)
-#29364 := [def-axiom]: #29363
-#29430 := [unit-resolution #29364 #29429]: #29342
-#29435 := (= #3257 #29336)
-#29433 := (= #29336 #3257)
-#29434 := [monotonicity #27142 #28386]: #29433
-#29436 := [symm #29434]: #29435
-#29438 := [trans #29436 #29430]: #29437
-#29440 := [monotonicity #29438]: #29439
-#29444 := [symm #29440]: #29443
-#29374 := (= #24996 #29371)
-#29379 := (or #25064 #29374)
-#29380 := [quant-inst #24996 #29340]: #29379
-#29428 := [unit-resolution #29380 #23312]: #29374
-#29445 := [trans #29428 #29444]: #28203
-#29320 := (not #28203)
-#28280 := (iff #28203 #28206)
-#29315 := (or #26210 #28280)
-#29316 := [quant-inst #3257 #24996]: #29315
-#29416 := [unit-resolution #29316 #23299]: #28280
-#28198 := (not #28206)
-#29424 := (iff #18556 #28198)
-#29422 := (iff #12575 #28206)
-#29420 := (iff #28206 #12575)
-#29421 := [monotonicity #29419]: #29420
-#29423 := [symm #29421]: #29422
-#29425 := [monotonicity #29423]: #29424
-#29417 := [hypothesis]: #18556
-#29426 := [mp #29417 #29425]: #28198
-#29317 := (not #28280)
-#29321 := (or #29317 #29320 #28206)
-#29322 := [def-axiom]: #29321
-#29427 := [unit-resolution #29322 #29426 #29416]: #29320
-#29446 := [unit-resolution #29427 #29445]: false
-#29447 := [lemma #29446]: #12575
-#30254 := [trans #29447 #30253]: #28206
-#28201 := (or #28200 #28198)
-#29376 := (or #26194 #28200 #28198)
-#29388 := (or #26194 #28201)
-#29387 := (iff #29388 #29376)
-#29390 := [rewrite]: #29387
-#29389 := [quant-inst #3257 #24996]: #29388
-#29391 := [mp #29389 #29390]: #29376
-#30255 := [unit-resolution #29391 #18284]: #28201
-#30256 := [unit-resolution #30255 #30254]: #28200
-#30267 := [symm #30256]: #30266
-#30270 := (= #29431 #28199)
-#29648 := (* #27068 #29368)
-#29651 := (+ #27318 #29648)
-#29654 := (f54 #24996 #29651)
-#30264 := (= #29654 #28199)
-#30258 := (= #29651 #28088)
-#30229 := (= #28088 #29651)
-#30230 := (* -1::Int #29651)
-#30231 := (+ #28088 #30230)
-#30232 := (<= #30231 0::Int)
-#29206 := (* -1::Int #27070)
-#29207 := (+ #24880 #29206)
-#29209 := (>= #29207 0::Int)
-#29205 := (= #24880 #27070)
-#30031 := (= #3043 #27070)
-#29986 := [symm #27275]: #30031
-#29987 := [trans #28885 #29986]: #29205
-#30032 := (not #29205)
-#30000 := (or #30032 #29209)
-#29997 := [th-lemma arith triangle-eq]: #30000
-#29984 := [unit-resolution #29997 #29987]: #29209
-#29700 := (* -1::Int #27318)
-#29701 := (+ #24880 #29700)
-#29702 := (<= #29701 0::Int)
-#29699 := (= #24880 #27318)
-#29989 := [symm #28883]: #29699
-#29990 := (not #29699)
-#29991 := (or #29990 #29702)
-#29992 := [th-lemma arith triangle-eq]: #29991
-#29993 := [unit-resolution #29992 #29989]: #29702
-#29377 := (f127 #29341)
-#29381 := (* -1::Int #29377)
-#29587 := (+ #28088 #29381)
-#29588 := (<= #29587 0::Int)
-#29586 := (= #28088 #29377)
-#30043 := (= #29377 #28088)
-#30035 := (= #29341 #3257)
-#30026 := (= #29341 #29336)
-#30034 := [symm #29430]: #30026
-#30042 := [trans #30034 #29434]: #30035
-#30041 := [monotonicity #30042]: #30043
-#30033 := [symm #30041]: #29586
-#30044 := (not #29586)
-#30045 := (or #30044 #29588)
-#30046 := [th-lemma arith triangle-eq]: #30045
-#30049 := [unit-resolution #30046 #30033]: #29588
-#29382 := (+ #28182 #29381)
-#29383 := (+ #27070 #29382)
-#29571 := (>= #29383 0::Int)
-#29384 := (= #29383 0::Int)
-#29559 := (or #25070 #29384)
-#29378 := (= #29340 #29377)
-#29560 := (or #25070 #29378)
-#29564 := (iff #29560 #29559)
-#29566 := (iff #29559 #29559)
-#29567 := [rewrite]: #29566
-#29385 := (iff #29378 #29384)
-#29386 := [rewrite]: #29385
-#29565 := [monotonicity #29386]: #29564
-#29568 := [trans #29565 #29567]: #29564
-#29563 := [quant-inst #24996 #29340]: #29560
-#29569 := [mp #29563 #29568]: #29559
-#30050 := [unit-resolution #29569 #23306]: #29384
-#30055 := (not #29384)
-#30058 := (or #30055 #29571)
-#30057 := [th-lemma arith triangle-eq]: #30058
-#30059 := [unit-resolution #30057 #30050]: #29571
-#29212 := (>= #27068 1::Int)
-#29210 := (= #27068 1::Int)
-#2998 := (f150 f19)
-#2999 := (= #2998 1::Int)
-#12057 := [asserted]: #2999
-#30060 := (= #27068 #2998)
-#30080 := [monotonicity #28386]: #30060
-#30081 := [trans #30080 #12057]: #29210
-#30082 := (not #29210)
-#30098 := (or #30082 #29212)
-#30099 := [th-lemma arith triangle-eq]: #30098
-#30056 := [unit-resolution #30099 #30081]: #29212
-#29211 := (<= #27068 1::Int)
-#30145 := (or #30082 #29211)
-#30146 := [th-lemma arith triangle-eq]: #30145
-#30147 := [unit-resolution #30146 #30081]: #29211
-#30028 := (not #29584)
-#30027 := (not #29702)
-#29999 := (not #29211)
-#29754 := (not #29212)
-#29998 := (not #29209)
-#29995 := (not #29571)
-#29994 := (not #29588)
-#30029 := (or #30232 #29994 #29995 #29998 #29754 #29999 #29754 #29999 #30027 #30028)
-#30030 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30029
-#30025 := [unit-resolution #30030 #30147 #30056 #30059 #29678 #30049 #29993 #29984]: #30232
-#30233 := (>= #30231 0::Int)
-#29208 := (<= #29207 0::Int)
-#30152 := (or #30032 #29208)
-#30153 := [th-lemma arith triangle-eq]: #30152
-#30154 := [unit-resolution #30153 #29987]: #29208
-#29703 := (>= #29701 0::Int)
-#30155 := (or #29990 #29703)
-#30156 := [th-lemma arith triangle-eq]: #30155
-#30157 := [unit-resolution #30156 #29989]: #29703
-#29589 := (>= #29587 0::Int)
-#30150 := (or #30044 #29589)
-#30151 := [th-lemma arith triangle-eq]: #30150
-#30148 := [unit-resolution #30151 #30033]: #29589
-#29570 := (<= #29383 0::Int)
-#30149 := (or #30055 #29570)
-#30158 := [th-lemma arith triangle-eq]: #30149
-#30159 := [unit-resolution #30158 #30050]: #29570
-#30162 := (not #29703)
-#30161 := (not #29208)
-#29784 := (not #29570)
-#30160 := (not #29589)
-#30163 := (or #30233 #30160 #29784 #30161 #29754 #29999 #29754 #29999 #30162 #30242)
-#30164 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30163
-#30165 := [unit-resolution #30164 #30147 #30056 #30159 #30237 #30148 #30157 #30154]: #30233
-#30169 := (not #30233)
-#30168 := (not #30232)
-#30178 := (or #30229 #30168 #30169)
-#30179 := [th-lemma arith triangle-eq]: #30178
-#30180 := [unit-resolution #30179 #30165 #30025]: #30229
-#30177 := [symm #30180]: #30258
-#30186 := [monotonicity #30177]: #30264
-#30268 := (= #29431 #29654)
-#29637 := (f77 #26182 #29368 #24996)
-#29657 := (= #29637 #29654)
-#29592 := (not #29657)
-#29638 := (f149 #29637 #26182)
-#29639 := (= f1 #29638)
-#29640 := (not #29639)
-#29597 := (or #29640 #29592)
-#29660 := (not #29597)
-#29684 := (or #27721 #29660)
-#29641 := (* #29368 #27068)
-#29642 := (+ #27318 #29641)
-#29643 := (f54 #24996 #29642)
-#29644 := (= #29637 #29643)
-#29645 := (not #29644)
-#29646 := (or #29645 #29640)
-#29647 := (not #29646)
-#29685 := (or #27721 #29647)
-#29687 := (iff #29685 #29684)
-#29689 := (iff #29684 #29684)
-#29690 := [rewrite]: #29689
-#29682 := (iff #29647 #29660)
-#29661 := (iff #29646 #29597)
-#29594 := (or #29592 #29640)
-#29598 := (iff #29594 #29597)
-#29599 := [rewrite]: #29598
-#29595 := (iff #29646 #29594)
-#29593 := (iff #29645 #29592)
-#29658 := (iff #29644 #29657)
-#29655 := (= #29643 #29654)
-#29652 := (= #29642 #29651)
-#29649 := (= #29641 #29648)
-#29650 := [rewrite]: #29649
-#29653 := [monotonicity #29650]: #29652
-#29656 := [monotonicity #29653]: #29655
-#29659 := [monotonicity #29656]: #29658
-#29591 := [monotonicity #29659]: #29593
-#29596 := [monotonicity #29591]: #29595
-#29662 := [trans #29596 #29599]: #29661
-#29683 := [monotonicity #29662]: #29682
-#29688 := [monotonicity #29683]: #29687
-#29691 := [trans #29688 #29690]: #29687
-#29686 := [quant-inst #26182 #29368 #24996]: #29685
-#29692 := [mp #29686 #29691]: #29684
-#30260 := [unit-resolution #29692 #21240]: #29660
-#29695 := (or #29597 #29657)
-#29696 := [def-axiom]: #29695
-#30261 := [unit-resolution #29696 #30260]: #29657
-#30262 := (= #29431 #29637)
-#30263 := [monotonicity #28791]: #30262
-#30269 := [trans #30263 #30261]: #30268
-#30187 := [trans #30269 #30186]: #30270
-#30188 := [trans #30187 #30267]: #30272
-#30189 := [monotonicity #30188]: #30274
-#30190 := [symm #30189]: #30276
-#30185 := [monotonicity #30190]: #30278
-#30191 := [trans #30185 #30281]: #30282
-#30192 := [trans #30191 #28789]: #30284
-#30194 := [monotonicity #30192]: #30193
-#30200 := [symm #30194]: #30199
-#30198 := [trans #14366 #30200]: #28498
-#29947 := (not #28498)
-#29948 := (or #28554 #29947)
-#29934 := [def-axiom]: #29948
-#30201 := [unit-resolution #29934 #30198]: #28554
-#30210 := (= #25501 #28512)
-#30212 := (= #28512 #25501)
-#30205 := (= #28202 f19)
-#30203 := (= #28202 #24996)
-#29392 := (or #29317 #28203 #28198)
-#29393 := [def-axiom]: #29392
-#30202 := [unit-resolution #29393 #30254 #29416]: #28203
-#30204 := [symm #30202]: #30203
-#30211 := [trans #30204 #28386]: #30205
-#30213 := [monotonicity #30211]: #30212
-#30216 := [symm #30213]: #30210
-#30217 := [trans #28841 #30216]: #28530
-#29890 := (not #28503)
-#30239 := (iff #12118 #29890)
-#30251 := (iff #12115 #28503)
-#30224 := (iff #28503 #12115)
-#30222 := (= #28502 #3053)
-#30220 := (= #28501 #3040)
-#30218 := (= #28501 #25117)
-#30219 := [monotonicity #30192]: #30218
-#30221 := [trans #30219 #28851]: #30220
-#30223 := [monotonicity #30221]: #30222
-#30288 := [monotonicity #30223]: #30224
-#30246 := [symm #30288]: #30251
-#30240 := [monotonicity #30246]: #30239
-#30238 := [mp #14369 #30240]: #29890
-#29517 := (f77 #27223 #29368 #24996)
-#29518 := (f69 #3220 #29517)
-#29519 := (f147 #29518)
-#29520 := (= f1 #29519)
-#29552 := (not #29520)
-#30315 := (iff #29552 #28509)
-#30313 := (iff #29520 #28508)
-#30311 := (iff #28508 #29520)
-#30309 := (= #28507 #29519)
-#30307 := (= #27834 #29518)
-#30305 := (= #29518 #27834)
-#30303 := (= #29517 #3257)
-#30301 := (= #29368 f309)
-#30302 := [symm #29674]: #30301
-#30304 := [monotonicity #28393 #30302 #28386]: #30303
-#30306 := [monotonicity #30304]: #30305
-#30308 := [symm #30306]: #30307
-#30310 := [monotonicity #30308]: #30309
-#30312 := [monotonicity #30310]: #30311
-#30314 := [symm #30312]: #30313
-#30316 := [monotonicity #30314]: #30315
-#29521 := (f35 f297 #29517)
-#29522 := (= f1 #29521)
-#29523 := (not #29522)
-#29527 := (or #29520 #29523)
-#29530 := (not #29527)
-#30297 := (or #29466 #29476 #29530)
-#29541 := (or #27254 #24846 #27235 #27238 #29466 #29476 #29530)
-#29524 := (or #29523 #29520)
-#29525 := (not #29524)
-#29526 := (or #27238 #29466 #29464 #24846 #27235 #29525)
-#29542 := (or #27254 #29526)
-#29549 := (iff #29542 #29541)
-#29536 := (or #24846 #27235 #27238 #29466 #29476 #29530)
-#29544 := (or #27254 #29536)
-#29547 := (iff #29544 #29541)
-#29548 := [rewrite]: #29547
-#29545 := (iff #29542 #29544)
-#29539 := (iff #29526 #29536)
-#29533 := (or #27238 #29466 #29476 #24846 #27235 #29530)
-#29537 := (iff #29533 #29536)
-#29538 := [rewrite]: #29537
-#29534 := (iff #29526 #29533)
-#29531 := (iff #29525 #29530)
-#29528 := (iff #29524 #29527)
-#29529 := [rewrite]: #29528
-#29532 := [monotonicity #29529]: #29531
-#29535 := [monotonicity #29480 #29532]: #29534
-#29540 := [trans #29535 #29538]: #29539
-#29546 := [monotonicity #29540]: #29545
-#29550 := [trans #29546 #29548]: #29549
-#29543 := [quant-inst #3039 #3043 #26182 #24998 #29368 #24996]: #29542
-#29551 := [mp #29543 #29550]: #29541
-#30298 := [unit-resolution #29551 #21684 #14351 #28797 #28426]: #30297
-#30299 := [unit-resolution #30298 #29681 #30245]: #29530
-#29553 := (or #29527 #29552)
-#29554 := [def-axiom]: #29553
-#30300 := [unit-resolution #29554 #30299]: #29552
-#30317 := [mp #30300 #30316]: #28509
-#29772 := (or #28548 #28508)
-#29773 := [def-axiom]: #29772
-#30318 := [unit-resolution #29773 #30317]: #28548
-#29907 := (or #28568 #28503 #28545 #28551 #28557)
-#29965 := [def-axiom]: #29907
-#30319 := [unit-resolution #29965 #30318 #30238 #30217 #30201 #30167]: false
-#30320 := [lemma #30319]: #28568
-#29805 := (or #28571 #28563)
-#29738 := [def-axiom]: #29805
-#30175 := [unit-resolution #29738 #30320]: #28571
-#28432 := (or #12578 #13656 #27235 #13801)
-#28375 := [hypothesis]: #13516
-#28210 := (f77 #27086 f309 #27607)
-#28211 := (f136 #28210 #27086)
-#28242 := (* -1::Int #28211)
-#28370 := (+ f309 #28242)
-#28371 := (<= #28370 0::Int)
-#28212 := (= f309 #28211)
-#28215 := (or #27129 #28212)
-#28216 := [quant-inst #27086 #3139]: #28215
-#28376 := [unit-resolution #28216 #17107]: #28212
-#28379 := (not #28212)
-#28380 := (or #28379 #28371)
-#28381 := [th-lemma arith triangle-eq]: #28380
-#28382 := [unit-resolution #28381 #28376]: #28371
-#28233 := (>= #28211 0::Int)
-#28234 := (not #28233)
-#28285 := (f77 #27223 #28211 #24996)
-#28289 := (f35 f297 #28285)
-#28290 := (= f1 #28289)
-#28291 := (not #28290)
-#28286 := (f69 #3220 #28285)
-#28287 := (f147 #28286)
-#28288 := (= f1 #28287)
-#28295 := (or #28288 #28291)
-#28402 := (iff #18559 #28291)
-#28400 := (iff #12578 #28290)
-#28398 := (iff #28290 #12578)
-#28396 := (= #28289 #3260)
-#28394 := (= #28285 #3257)
-#28387 := (= #28211 f309)
-#28388 := [symm #28376]: #28387
-#28395 := [monotonicity #28393 #28388 #28386]: #28394
-#28397 := [monotonicity #28395]: #28396
-#28399 := [monotonicity #28397]: #28398
-#28401 := [symm #28399]: #28400
-#28403 := [monotonicity #28401]: #28402
-#28383 := [hypothesis]: #18559
-#28404 := [mp #28383 #28403]: #28291
-#28323 := (or #28295 #28290)
-#28324 := [def-axiom]: #28323
-#28405 := [unit-resolution #28324 #28404]: #28295
-#28243 := (+ #24998 #28242)
-#28244 := (<= #28243 0::Int)
-#28415 := (not #28244)
-#28411 := [hypothesis]: #13802
-#28372 := (>= #28370 0::Int)
-#28412 := (or #28379 #28372)
-#28413 := [th-lemma arith triangle-eq]: #28412
-#28414 := [unit-resolution #28413 #28376]: #28372
-#28417 := (not #28372)
-#28418 := (or #28415 #28416 #28417 #13801)
-#28419 := [th-lemma arith assign-bounds 1 -1 -1]: #28418
-#28420 := [unit-resolution #28419 #28414 #28411 #28410]: #28415
-#28298 := (not #28295)
-#28428 := (or #28234 #28244 #28298)
-#28309 := (or #27254 #24846 #27235 #27238 #28234 #28244 #28298)
-#28292 := (or #28291 #28288)
-#28293 := (not #28292)
-#28231 := (+ #28211 #27164)
-#28232 := (>= #28231 0::Int)
-#28294 := (or #27238 #28234 #28232 #24846 #27235 #28293)
-#28310 := (or #27254 #28294)
-#28317 := (iff #28310 #28309)
-#28304 := (or #24846 #27235 #27238 #28234 #28244 #28298)
-#28312 := (or #27254 #28304)
-#28315 := (iff #28312 #28309)
-#28316 := [rewrite]: #28315
-#28313 := (iff #28310 #28312)
-#28307 := (iff #28294 #28304)
-#28301 := (or #27238 #28234 #28244 #24846 #27235 #28298)
-#28305 := (iff #28301 #28304)
-#28306 := [rewrite]: #28305
-#28302 := (iff #28294 #28301)
-#28299 := (iff #28293 #28298)
-#28296 := (iff #28292 #28295)
-#28297 := [rewrite]: #28296
-#28300 := [monotonicity #28297]: #28299
-#28247 := (iff #28232 #28244)
-#28236 := (+ #27164 #28211)
-#28239 := (>= #28236 0::Int)
-#28245 := (iff #28239 #28244)
-#28246 := [rewrite]: #28245
-#28240 := (iff #28232 #28239)
-#28237 := (= #28231 #28236)
-#28238 := [rewrite]: #28237
-#28241 := [monotonicity #28238]: #28240
-#28248 := [trans #28241 #28246]: #28247
-#28303 := [monotonicity #28248 #28300]: #28302
-#28308 := [trans #28303 #28306]: #28307
-#28314 := [monotonicity #28308]: #28313
-#28318 := [trans #28314 #28316]: #28317
-#28311 := [quant-inst #3039 #3043 #26182 #24998 #28211 #24996]: #28310
-#28319 := [mp #28311 #28318]: #28309
-#28429 := [unit-resolution #28319 #21684 #14351 #28427 #28426]: #28428
-#28430 := [unit-resolution #28429 #28420 #28405]: #28234
-#28431 := [th-lemma arith farkas 1 1 1 #28430 #28382 #28375]: false
-#28433 := [lemma #28431]: #28432
-#30142 := [unit-resolution #28433 #30141 #28797 #29673]: #12578
-#30170 := (or #28580 #18559 #28574)
-#30171 := [def-axiom]: #30170
-#30321 := [unit-resolution #30171 #30142 #30175]: #28580
-#29900 := (or #29899 #12584 #28577)
-#29898 := [def-axiom]: #29900
-#30323 := [unit-resolution #29898 #30321]: #30322
-#30324 := [unit-resolution #30323 #30215]: #12584
-#30424 := (+ f309 #18928)
-#30620 := (>= #30424 0::Int)
-#30702 := (not #30620)
-#30595 := (= f309 ?v0!14)
-#30648 := (not #30595)
-#30651 := [hypothesis]: #23457
-#24603 := (or #23454 #13708)
-#24604 := [def-axiom]: #24603
-#30652 := [unit-resolution #24604 #30651]: #13708
-#24587 := (+ f307 #13570)
-#24588 := (<= #24587 0::Int)
-#24593 := (or #23454 #12839)
-#24594 := [def-axiom]: #24593
-#30653 := [unit-resolution #24594 #30651]: #12839
-#30654 := (or #12857 #24588)
-#30655 := [th-lemma arith triangle-eq]: #30654
-#30656 := [unit-resolution #30655 #30653]: #24588
-#24484 := (not #18943)
-#30195 := [hypothesis]: #23421
-#24605 := (or #23454 #23418)
-#24606 := [def-axiom]: #24605
-#30176 := [unit-resolution #24606 #30195]: #23454
-#24549 := (or #23424 #23418)
-#24550 := [def-axiom]: #24549
-#30325 := [unit-resolution #24550 #30195]: #23424
-#30326 := (or #23433 #18565 #23427)
-#24559 := (or #23433 #18556 #18565 #23427)
-#24560 := [def-axiom]: #24559
-#30327 := [unit-resolution #24560 #29447]: #30326
-#30328 := [unit-resolution #30327 #30325 #30324]: #23433
-#29801 := (or #23430 #23457)
-#29776 := [hypothesis]: #23454
-#29777 := [hypothesis]: #23433
-#24555 := (or #23430 #12584)
-#24556 := [def-axiom]: #24555
-#29775 := [unit-resolution #24556 #29777]: #12584
-#29789 := (or #18565 #23469)
-#24657 := (or #23490 #23484)
-#24658 := [def-axiom]: #24657
-#29786 := [unit-resolution #24658 #30140]: #23484
-#27971 := (or #23472 #23487 #18559)
-#27967 := [hypothesis]: #12578
-#27968 := [hypothesis]: #23484
-#27930 := [hypothesis]: #23475
-#24627 := (or #23472 #12575)
-#24628 := [def-axiom]: #24627
-#27969 := [unit-resolution #24628 #27930]: #12575
-#24639 := (or #23478 #23472)
-#24640 := [def-axiom]: #24639
-#27964 := [unit-resolution #24640 #27930]: #23478
-#24649 := (or #23487 #18556 #18559 #23481)
-#24650 := [def-axiom]: #24649
-#27970 := [unit-resolution #24650 #27964 #27969 #27968 #27967]: false
-#27972 := [lemma #27970]: #27971
-#29787 := [unit-resolution #27972 #30142 #29786]: #23472
-#24633 := (or #23475 #18556 #18565 #23469)
-#24634 := [def-axiom]: #24633
-#29788 := [unit-resolution #24634 #29787]: #23472
-#29790 := [unit-resolution #29788 #29447]: #29789
-#29791 := [unit-resolution #29790 #29775]: #23469
-#24623 := (or #23466 #23460)
-#24624 := [def-axiom]: #24623
-#29792 := [unit-resolution #24624 #29791]: #23460
-#24565 := (or #23436 #23430)
-#24566 := [def-axiom]: #24565
-#29793 := [unit-resolution #24566 #29777]: #23436
-#29796 := (or #23445 #23439)
-#29794 := (or #23445 #18556 #23439)
-#24575 := (or #23445 #18556 #18559 #23439)
-#24576 := [def-axiom]: #24575
-#29795 := [unit-resolution #24576 #30142]: #29794
-#29797 := [unit-resolution #29795 #29447]: #29796
-#29798 := [unit-resolution #29797 #29793]: #23445
-#24583 := (or #23448 #23442)
-#24584 := [def-axiom]: #24583
-#29799 := [unit-resolution #24584 #29798]: #23448
-#24613 := (or #23463 #23451 #23457)
-#24614 := [def-axiom]: #24613
-#29800 := [unit-resolution #24614 #29799 #29792 #29776]: false
-#29802 := [lemma #29800]: #29801
-#30329 := [unit-resolution #29802 #30328 #30176]: false
-#30330 := [lemma #30329]: #23418
-#30607 := (or #23421 #23415)
-#15811 := (<= f296 4294967295::Int)
-#15814 := (iff #13441 #15811)
-#15805 := (+ 4294967295::Int #13442)
-#15808 := (>= #15805 0::Int)
-#15812 := (iff #15808 #15811)
-#15813 := [rewrite]: #15812
-#15809 := (iff #13441 #15808)
-#15806 := (= #13443 #15805)
-#15807 := [monotonicity #7642]: #15806
-#15810 := [monotonicity #15807]: #15809
-#15815 := [trans #15810 #15813]: #15814
-#14357 := [not-or-elim #14346]: #13446
-#14359 := [and-elim #14357]: #13441
-#15816 := [mp #14359 #15815]: #15811
-#29996 := [hypothesis]: #18597
-#29985 := [th-lemma arith farkas -1 -1 1 #30141 #29996 #15816]: false
-#29988 := [lemma #29985]: #15900
-#30605 := (or #23421 #18597 #23415)
-#30602 := (or #13656 #13534)
-#30603 := [th-lemma arith farkas 1 1]: #30602
-#30604 := [unit-resolution #30603 #29673]: #13534
-#24529 := (or #23421 #18594 #18597 #23415)
-#24530 := [def-axiom]: #24529
-#30606 := [unit-resolution #24530 #30604]: #30605
-#30608 := [unit-resolution #30606 #29988]: #30607
-#30609 := [unit-resolution #30608 #30330]: #23415
-#24519 := (or #23412 #23406)
-#24520 := [def-axiom]: #24519
-#30660 := [unit-resolution #24520 #30609]: #23406
-#24464 := (>= #13619 -1::Int)
-#24515 := (or #23412 #13618)
-#24516 := [def-axiom]: #24515
-#30610 := [unit-resolution #24516 #30609]: #13618
-#30611 := (or #13622 #24464)
-#30612 := [th-lemma arith triangle-eq]: #30611
-#30613 := [unit-resolution #30612 #30610]: #24464
-#29780 := (not #24464)
-#29781 := (or #29780 #13550)
-#29774 := [hypothesis]: #24464
-#29778 := [hypothesis]: #13555
-#29779 := [th-lemma arith farkas -1 1 1 #29778 #30141 #29774]: false
-#29782 := [lemma #29779]: #29781
-#30661 := [unit-resolution #29782 #30613]: #13550
-#24505 := (or #23409 #13555 #23403)
-#24506 := [def-axiom]: #24505
-#30662 := [unit-resolution #24506 #30661 #30660]: #23403
-#24497 := (or #23400 #23394)
-#24498 := [def-axiom]: #24497
-#30663 := [unit-resolution #24498 #30662]: #23394
-#24590 := (+ f308 #13592)
-#24592 := (>= #24590 0::Int)
-#24595 := (or #23454 #12842)
-#24596 := [def-axiom]: #24595
-#30664 := [unit-resolution #24596 #30651]: #12842
-#30665 := (or #12848 #24592)
-#30666 := [th-lemma arith triangle-eq]: #30665
-#30667 := [unit-resolution #30666 #30664]: #24592
-#30668 := (not #24592)
-#30671 := (or #13595 #30668)
-#30669 := (or #13595 #13979 #30668)
-#30670 := [th-lemma arith assign-bounds -1 -1]: #30669
-#30672 := [unit-resolution #30670 #30103]: #30671
-#30673 := [unit-resolution #30672 #30667]: #13595
-#30680 := (= #3153 #3299)
-#30678 := (= #3299 #3153)
-#30675 := (= #3298 #3152)
-#30674 := [symm #30664]: #3329
-#30676 := [monotonicity #30674]: #30675
-#30679 := [monotonicity #30676]: #30678
-#30681 := [symm #30679]: #30680
-#30682 := (= f315 #3153)
-#30677 := [symm #30653]: #3328
-#30683 := [trans #30677 #30101]: #30682
-#30684 := [trans #30683 #30681]: #12643
-#24469 := (or #22364 #22362 #13594)
-#24470 := [def-axiom]: #24469
-#30685 := [unit-resolution #24470 #30684 #30673]: #22364
-#24471 := (or #23388 #22363)
-#24472 := [def-axiom]: #24471
-#30686 := [unit-resolution #24472 #30685]: #23388
-#24493 := (or #23397 #23391 #22416)
-#24494 := [def-axiom]: #24493
-#30687 := [unit-resolution #24494 #30686 #30663]: #22416
-#24485 := (or #22411 #24484)
-#24486 := [def-axiom]: #24485
-#30688 := [unit-resolution #24486 #30687]: #24484
-#30632 := (not #24588)
-#30633 := (or #30631 #18943 #30632 #13707)
-#30626 := [hypothesis]: #13708
-#30627 := [hypothesis]: #24588
-#30628 := [hypothesis]: #24484
-#30629 := [hypothesis]: #30621
-#30630 := [th-lemma arith farkas 1 -1 -1 1 #30629 #30628 #30627 #30626]: false
-#30634 := [lemma #30630]: #30633
-#30689 := [unit-resolution #30634 #30688 #30656 #30652]: #30631
-#30625 := (or #30624 #30621)
-#30635 := [th-lemma arith triangle-eq]: #30625
-#30690 := [unit-resolution #30635 #30689]: #30624
-#30649 := (or #30648 #30591)
-#30644 := (= #18620 #3266)
-#30642 := (= #18619 #3257)
-#30640 := (= ?v0!14 f309)
-#30639 := [hypothesis]: #30595
-#30641 := [symm #30639]: #30640
-#30643 := [monotonicity #30641]: #30642
-#30645 := [monotonicity #30643]: #30644
-#30646 := [symm #30645]: #30591
-#30638 := [hypothesis]: #30624
-#30647 := [unit-resolution #30638 #30646]: false
-#30650 := [lemma #30647]: #30649
-#30691 := [unit-resolution #30650 #30690]: #30648
-#30705 := (or #30595 #30702)
-#30425 := (<= #30424 0::Int)
-#30436 := (+ f307 #18941)
-#30437 := (>= #30436 0::Int)
-#30692 := (not #30437)
-#30693 := (or #30692 #18943 #30632)
+#27835 := (+ f304 #19056)
+#27836 := (<= #27835 0::Int)
+#28008 := (not #27836)
+#28002 := [hypothesis]: #13781
+#24650 := (not #19058)
+#24651 := (or #22568 #24650)
+#24652 := [def-axiom]: #24651
+#28014 := [unit-resolution #24652 #28012]: #24650
+#28009 := (or #28008 #19058 #13782)
+#28003 := [hypothesis]: #27836
+#28006 := [hypothesis]: #24650
+#28007 := [th-lemma arith farkas -1 1 1 #28006 #28003 #28002]: false
+#28010 := [lemma #28007]: #28009
+#28015 := [unit-resolution #28010 #28014 #28002]: #28008
+#28019 := (or #27836 #27848)
+#24648 := (or #22568 #18720)
+#24649 := [def-axiom]: #24648
+#28016 := [unit-resolution #24649 #28012]: #18720
+#24646 := (or #22568 #18719)
+#24647 := [def-axiom]: #24646
+#28017 := [unit-resolution #24647 #28012]: #18719
+#27861 := (or #23356 #22552 #22553 #27836 #27848)
+#27824 := (+ #18724 #13986)
+#27825 := (<= #27824 0::Int)
+#27826 := (+ ?v0!15 #13517)
+#27827 := (>= #27826 0::Int)
+#27828 := (or #22553 #27827 #27825 #22552)
+#27862 := (or #23356 #27828)
+#27869 := (iff #27862 #27861)
+#27856 := (or #22552 #22553 #27836 #27848)
+#27864 := (or #23356 #27856)
+#27867 := (iff #27864 #27861)
+#27868 := [rewrite]: #27867
+#27865 := (iff #27862 #27864)
+#27859 := (iff #27828 #27856)
+#27853 := (or #22553 #27836 #27848 #22552)
+#27857 := (iff #27853 #27856)
+#27858 := [rewrite]: #27857
+#27854 := (iff #27828 #27853)
+#27851 := (iff #27825 #27848)
+#27841 := (+ #13986 #18724)
+#27844 := (<= #27841 0::Int)
+#27849 := (iff #27844 #27848)
+#27850 := [rewrite]: #27849
+#27845 := (iff #27825 #27844)
+#27842 := (= #27824 #27841)
+#27843 := [rewrite]: #27842
+#27846 := [monotonicity #27843]: #27845
+#27852 := [trans #27846 #27850]: #27851
+#27839 := (iff #27827 #27836)
+#27829 := (+ #13517 ?v0!15)
+#27832 := (>= #27829 0::Int)
+#27837 := (iff #27832 #27836)
+#27838 := [rewrite]: #27837
+#27833 := (iff #27827 #27832)
+#27830 := (= #27826 #27829)
+#27831 := [rewrite]: #27830
+#27834 := [monotonicity #27831]: #27833
+#27840 := [trans #27834 #27838]: #27839
+#27855 := [monotonicity #27840 #27852]: #27854
+#27860 := [trans #27855 #27858]: #27859
+#27866 := [monotonicity #27860]: #27865
+#27870 := [trans #27866 #27868]: #27869
+#27863 := [quant-inst #18718]: #27862
+#27871 := [mp #27863 #27870]: #27861
+#28020 := [unit-resolution #27871 #28018 #28017 #28016]: #28019
+#28021 := [unit-resolution #28020 #28015]: #27848
+#28022 := [th-lemma arith farkas -1 1 1 #28021 #28013 #28011]: false
+#28025 := [lemma #28022]: #28024
+#28116 := [unit-resolution #28025 #28115 #28018 #28112]: #22568
+#24662 := (or #23500 #23494 #22573)
+#24663 := [def-axiom]: #24662
+#28117 := [unit-resolution #24663 #28116 #28111]: #23494
+#24642 := (or #23491 #23483)
+#24643 := [def-axiom]: #24642
+#28118 := [unit-resolution #24643 #28117]: #23483
+#28031 := (or #23488 #27670 #27953 #27974 #27995)
+#27958 := (+ #27588 #13422)
+#27959 := (>= #27958 0::Int)
+#27966 := (= #27968 f308)
+#27969 := (not #27966)
+#27970 := (or #27969 #27670 #27959 #27953)
+#28032 := (or #23488 #27970)
+#28039 := (iff #28032 #28031)
+#28026 := (or #27670 #27953 #27974 #27995)
+#28034 := (or #23488 #28026)
+#28037 := (iff #28034 #28031)
+#28038 := [rewrite]: #28037
+#28035 := (iff #28032 #28034)
+#28029 := (iff #27970 #28026)
+#27975 := (or #27974 #27670 #27995 #27953)
+#28027 := (iff #27975 #28026)
+#28028 := [rewrite]: #28027
+#27976 := (iff #27970 #27975)
+#28005 := (iff #27959 #27995)
+#27989 := (+ #13422 #27588)
+#27986 := (>= #27989 0::Int)
+#27996 := (iff #27986 #27995)
+#28004 := [rewrite]: #27996
+#27992 := (iff #27959 #27986)
+#27990 := (= #27958 #27989)
+#27991 := [rewrite]: #27990
+#27993 := [monotonicity #27991]: #27992
+#27907 := [trans #27993 #28004]: #28005
+#27987 := (iff #27969 #27974)
+#27972 := (iff #27966 #27971)
+#27973 := [rewrite]: #27972
+#27988 := [monotonicity #27973]: #27987
+#27999 := [monotonicity #27988 #27907]: #27976
+#28030 := [trans #27999 #28028]: #28029
+#28036 := [monotonicity #28030]: #28035
+#28040 := [trans #28036 #28038]: #28039
+#28033 := [quant-inst #27588]: #28032
+#28041 := [mp #28033 #28040]: #28031
+#28120 := [unit-resolution #28041 #28118 #28110]: #28119
+#28121 := [unit-resolution #28120 #28109 #28104 #28095]: false
+#28123 := [lemma #28121]: #28122
+#30118 := [unit-resolution #28123 #30117 #30082 #30081 #30080 #30074]: #23503
+#24686 := (or #23512 #23472 #23506)
+#24687 := [def-axiom]: #24686
+#30119 := [unit-resolution #24687 #30118 #30079]: #23472
+#24634 := (or #23469 #13782)
+#24635 := [def-axiom]: #24634
+#30120 := [unit-resolution #24635 #30119]: #13782
+#30221 := (not #29564)
+#30222 := (or #30220 #28395 #30221 #13781)
+#30223 := [th-lemma arith assign-bounds 1 -1 -1]: #30222
+#30224 := [unit-resolution #30223 #28389 #30120 #30216]: #30220
+#29444 := (>= #29347 0::Int)
+#24712 := (or #23515 #13496)
+#24713 := [def-axiom]: #24712
+#29652 := [unit-resolution #24713 #29651]: #13496
+#29563 := (<= #29562 0::Int)
+#29655 := (or #29654 #29563)
+#29656 := [th-lemma arith triangle-eq]: #29655
+#29657 := [unit-resolution #29656 #29653]: #29563
+#29445 := (not #29444)
+#29658 := [hypothesis]: #29445
+#29659 := [th-lemma arith farkas 1 1 1 #29658 #29657 #29652]: false
+#29660 := [lemma #29659]: #29444
+#30226 := (or #29445 #29455 #29463)
+#29474 := (or #28618 #27142 #29445 #29455 #29463)
+#29440 := (or #29439 #29436 #29434 #29430)
+#29441 := (not #29440)
+#29442 := (+ #29347 #27143)
+#29443 := (>= #29442 0::Int)
+#29446 := (or #29445 #29443 #27142 #29441)
+#29475 := (or #28618 #29446)
+#29482 := (iff #29475 #29474)
+#29469 := (or #27142 #29445 #29455 #29463)
+#29477 := (or #28618 #29469)
+#29480 := (iff #29477 #29474)
+#29481 := [rewrite]: #29480
+#29478 := (iff #29475 #29477)
+#29472 := (iff #29446 #29469)
+#29466 := (or #29445 #29455 #27142 #29463)
+#29470 := (iff #29466 #29469)
+#29471 := [rewrite]: #29470
+#29467 := (iff #29446 #29466)
+#29464 := (iff #29441 #29463)
+#29461 := (iff #29440 #29460)
+#29462 := [rewrite]: #29461
+#29465 := [monotonicity #29462]: #29464
+#29458 := (iff #29443 #29455)
+#29447 := (+ #27143 #29347)
+#29450 := (>= #29447 0::Int)
+#29456 := (iff #29450 #29455)
+#29457 := [rewrite]: #29456
+#29451 := (iff #29443 #29450)
+#29448 := (= #29442 #29447)
+#29449 := [rewrite]: #29448
+#29452 := [monotonicity #29449]: #29451
+#29459 := [trans #29452 #29457]: #29458
+#29468 := [monotonicity #29459 #29465]: #29467
+#29473 := [trans #29468 #29471]: #29472
+#29479 := [monotonicity #29473]: #29478
+#29483 := [trans #29479 #29481]: #29482
+#29476 := [quant-inst #3032 #3036 #24975 #24977 #29347]: #29475
+#29484 := [mp #29476 #29483]: #29474
+#30227 := [unit-resolution #29484 #21004 #28852]: #30226
+#30228 := [unit-resolution #30227 #29660 #30224]: #29463
+#29492 := (or #29460 #29438)
+#29493 := [def-axiom]: #29492
+#30229 := [unit-resolution #29493 #30228]: #29438
+#30260 := [symm #30229]: #30259
+#30257 := (= #28473 #29437)
+#30255 := (= #27813 #29431)
+#30253 := (= #29431 #27813)
+#30251 := (= #29410 #3250)
+#28067 := (f117 #3250)
+#28178 := (f44 #24975 #28067)
+#30245 := (= #28178 #3250)
+#28179 := (= #3250 #28178)
+#28184 := (f49 #3250 #24975)
+#28185 := (= f1 #28184)
+#30231 := (= #3251 #28184)
+#29397 := (= #28184 #3251)
+#29398 := [monotonicity #28365]: #29397
+#30232 := [symm #29398]: #30231
+#28182 := (= #24975 #28181)
+#28161 := (* f304 #27047)
+#29319 := (+ #27049 #28161)
+#29320 := (f44 #24975 #29319)
+#29350 := (f14 #29320)
+#29422 := (= #29350 #28181)
+#29418 := (= #28181 #29350)
+#29416 := (= #3250 #29320)
+#29315 := (f67 #24812 f304 #24975)
+#29321 := (= #29315 #29320)
+#29322 := (not #29321)
+#29316 := (f139 #29315 #24812)
+#29317 := (= f1 #29316)
+#29318 := (not #29317)
+#29325 := (or #29318 #29322)
+#29328 := (not #29325)
+#29331 := (or #27700 #29328)
+#29323 := (or #29322 #29318)
+#29324 := (not #29323)
+#29332 := (or #27700 #29324)
+#29334 := (iff #29332 #29331)
+#29336 := (iff #29331 #29331)
+#29337 := [rewrite]: #29336
+#29329 := (iff #29324 #29328)
+#29326 := (iff #29323 #29325)
+#29327 := [rewrite]: #29326
+#29330 := [monotonicity #29327]: #29329
+#29335 := [monotonicity #29330]: #29334
+#29338 := [trans #29335 #29337]: #29334
+#29333 := [quant-inst #24812 #3132 #24975]: #29332
+#29339 := [mp #29333 #29338]: #29331
+#29408 := [unit-resolution #29339 #21220]: #29328
+#29342 := (or #29325 #29321)
+#29343 := [def-axiom]: #29342
+#29409 := [unit-resolution #29343 #29408]: #29321
+#29414 := (= #3250 #29315)
+#29412 := (= #29315 #3250)
+#29413 := [monotonicity #27121 #28365]: #29412
+#29415 := [symm #29413]: #29414
+#29417 := [trans #29415 #29409]: #29416
+#29419 := [monotonicity #29417]: #29418
+#29423 := [symm #29419]: #29422
+#29353 := (= #24975 #29350)
+#29358 := (or #25043 #29353)
+#29359 := [quant-inst #24975 #29319]: #29358
+#29407 := [unit-resolution #29359 #23256]: #29353
+#29424 := [trans #29407 #29423]: #28182
+#29299 := (not #28182)
+#28259 := (iff #28182 #28185)
+#29294 := (or #26189 #28259)
+#29295 := [quant-inst #3250 #24975]: #29294
+#29395 := [unit-resolution #29295 #23243]: #28259
+#28177 := (not #28185)
+#29403 := (iff #18536 #28177)
+#29401 := (iff #12555 #28185)
+#29399 := (iff #28185 #12555)
+#29400 := [monotonicity #29398]: #29399
+#29402 := [symm #29400]: #29401
+#29404 := [monotonicity #29402]: #29403
+#29396 := [hypothesis]: #18536
+#29405 := [mp #29396 #29404]: #28177
+#29296 := (not #28259)
+#29300 := (or #29296 #29299 #28185)
+#29301 := [def-axiom]: #29300
+#29406 := [unit-resolution #29301 #29405 #29395]: #29299
+#29425 := [unit-resolution #29406 #29424]: false
+#29426 := [lemma #29425]: #12555
+#30233 := [trans #29426 #30232]: #28185
+#28180 := (or #28179 #28177)
+#29355 := (or #26173 #28179 #28177)
+#29367 := (or #26173 #28180)
+#29366 := (iff #29367 #29355)
+#29369 := [rewrite]: #29366
+#29368 := [quant-inst #3250 #24975]: #29367
+#29370 := [mp #29368 #29369]: #29355
+#30234 := [unit-resolution #29370 #18239]: #28180
+#30235 := [unit-resolution #30234 #30233]: #28179
+#30246 := [symm #30235]: #30245
+#30249 := (= #29410 #28178)
+#29627 := (* #27047 #29347)
+#29630 := (+ #27297 #29627)
+#29633 := (f44 #24975 #29630)
+#30243 := (= #29633 #28178)
+#30237 := (= #29630 #28067)
+#30208 := (= #28067 #29630)
+#30209 := (* -1::Int #29630)
+#30210 := (+ #28067 #30209)
+#30211 := (<= #30210 0::Int)
+#29185 := (* -1::Int #27049)
+#29186 := (+ #24859 #29185)
+#29188 := (>= #29186 0::Int)
+#29184 := (= #24859 #27049)
+#30010 := (= #3036 #27049)
+#29965 := [symm #27254]: #30010
+#29966 := [trans #28864 #29965]: #29184
+#30011 := (not #29184)
+#29979 := (or #30011 #29188)
+#29976 := [th-lemma arith triangle-eq]: #29979
+#29963 := [unit-resolution #29976 #29966]: #29188
+#29679 := (* -1::Int #27297)
+#29680 := (+ #24859 #29679)
+#29681 := (<= #29680 0::Int)
+#29678 := (= #24859 #27297)
+#29968 := [symm #28862]: #29678
+#29969 := (not #29678)
+#29970 := (or #29969 #29681)
+#29971 := [th-lemma arith triangle-eq]: #29970
+#29972 := [unit-resolution #29971 #29968]: #29681
+#29356 := (f117 #29320)
+#29360 := (* -1::Int #29356)
+#29566 := (+ #28067 #29360)
+#29567 := (<= #29566 0::Int)
+#29565 := (= #28067 #29356)
+#30022 := (= #29356 #28067)
+#30014 := (= #29320 #3250)
+#30005 := (= #29320 #29315)
+#30013 := [symm #29409]: #30005
+#30021 := [trans #30013 #29413]: #30014
+#30020 := [monotonicity #30021]: #30022
+#30012 := [symm #30020]: #29565
+#30023 := (not #29565)
+#30024 := (or #30023 #29567)
+#30025 := [th-lemma arith triangle-eq]: #30024
+#30028 := [unit-resolution #30025 #30012]: #29567
+#29361 := (+ #28161 #29360)
+#29362 := (+ #27049 #29361)
+#29550 := (>= #29362 0::Int)
+#29363 := (= #29362 0::Int)
+#29538 := (or #25049 #29363)
+#29357 := (= #29319 #29356)
+#29539 := (or #25049 #29357)
+#29543 := (iff #29539 #29538)
+#29545 := (iff #29538 #29538)
+#29546 := [rewrite]: #29545
+#29364 := (iff #29357 #29363)
+#29365 := [rewrite]: #29364
+#29544 := [monotonicity #29365]: #29543
+#29547 := [trans #29544 #29546]: #29543
+#29542 := [quant-inst #24975 #29319]: #29539
+#29548 := [mp #29542 #29547]: #29538
+#30029 := [unit-resolution #29548 #23250]: #29363
+#30034 := (not #29363)
+#30037 := (or #30034 #29550)
+#30036 := [th-lemma arith triangle-eq]: #30037
+#30038 := [unit-resolution #30036 #30029]: #29550
+#29191 := (>= #27047 1::Int)
+#29189 := (= #27047 1::Int)
+#2964 := (f140 f9)
+#2965 := (= #2964 1::Int)
+#12004 := [asserted]: #2965
+#30039 := (= #27047 #2964)
+#30059 := [monotonicity #28365]: #30039
+#30060 := [trans #30059 #12004]: #29189
+#30061 := (not #29189)
+#30077 := (or #30061 #29191)
+#30078 := [th-lemma arith triangle-eq]: #30077
+#30035 := [unit-resolution #30078 #30060]: #29191
+#29190 := (<= #27047 1::Int)
+#30124 := (or #30061 #29190)
+#30125 := [th-lemma arith triangle-eq]: #30124
+#30126 := [unit-resolution #30125 #30060]: #29190
+#30007 := (not #29563)
+#30006 := (not #29681)
+#29978 := (not #29190)
+#29733 := (not #29191)
+#29977 := (not #29188)
+#29974 := (not #29550)
+#29973 := (not #29567)
+#30008 := (or #30211 #29973 #29974 #29977 #29733 #29978 #29733 #29978 #30006 #30007)
+#30009 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30008
+#30004 := [unit-resolution #30009 #30126 #30035 #30038 #29657 #30028 #29972 #29963]: #30211
+#30212 := (>= #30210 0::Int)
+#29187 := (<= #29186 0::Int)
+#30131 := (or #30011 #29187)
+#30132 := [th-lemma arith triangle-eq]: #30131
+#30133 := [unit-resolution #30132 #29966]: #29187
+#29682 := (>= #29680 0::Int)
+#30134 := (or #29969 #29682)
+#30135 := [th-lemma arith triangle-eq]: #30134
+#30136 := [unit-resolution #30135 #29968]: #29682
+#29568 := (>= #29566 0::Int)
+#30129 := (or #30023 #29568)
+#30130 := [th-lemma arith triangle-eq]: #30129
+#30127 := [unit-resolution #30130 #30012]: #29568
+#29549 := (<= #29362 0::Int)
+#30128 := (or #30034 #29549)
+#30137 := [th-lemma arith triangle-eq]: #30128
+#30138 := [unit-resolution #30137 #30029]: #29549
+#30141 := (not #29682)
+#30140 := (not #29187)
+#29763 := (not #29549)
+#30139 := (not #29568)
+#30142 := (or #30212 #30139 #29763 #30140 #29733 #29978 #29733 #29978 #30141 #30221)
+#30143 := [th-lemma arith assign-bounds -1 1 1 -1 -1 1 1 -1 -1]: #30142
+#30144 := [unit-resolution #30143 #30126 #30035 #30138 #30216 #30127 #30136 #30133]: #30212
+#30148 := (not #30212)
+#30147 := (not #30211)
+#30157 := (or #30208 #30147 #30148)
+#30158 := [th-lemma arith triangle-eq]: #30157
+#30159 := [unit-resolution #30158 #30144 #30004]: #30208
+#30156 := [symm #30159]: #30237
+#30165 := [monotonicity #30156]: #30243
+#30247 := (= #29410 #29633)
+#29616 := (f67 #26161 #29347 #24975)
+#29636 := (= #29616 #29633)
+#29571 := (not #29636)
+#29617 := (f139 #29616 #26161)
+#29618 := (= f1 #29617)
+#29619 := (not #29618)
+#29576 := (or #29619 #29571)
+#29639 := (not #29576)
+#29663 := (or #27700 #29639)
+#29620 := (* #29347 #27047)
+#29621 := (+ #27297 #29620)
+#29622 := (f44 #24975 #29621)
+#29623 := (= #29616 #29622)
+#29624 := (not #29623)
+#29625 := (or #29624 #29619)
+#29626 := (not #29625)
+#29664 := (or #27700 #29626)
+#29666 := (iff #29664 #29663)
+#29668 := (iff #29663 #29663)
+#29669 := [rewrite]: #29668
+#29661 := (iff #29626 #29639)
+#29640 := (iff #29625 #29576)
+#29573 := (or #29571 #29619)
+#29577 := (iff #29573 #29576)
+#29578 := [rewrite]: #29577
+#29574 := (iff #29625 #29573)
+#29572 := (iff #29624 #29571)
+#29637 := (iff #29623 #29636)
+#29634 := (= #29622 #29633)
+#29631 := (= #29621 #29630)
+#29628 := (= #29620 #29627)
+#29629 := [rewrite]: #29628
+#29632 := [monotonicity #29629]: #29631
+#29635 := [monotonicity #29632]: #29634
+#29638 := [monotonicity #29635]: #29637
+#29570 := [monotonicity #29638]: #29572
+#29575 := [monotonicity #29570]: #29574
+#29641 := [trans #29575 #29578]: #29640
+#29662 := [monotonicity #29641]: #29661
+#29667 := [monotonicity #29662]: #29666
+#29670 := [trans #29667 #29669]: #29666
+#29665 := [quant-inst #26161 #29347 #24975]: #29664
+#29671 := [mp #29665 #29670]: #29663
+#30239 := [unit-resolution #29671 #21220]: #29639
+#29674 := (or #29576 #29636)
+#29675 := [def-axiom]: #29674
+#30240 := [unit-resolution #29675 #30239]: #29636
+#30241 := (= #29410 #29616)
+#30242 := [monotonicity #28770]: #30241
+#30248 := [trans #30242 #30240]: #30247
+#30166 := [trans #30248 #30165]: #30249
+#30167 := [trans #30166 #30246]: #30251
+#30168 := [monotonicity #30167]: #30253
+#30169 := [symm #30168]: #30255
+#30164 := [monotonicity #30169]: #30257
+#30170 := [trans #30164 #30260]: #30261
+#30171 := [trans #30170 #28768]: #30263
+#30173 := [monotonicity #30171]: #30172
+#30179 := [symm #30173]: #30178
+#30177 := [trans #14346 #30179]: #28477
+#29926 := (not #28477)
+#29927 := (or #28533 #29926)
+#29913 := [def-axiom]: #29927
+#30180 := [unit-resolution #29913 #30177]: #28533
+#30189 := (= #25480 #28491)
+#30191 := (= #28491 #25480)
+#30184 := (= #28181 f9)
+#30182 := (= #28181 #24975)
+#29371 := (or #29296 #28182 #28177)
+#29372 := [def-axiom]: #29371
+#30181 := [unit-resolution #29372 #30233 #29395]: #28182
+#30183 := [symm #30181]: #30182
+#30190 := [trans #30183 #28365]: #30184
+#30192 := [monotonicity #30190]: #30191
+#30195 := [symm #30192]: #30189
+#30196 := [trans #28820 #30195]: #28509
+#29869 := (not #28482)
+#30218 := (iff #12098 #29869)
+#30230 := (iff #12095 #28482)
+#30203 := (iff #28482 #12095)
+#30201 := (= #28481 #3046)
+#30199 := (= #28480 #3033)
+#30197 := (= #28480 #25096)
+#30198 := [monotonicity #30171]: #30197
+#30200 := [trans #30198 #28830]: #30199
+#30202 := [monotonicity #30200]: #30201
+#30267 := [monotonicity #30202]: #30203
+#30225 := [symm #30267]: #30230
+#30219 := [monotonicity #30225]: #30218
+#30217 := [mp #14349 #30219]: #29869
+#29496 := (f67 #27202 #29347 #24975)
+#29497 := (f59 #3213 #29496)
+#29498 := (f137 #29497)
+#29499 := (= f1 #29498)
+#29531 := (not #29499)
+#30294 := (iff #29531 #28488)
+#30292 := (iff #29499 #28487)
+#30290 := (iff #28487 #29499)
+#30288 := (= #28486 #29498)
+#30286 := (= #27813 #29497)
+#30284 := (= #29497 #27813)
+#30282 := (= #29496 #3250)
+#30280 := (= #29347 f304)
+#30281 := [symm #29653]: #30280
+#30283 := [monotonicity #28372 #30281 #28365]: #30282
+#30285 := [monotonicity #30283]: #30284
+#30287 := [symm #30285]: #30286
+#30289 := [monotonicity #30287]: #30288
+#30291 := [monotonicity #30289]: #30290
+#30293 := [symm #30291]: #30292
+#30295 := [monotonicity #30293]: #30294
+#29500 := (f25 f292 #29496)
+#29501 := (= f1 #29500)
+#29502 := (not #29501)
+#29506 := (or #29499 #29502)
+#29509 := (not #29506)
+#30276 := (or #29445 #29455 #29509)
+#29520 := (or #27233 #24825 #27214 #27217 #29445 #29455 #29509)
+#29503 := (or #29502 #29499)
+#29504 := (not #29503)
+#29505 := (or #27217 #29445 #29443 #24825 #27214 #29504)
+#29521 := (or #27233 #29505)
+#29528 := (iff #29521 #29520)
+#29515 := (or #24825 #27214 #27217 #29445 #29455 #29509)
+#29523 := (or #27233 #29515)
+#29526 := (iff #29523 #29520)
+#29527 := [rewrite]: #29526
+#29524 := (iff #29521 #29523)
+#29518 := (iff #29505 #29515)
+#29512 := (or #27217 #29445 #29455 #24825 #27214 #29509)
+#29516 := (iff #29512 #29515)
+#29517 := [rewrite]: #29516
+#29513 := (iff #29505 #29512)
+#29510 := (iff #29504 #29509)
+#29507 := (iff #29503 #29506)
+#29508 := [rewrite]: #29507
+#29511 := [monotonicity #29508]: #29510
+#29514 := [monotonicity #29459 #29511]: #29513
+#29519 := [trans #29514 #29517]: #29518
+#29525 := [monotonicity #29519]: #29524
+#29529 := [trans #29525 #29527]: #29528
+#29522 := [quant-inst #3032 #3036 #26161 #24977 #29347 #24975]: #29521
+#29530 := [mp #29522 #29529]: #29520
+#30277 := [unit-resolution #29530 #21664 #14331 #28776 #28405]: #30276
+#30278 := [unit-resolution #30277 #29660 #30224]: #29509
+#29532 := (or #29506 #29531)
+#29533 := [def-axiom]: #29532
+#30279 := [unit-resolution #29533 #30278]: #29531
+#30296 := [mp #30279 #30295]: #28488
+#29751 := (or #28527 #28487)
+#29752 := [def-axiom]: #29751
+#30297 := [unit-resolution #29752 #30296]: #28527
+#29886 := (or #28547 #28482 #28524 #28530 #28536)
+#29944 := [def-axiom]: #29886
+#30298 := [unit-resolution #29944 #30297 #30217 #30196 #30180 #30146]: false
+#30299 := [lemma #30298]: #28547
+#29784 := (or #28550 #28542)
+#29717 := [def-axiom]: #29784
+#30154 := [unit-resolution #29717 #30299]: #28550
+#28411 := (or #12558 #13636 #27214 #13781)
+#28354 := [hypothesis]: #13496
+#28189 := (f67 #27065 f304 #27586)
+#28190 := (f126 #28189 #27065)
+#28221 := (* -1::Int #28190)
+#28349 := (+ f304 #28221)
+#28350 := (<= #28349 0::Int)
+#28191 := (= f304 #28190)
+#28194 := (or #27108 #28191)
+#28195 := [quant-inst #27065 #3132]: #28194
+#28355 := [unit-resolution #28195 #17062]: #28191
+#28358 := (not #28191)
+#28359 := (or #28358 #28350)
+#28360 := [th-lemma arith triangle-eq]: #28359
+#28361 := [unit-resolution #28360 #28355]: #28350
+#28212 := (>= #28190 0::Int)
+#28213 := (not #28212)
+#28264 := (f67 #27202 #28190 #24975)
+#28268 := (f25 f292 #28264)
+#28269 := (= f1 #28268)
+#28270 := (not #28269)
+#28265 := (f59 #3213 #28264)
+#28266 := (f137 #28265)
+#28267 := (= f1 #28266)
+#28274 := (or #28267 #28270)
+#28381 := (iff #18539 #28270)
+#28379 := (iff #12558 #28269)
+#28377 := (iff #28269 #12558)
+#28375 := (= #28268 #3253)
+#28373 := (= #28264 #3250)
+#28366 := (= #28190 f304)
+#28367 := [symm #28355]: #28366
+#28374 := [monotonicity #28372 #28367 #28365]: #28373
+#28376 := [monotonicity #28374]: #28375
+#28378 := [monotonicity #28376]: #28377
+#28380 := [symm #28378]: #28379
+#28382 := [monotonicity #28380]: #28381
+#28362 := [hypothesis]: #18539
+#28383 := [mp #28362 #28382]: #28270
+#28302 := (or #28274 #28269)
+#28303 := [def-axiom]: #28302
+#28384 := [unit-resolution #28303 #28383]: #28274
+#28222 := (+ #24977 #28221)
+#28223 := (<= #28222 0::Int)
+#28394 := (not #28223)
+#28390 := [hypothesis]: #13782
+#28351 := (>= #28349 0::Int)
+#28391 := (or #28358 #28351)
+#28392 := [th-lemma arith triangle-eq]: #28391
+#28393 := [unit-resolution #28392 #28355]: #28351
+#28396 := (not #28351)
+#28397 := (or #28394 #28395 #28396 #13781)
+#28398 := [th-lemma arith assign-bounds 1 -1 -1]: #28397
+#28399 := [unit-resolution #28398 #28393 #28390 #28389]: #28394
+#28277 := (not #28274)
+#28407 := (or #28213 #28223 #28277)
+#28288 := (or #27233 #24825 #27214 #27217 #28213 #28223 #28277)
+#28271 := (or #28270 #28267)
+#28272 := (not #28271)
+#28210 := (+ #28190 #27143)
+#28211 := (>= #28210 0::Int)
+#28273 := (or #27217 #28213 #28211 #24825 #27214 #28272)
+#28289 := (or #27233 #28273)
+#28296 := (iff #28289 #28288)
+#28283 := (or #24825 #27214 #27217 #28213 #28223 #28277)
+#28291 := (or #27233 #28283)
+#28294 := (iff #28291 #28288)
+#28295 := [rewrite]: #28294
+#28292 := (iff #28289 #28291)
+#28286 := (iff #28273 #28283)
+#28280 := (or #27217 #28213 #28223 #24825 #27214 #28277)
+#28284 := (iff #28280 #28283)
+#28285 := [rewrite]: #28284
+#28281 := (iff #28273 #28280)
+#28278 := (iff #28272 #28277)
+#28275 := (iff #28271 #28274)
+#28276 := [rewrite]: #28275
+#28279 := [monotonicity #28276]: #28278
+#28226 := (iff #28211 #28223)
+#28215 := (+ #27143 #28190)
+#28218 := (>= #28215 0::Int)
+#28224 := (iff #28218 #28223)
+#28225 := [rewrite]: #28224
+#28219 := (iff #28211 #28218)
+#28216 := (= #28210 #28215)
+#28217 := [rewrite]: #28216
+#28220 := [monotonicity #28217]: #28219
+#28227 := [trans #28220 #28225]: #28226
+#28282 := [monotonicity #28227 #28279]: #28281
+#28287 := [trans #28282 #28285]: #28286
+#28293 := [monotonicity #28287]: #28292
+#28297 := [trans #28293 #28295]: #28296
+#28290 := [quant-inst #3032 #3036 #26161 #24977 #28190 #24975]: #28289
+#28298 := [mp #28290 #28297]: #28288
+#28408 := [unit-resolution #28298 #21664 #14331 #28406 #28405]: #28407
+#28409 := [unit-resolution #28408 #28399 #28384]: #28213
+#28410 := [th-lemma arith farkas 1 1 1 #28409 #28361 #28354]: false
+#28412 := [lemma #28410]: #28411
+#30121 := [unit-resolution #28412 #30120 #28776 #29652]: #12558
+#30149 := (or #28559 #18539 #28553)
+#30150 := [def-axiom]: #30149
+#30300 := [unit-resolution #30150 #30121 #30154]: #28559
+#29879 := (or #29878 #12564 #28556)
+#29877 := [def-axiom]: #29879
+#30302 := [unit-resolution #29877 #30300]: #30301
+#30303 := [unit-resolution #30302 #30194]: #12564
+#30403 := (+ f304 #18908)
+#30599 := (>= #30403 0::Int)
+#30681 := (not #30599)
+#30574 := (= f304 ?v0!14)
+#30627 := (not #30574)
+#30630 := [hypothesis]: #23436
+#24582 := (or #23433 #13688)
+#24583 := [def-axiom]: #24582
+#30631 := [unit-resolution #24583 #30630]: #13688
+#24566 := (+ f302 #13550)
+#24567 := (<= #24566 0::Int)
+#24572 := (or #23433 #12819)
+#24573 := [def-axiom]: #24572
+#30632 := [unit-resolution #24573 #30630]: #12819
+#30633 := (or #12837 #24567)
+#30634 := [th-lemma arith triangle-eq]: #30633
+#30635 := [unit-resolution #30634 #30632]: #24567
+#24463 := (not #18923)
+#30174 := [hypothesis]: #23400
+#24584 := (or #23433 #23397)
+#24585 := [def-axiom]: #24584
+#30155 := [unit-resolution #24585 #30174]: #23433
+#24528 := (or #23403 #23397)
+#24529 := [def-axiom]: #24528
+#30304 := [unit-resolution #24529 #30174]: #23403
+#30305 := (or #23412 #18545 #23406)
+#24538 := (or #23412 #18536 #18545 #23406)
+#24539 := [def-axiom]: #24538
+#30306 := [unit-resolution #24539 #29426]: #30305
+#30307 := [unit-resolution #30306 #30304 #30303]: #23412
+#29780 := (or #23409 #23436)
+#29755 := [hypothesis]: #23433
+#29756 := [hypothesis]: #23412
+#24534 := (or #23409 #12564)
+#24535 := [def-axiom]: #24534
+#29754 := [unit-resolution #24535 #29756]: #12564
+#29768 := (or #18545 #23448)
+#24636 := (or #23469 #23463)
+#24637 := [def-axiom]: #24636
+#29765 := [unit-resolution #24637 #30119]: #23463
+#27950 := (or #23451 #23466 #18539)
+#27946 := [hypothesis]: #12558
+#27947 := [hypothesis]: #23463
+#27909 := [hypothesis]: #23454
+#24606 := (or #23451 #12555)
+#24607 := [def-axiom]: #24606
+#27948 := [unit-resolution #24607 #27909]: #12555
+#24618 := (or #23457 #23451)
+#24619 := [def-axiom]: #24618
+#27943 := [unit-resolution #24619 #27909]: #23457
+#24628 := (or #23466 #18536 #18539 #23460)
+#24629 := [def-axiom]: #24628
+#27949 := [unit-resolution #24629 #27943 #27948 #27947 #27946]: false
+#27951 := [lemma #27949]: #27950
+#29766 := [unit-resolution #27951 #30121 #29765]: #23451
+#24612 := (or #23454 #18536 #18545 #23448)
+#24613 := [def-axiom]: #24612
+#29767 := [unit-resolution #24613 #29766]: #23451
+#29769 := [unit-resolution #29767 #29426]: #29768
+#29770 := [unit-resolution #29769 #29754]: #23448
+#24602 := (or #23445 #23439)
+#24603 := [def-axiom]: #24602
+#29771 := [unit-resolution #24603 #29770]: #23439
+#24544 := (or #23415 #23409)
+#24545 := [def-axiom]: #24544
+#29772 := [unit-resolution #24545 #29756]: #23415
+#29775 := (or #23424 #23418)
+#29773 := (or #23424 #18536 #23418)
+#24554 := (or #23424 #18536 #18539 #23418)
+#24555 := [def-axiom]: #24554
+#29774 := [unit-resolution #24555 #30121]: #29773
+#29776 := [unit-resolution #29774 #29426]: #29775
+#29777 := [unit-resolution #29776 #29772]: #23424
+#24562 := (or #23427 #23421)
+#24563 := [def-axiom]: #24562
+#29778 := [unit-resolution #24563 #29777]: #23427
+#24592 := (or #23442 #23430 #23436)
+#24593 := [def-axiom]: #24592
+#29779 := [unit-resolution #24593 #29778 #29771 #29755]: false
+#29781 := [lemma #29779]: #29780
+#30308 := [unit-resolution #29781 #30307 #30155]: false
+#30309 := [lemma #30308]: #23397
+#30586 := (or #23400 #23394)
+#15791 := (<= f291 4294967295::Int)
+#15794 := (iff #13421 #15791)
+#15785 := (+ 4294967295::Int #13422)
+#15788 := (>= #15785 0::Int)
+#15792 := (iff #15788 #15791)
+#15793 := [rewrite]: #15792
+#15789 := (iff #13421 #15788)
+#15786 := (= #13423 #15785)
+#15787 := [monotonicity #7589]: #15786
+#15790 := [monotonicity #15787]: #15789
+#15795 := [trans #15790 #15793]: #15794
+#14337 := [not-or-elim #14326]: #13426
+#14339 := [and-elim #14337]: #13421
+#15796 := [mp #14339 #15795]: #15791
+#29975 := [hypothesis]: #18577
+#29964 := [th-lemma arith farkas -1 -1 1 #30120 #29975 #15796]: false
+#29967 := [lemma #29964]: #15880
+#30584 := (or #23400 #18577 #23394)
+#30581 := (or #13636 #13514)
+#30582 := [th-lemma arith farkas 1 1]: #30581
+#30583 := [unit-resolution #30582 #29652]: #13514
+#24508 := (or #23400 #18574 #18577 #23394)
+#24509 := [def-axiom]: #24508
+#30585 := [unit-resolution #24509 #30583]: #30584
+#30587 := [unit-resolution #30585 #29967]: #30586
+#30588 := [unit-resolution #30587 #30309]: #23394
+#24498 := (or #23391 #23385)
+#24499 := [def-axiom]: #24498
+#30639 := [unit-resolution #24499 #30588]: #23385
+#24443 := (>= #13599 -1::Int)
+#24494 := (or #23391 #13598)
+#24495 := [def-axiom]: #24494
+#30589 := [unit-resolution #24495 #30588]: #13598
+#30590 := (or #13602 #24443)
+#30591 := [th-lemma arith triangle-eq]: #30590
+#30592 := [unit-resolution #30591 #30589]: #24443
+#29759 := (not #24443)
+#29760 := (or #29759 #13530)
+#29753 := [hypothesis]: #24443
+#29757 := [hypothesis]: #13535
+#29758 := [th-lemma arith farkas -1 1 1 #29757 #30120 #29753]: false
+#29761 := [lemma #29758]: #29760
+#30640 := [unit-resolution #29761 #30592]: #13530
+#24484 := (or #23388 #13535 #23382)
+#24485 := [def-axiom]: #24484
+#30641 := [unit-resolution #24485 #30640 #30639]: #23382
+#24476 := (or #23379 #23373)
+#24477 := [def-axiom]: #24476
+#30642 := [unit-resolution #24477 #30641]: #23373
+#24569 := (+ f303 #13572)
+#24571 := (>= #24569 0::Int)
+#24574 := (or #23433 #12822)
+#24575 := [def-axiom]: #24574
+#30643 := [unit-resolution #24575 #30630]: #12822
+#30644 := (or #12828 #24571)
+#30645 := [th-lemma arith triangle-eq]: #30644
+#30646 := [unit-resolution #30645 #30643]: #24571
+#30647 := (not #24571)
+#30650 := (or #13575 #30647)
+#30648 := (or #13575 #13959 #30647)
+#30649 := [th-lemma arith assign-bounds -1 -1]: #30648
+#30651 := [unit-resolution #30649 #30082]: #30650
+#30652 := [unit-resolution #30651 #30646]: #13575
+#30659 := (= #3146 #3292)
+#30657 := (= #3292 #3146)
+#30654 := (= #3291 #3145)
+#30653 := [symm #30643]: #3322
+#30655 := [monotonicity #30653]: #30654
+#30658 := [monotonicity #30655]: #30657
+#30660 := [symm #30658]: #30659
+#30661 := (= f310 #3146)
+#30656 := [symm #30632]: #3321
+#30662 := [trans #30656 #30080]: #30661
+#30663 := [trans #30662 #30660]: #12623
+#24448 := (or #22344 #22342 #13574)
+#24449 := [def-axiom]: #24448
+#30664 := [unit-resolution #24449 #30663 #30652]: #22344
+#24450 := (or #23367 #22343)
+#24451 := [def-axiom]: #24450
+#30665 := [unit-resolution #24451 #30664]: #23367
+#24472 := (or #23376 #23370 #22396)
+#24473 := [def-axiom]: #24472
+#30666 := [unit-resolution #24473 #30665 #30642]: #22396
+#24464 := (or #22391 #24463)
+#24465 := [def-axiom]: #24464
+#30667 := [unit-resolution #24465 #30666]: #24463
+#30611 := (not #24567)
+#30612 := (or #30610 #18923 #30611 #13687)
+#30605 := [hypothesis]: #13688
+#30606 := [hypothesis]: #24567
+#30607 := [hypothesis]: #24463
+#30608 := [hypothesis]: #30600
+#30609 := [th-lemma arith farkas 1 -1 -1 1 #30608 #30607 #30606 #30605]: false
+#30613 := [lemma #30609]: #30612
+#30668 := [unit-resolution #30613 #30667 #30635 #30631]: #30610
+#30604 := (or #30603 #30600)
+#30614 := [th-lemma arith triangle-eq]: #30604
+#30669 := [unit-resolution #30614 #30668]: #30603
+#30628 := (or #30627 #30570)
+#30623 := (= #18600 #3259)
+#30621 := (= #18599 #3250)
+#30619 := (= ?v0!14 f304)
+#30618 := [hypothesis]: #30574
+#30620 := [symm #30618]: #30619
+#30622 := [monotonicity #30620]: #30621
+#30624 := [monotonicity #30622]: #30623
+#30625 := [symm #30624]: #30570
+#30617 := [hypothesis]: #30603
+#30626 := [unit-resolution #30617 #30625]: false
+#30629 := [lemma #30626]: #30628
+#30670 := [unit-resolution #30629 #30669]: #30627
+#30684 := (or #30574 #30681)
+#30404 := (<= #30403 0::Int)
+#30415 := (+ f302 #18921)
+#30416 := (>= #30415 0::Int)
+#30671 := (not #30416)
+#30672 := (or #30671 #18923 #30611)
+#30673 := [th-lemma arith assign-bounds -1 -1]: #30672
+#30674 := [unit-resolution #30673 #30635 #30667]: #30671
+#30677 := (or #30404 #30416)
+#24458 := (or #22391 #18596)
+#24459 := [def-axiom]: #24458
+#30675 := [unit-resolution #24459 #30666]: #18596
+#24456 := (or #22391 #18595)
+#24457 := [def-axiom]: #24456
+#30676 := [unit-resolution #24457 #30666]: #18595
+#30429 := (or #23356 #22375 #22376 #30404 #30416)
+#30392 := (+ #18600 #13986)
+#30393 := (<= #30392 0::Int)
+#30394 := (+ ?v0!14 #13517)
+#30395 := (>= #30394 0::Int)
+#30396 := (or #22376 #30395 #30393 #22375)
+#30430 := (or #23356 #30396)
+#30437 := (iff #30430 #30429)
+#30424 := (or #22375 #22376 #30404 #30416)
+#30432 := (or #23356 #30424)
+#30435 := (iff #30432 #30429)
+#30436 := [rewrite]: #30435
+#30433 := (iff #30430 #30432)
+#30427 := (iff #30396 #30424)
+#30421 := (or #22376 #30404 #30416 #22375)
+#30425 := (iff #30421 #30424)
+#30426 := [rewrite]: #30425
+#30422 := (iff #30396 #30421)
+#30419 := (iff #30393 #30416)
+#30409 := (+ #13986 #18600)
+#30412 := (<= #30409 0::Int)
+#30417 := (iff #30412 #30416)
+#30418 := [rewrite]: #30417
+#30413 := (iff #30393 #30412)
+#30410 := (= #30392 #30409)
+#30411 := [rewrite]: #30410
+#30414 := [monotonicity #30411]: #30413
+#30420 := [trans #30414 #30418]: #30419
+#30407 := (iff #30395 #30404)
+#30397 := (+ #13517 ?v0!14)
+#30400 := (>= #30397 0::Int)
+#30405 := (iff #30400 #30404)
+#30406 := [rewrite]: #30405
+#30401 := (iff #30395 #30400)
+#30398 := (= #30394 #30397)
+#30399 := [rewrite]: #30398
+#30402 := [monotonicity #30399]: #30401
+#30408 := [trans #30402 #30406]: #30407
+#30423 := [monotonicity #30408 #30420]: #30422
+#30428 := [trans #30423 #30426]: #30427
+#30434 := [monotonicity #30428]: #30433
+#30438 := [trans #30434 #30436]: #30437
+#30431 := [quant-inst #18594]: #30430
+#30439 := [mp #30431 #30438]: #30429
+#30678 := [unit-resolution #30439 #30074 #30676 #30675]: #30677
+#30679 := [unit-resolution #30678 #30674]: #30404
+#30680 := (not #30404)
+#30682 := (or #30574 #30680 #30681)
+#30683 := [th-lemma arith triangle-eq]: #30682
+#30685 := [unit-resolution #30683 #30679]: #30684
+#30686 := [unit-resolution #30685 #30670]: #30681
+#24460 := (not #18910)
+#24461 := (or #22391 #24460)
+#24462 := [def-axiom]: #24461
+#30687 := [unit-resolution #24462 #30666]: #24460
+#30688 := [th-lemma arith farkas -1 -1 1 #30687 #30592 #30686]: false
+#30689 := [lemma #30688]: #23433
+#26704 := [unit-resolution #29781 #30689]: #23409
+#26707 := [unit-resolution #30306 #26704 #30303]: #23406
+#24520 := (or #23403 #12581)
+#24521 := [def-axiom]: #24520
+#30535 := [unit-resolution #24521 #26707]: #12581
+#24514 := (or #23403 #12570)
+#24515 := [def-axiom]: #24514
+#30536 := [unit-resolution #24515 #26707]: #12570
+#30534 := [trans #30536 #30535]: #30322
+#30537 := (not #30322)
+#30538 := (or #30537 #30151)
+#30539 := [th-lemma arith triangle-eq]: #30538
+#30540 := [unit-resolution #30539 #30534]: #30151
+#30319 := (+ f304 #13572)
+#30321 := (>= #30319 0::Int)
+#24522 := (or #23403 #12584)
+#24523 := [def-axiom]: #24522
+#26708 := [unit-resolution #24523 #26707]: #12584
+#26709 := (or #12711 #30321)
+#30356 := [th-lemma arith triangle-eq]: #26709
+#30357 := [unit-resolution #30356 #26708]: #30321
+#30358 := [hypothesis]: #13574
+#30353 := [th-lemma arith farkas -1 1 1 #30358 #30357 #30120]: false
+#30359 := [lemma #30353]: #13575
+#30564 := (or #22344 #13574)
+#30554 := (= #3259 #3292)
+#30556 := (= #3292 #3259)
+#30542 := (= #3291 #3250)
+#30541 := [symm #26708]: #3271
+#30555 := [monotonicity #30541]: #30542
+#30557 := [monotonicity #30555]: #30556
+#30560 := [symm #30557]: #30554
+#30561 := (= f310 #3259)
+#30559 := [symm #30536]: #3262
+#30558 := [symm #30535]: #3269
+#30562 := [trans #30558 #30559]: #30561
+#30563 := [trans #30562 #30560]: #12623
+#30572 := [unit-resolution #24449 #30563]: #30564
+#30573 := [unit-resolution #30572 #30359]: #22344
+#30475 := [unit-resolution #24451 #30573]: #23367
+#30543 := [unit-resolution #24473 #30642]: #23373
+#30544 := [unit-resolution #30543 #30475]: #22396
+#30571 := [unit-resolution #24465 #30544]: #24463
+#30637 := (not #30151)
+#30638 := (or #30610 #18923 #30637)
+#30636 := [th-lemma arith assign-bounds -1 -1]: #30638
+#30690 := [unit-resolution #30636 #30571 #30540]: #30610
+#30691 := [unit-resolution #30614 #30690]: #30603
+#30692 := [unit-resolution #24462 #30544]: #24460
+#30693 := (or #30599 #18910 #29759)
 #30694 := [th-lemma arith assign-bounds -1 -1]: #30693
-#30695 := [unit-resolution #30694 #30656 #30688]: #30692
-#30698 := (or #30425 #30437)
-#24479 := (or #22411 #18616)
-#24480 := [def-axiom]: #24479
-#30696 := [unit-resolution #24480 #30687]: #18616
-#24477 := (or #22411 #18615)
-#24478 := [def-axiom]: #24477
-#30697 := [unit-resolution #24478 #30687]: #18615
-#30450 := (or #23377 #22395 #22396 #30425 #30437)
-#30413 := (+ #18620 #14006)
-#30414 := (<= #30413 0::Int)
-#30415 := (+ ?v0!14 #13537)
-#30416 := (>= #30415 0::Int)
-#30417 := (or #22396 #30416 #30414 #22395)
-#30451 := (or #23377 #30417)
-#30458 := (iff #30451 #30450)
-#30445 := (or #22395 #22396 #30425 #30437)
-#30453 := (or #23377 #30445)
-#30456 := (iff #30453 #30450)
-#30457 := [rewrite]: #30456
-#30454 := (iff #30451 #30453)
-#30448 := (iff #30417 #30445)
-#30442 := (or #22396 #30425 #30437 #22395)
-#30446 := (iff #30442 #30445)
-#30447 := [rewrite]: #30446
-#30443 := (iff #30417 #30442)
-#30440 := (iff #30414 #30437)
-#30430 := (+ #14006 #18620)
-#30433 := (<= #30430 0::Int)
-#30438 := (iff #30433 #30437)
-#30439 := [rewrite]: #30438
-#30434 := (iff #30414 #30433)
-#30431 := (= #30413 #30430)
-#30432 := [rewrite]: #30431
-#30435 := [monotonicity #30432]: #30434
-#30441 := [trans #30435 #30439]: #30440
-#30428 := (iff #30416 #30425)
-#30418 := (+ #13537 ?v0!14)
-#30421 := (>= #30418 0::Int)
-#30426 := (iff #30421 #30425)
-#30427 := [rewrite]: #30426
-#30422 := (iff #30416 #30421)
-#30419 := (= #30415 #30418)
-#30420 := [rewrite]: #30419
-#30423 := [monotonicity #30420]: #30422
-#30429 := [trans #30423 #30427]: #30428
-#30444 := [monotonicity #30429 #30441]: #30443
-#30449 := [trans #30444 #30447]: #30448
-#30455 := [monotonicity #30449]: #30454
-#30459 := [trans #30455 #30457]: #30458
-#30452 := [quant-inst #18614]: #30451
-#30460 := [mp #30452 #30459]: #30450
-#30699 := [unit-resolution #30460 #30095 #30697 #30696]: #30698
-#30700 := [unit-resolution #30699 #30695]: #30425
-#30701 := (not #30425)
-#30703 := (or #30595 #30701 #30702)
-#30704 := [th-lemma arith triangle-eq]: #30703
-#30706 := [unit-resolution #30704 #30700]: #30705
-#30707 := [unit-resolution #30706 #30691]: #30702
-#24481 := (not #18930)
-#24482 := (or #22411 #24481)
-#24483 := [def-axiom]: #24482
-#30708 := [unit-resolution #24483 #30687]: #24481
-#30709 := [th-lemma arith farkas -1 -1 1 #30708 #30613 #30707]: false
-#30710 := [lemma #30709]: #23454
-#26725 := [unit-resolution #29802 #30710]: #23430
-#26728 := [unit-resolution #30327 #26725 #30324]: #23427
-#24541 := (or #23424 #12601)
-#24542 := [def-axiom]: #24541
-#30556 := [unit-resolution #24542 #26728]: #12601
-#24535 := (or #23424 #12590)
-#24536 := [def-axiom]: #24535
-#30557 := [unit-resolution #24536 #26728]: #12590
-#30555 := [trans #30557 #30556]: #30343
-#30558 := (not #30343)
-#30559 := (or #30558 #30172)
-#30560 := [th-lemma arith triangle-eq]: #30559
-#30561 := [unit-resolution #30560 #30555]: #30172
-#30340 := (+ f309 #13592)
-#30342 := (>= #30340 0::Int)
-#24543 := (or #23424 #12604)
-#24544 := [def-axiom]: #24543
-#26729 := [unit-resolution #24544 #26728]: #12604
-#26730 := (or #12731 #30342)
-#30377 := [th-lemma arith triangle-eq]: #26730
-#30378 := [unit-resolution #30377 #26729]: #30342
-#30379 := [hypothesis]: #13594
-#30374 := [th-lemma arith farkas -1 1 1 #30379 #30378 #30141]: false
-#30380 := [lemma #30374]: #13595
-#30585 := (or #22364 #13594)
-#30575 := (= #3266 #3299)
-#30577 := (= #3299 #3266)
-#30563 := (= #3298 #3257)
-#30562 := [symm #26729]: #3278
-#30576 := [monotonicity #30562]: #30563
-#30578 := [monotonicity #30576]: #30577
-#30581 := [symm #30578]: #30575
-#30582 := (= f315 #3266)
-#30580 := [symm #30557]: #3269
-#30579 := [symm #30556]: #3276
-#30583 := [trans #30579 #30580]: #30582
-#30584 := [trans #30583 #30581]: #12643
-#30593 := [unit-resolution #24470 #30584]: #30585
-#30594 := [unit-resolution #30593 #30380]: #22364
-#30496 := [unit-resolution #24472 #30594]: #23388
-#30564 := [unit-resolution #24494 #30663]: #23394
-#30565 := [unit-resolution #30564 #30496]: #22416
-#30592 := [unit-resolution #24486 #30565]: #24484
-#30658 := (not #30172)
-#30659 := (or #30631 #18943 #30658)
-#30657 := [th-lemma arith assign-bounds -1 -1]: #30659
-#30711 := [unit-resolution #30657 #30592 #30561]: #30631
-#30712 := [unit-resolution #30635 #30711]: #30624
-#30713 := [unit-resolution #24483 #30565]: #24481
-#30714 := (or #30620 #18930 #29780)
-#30715 := [th-lemma arith assign-bounds -1 -1]: #30714
-#30716 := [unit-resolution #30715 #30713 #30613]: #30620
-#30724 := (or #30692 #18943)
-#30717 := [unit-resolution #29790 #30324]: #23469
-#30718 := [unit-resolution #24624 #30717]: #23460
-#30719 := [unit-resolution #24614 #30710 #30718]: #23451
-#24581 := (or #23448 #13707)
-#24582 := [def-axiom]: #24581
-#30720 := [unit-resolution #24582 #30719]: #13707
-#30721 := (or #24588 #30658 #13708)
-#30722 := [th-lemma arith assign-bounds 1 1]: #30721
-#30723 := [unit-resolution #30722 #30720 #30561]: #24588
-#30725 := [unit-resolution #30694 #30723]: #30724
-#30726 := [unit-resolution #30725 #30592]: #30692
-#30727 := [unit-resolution #24480 #30565]: #18616
-#30728 := [unit-resolution #24478 #30565]: #18615
-#30729 := [unit-resolution #30460 #30095 #30728 #30727 #30726]: #30425
-#30730 := [unit-resolution #30704 #30729 #30716]: #30595
-[unit-resolution #30650 #30730 #30712]: false
+#30695 := [unit-resolution #30694 #30692 #30592]: #30599
+#30703 := (or #30671 #18923)
+#30696 := [unit-resolution #29769 #30303]: #23448
+#30697 := [unit-resolution #24603 #30696]: #23439
+#30698 := [unit-resolution #24593 #30689 #30697]: #23430
+#24560 := (or #23427 #13687)
+#24561 := [def-axiom]: #24560
+#30699 := [unit-resolution #24561 #30698]: #13687
+#30700 := (or #24567 #30637 #13688)
+#30701 := [th-lemma arith assign-bounds 1 1]: #30700
+#30702 := [unit-resolution #30701 #30699 #30540]: #24567
+#30704 := [unit-resolution #30673 #30702]: #30703
+#30705 := [unit-resolution #30704 #30571]: #30671
+#30706 := [unit-resolution #24459 #30544]: #18596
+#30707 := [unit-resolution #24457 #30544]: #18595
+#30708 := [unit-resolution #30439 #30074 #30707 #30706 #30705]: #30404
+#30709 := [unit-resolution #30683 #30708 #30695]: #30574
+[unit-resolution #30629 #30709 #30691]: false
 unsat

--- a/src/HOL/Multivariate_Analysis/Integration.certs	Tue May 31 19:27:19 2011 +0200
+++ b/src/HOL/Multivariate_Analysis/Integration.certs	Tue May 31 19:28:03 2011 +0200
@@ -621,63 +621,282 @@
 #427 := [unit-resolution #411 #426]: #395
 [th-lemma arith farkas 2 1 2 3 1 1 #421 #319 #321 #414 #318 #427]: false
 unsat
-76aef63700c44d6a49155f473f80703718124469 57 0
+02d40f3e43c6a17458cd5dc30adbe4da03d87a0c 57 0
 #2 := false
-#37 := 0::Real
+#41 := 0::Real
 decl f12 :: (-> S5 Real)
 decl f13 :: (-> S4 S4 S5)
 decl f14 :: (-> S3 S4)
 decl f4 :: S3
 #8 := f4
-#45 := (f14 f4)
+#38 := (f14 f4)
 decl f10 :: S3
 #25 := f10
-#44 := (f14 f10)
-#46 := (f13 #44 #45)
-#47 := (f12 #46)
-#258 := (>= #47 0::Real)
-#260 := (not #258)
-#49 := (= #47 0::Real)
+#37 := (f14 f10)
+#39 := (f13 #37 #38)
+#40 := (f12 #39)
+#248 := (>= #40 0::Real)
+#250 := (not #248)
+#49 := (= #40 0::Real)
 #50 := (not #49)
 #134 := [asserted]: #50
-#266 := (or #49 #260)
-#48 := (<= #47 0::Real)
+#256 := (or #49 #250)
+#42 := (<= #40 0::Real)
+#132 := [asserted]: #42
+#249 := (not #42)
+#254 := (or #49 #249 #250)
+#255 := [th-lemma arith triangle-eq]: #254
+#257 := [unit-resolution #255 #132]: #256
+#258 := [unit-resolution #257 #134]: #250
+#44 := (:var 0 S4)
+#43 := (:var 1 S4)
+#45 := (f13 #43 #44)
+#241 := (pattern #45)
+#46 := (f12 #45)
+#137 := (>= #46 0::Real)
+#242 := (forall (vars (?v0 S4) (?v1 S4)) (:pat #241) #137)
+#139 := (forall (vars (?v0 S4) (?v1 S4)) #137)
+#245 := (iff #139 #242)
+#243 := (iff #137 #137)
+#244 := [refl]: #243
+#246 := [quant-intro #244]: #245
+#146 := (~ #139 #139)
+#148 := (~ #137 #137)
+#145 := [refl]: #148
+#143 := [nnf-pos #145]: #146
+#47 := (<= 0::Real #46)
+#48 := (forall (vars (?v0 S4) (?v1 S4)) #47)
+#140 := (iff #48 #139)
+#136 := (iff #47 #137)
+#138 := [rewrite]: #136
+#141 := [quant-intro #138]: #140
 #133 := [asserted]: #48
-#259 := (not #48)
-#264 := (or #49 #259 #260)
-#265 := [th-lemma arith triangle-eq]: #264
-#267 := [unit-resolution #265 #133]: #266
-#268 := [unit-resolution #267 #134]: #260
-#39 := (:var 0 S4)
-#38 := (:var 1 S4)
-#40 := (f13 #38 #39)
-#251 := (pattern #40)
-#41 := (f12 #40)
-#136 := (>= #41 0::Real)
-#252 := (forall (vars (?v0 S4) (?v1 S4)) (:pat #251) #136)
-#138 := (forall (vars (?v0 S4) (?v1 S4)) #136)
-#255 := (iff #138 #252)
-#253 := (iff #136 #136)
-#254 := [refl]: #253
-#256 := [quant-intro #254]: #255
-#165 := (~ #138 #138)
-#153 := (~ #136 #136)
-#154 := [refl]: #153
-#166 := [nnf-pos #154]: #165
-#42 := (<= 0::Real #41)
-#43 := (forall (vars (?v0 S4) (?v1 S4)) #42)
-#139 := (iff #43 #138)
-#135 := (iff #42 #136)
-#137 := [rewrite]: #135
-#140 := [quant-intro #137]: #139
-#132 := [asserted]: #43
-#141 := [mp #132 #140]: #138
-#167 := [mp~ #141 #166]: #138
-#257 := [mp #167 #256]: #252
-#261 := (not #252)
-#262 := (or #261 #258)
-#263 := [quant-inst #44 #45]: #262
-[unit-resolution #263 #257 #268]: false
+#142 := [mp #133 #141]: #139
+#144 := [mp~ #142 #143]: #139
+#247 := [mp #144 #246]: #242
+#251 := (not #242)
+#252 := (or #251 #248)
+#253 := [quant-inst #37 #38]: #252
+[unit-resolution #253 #247 #258]: false
+unsat
+d7759998d2972bb8616477c86659060b5a9117ad 218 0
+#2 := false
+#31 := 0::Real
+decl f3 :: (-> S2 S3 Real)
+decl f5 :: S3
+#9 := f5
+decl f10 :: S2
+#23 := f10
+#34 := (f3 f10 f5)
+#102 := -1::Real
+#348 := (* -1::Real #34)
+decl f6 :: S2
+#11 := f6
+#12 := (f3 f6 f5)
+#374 := (+ #12 #348)
+#375 := (>= #374 0::Real)
+#380 := (not #375)
+decl f4 :: S2
+#8 := f4
+#10 := (f3 f4 f5)
+#349 := (+ #10 #348)
+#350 := (<= #349 0::Real)
+#351 := (not #350)
+#383 := (or #351 #380)
+#386 := (not #383)
+#19 := (:var 0 S3)
+#26 := (f3 f6 #19)
+#318 := (pattern #26)
+#24 := (f3 f10 #19)
+#317 := (pattern #24)
+#22 := (f3 f4 #19)
+#316 := (pattern #22)
+decl f7 :: (-> S3 Int)
+#20 := (f7 #19)
+#315 := (pattern #20)
+#108 := (* -1::Real #26)
+#109 := (+ #24 #108)
+#110 := (<= #109 0::Real)
+#246 := (not #110)
+#103 := (* -1::Real #24)
+#104 := (+ #22 #103)
+#105 := (<= #104 0::Real)
+#245 := (not #105)
+#247 := (or #245 #246)
+#248 := (not #247)
+#40 := 0::Int
+#75 := -1::Int
+#89 := (* -1::Int #20)
+decl f8 :: (-> S4 S3)
+decl f9 :: S4
+#15 := f9
+#16 := (f8 f9)
+#17 := (f7 #16)
+#90 := (+ #17 #89)
+#91 := (<= #90 0::Int)
+#251 := (or #91 #248)
+#319 := (forall (vars (?v0 S3)) (:pat #315 #316 #317 #318) #251)
+#254 := (forall (vars (?v0 S3)) #251)
+#322 := (iff #254 #319)
+#320 := (iff #251 #251)
+#321 := [refl]: #320
+#323 := [quant-intro #321]: #322
+#113 := (and #105 #110)
+#116 := (or #91 #113)
+#119 := (forall (vars (?v0 S3)) #116)
+#255 := (iff #119 #254)
+#252 := (iff #116 #251)
+#249 := (iff #113 #248)
+#250 := [rewrite]: #249
+#253 := [monotonicity #250]: #252
+#256 := [quant-intro #253]: #255
+#239 := (~ #119 #119)
+#241 := (~ #116 #116)
+#242 := [refl]: #241
+#240 := [nnf-pos #242]: #239
+#27 := (<= #24 #26)
+#25 := (<= #22 #24)
+#28 := (and #25 #27)
+#21 := (< #20 #17)
+#29 := (implies #21 #28)
+#30 := (forall (vars (?v0 S3)) #29)
+#122 := (iff #30 #119)
+#74 := (not #21)
+#83 := (or #74 #28)
+#86 := (forall (vars (?v0 S3)) #83)
+#120 := (iff #86 #119)
+#117 := (iff #83 #116)
+#114 := (iff #28 #113)
+#111 := (iff #27 #110)
+#112 := [rewrite]: #111
+#106 := (iff #25 #105)
+#107 := [rewrite]: #106
+#115 := [monotonicity #107 #112]: #114
+#100 := (iff #74 #91)
+#92 := (not #91)
+#95 := (not #92)
+#98 := (iff #95 #91)
+#99 := [rewrite]: #98
+#96 := (iff #74 #95)
+#93 := (iff #21 #92)
+#94 := [rewrite]: #93
+#97 := [monotonicity #94]: #96
+#101 := [trans #97 #99]: #100
+#118 := [monotonicity #101 #115]: #117
+#121 := [quant-intro #118]: #120
+#87 := (iff #30 #86)
+#84 := (iff #29 #83)
+#85 := [rewrite]: #84
+#88 := [quant-intro #85]: #87
+#123 := [trans #88 #121]: #122
+#73 := [asserted]: #30
+#124 := [mp #73 #123]: #119
+#237 := [mp~ #124 #240]: #119
+#257 := [mp #237 #256]: #254
+#324 := [mp #257 #323]: #319
+#78 := (* -1::Int #17)
+#14 := (f7 f5)
+#79 := (+ #14 #78)
+#77 := (>= #79 0::Int)
+#76 := (not #77)
+#18 := (< #14 #17)
+#80 := (iff #18 #76)
+#81 := [rewrite]: #80
+#72 := [asserted]: #18
+#82 := [mp #72 #81]: #76
+#392 := (not #319)
+#393 := (or #392 #77 #386)
+#344 := (* -1::Real #12)
+#345 := (+ #34 #344)
+#346 := (<= #345 0::Real)
+#347 := (not #346)
+#352 := (or #351 #347)
+#353 := (not #352)
+#354 := (* -1::Int #14)
+#355 := (+ #17 #354)
+#356 := (<= #355 0::Int)
+#357 := (or #356 #353)
+#394 := (or #392 #357)
+#401 := (iff #394 #393)
+#389 := (or #77 #386)
+#396 := (or #392 #389)
+#399 := (iff #396 #393)
+#400 := [rewrite]: #399
+#397 := (iff #394 #396)
+#390 := (iff #357 #389)
+#387 := (iff #353 #386)
+#384 := (iff #352 #383)
+#381 := (iff #347 #380)
+#378 := (iff #346 #375)
+#368 := (+ #344 #34)
+#371 := (<= #368 0::Real)
+#376 := (iff #371 #375)
+#377 := [rewrite]: #376
+#372 := (iff #346 #371)
+#369 := (= #345 #368)
+#370 := [rewrite]: #369
+#373 := [monotonicity #370]: #372
+#379 := [trans #373 #377]: #378
+#382 := [monotonicity #379]: #381
+#385 := [monotonicity #382]: #384
+#388 := [monotonicity #385]: #387
+#366 := (iff #356 #77)
+#358 := (+ #354 #17)
+#361 := (<= #358 0::Int)
+#364 := (iff #361 #77)
+#365 := [rewrite]: #364
+#362 := (iff #356 #361)
+#359 := (= #355 #358)
+#360 := [rewrite]: #359
+#363 := [monotonicity #360]: #362
+#367 := [trans #363 #365]: #366
+#391 := [monotonicity #367 #388]: #390
+#398 := [monotonicity #391]: #397
+#402 := [trans #398 #400]: #401
+#395 := [quant-inst #9]: #394
+#403 := [mp #395 #402]: #393
+#530 := [unit-resolution #403 #82 #324]: #386
+#406 := (or #383 #375)
+#407 := [def-axiom]: #406
+#531 := [unit-resolution #407 #530]: #375
+#492 := (>= #349 0::Real)
+#541 := (not #492)
+#491 := (= #10 #34)
+#536 := (not #491)
+#127 := (= #12 #34)
+#135 := (not #127)
+#537 := (iff #135 #536)
+#534 := (iff #127 #491)
+#532 := (iff #491 #127)
+#13 := (= #10 #12)
+#71 := [asserted]: #13
+#533 := [monotonicity #71]: #532
+#535 := [symm #533]: #534
+#538 := [monotonicity #535]: #537
+#35 := (= #34 #12)
+#36 := (not #35)
+#136 := (iff #36 #135)
+#133 := (iff #35 #127)
+#134 := [rewrite]: #133
+#137 := [monotonicity #134]: #136
+#126 := [asserted]: #36
+#140 := [mp #126 #137]: #135
+#539 := [mp #140 #538]: #536
+#544 := (or #491 #541)
+#404 := (or #383 #350)
+#405 := [def-axiom]: #404
+#540 := [unit-resolution #405 #530]: #350
+#542 := (or #491 #351 #541)
+#543 := [th-lemma arith triangle-eq]: #542
+#545 := [unit-resolution #543 #540]: #544
+#546 := [unit-resolution #545 #539]: #541
+#486 := (+ #10 #344)
+#490 := (>= #486 0::Real)
+#547 := (not #13)
+#548 := (or #547 #490)
+#549 := [th-lemma arith triangle-eq]: #548
+#550 := [unit-resolution #549 #71]: #490
+[th-lemma arith farkas 1 -1 1 #550 #546 #531]: false
 unsat
 fe6d352e9186ccd9319b5d4bd3ff26ab342ba6c4 351 0
 #2 := false
@@ -1363,225 +1582,6 @@
 #735 := [th-lemma arith triangle-eq]: #734
 [unit-resolution #735 #732 #718]: false
 unsat
-d7759998d2972bb8616477c86659060b5a9117ad 218 0
-#2 := false
-#31 := 0::Real
-decl f3 :: (-> S2 S3 Real)
-decl f5 :: S3
-#9 := f5
-decl f10 :: S2
-#23 := f10
-#34 := (f3 f10 f5)
-#102 := -1::Real
-#348 := (* -1::Real #34)
-decl f6 :: S2
-#11 := f6
-#12 := (f3 f6 f5)
-#374 := (+ #12 #348)
-#375 := (>= #374 0::Real)
-#380 := (not #375)
-decl f4 :: S2
-#8 := f4
-#10 := (f3 f4 f5)
-#349 := (+ #10 #348)
-#350 := (<= #349 0::Real)
-#351 := (not #350)
-#383 := (or #351 #380)
-#386 := (not #383)
-#19 := (:var 0 S3)
-#26 := (f3 f6 #19)
-#318 := (pattern #26)
-#24 := (f3 f10 #19)
-#317 := (pattern #24)
-#22 := (f3 f4 #19)
-#316 := (pattern #22)
-decl f7 :: (-> S3 Int)
-#20 := (f7 #19)
-#315 := (pattern #20)
-#108 := (* -1::Real #26)
-#109 := (+ #24 #108)
-#110 := (<= #109 0::Real)
-#246 := (not #110)
-#103 := (* -1::Real #24)
-#104 := (+ #22 #103)
-#105 := (<= #104 0::Real)
-#245 := (not #105)
-#247 := (or #245 #246)
-#248 := (not #247)
-#40 := 0::Int
-#75 := -1::Int
-#89 := (* -1::Int #20)
-decl f8 :: (-> S4 S3)
-decl f9 :: S4
-#15 := f9
-#16 := (f8 f9)
-#17 := (f7 #16)
-#90 := (+ #17 #89)
-#91 := (<= #90 0::Int)
-#251 := (or #91 #248)
-#319 := (forall (vars (?v0 S3)) (:pat #315 #316 #317 #318) #251)
-#254 := (forall (vars (?v0 S3)) #251)
-#322 := (iff #254 #319)
-#320 := (iff #251 #251)
-#321 := [refl]: #320
-#323 := [quant-intro #321]: #322
-#113 := (and #105 #110)
-#116 := (or #91 #113)
-#119 := (forall (vars (?v0 S3)) #116)
-#255 := (iff #119 #254)
-#252 := (iff #116 #251)
-#249 := (iff #113 #248)
-#250 := [rewrite]: #249
-#253 := [monotonicity #250]: #252
-#256 := [quant-intro #253]: #255
-#239 := (~ #119 #119)
-#241 := (~ #116 #116)
-#242 := [refl]: #241
-#240 := [nnf-pos #242]: #239
-#27 := (<= #24 #26)
-#25 := (<= #22 #24)
-#28 := (and #25 #27)
-#21 := (< #20 #17)
-#29 := (implies #21 #28)
-#30 := (forall (vars (?v0 S3)) #29)
-#122 := (iff #30 #119)
-#74 := (not #21)
-#83 := (or #74 #28)
-#86 := (forall (vars (?v0 S3)) #83)
-#120 := (iff #86 #119)
-#117 := (iff #83 #116)
-#114 := (iff #28 #113)
-#111 := (iff #27 #110)
-#112 := [rewrite]: #111
-#106 := (iff #25 #105)
-#107 := [rewrite]: #106
-#115 := [monotonicity #107 #112]: #114
-#100 := (iff #74 #91)
-#92 := (not #91)
-#95 := (not #92)
-#98 := (iff #95 #91)
-#99 := [rewrite]: #98
-#96 := (iff #74 #95)
-#93 := (iff #21 #92)
-#94 := [rewrite]: #93
-#97 := [monotonicity #94]: #96
-#101 := [trans #97 #99]: #100
-#118 := [monotonicity #101 #115]: #117
-#121 := [quant-intro #118]: #120
-#87 := (iff #30 #86)
-#84 := (iff #29 #83)
-#85 := [rewrite]: #84
-#88 := [quant-intro #85]: #87
-#123 := [trans #88 #121]: #122
-#73 := [asserted]: #30
-#124 := [mp #73 #123]: #119
-#237 := [mp~ #124 #240]: #119
-#257 := [mp #237 #256]: #254
-#324 := [mp #257 #323]: #319
-#78 := (* -1::Int #17)
-#14 := (f7 f5)
-#79 := (+ #14 #78)
-#77 := (>= #79 0::Int)
-#76 := (not #77)
-#18 := (< #14 #17)
-#80 := (iff #18 #76)
-#81 := [rewrite]: #80
-#72 := [asserted]: #18
-#82 := [mp #72 #81]: #76
-#392 := (not #319)
-#393 := (or #392 #77 #386)
-#344 := (* -1::Real #12)
-#345 := (+ #34 #344)
-#346 := (<= #345 0::Real)
-#347 := (not #346)
-#352 := (or #351 #347)
-#353 := (not #352)
-#354 := (* -1::Int #14)
-#355 := (+ #17 #354)
-#356 := (<= #355 0::Int)
-#357 := (or #356 #353)
-#394 := (or #392 #357)
-#401 := (iff #394 #393)
-#389 := (or #77 #386)
-#396 := (or #392 #389)
-#399 := (iff #396 #393)
-#400 := [rewrite]: #399
-#397 := (iff #394 #396)
-#390 := (iff #357 #389)
-#387 := (iff #353 #386)
-#384 := (iff #352 #383)
-#381 := (iff #347 #380)
-#378 := (iff #346 #375)
-#368 := (+ #344 #34)
-#371 := (<= #368 0::Real)
-#376 := (iff #371 #375)
-#377 := [rewrite]: #376
-#372 := (iff #346 #371)
-#369 := (= #345 #368)
-#370 := [rewrite]: #369
-#373 := [monotonicity #370]: #372
-#379 := [trans #373 #377]: #378
-#382 := [monotonicity #379]: #381
-#385 := [monotonicity #382]: #384
-#388 := [monotonicity #385]: #387
-#366 := (iff #356 #77)
-#358 := (+ #354 #17)
-#361 := (<= #358 0::Int)
-#364 := (iff #361 #77)
-#365 := [rewrite]: #364
-#362 := (iff #356 #361)
-#359 := (= #355 #358)
-#360 := [rewrite]: #359
-#363 := [monotonicity #360]: #362
-#367 := [trans #363 #365]: #366
-#391 := [monotonicity #367 #388]: #390
-#398 := [monotonicity #391]: #397
-#402 := [trans #398 #400]: #401
-#395 := [quant-inst #9]: #394
-#403 := [mp #395 #402]: #393
-#530 := [unit-resolution #403 #82 #324]: #386
-#406 := (or #383 #375)
-#407 := [def-axiom]: #406
-#531 := [unit-resolution #407 #530]: #375
-#492 := (>= #349 0::Real)
-#541 := (not #492)
-#491 := (= #10 #34)
-#536 := (not #491)
-#127 := (= #12 #34)
-#135 := (not #127)
-#537 := (iff #135 #536)
-#534 := (iff #127 #491)
-#532 := (iff #491 #127)
-#13 := (= #10 #12)
-#71 := [asserted]: #13
-#533 := [monotonicity #71]: #532
-#535 := [symm #533]: #534
-#538 := [monotonicity #535]: #537
-#35 := (= #34 #12)
-#36 := (not #35)
-#136 := (iff #36 #135)
-#133 := (iff #35 #127)
-#134 := [rewrite]: #133
-#137 := [monotonicity #134]: #136
-#126 := [asserted]: #36
-#140 := [mp #126 #137]: #135
-#539 := [mp #140 #538]: #536
-#544 := (or #491 #541)
-#404 := (or #383 #350)
-#405 := [def-axiom]: #404
-#540 := [unit-resolution #405 #530]: #350
-#542 := (or #491 #351 #541)
-#543 := [th-lemma arith triangle-eq]: #542
-#545 := [unit-resolution #543 #540]: #544
-#546 := [unit-resolution #545 #539]: #541
-#486 := (+ #10 #344)
-#490 := (>= #486 0::Real)
-#547 := (not #13)
-#548 := (or #547 #490)
-#549 := [th-lemma arith triangle-eq]: #548
-#550 := [unit-resolution #549 #71]: #490
-[th-lemma arith farkas 1 -1 1 #550 #546 #531]: false
-unsat
 2e6294cf4cca8c6e762613c9c359f9400d601092 898 0
 #2 := false
 #11 := 0::Real

--- a/src/HOL/SMT_Examples/SMT_Examples.certs	Tue May 31 19:27:19 2011 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Tue May 31 19:28:03 2011 +0200
@@ -10487,6 +10487,67 @@
 unsat
 ERROR: line 11 column 83: invalid pattern.
 
+1953a39a3cc38daf2fde4846aa1d5cbc2ff95785 60 0
+#2 := false
+#8 := 0::Int
+decl ?v1!0 :: Int
+#67 := ?v1!0
+#70 := (<= ?v1!0 0::Int)
+#63 := (not #70)
+#11 := 1::Int
+#68 := (>= ?v1!0 1::Int)
+#69 := (not #68)
+#79 := (or #69 #63)
+#82 := (not #79)
+#64 := (or #63 #69)
+#71 := (not #64)
+#83 := (iff #71 #82)
+#80 := (iff #64 #79)
+#81 := [rewrite]: #80
+#84 := [monotonicity #81]: #83
+#9 := (:var 0 Int)
+#48 := (>= #9 1::Int)
+#46 := (not #48)
+#42 := (<= #9 0::Int)
+#43 := (not #42)
+#50 := (or #43 #46)
+#53 := (forall (vars (?v1 Int)) #50)
+#56 := (not #53)
+#72 := (~ #56 #71)
+#73 := [sk]: #72
+#12 := (< #9 1::Int)
+#10 := (< 0::Int #9)
+#13 := (or #10 #12)
+#14 := (forall (vars (?v0 Int) (?v1 Int)) #13)
+#15 := (not #14)
+#59 := (iff #15 #56)
+#36 := (forall (vars (?v1 Int)) #13)
+#39 := (not #36)
+#57 := (iff #39 #56)
+#54 := (iff #36 #53)
+#51 := (iff #13 #50)
+#47 := (iff #12 #46)
+#49 := [rewrite]: #47
+#44 := (iff #10 #43)
+#45 := [rewrite]: #44
+#52 := [monotonicity #45 #49]: #51
+#55 := [quant-intro #52]: #54
+#58 := [monotonicity #55]: #57
+#40 := (iff #15 #39)
+#37 := (iff #14 #36)
+#38 := [elim-unused]: #37
+#41 := [monotonicity #38]: #40
+#60 := [trans #41 #58]: #59
+#35 := [asserted]: #15
+#61 := [mp #35 #60]: #56
+#76 := [mp~ #61 #73]: #71
+#77 := [mp #76 #84]: #82
+#85 := [not-or-elim #77]: #70
+#78 := [not-or-elim #77]: #68
+#141 := [th-lemma arith farkas 1 1]: #64
+#142 := [unit-resolution #141 #78]: #63
+[unit-resolution #142 #85]: false
+unsat
 8f616b17d0807409dc26bfdf9593c5fcd06fb7e7 1 0
 unsat
 3eb9cf11ee8774c9212c37c265e7552f3b8f24a9 75 0
@@ -12849,7 +12910,7 @@
 #170 := [not-or-elim #167]: #169
 [th-lemma arith farkas -4 1 1 #170 #585 #559]: false
 unsat
-5a76ac61ccccc3cf413dd2cf808cc3df750b1eab 61 0
+b5c183bebb02d94d1f8b42e98316e9a15ecf822c 61 0
 #2 := false
 decl f7 :: S2
 #18 := f7
@@ -12888,10 +12949,10 @@
 #545 := (iff #43 #43)
 #546 := [refl]: #545
 #548 := [quant-intro #546]: #547
-#73 := (~ #46 #46)
-#71 := (~ #43 #43)
-#72 := [refl]: #71
-#74 := [nnf-pos #72]: #73
+#67 := (~ #46 #46)
+#65 := (~ #43 #43)
+#66 := [refl]: #65
+#72 := [nnf-pos #66]: #67
 #12 := (= #11 #8)
 #13 := (forall (vars (?v0 S2) (?v1 S3)) #12)
 #47 := (iff #13 #46)
@@ -12900,8 +12961,8 @@
 #48 := [quant-intro #45]: #47
 #42 := [asserted]: #13
 #51 := [mp #42 #48]: #46
-#63 := [mp~ #51 #74]: #46
-#549 := [mp #63 #548]: #544
+#73 := [mp~ #51 #72]: #46
+#549 := [mp #73 #548]: #544
 #213 := (not #544)
 #127 := (or #213 #125)
 #214 := [quant-inst #14 #15]: #127
@@ -12911,29 +12972,29 @@
 #61 := [not-or-elim #60]: #59
 [unit-resolution #61 #126]: false
 unsat
-23c03a2c075c99b6dd1e5fff0e14c35c8745e586 116 0
-#2 := false
-decl f3 :: (-> S4 S3)
-decl f12 :: S4
+cf92237c0d499778714b4e00f3fc6a25231e47a2 116 0
+#2 := false
+decl f8 :: (-> S5 S2)
+decl f12 :: S5
 #31 := f12
-#36 := (f3 f12)
-decl f8 :: (-> S5 S3)
-decl f9 :: S5
+#36 := (f8 f12)
+decl f3 :: (-> S4 S2)
+decl f9 :: S4
 #26 := f9
-#35 := (f8 f9)
+#35 := (f3 f9)
 #37 := (= #35 #36)
+decl f6 :: (-> S3 S2 S5)
+decl f10 :: S2
+#27 := f10
+decl f11 :: S3
+#28 := f11
+#32 := (f6 f11 f10)
+#277 := (f8 #32)
+#591 := (= #277 #36)
+#599 := (= #36 #277)
+#33 := (= f12 #32)
 decl f4 :: (-> S2 S3 S4)
-decl f10 :: S3
-#27 := f10
-decl f11 :: S2
-#28 := f11
-#32 := (f4 f11 f10)
-#183 := (f3 #32)
-#248 := (= #183 #36)
-#600 := (= #36 #183)
-#33 := (= f12 #32)
-decl f6 :: (-> S3 S2 S5)
-#29 := (f6 f10 f11)
+#29 := (f4 f10 f11)
 #30 := (= f9 #29)
 #34 := (and #30 #33)
 #91 := (not #34)
@@ -12949,27 +13010,61 @@
 #101 := [mp #90 #98]: #96
 #99 := [not-or-elim #101]: #34
 #102 := [and-elim #99]: #33
-#590 := [monotonicity #102]: #600
-#253 := [symm #590]: #248
-#592 := (= #35 #183)
+#594 := [monotonicity #102]: #599
+#249 := [symm #594]: #591
+#576 := (= #35 #277)
+#256 := (= f10 #277)
+#15 := (:var 0 S2)
+#14 := (:var 1 S3)
+#16 := (f6 #14 #15)
+#608 := (pattern #16)
+#23 := (f8 #16)
+#83 := (= #15 #23)
+#621 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #608) #83)
+#87 := (forall (vars (?v0 S3) (?v1 S2)) #83)
+#624 := (iff #87 #621)
+#622 := (iff #83 #83)
+#623 := [refl]: #622
+#625 := [quant-intro #623]: #624
+#124 := (~ #87 #87)
+#126 := (~ #83 #83)
+#127 := [refl]: #126
+#125 := [nnf-pos #127]: #124
+#24 := (= #23 #15)
+#25 := (forall (vars (?v0 S3) (?v1 S2)) #24)
+#88 := (iff #25 #87)
+#85 := (iff #24 #83)
+#86 := [rewrite]: #85
+#89 := [quant-intro #86]: #88
+#82 := [asserted]: #25
+#92 := [mp #82 #89]: #87
+#122 := [mp~ #92 #125]: #87
+#626 := [mp #122 #625]: #621
+#261 := (not #621)
+#262 := (or #261 #256)
+#596 := [quant-inst #28 #27]: #262
+#589 := [unit-resolution #596 #626]: #256
+#592 := (= #35 f10)
+#183 := (f3 #29)
+#248 := (= #183 f10)
 #270 := (= f10 #183)
 #9 := (:var 0 S3)
 #8 := (:var 1 S2)
 #10 := (f4 #8 #9)
 #601 := (pattern #10)
 #11 := (f3 #10)
-#60 := (= #9 #11)
+#60 := (= #8 #11)
 #602 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #601) #60)
 #63 := (forall (vars (?v0 S2) (?v1 S3)) #60)
 #605 := (iff #63 #602)
 #603 := (iff #60 #60)
 #604 := [refl]: #603
 #606 := [quant-intro #604]: #605
-#124 := (~ #63 #63)
-#122 := (~ #60 #60)
-#123 := [refl]: #122
-#125 := [nnf-pos #123]: #124
-#12 := (= #11 #9)
+#108 := (~ #63 #63)
+#117 := (~ #60 #60)
+#118 := [refl]: #117
+#109 := [nnf-pos #118]: #108
+#12 := (= #11 #8)
 #13 := (forall (vars (?v0 S2) (?v1 S3)) #12)
 #64 := (iff #13 #63)
 #61 := (iff #12 #60)
@@ -12977,58 +13072,24 @@
 #65 := [quant-intro #62]: #64
 #59 := [asserted]: #13
 #68 := [mp #59 #65]: #63
-#106 := [mp~ #68 #125]: #63
-#607 := [mp #106 #606]: #602
+#112 := [mp~ #68 #109]: #63
+#607 := [mp #112 #606]: #602
 #185 := (not #602)
 #272 := (or #185 #270)
-#263 := [quant-inst #28 #27]: #272
+#263 := [quant-inst #27 #28]: #272
 #382 := [unit-resolution #263 #607]: #270
-#591 := (= #35 f10)
-#277 := (f8 #29)
-#599 := (= #277 f10)
-#256 := (= f10 #277)
-#15 := (:var 0 S2)
-#14 := (:var 1 S3)
-#16 := (f6 #14 #15)
-#608 := (pattern #16)
-#23 := (f8 #16)
-#83 := (= #14 #23)
-#621 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #608) #83)
-#87 := (forall (vars (?v0 S3) (?v1 S2)) #83)
-#624 := (iff #87 #621)
-#622 := (iff #83 #83)
-#623 := [refl]: #622
-#625 := [quant-intro #623]: #624
-#112 := (~ #87 #87)
-#131 := (~ #83 #83)
-#132 := [refl]: #131
-#113 := [nnf-pos #132]: #112
-#24 := (= #23 #14)
-#25 := (forall (vars (?v0 S3) (?v1 S2)) #24)
-#88 := (iff #25 #87)
-#85 := (iff #24 #83)
-#86 := [rewrite]: #85
-#89 := [quant-intro #86]: #88
-#82 := [asserted]: #25
-#92 := [mp #82 #89]: #87
-#133 := [mp~ #92 #113]: #87
-#626 := [mp #133 #625]: #621
-#261 := (not #621)
-#262 := (or #261 #256)
-#596 := [quant-inst #27 #28]: #262
-#589 := [unit-resolution #596 #626]: #256
-#594 := [symm #589]: #599
-#597 := (= #35 #277)
+#253 := [symm #382]: #248
+#597 := (= #35 #183)
 #100 := [and-elim #99]: #30
 #598 := [monotonicity #100]: #597
-#249 := [trans #598 #594]: #591
-#233 := [trans #249 #382]: #592
-#576 := [trans #233 #253]: #37
+#233 := [trans #598 #253]: #592
+#237 := [trans #233 #589]: #576
+#238 := [trans #237 #249]: #37
 #103 := (not #37)
 #104 := [not-or-elim #101]: #103
-[unit-resolution #104 #576]: false
-unsat
-21925946f04e63dea2f01d8f4ea201edb55fb97e 192 0
+[unit-resolution #104 #238]: false
+unsat
+683ecf2fabb84eab2c1f7b22612c683b9106d640 192 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f5 :: S3
@@ -13049,81 +13110,81 @@
 #38 := (f4 #36 f7 f10)
 #39 := (f3 #38 f5)
 #41 := (= #39 #40)
-#242 := (f3 #36 f6)
-#233 := (f4 f8 f6 #242)
-#571 := (f3 #233 f5)
-#574 := (= #571 #40)
-#579 := (= #40 #571)
-#575 := (= #242 #571)
+#176 := (f3 #36 f6)
+#573 := (f4 f8 f6 #176)
+#541 := (f3 #573 f5)
+#542 := (= #541 #40)
+#545 := (= #40 #541)
+#536 := (= #176 #541)
 #28 := (= f5 f6)
-#580 := (ite #28 #575 #579)
-#12 := (:var 0 S3)
-#10 := (:var 1 S4)
-#9 := (:var 2 S3)
-#8 := (:var 3 S2)
-#11 := (f4 #8 #9 #10)
-#13 := (f3 #11 #12)
-#594 := (pattern #13)
-#15 := (f3 #8 #12)
-#119 := (= #13 #15)
-#118 := (= #10 #13)
-#64 := (= #9 #12)
-#104 := (ite #64 #118 #119)
-#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104)
+#377 := (ite #28 #536 #545)
+#19 := (:var 0 S3)
+#17 := (:var 1 S4)
+#16 := (:var 2 S3)
+#15 := (:var 3 S2)
+#18 := (f4 #15 #16 #17)
+#20 := (f3 #18 #19)
+#602 := (pattern #20)
+#22 := (f3 #15 #19)
+#119 := (= #20 #22)
+#118 := (= #17 #20)
+#71 := (= #16 #19)
+#104 := (ite #71 #118 #119)
+#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #602) #104)
 #111 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104)
-#598 := (iff #111 #595)
-#596 := (iff #104 #104)
-#597 := [refl]: #596
-#599 := [quant-intro #597]: #598
-#67 := (ite #64 #10 #15)
-#70 := (= #13 #67)
-#73 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #70)
-#108 := (iff #73 #111)
-#105 := (iff #70 #104)
+#606 := (iff #111 #603)
+#604 := (iff #104 #104)
+#605 := [refl]: #604
+#607 := [quant-intro #605]: #606
+#75 := (ite #71 #17 #22)
+#78 := (= #20 #75)
+#81 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #78)
+#108 := (iff #81 #111)
+#105 := (iff #78 #104)
 #110 := [rewrite]: #105
 #109 := [quant-intro #110]: #108
-#114 := (~ #73 #73)
-#112 := (~ #70 #70)
-#113 := [refl]: #112
-#115 := [nnf-pos #113]: #114
-#14 := (= #12 #9)
-#16 := (ite #14 #10 #15)
-#17 := (= #13 #16)
-#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
-#74 := (iff #18 #73)
-#71 := (iff #17 #70)
-#68 := (= #16 #67)
-#65 := (iff #14 #64)
-#66 := [rewrite]: #65
-#69 := [monotonicity #66]: #68
-#72 := [monotonicity #69]: #71
-#75 := [quant-intro #72]: #74
-#63 := [asserted]: #18
-#78 := [mp #63 #75]: #73
-#100 := [mp~ #78 #115]: #73
-#106 := [mp #100 #109]: #111
-#600 := [mp #106 #599]: #595
-#269 := (not #595)
-#567 := (or #269 #580)
-#570 := (= f6 f5)
-#576 := (ite #570 #575 #574)
-#568 := (or #269 #576)
-#290 := (iff #568 #567)
-#292 := (iff #567 #567)
-#278 := [rewrite]: #292
-#578 := (iff #576 #580)
-#217 := (iff #574 #579)
-#218 := [rewrite]: #217
-#212 := (iff #570 #28)
-#577 := [rewrite]: #212
-#581 := [monotonicity #577 #218]: #578
-#291 := [monotonicity #581]: #290
-#293 := [trans #291 #278]: #290
-#274 := [quant-inst #34 #27 #242 #26]: #568
-#184 := [mp #274 #293]: #567
-#529 := [unit-resolution #184 #600]: #580
-#563 := (not #580)
-#516 := (or #563 #579)
+#102 := (~ #81 #81)
+#101 := (~ #78 #78)
+#116 := [refl]: #101
+#103 := [nnf-pos #116]: #102
+#21 := (= #19 #16)
+#23 := (ite #21 #17 #22)
+#24 := (= #20 #23)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #24)
+#82 := (iff #25 #81)
+#79 := (iff #24 #78)
+#76 := (= #23 #75)
+#73 := (iff #21 #71)
+#74 := [rewrite]: #73
+#77 := [monotonicity #74]: #76
+#80 := [monotonicity #77]: #79
+#83 := [quant-intro #80]: #82
+#70 := [asserted]: #25
+#86 := [mp #70 #83]: #81
+#117 := [mp~ #86 #103]: #81
+#106 := [mp #117 #109]: #111
+#608 := [mp #106 #607]: #603
+#254 := (not #603)
+#533 := (or #254 #377)
+#537 := (= f6 f5)
+#543 := (ite #537 #536 #542)
+#534 := (or #254 #543)
+#535 := (iff #534 #533)
+#418 := (iff #533 #533)
+#419 := [rewrite]: #418
+#530 := (iff #543 #377)
+#374 := (iff #542 #545)
+#376 := [rewrite]: #374
+#544 := (iff #537 #28)
+#538 := [rewrite]: #544
+#531 := [monotonicity #538 #376]: #530
+#417 := [monotonicity #531]: #535
+#378 := [trans #417 #419]: #535
+#532 := [quant-inst #34 #27 #176 #26]: #534
+#526 := [mp #532 #378]: #533
+#529 := [unit-resolution #526 #608]: #377
+#428 := (not #377)
+#516 := (or #428 #545)
 #29 := (not #28)
 #31 := (= f5 f7)
 #32 := (not #31)
@@ -13141,80 +13202,80 @@
 #95 := [mp #84 #92]: #90
 #93 := [not-or-elim #95]: #33
 #94 := [and-elim #93]: #29
-#287 := (or #563 #28 #579)
-#561 := [def-axiom]: #287
-#518 := [unit-resolution #561 #94]: #516
-#510 := [unit-resolution #518 #529]: #579
-#512 := [symm #510]: #574
-#513 := (= #39 #571)
-#176 := (f3 #36 f5)
-#522 := (= #176 #571)
-#521 := (= #571 #176)
-#528 := (= #233 #36)
-#434 := (= #242 f9)
-#585 := (= f9 #242)
-#21 := (:var 0 S4)
-#20 := (:var 1 S3)
-#19 := (:var 2 S2)
-#22 := (f4 #19 #20 #21)
-#601 := (pattern #22)
-#23 := (f3 #22 #20)
-#77 := (= #21 #23)
-#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #601) #77)
-#81 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #77)
-#602 := (iff #81 #603)
-#605 := (iff #603 #603)
-#606 := [rewrite]: #605
-#604 := [rewrite]: #602
-#607 := [trans #604 #606]: #602
-#102 := (~ #81 #81)
-#101 := (~ #77 #77)
-#116 := [refl]: #101
-#103 := [nnf-pos #116]: #102
-#24 := (= #23 #21)
-#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
-#82 := (iff #25 #81)
-#79 := (iff #24 #77)
-#80 := [rewrite]: #79
-#83 := [quant-intro #80]: #82
-#76 := [asserted]: #25
-#86 := [mp #76 #83]: #81
-#117 := [mp~ #86 #103]: #81
-#608 := [mp #117 #607]: #603
-#230 := (not #603)
-#231 := (or #230 #585)
-#232 := [quant-inst #34 #27 #35]: #231
-#433 := [unit-resolution #232 #608]: #585
+#527 := (or #428 #28 #545)
+#412 := [def-axiom]: #527
+#518 := [unit-resolution #412 #94]: #516
+#510 := [unit-resolution #518 #529]: #545
+#512 := [symm #510]: #542
+#513 := (= #39 #541)
+#267 := (f3 #36 f5)
+#522 := (= #267 #541)
+#521 := (= #541 #267)
+#528 := (= #573 #36)
+#434 := (= #176 f9)
+#263 := (= f9 #176)
+#10 := (:var 0 S4)
+#9 := (:var 1 S3)
+#8 := (:var 2 S2)
+#11 := (f4 #8 #9 #10)
+#594 := (pattern #11)
+#12 := (f3 #11 #9)
+#64 := (= #10 #12)
+#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #594) #64)
+#67 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #64)
+#595 := (iff #67 #596)
+#598 := (iff #596 #596)
+#599 := [rewrite]: #598
+#597 := [rewrite]: #595
+#600 := [trans #597 #599]: #595
+#114 := (~ #67 #67)
+#112 := (~ #64 #64)
+#113 := [refl]: #112
+#115 := [nnf-pos #113]: #114
+#13 := (= #12 #10)
+#14 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #13)
+#68 := (iff #14 #67)
+#65 := (iff #13 #64)
+#66 := [rewrite]: #65
+#69 := [quant-intro #66]: #68
+#63 := [asserted]: #14
+#72 := [mp #63 #69]: #67
+#100 := [mp~ #72 #115]: #67
+#601 := [mp #100 #600]: #596
+#178 := (not #596)
+#265 := (or #178 #263)
+#256 := [quant-inst #34 #27 #35]: #265
+#433 := [unit-resolution #256 #601]: #263
 #435 := [symm #433]: #434
 #525 := [monotonicity #435]: #528
 #517 := [monotonicity #525]: #521
 #511 := [symm #517]: #522
-#263 := (= #39 #176)
-#177 := (= f10 #39)
-#267 := (ite #31 #177 #263)
-#266 := (or #269 #267)
-#264 := (= f7 f5)
-#178 := (ite #264 #177 #263)
-#270 := (or #269 #178)
-#586 := (iff #270 #266)
-#243 := (iff #266 #266)
-#375 := [rewrite]: #243
-#268 := (iff #178 #267)
-#265 := (iff #264 #31)
-#256 := [rewrite]: #265
-#196 := [monotonicity #256]: #268
-#588 := [monotonicity #196]: #586
-#582 := [trans #588 #375]: #586
-#249 := [quant-inst #36 #30 #37 #26]: #270
-#254 := [mp #249 #582]: #266
-#507 := [unit-resolution #254 #600]: #267
-#255 := (not #267)
-#509 := (or #255 #263)
+#268 := (= #39 #267)
+#266 := (= f10 #39)
+#243 := (ite #31 #266 #268)
+#255 := (or #254 #243)
+#270 := (= f7 f5)
+#249 := (ite #270 #266 #268)
+#589 := (or #254 #249)
+#591 := (iff #589 #255)
+#587 := (iff #255 #255)
+#593 := [rewrite]: #587
+#375 := (iff #249 #243)
+#586 := (iff #270 #31)
+#588 := [rewrite]: #586
+#582 := [monotonicity #588]: #375
+#592 := [monotonicity #582]: #591
+#583 := [trans #592 #593]: #591
+#590 := [quant-inst #36 #30 #37 #26]: #589
+#241 := [mp #590 #583]: #255
+#507 := [unit-resolution #241 #608]: #243
+#246 := (not #243)
+#509 := (or #246 #268)
 #96 := [and-elim #93]: #32
-#591 := (or #255 #31 #263)
-#592 := [def-axiom]: #591
-#519 := [unit-resolution #592 #96]: #509
-#520 := [unit-resolution #519 #507]: #263
+#585 := (or #246 #31 #268)
+#226 := [def-axiom]: #585
+#519 := [unit-resolution #226 #96]: #509
+#520 := [unit-resolution #519 #507]: #268
 #514 := [trans #520 #511]: #513
 #508 := [trans #514 #512]: #41
 #97 := (not #41)
@@ -13318,9 +13379,9 @@
 #94 := [not-or-elim #88]: #93
 [mp #94 #115]: false
 unsat
-b9360163b10b7a2a34fb792ababcc1898c7e5b1c 138 0
-#2 := false
-decl f3 :: (-> S2 S2)
+55388cf0134b951cf42c3bbd8cd933c386d4af72 138 0
+#2 := false
+decl f4 :: (-> S2 S2)
 decl f5 :: (-> Int S2)
 decl f6 :: (-> Int Int)
 decl f7 :: Int
@@ -13328,49 +13389,49 @@
 #19 := (f6 f7)
 #20 := (f6 #19)
 #21 := (f5 #20)
-#22 := (f3 #21)
+#22 := (f4 #21)
 #70 := (= #21 #22)
 #106 := (not #70)
-decl f4 :: (-> S1 S1)
+decl f3 :: (-> S1 S1)
 decl f1 :: S1
 #4 := f1
-#24 := (f4 f1)
+#24 := (f3 f1)
 #74 := (= f1 #24)
 #107 := (not #74)
 #579 := [hypothesis]: #107
-#12 := (:var 0 S1)
-#13 := (f4 #12)
-#598 := (pattern #13)
-#60 := (= f1 #12)
-#56 := (= f1 #13)
-#63 := (iff #56 #60)
-#599 := (forall (vars (?v0 S1)) (:pat #598) #63)
-#66 := (forall (vars (?v0 S1)) #63)
-#602 := (iff #66 #599)
-#600 := (iff #63 #63)
-#601 := [refl]: #600
-#603 := [quant-intro #601]: #602
-#94 := (~ #66 #66)
-#93 := (~ #63 #63)
-#104 := [refl]: #93
-#95 := [nnf-pos #104]: #94
-#15 := (= #12 f1)
-#14 := (= #13 f1)
-#16 := (iff #14 #15)
-#17 := (forall (vars (?v0 S1)) #16)
-#67 := (iff #17 #66)
-#64 := (iff #16 #63)
-#61 := (iff #15 #60)
-#62 := [rewrite]: #61
-#58 := (iff #14 #56)
-#59 := [rewrite]: #58
-#65 := [monotonicity #59 #62]: #64
-#68 := [quant-intro #65]: #67
-#55 := [asserted]: #17
-#71 := [mp #55 #68]: #66
-#105 := [mp~ #71 #95]: #66
-#604 := [mp #105 #603]: #599
-#265 := (not #599)
+#8 := (:var 0 S1)
+#9 := (f3 #8)
+#591 := (pattern #9)
+#52 := (= f1 #8)
+#49 := (= f1 #9)
+#55 := (iff #49 #52)
+#592 := (forall (vars (?v0 S1)) (:pat #591) #55)
+#58 := (forall (vars (?v0 S1)) #55)
+#595 := (iff #58 #592)
+#593 := (iff #55 #55)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#102 := (~ #58 #58)
+#100 := (~ #55 #55)
+#101 := [refl]: #100
+#103 := [nnf-pos #101]: #102
+#11 := (= #8 f1)
+#10 := (= #9 f1)
+#12 := (iff #10 #11)
+#13 := (forall (vars (?v0 S1)) #12)
+#59 := (iff #13 #58)
+#56 := (iff #12 #55)
+#53 := (iff #11 #52)
+#54 := [rewrite]: #53
+#50 := (iff #10 #49)
+#51 := [rewrite]: #50
+#57 := [monotonicity #51 #54]: #56
+#60 := [quant-intro #57]: #59
+#48 := [asserted]: #13
+#63 := [mp #48 #60]: #58
+#91 := [mp~ #63 #103]: #58
+#597 := [mp #91 #596]: #592
+#265 := (not #592)
 #193 := (or #265 #74)
 #173 := (= f1 f1)
 #260 := (iff #74 #173)
@@ -13392,7 +13453,7 @@
 #240 := [trans #246 #585]: #267
 #263 := [quant-inst #4]: #266
 #372 := [mp #263 #240]: #193
-#251 := [unit-resolution #372 #604 #579]: false
+#251 := [unit-resolution #372 #597 #579]: false
 #252 := [lemma #251]: #74
 #96 := (or #106 #107)
 #84 := (and #70 #74)
@@ -13428,493 +13489,758 @@
 #92 := [mp #69 #89]: #87
 #115 := [mp #92 #114]: #96
 #586 := [unit-resolution #115 #252]: #106
-#8 := (:var 0 S2)
-#9 := (f3 #8)
-#591 := (pattern #9)
-#49 := (= #8 #9)
-#592 := (forall (vars (?v0 S2)) (:pat #591) #49)
-#52 := (forall (vars (?v0 S2)) #49)
-#595 := (iff #52 #592)
-#593 := (iff #49 #49)
-#594 := [refl]: #593
-#596 := [quant-intro #594]: #595
-#102 := (~ #52 #52)
-#100 := (~ #49 #49)
-#101 := [refl]: #100
-#103 := [nnf-pos #101]: #102
-#10 := (= #9 #8)
-#11 := (forall (vars (?v0 S2)) #10)
-#53 := (iff #11 #52)
-#50 := (iff #10 #49)
-#51 := [rewrite]: #50
-#54 := [quant-intro #51]: #53
-#48 := [asserted]: #11
-#57 := [mp #48 #54]: #52
-#91 := [mp~ #57 #103]: #52
-#597 := [mp #91 #596]: #592
-#588 := (not #592)
+#14 := (:var 0 S2)
+#15 := (f4 #14)
+#598 := (pattern #15)
+#62 := (= #14 #15)
+#599 := (forall (vars (?v0 S2)) (:pat #598) #62)
+#66 := (forall (vars (?v0 S2)) #62)
+#602 := (iff #66 #599)
+#600 := (iff #62 #62)
+#601 := [refl]: #600
+#603 := [quant-intro #601]: #602
+#94 := (~ #66 #66)
+#93 := (~ #62 #62)
+#104 := [refl]: #93
+#95 := [nnf-pos #104]: #94
+#16 := (= #15 #14)
+#17 := (forall (vars (?v0 S2)) #16)
+#67 := (iff #17 #66)
+#64 := (iff #16 #62)
+#65 := [rewrite]: #64
+#68 := [quant-intro #65]: #67
+#61 := [asserted]: #17
+#71 := [mp #61 #68]: #66
+#105 := [mp~ #71 #95]: #66
+#604 := [mp #105 #603]: #599
+#588 := (not #599)
 #589 := (or #588 #70)
 #584 := [quant-inst #21]: #589
-[unit-resolution #584 #597 #586]: false
-unsat
-81c1cc5fc7edfc96b965f4e15b374acf04ca9046 458 0
-#2 := false
-decl f8 :: (-> S2 S4 S4)
-decl f9 :: S4
-#29 := f9
+[unit-resolution #584 #604 #586]: false
+unsat
+c2e9404480cb814492148c359fbbbb3b0e606571 54 0
+#2 := false
+#1 := true
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S1 S1)
+decl f2 :: S1
+#5 := f2
+decl f4 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#10 := (= #9 f1)
+#11 := (exists (vars (?v0 S2)) #10)
+#12 := (ite #11 f1 f2)
+#13 := (f3 #12)
+#14 := (= #13 f1)
+#15 := (implies #14 true)
+#16 := (not #15)
+#69 := (iff #16 false)
+#64 := (not true)
+#67 := (iff #64 false)
+#68 := [rewrite]: #67
+#65 := (iff #16 #64)
+#62 := (iff #15 true)
+#37 := (= f1 #9)
+#40 := (exists (vars (?v0 S2)) #37)
+#43 := (ite #40 f1 f2)
+#46 := (f3 #43)
+#52 := (= f1 #46)
+#57 := (implies #52 true)
+#60 := (iff #57 true)
+#61 := [rewrite]: #60
+#58 := (iff #15 #57)
+#55 := (iff #14 #52)
+#49 := (= #46 f1)
+#53 := (iff #49 #52)
+#54 := [rewrite]: #53
+#50 := (iff #14 #49)
+#47 := (= #13 #46)
+#44 := (= #12 #43)
+#41 := (iff #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [quant-intro #39]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#66 := [monotonicity #63]: #65
+#70 := [trans #66 #68]: #69
+#36 := [asserted]: #16
+[mp #36 #70]: false
+unsat
+343488aeda93da0c02f8ac1558cbc54ab37a2bb9 54 0
+#2 := false
+#1 := true
+decl f1 :: S1
+#4 := f1
+decl f3 :: (-> S1 S1)
+decl f2 :: S1
+#5 := f2
+decl f4 :: (-> S2 S1)
+#8 := (:var 0 S2)
+#9 := (f4 #8)
+#10 := (= #9 f1)
+#11 := (forall (vars (?v0 S2)) #10)
+#12 := (ite #11 f1 f2)
+#13 := (f3 #12)
+#14 := (= #13 f1)
+#15 := (implies #14 true)
+#16 := (not #15)
+#69 := (iff #16 false)
+#64 := (not true)
+#67 := (iff #64 false)
+#68 := [rewrite]: #67
+#65 := (iff #16 #64)
+#62 := (iff #15 true)
+#37 := (= f1 #9)
+#40 := (forall (vars (?v0 S2)) #37)
+#43 := (ite #40 f1 f2)
+#46 := (f3 #43)
+#52 := (= f1 #46)
+#57 := (implies #52 true)
+#60 := (iff #57 true)
+#61 := [rewrite]: #60
+#58 := (iff #15 #57)
+#55 := (iff #14 #52)
+#49 := (= #46 f1)
+#53 := (iff #49 #52)
+#54 := [rewrite]: #53
+#50 := (iff #14 #49)
+#47 := (= #13 #46)
+#44 := (= #12 #43)
+#41 := (iff #11 #40)
+#38 := (iff #10 #37)
+#39 := [rewrite]: #38
+#42 := [quant-intro #39]: #41
+#45 := [monotonicity #42]: #44
+#48 := [monotonicity #45]: #47
+#51 := [monotonicity #48]: #50
+#56 := [trans #51 #54]: #55
+#59 := [monotonicity #56]: #58
+#63 := [trans #59 #61]: #62
+#66 := [monotonicity #63]: #65
+#70 := [trans #66 #68]: #69
+#36 := [asserted]: #16
+[mp #36 #70]: false
+unsat
+46a14fd6aa65cfd8a30d4b0b44a855a19c19f288 8 0
+#2 := false
+#1 := true
+#24 := (not true)
+#53 := (iff #24 false)
+#55 := [rewrite]: #53
+#52 := [asserted]: #24
+[mp #52 #55]: false
+unsat
+ad406fc43130e24f380abadc1fc8a246fab490af 145 0
+#2 := false
+decl f3 :: (-> S2 Int S1)
+#22 := 42::Int
+decl f4 :: (-> S3 Int S2)
+#20 := 3::Int
+decl f6 :: S3
+#18 := f6
+#21 := (f4 f6 3::Int)
+#23 := (f3 #21 42::Int)
+decl f1 :: S1
+#4 := f1
+#86 := (= f1 #23)
+decl f5 :: S3
+#8 := f5
+#255 := (f4 f5 3::Int)
+#246 := (f3 #255 42::Int)
+#568 := (= #246 #23)
+#207 := (= #23 #246)
+#202 := (= #21 #255)
+#558 := (= #255 #21)
+#83 := (= f5 f6)
+#92 := (not #83)
+#93 := (or #92 #86)
+#98 := (not #93)
+#24 := (= #23 f1)
+#19 := (= f6 f5)
+#25 := (implies #19 #24)
+#26 := (not #25)
+#99 := (iff #26 #98)
+#96 := (iff #25 #93)
+#89 := (implies #83 #86)
+#94 := (iff #89 #93)
+#95 := [rewrite]: #94
+#90 := (iff #25 #89)
+#87 := (iff #24 #86)
+#88 := [rewrite]: #87
+#84 := (iff #19 #83)
+#85 := [rewrite]: #84
+#91 := [monotonicity #85 #88]: #90
+#97 := [trans #91 #95]: #96
+#100 := [monotonicity #97]: #99
+#82 := [asserted]: #26
+#103 := [mp #82 #100]: #98
+#101 := [not-or-elim #103]: #83
+#564 := [monotonicity #101]: #558
+#565 := [symm #564]: #202
+#208 := [monotonicity #565]: #207
+#566 := [symm #208]: #568
+#257 := (= f1 #246)
+#11 := (:var 0 Int)
+#9 := (:var 1 Int)
+#10 := (f4 f5 #9)
+#12 := (f3 #10 #11)
+#13 := (pattern #12)
+#64 := 0::Int
+#61 := -1::Int
+#62 := (* -1::Int #11)
+#63 := (+ #9 #62)
+#65 := (<= #63 0::Int)
+#47 := (= f1 #12)
+#71 := (iff #47 #65)
+#76 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #13) #71)
+#116 := (~ #76 #76)
+#114 := (~ #71 #71)
+#115 := [refl]: #114
+#117 := [nnf-pos #115]: #116
+#15 := (<= #9 #11)
+#14 := (= #12 f1)
+#16 := (iff #14 #15)
+#17 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #13) #16)
+#79 := (iff #17 #76)
+#53 := (iff #15 #47)
+#58 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #13) #53)
+#77 := (iff #58 #76)
+#74 := (iff #53 #71)
+#68 := (iff #65 #47)
+#72 := (iff #68 #71)
+#73 := [rewrite]: #72
+#69 := (iff #53 #68)
+#66 := (iff #15 #65)
+#67 := [rewrite]: #66
+#70 := [monotonicity #67]: #69
+#75 := [trans #70 #73]: #74
+#78 := [quant-intro #75]: #77
+#59 := (iff #17 #58)
+#56 := (iff #16 #53)
+#50 := (iff #47 #15)
+#54 := (iff #50 #53)
+#55 := [rewrite]: #54
+#51 := (iff #16 #50)
+#48 := (iff #14 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#57 := [trans #52 #55]: #56
+#60 := [quant-intro #57]: #59
+#80 := [trans #60 #78]: #79
+#46 := [asserted]: #17
+#81 := [mp #46 #80]: #76
+#106 := [mp~ #81 #117]: #76
+#557 := (not #76)
+#220 := (or #557 #257)
+#168 := (* -1::Int 42::Int)
+#253 := (+ 3::Int #168)
+#254 := (<= #253 0::Int)
+#258 := (iff #257 #254)
+#221 := (or #557 #258)
+#223 := (iff #221 #220)
+#560 := (iff #220 #220)
+#561 := [rewrite]: #560
+#573 := (iff #258 #257)
+#1 := true
+#571 := (iff #257 true)
+#572 := (iff #571 #257)
+#232 := [rewrite]: #572
+#231 := (iff #258 #571)
+#575 := (iff #254 true)
+#576 := -39::Int
+#245 := (<= -39::Int 0::Int)
+#579 := (iff #245 true)
+#580 := [rewrite]: #579
+#577 := (iff #254 #245)
+#570 := (= #253 -39::Int)
+#186 := -42::Int
+#260 := (+ 3::Int -42::Int)
+#233 := (= #260 -39::Int)
+#363 := [rewrite]: #233
+#239 := (= #253 #260)
+#259 := (= #168 -42::Int)
+#256 := [rewrite]: #259
+#574 := [monotonicity #256]: #239
+#244 := [trans #574 #363]: #570
+#578 := [monotonicity #244]: #577
+#581 := [trans #578 #580]: #575
+#236 := [monotonicity #581]: #231
+#216 := [trans #236 #232]: #573
+#559 := [monotonicity #216]: #223
+#562 := [trans #559 #561]: #223
+#222 := [quant-inst #20 #22]: #221
+#563 := [mp #222 #562]: #220
+#567 := [unit-resolution #563 #106]: #257
+#569 := [trans #567 #566]: #86
+#102 := (not #86)
+#104 := [not-or-elim #103]: #102
+[unit-resolution #104 #569]: false
+unsat
+05590bf1e80ec72a93326bf55eec9fe7b56de9d9 458 0
+#2 := false
+decl f12 :: (-> S2 S4 S4)
+decl f8 :: S4
+#19 := f8
 decl f5 :: (-> Int S2)
-#39 := 2::Int
-#40 := (f5 2::Int)
-#41 := (f8 #40 f9)
+#65 := 2::Int
+#66 := (f5 2::Int)
+#67 := (f12 #66 f8)
 #13 := 1::Int
-#35 := (f5 1::Int)
-#42 := (f8 #35 #41)
+#61 := (f5 1::Int)
+#68 := (f12 #61 #67)
 decl f7 :: (-> S3 S4 S4)
-#36 := (f8 #35 f9)
-#33 := 0::Int
-#34 := (f5 0::Int)
-#37 := (f8 #34 #36)
+#62 := (f12 #61 f8)
+#59 := 0::Int
+#60 := (f5 0::Int)
+#63 := (f12 #60 #62)
 decl f4 :: S3
 #8 := f4
-#38 := (f7 f4 #37)
-#43 := (= #38 #42)
-#275 := (f7 f4 #36)
+#64 := (f7 f4 #63)
+#69 := (= #64 #68)
+#339 := (f7 f4 #62)
 decl f3 :: (-> S3 S2 S2)
-#360 := (f3 f4 #34)
-#276 := (f8 #360 #275)
-#317 := (= #276 #42)
-#316 := (= #42 #276)
-#369 := (= #41 #275)
-#530 := (f7 f4 f9)
-#531 := (f3 f4 #35)
-#624 := (f8 #531 #530)
-#377 := (= #624 #275)
-#621 := (= #275 #624)
-#20 := (:var 0 S4)
-#18 := (:var 2 S3)
-#24 := (f7 #18 #20)
-#19 := (:var 1 S2)
-#23 := (f3 #18 #19)
-#25 := (f8 #23 #24)
-#691 := (pattern #25)
-#21 := (f8 #19 #20)
-#22 := (f7 #18 #21)
-#690 := (pattern #22)
-#26 := (= #22 #25)
-#692 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #690 #691) #26)
-#27 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #26)
-#695 := (iff #27 #692)
-#693 := (iff #26 #26)
-#694 := [refl]: #693
-#696 := [quant-intro #694]: #695
-#190 := (~ #27 #27)
-#189 := (~ #26 #26)
-#208 := [refl]: #189
-#191 := [nnf-pos #208]: #190
-#91 := [asserted]: #27
-#209 := [mp~ #91 #191]: #27
-#697 := [mp #209 #696]: #692
-#364 := (not #692)
-#614 := (or #364 #621)
-#606 := [quant-inst #8 #35 #29]: #614
-#414 := [unit-resolution #606 #697]: #621
-#378 := [symm #414]: #377
-#395 := (= #41 #624)
-#618 := (= f9 #530)
-#28 := (:var 0 S3)
-#30 := (f7 #28 f9)
-#698 := (pattern #30)
-#94 := (= f9 #30)
-#699 := (forall (vars (?v0 S3)) (:pat #698) #94)
-#97 := (forall (vars (?v0 S3)) #94)
-#702 := (iff #97 #699)
-#700 := (iff #94 #94)
-#701 := [refl]: #700
-#703 := [quant-intro #701]: #702
-#192 := (~ #97 #97)
-#210 := (~ #94 #94)
-#211 := [refl]: #210
-#193 := [nnf-pos #211]: #192
-#31 := (= #30 f9)
-#32 := (forall (vars (?v0 S3)) #31)
-#98 := (iff #32 #97)
-#95 := (iff #31 #94)
-#96 := [rewrite]: #95
-#99 := [quant-intro #96]: #98
-#92 := [asserted]: #32
-#102 := [mp #92 #99]: #97
-#212 := [mp~ #102 #193]: #97
-#704 := [mp #212 #703]: #699
-#609 := (not #699)
-#610 := (or #609 #618)
-#604 := [quant-inst #8]: #610
-#415 := [unit-resolution #604 #704]: #618
-#394 := (= #40 #531)
+#424 := (f3 f4 #60)
+#340 := (f12 #424 #339)
+#381 := (= #340 #68)
+#380 := (= #68 #340)
+#433 := (= #67 #339)
+#594 := (f7 f4 f8)
+#595 := (f3 f4 #61)
+#688 := (f12 #595 #594)
+#441 := (= #688 #339)
+#685 := (= #339 #688)
+#34 := (:var 0 S4)
+#32 := (:var 2 S3)
+#38 := (f7 #32 #34)
+#33 := (:var 1 S2)
+#37 := (f3 #32 #33)
+#39 := (f12 #37 #38)
+#776 := (pattern #39)
+#35 := (f12 #33 #34)
+#36 := (f7 #32 #35)
+#775 := (pattern #36)
+#40 := (= #36 #39)
+#777 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) (:pat #775 #776) #40)
+#41 := (forall (vars (?v0 S3) (?v1 S2) (?v2 S4)) #40)
+#780 := (iff #41 #777)
+#778 := (iff #40 #40)
+#779 := [refl]: #778
+#781 := [quant-intro #779]: #780
+#240 := (~ #41 #41)
+#268 := (~ #40 #40)
+#269 := [refl]: #268
+#241 := [nnf-pos #269]: #240
+#141 := [asserted]: #41
+#270 := [mp~ #141 #241]: #41
+#782 := [mp #270 #781]: #777
+#428 := (not #777)
+#678 := (or #428 #685)
+#670 := [quant-inst #8 #61 #19]: #678
+#478 := [unit-resolution #670 #782]: #685
+#442 := [symm #478]: #441
+#459 := (= #67 #688)
+#682 := (= f8 #594)
+#18 := (:var 0 S3)
+#20 := (f7 #18 f8)
+#754 := (pattern #20)
+#118 := (= f8 #20)
+#755 := (forall (vars (?v0 S3)) (:pat #754) #118)
+#122 := (forall (vars (?v0 S3)) #118)
+#758 := (iff #122 #755)
+#756 := (iff #118 #118)
+#757 := [refl]: #756
+#759 := [quant-intro #757]: #758
+#234 := (~ #122 #122)
+#233 := (~ #118 #118)
+#260 := [refl]: #233
+#235 := [nnf-pos #260]: #234
+#21 := (= #20 f8)
+#22 := (forall (vars (?v0 S3)) #21)
+#123 := (iff #22 #122)
+#120 := (iff #21 #118)
+#121 := [rewrite]: #120
+#124 := [quant-intro #121]: #123
+#117 := [asserted]: #22
+#127 := [mp #117 #124]: #122
+#261 := [mp~ #127 #235]: #122
+#760 := [mp #261 #759]: #755
+#673 := (not #755)
+#674 := (or #673 #682)
+#668 := [quant-inst #8]: #674
+#479 := [unit-resolution #668 #760]: #682
+#458 := (= #66 #595)
 decl f6 :: (-> S2 Int)
-#677 := (f6 #35)
-#607 := (+ 1::Int #677)
-#608 := (f5 #607)
-#391 := (= #608 #531)
-#611 := (= #531 #608)
+#741 := (f6 #61)
+#671 := (+ 1::Int #741)
+#672 := (f5 #671)
+#455 := (= #672 #595)
+#675 := (= #595 #672)
 #9 := (:var 0 S2)
 #10 := (f3 f4 #9)
 #11 := (pattern #10)
 #12 := (f6 #9)
-#79 := (+ 1::Int #12)
-#82 := (f5 #79)
-#85 := (= #10 #82)
-#88 := (forall (vars (?v0 S2)) (:pat #11) #85)
-#206 := (~ #88 #88)
-#204 := (~ #85 #85)
-#205 := [refl]: #204
-#207 := [nnf-pos #205]: #206
+#105 := (+ 1::Int #12)
+#108 := (f5 #105)
+#111 := (= #10 #108)
+#114 := (forall (vars (?v0 S2)) (:pat #11) #111)
+#258 := (~ #114 #114)
+#256 := (~ #111 #111)
+#257 := [refl]: #256
+#259 := [nnf-pos #257]: #258
 #14 := (+ #12 1::Int)
 #15 := (f5 #14)
 #16 := (= #10 #15)
 #17 := (forall (vars (?v0 S2)) (:pat #11) #16)
-#89 := (iff #17 #88)
-#86 := (iff #16 #85)
-#83 := (= #15 #82)
-#80 := (= #14 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#87 := [monotonicity #84]: #86
-#90 := [quant-intro #87]: #89
-#78 := [asserted]: #17
-#93 := [mp #78 #90]: #88
-#188 := [mp~ #93 #207]: #88
-#616 := (not #88)
-#598 := (or #616 #611)
-#599 := [quant-inst #35]: #598
-#416 := [unit-resolution #599 #188]: #611
-#392 := [symm #416]: #391
-#384 := (= #40 #608)
-#554 := (f6 #608)
-#445 := (f5 #554)
-#452 := (= #445 #608)
-#705 := (pattern #12)
-#45 := (f5 #12)
-#103 := (= #9 #45)
-#706 := (forall (vars (?v0 S2)) (:pat #705) #103)
-#106 := (forall (vars (?v0 S2)) #103)
-#707 := (iff #106 #706)
-#709 := (iff #706 #706)
-#710 := [rewrite]: #709
-#708 := [rewrite]: #707
-#711 := [trans #708 #710]: #707
-#194 := (~ #106 #106)
-#213 := (~ #103 #103)
-#214 := [refl]: #213
-#195 := [nnf-pos #214]: #194
-#46 := (= #45 #9)
-#47 := (forall (vars (?v0 S2)) #46)
-#107 := (iff #47 #106)
-#104 := (iff #46 #103)
-#105 := [rewrite]: #104
-#108 := [quant-intro #105]: #107
-#101 := [asserted]: #47
-#111 := [mp #101 #108]: #106
-#196 := [mp~ #111 #195]: #106
-#712 := [mp #196 #711]: #706
-#458 := (not #706)
-#453 := (or #458 #452)
-#448 := (= #608 #445)
-#456 := (or #458 #448)
-#447 := (iff #456 #453)
-#450 := (iff #453 #453)
-#446 := [rewrite]: #450
-#454 := (iff #448 #452)
-#455 := [rewrite]: #454
-#449 := [monotonicity #455]: #447
-#451 := [trans #449 #446]: #447
-#444 := [quant-inst #608]: #456
-#441 := [mp #444 #451]: #453
-#417 := [unit-resolution #441 #712]: #452
-#401 := (= #40 #445)
-#400 := (= 2::Int #554)
-#397 := (= #554 2::Int)
-#602 := -1::Int
-#540 := (* -1::Int #677)
-#541 := (+ #554 #540)
-#498 := (<= #541 1::Int)
-#516 := (= #541 1::Int)
-#542 := (>= #677 -1::Int)
-#552 := (>= #677 1::Int)
-#387 := (= #677 1::Int)
-#48 := (:var 0 Int)
-#50 := (f5 #48)
-#713 := (pattern #50)
-#128 := (>= #48 0::Int)
-#129 := (not #128)
-#51 := (f6 #50)
-#110 := (= #48 #51)
-#135 := (or #110 #129)
-#714 := (forall (vars (?v0 Int)) (:pat #713) #135)
-#140 := (forall (vars (?v0 Int)) #135)
-#717 := (iff #140 #714)
-#715 := (iff #135 #135)
-#716 := [refl]: #715
-#718 := [quant-intro #716]: #717
-#198 := (~ #140 #140)
-#197 := (~ #135 #135)
-#215 := [refl]: #197
-#199 := [nnf-pos #215]: #198
-#52 := (= #51 #48)
-#49 := (<= 0::Int #48)
-#53 := (implies #49 #52)
-#54 := (forall (vars (?v0 Int)) #53)
-#143 := (iff #54 #140)
-#117 := (not #49)
-#118 := (or #117 #110)
-#123 := (forall (vars (?v0 Int)) #118)
-#141 := (iff #123 #140)
-#138 := (iff #118 #135)
-#132 := (or #129 #110)
-#136 := (iff #132 #135)
-#137 := [rewrite]: #136
-#133 := (iff #118 #132)
-#130 := (iff #117 #129)
-#126 := (iff #49 #128)
-#127 := [rewrite]: #126
-#131 := [monotonicity #127]: #130
-#134 := [monotonicity #131]: #133
-#139 := [trans #134 #137]: #138
-#142 := [quant-intro #139]: #141
-#124 := (iff #54 #123)
-#121 := (iff #53 #118)
-#114 := (implies #49 #110)
-#119 := (iff #114 #118)
-#120 := [rewrite]: #119
-#115 := (iff #53 #114)
-#112 := (iff #52 #110)
-#113 := [rewrite]: #112
-#116 := [monotonicity #113]: #115
-#122 := [trans #116 #120]: #121
-#125 := [quant-intro #122]: #124
-#144 := [trans #125 #142]: #143
-#109 := [asserted]: #54
-#145 := [mp #109 #144]: #140
-#216 := [mp~ #145 #199]: #140
-#719 := [mp #216 #718]: #714
-#323 := (not #714)
-#374 := (or #323 #387)
-#676 := (>= 1::Int 0::Int)
-#674 := (not #676)
-#663 := (= 1::Int #677)
-#664 := (or #663 #674)
-#375 := (or #323 #664)
-#654 := (iff #375 #374)
-#651 := (iff #374 #374)
-#655 := [rewrite]: #651
-#372 := (iff #664 #387)
-#383 := (or #387 false)
-#658 := (iff #383 #387)
-#662 := [rewrite]: #658
-#657 := (iff #664 #383)
-#660 := (iff #674 false)
+#115 := (iff #17 #114)
+#112 := (iff #16 #111)
+#109 := (= #15 #108)
+#106 := (= #14 #105)
+#107 := [rewrite]: #106
+#110 := [monotonicity #107]: #109
+#113 := [monotonicity #110]: #112
+#116 := [quant-intro #113]: #115
+#104 := [asserted]: #17
+#119 := [mp #104 #116]: #114
+#232 := [mp~ #119 #259]: #114
+#680 := (not #114)
+#662 := (or #680 #675)
+#663 := [quant-inst #61]: #662
+#480 := [unit-resolution #663 #232]: #675
+#456 := [symm #480]: #455
+#448 := (= #66 #672)
+#618 := (f6 #672)
+#509 := (f5 #618)
+#516 := (= #509 #672)
+#799 := (pattern #12)
+#71 := (f5 #12)
+#147 := (= #9 #71)
+#800 := (forall (vars (?v0 S2)) (:pat #799) #147)
+#150 := (forall (vars (?v0 S2)) #147)
+#801 := (iff #150 #800)
+#803 := (iff #800 #800)
+#804 := [rewrite]: #803
+#802 := [rewrite]: #801
+#805 := [trans #802 #804]: #801
+#246 := (~ #150 #150)
+#277 := (~ #147 #147)
+#278 := [refl]: #277
+#247 := [nnf-pos #278]: #246
+#72 := (= #71 #9)
+#73 := (forall (vars (?v0 S2)) #72)
+#151 := (iff #73 #150)
+#148 := (iff #72 #147)
+#149 := [rewrite]: #148
+#152 := [quant-intro #149]: #151
+#146 := [asserted]: #73
+#155 := [mp #146 #152]: #150
+#248 := [mp~ #155 #247]: #150
+#806 := [mp #248 #805]: #800
+#522 := (not #800)
+#517 := (or #522 #516)
+#512 := (= #672 #509)
+#520 := (or #522 #512)
+#511 := (iff #520 #517)
+#514 := (iff #517 #517)
+#510 := [rewrite]: #514
+#518 := (iff #512 #516)
+#519 := [rewrite]: #518
+#513 := [monotonicity #519]: #511
+#515 := [trans #513 #510]: #511
+#508 := [quant-inst #672]: #520
+#505 := [mp #508 #515]: #517
+#481 := [unit-resolution #505 #806]: #516
+#465 := (= #66 #509)
+#464 := (= 2::Int #618)
+#461 := (= #618 2::Int)
+#666 := -1::Int
+#604 := (* -1::Int #741)
+#605 := (+ #618 #604)
+#562 := (<= #605 1::Int)
+#580 := (= #605 1::Int)
+#606 := (>= #741 -1::Int)
+#616 := (>= #741 1::Int)
+#451 := (= #741 1::Int)
+#74 := (:var 0 Int)
+#76 := (f5 #74)
+#807 := (pattern #76)
+#172 := (>= #74 0::Int)
+#173 := (not #172)
+#77 := (f6 #76)
+#154 := (= #74 #77)
+#179 := (or #154 #173)
+#808 := (forall (vars (?v0 Int)) (:pat #807) #179)
+#184 := (forall (vars (?v0 Int)) #179)
+#811 := (iff #184 #808)
+#809 := (iff #179 #179)
+#810 := [refl]: #809
+#812 := [quant-intro #810]: #811
+#250 := (~ #184 #184)
+#249 := (~ #179 #179)
+#279 := [refl]: #249
+#251 := [nnf-pos #279]: #250
+#78 := (= #77 #74)
+#75 := (<= 0::Int #74)
+#79 := (implies #75 #78)
+#80 := (forall (vars (?v0 Int)) #79)
+#187 := (iff #80 #184)
+#161 := (not #75)
+#162 := (or #161 #154)
+#167 := (forall (vars (?v0 Int)) #162)
+#185 := (iff #167 #184)
+#182 := (iff #162 #179)
+#176 := (or #173 #154)
+#180 := (iff #176 #179)
+#181 := [rewrite]: #180
+#177 := (iff #162 #176)
+#174 := (iff #161 #173)
+#170 := (iff #75 #172)
+#171 := [rewrite]: #170
+#175 := [monotonicity #171]: #174
+#178 := [monotonicity #175]: #177
+#183 := [trans #178 #181]: #182
+#186 := [quant-intro #183]: #185
+#168 := (iff #80 #167)
+#165 := (iff #79 #162)
+#158 := (implies #75 #154)
+#163 := (iff #158 #162)
+#164 := [rewrite]: #163
+#159 := (iff #79 #158)
+#156 := (iff #78 #154)
+#157 := [rewrite]: #156
+#160 := [monotonicity #157]: #159
+#166 := [trans #160 #164]: #165
+#169 := [quant-intro #166]: #168
+#188 := [trans #169 #186]: #187
+#153 := [asserted]: #80
+#189 := [mp #153 #188]: #184
+#280 := [mp~ #189 #251]: #184
+#813 := [mp #280 #812]: #808
+#387 := (not #808)
+#438 := (or #387 #451)
+#740 := (>= 1::Int 0::Int)
+#738 := (not #740)
+#727 := (= 1::Int #741)
+#728 := (or #727 #738)
+#439 := (or #387 #728)
+#718 := (iff #439 #438)
+#715 := (iff #438 #438)
+#719 := [rewrite]: #715
+#436 := (iff #728 #451)
+#447 := (or #451 false)
+#722 := (iff #447 #451)
+#726 := [rewrite]: #722
+#721 := (iff #728 #447)
+#724 := (iff #738 false)
 #1 := true
-#351 := (not true)
-#686 := (iff #351 false)
-#687 := [rewrite]: #686
-#282 := (iff #674 #351)
-#388 := (iff #676 true)
-#389 := [rewrite]: #388
-#659 := [monotonicity #389]: #282
-#382 := [trans #659 #687]: #660
-#371 := (iff #663 #387)
-#386 := [rewrite]: #371
-#661 := [monotonicity #386 #382]: #657
-#373 := [trans #661 #662]: #372
-#368 := [monotonicity #373]: #654
-#652 := [trans #368 #655]: #654
-#653 := [quant-inst #13]: #375
-#656 := [mp #653 #652]: #374
-#418 := [unit-resolution #656 #719]: #387
-#419 := (not #387)
-#420 := (or #419 #552)
-#421 := [th-lemma arith triangle-eq]: #420
-#422 := [unit-resolution #421 #418]: #552
-#423 := (not #552)
-#424 := (or #423 #542)
-#413 := [th-lemma arith farkas 1 1]: #424
-#425 := [unit-resolution #413 #422]: #542
-#476 := (not #542)
-#521 := (or #323 #516 #476)
-#553 := (>= #607 0::Int)
-#549 := (not #553)
-#534 := (= #607 #554)
-#480 := (or #534 #549)
-#522 := (or #323 #480)
-#495 := (iff #522 #521)
-#511 := (or #516 #476)
-#512 := (or #323 #511)
-#489 := (iff #512 #521)
-#494 := [rewrite]: #489
-#533 := (iff #522 #512)
-#518 := (iff #480 #511)
-#507 := (iff #549 #476)
-#510 := (iff #553 #542)
-#517 := [rewrite]: #510
-#509 := [monotonicity #517]: #507
-#535 := (iff #534 #516)
-#536 := [rewrite]: #535
-#520 := [monotonicity #536 #509]: #518
-#488 := [monotonicity #520]: #533
-#496 := [trans #488 #494]: #495
-#532 := [quant-inst #607]: #522
-#497 := [mp #532 #496]: #521
-#402 := [unit-resolution #497 #719 #425]: #516
-#404 := (not #516)
-#405 := (or #404 #498)
-#406 := [th-lemma arith triangle-eq]: #405
-#407 := [unit-resolution #406 #402]: #498
-#499 := (>= #541 1::Int)
-#408 := (or #404 #499)
-#409 := [th-lemma arith triangle-eq]: #408
-#410 := [unit-resolution #409 #402]: #499
-#551 := (<= #677 1::Int)
-#403 := (or #419 #551)
-#411 := [th-lemma arith triangle-eq]: #403
-#396 := [unit-resolution #411 #418]: #551
-#398 := [th-lemma arith eq-propagate -1 -1 -1 -1 #422 #396 #410 #407]: #397
-#399 := [symm #398]: #400
-#390 := [monotonicity #399]: #401
-#393 := [trans #390 #417]: #384
-#385 := [trans #393 #392]: #394
-#376 := [monotonicity #385 #415]: #395
-#379 := [trans #376 #378]: #369
-#310 := (= #35 #360)
-#363 := (f6 #34)
-#625 := (+ 1::Int #363)
-#612 := (f5 #625)
-#320 := (= #612 #360)
-#603 := (= #360 #612)
-#617 := (or #616 #603)
-#613 := [quant-inst #34]: #617
-#380 := [unit-resolution #613 #188]: #603
-#321 := [symm #380]: #320
-#319 := (= #35 #612)
-#600 := (f6 #612)
-#485 := (f5 #600)
-#469 := (= #485 #612)
-#459 := (or #458 #469)
-#486 := (= #612 #485)
-#460 := (or #458 #486)
-#463 := (iff #460 #459)
-#306 := (iff #459 #459)
-#465 := [rewrite]: #306
-#487 := (iff #486 #469)
-#457 := [rewrite]: #487
-#464 := [monotonicity #457]: #463
-#461 := [trans #464 #465]: #463
-#462 := [quant-inst #612]: #460
-#466 := [mp #462 #461]: #459
-#370 := [unit-resolution #466 #712]: #469
-#337 := (= #35 #485)
-#336 := (= 1::Int #600)
-#334 := (= #600 1::Int)
-#588 := (* -1::Int #600)
-#589 := (+ #363 #588)
-#559 := (<= #589 -1::Int)
-#591 := (= #589 -1::Int)
-#590 := (>= #363 -1::Int)
-#615 := (>= #363 0::Int)
-#340 := (= #363 0::Int)
-#665 := (or #323 #340)
-#362 := (>= 0::Int 0::Int)
-#353 := (not #362)
-#367 := (= 0::Int #363)
-#346 := (or #367 #353)
-#327 := (or #323 #346)
-#329 := (iff #327 #665)
-#667 := (iff #665 #665)
-#668 := [rewrite]: #667
-#339 := (iff #346 #340)
-#689 := (or #340 false)
-#343 := (iff #689 #340)
-#680 := [rewrite]: #343
-#679 := (iff #346 #689)
-#688 := (iff #353 false)
-#352 := (iff #353 #351)
-#471 := (iff #362 true)
-#678 := [rewrite]: #471
-#685 := [monotonicity #678]: #352
-#683 := [trans #685 #687]: #688
-#682 := (iff #367 #340)
-#684 := [rewrite]: #682
-#338 := [monotonicity #684 #683]: #679
-#681 := [trans #338 #680]: #339
-#330 := [monotonicity #681]: #329
-#669 := [trans #330 #668]: #329
-#328 := [quant-inst #33]: #327
-#670 := [mp #328 #669]: #665
-#381 := [unit-resolution #670 #719]: #340
-#347 := (not #340)
-#349 := (or #347 #615)
-#350 := [th-lemma arith triangle-eq]: #349
-#341 := [unit-resolution #350 #381]: #615
-#354 := (not #615)
-#355 := (or #354 #590)
-#356 := [th-lemma arith farkas 1 1]: #355
-#357 := [unit-resolution #356 #341]: #590
-#575 := (not #590)
-#576 := (or #323 #575 #591)
-#595 := (>= #625 0::Int)
-#596 := (not #595)
-#601 := (= #625 #600)
-#597 := (or #601 #596)
-#587 := (or #323 #597)
-#572 := (iff #587 #576)
-#582 := (or #575 #591)
-#566 := (or #323 #582)
-#570 := (iff #566 #576)
-#571 := [rewrite]: #570
-#568 := (iff #587 #566)
-#585 := (iff #597 #582)
-#579 := (or #591 #575)
-#583 := (iff #579 #582)
-#584 := [rewrite]: #583
-#580 := (iff #597 #579)
-#577 := (iff #596 #575)
-#594 := (iff #595 #590)
-#574 := [rewrite]: #594
-#578 := [monotonicity #574]: #577
-#592 := (iff #601 #591)
-#593 := [rewrite]: #592
-#581 := [monotonicity #593 #578]: #580
-#586 := [trans #581 #584]: #585
-#569 := [monotonicity #586]: #568
-#567 := [trans #569 #571]: #572
-#565 := [quant-inst #625]: #587
-#573 := [mp #565 #567]: #576
-#358 := [unit-resolution #573 #719 #357]: #591
-#348 := (not #591)
-#359 := (or #348 #559)
-#342 := [th-lemma arith triangle-eq]: #359
-#344 := [unit-resolution #342 #358]: #559
-#555 := (>= #589 -1::Int)
-#345 := (or #348 #555)
-#324 := [th-lemma arith triangle-eq]: #345
-#326 := [unit-resolution #324 #358]: #555
-#605 := (<= #363 0::Int)
-#331 := (or #347 #605)
-#332 := [th-lemma arith triangle-eq]: #331
-#333 := [unit-resolution #332 #381]: #605
-#335 := [th-lemma arith eq-propagate -1 -1 1 1 #341 #333 #326 #344]: #334
-#325 := [symm #335]: #336
-#318 := [monotonicity #325]: #337
-#322 := [trans #318 #370]: #319
-#312 := [trans #322 #321]: #310
-#311 := [monotonicity #312 #379]: #316
-#292 := [symm #311]: #317
-#361 := (= #38 #276)
-#365 := (or #364 #361)
-#366 := [quant-inst #8 #34 #36]: #365
-#313 := [unit-resolution #366 #697]: #361
-#296 := [trans #313 #292]: #43
-#44 := (not #43)
-#100 := [asserted]: #44
-[unit-resolution #100 #296]: false
+#415 := (not true)
+#750 := (iff #415 false)
+#751 := [rewrite]: #750
+#346 := (iff #738 #415)
+#452 := (iff #740 true)
+#453 := [rewrite]: #452
+#723 := [monotonicity #453]: #346
+#446 := [trans #723 #751]: #724
+#435 := (iff #727 #451)
+#450 := [rewrite]: #435
+#725 := [monotonicity #450 #446]: #721
+#437 := [trans #725 #726]: #436
+#432 := [monotonicity #437]: #718
+#716 := [trans #432 #719]: #718
+#717 := [quant-inst #13]: #439
+#720 := [mp #717 #716]: #438
+#482 := [unit-resolution #720 #813]: #451
+#483 := (not #451)
+#484 := (or #483 #616)
+#485 := [th-lemma arith triangle-eq]: #484
+#486 := [unit-resolution #485 #482]: #616
+#487 := (not #616)
+#488 := (or #487 #606)
+#477 := [th-lemma arith farkas 1 1]: #488
+#489 := [unit-resolution #477 #486]: #606
+#540 := (not #606)
+#585 := (or #387 #580 #540)
+#617 := (>= #671 0::Int)
+#613 := (not #617)
+#598 := (= #671 #618)
+#544 := (or #598 #613)
+#586 := (or #387 #544)
+#559 := (iff #586 #585)
+#575 := (or #580 #540)
+#576 := (or #387 #575)
+#553 := (iff #576 #585)
+#558 := [rewrite]: #553
+#597 := (iff #586 #576)
+#582 := (iff #544 #575)
+#571 := (iff #613 #540)
+#574 := (iff #617 #606)
+#581 := [rewrite]: #574
+#573 := [monotonicity #581]: #571
+#599 := (iff #598 #580)
+#600 := [rewrite]: #599
+#584 := [monotonicity #600 #573]: #582
+#552 := [monotonicity #584]: #597
+#560 := [trans #552 #558]: #559
+#596 := [quant-inst #671]: #586
+#561 := [mp #596 #560]: #585
+#466 := [unit-resolution #561 #813 #489]: #580
+#468 := (not #580)
+#469 := (or #468 #562)
+#470 := [th-lemma arith triangle-eq]: #469
+#471 := [unit-resolution #470 #466]: #562
+#563 := (>= #605 1::Int)
+#472 := (or #468 #563)
+#473 := [th-lemma arith triangle-eq]: #472
+#474 := [unit-resolution #473 #466]: #563
+#615 := (<= #741 1::Int)
+#467 := (or #483 #615)
+#475 := [th-lemma arith triangle-eq]: #467
+#460 := [unit-resolution #475 #482]: #615
+#462 := [th-lemma arith eq-propagate -1 -1 -1 -1 #486 #460 #474 #471]: #461
+#463 := [symm #462]: #464
+#454 := [monotonicity #463]: #465
+#457 := [trans #454 #481]: #448
+#449 := [trans #457 #456]: #458
+#440 := [monotonicity #449 #479]: #459
+#443 := [trans #440 #442]: #433
+#374 := (= #61 #424)
+#427 := (f6 #60)
+#689 := (+ 1::Int #427)
+#676 := (f5 #689)
+#384 := (= #676 #424)
+#667 := (= #424 #676)
+#681 := (or #680 #667)
+#677 := [quant-inst #60]: #681
+#444 := [unit-resolution #677 #232]: #667
+#385 := [symm #444]: #384
+#383 := (= #61 #676)
+#664 := (f6 #676)
+#549 := (f5 #664)
+#533 := (= #549 #676)
+#523 := (or #522 #533)
+#550 := (= #676 #549)
+#524 := (or #522 #550)
+#527 := (iff #524 #523)
+#370 := (iff #523 #523)
+#529 := [rewrite]: #370
+#551 := (iff #550 #533)
+#521 := [rewrite]: #551
+#528 := [monotonicity #521]: #527
+#525 := [trans #528 #529]: #527
+#526 := [quant-inst #676]: #524
+#530 := [mp #526 #525]: #523
+#434 := [unit-resolution #530 #806]: #533
+#401 := (= #61 #549)
+#400 := (= 1::Int #664)
+#398 := (= #664 1::Int)
+#652 := (* -1::Int #664)
+#653 := (+ #427 #652)
+#623 := (<= #653 -1::Int)
+#655 := (= #653 -1::Int)
+#654 := (>= #427 -1::Int)
+#679 := (>= #427 0::Int)
+#404 := (= #427 0::Int)
+#729 := (or #387 #404)
+#426 := (>= 0::Int 0::Int)
+#417 := (not #426)
+#431 := (= 0::Int #427)
+#410 := (or #431 #417)
+#391 := (or #387 #410)
+#393 := (iff #391 #729)
+#731 := (iff #729 #729)
+#732 := [rewrite]: #731
+#403 := (iff #410 #404)
+#753 := (or #404 false)
+#407 := (iff #753 #404)
+#744 := [rewrite]: #407
+#743 := (iff #410 #753)
+#752 := (iff #417 false)
+#416 := (iff #417 #415)
+#535 := (iff #426 true)
+#742 := [rewrite]: #535
+#749 := [monotonicity #742]: #416
+#747 := [trans #749 #751]: #752
+#746 := (iff #431 #404)
+#748 := [rewrite]: #746
+#402 := [monotonicity #748 #747]: #743
+#745 := [trans #402 #744]: #403
+#394 := [monotonicity #745]: #393
+#733 := [trans #394 #732]: #393
+#392 := [quant-inst #59]: #391
+#734 := [mp #392 #733]: #729
+#445 := [unit-resolution #734 #813]: #404
+#411 := (not #404)
+#413 := (or #411 #679)
+#414 := [th-lemma arith triangle-eq]: #413
+#405 := [unit-resolution #414 #445]: #679
+#418 := (not #679)
+#419 := (or #418 #654)
+#420 := [th-lemma arith farkas 1 1]: #419
+#421 := [unit-resolution #420 #405]: #654
+#639 := (not #654)
+#640 := (or #387 #639 #655)
+#659 := (>= #689 0::Int)
+#660 := (not #659)
+#665 := (= #689 #664)
+#661 := (or #665 #660)
+#651 := (or #387 #661)
+#636 := (iff #651 #640)
+#646 := (or #639 #655)
+#630 := (or #387 #646)
+#634 := (iff #630 #640)
+#635 := [rewrite]: #634
+#632 := (iff #651 #630)
+#649 := (iff #661 #646)
+#643 := (or #655 #639)
+#647 := (iff #643 #646)
+#648 := [rewrite]: #647
+#644 := (iff #661 #643)
+#641 := (iff #660 #639)
+#658 := (iff #659 #654)
+#638 := [rewrite]: #658
+#642 := [monotonicity #638]: #641
+#656 := (iff #665 #655)
+#657 := [rewrite]: #656
+#645 := [monotonicity #657 #642]: #644
+#650 := [trans #645 #648]: #649
+#633 := [monotonicity #650]: #632
+#631 := [trans #633 #635]: #636
+#629 := [quant-inst #689]: #651
+#637 := [mp #629 #631]: #640
+#422 := [unit-resolution #637 #813 #421]: #655
+#412 := (not #655)
+#423 := (or #412 #623)
+#406 := [th-lemma arith triangle-eq]: #423
+#408 := [unit-resolution #406 #422]: #623
+#619 := (>= #653 -1::Int)
+#409 := (or #412 #619)
+#388 := [th-lemma arith triangle-eq]: #409
+#390 := [unit-resolution #388 #422]: #619
+#669 := (<= #427 0::Int)
+#395 := (or #411 #669)
+#396 := [th-lemma arith triangle-eq]: #395
+#397 := [unit-resolution #396 #445]: #669
+#399 := [th-lemma arith eq-propagate -1 -1 1 1 #405 #397 #390 #408]: #398
+#389 := [symm #399]: #400
+#382 := [monotonicity #389]: #401
+#386 := [trans #382 #434]: #383
+#376 := [trans #386 #385]: #374
+#375 := [monotonicity #376 #443]: #380
+#356 := [symm #375]: #381
+#425 := (= #64 #340)
+#429 := (or #428 #425)
+#430 := [quant-inst #8 #60 #62]: #429
+#377 := [unit-resolution #430 #782]: #425
+#360 := [trans #377 #356]: #69
+#70 := (not #69)
+#145 := [asserted]: #70
+[unit-resolution #145 #360]: false
 unsat
 b18aa009c5b54d915c2c9feecd9762a9bb0c27b5 38 0
 #2 := false
@@ -14332,536 +14658,37 @@
 unsat
 cbddab0a93fe2901d1f5dd30bb313d7532a1c531 1 0
 unsat
-a7ba12fdd24a1cfe15f53475941aaf6855022b7f 76 0
-#2 := false
-decl f28 :: (-> Int S1)
-#107 := 1::Int
-#108 := (f28 1::Int)
-decl f1 :: S1
-#4 := f1
-#382 := (= f1 #108)
-#386 := (not #382)
-#109 := (= #108 f1)
-#110 := (not #109)
-#387 := (iff #110 #386)
-#384 := (iff #109 #382)
-#385 := [rewrite]: #384
-#388 := [monotonicity #385]: #387
-#381 := [asserted]: #110
-#391 := [mp #381 #388]: #386
-#96 := (:var 0 Int)
-#97 := (f28 #96)
-#965 := (pattern #97)
-#354 := (= f1 #97)
-#966 := (forall (vars (?v0 Int)) (:pat #965) #354)
-#378 := (forall (vars (?v0 Int)) #354)
-#969 := (iff #378 #966)
-#967 := (iff #354 #354)
-#968 := [refl]: #967
-#970 := [quant-intro #968]: #969
-#407 := (~ #378 #378)
-#437 := (~ #354 #354)
-#438 := [refl]: #437
-#408 := [nnf-pos #438]: #407
-decl f3 :: (-> S2 S1)
-decl f29 :: (-> Int S2 S2)
-decl f30 :: S2
-#99 := f30
-#100 := (f29 #96 f30)
-#101 := (f3 #100)
-#102 := (= #101 f1)
-#103 := (not #102)
-#104 := (or #102 #103)
-#98 := (= #97 f1)
-#105 := (and #98 #104)
-#106 := (forall (vars (?v0 Int)) #105)
-#379 := (iff #106 #378)
-#376 := (iff #105 #354)
-#1 := true
-#371 := (and #354 true)
-#374 := (iff #371 #354)
-#375 := [rewrite]: #374
-#372 := (iff #105 #371)
-#369 := (iff #104 true)
-#358 := (= f1 #101)
-#361 := (not #358)
-#364 := (or #358 #361)
-#367 := (iff #364 true)
-#368 := [rewrite]: #367
-#365 := (iff #104 #364)
-#362 := (iff #103 #361)
-#359 := (iff #102 #358)
-#360 := [rewrite]: #359
-#363 := [monotonicity #360]: #362
-#366 := [monotonicity #360 #363]: #365
-#370 := [trans #366 #368]: #369
-#356 := (iff #98 #354)
-#357 := [rewrite]: #356
-#373 := [monotonicity #357 #370]: #372
-#377 := [trans #373 #375]: #376
-#380 := [quant-intro #377]: #379
-#353 := [asserted]: #106
-#383 := [mp #353 #380]: #378
-#439 := [mp~ #383 #408]: #378
-#971 := [mp #439 #970]: #966
-#494 := (not #966)
-#579 := (or #494 #382)
-#580 := [quant-inst #107]: #579
-[unit-resolution #580 #971 #391]: false
-unsat
-24f7b95c280da62e693df186e53d1c34ad016474 421 0
-#2 := false
-decl f19 :: (-> S8 S3)
-decl f22 :: (-> S1 S8)
+8dfc32ec0576a35c6d7e7c764cb46b73661ecad4 76 0
+#2 := false
+decl f3 :: (-> Int S1)
+#63 := 1::Int
+#64 := (f3 1::Int)
 decl f1 :: S1
 #4 := f1
-#101 := (f22 f1)
-#102 := (f19 #101)
-decl f17 :: (-> S7 S3)
-decl f21 :: (-> Int S7)
-#98 := 3::Int
-#99 := (f21 3::Int)
-#100 := (f17 #99)
-#103 := (= #100 #102)
-decl f16 :: (-> S4 S3)
-decl f8 :: (-> S1 S4 S4)
-decl f10 :: S4
-#35 := f10
-#884 := (f8 f1 f10)
-#886 := (f16 #884)
-#640 := (= #886 #102)
-#553 := (= #102 #886)
-#91 := (:var 0 S1)
-#94 := (f8 #91 f10)
-#959 := (pattern #94)
-#92 := (f22 #91)
-#958 := (pattern #92)
-#95 := (f16 #94)
-#93 := (f19 #92)
-#96 := (= #93 #95)
-#960 := (forall (vars (?v0 S1)) (:pat #958 #959) #96)
-#97 := (forall (vars (?v0 S1)) #96)
-#963 := (iff #97 #960)
-#961 := (iff #96 #96)
-#962 := [refl]: #961
-#964 := [quant-intro #962]: #963
-#386 := (~ #97 #97)
-#385 := (~ #96 #96)
-#382 := [refl]: #385
-#387 := [nnf-pos #382]: #386
-#267 := [asserted]: #97
-#383 := [mp~ #267 #387]: #97
-#965 := [mp #383 #964]: #960
-#888 := (not #960)
-#889 := (or #888 #553)
-#890 := [quant-inst #4]: #889
-#658 := [unit-resolution #890 #965]: #553
-#644 := [symm #658]: #640
-#629 := (= #100 #886)
-decl f7 :: (-> S4 S3)
-#849 := (f7 #884)
-#844 := (= #849 #886)
-#22 := (:var 0 S4)
-#71 := (f16 #22)
-#943 := (pattern #71)
-#25 := (f7 #22)
-#942 := (pattern #25)
-#247 := (= #25 #71)
-#944 := (forall (vars (?v0 S4)) (:pat #942 #943) #247)
-#251 := (forall (vars (?v0 S4)) #247)
-#947 := (iff #251 #944)
-#945 := (iff #247 #247)
-#946 := [refl]: #945
-#948 := [quant-intro #946]: #947
-#374 := (~ #251 #251)
-#415 := (~ #247 #247)
-#416 := [refl]: #415
-#375 := [nnf-pos #416]: #374
-#72 := (= #71 #25)
-#73 := (forall (vars (?v0 S4)) #72)
-#252 := (iff #73 #251)
-#249 := (iff #72 #247)
-#250 := [rewrite]: #249
-#253 := [quant-intro #250]: #252
-#246 := [asserted]: #73
-#256 := [mp #246 #253]: #251
-#417 := [mp~ #256 #375]: #251
-#949 := [mp #417 #948]: #944
-#568 := (not #944)
-#693 := (or #568 #844)
-#694 := [quant-inst #884]: #693
-#655 := [unit-resolution #694 #949]: #844
-#630 := (= #100 #849)
-decl f5 :: (-> Int S3)
-decl f6 :: (-> S3 Int)
-#36 := (f7 f10)
-#846 := (f6 #36)
-#15 := 1::Int
-#852 := (+ 1::Int #846)
-#695 := (f5 #852)
-#838 := (= #695 #849)
-#21 := (:var 1 S1)
-#23 := (f8 #21 #22)
-#899 := (pattern #23)
-#26 := (f6 #25)
-#164 := (+ 1::Int #26)
-#169 := (f5 #164)
-#24 := (f7 #23)
-#172 := (= #24 #169)
-#900 := (forall (vars (?v0 S1) (?v1 S4)) (:pat #899) #172)
-#175 := (forall (vars (?v0 S1) (?v1 S4)) #172)
-#903 := (iff #175 #900)
-#901 := (iff #172 #172)
-#902 := [refl]: #901
-#904 := [quant-intro #902]: #903
-#358 := (~ #175 #175)
-#357 := (~ #172 #172)
-#402 := [refl]: #357
-#359 := [nnf-pos #402]: #358
-#14 := 0::Int
-#16 := (+ 0::Int 1::Int)
-#27 := (+ #26 #16)
-#28 := (f5 #27)
-#29 := (= #24 #28)
-#30 := (forall (vars (?v0 S1) (?v1 S4)) #29)
-#176 := (iff #30 #175)
-#173 := (iff #29 #172)
-#170 := (= #28 #169)
-#167 := (= #27 #164)
-#160 := (+ #26 1::Int)
-#165 := (= #160 #164)
-#166 := [rewrite]: #165
-#162 := (= #27 #160)
-#140 := (= #16 1::Int)
-#141 := [rewrite]: #140
-#163 := [monotonicity #141]: #162
-#168 := [trans #163 #166]: #167
-#171 := [monotonicity #168]: #170
-#174 := [monotonicity #171]: #173
-#177 := [quant-intro #174]: #176
-#159 := [asserted]: #30
-#180 := [mp #159 #177]: #175
-#403 := [mp~ #180 #359]: #175
-#905 := [mp #403 #904]: #900
-#834 := (not #900)
-#835 := (or #834 #838)
-#837 := (= #849 #695)
-#841 := (or #834 #837)
-#836 := (iff #841 #835)
-#672 := (iff #835 #835)
-#674 := [rewrite]: #672
-#839 := (iff #837 #838)
-#840 := [rewrite]: #839
-#843 := [monotonicity #840]: #836
-#675 := [trans #843 #674]: #836
-#842 := [quant-inst #4 #35]: #841
-#828 := [mp #842 #675]: #835
-#657 := [unit-resolution #828 #905]: #838
-#642 := (= #100 #695)
-decl f3 :: (-> S2 S3)
-decl f9 :: S2
-#31 := f9
-#32 := (f3 f9)
-#854 := (f6 #32)
-#858 := (+ 1::Int #854)
-#847 := (f5 #858)
-#636 := (= #847 #695)
-#648 := (= #695 #847)
-#654 := (= #852 #858)
-#647 := (= 1::Int #858)
-#687 := (= #858 1::Int)
-#831 := (<= #854 0::Int)
-#829 := (= #854 0::Int)
-#33 := (f5 0::Int)
-#885 := (f6 #33)
-#882 := (= #885 0::Int)
-#84 := (:var 0 Int)
-#111 := (f5 #84)
-#974 := (pattern #111)
-#296 := (>= #84 0::Int)
-#297 := (not #296)
-#112 := (f6 #111)
-#278 := (= #84 #112)
-#303 := (or #278 #297)
-#975 := (forall (vars (?v0 Int)) (:pat #974) #303)
-#308 := (forall (vars (?v0 Int)) #303)
-#978 := (iff #308 #975)
-#976 := (iff #303 #303)
-#977 := [refl]: #976
-#979 := [quant-intro #977]: #978
-#392 := (~ #308 #308)
-#391 := (~ #303 #303)
-#378 := [refl]: #391
-#393 := [nnf-pos #378]: #392
-#113 := (= #112 #84)
-#110 := (<= 0::Int #84)
-#114 := (implies #110 #113)
-#115 := (forall (vars (?v0 Int)) #114)
-#311 := (iff #115 #308)
-#285 := (not #110)
-#286 := (or #285 #278)
-#291 := (forall (vars (?v0 Int)) #286)
-#309 := (iff #291 #308)
-#306 := (iff #286 #303)
-#300 := (or #297 #278)
-#304 := (iff #300 #303)
-#305 := [rewrite]: #304
-#301 := (iff #286 #300)
-#298 := (iff #285 #297)
-#294 := (iff #110 #296)
-#295 := [rewrite]: #294
-#299 := [monotonicity #295]: #298
-#302 := [monotonicity #299]: #301
-#307 := [trans #302 #305]: #306
-#310 := [quant-intro #307]: #309
-#292 := (iff #115 #291)
-#289 := (iff #114 #286)
-#282 := (implies #110 #278)
-#287 := (iff #282 #286)
-#288 := [rewrite]: #287
-#283 := (iff #114 #282)
-#280 := (iff #113 #278)
-#281 := [rewrite]: #280
-#284 := [monotonicity #281]: #283
-#290 := [trans #284 #288]: #289
-#293 := [quant-intro #290]: #292
-#312 := [trans #293 #310]: #311
-#277 := [asserted]: #115
-#313 := [mp #277 #312]: #308
-#379 := [mp~ #313 #393]: #308
-#980 := [mp #379 #979]: #975
-#875 := (not #975)
-#877 := (or #875 #882)
-#554 := (>= 0::Int 0::Int)
-#887 := (not #554)
-#891 := (= 0::Int #885)
-#881 := (or #891 #887)
-#516 := (or #875 #881)
-#878 := (iff #516 #877)
-#879 := (iff #877 #877)
-#865 := [rewrite]: #879
-#874 := (iff #881 #882)
-#870 := (or #882 false)
-#873 := (iff #870 #882)
-#868 := [rewrite]: #873
-#871 := (iff #881 #870)
-#532 := (iff #887 false)
-#1 := true
-#525 := (not true)
-#530 := (iff #525 false)
-#531 := [rewrite]: #530
-#867 := (iff #887 #525)
-#541 := (iff #554 true)
-#883 := [rewrite]: #541
-#529 := [monotonicity #883]: #867
-#869 := [trans #529 #531]: #532
-#540 := (iff #891 #882)
-#545 := [rewrite]: #540
-#872 := [monotonicity #545 #869]: #871
-#511 := [trans #872 #868]: #874
-#876 := [monotonicity #511]: #878
-#866 := [trans #876 #865]: #878
-#517 := [quant-inst #14]: #516
-#573 := [mp #517 #866]: #877
-#707 := [unit-resolution #573 #980]: #882
-#669 := (= #854 #885)
-#34 := (= #32 #33)
-#178 := [asserted]: #34
-#670 := [monotonicity #178]: #669
-#677 := [trans #670 #707]: #829
-#679 := (not #829)
-#680 := (or #679 #831)
-#681 := [th-lemma arith triangle-eq]: #680
-#683 := [unit-resolution #681 #677]: #831
-#832 := (>= #854 0::Int)
-#684 := (or #679 #832)
-#685 := [th-lemma arith triangle-eq]: #684
-#686 := [unit-resolution #685 #677]: #832
-#688 := [th-lemma arith eq-propagate -1 -1 #686 #683]: #687
-#650 := [symm #688]: #647
-#663 := (= #852 1::Int)
-#833 := (<= #846 0::Int)
-#830 := (= #846 0::Int)
-#689 := (= #846 #885)
-#37 := (= #36 #33)
-#181 := (= #33 #36)
-#182 := (iff #37 #181)
-#183 := [rewrite]: #182
-#179 := [asserted]: #37
-#186 := [mp #179 #183]: #181
-#671 := [symm #186]: #37
-#659 := [monotonicity #671]: #689
-#660 := [trans #659 #707]: #830
-#661 := (not #830)
-#662 := (or #661 #833)
-#664 := [th-lemma arith triangle-eq]: #662
-#665 := [unit-resolution #664 #660]: #833
-#715 := (>= #846 0::Int)
-#666 := (or #661 #715)
-#508 := [th-lemma arith triangle-eq]: #666
-#667 := [unit-resolution #508 #660]: #715
-#668 := [th-lemma arith eq-propagate -1 -1 #667 #665]: #663
-#656 := [trans #668 #650]: #654
-#653 := [monotonicity #656]: #648
-#639 := [symm #653]: #636
-#638 := (= #100 #847)
-decl f4 :: (-> Int S2 S2)
-#563 := (f4 3::Int f9)
-#585 := (f3 #563)
-#848 := (= #585 #847)
-#9 := (:var 0 S2)
-#8 := (:var 1 Int)
-#10 := (f4 #8 #9)
-#892 := (pattern #10)
-#12 := (f3 #9)
-#13 := (f6 #12)
-#145 := (+ 1::Int #13)
-#150 := (f5 #145)
-#11 := (f3 #10)
-#153 := (= #11 #150)
-#893 := (forall (vars (?v0 Int) (?v1 S2)) (:pat #892) #153)
-#156 := (forall (vars (?v0 Int) (?v1 S2)) #153)
-#896 := (iff #156 #893)
-#894 := (iff #153 #153)
-#895 := [refl]: #894
-#897 := [quant-intro #895]: #896
-#400 := (~ #156 #156)
-#398 := (~ #153 #153)
-#399 := [refl]: #398
-#401 := [nnf-pos #399]: #400
-#17 := (+ #13 #16)
-#18 := (f5 #17)
-#19 := (= #11 #18)
-#20 := (forall (vars (?v0 Int) (?v1 S2)) #19)
-#157 := (iff #20 #156)
-#154 := (iff #19 #153)
-#151 := (= #18 #150)
-#148 := (= #17 #145)
-#142 := (+ #13 1::Int)
-#146 := (= #142 #145)
-#147 := [rewrite]: #146
-#143 := (= #17 #142)
-#144 := [monotonicity #141]: #143
-#149 := [trans #144 #147]: #148
-#152 := [monotonicity #149]: #151
-#155 := [monotonicity #152]: #154
-#158 := [quant-intro #155]: #157
-#139 := [asserted]: #20
-#161 := [mp #139 #158]: #156
-#356 := [mp~ #161 #401]: #156
-#898 := [mp #356 #897]: #893
-#845 := (not #893)
-#850 := (or #845 #848)
-#851 := [quant-inst #98 #31]: #850
-#706 := [unit-resolution #851 #898]: #848
-#637 := (= #100 #585)
-decl f15 :: (-> S2 S3)
-#567 := (f15 #563)
-#863 := (= #567 #585)
-#68 := (f15 #9)
-#935 := (pattern #68)
-#934 := (pattern #12)
-#239 := (= #12 #68)
-#936 := (forall (vars (?v0 S2)) (:pat #934 #935) #239)
-#243 := (forall (vars (?v0 S2)) #239)
-#939 := (iff #243 #936)
-#937 := (iff #239 #239)
-#938 := [refl]: #937
-#940 := [quant-intro #938]: #939
-#372 := (~ #243 #243)
-#412 := (~ #239 #239)
-#413 := [refl]: #412
-#373 := [nnf-pos #413]: #372
-#69 := (= #68 #12)
-#70 := (forall (vars (?v0 S2)) #69)
-#244 := (iff #70 #243)
-#241 := (iff #69 #239)
-#242 := [rewrite]: #241
-#245 := [quant-intro #242]: #244
-#238 := [asserted]: #70
-#248 := [mp #238 #245]: #243
-#414 := [mp~ #248 #373]: #243
-#941 := [mp #414 #940]: #936
-#564 := (not #936)
-#574 := (or #564 #863)
-#859 := (= #585 #567)
-#575 := (or #564 #859)
-#577 := (iff #575 #574)
-#856 := (iff #574 #574)
-#570 := [rewrite]: #856
-#860 := (iff #859 #863)
-#864 := [rewrite]: #860
-#855 := [monotonicity #864]: #577
-#853 := [trans #855 #570]: #577
-#576 := [quant-inst #563]: #575
-#857 := [mp #576 #853]: #574
-#705 := [unit-resolution #857 #941]: #863
-#548 := (= #100 #567)
-#87 := (f4 #84 f9)
-#951 := (pattern #87)
-#85 := (f21 #84)
-#950 := (pattern #85)
-#88 := (f15 #87)
-#86 := (f17 #85)
-#89 := (= #86 #88)
-#952 := (forall (vars (?v0 Int)) (:pat #950 #951) #89)
-#90 := (forall (vars (?v0 Int)) #89)
-#955 := (iff #90 #952)
-#953 := (iff #89 #89)
-#954 := [refl]: #953
-#956 := [quant-intro #954]: #955
-#376 := (~ #90 #90)
-#418 := (~ #89 #89)
-#419 := [refl]: #418
-#377 := [nnf-pos #419]: #376
-#266 := [asserted]: #90
-#384 := [mp~ #266 #377]: #90
-#957 := [mp #384 #956]: #952
-#542 := (not #952)
-#673 := (or #542 #548)
-#880 := [quant-inst #98]: #673
-#646 := [unit-resolution #880 #957]: #548
-#645 := [trans #646 #705]: #637
-#641 := [trans #645 #706]: #638
-#628 := [trans #641 #639]: #642
-#631 := [trans #628 #657]: #630
-#632 := [trans #631 #655]: #629
-#614 := [trans #632 #644]: #103
-#104 := (not #103)
-#269 := [asserted]: #104
-[unit-resolution #269 #614]: false
-unsat
-b5935b8a85a2e047200d1ea44e320dc9dcfbbbbc 76 0
-#2 := false
-decl f3 :: (-> Int S1)
-#118 := 1::Int
-#119 := (f3 1::Int)
-decl f1 :: S1
-#4 := f1
-#421 := (= f1 #119)
-#425 := (not #421)
-#120 := (= #119 f1)
-#121 := (not #120)
-#426 := (iff #121 #425)
-#423 := (iff #120 #421)
-#424 := [rewrite]: #423
-#427 := [monotonicity #424]: #426
-#420 := [asserted]: #121
-#430 := [mp #420 #427]: #425
+#226 := (= f1 #64)
+#230 := (not #226)
+#65 := (= #64 f1)
+#66 := (not #65)
+#231 := (iff #66 #230)
+#228 := (iff #65 #226)
+#229 := [rewrite]: #228
+#232 := [monotonicity #229]: #231
+#225 := [asserted]: #66
+#235 := [mp #225 #232]: #230
 #8 := (:var 0 Int)
 #9 := (f3 #8)
-#953 := (pattern #9)
-#142 := (= f1 #9)
-#954 := (forall (vars (?v0 Int)) (:pat #953) #142)
-#165 := (forall (vars (?v0 Int)) #142)
-#957 := (iff #165 #954)
-#955 := (iff #142 #142)
-#956 := [refl]: #955
-#958 := [quant-intro #956]: #957
-#456 := (~ #165 #165)
-#454 := (~ #142 #142)
-#455 := [refl]: #454
-#457 := [nnf-pos #455]: #456
+#733 := (pattern #9)
+#87 := (= f1 #9)
+#734 := (forall (vars (?v0 Int)) (:pat #733) #87)
+#110 := (forall (vars (?v0 Int)) #87)
+#737 := (iff #110 #734)
+#735 := (iff #87 #87)
+#736 := [refl]: #735
+#738 := [quant-intro #736]: #737
+#251 := (~ #110 #110)
+#249 := (~ #87 #87)
+#250 := [refl]: #249
+#252 := [nnf-pos #250]: #251
 decl f4 :: (-> S2 S1)
 decl f5 :: (-> Int S2 S2)
 decl f6 :: S2
@@ -14874,363 +14701,451 @@
 #10 := (= #9 f1)
 #17 := (and #10 #16)
 #18 := (forall (vars (?v0 Int)) #17)
-#166 := (iff #18 #165)
-#163 := (iff #17 #142)
-#1 := true
-#158 := (and #142 true)
-#161 := (iff #158 #142)
-#162 := [rewrite]: #161
-#159 := (iff #17 #158)
-#156 := (iff #16 true)
-#145 := (= f1 #13)
-#148 := (not #145)
-#151 := (or #145 #148)
-#154 := (iff #151 true)
-#155 := [rewrite]: #154
-#152 := (iff #16 #151)
-#149 := (iff #15 #148)
-#146 := (iff #14 #145)
-#147 := [rewrite]: #146
-#150 := [monotonicity #147]: #149
-#153 := [monotonicity #147 #150]: #152
-#157 := [trans #153 #155]: #156
-#143 := (iff #10 #142)
-#144 := [rewrite]: #143
-#160 := [monotonicity #144 #157]: #159
-#164 := [trans #160 #162]: #163
-#167 := [quant-intro #164]: #166
-#141 := [asserted]: #18
-#170 := [mp #141 #167]: #165
-#429 := [mp~ #170 #457]: #165
-#959 := [mp #429 #958]: #954
-#538 := (not #954)
-#623 := (or #538 #421)
-#624 := [quant-inst #118]: #623
-[unit-resolution #624 #959 #430]: false
-unsat
-c2e9404480cb814492148c359fbbbb3b0e606571 54 0
-#2 := false
+#111 := (iff #18 #110)
+#108 := (iff #17 #87)
 #1 := true
-decl f1 :: S1
-#4 := f1
-decl f3 :: (-> S1 S1)
-decl f2 :: S1
-#5 := f2
-decl f4 :: (-> S2 S1)
-#8 := (:var 0 S2)
-#9 := (f4 #8)
-#10 := (= #9 f1)
-#11 := (exists (vars (?v0 S2)) #10)
-#12 := (ite #11 f1 f2)
-#13 := (f3 #12)
-#14 := (= #13 f1)
-#15 := (implies #14 true)
-#16 := (not #15)
-#69 := (iff #16 false)
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #16 #64)
-#62 := (iff #15 true)
-#37 := (= f1 #9)
-#40 := (exists (vars (?v0 S2)) #37)
-#43 := (ite #40 f1 f2)
-#46 := (f3 #43)
-#52 := (= f1 #46)
-#57 := (implies #52 true)
-#60 := (iff #57 true)
-#61 := [rewrite]: #60
-#58 := (iff #15 #57)
-#55 := (iff #14 #52)
-#49 := (= #46 f1)
-#53 := (iff #49 #52)
-#54 := [rewrite]: #53
-#50 := (iff #14 #49)
-#47 := (= #13 #46)
-#44 := (= #12 #43)
-#41 := (iff #11 #40)
-#38 := (iff #10 #37)
-#39 := [rewrite]: #38
-#42 := [quant-intro #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#56 := [trans #51 #54]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#36 := [asserted]: #16
-[mp #36 #70]: false
-unsat
-343488aeda93da0c02f8ac1558cbc54ab37a2bb9 54 0
-#2 := false
-#1 := true
+#103 := (and #87 true)
+#106 := (iff #103 #87)
+#107 := [rewrite]: #106
+#104 := (iff #17 #103)
+#101 := (iff #16 true)
+#90 := (= f1 #13)
+#93 := (not #90)
+#96 := (or #90 #93)
+#99 := (iff #96 true)
+#100 := [rewrite]: #99
+#97 := (iff #16 #96)
+#94 := (iff #15 #93)
+#91 := (iff #14 #90)
+#92 := [rewrite]: #91
+#95 := [monotonicity #92]: #94
+#98 := [monotonicity #92 #95]: #97
+#102 := [trans #98 #100]: #101
+#88 := (iff #10 #87)
+#89 := [rewrite]: #88
+#105 := [monotonicity #89 #102]: #104
+#109 := [trans #105 #107]: #108
+#112 := [quant-intro #109]: #111
+#86 := [asserted]: #18
+#115 := [mp #86 #112]: #110
+#234 := [mp~ #115 #252]: #110
+#739 := [mp #234 #738]: #734
+#318 := (not #734)
+#403 := (or #318 #226)
+#404 := [quant-inst #63]: #403
+[unit-resolution #404 #739 #235]: false
+unsat
+9dee92579ae791dc7235ea6e43e7e7da09fc5b4d 413 0
+#2 := false
+decl f3 :: (-> S2 S3)
+decl f4 :: (-> S1 S2)
 decl f1 :: S1
 #4 := f1
-decl f3 :: (-> S1 S1)
-decl f2 :: S1
-#5 := f2
-decl f4 :: (-> S2 S1)
-#8 := (:var 0 S2)
+#101 := (f4 f1)
+#102 := (f3 #101)
+decl f8 :: (-> S5 S3)
+decl f9 :: (-> Int S5)
+#98 := 3::Int
+#99 := (f9 3::Int)
+#100 := (f8 #99)
+#103 := (= #100 #102)
+decl f5 :: (-> S4 S3)
+decl f6 :: (-> S1 S4 S4)
+decl f7 :: S4
+#11 := f7
+#471 := (f6 f1 f7)
+#555 := (f5 #471)
+#637 := (= #555 #102)
+#556 := (= #102 #555)
+#8 := (:var 0 S1)
+#12 := (f6 #8 f7)
+#876 := (pattern #12)
 #9 := (f4 #8)
-#10 := (= #9 f1)
-#11 := (forall (vars (?v0 S2)) #10)
-#12 := (ite #11 f1 f2)
-#13 := (f3 #12)
-#14 := (= #13 f1)
-#15 := (implies #14 true)
-#16 := (not #15)
-#69 := (iff #16 false)
-#64 := (not true)
-#67 := (iff #64 false)
-#68 := [rewrite]: #67
-#65 := (iff #16 #64)
-#62 := (iff #15 true)
-#37 := (= f1 #9)
-#40 := (forall (vars (?v0 S2)) #37)
-#43 := (ite #40 f1 f2)
-#46 := (f3 #43)
-#52 := (= f1 #46)
-#57 := (implies #52 true)
-#60 := (iff #57 true)
-#61 := [rewrite]: #60
-#58 := (iff #15 #57)
-#55 := (iff #14 #52)
-#49 := (= #46 f1)
-#53 := (iff #49 #52)
-#54 := [rewrite]: #53
-#50 := (iff #14 #49)
-#47 := (= #13 #46)
-#44 := (= #12 #43)
-#41 := (iff #11 #40)
-#38 := (iff #10 #37)
-#39 := [rewrite]: #38
-#42 := [quant-intro #39]: #41
-#45 := [monotonicity #42]: #44
-#48 := [monotonicity #45]: #47
-#51 := [monotonicity #48]: #50
-#56 := [trans #51 #54]: #55
-#59 := [monotonicity #56]: #58
-#63 := [trans #59 #61]: #62
-#66 := [monotonicity #63]: #65
-#70 := [trans #66 #68]: #69
-#36 := [asserted]: #16
-[mp #36 #70]: false
-unsat
-1953a39a3cc38daf2fde4846aa1d5cbc2ff95785 60 0
-#2 := false
-#8 := 0::Int
-decl ?v1!0 :: Int
-#67 := ?v1!0
-#70 := (<= ?v1!0 0::Int)
-#63 := (not #70)
-#11 := 1::Int
-#68 := (>= ?v1!0 1::Int)
-#69 := (not #68)
-#79 := (or #69 #63)
-#82 := (not #79)
-#64 := (or #63 #69)
-#71 := (not #64)
-#83 := (iff #71 #82)
-#80 := (iff #64 #79)
-#81 := [rewrite]: #80
-#84 := [monotonicity #81]: #83
-#9 := (:var 0 Int)
-#48 := (>= #9 1::Int)
-#46 := (not #48)
-#42 := (<= #9 0::Int)
-#43 := (not #42)
-#50 := (or #43 #46)
-#53 := (forall (vars (?v1 Int)) #50)
-#56 := (not #53)
-#72 := (~ #56 #71)
-#73 := [sk]: #72
-#12 := (< #9 1::Int)
-#10 := (< 0::Int #9)
-#13 := (or #10 #12)
-#14 := (forall (vars (?v0 Int) (?v1 Int)) #13)
-#15 := (not #14)
-#59 := (iff #15 #56)
-#36 := (forall (vars (?v1 Int)) #13)
-#39 := (not #36)
-#57 := (iff #39 #56)
-#54 := (iff #36 #53)
-#51 := (iff #13 #50)
-#47 := (iff #12 #46)
-#49 := [rewrite]: #47
-#44 := (iff #10 #43)
-#45 := [rewrite]: #44
-#52 := [monotonicity #45 #49]: #51
-#55 := [quant-intro #52]: #54
-#58 := [monotonicity #55]: #57
-#40 := (iff #15 #39)
-#37 := (iff #14 #36)
-#38 := [elim-unused]: #37
-#41 := [monotonicity #38]: #40
-#60 := [trans #41 #58]: #59
-#35 := [asserted]: #15
-#61 := [mp #35 #60]: #56
-#76 := [mp~ #61 #73]: #71
-#77 := [mp #76 #84]: #82
-#85 := [not-or-elim #77]: #70
-#78 := [not-or-elim #77]: #68
-#141 := [th-lemma arith farkas 1 1]: #64
-#142 := [unit-resolution #141 #78]: #63
-[unit-resolution #142 #85]: false
-unsat
-4d18c87aa576f201e48ea20e31f11fb8675b59d4 8 0
-#2 := false
+#875 := (pattern #9)
+#13 := (f5 #12)
+#10 := (f3 #9)
+#14 := (= #10 #13)
+#877 := (forall (vars (?v0 S1)) (:pat #875 #876) #14)
+#15 := (forall (vars (?v0 S1)) #14)
+#880 := (iff #15 #877)
+#878 := (iff #14 #14)
+#879 := [refl]: #878
+#881 := [quant-intro #879]: #880
+#435 := (~ #15 #15)
+#437 := (~ #14 #14)
+#438 := [refl]: #437
+#436 := [nnf-pos #438]: #435
+#139 := [asserted]: #15
+#427 := [mp~ #139 #436]: #15
+#882 := [mp #427 #881]: #877
+#559 := (not #877)
+#560 := (or #559 #556)
+#561 := [quant-inst #4]: #560
+#718 := [unit-resolution #561 #882]: #556
+#639 := [symm #718]: #637
+#636 := (= #100 #555)
+decl f16 :: (-> S4 S3)
+#578 := (f16 #471)
+#630 := (= #578 #555)
+#842 := (= #555 #578)
+#39 := (:var 0 S4)
+#41 := (f16 #39)
+#900 := (pattern #41)
+#40 := (f5 #39)
+#899 := (pattern #40)
+#42 := (= #40 #41)
+#901 := (forall (vars (?v0 S4)) (:pat #899 #900) #42)
+#43 := (forall (vars (?v0 S4)) #42)
+#904 := (iff #43 #901)
+#902 := (iff #42 #42)
+#903 := [refl]: #902
+#905 := [quant-intro #903]: #904
+#398 := (~ #43 #43)
+#406 := (~ #42 #42)
+#397 := [refl]: #406
+#395 := [nnf-pos #397]: #398
+#153 := [asserted]: #43
+#396 := [mp~ #153 #395]: #43
+#906 := [mp #396 #905]: #901
+#871 := (not #901)
+#847 := (or #871 #842)
+#567 := [quant-inst #471]: #847
+#673 := [unit-resolution #567 #906]: #842
+#633 := [symm #673]: #630
+#635 := (= #100 #578)
+decl f18 :: (-> Int S3)
+decl f20 :: (-> S3 Int)
+#84 := (f16 f7)
+#846 := (f20 #84)
+#63 := 1::Int
+#843 := (+ 1::Int #846)
+#568 := (f18 #843)
+#570 := (= #568 #578)
+#70 := (:var 1 S1)
+#71 := (f6 #70 #39)
+#942 := (pattern #71)
+#93 := (f20 #41)
+#237 := (+ 1::Int #93)
+#242 := (f18 #237)
+#92 := (f16 #71)
+#245 := (= #92 #242)
+#943 := (forall (vars (?v0 S1) (?v1 S4)) (:pat #942) #245)
+#248 := (forall (vars (?v0 S1) (?v1 S4)) #245)
+#946 := (iff #248 #943)
+#944 := (iff #245 #245)
+#945 := [refl]: #944
+#947 := [quant-intro #945]: #946
+#364 := (~ #248 #248)
+#362 := (~ #245 #245)
+#363 := [refl]: #362
+#365 := [nnf-pos #363]: #364
+#46 := 0::Int
+#64 := (+ 0::Int 1::Int)
+#94 := (+ #93 #64)
+#95 := (f18 #94)
+#96 := (= #92 #95)
+#97 := (forall (vars (?v0 S1) (?v1 S4)) #96)
+#249 := (iff #97 #248)
+#246 := (iff #96 #245)
+#243 := (= #95 #242)
+#240 := (= #94 #237)
+#233 := (+ #93 1::Int)
+#238 := (= #233 #237)
+#239 := [rewrite]: #238
+#235 := (= #94 #233)
+#164 := (= #64 1::Int)
+#166 := [rewrite]: #164
+#236 := [monotonicity #166]: #235
+#241 := [trans #236 #239]: #240
+#244 := [monotonicity #241]: #243
+#247 := [monotonicity #244]: #246
+#250 := [quant-intro #247]: #249
+#232 := [asserted]: #97
+#253 := [mp #232 #250]: #248
+#366 := [mp~ #253 #365]: #248
+#948 := [mp #366 #947]: #943
+#563 := (not #943)
+#836 := (or #563 #570)
+#569 := (= #578 #568)
+#840 := (or #563 #569)
+#841 := (iff #840 #836)
+#831 := (iff #836 #836)
+#832 := [rewrite]: #831
+#838 := (iff #569 #570)
+#839 := [rewrite]: #838
+#830 := [monotonicity #839]: #841
+#827 := [trans #830 #832]: #841
+#837 := [quant-inst #4 #11]: #840
+#828 := [mp #837 #827]: #836
+#680 := [unit-resolution #828 #948]: #570
+#632 := (= #100 #568)
+decl f15 :: (-> S6 S3)
+decl f12 :: S6
+#19 := f12
+#82 := (f15 f12)
+#829 := (f20 #82)
+#835 := (+ 1::Int #829)
+#678 := (f18 #835)
+#646 := (= #678 #568)
+#645 := (= #835 #843)
+#643 := (= 1::Int #843)
+#652 := (= #843 1::Int)
+#814 := (<= #846 0::Int)
+#812 := (= #846 0::Int)
+#47 := (f18 0::Int)
+#868 := (f20 #47)
+#865 := (= #868 0::Int)
+#16 := (:var 0 Int)
+#111 := (f18 #16)
+#957 := (pattern #111)
+#279 := (>= #16 0::Int)
+#280 := (not #279)
+#112 := (f20 #111)
+#261 := (= #16 #112)
+#286 := (or #261 #280)
+#958 := (forall (vars (?v0 Int)) (:pat #957) #286)
+#291 := (forall (vars (?v0 Int)) #286)
+#961 := (iff #291 #958)
+#959 := (iff #286 #286)
+#960 := [refl]: #959
+#962 := [quant-intro #960]: #961
+#378 := (~ #291 #291)
+#372 := (~ #286 #286)
+#377 := [refl]: #372
+#379 := [nnf-pos #377]: #378
+#113 := (= #112 #16)
+#110 := (<= 0::Int #16)
+#114 := (implies #110 #113)
+#115 := (forall (vars (?v0 Int)) #114)
+#294 := (iff #115 #291)
+#268 := (not #110)
+#269 := (or #268 #261)
+#274 := (forall (vars (?v0 Int)) #269)
+#292 := (iff #274 #291)
+#289 := (iff #269 #286)
+#283 := (or #280 #261)
+#287 := (iff #283 #286)
+#288 := [rewrite]: #287
+#284 := (iff #269 #283)
+#281 := (iff #268 #280)
+#277 := (iff #110 #279)
+#278 := [rewrite]: #277
+#282 := [monotonicity #278]: #281
+#285 := [monotonicity #282]: #284
+#290 := [trans #285 #288]: #289
+#293 := [quant-intro #290]: #292
+#275 := (iff #115 #274)
+#272 := (iff #114 #269)
+#265 := (implies #110 #261)
+#270 := (iff #265 #269)
+#271 := [rewrite]: #270
+#266 := (iff #114 #265)
+#263 := (iff #113 #261)
+#264 := [rewrite]: #263
+#267 := [monotonicity #264]: #266
+#273 := [trans #267 #271]: #272
+#276 := [quant-intro #273]: #275
+#295 := [trans #276 #293]: #294
+#260 := [asserted]: #115
+#296 := [mp #260 #295]: #291
+#380 := [mp~ #296 #379]: #291
+#963 := [mp #380 #962]: #958
+#858 := (not #958)
+#860 := (or #858 #865)
+#656 := (>= 0::Int 0::Int)
+#870 := (not #656)
+#874 := (= 0::Int #868)
+#864 := (or #874 #870)
+#509 := (or #858 #864)
+#861 := (iff #509 #860)
+#862 := (iff #860 #860)
+#848 := [rewrite]: #862
+#857 := (iff #864 #865)
+#853 := (or #865 false)
+#856 := (iff #853 #865)
+#851 := [rewrite]: #856
+#854 := (iff #864 #853)
+#525 := (iff #870 false)
 #1 := true
-#33 := (not true)
-#63 := (iff #33 false)
-#65 := [rewrite]: #63
-#62 := [asserted]: #33
-[mp #62 #65]: false
-unsat
-ad406fc43130e24f380abadc1fc8a246fab490af 145 0
-#2 := false
-decl f3 :: (-> S2 Int S1)
-#22 := 42::Int
-decl f4 :: (-> S3 Int S2)
-#20 := 3::Int
-decl f6 :: S3
-#18 := f6
-#21 := (f4 f6 3::Int)
-#23 := (f3 #21 42::Int)
-decl f1 :: S1
-#4 := f1
-#86 := (= f1 #23)
-decl f5 :: S3
-#8 := f5
-#255 := (f4 f5 3::Int)
-#246 := (f3 #255 42::Int)
-#568 := (= #246 #23)
-#207 := (= #23 #246)
-#202 := (= #21 #255)
-#558 := (= #255 #21)
-#83 := (= f5 f6)
-#92 := (not #83)
-#93 := (or #92 #86)
-#98 := (not #93)
-#24 := (= #23 f1)
-#19 := (= f6 f5)
-#25 := (implies #19 #24)
-#26 := (not #25)
-#99 := (iff #26 #98)
-#96 := (iff #25 #93)
-#89 := (implies #83 #86)
-#94 := (iff #89 #93)
-#95 := [rewrite]: #94
-#90 := (iff #25 #89)
-#87 := (iff #24 #86)
-#88 := [rewrite]: #87
-#84 := (iff #19 #83)
-#85 := [rewrite]: #84
-#91 := [monotonicity #85 #88]: #90
-#97 := [trans #91 #95]: #96
-#100 := [monotonicity #97]: #99
-#82 := [asserted]: #26
-#103 := [mp #82 #100]: #98
-#101 := [not-or-elim #103]: #83
-#564 := [monotonicity #101]: #558
-#565 := [symm #564]: #202
-#208 := [monotonicity #565]: #207
-#566 := [symm #208]: #568
-#257 := (= f1 #246)
-#11 := (:var 0 Int)
-#9 := (:var 1 Int)
-#10 := (f4 f5 #9)
-#12 := (f3 #10 #11)
-#13 := (pattern #12)
-#64 := 0::Int
-#61 := -1::Int
-#62 := (* -1::Int #11)
-#63 := (+ #9 #62)
-#65 := (<= #63 0::Int)
-#47 := (= f1 #12)
-#71 := (iff #47 #65)
-#76 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #13) #71)
-#116 := (~ #76 #76)
-#114 := (~ #71 #71)
-#115 := [refl]: #114
-#117 := [nnf-pos #115]: #116
-#15 := (<= #9 #11)
-#14 := (= #12 f1)
-#16 := (iff #14 #15)
-#17 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #13) #16)
-#79 := (iff #17 #76)
-#53 := (iff #15 #47)
-#58 := (forall (vars (?v0 Int) (?v1 Int)) (:pat #13) #53)
-#77 := (iff #58 #76)
-#74 := (iff #53 #71)
-#68 := (iff #65 #47)
-#72 := (iff #68 #71)
-#73 := [rewrite]: #72
-#69 := (iff #53 #68)
-#66 := (iff #15 #65)
-#67 := [rewrite]: #66
-#70 := [monotonicity #67]: #69
-#75 := [trans #70 #73]: #74
-#78 := [quant-intro #75]: #77
-#59 := (iff #17 #58)
-#56 := (iff #16 #53)
-#50 := (iff #47 #15)
-#54 := (iff #50 #53)
-#55 := [rewrite]: #54
-#51 := (iff #16 #50)
-#48 := (iff #14 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#57 := [trans #52 #55]: #56
-#60 := [quant-intro #57]: #59
-#80 := [trans #60 #78]: #79
-#46 := [asserted]: #17
-#81 := [mp #46 #80]: #76
-#106 := [mp~ #81 #117]: #76
-#557 := (not #76)
-#220 := (or #557 #257)
-#168 := (* -1::Int 42::Int)
-#253 := (+ 3::Int #168)
-#254 := (<= #253 0::Int)
-#258 := (iff #257 #254)
-#221 := (or #557 #258)
-#223 := (iff #221 #220)
-#560 := (iff #220 #220)
-#561 := [rewrite]: #560
-#573 := (iff #258 #257)
-#1 := true
-#571 := (iff #257 true)
-#572 := (iff #571 #257)
-#232 := [rewrite]: #572
-#231 := (iff #258 #571)
-#575 := (iff #254 true)
-#576 := -39::Int
-#245 := (<= -39::Int 0::Int)
-#579 := (iff #245 true)
-#580 := [rewrite]: #579
-#577 := (iff #254 #245)
-#570 := (= #253 -39::Int)
-#186 := -42::Int
-#260 := (+ 3::Int -42::Int)
-#233 := (= #260 -39::Int)
-#363 := [rewrite]: #233
-#239 := (= #253 #260)
-#259 := (= #168 -42::Int)
-#256 := [rewrite]: #259
-#574 := [monotonicity #256]: #239
-#244 := [trans #574 #363]: #570
-#578 := [monotonicity #244]: #577
-#581 := [trans #578 #580]: #575
-#236 := [monotonicity #581]: #231
-#216 := [trans #236 #232]: #573
-#559 := [monotonicity #216]: #223
-#562 := [trans #559 #561]: #223
-#222 := [quant-inst #20 #22]: #221
-#563 := [mp #222 #562]: #220
-#567 := [unit-resolution #563 #106]: #257
-#569 := [trans #567 #566]: #86
-#102 := (not #86)
-#104 := [not-or-elim #103]: #102
-[unit-resolution #104 #569]: false
-unsat
+#518 := (not true)
+#523 := (iff #518 false)
+#524 := [rewrite]: #523
+#850 := (iff #870 #518)
+#534 := (iff #656 true)
+#866 := [rewrite]: #534
+#522 := [monotonicity #866]: #850
+#852 := [trans #522 #524]: #525
+#533 := (iff #874 #865)
+#538 := [rewrite]: #533
+#855 := [monotonicity #538 #852]: #854
+#504 := [trans #855 #851]: #857
+#859 := [monotonicity #504]: #861
+#849 := [trans #859 #848]: #861
+#510 := [quant-inst #46]: #509
+#566 := [mp #510 #849]: #860
+#681 := [unit-resolution #566 #963]: #865
+#683 := (= #846 #868)
+#85 := (= #84 #47)
+#209 := (= #47 #84)
+#211 := (iff #85 #209)
+#212 := [rewrite]: #211
+#208 := [asserted]: #85
+#215 := [mp #208 #212]: #209
+#682 := [symm #215]: #85
+#684 := [monotonicity #682]: #683
+#685 := [trans #684 #681]: #812
+#686 := (not #812)
+#687 := (or #686 #814)
+#688 := [th-lemma arith triangle-eq]: #687
+#689 := [unit-resolution #688 #685]: #814
+#815 := (>= #846 0::Int)
+#690 := (or #686 #815)
+#675 := [th-lemma arith triangle-eq]: #690
+#691 := [unit-resolution #675 #685]: #815
+#653 := [th-lemma arith eq-propagate -1 -1 #691 #689]: #652
+#644 := [symm #653]: #643
+#672 := (= #835 1::Int)
+#816 := (<= #829 0::Int)
+#813 := (= #829 0::Int)
+#662 := (= #829 #868)
+#83 := (= #82 #47)
+#204 := (= #47 #82)
+#206 := (iff #83 #204)
+#207 := [rewrite]: #206
+#203 := [asserted]: #83
+#210 := [mp #203 #207]: #204
+#660 := [symm #210]: #83
+#663 := [monotonicity #660]: #662
+#664 := [trans #663 #681]: #813
+#666 := (not #813)
+#667 := (or #666 #816)
+#668 := [th-lemma arith triangle-eq]: #667
+#669 := [unit-resolution #668 #664]: #816
+#698 := (>= #829 0::Int)
+#670 := (or #666 #698)
+#671 := [th-lemma arith triangle-eq]: #670
+#654 := [unit-resolution #671 #664]: #698
+#642 := [th-lemma arith eq-propagate -1 -1 #654 #669]: #672
+#647 := [trans #642 #644]: #645
+#651 := [monotonicity #647]: #646
+#641 := (= #100 #678)
+decl f11 :: (-> Int S6 S6)
+#557 := (f11 3::Int f12)
+#833 := (f15 #557)
+#820 := (= #833 #678)
+#821 := (= #678 #833)
+#34 := (:var 0 S6)
+#55 := (:var 1 Int)
+#56 := (f11 #55 #34)
+#935 := (pattern #56)
+#36 := (f15 #34)
+#87 := (f20 #36)
+#218 := (+ 1::Int #87)
+#223 := (f18 #218)
+#86 := (f15 #56)
+#226 := (= #86 #223)
+#936 := (forall (vars (?v0 Int) (?v1 S6)) (:pat #935) #226)
+#229 := (forall (vars (?v0 Int) (?v1 S6)) #226)
+#939 := (iff #229 #936)
+#937 := (iff #226 #226)
+#938 := [refl]: #937
+#940 := [quant-intro #938]: #939
+#359 := (~ #229 #229)
+#357 := (~ #226 #226)
+#358 := [refl]: #357
+#360 := [nnf-pos #358]: #359
+#88 := (+ #87 #64)
+#89 := (f18 #88)
+#90 := (= #86 #89)
+#91 := (forall (vars (?v0 Int) (?v1 S6)) #90)
+#230 := (iff #91 #229)
+#227 := (iff #90 #226)
+#224 := (= #89 #223)
+#221 := (= #88 #218)
+#214 := (+ #87 1::Int)
+#219 := (= #214 #218)
+#220 := [rewrite]: #219
+#216 := (= #88 #214)
+#217 := [monotonicity #166]: #216
+#222 := [trans #217 #220]: #221
+#225 := [monotonicity #222]: #224
+#228 := [monotonicity #225]: #227
+#231 := [quant-intro #228]: #230
+#213 := [asserted]: #91
+#234 := [mp #213 #231]: #229
+#361 := [mp~ #234 #360]: #229
+#941 := [mp #361 #940]: #936
+#817 := (not #936)
+#818 := (or #817 #821)
+#824 := (or #817 #820)
+#819 := (iff #824 #818)
+#655 := (iff #818 #818)
+#657 := [rewrite]: #655
+#822 := (iff #820 #821)
+#823 := [rewrite]: #822
+#826 := [monotonicity #823]: #819
+#658 := [trans #826 #657]: #819
+#825 := [quant-inst #98 #19]: #824
+#811 := [mp #825 #658]: #818
+#648 := [unit-resolution #811 #941]: #821
+#650 := [symm #648]: #820
+#640 := (= #100 #833)
+decl f10 :: (-> S6 S3)
+#548 := (f10 #557)
+#834 := (= #548 #833)
+#892 := (pattern #36)
+#35 := (f10 #34)
+#891 := (pattern #35)
+#37 := (= #35 #36)
+#893 := (forall (vars (?v0 S6)) (:pat #891 #892) #37)
+#38 := (forall (vars (?v0 S6)) #37)
+#896 := (iff #38 #893)
+#894 := (iff #37 #37)
+#895 := [refl]: #894
+#897 := [quant-intro #895]: #896
+#407 := (~ #38 #38)
+#415 := (~ #37 #37)
+#416 := [refl]: #415
+#408 := [nnf-pos #416]: #407
+#152 := [asserted]: #38
+#405 := [mp~ #152 #408]: #38
+#898 := [mp #405 #897]: #893
+#863 := (not #893)
+#676 := (or #863 #834)
+#677 := [quant-inst #557]: #676
+#649 := [unit-resolution #677 #898]: #834
+#558 := (= #100 #548)
+#20 := (f11 #16 f12)
+#884 := (pattern #20)
+#17 := (f9 #16)
+#883 := (pattern #17)
+#21 := (f10 #20)
+#18 := (f8 #17)
+#22 := (= #18 #21)
+#885 := (forall (vars (?v0 Int)) (:pat #883 #884) #22)
+#23 := (forall (vars (?v0 Int)) #22)
+#888 := (iff #23 #885)
+#886 := (iff #22 #22)
+#887 := [refl]: #886
+#889 := [quant-intro #887]: #888
+#426 := (~ #23 #23)
+#428 := (~ #22 #22)
+#425 := [refl]: #428
+#417 := [nnf-pos #425]: #426
+#140 := [asserted]: #23
+#418 := [mp~ #140 #417]: #23
+#890 := [mp #418 #889]: #885
+#867 := (not #885)
+#869 := (or #867 #558)
+#535 := [quant-inst #98]: #869
+#501 := [unit-resolution #535 #890]: #558
+#638 := [trans #501 #649]: #640
+#629 := [trans #638 #650]: #641
+#634 := [trans #629 #651]: #632
+#631 := [trans #634 #680]: #635
+#626 := [trans #631 #633]: #636
+#616 := [trans #626 #639]: #103
+#104 := (not #103)
+#251 := [asserted]: #104
+[unit-resolution #251 #616]: false
+unsat

--- a/src/HOL/SMT_Examples/SMT_Tests.certs	Tue May 31 19:27:19 2011 +0200
+++ b/src/HOL/SMT_Examples/SMT_Tests.certs	Tue May 31 19:28:03 2011 +0200
@@ -8874,6 +8874,379 @@
 #34 := [asserted]: #14
 [mp #34 #57]: false
 unsat
+e82a6cc10c3ef4d2130dbd751caaaa2ceb41a37f 138 0
+#2 := false
+decl f4 :: S2
+#9 := f4
+decl f3 :: S2
+#8 := f3
+#152 := (= f3 f4)
+decl inj!0 :: (-> S3 S2)
+decl f6 :: (-> S2 S3)
+#22 := (f6 f4)
+#207 := (inj!0 #22)
+#208 := (= #207 f4)
+#209 := (= f4 #207)
+#14 := (:var 0 S2)
+#15 := (f6 #14)
+#89 := (pattern #15)
+#88 := (inj!0 #15)
+#85 := (= #88 #14)
+#570 := (forall (vars (k!0 S2)) (:pat #89) #85)
+#90 := (forall (vars (k!0 S2)) (:pat #89) #85)
+#571 := (iff #90 #570)
+#573 := (iff #570 #570)
+#574 := [rewrite]: #573
+#572 := [rewrite]: #571
+#575 := [trans #572 #574]: #571
+#12 := (:var 1 S2)
+#47 := (= #12 #14)
+#13 := (f6 #12)
+#16 := (= #13 #15)
+#53 := (not #16)
+#54 := (or #53 #47)
+#59 := (forall (vars (?v0 S2) (?v1 S2)) #54)
+#86 := (iff #59 #90)
+#83 := [rewrite]: #86
+#93 := (~ #59 #59)
+#91 := (~ #54 #54)
+#92 := [refl]: #91
+#94 := [nnf-pos #92]: #93
+decl f5 :: S2
+#10 := f5
+#11 := (distinct f3 f4 f5)
+#62 := (and #11 #59)
+#68 := (not #62)
+#21 := (f6 f3)
+#23 := (= #21 #22)
+#24 := (not #23)
+#69 := (or #24 #68)
+#74 := (not #69)
+#17 := (= #14 #12)
+#18 := (implies #16 #17)
+#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
+#20 := (and #11 #19)
+#25 := (implies #20 #24)
+#26 := (not #25)
+#75 := (iff #26 #74)
+#72 := (iff #25 #69)
+#65 := (implies #62 #24)
+#70 := (iff #65 #69)
+#71 := [rewrite]: #70
+#66 := (iff #25 #65)
+#63 := (iff #20 #62)
+#60 := (iff #19 #59)
+#57 := (iff #18 #54)
+#50 := (implies #16 #47)
+#55 := (iff #50 #54)
+#56 := [rewrite]: #55
+#51 := (iff #18 #50)
+#48 := (iff #17 #47)
+#49 := [rewrite]: #48
+#52 := [monotonicity #49]: #51
+#58 := [trans #52 #56]: #57
+#61 := [quant-intro #58]: #60
+#64 := [monotonicity #61]: #63
+#67 := [monotonicity #64]: #66
+#73 := [trans #67 #71]: #72
+#76 := [monotonicity #73]: #75
+#46 := [asserted]: #26
+#79 := [mp #46 #76]: #74
+#78 := [not-or-elim #79]: #62
+#81 := [and-elim #78]: #59
+#87 := [mp~ #81 #94]: #59
+#84 := [mp #87 #83]: #90
+#576 := [mp #84 #575]: #570
+#569 := (not #570)
+#549 := (or #569 #209)
+#550 := (or #569 #208)
+#546 := (iff #550 #549)
+#188 := (iff #549 #549)
+#553 := [rewrite]: #188
+#547 := (iff #208 #209)
+#548 := [rewrite]: #547
+#552 := [monotonicity #548]: #546
+#555 := [trans #552 #553]: #546
+#551 := [quant-inst #9]: #550
+#193 := [mp #551 #555]: #549
+#543 := [unit-resolution #193 #576]: #209
+#254 := [symm #543]: #208
+#269 := (= f3 #207)
+#565 := (inj!0 #21)
+#267 := (= #565 #207)
+#250 := (= #207 #565)
+#554 := (= #22 #21)
+#77 := [not-or-elim #79]: #23
+#557 := [symm #77]: #554
+#266 := [monotonicity #557]: #250
+#268 := [symm #266]: #267
+#567 := (= f3 #565)
+#559 := (or #569 #567)
+#566 := (= #565 f3)
+#217 := (or #569 #566)
+#560 := (iff #217 #559)
+#561 := (iff #559 #559)
+#202 := [rewrite]: #561
+#568 := (iff #566 #567)
+#563 := [rewrite]: #568
+#218 := [monotonicity #563]: #560
+#545 := [trans #218 #202]: #560
+#222 := [quant-inst #8]: #217
+#206 := [mp #222 #545]: #559
+#544 := [unit-resolution #206 #576]: #567
+#160 := [trans #544 #268]: #269
+#539 := [trans #160 #254]: #152
+#239 := (not #152)
+#154 := (= f4 f5)
+#241 := (not #154)
+#153 := (= f3 f5)
+#240 := (not #153)
+#232 := (and #239 #240 #241)
+#80 := [and-elim #78]: #11
+#219 := (not #11)
+#351 := (or #219 #232)
+#558 := [def-axiom]: #351
+#194 := [unit-resolution #558 #80]: #232
+#243 := (not #232)
+#244 := (or #243 #239)
+#172 := [def-axiom]: #244
+#556 := [unit-resolution #172 #194]: #239
+[unit-resolution #556 #539]: false
+unsat
+03a4fcd182047beb0b3be329b34440294749812c 117 0
+#2 := false
+decl f5 :: S3
+#18 := f5
+decl f4 :: S3
+#17 := f4
+#19 := (= f4 f5)
+decl inj!0 :: (-> S2 S4 S3)
+decl f3 :: (-> S2 S3 S4)
+decl f6 :: S2
+#22 := f6
+#24 := (f3 f6 f5)
+#565 := (inj!0 f6 #24)
+#220 := (= #565 f5)
+#352 := (= f5 #565)
+#9 := (:var 1 S3)
+#87 := (:var 0 S2)
+#84 := (f3 #87 #9)
+#85 := (pattern #84)
+#88 := (inj!0 #87 #84)
+#89 := (= #88 #9)
+#82 := (forall (vars (k!0 S2) (k!1 S3)) (:pat #85) #89)
+#11 := (:var 0 S3)
+#14 := (= #9 #11)
+#8 := (:var 2 S2)
+#12 := (f3 #8 #11)
+#10 := (f3 #8 #9)
+#13 := (= #10 #12)
+#49 := (not #13)
+#50 := (or #49 #14)
+#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #50)
+#83 := (iff #53 #82)
+#94 := [rewrite]: #83
+#92 := (~ #53 #53)
+#90 := (~ #50 #50)
+#91 := [refl]: #90
+#93 := [nnf-pos #91]: #92
+#20 := (not #19)
+#59 := (and #20 #53)
+#67 := (not #59)
+#23 := (f3 f6 f4)
+#25 := (= #23 #24)
+#26 := (not #25)
+#68 := (or #26 #67)
+#73 := (not #68)
+#15 := (implies #13 #14)
+#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #15)
+#21 := (and #16 #20)
+#27 := (implies #21 #26)
+#28 := (not #27)
+#74 := (iff #28 #73)
+#71 := (iff #27 #68)
+#64 := (implies #59 #26)
+#69 := (iff #64 #68)
+#70 := [rewrite]: #69
+#65 := (iff #27 #64)
+#62 := (iff #21 #59)
+#56 := (and #53 #20)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #21 #56)
+#54 := (iff #16 #53)
+#51 := (iff #15 #50)
+#52 := [rewrite]: #51
+#55 := [quant-intro #52]: #54
+#58 := [monotonicity #55]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #63]: #65
+#72 := [trans #66 #70]: #71
+#75 := [monotonicity #72]: #74
+#48 := [asserted]: #28
+#78 := [mp #48 #75]: #73
+#77 := [not-or-elim #78]: #59
+#80 := [and-elim #77]: #53
+#86 := [mp~ #80 #93]: #53
+#95 := [mp #86 #94]: #82
+#242 := (not #82)
+#232 := (or #242 #352)
+#566 := (or #242 #220)
+#568 := (iff #566 #232)
+#564 := (iff #232 #232)
+#570 := [rewrite]: #564
+#559 := (iff #220 #352)
+#231 := [rewrite]: #559
+#569 := [monotonicity #231]: #568
+#560 := [trans #569 #570]: #568
+#567 := [quant-inst #18 #22]: #566
+#218 := [mp #567 #560]: #232
+#219 := [unit-resolution #218 #95]: #352
+#209 := [symm #219]: #220
+#210 := (= f4 #565)
+#153 := (inj!0 f6 #23)
+#207 := (= #153 #565)
+#203 := (= #565 #153)
+#223 := (= #24 #23)
+#76 := [not-or-elim #78]: #25
+#561 := [symm #76]: #223
+#546 := [monotonicity #561]: #203
+#208 := [symm #546]: #207
+#154 := (= f4 #153)
+#233 := (or #242 #154)
+#240 := (= #153 f4)
+#244 := (or #242 #240)
+#173 := (iff #244 #233)
+#243 := (iff #233 #233)
+#247 := [rewrite]: #243
+#241 := (iff #240 #154)
+#155 := [rewrite]: #241
+#246 := [monotonicity #155]: #173
+#226 := [trans #246 #247]: #173
+#245 := [quant-inst #17 #22]: #244
+#563 := [mp #245 #226]: #233
+#562 := [unit-resolution #563 #95]: #154
+#548 := [trans #562 #208]: #210
+#549 := [trans #548 #209]: #19
+#79 := [and-elim #77]: #20
+[unit-resolution #79 #549]: false
+unsat
+16237d3c6ed6b1b0d94625f503401c43285f9eec 115 0
+#2 := false
+decl f5 :: S2
+#18 := f5
+decl f4 :: S2
+#17 := f4
+#19 := (= f4 f5)
+decl inj!0 :: (-> S3 S4 S2)
+decl f3 :: (-> S2 S3 S4)
+decl f6 :: S3
+#22 := f6
+#24 := (f3 f5 f6)
+#563 := (inj!0 f6 #24)
+#218 := (= #563 f5)
+#350 := (= f5 #563)
+#9 := (:var 1 S3)
+#11 := (:var 0 S2)
+#12 := (f3 #11 #9)
+#88 := (pattern #12)
+#87 := (inj!0 #9 #12)
+#84 := (= #87 #11)
+#89 := (forall (vars (k!0 S2) (k!1 S3)) (:pat #88) #84)
+#8 := (:var 2 S2)
+#14 := (= #8 #11)
+#10 := (f3 #8 #9)
+#13 := (= #10 #12)
+#49 := (not #13)
+#50 := (or #49 #14)
+#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #50)
+#85 := (iff #53 #89)
+#82 := [rewrite]: #85
+#92 := (~ #53 #53)
+#90 := (~ #50 #50)
+#91 := [refl]: #90
+#93 := [nnf-pos #91]: #92
+#20 := (not #19)
+#59 := (and #20 #53)
+#67 := (not #59)
+#23 := (f3 f4 f6)
+#25 := (= #23 #24)
+#26 := (not #25)
+#68 := (or #26 #67)
+#73 := (not #68)
+#15 := (implies #13 #14)
+#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #15)
+#21 := (and #16 #20)
+#27 := (implies #21 #26)
+#28 := (not #27)
+#74 := (iff #28 #73)
+#71 := (iff #27 #68)
+#64 := (implies #59 #26)
+#69 := (iff #64 #68)
+#70 := [rewrite]: #69
+#65 := (iff #27 #64)
+#62 := (iff #21 #59)
+#56 := (and #53 #20)
+#60 := (iff #56 #59)
+#61 := [rewrite]: #60
+#57 := (iff #21 #56)
+#54 := (iff #16 #53)
+#51 := (iff #15 #50)
+#52 := [rewrite]: #51
+#55 := [quant-intro #52]: #54
+#58 := [monotonicity #55]: #57
+#63 := [trans #58 #61]: #62
+#66 := [monotonicity #63]: #65
+#72 := [trans #66 #70]: #71
+#75 := [monotonicity #72]: #74
+#48 := [asserted]: #28
+#78 := [mp #48 #75]: #73
+#77 := [not-or-elim #78]: #59
+#80 := [and-elim #77]: #53
+#86 := [mp~ #80 #93]: #53
+#83 := [mp #86 #82]: #89
+#240 := (not #89)
+#230 := (or #240 #350)
+#564 := (or #240 #218)
+#566 := (iff #564 #230)
+#562 := (iff #230 #230)
+#568 := [rewrite]: #562
+#557 := (iff #218 #350)
+#229 := [rewrite]: #557
+#567 := [monotonicity #229]: #566
+#558 := [trans #567 #568]: #566
+#565 := [quant-inst #22 #18]: #564
+#216 := [mp #565 #558]: #230
+#217 := [unit-resolution #216 #83]: #350
+#207 := [symm #217]: #218
+#208 := (= f4 #563)
+#151 := (inj!0 f6 #23)
+#205 := (= #151 #563)
+#201 := (= #563 #151)
+#221 := (= #24 #23)
+#76 := [not-or-elim #78]: #25
+#559 := [symm #76]: #221
+#544 := [monotonicity #559]: #201
+#206 := [symm #544]: #205
+#152 := (= f4 #151)
+#231 := (or #240 #152)
+#238 := (= #151 f4)
+#242 := (or #240 #238)
+#171 := (iff #242 #231)
+#241 := (iff #231 #231)
+#245 := [rewrite]: #241
+#239 := (iff #238 #152)
+#153 := [rewrite]: #239
+#244 := [monotonicity #153]: #171
+#224 := [trans #244 #245]: #171
+#243 := [quant-inst #22 #17]: #242
+#561 := [mp #243 #224]: #231
+#560 := [unit-resolution #561 #83]: #152
+#546 := [trans #560 #206]: #208
+#547 := [trans #546 #207]: #19
+#79 := [and-elim #77]: #20
+[unit-resolution #79 #547]: false
+unsat
 3aff166df9d8da7d607b1c699d438273dc2fad39 38 0
 #2 := false
 decl f3 :: (-> S2 S2)
@@ -49664,142 +50037,141 @@
 #87 := [and-elim #86]: #46
 [th-lemma arith farkas 1 1 1 #87 #88 #89]: false
 unsat
-dc92b7d4afd6ba08cfa13227dfc8532cdbeb39b8 43 0
-#2 := false
-decl f4 :: (-> S2 S3)
-decl f3 :: (-> S3 S3 S2)
-decl f7 :: S3
+267c94908fa1cba1e9bb1ecaaa4c65058e972cc1 43 0
+#2 := false
+decl f3 :: (-> S3 S2)
+decl f4 :: (-> S2 S2 S3)
+decl f7 :: S2
 #24 := f7
-decl f6 :: S3
+decl f6 :: S2
 #23 := f6
-#25 := (f3 f6 f7)
-#26 := (f4 #25)
+#25 := (f4 f6 f7)
+#26 := (f3 #25)
 #27 := (= f6 #26)
 #28 := (not #27)
 #71 := [asserted]: #28
-#15 := (:var 0 S3)
-#14 := (:var 1 S3)
-#16 := (f3 #14 #15)
-#572 := (pattern #16)
-#20 := (f4 #16)
-#64 := (= #14 #20)
-#579 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #572) #64)
-#68 := (forall (vars (?v0 S3) (?v1 S3)) #64)
-#582 := (iff #68 #579)
-#580 := (iff #64 #64)
-#581 := [refl]: #580
-#583 := [quant-intro #581]: #582
-#78 := (~ #68 #68)
-#90 := (~ #64 #64)
-#91 := [refl]: #90
-#79 := [nnf-pos #91]: #78
-#21 := (= #20 #14)
-#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
-#69 := (iff #22 #68)
-#66 := (iff #21 #64)
-#67 := [rewrite]: #66
-#70 := [quant-intro #67]: #69
-#63 := [asserted]: #22
-#73 := [mp #63 #70]: #68
-#92 := [mp~ #73 #79]: #68
-#584 := [mp #92 #583]: #579
-#240 := (not #579)
-#219 := (or #240 #27)
-#556 := [quant-inst #23 #24]: #219
-[unit-resolution #556 #584 #71]: false
-unsat
-78a9d9bd4030219f6f6fc3a3d77e6844fcb4a19d 43 0
-#2 := false
-decl f5 :: (-> S2 S3)
-decl f3 :: (-> S3 S3 S2)
-decl f6 :: S3
+#9 := (:var 0 S2)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#564 := (pattern #10)
+#11 := (f3 #10)
+#49 := (= #8 #11)
+#565 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #564) #49)
+#52 := (forall (vars (?v0 S2) (?v1 S2)) #49)
+#568 := (iff #52 #565)
+#566 := (iff #49 #49)
+#567 := [refl]: #566
+#569 := [quant-intro #567]: #568
+#76 := (~ #52 #52)
+#83 := (~ #49 #49)
+#84 := [refl]: #83
+#77 := [nnf-pos #84]: #76
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#53 := (iff #13 #52)
+#50 := (iff #12 #49)
+#51 := [rewrite]: #50
+#54 := [quant-intro #51]: #53
+#48 := [asserted]: #13
+#57 := [mp #48 #54]: #52
+#78 := [mp~ #57 #77]: #52
+#570 := [mp #78 #569]: #565
+#147 := (not #565)
+#234 := (or #147 #27)
+#148 := [quant-inst #23 #24]: #234
+[unit-resolution #148 #570 #71]: false
+unsat
+eba38932115d0bb0963b99e993a7e1b0dfff5581 43 0
+#2 := false
+decl f5 :: (-> S3 S2)
+decl f4 :: (-> S2 S2 S3)
+decl f6 :: S2
 #23 := f6
-decl f7 :: S3
+decl f7 :: S2
 #24 := f7
-#25 := (f3 f7 f6)
+#25 := (f4 f7 f6)
 #26 := (f5 #25)
 #27 := (= f6 #26)
 #28 := (not #27)
 #71 := [asserted]: #28
-#15 := (:var 0 S3)
-#14 := (:var 1 S3)
-#16 := (f3 #14 #15)
-#572 := (pattern #16)
-#17 := (f5 #16)
-#56 := (= #15 #17)
-#573 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #572) #56)
-#60 := (forall (vars (?v0 S3) (?v1 S3)) #56)
-#576 := (iff #60 #573)
-#574 := (iff #56 #56)
-#575 := [refl]: #574
-#577 := [quant-intro #575]: #576
-#76 := (~ #60 #60)
-#75 := (~ #56 #56)
-#88 := [refl]: #75
-#77 := [nnf-pos #88]: #76
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
-#61 := (iff #19 #60)
-#58 := (iff #18 #56)
+#9 := (:var 0 S2)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#564 := (pattern #10)
+#14 := (f5 #10)
+#56 := (= #9 #14)
+#571 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #564) #56)
+#60 := (forall (vars (?v0 S2) (?v1 S2)) #56)
+#574 := (iff #60 #571)
+#572 := (iff #56 #56)
+#573 := [refl]: #572
+#575 := [quant-intro #573]: #574
+#85 := (~ #60 #60)
+#81 := (~ #56 #56)
+#82 := [refl]: #81
+#86 := [nnf-pos #82]: #85
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
+#61 := (iff #16 #60)
+#58 := (iff #15 #56)
 #59 := [rewrite]: #58
 #62 := [quant-intro #59]: #61
-#55 := [asserted]: #19
+#55 := [asserted]: #16
 #65 := [mp #55 #62]: #60
-#89 := [mp~ #65 #77]: #60
-#578 := [mp #89 #577]: #573
-#238 := (not #573)
-#166 := (or #238 #27)
-#239 := [quant-inst #24 #23]: #166
-[unit-resolution #239 #578 #71]: false
-unsat
-5b1fa50c4a946d66cbeae41049a8c24d25af0430 87 0
-#2 := false
-decl f7 :: S3
+#87 := [mp~ #65 #86]: #60
+#576 := [mp #87 #575]: #571
+#237 := (not #571)
+#238 := (or #237 #27)
+#166 := [quant-inst #24 #23]: #238
+[unit-resolution #166 #576 #71]: false
+unsat
+4756e085d79123f082e8dd0ab05d9846a56e2ff2 85 0
+#2 := false
+decl f7 :: S2
 #24 := f7
-decl f6 :: S3
+decl f6 :: S2
 #23 := f6
 #28 := (= f6 f7)
-decl f5 :: (-> S2 S3)
-decl f3 :: (-> S3 S3 S2)
-#25 := (f3 f6 f7)
-#246 := (f5 #25)
-#189 := (= #246 f7)
-#243 := (= f7 #246)
-#15 := (:var 0 S3)
-#14 := (:var 1 S3)
-#16 := (f3 #14 #15)
-#579 := (pattern #16)
-#17 := (f5 #16)
-#58 := (= #15 #17)
-#580 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #579) #58)
-#62 := (forall (vars (?v0 S3) (?v1 S3)) #58)
-#583 := (iff #62 #580)
-#581 := (iff #58 #58)
-#582 := [refl]: #581
-#584 := [quant-intro #582]: #583
-#83 := (~ #62 #62)
-#82 := (~ #58 #58)
-#95 := [refl]: #82
-#84 := [nnf-pos #95]: #83
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
-#63 := (iff #19 #62)
-#60 := (iff #18 #58)
-#61 := [rewrite]: #60
-#64 := [quant-intro #61]: #63
-#57 := [asserted]: #19
-#67 := [mp #57 #64]: #62
-#96 := [mp~ #67 #84]: #62
-#585 := [mp #96 #584]: #580
-#563 := (not #580)
-#565 := (or #563 #243)
-#220 := [quant-inst #23 #24]: #565
-#548 := [unit-resolution #220 #585]: #243
-#554 := [symm #548]: #189
-#556 := (= f6 #246)
-#26 := (f3 f7 f6)
-#352 := (f5 #26)
-#547 := (= #352 #246)
+decl f3 :: (-> S3 S2)
+decl f4 :: (-> S2 S2 S3)
+#26 := (f4 f7 f6)
+#352 := (f3 #26)
+#551 := (= #352 f7)
+#559 := (= f7 #352)
+#9 := (:var 0 S2)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#571 := (pattern #10)
+#11 := (f3 #10)
+#51 := (= #8 #11)
+#572 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #571) #51)
+#54 := (forall (vars (?v0 S2) (?v1 S2)) #51)
+#575 := (iff #54 #572)
+#573 := (iff #51 #51)
+#574 := [refl]: #573
+#576 := [quant-intro #574]: #575
+#93 := (~ #54 #54)
+#91 := (~ #51 #51)
+#92 := [refl]: #91
+#94 := [nnf-pos #92]: #93
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#55 := (iff #13 #54)
+#52 := (iff #12 #51)
+#53 := [rewrite]: #52
+#56 := [quant-intro #53]: #55
+#50 := [asserted]: #13
+#59 := [mp #50 #56]: #54
+#80 := [mp~ #59 #94]: #54
+#577 := [mp #80 #576]: #572
+#563 := (not #572)
+#569 := (or #563 #559)
+#564 := [quant-inst #24 #23]: #569
+#210 := [unit-resolution #564 #577]: #559
+#552 := [symm #210]: #551
+#547 := (= f6 #352)
+#25 := (f4 f6 f7)
+#246 := (f3 #25)
 #549 := (= #246 #352)
 #27 := (= #25 #26)
 #562 := (= #26 #25)
@@ -49825,39 +50197,38 @@
 #207 := [unit-resolution #570 #546]: false
 #208 := [lemma #207]: #27
 #550 := [monotonicity #208]: #549
-#553 := [symm #550]: #547
-#559 := (= f6 #352)
-#569 := (or #563 #559)
-#564 := [quant-inst #24 #23]: #569
-#210 := [unit-resolution #564 #585]: #559
-#194 := [trans #210 #553]: #556
-#195 := [trans #194 #554]: #28
+#243 := (= f6 #246)
+#565 := (or #563 #243)
+#220 := [quant-inst #23 #24]: #565
+#548 := [unit-resolution #220 #577]: #243
+#553 := [trans #548 #550]: #547
+#189 := [trans #553 #552]: #28
 #242 := (not #28)
 #245 := (or #242 #74)
 #233 := (or #242 #74 #153)
 #244 := [def-axiom]: #233
 #173 := [unit-resolution #244 #81]: #245
 #209 := [unit-resolution #173 #208]: #242
-[unit-resolution #209 #195]: false
-unsat
-55451993392a339d9aeab45ab57333ada99d25e7 155 0
-#2 := false
-decl f9 :: S3
+[unit-resolution #209 #189]: false
+unsat
+ada08cd4b21eae33a592930e9a97acc08f923d51 155 0
+#2 := false
+decl f9 :: S2
 #27 := f9
-decl f7 :: S3
+decl f7 :: S2
 #24 := f7
 #31 := (= f7 f9)
 #105 := (not #31)
-decl f8 :: S3
+decl f8 :: S2
 #26 := f8
-decl f6 :: S3
+decl f6 :: S2
 #23 := f6
 #30 := (= f6 f8)
 #104 := (not #30)
 #91 := (or #104 #105)
-decl f3 :: (-> S3 S3 S2)
-#28 := (f3 f8 f9)
-#25 := (f3 f6 f7)
+decl f4 :: (-> S2 S2 S3)
+#28 := (f4 f8 f9)
+#25 := (f4 f6 f7)
 #29 := (= #25 #28)
 #92 := (not #91)
 #243 := [hypothesis]: #92
@@ -49901,43 +50272,43 @@
 #586 := [unit-resolution #587 #243]: #78
 #234 := [unit-resolution #586 #233]: false
 #572 := [lemma #234]: #91
-decl f5 :: (-> S2 S3)
-#591 := (f5 #28)
-#577 := (= #591 f9)
-#592 := (= f9 #591)
-#15 := (:var 0 S3)
-#14 := (:var 1 S3)
-#16 := (f3 #14 #15)
-#603 := (pattern #16)
-#17 := (f5 #16)
-#62 := (= #15 #17)
-#604 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #603) #62)
-#66 := (forall (vars (?v0 S3) (?v1 S3)) #62)
-#607 := (iff #66 #604)
-#605 := (iff #62 #62)
-#606 := [refl]: #605
-#608 := [quant-intro #606]: #607
-#87 := (~ #66 #66)
-#86 := (~ #62 #62)
-#99 := [refl]: #86
-#88 := [nnf-pos #99]: #87
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
-#67 := (iff #19 #66)
-#64 := (iff #18 #62)
-#65 := [rewrite]: #64
-#68 := [quant-intro #65]: #67
-#61 := [asserted]: #19
-#71 := [mp #61 #68]: #66
-#100 := [mp~ #71 #88]: #66
-#609 := [mp #100 #608]: #604
-#255 := (not #604)
+decl f3 :: (-> S3 S2)
+#591 := (f3 #28)
+#577 := (= #591 f8)
+#592 := (= f8 #591)
+#9 := (:var 0 S2)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#595 := (pattern #10)
+#11 := (f3 #10)
+#55 := (= #8 #11)
+#596 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #595) #55)
+#58 := (forall (vars (?v0 S2) (?v1 S2)) #55)
+#599 := (iff #58 #596)
+#597 := (iff #55 #55)
+#598 := [refl]: #597
+#600 := [quant-intro #598]: #599
+#97 := (~ #58 #58)
+#95 := (~ #55 #55)
+#96 := [refl]: #95
+#98 := [nnf-pos #96]: #97
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#59 := (iff #13 #58)
+#56 := (iff #12 #55)
+#57 := [rewrite]: #56
+#60 := [quant-intro #57]: #59
+#54 := [asserted]: #13
+#63 := [mp #54 #60]: #58
+#84 := [mp~ #63 #98]: #58
+#601 := [mp #84 #600]: #596
+#255 := (not #596)
 #247 := (or #255 #592)
 #585 := [quant-inst #26 #27]: #247
-#573 := [unit-resolution #585 #609]: #592
+#573 := [unit-resolution #585 #601]: #592
 #213 := [symm #573]: #577
-#578 := (= f7 #591)
-#589 := (f5 #25)
+#578 := (= f6 #591)
+#589 := (f3 #25)
 #576 := (= #589 #591)
 #197 := (or #29 #92)
 #268 := (or #29 #92 #257)
@@ -49945,127 +50316,127 @@
 #270 := [unit-resolution #269 #119]: #197
 #574 := [unit-resolution #270 #572]: #29
 #571 := [monotonicity #574]: #576
-#244 := (= f7 #589)
+#244 := (= f6 #589)
 #256 := (or #255 #244)
 #590 := [quant-inst #23 #24]: #256
-#575 := [unit-resolution #590 #609]: #244
+#575 := [unit-resolution #590 #601]: #244
 #580 := [trans #575 #571]: #578
-#218 := [trans #580 #213]: #31
-decl f4 :: (-> S2 S3)
-#584 := (f4 #28)
-#568 := (= #584 f8)
-#242 := (= f8 #584)
-#20 := (f4 #16)
-#70 := (= #14 #20)
-#610 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #603) #70)
-#74 := (forall (vars (?v0 S3) (?v1 S3)) #70)
-#613 := (iff #74 #610)
-#611 := (iff #70 #70)
-#612 := [refl]: #611
-#614 := [quant-intro #612]: #613
-#89 := (~ #74 #74)
-#101 := (~ #70 #70)
-#102 := [refl]: #101
-#90 := [nnf-pos #102]: #89
-#21 := (= #20 #14)
-#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
-#75 := (iff #22 #74)
-#72 := (iff #21 #70)
-#73 := [rewrite]: #72
-#76 := [quant-intro #73]: #75
-#69 := [asserted]: #22
-#79 := [mp #69 #76]: #74
-#103 := [mp~ #79 #90]: #74
-#615 := [mp #103 #614]: #610
-#593 := (not #610)
+#218 := [trans #580 #213]: #30
+decl f5 :: (-> S3 S2)
+#584 := (f5 #28)
+#568 := (= #584 f9)
+#242 := (= f9 #584)
+#14 := (f5 #10)
+#62 := (= #9 #14)
+#602 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #595) #62)
+#66 := (forall (vars (?v0 S2) (?v1 S2)) #62)
+#605 := (iff #66 #602)
+#603 := (iff #62 #62)
+#604 := [refl]: #603
+#606 := [quant-intro #604]: #605
+#87 := (~ #66 #66)
+#86 := (~ #62 #62)
+#99 := [refl]: #86
+#88 := [nnf-pos #99]: #87
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
+#67 := (iff #16 #66)
+#64 := (iff #15 #62)
+#65 := [rewrite]: #64
+#68 := [quant-intro #65]: #67
+#61 := [asserted]: #16
+#71 := [mp #61 #68]: #66
+#100 := [mp~ #71 #88]: #66
+#607 := [mp #100 #606]: #602
+#593 := (not #602)
 #227 := (or #593 #242)
 #570 := [quant-inst #26 #27]: #227
-#219 := [unit-resolution #570 #615]: #242
+#219 := [unit-resolution #570 #607]: #242
 #569 := [symm #219]: #568
-#275 := (= f6 #584)
-#376 := (f4 #25)
+#275 := (= f7 #584)
+#376 := (f5 #25)
 #579 := (= #376 #584)
 #582 := [monotonicity #574]: #579
-#583 := (= f6 #376)
+#583 := (= f7 #376)
 #588 := (or #593 #583)
 #594 := [quant-inst #23 #24]: #588
-#581 := [unit-resolution #594 #615]: #583
+#581 := [unit-resolution #594 #607]: #583
 #291 := [trans #581 #582]: #275
-#292 := [trans #291 #569]: #30
+#292 := [trans #291 #569]: #31
 #179 := (or #92 #104 #105)
 #266 := [def-axiom]: #179
 [unit-resolution #266 #292 #218 #572]: false
 unsat
-be42530dd2762a091effcef8ad846d02ec16506c 91 0
-#2 := false
-decl f12 :: S3
+39134e03a4a206aeb5e8ee58e8edb86a602fc708 91 0
+#2 := false
+decl f12 :: S2
 #42 := f12
-decl f9 :: S3
+decl f9 :: S2
 #36 := f9
 #49 := (= f9 f12)
-decl f7 :: (-> S5 S3)
-decl f6 :: (-> S3 S2 S5)
-decl f3 :: (-> S3 S4 S2)
-decl f14 :: S4
+decl f3 :: (-> S4 S2)
+decl f4 :: (-> S2 S3 S4)
+decl f6 :: (-> S2 S5 S3)
+decl f14 :: S5
 #44 := f14
-decl f13 :: S3
+decl f13 :: S2
 #43 := f13
-#45 := (f3 f13 f14)
-#46 := (f6 f12 #45)
-#47 := (f7 #46)
-decl f11 :: S4
+#45 := (f6 f13 f14)
+#46 := (f4 f12 #45)
+#47 := (f3 #46)
+decl f11 :: S5
 #38 := f11
-decl f10 :: S3
+decl f10 :: S2
 #37 := f10
-#39 := (f3 f10 f11)
-#40 := (f6 f9 #39)
-#41 := (f7 #40)
+#39 := (f6 f10 f11)
+#40 := (f4 f9 #39)
+#41 := (f3 #40)
 #48 := (= #41 #47)
 #50 := (iff #48 #49)
 #327 := (iff #49 #48)
-#613 := (= f12 #47)
-#8 := (:var 0 S2)
-#20 := (:var 1 S3)
-#26 := (f6 #20 #8)
-#654 := (pattern #26)
-#33 := (f7 #26)
-#111 := (= #20 #33)
-#667 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #654) #111)
-#115 := (forall (vars (?v0 S3) (?v1 S2)) #111)
-#670 := (iff #115 #667)
-#668 := (iff #111 #111)
-#669 := [refl]: #668
-#671 := [quant-intro #669]: #670
-#136 := (~ #115 #115)
-#157 := (~ #111 #111)
-#158 := [refl]: #157
-#137 := [nnf-pos #158]: #136
-#34 := (= #33 #20)
-#35 := (forall (vars (?v0 S3) (?v1 S2)) #34)
-#116 := (iff #35 #115)
-#113 := (iff #34 #111)
-#114 := [rewrite]: #113
-#117 := [quant-intro #114]: #116
-#110 := [asserted]: #35
-#120 := [mp #110 #117]: #115
-#159 := [mp~ #120 #137]: #115
-#672 := [mp #159 #671]: #667
-#249 := (not #667)
-#618 := (or #249 #613)
-#604 := [quant-inst #42 #45]: #618
-#605 := [unit-resolution #604 #672]: #613
-#270 := (= f9 #41)
-#614 := (or #249 #270)
-#616 := [quant-inst #36 #39]: #614
-#311 := [unit-resolution #616 #672]: #270
+#280 := (= f12 #47)
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#631 := (pattern #10)
+#11 := (f3 #10)
+#72 := (= #8 #11)
+#632 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #631) #72)
+#75 := (forall (vars (?v0 S2) (?v1 S3)) #72)
+#635 := (iff #75 #632)
+#633 := (iff #72 #72)
+#634 := [refl]: #633
+#636 := [quant-intro #634]: #635
+#128 := (~ #75 #75)
+#139 := (~ #72 #72)
+#140 := [refl]: #139
+#129 := [nnf-pos #140]: #128
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S3)) #12)
+#76 := (iff #13 #75)
+#73 := (iff #12 #72)
+#74 := [rewrite]: #73
+#77 := [quant-intro #74]: #76
+#71 := [asserted]: #13
+#80 := [mp #71 #77]: #75
+#132 := [mp~ #80 #129]: #75
+#637 := [mp #132 #636]: #632
+#286 := (not #632)
+#627 := (or #286 #280)
+#628 := [quant-inst #42 #45]: #627
+#605 := [unit-resolution #628 #637]: #280
+#306 := (= f9 #41)
+#623 := (or #286 #306)
+#625 := [quant-inst #36 #39]: #623
+#311 := [unit-resolution #625 #637]: #306
 #328 := [monotonicity #311 #605]: #327
 #329 := [symm #328]: #50
 #302 := (not #49)
 #119 := (not #48)
 #315 := (iff #119 #302)
 #330 := [monotonicity #329]: #315
-#254 := [hypothesis]: #119
-#221 := [mp #254 #330]: #302
+#617 := [hypothesis]: #119
+#221 := [mp #617 #330]: #302
 #301 := (or #49 #48)
 #121 := (iff #49 #119)
 #51 := (not #50)
@@ -50077,7 +50448,7 @@
 #300 := (or #49 #48 #213)
 #214 := [def-axiom]: #300
 #215 := [unit-resolution #214 #126]: #301
-#615 := [unit-resolution #215 #254]: #49
+#615 := [unit-resolution #215 #617]: #49
 #600 := [unit-resolution #615 #221]: false
 #601 := [lemma #600]: #48
 #324 := [mp #601 #329]: #49
@@ -50088,102 +50459,102 @@
 #323 := [unit-resolution #233 #601]: #302
 [unit-resolution #323 #324]: false
 unsat
-703ada2cefd34540ab26d41eac317697843d015a 210 0
-#2 := false
-decl f14 :: S4
+f188cd132a2dfe3292e7656a282b6a08809558ea 210 0
+#2 := false
+decl f14 :: S5
 #44 := f14
-decl f11 :: S4
+decl f11 :: S5
 #38 := f11
 #50 := (= f11 f14)
-#163 := (not #50)
-decl f13 :: S3
+#159 := (not #50)
+decl f13 :: S2
 #43 := f13
-decl f10 :: S3
+decl f10 :: S2
 #37 := f10
 #49 := (= f10 f13)
-#162 := (not #49)
-#140 := (or #162 #163)
-decl f8 :: (-> S5 S2)
-decl f6 :: (-> S3 S2 S5)
-decl f3 :: (-> S3 S4 S2)
-#45 := (f3 f13 f14)
-decl f12 :: S3
+#158 := (not #49)
+#160 := (or #158 #159)
+decl f7 :: (-> S4 S3)
+decl f4 :: (-> S2 S3 S4)
+decl f6 :: (-> S2 S5 S3)
+#45 := (f6 f13 f14)
+decl f12 :: S2
 #42 := f12
-#46 := (f6 f12 #45)
-#47 := (f8 #46)
-#39 := (f3 f10 f11)
-decl f9 :: S3
+#46 := (f4 f12 #45)
+#47 := (f7 #46)
+#39 := (f6 f10 f11)
+decl f9 :: S2
 #36 := f9
-#40 := (f6 f9 #39)
-#41 := (f8 #40)
+#40 := (f4 f9 #39)
+#41 := (f7 #40)
 #48 := (= #41 #47)
-#271 := (= #45 #47)
-#8 := (:var 0 S2)
-#20 := (:var 1 S3)
-#26 := (f6 #20 #8)
-#676 := (pattern #26)
-#27 := (f8 #26)
-#97 := (= #8 #27)
-#677 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #676) #97)
-#101 := (forall (vars (?v0 S3) (?v1 S2)) #97)
-#680 := (iff #101 #677)
-#678 := (iff #97 #97)
-#679 := [refl]: #678
-#681 := [quant-intro #679]: #680
-#134 := (~ #101 #101)
-#153 := (~ #97 #97)
-#154 := [refl]: #153
-#135 := [nnf-pos #154]: #134
-#28 := (= #27 #8)
-#29 := (forall (vars (?v0 S3) (?v1 S2)) #28)
-#102 := (iff #29 #101)
-#99 := (iff #28 #97)
-#100 := [rewrite]: #99
-#103 := [quant-intro #100]: #102
-#96 := [asserted]: #29
-#106 := [mp #96 #103]: #101
-#155 := [mp~ #106 #135]: #101
-#682 := [mp #155 #681]: #677
-#636 := (not #677)
-#627 := (or #636 #271)
-#333 := [quant-inst #42 #45]: #627
-#337 := [unit-resolution #333 #682]: #271
+#652 := (= #45 #47)
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#653 := (pattern #10)
+#19 := (f7 #10)
+#89 := (= #9 #19)
+#667 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #653) #89)
+#93 := (forall (vars (?v0 S2) (?v1 S3)) #89)
+#670 := (iff #93 #667)
+#668 := (iff #89 #89)
+#669 := [refl]: #668
+#671 := [quant-intro #669]: #670
+#152 := (~ #93 #93)
+#150 := (~ #89 #89)
+#151 := [refl]: #150
+#153 := [nnf-pos #151]: #152
+#20 := (= #19 #9)
+#21 := (forall (vars (?v0 S2) (?v1 S3)) #20)
+#94 := (iff #21 #93)
+#91 := (iff #20 #89)
+#92 := [rewrite]: #91
+#95 := [quant-intro #92]: #94
+#88 := [asserted]: #21
+#98 := [mp #88 #95]: #93
+#154 := [mp~ #98 #153]: #93
+#672 := [mp #154 #671]: #667
+#650 := (not #667)
+#301 := (or #650 #652)
+#644 := [quant-inst #42 #45]: #301
+#337 := [unit-resolution #644 #672]: #652
 #624 := (= #41 #45)
 #346 := (= #39 #45)
-#141 := (not #140)
-#626 := [hypothesis]: #141
-#236 := (or #140 #50)
+#161 := (not #160)
+#333 := [hypothesis]: #161
+#236 := (or #160 #50)
 #323 := [def-axiom]: #236
-#352 := [unit-resolution #323 #626]: #50
-#235 := (or #140 #49)
+#352 := [unit-resolution #323 #333]: #50
+#235 := (or #160 #49)
 #322 := [def-axiom]: #235
-#243 := [unit-resolution #322 #626]: #49
+#243 := [unit-resolution #322 #333]: #49
 #620 := [monotonicity #243 #352]: #346
 #623 := (= #41 #39)
-#633 := (= #39 #41)
-#638 := (or #636 #633)
-#276 := [quant-inst #36 #39]: #638
-#622 := [unit-resolution #276 #682]: #633
+#434 := (= #39 #41)
+#651 := (or #650 #434)
+#646 := [quant-inst #36 #39]: #651
+#622 := [unit-resolution #646 #672]: #434
 #345 := [symm #622]: #623
 #621 := [trans #345 #620]: #624
 #625 := [trans #621 #337]: #48
 #121 := (not #48)
-#308 := (or #121 #140)
-#172 := (iff #48 #140)
+#308 := (or #121 #160)
+#172 := (iff #48 #160)
 #51 := (and #49 #50)
 #123 := (iff #51 #121)
 #175 := (iff #123 #172)
-#167 := (iff #140 #48)
+#167 := (iff #160 #48)
 #173 := (iff #167 #172)
 #174 := [rewrite]: #173
 #170 := (iff #123 #167)
-#164 := (iff #141 #121)
+#164 := (iff #161 #121)
 #168 := (iff #164 #167)
 #169 := [rewrite]: #168
 #165 := (iff #123 #164)
-#142 := (iff #51 #141)
-#143 := [rewrite]: #142
-#166 := [monotonicity #143]: #165
+#162 := (iff #51 #161)
+#163 := [rewrite]: #162
+#166 := [monotonicity #163]: #165
 #171 := [trans #166 #169]: #170
 #176 := [trans #171 #174]: #175
 #52 := (iff #48 #51)
@@ -50194,224 +50565,224 @@
 #128 := [mp #120 #125]: #123
 #177 := [mp #128 #176]: #172
 #315 := (not #172)
-#325 := (or #121 #140 #315)
+#325 := (or #121 #160 #315)
 #329 := [def-axiom]: #325
 #645 := [unit-resolution #329 #177]: #308
-#349 := [unit-resolution #645 #626]: #121
+#349 := [unit-resolution #645 #333]: #121
 #334 := [unit-resolution #349 #625]: false
-#335 := [lemma #334]: #140
-decl f5 :: (-> S2 S4)
-#285 := (f5 #45)
-#609 := (= #285 f14)
-#628 := (= f14 #285)
-#21 := (:var 0 S4)
-#22 := (f3 #20 #21)
-#669 := (pattern #22)
-#23 := (f5 #22)
-#89 := (= #21 #23)
-#670 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #669) #89)
-#93 := (forall (vars (?v0 S3) (?v1 S4)) #89)
-#673 := (iff #93 #670)
-#671 := (iff #89 #89)
-#672 := [refl]: #671
-#674 := [quant-intro #672]: #673
-#132 := (~ #93 #93)
-#150 := (~ #89 #89)
-#151 := [refl]: #150
-#133 := [nnf-pos #151]: #132
-#24 := (= #23 #21)
-#25 := (forall (vars (?v0 S3) (?v1 S4)) #24)
-#94 := (iff #25 #93)
-#91 := (iff #24 #89)
-#92 := [rewrite]: #91
-#95 := [quant-intro #92]: #94
-#88 := [asserted]: #25
-#98 := [mp #88 #95]: #93
-#152 := [mp~ #98 #133]: #93
-#675 := [mp #152 #674]: #670
-#643 := (not #670)
-#631 := (or #643 #628)
-#632 := [quant-inst #43 #44]: #631
-#336 := [unit-resolution #632 #675]: #628
+#335 := [lemma #334]: #160
+decl f5 :: (-> S3 S2)
+#292 := (f5 #45)
+#609 := (= #292 f13)
+#630 := (= f13 #292)
+#14 := (:var 0 S5)
+#15 := (f6 #8 #14)
+#660 := (pattern #15)
+#16 := (f5 #15)
+#81 := (= #8 #16)
+#661 := (forall (vars (?v0 S2) (?v1 S5)) (:pat #660) #81)
+#85 := (forall (vars (?v0 S2) (?v1 S5)) #81)
+#664 := (iff #85 #661)
+#662 := (iff #81 #81)
+#663 := [refl]: #662
+#665 := [quant-intro #663]: #664
+#145 := (~ #85 #85)
+#139 := (~ #81 #81)
+#140 := [refl]: #139
+#146 := [nnf-pos #140]: #145
+#17 := (= #16 #8)
+#18 := (forall (vars (?v0 S2) (?v1 S5)) #17)
+#86 := (iff #18 #85)
+#83 := (iff #17 #81)
+#84 := [rewrite]: #83
+#87 := [quant-intro #84]: #86
+#80 := [asserted]: #18
+#90 := [mp #80 #87]: #85
+#147 := [mp~ #90 #146]: #85
+#666 := [mp #147 #665]: #661
+#289 := (not #661)
+#635 := (or #289 #630)
+#271 := [quant-inst #43 #44]: #635
+#336 := [unit-resolution #271 #666]: #630
 #610 := [symm #336]: #609
-#605 := (= f11 #285)
-#651 := (f5 #39)
-#619 := (= #651 #285)
+#605 := (= f10 #292)
+#642 := (f5 #39)
+#619 := (= #642 #292)
 #616 := (= #47 #45)
 #617 := [symm #337]: #616
 #330 := (= #39 #47)
-#255 := (or #48 #141)
-#326 := (or #48 #141 #315)
+#255 := (or #48 #161)
+#326 := (or #48 #161 #315)
 #327 := [def-axiom]: #326
 #328 := [unit-resolution #327 #177]: #255
 #338 := [unit-resolution #328 #335]: #48
 #614 := [trans #622 #338]: #330
 #618 := [trans #614 #617]: #346
 #608 := [monotonicity #618]: #619
-#646 := (= f11 #651)
-#301 := (or #643 #646)
-#644 := [quant-inst #37 #38]: #301
-#615 := [unit-resolution #644 #675]: #646
+#643 := (= f10 #642)
+#290 := (or #289 #643)
+#291 := [quant-inst #37 #38]: #290
+#615 := [unit-resolution #291 #666]: #643
 #606 := [trans #615 #608]: #605
-#611 := [trans #606 #610]: #50
-decl f4 :: (-> S2 S3)
-#292 := (f4 #45)
-#455 := (= #292 f13)
-#630 := (= f13 #292)
-#30 := (f4 #22)
-#105 := (= #20 #30)
-#683 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #669) #105)
-#109 := (forall (vars (?v0 S3) (?v1 S4)) #105)
-#686 := (iff #109 #683)
-#684 := (iff #105 #105)
-#685 := [refl]: #684
-#687 := [quant-intro #685]: #686
-#136 := (~ #109 #109)
-#156 := (~ #105 #105)
-#157 := [refl]: #156
-#137 := [nnf-pos #157]: #136
-#31 := (= #30 #20)
-#32 := (forall (vars (?v0 S3) (?v1 S4)) #31)
-#110 := (iff #32 #109)
-#107 := (iff #31 #105)
-#108 := [rewrite]: #107
-#111 := [quant-intro #108]: #110
-#104 := [asserted]: #32
-#114 := [mp #104 #111]: #109
-#158 := [mp~ #114 #137]: #109
-#688 := [mp #158 #687]: #683
-#289 := (not #683)
-#629 := (or #289 #630)
-#635 := [quant-inst #43 #44]: #629
-#612 := [unit-resolution #635 #688]: #630
+#611 := [trans #606 #610]: #49
+decl f8 :: (-> S3 S5)
+#634 := (f8 #45)
+#455 := (= #634 f14)
+#629 := (= f14 #634)
+#22 := (f8 #15)
+#97 := (= #14 #22)
+#673 := (forall (vars (?v0 S2) (?v1 S5)) (:pat #660) #97)
+#101 := (forall (vars (?v0 S2) (?v1 S5)) #97)
+#676 := (iff #101 #673)
+#674 := (iff #97 #97)
+#675 := [refl]: #674
+#677 := [quant-intro #675]: #676
+#143 := (~ #101 #101)
+#148 := (~ #97 #97)
+#149 := [refl]: #148
+#144 := [nnf-pos #149]: #143
+#23 := (= #22 #14)
+#24 := (forall (vars (?v0 S2) (?v1 S5)) #23)
+#102 := (iff #24 #101)
+#99 := (iff #23 #97)
+#100 := [rewrite]: #99
+#103 := [quant-intro #100]: #102
+#96 := [asserted]: #24
+#106 := [mp #96 #103]: #101
+#155 := [mp~ #106 #144]: #101
+#678 := [mp #155 #677]: #673
+#631 := (not #673)
+#276 := (or #631 #629)
+#277 := [quant-inst #43 #44]: #276
+#612 := [unit-resolution #277 #678]: #629
 #456 := [symm #612]: #455
-#598 := (= f10 #292)
-#300 := (f4 #39)
-#613 := (= #300 #292)
+#598 := (= f11 #634)
+#285 := (f8 #39)
+#613 := (= #285 #634)
 #454 := [monotonicity #618]: #613
-#305 := (= f10 #300)
-#290 := (or #289 #305)
-#291 := [quant-inst #37 #38]: #290
-#607 := [unit-resolution #291 #688]: #305
+#628 := (= f11 #285)
+#632 := (or #631 #628)
+#633 := [quant-inst #37 #38]: #632
+#607 := [unit-resolution #633 #678]: #628
 #599 := [trans #607 #454]: #598
-#600 := [trans #599 #456]: #49
-#237 := (or #141 #162 #163)
+#600 := [trans #599 #456]: #50
+#237 := (or #161 #158 #159)
 #324 := [def-axiom]: #237
 [unit-resolution #324 #600 #611 #335]: false
 unsat
-b85ad566d41295cad233b645b03aa0d599f756ba 144 0
-#2 := false
-decl f13 :: S3
+bb6d90f8a24326b7dc1b50e80f594ff94486f0cc 144 0
+#2 := false
+decl f13 :: S2
 #44 := f13
-decl f10 :: S3
+decl f10 :: S2
 #37 := f10
 #51 := (= f10 f13)
-decl f4 :: (-> S2 S3)
-decl f8 :: (-> S5 S2)
-decl f6 :: (-> S3 S2 S5)
-decl f3 :: (-> S3 S4 S2)
-decl f14 :: S4
+decl f5 :: (-> S3 S2)
+decl f7 :: (-> S4 S3)
+decl f4 :: (-> S2 S3 S4)
+decl f6 :: (-> S2 S5 S3)
+decl f14 :: S5
 #45 := f14
-#46 := (f3 f13 f14)
-decl f12 :: S3
+#46 := (f6 f13 f14)
+decl f12 :: S2
 #43 := f12
-#47 := (f6 f12 #46)
-#48 := (f8 #47)
-#49 := (f4 #48)
-decl f11 :: S4
+#47 := (f4 f12 #46)
+#48 := (f7 #47)
+#49 := (f5 #48)
+decl f11 :: S5
 #38 := f11
-#39 := (f3 f10 f11)
-decl f9 :: S3
+#39 := (f6 f10 f11)
+decl f9 :: S2
 #36 := f9
-#40 := (f6 f9 #39)
-#41 := (f8 #40)
-#42 := (f4 #41)
+#40 := (f4 f9 #39)
+#41 := (f7 #40)
+#42 := (f5 #41)
 #50 := (= #42 #49)
 #52 := (iff #50 #51)
 #318 := (= #49 f13)
-#609 := (f4 #46)
-#315 := (= #609 f13)
-#615 := (= f13 #609)
-#21 := (:var 0 S4)
-#20 := (:var 1 S3)
-#22 := (f3 #20 #21)
-#649 := (pattern #22)
-#30 := (f4 #22)
-#105 := (= #20 #30)
-#663 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #649) #105)
-#109 := (forall (vars (?v0 S3) (?v1 S4)) #105)
-#666 := (iff #109 #663)
-#664 := (iff #105 #105)
-#665 := [refl]: #664
-#667 := [quant-intro #665]: #666
-#136 := (~ #109 #109)
-#156 := (~ #105 #105)
-#157 := [refl]: #156
-#137 := [nnf-pos #157]: #136
-#31 := (= #30 #20)
-#32 := (forall (vars (?v0 S3) (?v1 S4)) #31)
-#110 := (iff #32 #109)
-#107 := (iff #31 #105)
-#108 := [rewrite]: #107
-#111 := [quant-intro #108]: #110
-#104 := [asserted]: #32
-#114 := [mp #104 #111]: #109
-#158 := [mp~ #114 #137]: #109
-#668 := [mp #158 #667]: #663
-#612 := (not #663)
-#257 := (or #612 #615)
-#619 := [quant-inst #44 #45]: #257
-#326 := [unit-resolution #619 #668]: #615
+#265 := (f5 #46)
+#315 := (= #265 f13)
+#608 := (= f13 #265)
+#14 := (:var 0 S5)
+#8 := (:var 1 S2)
+#15 := (f6 #8 #14)
+#640 := (pattern #15)
+#16 := (f5 #15)
+#81 := (= #8 #16)
+#641 := (forall (vars (?v0 S2) (?v1 S5)) (:pat #640) #81)
+#85 := (forall (vars (?v0 S2) (?v1 S5)) #81)
+#644 := (iff #85 #641)
+#642 := (iff #81 #81)
+#643 := [refl]: #642
+#645 := [quant-intro #643]: #644
+#133 := (~ #85 #85)
+#138 := (~ #81 #81)
+#132 := [refl]: #138
+#134 := [nnf-pos #132]: #133
+#17 := (= #16 #8)
+#18 := (forall (vars (?v0 S2) (?v1 S5)) #17)
+#86 := (iff #18 #85)
+#83 := (iff #17 #81)
+#84 := [rewrite]: #83
+#87 := [quant-intro #84]: #86
+#80 := [asserted]: #18
+#90 := [mp #80 #87]: #85
+#135 := [mp~ #90 #134]: #85
+#646 := [mp #135 #645]: #641
+#623 := (not #641)
+#611 := (or #623 #608)
+#612 := [quant-inst #44 #45]: #611
+#326 := [unit-resolution #612 #646]: #608
 #316 := [symm #326]: #315
-#605 := (= #49 #609)
+#605 := (= #49 #265)
 #604 := (= #48 #46)
-#617 := (= #46 #48)
-#8 := (:var 0 S2)
-#26 := (f6 #20 #8)
-#656 := (pattern #26)
-#27 := (f8 #26)
-#97 := (= #8 #27)
-#657 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #656) #97)
-#101 := (forall (vars (?v0 S3) (?v1 S2)) #97)
-#660 := (iff #101 #657)
-#658 := (iff #97 #97)
-#659 := [refl]: #658
-#661 := [quant-intro #659]: #660
-#134 := (~ #101 #101)
-#153 := (~ #97 #97)
-#154 := [refl]: #153
-#135 := [nnf-pos #154]: #134
-#28 := (= #27 #8)
-#29 := (forall (vars (?v0 S3) (?v1 S2)) #28)
-#102 := (iff #29 #101)
-#99 := (iff #28 #97)
-#100 := [rewrite]: #99
-#103 := [quant-intro #100]: #102
-#96 := [asserted]: #29
-#106 := [mp #96 #103]: #101
-#155 := [mp~ #106 #135]: #101
-#662 := [mp #155 #661]: #657
-#620 := (not #657)
-#332 := (or #620 #617)
-#223 := [quant-inst #43 #46]: #332
-#600 := [unit-resolution #223 #662]: #617
+#628 := (= #46 #48)
+#9 := (:var 0 S3)
+#10 := (f4 #8 #9)
+#633 := (pattern #10)
+#19 := (f7 #10)
+#89 := (= #9 #19)
+#647 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #633) #89)
+#93 := (forall (vars (?v0 S2) (?v1 S3)) #89)
+#650 := (iff #93 #647)
+#648 := (iff #89 #89)
+#649 := [refl]: #648
+#651 := [quant-intro #649]: #650
+#142 := (~ #93 #93)
+#136 := (~ #89 #89)
+#141 := [refl]: #136
+#143 := [nnf-pos #141]: #142
+#20 := (= #19 #9)
+#21 := (forall (vars (?v0 S2) (?v1 S3)) #20)
+#94 := (iff #21 #93)
+#91 := (iff #20 #89)
+#92 := [rewrite]: #91
+#95 := [quant-intro #92]: #94
+#88 := [asserted]: #21
+#98 := [mp #88 #95]: #93
+#148 := [mp~ #98 #143]: #93
+#652 := [mp #148 #651]: #647
+#621 := (not #647)
+#632 := (or #621 #628)
+#622 := [quant-inst #43 #46]: #632
+#600 := [unit-resolution #622 #652]: #628
 #601 := [symm #600]: #604
 #314 := [monotonicity #601]: #605
 #596 := [trans #314 #316]: #318
 #590 := (= #42 f10)
-#608 := (f4 #39)
-#588 := (= #608 f10)
-#269 := (= f10 #608)
-#613 := (or #612 #269)
-#614 := [quant-inst #37 #38]: #613
-#597 := [unit-resolution #614 #668]: #269
+#629 := (f5 #39)
+#588 := (= #629 f10)
+#626 := (= f10 #629)
+#281 := (or #623 #626)
+#624 := [quant-inst #37 #38]: #281
+#597 := [unit-resolution #624 #646]: #626
 #589 := [symm #597]: #588
-#595 := (= #42 #608)
+#595 := (= #42 #629)
 #594 := (= #41 #39)
-#618 := (= #39 #41)
-#606 := (or #620 #618)
-#607 := [quant-inst #36 #39]: #606
-#310 := [unit-resolution #607 #662]: #618
+#309 := (= #39 #41)
+#293 := (or #621 #309)
+#294 := [quant-inst #36 #39]: #293
+#310 := [unit-resolution #294 #652]: #309
 #598 := [symm #310]: #594
 #599 := [monotonicity #598]: #595
 #585 := [trans #599 #589]: #590
@@ -50420,8 +50791,8 @@
 #121 := (not #50)
 #591 := (iff #121 #304)
 #592 := [monotonicity #586]: #591
-#317 := [hypothesis]: #121
-#587 := [mp #317 #592]: #304
+#223 := [hypothesis]: #121
+#587 := [mp #223 #592]: #304
 #303 := (or #51 #50)
 #123 := (iff #51 #121)
 #53 := (not #52)
@@ -50433,7 +50804,7 @@
 #302 := (or #51 #50 #215)
 #216 := [def-axiom]: #302
 #217 := [unit-resolution #216 #128]: #303
-#602 := [unit-resolution #217 #317]: #51
+#602 := [unit-resolution #217 #223]: #51
 #593 := [unit-resolution #602 #587]: false
 #434 := [lemma #593]: #50
 #436 := [mp #434 #586]: #51
@@ -50444,119 +50815,119 @@
 #435 := [unit-resolution #235 #434]: #304
 [unit-resolution #435 #436]: false
 unsat
-b6231ad6e1765a00bbbe9f66100da15b0775b711 144 0
-#2 := false
-decl f14 :: S4
+ff464dff75d057630c9c6f2ae16d33617edf611b 144 0
+#2 := false
+decl f14 :: S5
 #45 := f14
-decl f11 :: S4
+decl f11 :: S5
 #38 := f11
 #51 := (= f11 f14)
-decl f5 :: (-> S2 S4)
-decl f8 :: (-> S5 S2)
-decl f6 :: (-> S3 S2 S5)
-decl f3 :: (-> S3 S4 S2)
-decl f13 :: S3
+decl f8 :: (-> S3 S5)
+decl f7 :: (-> S4 S3)
+decl f4 :: (-> S2 S3 S4)
+decl f6 :: (-> S2 S5 S3)
+decl f13 :: S2
 #44 := f13
-#46 := (f3 f13 f14)
-decl f12 :: S3
+#46 := (f6 f13 f14)
+decl f12 :: S2
 #43 := f12
-#47 := (f6 f12 #46)
-#48 := (f8 #47)
-#49 := (f5 #48)
-decl f10 :: S3
+#47 := (f4 f12 #46)
+#48 := (f7 #47)
+#49 := (f8 #48)
+decl f10 :: S2
 #37 := f10
-#39 := (f3 f10 f11)
-decl f9 :: S3
+#39 := (f6 f10 f11)
+decl f9 :: S2
 #36 := f9
-#40 := (f6 f9 #39)
-#41 := (f8 #40)
-#42 := (f5 #41)
+#40 := (f4 f9 #39)
+#41 := (f7 #40)
+#42 := (f8 #41)
 #50 := (= #42 #49)
 #52 := (iff #50 #51)
 #318 := (= #49 f14)
-#610 := (f5 #46)
-#315 := (= #610 f14)
-#611 := (= f14 #610)
-#21 := (:var 0 S4)
-#20 := (:var 1 S3)
-#22 := (f3 #20 #21)
-#649 := (pattern #22)
-#23 := (f5 #22)
-#89 := (= #21 #23)
-#650 := (forall (vars (?v0 S3) (?v1 S4)) (:pat #649) #89)
-#93 := (forall (vars (?v0 S3) (?v1 S4)) #89)
-#653 := (iff #93 #650)
-#651 := (iff #89 #89)
-#652 := [refl]: #651
-#654 := [quant-intro #652]: #653
-#132 := (~ #93 #93)
-#150 := (~ #89 #89)
-#151 := [refl]: #150
-#133 := [nnf-pos #151]: #132
-#24 := (= #23 #21)
-#25 := (forall (vars (?v0 S3) (?v1 S4)) #24)
-#94 := (iff #25 #93)
-#91 := (iff #24 #89)
+#272 := (f8 #46)
+#315 := (= #272 f14)
+#610 := (= f14 #272)
+#14 := (:var 0 S5)
+#8 := (:var 1 S2)
+#15 := (f6 #8 #14)
+#640 := (pattern #15)
+#22 := (f8 #15)
+#97 := (= #14 #22)
+#653 := (forall (vars (?v0 S2) (?v1 S5)) (:pat #640) #97)
+#101 := (forall (vars (?v0 S2) (?v1 S5)) #97)
+#656 := (iff #101 #653)
+#654 := (iff #97 #97)
+#655 := [refl]: #654
+#657 := [quant-intro #655]: #656
+#151 := (~ #101 #101)
+#149 := (~ #97 #97)
+#150 := [refl]: #149
+#152 := [nnf-pos #150]: #151
+#23 := (= #22 #14)
+#24 := (forall (vars (?v0 S2) (?v1 S5)) #23)
+#102 := (iff #24 #101)
+#99 := (iff #23 #97)
+#100 := [rewrite]: #99
+#103 := [quant-intro #100]: #102
+#96 := [asserted]: #24
+#106 := [mp #96 #103]: #101
+#153 := [mp~ #106 #152]: #101
+#658 := [mp #153 #657]: #653
+#269 := (not #653)
+#609 := (or #269 #610)
+#615 := [quant-inst #44 #45]: #609
+#326 := [unit-resolution #615 #658]: #610
+#316 := [symm #326]: #315
+#605 := (= #49 #272)
+#604 := (= #48 #46)
+#628 := (= #46 #48)
+#9 := (:var 0 S3)
+#10 := (f4 #8 #9)
+#633 := (pattern #10)
+#19 := (f7 #10)
+#89 := (= #9 #19)
+#647 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #633) #89)
+#93 := (forall (vars (?v0 S2) (?v1 S3)) #89)
+#650 := (iff #93 #647)
+#648 := (iff #89 #89)
+#649 := [refl]: #648
+#651 := [quant-intro #649]: #650
+#142 := (~ #93 #93)
+#140 := (~ #89 #89)
+#141 := [refl]: #140
+#143 := [nnf-pos #141]: #142
+#20 := (= #19 #9)
+#21 := (forall (vars (?v0 S2) (?v1 S3)) #20)
+#94 := (iff #21 #93)
+#91 := (iff #20 #89)
 #92 := [rewrite]: #91
 #95 := [quant-intro #92]: #94
-#88 := [asserted]: #25
+#88 := [asserted]: #21
 #98 := [mp #88 #95]: #93
-#152 := [mp~ #98 #133]: #93
-#655 := [mp #152 #654]: #650
-#270 := (not #650)
-#251 := (or #270 #611)
-#616 := [quant-inst #44 #45]: #251
-#326 := [unit-resolution #616 #655]: #611
-#316 := [symm #326]: #315
-#605 := (= #49 #610)
-#604 := (= #48 #46)
-#617 := (= #46 #48)
-#8 := (:var 0 S2)
-#26 := (f6 #20 #8)
-#656 := (pattern #26)
-#27 := (f8 #26)
-#97 := (= #8 #27)
-#657 := (forall (vars (?v0 S3) (?v1 S2)) (:pat #656) #97)
-#101 := (forall (vars (?v0 S3) (?v1 S2)) #97)
-#660 := (iff #101 #657)
-#658 := (iff #97 #97)
-#659 := [refl]: #658
-#661 := [quant-intro #659]: #660
-#134 := (~ #101 #101)
-#153 := (~ #97 #97)
-#154 := [refl]: #153
-#135 := [nnf-pos #154]: #134
-#28 := (= #27 #8)
-#29 := (forall (vars (?v0 S3) (?v1 S2)) #28)
-#102 := (iff #29 #101)
-#99 := (iff #28 #97)
-#100 := [rewrite]: #99
-#103 := [quant-intro #100]: #102
-#96 := [asserted]: #29
-#106 := [mp #96 #103]: #101
-#155 := [mp~ #106 #135]: #101
-#662 := [mp #155 #661]: #657
-#620 := (not #657)
-#332 := (or #620 #617)
-#223 := [quant-inst #43 #46]: #332
-#600 := [unit-resolution #223 #662]: #617
+#148 := [mp~ #98 #143]: #93
+#652 := [mp #148 #651]: #647
+#621 := (not #647)
+#632 := (or #621 #628)
+#622 := [quant-inst #43 #46]: #632
+#600 := [unit-resolution #622 #652]: #628
 #601 := [symm #600]: #604
 #314 := [monotonicity #601]: #605
 #596 := [trans #314 #316]: #318
 #590 := (= #42 f11)
-#623 := (f5 #39)
-#588 := (= #623 f11)
-#281 := (= f11 #623)
-#271 := (or #270 #281)
-#272 := [quant-inst #37 #38]: #271
-#597 := [unit-resolution #272 #655]: #281
+#280 := (f8 #39)
+#588 := (= #280 f11)
+#285 := (= f11 #280)
+#270 := (or #269 #285)
+#271 := [quant-inst #37 #38]: #270
+#597 := [unit-resolution #271 #658]: #285
 #589 := [symm #597]: #588
-#595 := (= #42 #623)
+#595 := (= #42 #280)
 #594 := (= #41 #39)
-#618 := (= #39 #41)
-#606 := (or #620 #618)
-#607 := [quant-inst #36 #39]: #606
-#310 := [unit-resolution #607 #662]: #618
+#309 := (= #39 #41)
+#293 := (or #621 #309)
+#294 := [quant-inst #36 #39]: #293
+#310 := [unit-resolution #294 #652]: #309
 #598 := [symm #310]: #594
 #599 := [monotonicity #598]: #595
 #585 := [trans #599 #589]: #590
@@ -50565,8 +50936,8 @@
 #121 := (not #50)
 #591 := (iff #121 #304)
 #592 := [monotonicity #586]: #591
-#317 := [hypothesis]: #121
-#587 := [mp #317 #592]: #304
+#223 := [hypothesis]: #121
+#587 := [mp #223 #592]: #304
 #303 := (or #51 #50)
 #123 := (iff #51 #121)
 #53 := (not #52)
@@ -50578,7 +50949,7 @@
 #302 := (or #51 #50 #215)
 #216 := [def-axiom]: #302
 #217 := [unit-resolution #216 #128]: #303
-#602 := [unit-resolution #217 #317]: #51
+#602 := [unit-resolution #217 #223]: #51
 #593 := [unit-resolution #602 #587]: false
 #434 := [lemma #593]: #50
 #436 := [mp #434 #586]: #51
@@ -50589,88 +50960,88 @@
 #435 := [unit-resolution #235 #434]: #304
 [unit-resolution #435 #436]: false
 unsat
-8157d199c7019faf223d954e5ed37245ebb98783 103 0
-#2 := false
-decl f7 :: S3
+c3d12f254b9672d4ea71a3aff4f3729162212903 103 0
+#2 := false
+decl f7 :: S2
 #24 := f7
-decl f6 :: S3
+decl f6 :: S2
 #23 := f6
 #29 := (= f6 f7)
-decl f5 :: (-> S2 S3)
-decl f3 :: (-> S3 S3 S2)
-#25 := (f3 f6 f7)
+decl f5 :: (-> S3 S2)
+decl f4 :: (-> S2 S2 S3)
+#25 := (f4 f6 f7)
 #27 := (f5 #25)
-decl f4 :: (-> S2 S3)
-#26 := (f4 #25)
+decl f3 :: (-> S3 S2)
+#26 := (f3 #25)
 #28 := (= #26 #27)
 #30 := (iff #28 #29)
 #561 := (iff #29 #28)
-#248 := (= f7 #27)
-#15 := (:var 0 S3)
-#14 := (:var 1 S3)
-#16 := (f3 #14 #15)
-#580 := (pattern #16)
-#17 := (f5 #16)
-#59 := (= #15 #17)
-#581 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #580) #59)
-#63 := (forall (vars (?v0 S3) (?v1 S3)) #59)
-#584 := (iff #63 #581)
-#582 := (iff #59 #59)
-#583 := [refl]: #582
-#585 := [quant-intro #583]: #584
-#84 := (~ #63 #63)
-#83 := (~ #59 #59)
-#96 := [refl]: #83
-#85 := [nnf-pos #96]: #84
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
-#64 := (iff #19 #63)
-#61 := (iff #18 #59)
+#244 := (= f7 #27)
+#9 := (:var 0 S2)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#572 := (pattern #10)
+#14 := (f5 #10)
+#59 := (= #9 #14)
+#579 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #572) #59)
+#63 := (forall (vars (?v0 S2) (?v1 S2)) #59)
+#582 := (iff #63 #579)
+#580 := (iff #59 #59)
+#581 := [refl]: #580
+#583 := [quant-intro #581]: #582
+#87 := (~ #63 #63)
+#85 := (~ #59 #59)
+#86 := [refl]: #85
+#88 := [nnf-pos #86]: #87
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
+#64 := (iff #16 #63)
+#61 := (iff #15 #59)
 #62 := [rewrite]: #61
 #65 := [quant-intro #62]: #64
-#58 := [asserted]: #19
+#58 := [asserted]: #16
 #68 := [mp #58 #65]: #63
-#97 := [mp~ #68 #85]: #63
-#586 := [mp #97 #585]: #581
-#560 := (not #581)
-#232 := (or #560 #248)
-#233 := [quant-inst #23 #24]: #232
-#565 := [unit-resolution #233 #586]: #248
-#227 := (= f6 #26)
-#20 := (f4 #16)
-#67 := (= #14 #20)
-#587 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #580) #67)
-#71 := (forall (vars (?v0 S3) (?v1 S3)) #67)
-#590 := (iff #71 #587)
-#588 := (iff #67 #67)
-#589 := [refl]: #588
-#591 := [quant-intro #589]: #590
-#86 := (~ #71 #71)
-#98 := (~ #67 #67)
-#99 := [refl]: #98
-#87 := [nnf-pos #99]: #86
-#21 := (= #20 #14)
-#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
-#72 := (iff #22 #71)
-#69 := (iff #21 #67)
-#70 := [rewrite]: #69
-#73 := [quant-intro #70]: #72
-#66 := [asserted]: #22
-#76 := [mp #66 #73]: #71
-#100 := [mp~ #76 #87]: #71
-#592 := [mp #100 #591]: #587
-#568 := (not #587)
-#569 := (or #568 #227)
-#570 := [quant-inst #23 #24]: #569
-#571 := [unit-resolution #570 #592]: #227
+#91 := [mp~ #68 #88]: #63
+#584 := [mp #91 #583]: #579
+#353 := (not #579)
+#560 := (or #353 #244)
+#232 := [quant-inst #23 #24]: #560
+#565 := [unit-resolution #232 #584]: #244
+#247 := (= f6 #26)
+#11 := (f3 #10)
+#52 := (= #8 #11)
+#573 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #572) #52)
+#55 := (forall (vars (?v0 S2) (?v1 S2)) #52)
+#576 := (iff #55 #573)
+#574 := (iff #52 #52)
+#575 := [refl]: #574
+#577 := [quant-intro #575]: #576
+#89 := (~ #55 #55)
+#94 := (~ #52 #52)
+#95 := [refl]: #94
+#90 := [nnf-pos #95]: #89
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#56 := (iff #13 #55)
+#53 := (iff #12 #52)
+#54 := [rewrite]: #53
+#57 := [quant-intro #54]: #56
+#51 := [asserted]: #13
+#60 := [mp #51 #57]: #55
+#84 := [mp~ #60 #90]: #55
+#578 := [mp #84 #577]: #573
+#227 := (not #573)
+#564 := (or #227 #247)
+#566 := [quant-inst #23 #24]: #564
+#571 := [unit-resolution #566 #578]: #247
 #219 := [monotonicity #571 #565]: #561
 #224 := [symm #219]: #30
 #243 := (not #29)
 #75 := (not #28)
 #562 := (iff #75 #243)
 #220 := [monotonicity #224]: #562
-#353 := [hypothesis]: #75
-#563 := [mp #353 #220]: #243
+#233 := [hypothesis]: #75
+#563 := [mp #233 #220]: #243
 #242 := (or #29 #28)
 #77 := (iff #29 #75)
 #31 := (not #30)
@@ -50682,7 +51053,7 @@
 #241 := (or #29 #28 #154)
 #155 := [def-axiom]: #241
 #156 := [unit-resolution #155 #82]: #242
-#567 := [unit-resolution #156 #353]: #29
+#567 := [unit-resolution #156 #233]: #29
 #204 := [unit-resolution #567 #563]: false
 #547 := [lemma #204]: #28
 #209 := [mp #547 #224]: #29
@@ -50693,28 +51064,28 @@
 #208 := [unit-resolution #174 #547]: #243
 [unit-resolution #208 #209]: false
 unsat
-14ec8583ed83b806bed26d093fab6c858f541eb6 111 0
-#2 := false
-decl f5 :: (-> S2 S3)
-decl f9 :: S2
+df71e79ae4d3b6ca6b9e37bd4464bcbb19ac1ad4 111 0
+#2 := false
+decl f5 :: (-> S3 S2)
+decl f9 :: S3
 #28 := f9
 #33 := (f5 f9)
-decl f4 :: (-> S2 S3)
-decl f6 :: S2
+decl f3 :: (-> S3 S2)
+decl f6 :: S3
 #23 := f6
-#32 := (f4 f6)
+#32 := (f3 f6)
 #34 := (= #32 #33)
-decl f3 :: (-> S3 S3 S2)
-decl f7 :: S3
+decl f4 :: (-> S2 S2 S3)
+decl f7 :: S2
 #24 := f7
-decl f8 :: S3
+decl f8 :: S2
 #25 := f8
-#29 := (f3 f8 f7)
-#169 := (f5 #29)
-#223 := (= #169 #33)
-#233 := (= #33 #169)
+#29 := (f4 f8 f7)
+#261 := (f5 #29)
+#223 := (= #261 #33)
+#233 := (= #33 #261)
 #30 := (= f9 #29)
-#26 := (f3 f7 f8)
+#26 := (f4 f7 f8)
 #27 := (= f6 #26)
 #31 := (and #27 #30)
 #80 := (not #31)
@@ -50732,70 +51103,70 @@
 #91 := [and-elim #88]: #30
 #576 := [monotonicity #91]: #233
 #224 := [symm #576]: #223
-#564 := (= #32 #169)
-#579 := (= f7 #169)
-#15 := (:var 0 S3)
-#14 := (:var 1 S3)
-#16 := (f3 #14 #15)
-#593 := (pattern #16)
-#17 := (f5 #16)
-#64 := (= #15 #17)
-#594 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #593) #64)
-#68 := (forall (vars (?v0 S3) (?v1 S3)) #64)
-#597 := (iff #68 #594)
-#595 := (iff #64 #64)
-#596 := [refl]: #595
-#598 := [quant-intro #596]: #597
-#97 := (~ #68 #68)
-#96 := (~ #64 #64)
-#113 := [refl]: #96
-#98 := [nnf-pos #113]: #97
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
-#69 := (iff #19 #68)
-#66 := (iff #18 #64)
+#564 := (= #32 #261)
+#240 := (= f7 #261)
+#9 := (:var 0 S2)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#585 := (pattern #10)
+#14 := (f5 #10)
+#64 := (= #9 #14)
+#592 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #585) #64)
+#68 := (forall (vars (?v0 S2) (?v1 S2)) #64)
+#595 := (iff #68 #592)
+#593 := (iff #64 #64)
+#594 := [refl]: #593
+#596 := [quant-intro #594]: #595
+#100 := (~ #68 #68)
+#98 := (~ #64 #64)
+#99 := [refl]: #98
+#101 := [nnf-pos #99]: #100
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S2)) #15)
+#69 := (iff #16 #68)
+#66 := (iff #15 #64)
 #67 := [rewrite]: #66
 #70 := [quant-intro #67]: #69
-#63 := [asserted]: #19
+#63 := [asserted]: #16
 #73 := [mp #63 #70]: #68
-#114 := [mp~ #73 #98]: #68
-#599 := [mp #114 #598]: #594
-#234 := (not #594)
-#583 := (or #234 #579)
-#578 := [quant-inst #25 #24]: #583
-#584 := [unit-resolution #578 #599]: #579
+#104 := [mp~ #73 #101]: #68
+#597 := [mp #104 #596]: #592
+#187 := (not #592)
+#573 := (or #187 #240)
+#245 := [quant-inst #25 #24]: #573
+#584 := [unit-resolution #245 #597]: #240
 #562 := (= #32 f7)
-#254 := (f4 #26)
-#221 := (= #254 f7)
-#261 := (= f7 #254)
-#20 := (f4 #16)
-#72 := (= #14 #20)
-#600 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #593) #72)
-#76 := (forall (vars (?v0 S3) (?v1 S3)) #72)
-#603 := (iff #76 #600)
-#601 := (iff #72 #72)
-#602 := [refl]: #601
-#604 := [quant-intro #602]: #603
-#99 := (~ #76 #76)
-#115 := (~ #72 #72)
-#116 := [refl]: #115
-#100 := [nnf-pos #116]: #99
-#21 := (= #20 #14)
-#22 := (forall (vars (?v0 S3) (?v1 S3)) #21)
-#77 := (iff #22 #76)
-#74 := (iff #21 #72)
-#75 := [rewrite]: #74
-#78 := [quant-intro #75]: #77
-#71 := [asserted]: #22
-#81 := [mp #71 #78]: #76
-#117 := [mp~ #81 #100]: #76
-#605 := [mp #117 #604]: #600
-#246 := (not #600)
-#580 := (or #246 #261)
-#581 := [quant-inst #24 #25]: #580
-#582 := [unit-resolution #581 #605]: #261
-#222 := [symm #582]: #221
-#237 := (= #32 #254)
+#167 := (f3 #26)
+#221 := (= #167 f7)
+#254 := (= f7 #167)
+#11 := (f3 #10)
+#57 := (= #8 #11)
+#586 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #585) #57)
+#60 := (forall (vars (?v0 S2) (?v1 S2)) #57)
+#589 := (iff #60 #586)
+#587 := (iff #57 #57)
+#588 := [refl]: #587
+#590 := [quant-intro #588]: #589
+#102 := (~ #60 #60)
+#107 := (~ #57 #57)
+#108 := [refl]: #107
+#103 := [nnf-pos #108]: #102
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#61 := (iff #13 #60)
+#58 := (iff #12 #57)
+#59 := [rewrite]: #58
+#62 := [quant-intro #59]: #61
+#56 := [asserted]: #13
+#65 := [mp #56 #62]: #60
+#97 := [mp~ #65 #103]: #60
+#591 := [mp #97 #590]: #586
+#169 := (not #586)
+#256 := (or #169 #254)
+#247 := [quant-inst #24 #25]: #256
+#578 := [unit-resolution #247 #591]: #254
+#222 := [symm #578]: #221
+#237 := (= #32 #167)
 #89 := [and-elim #88]: #27
 #575 := [monotonicity #89]: #237
 #563 := [trans #575 #222]: #562
@@ -50805,23 +51176,57 @@
 #93 := [not-or-elim #90]: #92
 [unit-resolution #93 #566]: false
 unsat
-139963e49c370526a172ba9c7501eab1a4a7d779 113 0
-#2 := false
-decl f3 :: (-> S3 S3 S2)
-decl f4 :: (-> S2 S3)
-decl f6 :: S2
+e078bb600df2bd0f41e49114d3117704e2a9b9b4 117 0
+#2 := false
+decl f4 :: (-> S2 S2 S3)
+decl f3 :: (-> S3 S2)
+decl f6 :: S3
 #23 := f6
-#24 := (f4 f6)
-decl f5 :: (-> S2 S3)
+#24 := (f3 f6)
+decl f5 :: (-> S3 S2)
 #25 := (f5 f6)
-#27 := (f3 #25 #24)
+#27 := (f4 #25 #24)
 #28 := (= f6 #27)
-#246 := (f3 #24 #25)
-#550 := (= #246 #27)
-#548 := (= #27 #246)
+#352 := (f4 #24 #25)
+#553 := (= #352 #27)
+#552 := (= #27 #352)
 #26 := (= #24 #25)
-#247 := (f5 #27)
-#561 := (= #247 #25)
+#246 := (f3 #27)
+#546 := (= #246 #25)
+#243 := (= #25 #246)
+#9 := (:var 0 S2)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#571 := (pattern #10)
+#11 := (f3 #10)
+#51 := (= #8 #11)
+#572 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #571) #51)
+#54 := (forall (vars (?v0 S2) (?v1 S2)) #51)
+#575 := (iff #54 #572)
+#573 := (iff #51 #51)
+#574 := [refl]: #573
+#576 := [quant-intro #574]: #575
+#88 := (~ #54 #54)
+#93 := (~ #51 #51)
+#94 := [refl]: #93
+#89 := [nnf-pos #94]: #88
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S2)) #12)
+#55 := (iff #13 #54)
+#52 := (iff #12 #51)
+#53 := [rewrite]: #52
+#56 := [quant-intro #53]: #55
+#50 := [asserted]: #13
+#59 := [mp #50 #56]: #54
+#83 := [mp~ #59 #89]: #54
+#577 := [mp #83 #576]: #572
+#563 := (not #572)
+#565 := (or #563 #243)
+#220 := [quant-inst #25 #24]: #565
+#223 := [unit-resolution #220 #577]: #243
+#207 := [symm #223]: #546
+#562 := (= #24 #246)
+#561 := (= #246 #24)
 #560 := (= #27 f6)
 #74 := (not #26)
 #567 := [hypothesis]: #74
@@ -50840,948 +51245,938 @@
 #568 := [unit-resolution #155 #567]: #28
 #218 := [symm #568]: #560
 #219 := [monotonicity #218]: #561
-#226 := (= #24 #247)
-#15 := (:var 0 S3)
-#14 := (:var 1 S3)
-#16 := (f3 #14 #15)
-#579 := (pattern #16)
-#17 := (f5 #16)
-#58 := (= #15 #17)
-#580 := (forall (vars (?v0 S3) (?v1 S3)) (:pat #579) #58)
-#62 := (forall (vars (?v0 S3) (?v1 S3)) #58)
-#583 := (iff #62 #580)
-#581 := (iff #58 #58)
-#582 := [refl]: #581
-#584 := [quant-intro #582]: #583
-#83 := (~ #62 #62)
-#82 := (~ #58 #58)
-#95 := [refl]: #82
-#84 := [nnf-pos #95]: #83
-#18 := (= #17 #15)
-#19 := (forall (vars (?v0 S3) (?v1 S3)) #18)
-#63 := (iff #19 #62)
-#60 := (iff #18 #58)
-#61 := [rewrite]: #60
-#64 := [quant-intro #61]: #63
-#57 := [asserted]: #19
-#67 := [mp #57 #64]: #62
-#96 := [mp~ #67 #84]: #62
-#585 := [mp #96 #584]: #580
-#231 := (not #580)
-#232 := (or #231 #226)
-#566 := [quant-inst #25 #24]: #232
-#223 := [unit-resolution #566 #585]: #226
-#562 := [trans #223 #219]: #26
-#203 := [unit-resolution #567 #562]: false
-#546 := [lemma #203]: #26
-#208 := (= #25 #24)
-#209 := [symm #546]: #208
-#549 := [monotonicity #209 #546]: #548
-#551 := [symm #549]: #550
-#243 := (= f6 #246)
-#8 := (:var 0 S2)
-#10 := (f5 #8)
-#572 := (pattern #10)
-#9 := (f4 #8)
-#571 := (pattern #9)
-#11 := (f3 #9 #10)
-#51 := (= #8 #11)
-#573 := (forall (vars (?v0 S2)) (:pat #571 #572) #51)
-#54 := (forall (vars (?v0 S2)) #51)
-#576 := (iff #54 #573)
-#574 := (iff #51 #51)
-#575 := [refl]: #574
-#577 := [quant-intro #575]: #576
-#93 := (~ #54 #54)
-#91 := (~ #51 #51)
+#203 := [symm #219]: #562
+#208 := [trans #203 #207]: #26
+#209 := [unit-resolution #567 #208]: false
+#210 := [lemma #209]: #26
+#549 := (= #25 #24)
+#550 := [symm #210]: #549
+#547 := [monotonicity #550 #210]: #552
+#189 := [symm #547]: #553
+#559 := (= f6 #352)
+#17 := (:var 0 S3)
+#19 := (f5 #17)
+#585 := (pattern #19)
+#18 := (f3 #17)
+#584 := (pattern #18)
+#20 := (f4 #18 #19)
+#66 := (= #17 #20)
+#586 := (forall (vars (?v0 S3)) (:pat #584 #585) #66)
+#70 := (forall (vars (?v0 S3)) #66)
+#589 := (iff #70 #586)
+#587 := (iff #66 #66)
+#588 := [refl]: #587
+#590 := [quant-intro #588]: #589
+#95 := (~ #70 #70)
+#91 := (~ #66 #66)
 #92 := [refl]: #91
-#94 := [nnf-pos #92]: #93
-#12 := (= #11 #8)
-#13 := (forall (vars (?v0 S2)) #12)
-#55 := (iff #13 #54)
-#52 := (iff #12 #51)
-#53 := [rewrite]: #52
-#56 := [quant-intro #53]: #55
-#50 := [asserted]: #13
-#59 := [mp #50 #56]: #54
-#80 := [mp~ #59 #94]: #54
-#578 := [mp #80 #577]: #573
-#563 := (not #573)
-#565 := (or #563 #243)
-#220 := [quant-inst #23]: #565
-#210 := [unit-resolution #220 #578]: #243
-#552 := [trans #210 #551]: #28
+#96 := [nnf-pos #92]: #95
+#21 := (= #20 #17)
+#22 := (forall (vars (?v0 S3)) #21)
+#71 := (iff #22 #70)
+#68 := (iff #21 #66)
+#69 := [rewrite]: #68
+#72 := [quant-intro #69]: #71
+#65 := [asserted]: #22
+#75 := [mp #65 #72]: #70
+#97 := [mp~ #75 #96]: #70
+#591 := [mp #97 #590]: #586
+#569 := (not #586)
+#564 := (or #569 #559)
+#570 := [quant-inst #23]: #564
+#551 := [unit-resolution #570 #591]: #559
+#554 := [trans #551 #189]: #28
 #242 := (not #28)
 #245 := (or #242 #74)
 #233 := (or #242 #74 #153)
 #244 := [def-axiom]: #233
 #173 := [unit-resolution #244 #81]: #245
-#207 := [unit-resolution #173 #546]: #242
-[unit-resolution #207 #552]: false
-unsat
-49afcc0d7e8a703cc498df193e407add0e832e10 72 0
-#2 := false
-decl f4 :: (-> S4 S5 S5)
-decl f9 :: S5
-#22 := f9
-decl f16 :: S4
-#59 := f16
-#60 := (f4 f16 f9)
-#270 := (f4 f16 #60)
-#343 := (= f9 #270)
-#320 := (= #60 #270)
-#336 := (= #270 #60)
-#61 := (= #60 f9)
-#146 := (= f9 #60)
+#548 := [unit-resolution #173 #210]: #242
+[unit-resolution #548 #554]: false
+unsat
+e0d0d958c704cd740ed0ffb718fec05abf4295fd 82 0
+#2 := false
+decl f4 :: (-> S2 S3 S3)
+decl f6 :: S3
+#26 := f6
+decl f14 :: S2
+#57 := f14
+#58 := (f4 f14 f6)
+#269 := (f4 f14 #58)
+#357 := (= f6 #269)
+#319 := (= #58 #269)
+#335 := (= #269 #58)
+#59 := (= #58 f6)
+#145 := (= f6 #58)
+#60 := (not #59)
+#61 := (not #60)
+#156 := (iff #61 #145)
+#148 := (not #145)
+#151 := (not #148)
+#154 := (iff #151 #145)
+#155 := [rewrite]: #154
+#152 := (iff #61 #151)
+#149 := (iff #60 #148)
+#146 := (iff #59 #145)
+#147 := [rewrite]: #146
+#150 := [monotonicity #147]: #149
+#153 := [monotonicity #150]: #152
+#157 := [trans #153 #155]: #156
+#143 := [asserted]: #61
+#160 := [mp #143 #157]: #145
+#676 := [symm #160]: #59
+#678 := [monotonicity #676]: #335
+#662 := [symm #678]: #319
+#323 := [trans #160 #662]: #357
+#349 := (not #357)
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#687 := (pattern #10)
+#30 := (= #10 f6)
+#31 := (not #30)
+#707 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #687) #31)
+#32 := (forall (vars (?v0 S2) (?v1 S3)) #31)
+#710 := (iff #32 #707)
+#708 := (iff #31 #31)
+#709 := [refl]: #708
+#711 := [quant-intro #709]: #710
+#194 := (~ #32 #32)
+#192 := (~ #31 #31)
+#193 := [refl]: #192
+#195 := [nnf-pos #193]: #194
+#27 := (= f6 #10)
+#28 := (not #27)
+#29 := (forall (vars (?v0 S2) (?v1 S3)) #28)
+#122 := (iff #29 #32)
+#120 := (iff #28 #31)
+#117 := (iff #27 #30)
+#119 := [rewrite]: #117
+#121 := [monotonicity #119]: #120
+#123 := [quant-intro #121]: #122
+#116 := [asserted]: #29
+#126 := [mp #116 #123]: #32
+#196 := [mp~ #126 #195]: #32
+#712 := [mp #196 #711]: #707
+#289 := (not #707)
+#362 := (or #289 #349)
+#356 := (= #269 f6)
+#270 := (not #356)
+#359 := (or #289 #270)
+#342 := (iff #359 #362)
+#681 := (iff #362 #362)
+#336 := [rewrite]: #681
+#360 := (iff #270 #349)
+#271 := (iff #356 #357)
+#358 := [rewrite]: #271
+#361 := [monotonicity #358]: #360
+#679 := [monotonicity #361]: #342
+#468 := [trans #679 #336]: #342
+#363 := [quant-inst #57 #58]: #359
+#675 := [mp #363 #468]: #362
+#686 := [unit-resolution #675 #712]: #349
+[unit-resolution #686 #323]: false
+unsat
+08e36b4206627321e9ef13c16c3c6ff1083524c9 69 0
+#2 := false
+decl f4 :: (-> S2 S3 S3)
+decl f6 :: S3
+#26 := f6
+decl f15 :: S2
+#58 := f15
+#59 := (f4 f15 f6)
+decl f14 :: S2
+#57 := f14
+#60 := (f4 f14 #59)
+#147 := (= f6 #60)
+#61 := (= #60 f6)
 #62 := (not #61)
 #63 := (not #62)
-#158 := (iff #63 #146)
-#150 := (not #146)
+#158 := (iff #63 #147)
+#150 := (not #147)
 #153 := (not #150)
-#156 := (iff #153 #146)
+#156 := (iff #153 #147)
 #157 := [rewrite]: #156
 #154 := (iff #63 #153)
 #151 := (iff #62 #150)
-#148 := (iff #61 #146)
+#148 := (iff #61 #147)
 #149 := [rewrite]: #148
 #152 := [monotonicity #149]: #151
 #155 := [monotonicity #152]: #154
 #159 := [trans #155 #157]: #158
 #145 := [asserted]: #63
-#162 := [mp #145 #159]: #146
-#678 := [symm #162]: #61
-#679 := [monotonicity #678]: #336
-#663 := [symm #679]: #320
-#324 := [trans #162 #663]: #343
-#337 := (not #343)
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#717 := (pattern #12)
-#38 := (= #12 f9)
-#39 := (not #38)
-#718 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #717) #39)
-#40 := (forall (vars (?v0 S4) (?v1 S5)) #39)
-#721 := (iff #40 #718)
-#719 := (iff #39 #39)
-#720 := [refl]: #719
-#722 := [quant-intro #720]: #721
-#165 := (~ #40 #40)
-#167 := (~ #39 #39)
-#164 := [refl]: #167
-#161 := [nnf-pos #164]: #165
-#100 := [asserted]: #40
-#163 := [mp~ #100 #161]: #40
-#723 := [mp #163 #722]: #718
-#348 := (not #718)
-#349 := (or #348 #337)
-#362 := (= #270 f9)
-#290 := (not #362)
-#683 := (or #348 #290)
-#685 := (iff #683 #349)
-#681 := (iff #349 #349)
-#687 := [rewrite]: #681
-#469 := (iff #290 #337)
-#680 := (iff #362 #343)
-#682 := [rewrite]: #680
-#676 := [monotonicity #682]: #469
-#686 := [monotonicity #676]: #685
-#677 := [trans #686 #687]: #685
-#684 := [quant-inst #59 #60]: #683
-#335 := [mp #684 #677]: #349
-#340 := [unit-resolution #335 #723]: #337
-[unit-resolution #340 #324]: false
-unsat
-04befb37cbbc5695f38171536eac721870f8c5ee 59 0
-#2 := false
-decl f4 :: (-> S4 S5 S5)
-decl f9 :: S5
-#22 := f9
-decl f17 :: S4
-#60 := f17
-#61 := (f4 f17 f9)
-decl f16 :: S4
+#162 := [mp #145 #159]: #147
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#689 := (pattern #10)
+#30 := (= #10 f6)
+#31 := (not #30)
+#709 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #689) #31)
+#32 := (forall (vars (?v0 S2) (?v1 S3)) #31)
+#712 := (iff #32 #709)
+#710 := (iff #31 #31)
+#711 := [refl]: #710
+#713 := [quant-intro #711]: #712
+#196 := (~ #32 #32)
+#194 := (~ #31 #31)
+#195 := [refl]: #194
+#197 := [nnf-pos #195]: #196
+#27 := (= f6 #10)
+#28 := (not #27)
+#29 := (forall (vars (?v0 S2) (?v1 S3)) #28)
+#124 := (iff #29 #32)
+#122 := (iff #28 #31)
+#119 := (iff #27 #30)
+#121 := [rewrite]: #119
+#123 := [monotonicity #121]: #122
+#125 := [quant-intro #123]: #124
+#118 := [asserted]: #29
+#128 := [mp #118 #125]: #32
+#198 := [mp~ #128 #197]: #32
+#714 := [mp #198 #713]: #709
+#364 := (not #709)
+#649 := (or #364 #150)
+#490 := (or #364 #62)
+#636 := (iff #490 #649)
+#631 := (iff #649 #649)
+#632 := [rewrite]: #631
+#637 := [monotonicity #152]: #636
+#638 := [trans #637 #632]: #636
+#635 := [quant-inst #57 #59]: #490
+#639 := [mp #635 #638]: #649
+[unit-resolution #639 #714 #162]: false
+unsat
+e3c83bfe7d36b6dbe01f810a411eecc94e2d0020 136 0
+#2 := false
+decl f4 :: (-> S2 S3 S3)
+decl f6 :: S3
+#26 := f6
+decl f15 :: S2
+#58 := f15
+#62 := (f4 f15 f6)
+decl f14 :: S2
+#57 := f14
+#61 := (f4 f14 f6)
+#63 := (= #61 #62)
+#59 := (= f14 f15)
+#310 := (iff #59 #63)
+#657 := (not #310)
+#64 := (not #63)
+#150 := (or #59 #64)
+#153 := (not #150)
+#60 := (not #59)
+#65 := (implies #60 #64)
+#66 := (not #65)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#148 := [asserted]: #66
+#158 := [mp #148 #155]: #153
+#157 := [not-or-elim #158]: #63
+#156 := [not-or-elim #158]: #60
+#379 := (or #657 #59 #64)
+#380 := [def-axiom]: #379
+#616 := [unit-resolution #380 #156 #157]: #657
+#18 := (:var 2 S3)
+#17 := (:var 3 S2)
+#19 := (f4 #17 #18)
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#700 := (pattern #10 #19)
+#109 := (= #9 #18)
+#163 := (not #109)
+#106 := (= #8 #17)
+#162 := (not #106)
+#160 := (or #162 #163)
+#161 := (not #160)
+#102 := (= #10 #19)
+#205 := (iff #102 #161)
+#701 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) (:pat #700) #205)
+#208 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #205)
+#704 := (iff #208 #701)
+#702 := (iff #205 #205)
+#703 := [refl]: #702
+#705 := [quant-intro #703]: #704
+#112 := (and #106 #109)
+#115 := (iff #102 #112)
+#118 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #115)
+#209 := (iff #118 #208)
+#206 := (iff #115 #205)
+#203 := (iff #112 #161)
+#204 := [rewrite]: #203
+#207 := [monotonicity #204]: #206
+#210 := [quant-intro #207]: #209
+#191 := (~ #118 #118)
+#177 := (~ #115 #115)
+#178 := [refl]: #177
+#192 := [nnf-pos #178]: #191
+#22 := (= #18 #9)
+#21 := (= #17 #8)
+#23 := (and #21 #22)
+#20 := (= #19 #10)
+#24 := (iff #20 #23)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2) (?v3 S3)) #24)
+#119 := (iff #25 #118)
+#116 := (iff #24 #115)
+#113 := (iff #23 #112)
+#110 := (iff #22 #109)
+#111 := [rewrite]: #110
+#107 := (iff #21 #106)
+#108 := [rewrite]: #107
+#114 := [monotonicity #108 #111]: #113
+#104 := (iff #20 #102)
+#105 := [rewrite]: #104
+#117 := [monotonicity #105 #114]: #116
+#120 := [quant-intro #117]: #119
+#101 := [asserted]: #25
+#123 := [mp #101 #120]: #118
+#193 := [mp~ #123 #192]: #118
+#211 := [mp #193 #210]: #208
+#706 := [mp #211 #705]: #701
+#660 := (not #701)
+#661 := (or #660 #310)
+#675 := (= f6 f6)
+#347 := (not #675)
+#348 := (or #60 #347)
+#682 := (not #348)
+#683 := (iff #63 #682)
+#367 := (or #660 #683)
+#384 := (iff #367 #661)
+#371 := (iff #661 #661)
+#386 := [rewrite]: #371
+#671 := (iff #683 #310)
+#305 := (iff #63 #59)
+#311 := (iff #305 #310)
+#673 := [rewrite]: #311
+#670 := (iff #683 #305)
+#663 := (iff #682 #59)
+#664 := (not #60)
+#667 := (iff #664 #59)
+#668 := [rewrite]: #667
+#665 := (iff #682 #664)
+#325 := (iff #348 #60)
+#678 := (or #60 false)
+#323 := (iff #678 #60)
+#324 := [rewrite]: #323
+#319 := (iff #348 #678)
+#677 := (iff #347 false)
+#1 := true
+#680 := (not true)
+#334 := (iff #680 false)
+#339 := [rewrite]: #334
+#686 := (iff #347 #680)
+#684 := (iff #675 true)
+#685 := [rewrite]: #684
+#676 := [monotonicity #685]: #686
+#335 := [trans #676 #339]: #677
+#662 := [monotonicity #335]: #319
+#326 := [trans #662 #324]: #325
+#666 := [monotonicity #326]: #665
+#669 := [trans #666 #668]: #663
+#672 := [monotonicity #669]: #670
+#674 := [trans #672 #673]: #671
+#385 := [monotonicity #674]: #384
+#277 := [trans #385 #386]: #384
+#383 := [quant-inst #58 #26 #57 #26]: #367
+#656 := [mp #383 #277]: #661
+[unit-resolution #656 #706 #616]: false
+unsat
+8500def9bd98753ab4a7655e9231b63171fa5f04 50 0
+#2 := false
+decl f3 :: (-> S3 S2)
+decl f4 :: (-> S2 S3 S3)
+decl f15 :: S3
+#58 := f15
+decl f14 :: S2
+#57 := f14
+#59 := (f4 f14 f15)
+#60 := (f3 #59)
+#146 := (= f14 #60)
+#149 := (not #146)
+#61 := (= #60 f14)
+#62 := (not #61)
+#150 := (iff #62 #149)
+#147 := (iff #61 #146)
+#148 := [rewrite]: #147
+#151 := [monotonicity #148]: #150
+#144 := [asserted]: #62
+#154 := [mp #144 #151]: #149
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#681 := (pattern #10)
+#11 := (f3 #10)
+#83 := (= #8 #11)
+#682 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #681) #83)
+#86 := (forall (vars (?v0 S2) (?v1 S3)) #83)
+#685 := (iff #86 #682)
+#683 := (iff #83 #83)
+#684 := [refl]: #683
+#686 := [quant-intro #684]: #685
+#170 := (~ #86 #86)
+#177 := (~ #83 #83)
+#178 := [refl]: #177
+#171 := [nnf-pos #178]: #170
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S3)) #12)
+#87 := (iff #13 #86)
+#84 := (iff #12 #83)
+#85 := [rewrite]: #84
+#88 := [quant-intro #85]: #87
+#82 := [asserted]: #13
+#91 := [mp #82 #88]: #86
+#125 := [mp~ #91 #171]: #86
+#687 := [mp #125 #686]: #682
+#342 := (not #682)
+#676 := (or #342 #146)
+#677 := [quant-inst #57 #58]: #676
+[unit-resolution #677 #687 #154]: false
+unsat
+a4455fa26a2bf5d21921399b4d6f0e721daff1a2 50 0
+#2 := false
+decl f5 :: (-> S3 S3)
+decl f4 :: (-> S2 S3 S3)
+decl f15 :: S3
+#58 := f15
+decl f14 :: S2
+#57 := f14
+#59 := (f4 f14 f15)
+#60 := (f5 #59)
+#146 := (= f15 #60)
+#149 := (not #146)
+#61 := (= #60 f15)
+#62 := (not #61)
+#150 := (iff #62 #149)
+#147 := (iff #61 #146)
+#148 := [rewrite]: #147
+#151 := [monotonicity #148]: #150
+#144 := [asserted]: #62
+#154 := [mp #144 #151]: #149
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#681 := (pattern #10)
+#14 := (f5 #10)
+#90 := (= #9 #14)
+#688 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #681) #90)
+#94 := (forall (vars (?v0 S2) (?v1 S3)) #90)
+#691 := (iff #94 #688)
+#689 := (iff #90 #90)
+#690 := [refl]: #689
+#692 := [quant-intro #690]: #691
+#158 := (~ #94 #94)
+#165 := (~ #90 #90)
+#166 := [refl]: #165
+#159 := [nnf-pos #166]: #158
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
+#95 := (iff #16 #94)
+#92 := (iff #15 #90)
+#93 := [rewrite]: #92
+#96 := [quant-intro #93]: #95
+#89 := [asserted]: #16
+#99 := [mp #89 #96]: #94
+#160 := [mp~ #99 #159]: #94
+#693 := [mp #160 #692]: #688
+#674 := (not #688)
+#680 := (or #674 #146)
+#670 := [quant-inst #57 #58]: #680
+[unit-resolution #670 #693 #154]: false
+unsat
+65f5926fa55a56a20b93bf43ca8b606d7a725e83 56 0
+#2 := false
+decl f3 :: (-> S3 S2)
+decl f4 :: (-> S2 S3 S3)
+decl f6 :: S3
+#26 := f6
+decl f16 :: S2
 #59 := f16
-#62 := (f4 f16 #61)
-#148 := (= f9 #62)
-#63 := (= #62 f9)
-#64 := (not #63)
+#60 := (f4 f16 f6)
+decl f15 :: S2
+#58 := f15
+#61 := (f4 f15 #60)
+decl f14 :: S2
+#57 := f14
+#62 := (f4 f14 #61)
+#63 := (f3 #62)
+#149 := (= f14 #63)
+#152 := (not #149)
+#64 := (= #63 f14)
 #65 := (not #64)
-#160 := (iff #65 #148)
-#152 := (not #148)
-#155 := (not #152)
-#158 := (iff #155 #148)
-#159 := [rewrite]: #158
-#156 := (iff #65 #155)
-#153 := (iff #64 #152)
-#150 := (iff #63 #148)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
+#151 := [rewrite]: #150
+#154 := [monotonicity #151]: #153
+#147 := [asserted]: #65
+#157 := [mp #147 #154]: #152
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#684 := (pattern #10)
+#11 := (f3 #10)
+#86 := (= #8 #11)
+#685 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #684) #86)
+#89 := (forall (vars (?v0 S2) (?v1 S3)) #86)
+#688 := (iff #89 #685)
+#686 := (iff #86 #86)
+#687 := [refl]: #686
+#689 := [quant-intro #687]: #688
+#169 := (~ #89 #89)
+#128 := (~ #86 #86)
+#168 := [refl]: #128
+#159 := [nnf-pos #168]: #169
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S3)) #12)
+#90 := (iff #13 #89)
+#87 := (iff #12 #86)
+#88 := [rewrite]: #87
+#91 := [quant-intro #88]: #90
+#85 := [asserted]: #13
+#94 := [mp #85 #91]: #89
+#160 := [mp~ #94 #159]: #89
+#690 := [mp #160 #689]: #685
+#618 := (not #685)
+#436 := (or #618 #149)
+#429 := [quant-inst #57 #61]: #436
+[unit-resolution #429 #690 #157]: false
+unsat
+d48bb23843eefa7d190bfd37fdd1c5737b414ba9 56 0
+#2 := false
+decl f5 :: (-> S3 S3)
+decl f4 :: (-> S2 S3 S3)
+decl f6 :: S3
+#26 := f6
+decl f16 :: S2
+#59 := f16
+#60 := (f4 f16 f6)
+decl f15 :: S2
+#58 := f15
+#61 := (f4 f15 #60)
+decl f14 :: S2
+#57 := f14
+#62 := (f4 f14 #61)
+#63 := (f5 #62)
+#149 := (= #61 #63)
+#152 := (not #149)
+#64 := (= #63 #61)
+#65 := (not #64)
+#153 := (iff #65 #152)
+#150 := (iff #64 #149)
 #151 := [rewrite]: #150
 #154 := [monotonicity #151]: #153
-#157 := [monotonicity #154]: #156
-#161 := [trans #157 #159]: #160
 #147 := [asserted]: #65
-#164 := [mp #147 #161]: #148
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#719 := (pattern #12)
-#38 := (= #12 f9)
-#39 := (not #38)
-#720 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #719) #39)
-#40 := (forall (vars (?v0 S4) (?v1 S5)) #39)
-#723 := (iff #40 #720)
-#721 := (iff #39 #39)
-#722 := [refl]: #721
-#724 := [quant-intro #722]: #723
-#167 := (~ #40 #40)
-#169 := (~ #39 #39)
-#166 := [refl]: #169
-#163 := [nnf-pos #166]: #167
-#102 := [asserted]: #40
-#165 := [mp~ #102 #163]: #40
-#725 := [mp #165 #724]: #720
-#351 := (not #720)
-#635 := (or #351 #152)
-#636 := (or #351 #64)
-#633 := (iff #636 #635)
-#640 := (iff #635 #635)
-#634 := [rewrite]: #640
-#639 := [monotonicity #154]: #633
-#641 := [trans #639 #634]: #633
-#632 := [quant-inst #59 #61]: #636
-#470 := [mp #632 #641]: #635
-[unit-resolution #470 #725 #164]: false
-unsat
-b0341ff23e5abb796f1191ac954b55a496b57644 136 0
-#2 := false
-decl f4 :: (-> S4 S5 S5)
-decl f9 :: S5
-#22 := f9
-decl f17 :: S4
-#60 := f17
-#64 := (f4 f17 f9)
-decl f16 :: S4
+#157 := [mp #147 #154]: #152
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#684 := (pattern #10)
+#14 := (f5 #10)
+#93 := (= #9 #14)
+#691 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #684) #93)
+#97 := (forall (vars (?v0 S2) (?v1 S3)) #93)
+#694 := (iff #97 #691)
+#692 := (iff #93 #93)
+#693 := [refl]: #692
+#695 := [quant-intro #693]: #694
+#165 := (~ #97 #97)
+#163 := (~ #93 #93)
+#164 := [refl]: #163
+#170 := [nnf-pos #164]: #165
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
+#98 := (iff #16 #97)
+#95 := (iff #15 #93)
+#96 := [rewrite]: #95
+#99 := [quant-intro #96]: #98
+#92 := [asserted]: #16
+#102 := [mp #92 #99]: #97
+#171 := [mp~ #102 #170]: #97
+#696 := [mp #171 #695]: #691
+#600 := (not #691)
+#433 := (or #600 #149)
+#434 := [quant-inst #57 #61]: #433
+[unit-resolution #434 #696 #157]: false
+unsat
+6b5ffaa8a4665068d38b31a11461bd89d95e477d 95 0
+#2 := false
+decl f3 :: (-> S3 S2)
+decl f5 :: (-> S3 S3)
+decl f4 :: (-> S2 S3 S3)
+decl f6 :: S3
+#26 := f6
+decl f16 :: S2
 #59 := f16
-#63 := (f4 f16 f9)
-#65 := (= #63 #64)
-#61 := (= f16 f17)
-#386 := (iff #61 #65)
-#373 := (not #386)
+#60 := (f4 f16 f6)
+decl f15 :: S2
+#58 := f15
+#61 := (f4 f15 #60)
+decl f14 :: S2
+#57 := f14
+#62 := (f4 f14 #61)
+#63 := (f5 #62)
+#64 := (f3 #63)
+#150 := (= f15 #64)
+#502 := (f3 #61)
+#407 := (= #502 #64)
+#422 := (= #64 #502)
+#434 := (= #63 #61)
+#437 := (= #61 #63)
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#685 := (pattern #10)
+#14 := (f5 #10)
+#94 := (= #9 #14)
+#692 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #685) #94)
+#98 := (forall (vars (?v0 S2) (?v1 S3)) #94)
+#695 := (iff #98 #692)
+#693 := (iff #94 #94)
+#694 := [refl]: #693
+#696 := [quant-intro #694]: #695
+#162 := (~ #98 #98)
+#160 := (~ #94 #94)
+#161 := [refl]: #160
+#163 := [nnf-pos #161]: #162
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
+#99 := (iff #16 #98)
+#96 := (iff #15 #94)
+#97 := [rewrite]: #96
+#100 := [quant-intro #97]: #99
+#93 := [asserted]: #16
+#103 := [mp #93 #100]: #98
+#164 := [mp~ #103 #163]: #98
+#697 := [mp #164 #696]: #692
+#601 := (not #692)
+#435 := (or #601 #437)
+#421 := [quant-inst #57 #61]: #435
+#430 := [unit-resolution #421 #697]: #437
+#423 := [symm #430]: #434
+#425 := [monotonicity #423]: #422
+#409 := [symm #425]: #407
+#504 := (= f15 #502)
+#11 := (f3 #10)
+#87 := (= #8 #11)
+#686 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #685) #87)
+#90 := (forall (vars (?v0 S2) (?v1 S3)) #87)
+#689 := (iff #90 #686)
+#687 := (iff #87 #87)
+#688 := [refl]: #687
+#690 := [quant-intro #688]: #689
+#173 := (~ #90 #90)
+#129 := (~ #87 #87)
+#172 := [refl]: #129
+#165 := [nnf-pos #172]: #173
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S3)) #12)
+#91 := (iff #13 #90)
+#88 := (iff #12 #87)
+#89 := [rewrite]: #88
+#92 := [quant-intro #89]: #91
+#86 := [asserted]: #13
+#95 := [mp #86 #92]: #90
+#166 := [mp~ #95 #165]: #90
+#691 := [mp #166 #690]: #686
+#619 := (not #686)
+#515 := (or #619 #504)
+#516 := [quant-inst #58 #60]: #515
+#424 := [unit-resolution #516 #691]: #504
+#410 := [trans #424 #409]: #150
+#153 := (not #150)
+#65 := (= #64 f15)
 #66 := (not #65)
-#151 := (or #61 #66)
-#155 := (not #151)
-#62 := (not #61)
-#67 := (implies #62 #66)
-#68 := (not #67)
-#156 := (iff #68 #155)
-#153 := (iff #67 #151)
-#154 := [rewrite]: #153
-#157 := [monotonicity #154]: #156
-#150 := [asserted]: #68
-#160 := [mp #150 #157]: #155
-#159 := [not-or-elim #160]: #65
-#158 := [not-or-elim #160]: #62
-#651 := (or #373 #61 #66)
-#652 := [def-axiom]: #651
-#621 := [unit-resolution #652 #158 #159]: #373
-#45 := (:var 2 S5)
-#44 := (:var 3 S4)
-#46 := (f4 #44 #45)
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#724 := (pattern #12 #46)
-#122 := (= #11 #45)
-#201 := (not #122)
-#119 := (= #10 #44)
-#200 := (not #119)
-#202 := (or #200 #201)
-#203 := (not #202)
-#115 := (= #12 #46)
-#206 := (iff #115 #203)
-#725 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S4) (?v3 S5)) (:pat #724) #206)
-#209 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S4) (?v3 S5)) #206)
-#728 := (iff #209 #725)
-#726 := (iff #206 #206)
-#727 := [refl]: #726
-#729 := [quant-intro #727]: #728
-#125 := (and #119 #122)
-#128 := (iff #115 #125)
-#131 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S4) (?v3 S5)) #128)
-#210 := (iff #131 #209)
-#207 := (iff #128 #206)
-#204 := (iff #125 #203)
-#205 := [rewrite]: #204
-#208 := [monotonicity #205]: #207
-#211 := [quant-intro #208]: #210
-#187 := (~ #131 #131)
-#162 := (~ #128 #128)
-#163 := [refl]: #162
-#188 := [nnf-pos #163]: #187
-#49 := (= #45 #11)
-#48 := (= #44 #10)
-#50 := (and #48 #49)
-#47 := (= #46 #12)
-#51 := (iff #47 #50)
-#52 := (forall (vars (?v0 S4) (?v1 S5) (?v2 S4) (?v3 S5)) #51)
-#132 := (iff #52 #131)
-#129 := (iff #51 #128)
-#126 := (iff #50 #125)
-#123 := (iff #49 #122)
-#124 := [rewrite]: #123
-#120 := (iff #48 #119)
-#121 := [rewrite]: #120
-#127 := [monotonicity #121 #124]: #126
-#117 := (iff #47 #115)
-#118 := [rewrite]: #117
-#130 := [monotonicity #118 #127]: #129
-#133 := [quant-intro #130]: #132
-#114 := [asserted]: #52
-#136 := [mp #114 #133]: #131
-#189 := [mp~ #136 #188]: #131
-#212 := [mp #189 #211]: #209
-#730 := [mp #212 #729]: #725
-#658 := (not #725)
-#380 := (or #658 #386)
-#335 := (= f9 f9)
-#340 := (not #335)
-#678 := (or #62 #340)
-#336 := (not #678)
-#679 := (iff #65 #336)
-#381 := (or #658 #679)
-#659 := (iff #381 #380)
-#660 := (iff #380 #380)
-#369 := [rewrite]: #660
-#278 := (iff #679 #386)
-#368 := (iff #65 #61)
-#372 := (iff #368 #386)
-#387 := [rewrite]: #372
-#384 := (iff #679 #368)
-#661 := (iff #336 #61)
-#311 := (not #62)
-#672 := (iff #311 #61)
-#675 := [rewrite]: #672
-#312 := (iff #336 #311)
-#671 := (iff #678 #62)
-#668 := (or #62 false)
-#670 := (iff #668 #62)
-#306 := [rewrite]: #670
-#669 := (iff #678 #668)
-#666 := (iff #340 false)
-#1 := true
-#324 := (not true)
-#327 := (iff #324 false)
-#665 := [rewrite]: #327
-#325 := (iff #340 #324)
-#320 := (iff #335 true)
-#663 := [rewrite]: #320
-#326 := [monotonicity #663]: #325
-#667 := [trans #326 #665]: #666
-#664 := [monotonicity #667]: #669
-#673 := [trans #664 #306]: #671
-#674 := [monotonicity #673]: #312
-#662 := [trans #674 #675]: #661
-#385 := [monotonicity #662]: #384
-#657 := [trans #385 #387]: #278
-#656 := [monotonicity #657]: #659
-#370 := [trans #656 #369]: #659
-#655 := [quant-inst #60 #22 #59 #22]: #381
-#371 := [mp #655 #370]: #380
-[unit-resolution #371 #730 #621]: false
-unsat
-fff2cbf089f9102929d14127f6531c5541969006 50 0
-#2 := false
-decl f15 :: (-> S5 S4)
-decl f4 :: (-> S4 S5 S5)
-decl f17 :: S5
-#60 := f17
-decl f16 :: S4
-#59 := f16
-#61 := (f4 f16 f17)
-#62 := (f15 #61)
-#147 := (= f16 #62)
-#151 := (not #147)
-#63 := (= #62 f16)
-#64 := (not #63)
-#152 := (iff #64 #151)
-#149 := (iff #63 #147)
-#150 := [rewrite]: #149
-#153 := [monotonicity #150]: #152
-#146 := [asserted]: #64
-#156 := [mp #146 #153]: #151
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#711 := (pattern #12)
-#56 := (f15 #12)
-#139 := (= #10 #56)
-#731 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #711) #139)
-#143 := (forall (vars (?v0 S4) (?v1 S5)) #139)
-#734 := (iff #143 #731)
-#732 := (iff #139 #139)
-#733 := [refl]: #732
-#735 := [quant-intro #733]: #734
-#191 := (~ #143 #143)
-#189 := (~ #139 #139)
-#190 := [refl]: #189
-#192 := [nnf-pos #190]: #191
-#57 := (= #56 #10)
-#58 := (forall (vars (?v0 S4) (?v1 S5)) #57)
-#144 := (iff #58 #143)
-#141 := (iff #57 #139)
-#142 := [rewrite]: #141
-#145 := [quant-intro #142]: #144
-#138 := [asserted]: #58
-#148 := [mp #138 #145]: #143
-#193 := [mp~ #148 #192]: #143
-#736 := [mp #193 #735]: #731
-#265 := (not #731)
-#352 := (or #265 #147)
-#266 := [quant-inst #59 #60]: #352
-[unit-resolution #266 #736 #156]: false
-unsat
-affee22ddd78a2e982940d231a35763dd8db5ff1 50 0
-#2 := false
-decl f14 :: (-> S5 S5)
-decl f4 :: (-> S4 S5 S5)
-decl f17 :: S5
-#60 := f17
-decl f16 :: S4
-#59 := f16
-#61 := (f4 f16 f17)
-#62 := (f14 #61)
-#147 := (= f17 #62)
-#151 := (not #147)
-#63 := (= #62 f17)
-#64 := (not #63)
-#152 := (iff #64 #151)
-#149 := (iff #63 #147)
-#150 := [rewrite]: #149
-#153 := [monotonicity #150]: #152
-#146 := [asserted]: #64
-#156 := [mp #146 #153]: #151
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#711 := (pattern #12)
-#53 := (f14 #12)
-#131 := (= #11 #53)
-#725 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #711) #131)
-#135 := (forall (vars (?v0 S4) (?v1 S5)) #131)
-#728 := (iff #135 #725)
-#726 := (iff #131 #131)
-#727 := [refl]: #726
-#729 := [quant-intro #727]: #728
-#186 := (~ #135 #135)
-#184 := (~ #131 #131)
-#185 := [refl]: #184
-#187 := [nnf-pos #185]: #186
-#54 := (= #53 #11)
-#55 := (forall (vars (?v0 S4) (?v1 S5)) #54)
-#136 := (iff #55 #135)
-#133 := (iff #54 #131)
-#134 := [rewrite]: #133
-#137 := [quant-intro #134]: #136
-#130 := [asserted]: #55
-#140 := [mp #130 #137]: #135
-#188 := [mp~ #140 #187]: #135
-#730 := [mp #188 #729]: #725
-#355 := (not #725)
-#356 := (or #355 #147)
-#284 := [quant-inst #59 #60]: #356
-[unit-resolution #284 #730 #156]: false
-unsat
-9aafa835b8aaa001d18bcde9a4c11eddfa9c9649 56 0
-#2 := false
-decl f15 :: (-> S5 S4)
-decl f4 :: (-> S4 S5 S5)
-decl f9 :: S5
-#22 := f9
-decl f18 :: S4
-#61 := f18
-#62 := (f4 f18 f9)
-decl f17 :: S4
-#60 := f17
-#63 := (f4 f17 #62)
-decl f16 :: S4
-#59 := f16
-#64 := (f4 f16 #63)
-#65 := (f15 #64)
-#150 := (= f16 #65)
-#154 := (not #150)
-#66 := (= #65 f16)
-#67 := (not #66)
-#155 := (iff #67 #154)
-#152 := (iff #66 #150)
-#153 := [rewrite]: #152
-#156 := [monotonicity #153]: #155
-#149 := [asserted]: #67
-#159 := [mp #149 #156]: #154
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#714 := (pattern #12)
-#56 := (f15 #12)
-#142 := (= #10 #56)
-#734 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #714) #142)
-#146 := (forall (vars (?v0 S4) (?v1 S5)) #142)
-#737 := (iff #146 #734)
-#735 := (iff #142 #142)
-#736 := [refl]: #735
-#738 := [quant-intro #736]: #737
-#194 := (~ #146 #146)
-#192 := (~ #142 #142)
-#193 := [refl]: #192
-#195 := [nnf-pos #193]: #194
-#57 := (= #56 #10)
-#58 := (forall (vars (?v0 S4) (?v1 S5)) #57)
-#147 := (iff #58 #146)
-#144 := (iff #57 #142)
-#145 := [rewrite]: #144
-#148 := [quant-intro #145]: #147
-#141 := [asserted]: #58
-#151 := [mp #141 #148]: #146
-#196 := [mp~ #151 #195]: #146
-#739 := [mp #196 #738]: #734
-#269 := (not #734)
-#516 := (or #269 #150)
-#517 := [quant-inst #59 #63]: #516
-[unit-resolution #517 #739 #159]: false
-unsat
-5f1277eca9b4949514eac16a5c81e154e20379e5 56 0
-#2 := false
-decl f14 :: (-> S5 S5)
-decl f4 :: (-> S4 S5 S5)
-decl f9 :: S5
-#22 := f9
-decl f18 :: S4
-#61 := f18
-#62 := (f4 f18 f9)
-decl f17 :: S4
-#60 := f17
-#63 := (f4 f17 #62)
-decl f16 :: S4
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#148 := [asserted]: #66
+#158 := [mp #148 #155]: #153
+[unit-resolution #158 #410]: false
+unsat
+3c9960275d5862cae6ae020dd19199bbe60db8f3 71 0
+#2 := false
+decl f5 :: (-> S3 S3)
+decl f4 :: (-> S2 S3 S3)
+decl f6 :: S3
+#26 := f6
+decl f16 :: S2
 #59 := f16
-#64 := (f4 f16 #63)
-#65 := (f14 #64)
-#150 := (= #63 #65)
-#154 := (not #150)
-#66 := (= #65 #63)
-#67 := (not #66)
-#155 := (iff #67 #154)
-#152 := (iff #66 #150)
-#153 := [rewrite]: #152
-#156 := [monotonicity #153]: #155
-#149 := [asserted]: #67
-#159 := [mp #149 #156]: #154
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#714 := (pattern #12)
-#53 := (f14 #12)
-#134 := (= #11 #53)
-#728 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #714) #134)
-#138 := (forall (vars (?v0 S4) (?v1 S5)) #134)
-#731 := (iff #138 #728)
-#729 := (iff #134 #134)
-#730 := [refl]: #729
-#732 := [quant-intro #730]: #731
-#189 := (~ #138 #138)
-#187 := (~ #134 #134)
-#188 := [refl]: #187
-#190 := [nnf-pos #188]: #189
-#54 := (= #53 #11)
-#55 := (forall (vars (?v0 S4) (?v1 S5)) #54)
-#139 := (iff #55 #138)
-#136 := (iff #54 #134)
-#137 := [rewrite]: #136
-#140 := [quant-intro #137]: #139
-#133 := [asserted]: #55
-#143 := [mp #133 #140]: #138
-#191 := [mp~ #143 #190]: #138
-#733 := [mp #191 #732]: #728
-#287 := (not #728)
-#528 := (or #287 #150)
-#483 := [quant-inst #59 #63]: #528
-[unit-resolution #483 #733 #159]: false
-unsat
-3d958afb574f2b777d342f1a937e466d602feddd 95 0
-#2 := false
-decl f15 :: (-> S5 S4)
-decl f14 :: (-> S5 S5)
-decl f4 :: (-> S4 S5 S5)
-decl f9 :: S5
-#22 := f9
-decl f18 :: S4
-#61 := f18
-#62 := (f4 f18 f9)
-decl f17 :: S4
-#60 := f17
-#63 := (f4 f17 #62)
-decl f16 :: S4
-#59 := f16
-#64 := (f4 f16 #63)
-#65 := (f14 #64)
-#66 := (f15 #65)
-#151 := (= f17 #66)
-#617 := (f15 #63)
-#435 := (= #617 #66)
-#439 := (= #66 #617)
-#434 := (= #65 #63)
-#517 := (= #63 #65)
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#715 := (pattern #12)
-#53 := (f14 #12)
-#135 := (= #11 #53)
-#729 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #715) #135)
-#139 := (forall (vars (?v0 S4) (?v1 S5)) #135)
-#732 := (iff #139 #729)
-#730 := (iff #135 #135)
-#731 := [refl]: #730
-#733 := [quant-intro #731]: #732
-#190 := (~ #139 #139)
-#188 := (~ #135 #135)
-#189 := [refl]: #188
-#191 := [nnf-pos #189]: #190
-#54 := (= #53 #11)
-#55 := (forall (vars (?v0 S4) (?v1 S5)) #54)
-#140 := (iff #55 #139)
-#137 := (iff #54 #135)
-#138 := [rewrite]: #137
-#141 := [quant-intro #138]: #140
-#134 := [asserted]: #55
-#144 := [mp #134 #141]: #139
-#192 := [mp~ #144 #191]: #139
-#734 := [mp #192 #733]: #729
-#288 := (not #729)
-#484 := (or #288 #517)
-#485 := [quant-inst #59 #63]: #484
-#433 := [unit-resolution #485 #734]: #517
-#438 := [symm #433]: #434
-#432 := [monotonicity #438]: #439
-#436 := [symm #432]: #435
-#621 := (= f17 #617)
-#56 := (f15 #12)
-#143 := (= #10 #56)
-#735 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #715) #143)
-#147 := (forall (vars (?v0 S4) (?v1 S5)) #143)
-#738 := (iff #147 #735)
-#736 := (iff #143 #143)
-#737 := [refl]: #736
-#739 := [quant-intro #737]: #738
-#195 := (~ #147 #147)
-#193 := (~ #143 #143)
-#194 := [refl]: #193
-#196 := [nnf-pos #194]: #195
-#57 := (= #56 #10)
-#58 := (forall (vars (?v0 S4) (?v1 S5)) #57)
-#148 := (iff #58 #147)
-#145 := (iff #57 #143)
-#146 := [rewrite]: #145
-#149 := [quant-intro #146]: #148
-#142 := [asserted]: #58
-#152 := [mp #142 #149]: #147
-#197 := [mp~ #152 #196]: #147
-#740 := [mp #197 #739]: #735
-#270 := (not #735)
-#602 := (or #270 #621)
-#599 := [quant-inst #60 #62]: #602
-#431 := [unit-resolution #599 #740]: #621
-#422 := [trans #431 #436]: #151
-#155 := (not #151)
-#67 := (= #66 f17)
-#68 := (not #67)
-#156 := (iff #68 #155)
-#153 := (iff #67 #151)
-#154 := [rewrite]: #153
-#157 := [monotonicity #154]: #156
-#150 := [asserted]: #68
-#160 := [mp #150 #157]: #155
-[unit-resolution #160 #422]: false
-unsat
-27c15c60b6aaec6351efe83812dce879a8ad44d1 71 0
-#2 := false
-decl f14 :: (-> S5 S5)
-decl f4 :: (-> S4 S5 S5)
+#60 := (f4 f16 f6)
+decl f15 :: S2
+#58 := f15
+#61 := (f4 f15 #60)
+decl f14 :: S2
+#57 := f14
+#62 := (f4 f14 #61)
+#63 := (f5 #62)
+#64 := (f5 #63)
+#150 := (= #60 #64)
+#506 := (f5 #61)
+#407 := (= #506 #64)
+#422 := (= #64 #506)
+#434 := (= #63 #61)
+#437 := (= #61 #63)
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#685 := (pattern #10)
+#14 := (f5 #10)
+#94 := (= #9 #14)
+#692 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #685) #94)
+#98 := (forall (vars (?v0 S2) (?v1 S3)) #94)
+#695 := (iff #98 #692)
+#693 := (iff #94 #94)
+#694 := [refl]: #693
+#696 := [quant-intro #694]: #695
+#166 := (~ #98 #98)
+#164 := (~ #94 #94)
+#165 := [refl]: #164
+#171 := [nnf-pos #165]: #166
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
+#99 := (iff #16 #98)
+#96 := (iff #15 #94)
+#97 := [rewrite]: #96
+#100 := [quant-intro #97]: #99
+#93 := [asserted]: #16
+#103 := [mp #93 #100]: #98
+#172 := [mp~ #103 #171]: #98
+#697 := [mp #172 #696]: #692
+#601 := (not #692)
+#435 := (or #601 #437)
+#421 := [quant-inst #57 #61]: #435
+#430 := [unit-resolution #421 #697]: #437
+#423 := [symm #430]: #434
+#425 := [monotonicity #423]: #422
+#409 := [symm #425]: #407
+#513 := (= #60 #506)
+#507 := (or #601 #513)
+#528 := [quant-inst #58 #60]: #507
+#424 := [unit-resolution #528 #697]: #513
+#410 := [trans #424 #409]: #150
+#153 := (not #150)
+#65 := (= #64 #60)
+#66 := (not #65)
+#154 := (iff #66 #153)
+#151 := (iff #65 #150)
+#152 := [rewrite]: #151
+#155 := [monotonicity #152]: #154
+#148 := [asserted]: #66
+#158 := [mp #148 #155]: #153
+[unit-resolution #158 #410]: false
+unsat
+d5569cbebc9c95b668e726d7b9e33fb967151908 97 0
+#2 := false
+decl f3 :: (-> S4 S2)
+decl f6 :: (-> S5 S4)
+decl f7 :: (-> S4 S5 S5)
 decl f9 :: S5
-#22 := f9
-decl f18 :: S4
-#61 := f18
-#62 := (f4 f18 f9)
-decl f17 :: S4
-#60 := f17
-#63 := (f4 f17 #62)
-decl f16 :: S4
-#59 := f16
-#64 := (f4 f16 #63)
-#65 := (f14 #64)
-#66 := (f14 #65)
-#151 := (= #62 #66)
-#608 := (f14 #63)
-#435 := (= #608 #66)
-#439 := (= #66 #608)
-#434 := (= #65 #63)
-#517 := (= #63 #65)
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#715 := (pattern #12)
-#53 := (f14 #12)
-#135 := (= #11 #53)
-#729 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #715) #135)
-#139 := (forall (vars (?v0 S4) (?v1 S5)) #135)
-#732 := (iff #139 #729)
-#730 := (iff #135 #135)
-#731 := [refl]: #730
-#733 := [quant-intro #731]: #732
-#190 := (~ #139 #139)
-#188 := (~ #135 #135)
-#189 := [refl]: #188
-#191 := [nnf-pos #189]: #190
-#54 := (= #53 #11)
-#55 := (forall (vars (?v0 S4) (?v1 S5)) #54)
-#140 := (iff #55 #139)
-#137 := (iff #54 #135)
-#138 := [rewrite]: #137
-#141 := [quant-intro #138]: #140
-#134 := [asserted]: #55
-#144 := [mp #134 #141]: #139
-#192 := [mp~ #144 #191]: #139
-#734 := [mp #192 #733]: #729
-#288 := (not #729)
-#484 := (or #288 #517)
-#485 := [quant-inst #59 #63]: #484
-#433 := [unit-resolution #485 #734]: #517
-#438 := [symm #433]: #434
-#432 := [monotonicity #438]: #439
-#436 := [symm #432]: #435
-#610 := (= #62 #608)
-#612 := (or #288 #610)
-#613 := [quant-inst #60 #62]: #612
-#431 := [unit-resolution #613 #734]: #610
-#422 := [trans #431 #436]: #151
-#155 := (not #151)
-#67 := (= #66 #62)
-#68 := (not #67)
-#156 := (iff #68 #155)
-#153 := (iff #67 #151)
-#154 := [rewrite]: #153
-#157 := [monotonicity #154]: #156
-#150 := [asserted]: #68
-#160 := [mp #150 #157]: #155
-[unit-resolution #160 #422]: false
-unsat
-a98c8f96e82461af4b3fef055b4043eba1bf782f 97 0
-#2 := false
-decl f17 :: (-> S4 S15)
-decl f15 :: (-> S5 S4)
-decl f4 :: (-> S4 S5 S5)
+#41 := f9
+decl f4 :: (-> S2 S3 S4)
+decl f18 :: S3
+#73 := f18
+decl f17 :: S2
+#72 := f17
+#74 := (f4 f17 f18)
+#75 := (f7 #74 f9)
+#76 := (f6 #75)
+#77 := (f3 #76)
+#187 := (= f17 #77)
+#319 := (f3 #74)
+#360 := (= #319 #77)
+#720 := (= #77 #319)
+#716 := (= #76 #74)
+#712 := (= #74 #76)
+#24 := (:var 0 S5)
+#23 := (:var 1 S4)
+#25 := (f7 #23 #24)
+#758 := (pattern #25)
+#26 := (f6 #25)
+#123 := (= #23 #26)
+#759 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #758) #123)
+#127 := (forall (vars (?v0 S4) (?v1 S5)) #123)
+#762 := (iff #127 #759)
+#760 := (iff #123 #123)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#213 := (~ #127 #127)
+#211 := (~ #123 #123)
+#212 := [refl]: #211
+#220 := [nnf-pos #212]: #213
+#27 := (= #26 #23)
+#28 := (forall (vars (?v0 S4) (?v1 S5)) #27)
+#128 := (iff #28 #127)
+#125 := (iff #27 #123)
+#126 := [rewrite]: #125
+#129 := [quant-intro #126]: #128
+#122 := [asserted]: #28
+#132 := [mp #122 #129]: #127
+#221 := [mp~ #132 #220]: #127
+#764 := [mp #221 #763]: #759
+#375 := (not #759)
+#376 := (or #375 #712)
+#714 := [quant-inst #74 #41]: #376
+#715 := [unit-resolution #714 #764]: #712
+#719 := [symm #715]: #716
+#722 := [monotonicity #719]: #720
+#361 := [symm #722]: #360
+#406 := (= f17 #319)
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#737 := (pattern #10)
+#11 := (f3 #10)
+#100 := (= #8 #11)
+#738 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #737) #100)
+#103 := (forall (vars (?v0 S2) (?v1 S3)) #100)
+#741 := (iff #103 #738)
+#739 := (iff #100 #100)
+#740 := [refl]: #739
+#742 := [quant-intro #740]: #741
+#219 := (~ #103 #103)
+#166 := (~ #100 #100)
+#218 := [refl]: #166
+#209 := [nnf-pos #218]: #219
+#12 := (= #11 #8)
+#13 := (forall (vars (?v0 S2) (?v1 S3)) #12)
+#104 := (iff #13 #103)
+#101 := (iff #12 #100)
+#102 := [rewrite]: #101
+#105 := [quant-intro #102]: #104
+#99 := [asserted]: #13
+#108 := [mp #99 #105]: #103
+#210 := [mp~ #108 #209]: #103
+#743 := [mp #210 #742]: #738
+#321 := (not #738)
+#408 := (or #321 #406)
+#399 := [quant-inst #72 #73]: #408
+#355 := [unit-resolution #399 #743]: #406
+#723 := [trans #355 #361]: #187
+#190 := (not #187)
+#78 := (= #77 f17)
+#79 := (not #78)
+#191 := (iff #79 #190)
+#188 := (iff #78 #187)
+#189 := [rewrite]: #188
+#192 := [monotonicity #189]: #191
+#185 := [asserted]: #79
+#195 := [mp #185 #192]: #190
+[unit-resolution #195 #723]: false
+unsat
+4d4a4abaf885c3c42662c956779a33f9969b3641 97 0
+#2 := false
+decl f5 :: (-> S4 S3)
+decl f6 :: (-> S5 S4)
+decl f7 :: (-> S4 S5 S5)
 decl f9 :: S5
-#22 := f9
-decl f16 :: (-> S15 S16 S4)
-decl f20 :: S16
-#75 := f20
-decl f19 :: S15
-#74 := f19
-#76 := (f16 f19 f20)
-#77 := (f4 #76 f9)
-#78 := (f15 #77)
-#79 := (f17 #78)
-#188 := (= f19 #79)
-#374 := (f17 #76)
-#361 := (= #374 #79)
-#721 := (= #79 #374)
-#717 := (= #78 #76)
-#320 := (= #76 #78)
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#767 := (pattern #12)
-#56 := (f15 #12)
-#156 := (= #10 #56)
-#787 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #767) #156)
-#160 := (forall (vars (?v0 S4) (?v1 S5)) #156)
-#790 := (iff #160 #787)
-#788 := (iff #156 #156)
-#789 := [refl]: #788
-#791 := [quant-intro #789]: #790
-#232 := (~ #160 #160)
-#230 := (~ #156 #156)
-#231 := [refl]: #230
-#233 := [nnf-pos #231]: #232
-#57 := (= #56 #10)
-#58 := (forall (vars (?v0 S4) (?v1 S5)) #57)
-#161 := (iff #58 #160)
-#158 := (iff #57 #156)
-#159 := [rewrite]: #158
-#162 := [quant-intro #159]: #161
-#155 := [asserted]: #58
-#165 := [mp #155 #162]: #160
-#234 := [mp~ #165 #233]: #160
-#792 := [mp #234 #791]: #787
-#408 := (not #787)
-#322 := (or #408 #320)
-#409 := [quant-inst #76 #22]: #322
-#716 := [unit-resolution #409 #792]: #320
-#720 := [symm #716]: #717
-#723 := [monotonicity #720]: #721
-#362 := [symm #723]: #361
-#375 := (= f19 #374)
-#66 := (:var 0 S16)
-#65 := (:var 1 S15)
-#67 := (f16 #65 #66)
-#801 := (pattern #67)
-#71 := (f17 #67)
-#180 := (= #65 #71)
-#808 := (forall (vars (?v0 S15) (?v1 S16)) (:pat #801) #180)
-#184 := (forall (vars (?v0 S15) (?v1 S16)) #180)
-#811 := (iff #184 #808)
-#809 := (iff #180 #180)
-#810 := [refl]: #809
-#812 := [quant-intro #810]: #811
-#247 := (~ #184 #184)
-#245 := (~ #180 #180)
-#246 := [refl]: #245
-#248 := [nnf-pos #246]: #247
-#72 := (= #71 #65)
-#73 := (forall (vars (?v0 S15) (?v1 S16)) #72)
-#185 := (iff #73 #184)
-#182 := (iff #72 #180)
-#183 := [rewrite]: #182
-#186 := [quant-intro #183]: #185
-#179 := [asserted]: #73
-#189 := [mp #179 #186]: #184
-#249 := [mp~ #189 #248]: #184
-#813 := [mp #249 #812]: #808
-#718 := (not #808)
-#719 := (or #718 #375)
-#714 := [quant-inst #74 #75]: #719
-#356 := [unit-resolution #714 #813]: #375
-#724 := [trans #356 #362]: #188
-#192 := (not #188)
-#80 := (= #79 f19)
-#81 := (not #80)
-#193 := (iff #81 #192)
-#190 := (iff #80 #188)
-#191 := [rewrite]: #190
-#194 := [monotonicity #191]: #193
-#187 := [asserted]: #81
-#197 := [mp #187 #194]: #192
-[unit-resolution #197 #724]: false
-unsat
-81664cdfae8156255b7987f37aef4ab63fd862c1 97 0
-#2 := false
-decl f18 :: (-> S4 S16)
-decl f15 :: (-> S5 S4)
-decl f4 :: (-> S4 S5 S5)
-decl f9 :: S5
-#22 := f9
-decl f16 :: (-> S15 S16 S4)
-decl f20 :: S16
-#75 := f20
-decl f19 :: S15
-#74 := f19
-#76 := (f16 f19 f20)
-#77 := (f4 #76 f9)
-#78 := (f15 #77)
-#79 := (f18 #78)
-#188 := (= f20 #79)
-#728 := (f18 #76)
-#361 := (= #728 #79)
-#721 := (= #79 #728)
-#717 := (= #78 #76)
-#320 := (= #76 #78)
-#11 := (:var 0 S5)
-#10 := (:var 1 S4)
-#12 := (f4 #10 #11)
-#767 := (pattern #12)
-#56 := (f15 #12)
-#156 := (= #10 #56)
-#787 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #767) #156)
-#160 := (forall (vars (?v0 S4) (?v1 S5)) #156)
-#790 := (iff #160 #787)
-#788 := (iff #156 #156)
-#789 := [refl]: #788
-#791 := [quant-intro #789]: #790
-#232 := (~ #160 #160)
-#230 := (~ #156 #156)
-#231 := [refl]: #230
-#233 := [nnf-pos #231]: #232
-#57 := (= #56 #10)
-#58 := (forall (vars (?v0 S4) (?v1 S5)) #57)
-#161 := (iff #58 #160)
-#158 := (iff #57 #156)
-#159 := [rewrite]: #158
-#162 := [quant-intro #159]: #161
-#155 := [asserted]: #58
-#165 := [mp #155 #162]: #160
-#234 := [mp~ #165 #233]: #160
-#792 := [mp #234 #791]: #787
-#408 := (not #787)
-#322 := (or #408 #320)
-#409 := [quant-inst #76 #22]: #322
-#716 := [unit-resolution #409 #792]: #320
-#720 := [symm #716]: #717
-#723 := [monotonicity #720]: #721
-#362 := [symm #723]: #361
-#386 := (= f20 #728)
-#66 := (:var 0 S16)
-#65 := (:var 1 S15)
-#67 := (f16 #65 #66)
-#801 := (pattern #67)
-#68 := (f18 #67)
-#172 := (= #66 #68)
-#802 := (forall (vars (?v0 S15) (?v1 S16)) (:pat #801) #172)
-#176 := (forall (vars (?v0 S15) (?v1 S16)) #172)
-#805 := (iff #176 #802)
-#803 := (iff #172 #172)
-#804 := [refl]: #803
-#806 := [quant-intro #804]: #805
-#242 := (~ #176 #176)
-#240 := (~ #172 #172)
-#241 := [refl]: #240
-#243 := [nnf-pos #241]: #242
-#69 := (= #68 #66)
-#70 := (forall (vars (?v0 S15) (?v1 S16)) #69)
-#177 := (iff #70 #176)
-#174 := (iff #69 #172)
-#175 := [rewrite]: #174
-#178 := [quant-intro #175]: #177
-#171 := [asserted]: #70
-#181 := [mp #171 #178]: #176
-#244 := [mp~ #181 #243]: #176
-#807 := [mp #244 #806]: #802
-#376 := (not #802)
-#377 := (or #376 #386)
-#715 := [quant-inst #74 #75]: #377
-#356 := [unit-resolution #715 #807]: #386
-#724 := [trans #356 #362]: #188
-#192 := (not #188)
-#80 := (= #79 f20)
-#81 := (not #80)
-#193 := (iff #81 #192)
-#190 := (iff #80 #188)
-#191 := [rewrite]: #190
-#194 := [monotonicity #191]: #193
-#187 := [asserted]: #81
-#197 := [mp #187 #194]: #192
-[unit-resolution #197 #724]: false
-unsat
-cf613377475a54ad92f6fa8003d09874c4dd987e 27 0
-#2 := false
-decl f11 :: (-> S4 Int)
-decl f13 :: S4
+#41 := f9
+decl f4 :: (-> S2 S3 S4)
+decl f18 :: S3
+#73 := f18
+decl f17 :: S2
+#72 := f17
+#74 := (f4 f17 f18)
+#75 := (f7 #74 f9)
+#76 := (f6 #75)
+#77 := (f5 #76)
+#187 := (= f18 #77)
+#320 := (f5 #74)
+#360 := (= #320 #77)
+#720 := (= #77 #320)
+#716 := (= #76 #74)
+#712 := (= #74 #76)
+#24 := (:var 0 S5)
+#23 := (:var 1 S4)
+#25 := (f7 #23 #24)
+#758 := (pattern #25)
+#26 := (f6 #25)
+#123 := (= #23 #26)
+#759 := (forall (vars (?v0 S4) (?v1 S5)) (:pat #758) #123)
+#127 := (forall (vars (?v0 S4) (?v1 S5)) #123)
+#762 := (iff #127 #759)
+#760 := (iff #123 #123)
+#761 := [refl]: #760
+#763 := [quant-intro #761]: #762
+#213 := (~ #127 #127)
+#211 := (~ #123 #123)
+#212 := [refl]: #211
+#220 := [nnf-pos #212]: #213
+#27 := (= #26 #23)
+#28 := (forall (vars (?v0 S4) (?v1 S5)) #27)
+#128 := (iff #28 #127)
+#125 := (iff #27 #123)
+#126 := [rewrite]: #125
+#129 := [quant-intro #126]: #128
+#122 := [asserted]: #28
+#132 := [mp #122 #129]: #127
+#221 := [mp~ #132 #220]: #127
+#764 := [mp #221 #763]: #759
+#375 := (not #759)
+#376 := (or #375 #712)
+#714 := [quant-inst #74 #41]: #376
+#715 := [unit-resolution #714 #764]: #712
+#719 := [symm #715]: #716
+#722 := [monotonicity #719]: #720
+#361 := [symm #722]: #360
+#407 := (= f18 #320)
+#9 := (:var 0 S3)
+#8 := (:var 1 S2)
+#10 := (f4 #8 #9)
+#737 := (pattern #10)
+#14 := (f5 #10)
+#107 := (= #9 #14)
+#744 := (forall (vars (?v0 S2) (?v1 S3)) (:pat #737) #107)
+#111 := (forall (vars (?v0 S2) (?v1 S3)) #107)
+#747 := (iff #111 #744)
+#745 := (iff #107 #107)
+#746 := [refl]: #745
+#748 := [quant-intro #746]: #747
+#199 := (~ #111 #111)
+#204 := (~ #107 #107)
+#205 := [refl]: #204
+#200 := [nnf-pos #205]: #199
+#15 := (= #14 #9)
+#16 := (forall (vars (?v0 S2) (?v1 S3)) #15)
+#112 := (iff #16 #111)
+#109 := (iff #15 #107)
+#110 := [rewrite]: #109
+#113 := [quant-intro #110]: #112
+#106 := [asserted]: #16
+#116 := [mp #106 #113]: #111
+#201 := [mp~ #116 #200]: #111
+#749 := [mp #201 #748]: #744
+#339 := (not #744)
+#412 := (or #339 #407)
+#409 := [quant-inst #72 #73]: #412
+#355 := [unit-resolution #409 #749]: #407
+#723 := [trans #355 #361]: #187
+#190 := (not #187)
+#78 := (= #77 f18)
+#79 := (not #78)
+#191 := (iff #79 #190)
+#188 := (iff #78 #187)
+#189 := [rewrite]: #188
+#192 := [monotonicity #189]: #191
+#185 := [asserted]: #79
+#195 := [mp #185 #192]: #190
+[unit-resolution #195 #723]: false
+unsat
+fc1ad556fda894d36996e3ba12e97af8ee530a7a 27 0
+#2 := false
+decl f3 :: (-> S3 Int)
+decl f13 :: S3
 #39 := f13
-#42 := (f11 f13)
-decl f12 :: S4
+#42 := (f3 f13)
+decl f12 :: S3
 #38 := f12
-#41 := (f11 f12)
+#41 := (f3 f12)
 #43 := (= #41 #42)
 #40 := (= f12 f13)
-#92 := (not #40)
-#94 := (or #92 #43)
+#93 := (not #40)
+#94 := (or #93 #43)
 #97 := (not #94)
 #44 := (implies #40 #43)
 #45 := (not #44)
@@ -51789,27 +52184,27 @@
 #95 := (iff #44 #94)
 #96 := [rewrite]: #95
 #99 := [monotonicity #96]: #98
-#91 := [asserted]: #45
-#102 := [mp #91 #99]: #97
+#92 := [asserted]: #45
+#102 := [mp #92 #99]: #97
 #100 := [not-or-elim #102]: #40
 #277 := [monotonicity #100]: #43
 #101 := (not #43)
 #103 := [not-or-elim #102]: #101
 [unit-resolution #103 #277]: false
 unsat
-6d6860bfe81ec3edbe1c99a18aabbf9ae1253e74 27 0
-#2 := false
-decl f10 :: (-> S4 Int)
-decl f13 :: S4
+3d75464ef9b91ba83a371b9375e6be1c3ceb4398 27 0
+#2 := false
+decl f5 :: (-> S3 Int)
+decl f13 :: S3
 #39 := f13
-#42 := (f10 f13)
-decl f12 :: S4
+#42 := (f5 f13)
+decl f12 :: S3
 #38 := f12
-#41 := (f10 f12)
+#41 := (f5 f12)
 #43 := (= #41 #42)
 #40 := (= f12 f13)
-#92 := (not #40)
-#94 := (or #92 #43)
+#93 := (not #40)
+#94 := (or #93 #43)
 #97 := (not #94)
 #44 := (implies #40 #43)
 #45 := (not #44)
@@ -51817,299 +52212,299 @@
 #95 := (iff #44 #94)
 #96 := [rewrite]: #95
 #99 := [monotonicity #96]: #98
-#91 := [asserted]: #45
-#102 := [mp #91 #99]: #97
+#92 := [asserted]: #45
+#102 := [mp #92 #99]: #97
 #100 := [not-or-elim #102]: #40
 #277 := [monotonicity #100]: #43
 #101 := (not #43)
 #103 := [not-or-elim #102]: #101
 [unit-resolution #103 #277]: false
 unsat
-ef081363dddbf9a4a6afa336a6060e79996228d7 27 0
-#2 := false
-decl f11 :: (-> S4 Int)
-decl f13 :: S4
+b52ec4a4e709ed2db07ff39779e54b0c585650ac 27 0
+#2 := false
+decl f3 :: (-> S3 Int)
+decl f13 :: S3
 #40 := f13
-#41 := (f11 f13)
-decl f12 :: S4
+#41 := (f3 f13)
+decl f12 :: S3
 #38 := f12
-#39 := (f11 f12)
+#39 := (f3 f12)
 #42 := (= #39 #41)
 #44 := (= f12 f13)
 #45 := (not #44)
-#94 := (or #42 #45)
-#98 := (not #94)
+#95 := (or #42 #45)
+#98 := (not #95)
 #43 := (not #42)
 #46 := (implies #43 #45)
 #47 := (not #46)
 #99 := (iff #47 #98)
-#96 := (iff #46 #94)
+#96 := (iff #46 #95)
 #97 := [rewrite]: #96
 #100 := [monotonicity #97]: #99
-#93 := [asserted]: #47
-#103 := [mp #93 #100]: #98
+#94 := [asserted]: #47
+#103 := [mp #94 #100]: #98
 #102 := [not-or-elim #103]: #44
 #277 := [monotonicity #102]: #42
 #101 := [not-or-elim #103]: #43
 [unit-resolution #101 #277]: false
 unsat
-903c4f7ca1d07607d314979b3f7a41a8fc46e4c9 27 0
-#2 := false
-decl f10 :: (-> S4 Int)
-decl f13 :: S4
+85a96de82cde48a962b310ed2706004c2ae2bf3c 27 0
+#2 := false
+decl f5 :: (-> S3 Int)
+decl f13 :: S3
 #40 := f13
-#41 := (f10 f13)
-decl f12 :: S4
+#41 := (f5 f13)
+decl f12 :: S3
 #38 := f12
-#39 := (f10 f12)
+#39 := (f5 f12)
 #42 := (= #39 #41)
 #44 := (= f12 f13)
 #45 := (not #44)
-#94 := (or #42 #45)
-#98 := (not #94)
+#95 := (or #42 #45)
+#98 := (not #95)
 #43 := (not #42)
 #46 := (implies #43 #45)
 #47 := (not #46)
 #99 := (iff #47 #98)
-#96 := (iff #46 #94)
+#96 := (iff #46 #95)
 #97 := [rewrite]: #96
 #100 := [monotonicity #97]: #99
-#93 := [asserted]: #47
-#103 := [mp #93 #100]: #98
+#94 := [asserted]: #47
+#103 := [mp #94 #100]: #98
 #102 := [not-or-elim #103]: #44
 #277 := [monotonicity #102]: #42
 #101 := [not-or-elim #103]: #43
 [unit-resolution #101 #277]: false
 unsat
-c2ddf97e343f0f179028b651e27488b381d9b232 54 0
+9701cdd9448439fa34387c2ec3bdc4fe35ec7bdc 54 0
 #2 := false
 #38 := 3::Int
-decl f11 :: (-> S4 Int)
-decl f4 :: (-> Int Int S3 S4)
-decl f12 :: S3
+decl f3 :: (-> S3 Int)
+decl f4 :: (-> Int Int S2 S3)
+decl f12 :: S2
 #40 := f12
 #39 := 4::Int
 #41 := (f4 3::Int 4::Int f12)
-#42 := (f11 #41)
+#42 := (f3 #41)
 #43 := (= #42 3::Int)
 #44 := (not #43)
-#90 := [asserted]: #44
-#11 := (:var 0 S3)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f4 #9 #10 #11)
-#214 := (pattern #12)
-#35 := (f11 #12)
-#83 := (= #9 #35)
-#227 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) (:pat #214) #83)
-#87 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #83)
-#230 := (iff #87 #227)
-#228 := (iff #83 #83)
-#229 := [refl]: #228
-#231 := [quant-intro #229]: #230
-#130 := (~ #87 #87)
-#128 := (~ #83 #83)
-#129 := [refl]: #128
-#131 := [nnf-pos #129]: #130
-#36 := (= #35 #9)
-#37 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #36)
-#88 := (iff #37 #87)
-#85 := (iff #36 #83)
-#86 := [rewrite]: #85
-#89 := [quant-intro #86]: #88
-#82 := [asserted]: #37
-#92 := [mp #82 #89]: #87
-#132 := [mp~ #92 #131]: #87
-#232 := [mp #132 #231]: #227
-#233 := (not #227)
-#234 := (or #233 #43)
-#91 := (= 3::Int #42)
-#235 := (or #233 #91)
-#237 := (iff #235 #234)
-#239 := (iff #234 #234)
-#240 := [rewrite]: #239
-#98 := (iff #91 #43)
+#91 := [asserted]: #44
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f4 #8 #9 #10)
+#190 := (pattern #11)
+#12 := (f3 #11)
+#65 := (= #8 #12)
+#191 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #190) #65)
+#68 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #65)
+#194 := (iff #68 #191)
+#192 := (iff #65 #65)
+#193 := [refl]: #192
+#195 := [quant-intro #193]: #194
+#105 := (~ #68 #68)
+#103 := (~ #65 #65)
+#104 := [refl]: #103
+#106 := [nnf-pos #104]: #105
+#13 := (= #12 #8)
+#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
+#69 := (iff #14 #68)
+#66 := (iff #13 #65)
+#67 := [rewrite]: #66
+#70 := [quant-intro #67]: #69
+#64 := [asserted]: #14
+#73 := [mp #64 #70]: #68
+#107 := [mp~ #73 #106]: #68
+#196 := [mp #107 #195]: #191
+#235 := (not #191)
+#236 := (or #235 #43)
+#92 := (= 3::Int #42)
+#240 := (or #235 #92)
+#242 := (iff #240 #236)
+#244 := (iff #236 #236)
+#245 := [rewrite]: #244
+#98 := (iff #92 #43)
 #99 := [rewrite]: #98
-#238 := [monotonicity #99]: #237
-#241 := [trans #238 #240]: #237
-#236 := [quant-inst #38 #39 #40]: #235
-#242 := [mp #236 #241]: #234
-[unit-resolution #242 #232 #90]: false
-unsat
-57a3abfe79abd00a70bcda611ae3d757ad63951c 54 0
+#243 := [monotonicity #99]: #242
+#246 := [trans #243 #245]: #242
+#241 := [quant-inst #38 #39 #40]: #240
+#247 := [mp #241 #246]: #236
+[unit-resolution #247 #196 #91]: false
+unsat
+3a7987f9f2406e33255cc3f658f066dbd894644a 54 0
 #2 := false
 #39 := 4::Int
-decl f10 :: (-> S4 Int)
-decl f4 :: (-> Int Int S3 S4)
-decl f12 :: S3
+decl f5 :: (-> S3 Int)
+decl f4 :: (-> Int Int S2 S3)
+decl f12 :: S2
 #40 := f12
 #38 := 3::Int
 #41 := (f4 3::Int 4::Int f12)
-#42 := (f10 #41)
+#42 := (f5 #41)
 #43 := (= #42 4::Int)
 #44 := (not #43)
-#90 := [asserted]: #44
-#11 := (:var 0 S3)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f4 #9 #10 #11)
-#214 := (pattern #12)
-#32 := (f10 #12)
-#75 := (= #10 #32)
-#221 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) (:pat #214) #75)
-#79 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #75)
-#224 := (iff #79 #221)
-#222 := (iff #75 #75)
-#223 := [refl]: #222
-#225 := [quant-intro #223]: #224
-#125 := (~ #79 #79)
-#123 := (~ #75 #75)
-#124 := [refl]: #123
-#126 := [nnf-pos #124]: #125
-#33 := (= #32 #10)
-#34 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #33)
-#80 := (iff #34 #79)
-#77 := (iff #33 #75)
-#78 := [rewrite]: #77
-#81 := [quant-intro #78]: #80
-#74 := [asserted]: #34
-#84 := [mp #74 #81]: #79
-#127 := [mp~ #84 #126]: #79
-#226 := [mp #127 #225]: #221
-#248 := (not #221)
-#249 := (or #248 #43)
-#91 := (= 4::Int #42)
-#250 := (or #248 #91)
-#252 := (iff #250 #249)
-#254 := (iff #249 #249)
-#255 := [rewrite]: #254
-#98 := (iff #91 #43)
+#91 := [asserted]: #44
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f4 #8 #9 #10)
+#190 := (pattern #11)
+#15 := (f5 #11)
+#72 := (= #9 #15)
+#197 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #190) #72)
+#76 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #72)
+#200 := (iff #76 #197)
+#198 := (iff #72 #72)
+#199 := [refl]: #198
+#201 := [quant-intro #199]: #200
+#110 := (~ #76 #76)
+#108 := (~ #72 #72)
+#109 := [refl]: #108
+#111 := [nnf-pos #109]: #110
+#16 := (= #15 #9)
+#17 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #16)
+#77 := (iff #17 #76)
+#74 := (iff #16 #72)
+#75 := [rewrite]: #74
+#78 := [quant-intro #75]: #77
+#71 := [asserted]: #17
+#81 := [mp #71 #78]: #76
+#112 := [mp~ #81 #111]: #76
+#202 := [mp #112 #201]: #197
+#253 := (not #197)
+#254 := (or #253 #43)
+#92 := (= 4::Int #42)
+#255 := (or #253 #92)
+#257 := (iff #255 #254)
+#259 := (iff #254 #254)
+#260 := [rewrite]: #259
+#98 := (iff #92 #43)
 #99 := [rewrite]: #98
-#253 := [monotonicity #99]: #252
-#256 := [trans #253 #255]: #252
-#251 := [quant-inst #38 #39 #40]: #250
-#257 := [mp #251 #256]: #249
-[unit-resolution #257 #226 #90]: false
-unsat
-1627078085337168675bc7c62614c7f389cf7cb9 109 0
+#258 := [monotonicity #99]: #257
+#261 := [trans #258 #260]: #257
+#256 := [quant-inst #38 #39 #40]: #255
+#262 := [mp #256 #261]: #254
+[unit-resolution #262 #202 #91]: false
+unsat
+2a9b9fb7f75472ed7447a04c770c82842793429a 109 0
 #2 := false
 #39 := 4::Int
 #38 := 3::Int
 #269 := (= 3::Int 4::Int)
 #271 := (iff #269 false)
 #272 := [rewrite]: #271
-decl f10 :: (-> S4 Int)
-decl f4 :: (-> Int Int S3 S4)
-decl f12 :: S3
+decl f5 :: (-> S3 Int)
+decl f4 :: (-> Int Int S2 S3)
+decl f12 :: S2
 #40 := f12
 #41 := (f4 3::Int 4::Int f12)
-#43 := (f10 #41)
-#245 := (= #43 4::Int)
-#11 := (:var 0 S3)
-#10 := (:var 1 Int)
-#9 := (:var 2 Int)
-#12 := (f4 #9 #10 #11)
-#209 := (pattern #12)
-#32 := (f10 #12)
-#77 := (= #10 #32)
-#216 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) (:pat #209) #77)
-#81 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #77)
-#219 := (iff #81 #216)
-#217 := (iff #77 #77)
-#218 := [refl]: #217
-#220 := [quant-intro #218]: #219
-#120 := (~ #81 #81)
-#118 := (~ #77 #77)
-#119 := [refl]: #118
-#121 := [nnf-pos #119]: #120
-#33 := (= #32 #10)
-#34 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #33)
-#82 := (iff #34 #81)
-#79 := (iff #33 #77)
-#80 := [rewrite]: #79
-#83 := [quant-intro #80]: #82
-#76 := [asserted]: #34
-#86 := [mp #76 #83]: #81
-#122 := [mp~ #86 #121]: #81
-#221 := [mp #122 #220]: #216
-#246 := (not #216)
-#247 := (or #246 #245)
-#242 := (= 4::Int #43)
-#248 := (or #246 #242)
-#250 := (iff #248 #247)
-#252 := (iff #247 #247)
-#253 := [rewrite]: #252
-#243 := (iff #242 #245)
-#244 := [rewrite]: #243
-#251 := [monotonicity #244]: #250
-#254 := [trans #251 #253]: #250
-#249 := [quant-inst #38 #39 #40]: #248
-#255 := [mp #249 #254]: #247
-#258 := [unit-resolution #255 #221]: #245
+#43 := (f5 #41)
+#250 := (= #43 4::Int)
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f4 #8 #9 #10)
+#185 := (pattern #11)
+#15 := (f5 #11)
+#74 := (= #9 #15)
+#192 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #185) #74)
+#78 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #74)
+#195 := (iff #78 #192)
+#193 := (iff #74 #74)
+#194 := [refl]: #193
+#196 := [quant-intro #194]: #195
+#105 := (~ #78 #78)
+#103 := (~ #74 #74)
+#104 := [refl]: #103
+#106 := [nnf-pos #104]: #105
+#16 := (= #15 #9)
+#17 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #16)
+#79 := (iff #17 #78)
+#76 := (iff #16 #74)
+#77 := [rewrite]: #76
+#80 := [quant-intro #77]: #79
+#73 := [asserted]: #17
+#83 := [mp #73 #80]: #78
+#107 := [mp~ #83 #106]: #78
+#197 := [mp #107 #196]: #192
+#251 := (not #192)
+#252 := (or #251 #250)
+#247 := (= 4::Int #43)
+#253 := (or #251 #247)
+#255 := (iff #253 #252)
+#257 := (iff #252 #252)
+#258 := [rewrite]: #257
+#248 := (iff #247 #250)
+#249 := [rewrite]: #248
+#256 := [monotonicity #249]: #255
+#259 := [trans #256 #258]: #255
+#254 := [quant-inst #38 #39 #40]: #253
+#260 := [mp #254 #259]: #252
+#261 := [unit-resolution #260 #197]: #250
 #267 := (= 3::Int #43)
 #265 := (= #43 3::Int)
-decl f11 :: (-> S4 Int)
-#42 := (f11 #41)
-#231 := (= #42 3::Int)
-#35 := (f11 #12)
-#85 := (= #9 #35)
-#222 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) (:pat #209) #85)
-#89 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #85)
-#225 := (iff #89 #222)
-#223 := (iff #85 #85)
-#224 := [refl]: #223
-#226 := [quant-intro #224]: #225
-#125 := (~ #89 #89)
-#123 := (~ #85 #85)
-#124 := [refl]: #123
-#126 := [nnf-pos #124]: #125
-#36 := (= #35 #9)
-#37 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #36)
-#90 := (iff #37 #89)
-#87 := (iff #36 #85)
-#88 := [rewrite]: #87
-#91 := [quant-intro #88]: #90
-#84 := [asserted]: #37
-#94 := [mp #84 #91]: #89
-#127 := [mp~ #94 #126]: #89
-#227 := [mp #127 #226]: #222
-#232 := (not #222)
-#233 := (or #232 #231)
-#228 := (= 3::Int #42)
-#234 := (or #232 #228)
-#236 := (iff #234 #233)
-#238 := (iff #233 #233)
-#239 := [rewrite]: #238
-#229 := (iff #228 #231)
-#230 := [rewrite]: #229
-#237 := [monotonicity #230]: #236
-#240 := [trans #237 #239]: #236
-#235 := [quant-inst #38 #39 #40]: #234
-#241 := [mp #235 #240]: #233
-#259 := [unit-resolution #241 #227]: #231
+decl f3 :: (-> S3 Int)
+#42 := (f3 #41)
+#236 := (= #42 3::Int)
+#12 := (f3 #11)
+#67 := (= #8 #12)
+#186 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #185) #67)
+#70 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #67)
+#189 := (iff #70 #186)
+#187 := (iff #67 #67)
+#188 := [refl]: #187
+#190 := [quant-intro #188]: #189
+#100 := (~ #70 #70)
+#97 := (~ #67 #67)
+#99 := [refl]: #97
+#101 := [nnf-pos #99]: #100
+#13 := (= #12 #8)
+#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
+#71 := (iff #14 #70)
+#68 := (iff #13 #67)
+#69 := [rewrite]: #68
+#72 := [quant-intro #69]: #71
+#66 := [asserted]: #14
+#75 := [mp #66 #72]: #70
+#102 := [mp~ #75 #101]: #70
+#191 := [mp #102 #190]: #186
+#237 := (not #186)
+#238 := (or #237 #236)
+#230 := (= 3::Int #42)
+#239 := (or #237 #230)
+#241 := (iff #239 #238)
+#243 := (iff #238 #238)
+#244 := [rewrite]: #243
+#231 := (iff #230 #236)
+#235 := [rewrite]: #231
+#242 := [monotonicity #235]: #241
+#245 := [trans #242 #244]: #241
+#240 := [quant-inst #38 #39 #40]: #239
+#246 := [mp #240 #245]: #238
+#262 := [unit-resolution #246 #191]: #236
 #263 := (= #43 #42)
 #44 := (= #42 #43)
 #45 := (not #44)
 #46 := (not #45)
-#93 := (iff #46 #44)
-#95 := [rewrite]: #93
-#92 := [asserted]: #46
-#98 := [mp #92 #95]: #44
+#94 := (iff #46 #44)
+#95 := [rewrite]: #94
+#93 := [asserted]: #46
+#98 := [mp #93 #95]: #44
 #264 := [symm #98]: #263
-#266 := [trans #264 #259]: #265
+#266 := [trans #264 #262]: #265
 #268 := [symm #266]: #267
-#270 := [trans #268 #258]: #269
+#270 := [trans #268 #261]: #269
 [mp #270 #272]: false
 unsat
-5633d72176578081af78ab5b81311524f1bf4c82 73 0
-#2 := false
-decl f6 :: (-> Int Int S4 S5)
-decl f13 :: S4
+2e54a746615da0b9042b7a1c7abdcba21277b942 73 0
+#2 := false
+decl f6 :: (-> Int Int S3 S4)
+decl f13 :: S3
 #47 := f13
 #46 := 4::Int
 #12 := 5::Int
 #50 := (f6 5::Int 4::Int f13)
-decl f9 :: (-> S2 S5 S5)
+decl f9 :: (-> S2 S4 S4)
 #45 := 3::Int
 #48 := (f6 3::Int 4::Int f13)
 decl f4 :: S2
@@ -52117,12 +52512,12 @@
 #49 := (f9 f4 #48)
 #51 := (= #49 #50)
 decl f3 :: (-> S2 Int Int)
-#302 := (f3 f4 3::Int)
-#303 := (f6 #302 4::Int f13)
-#343 := (= #303 #50)
-#341 := (= #50 #303)
-#335 := (= 5::Int #302)
-#331 := (= #302 5::Int)
+#304 := (f3 f4 3::Int)
+#305 := (f6 #304 4::Int f13)
+#343 := (= #305 #50)
+#341 := (= #50 #305)
+#335 := (= 5::Int #304)
+#333 := (= #304 5::Int)
 #9 := (:var 0 Int)
 #10 := (f3 f4 #9)
 #11 := (pattern #10)
@@ -52135,68 +52530,68 @@
 #72 := [asserted]: #14
 #106 := [mp~ #72 #105]: #14
 #336 := (not #14)
-#337 := (or #336 #331)
+#337 := (or #336 #333)
 #338 := [quant-inst #45]: #337
-#332 := [unit-resolution #338 #106]: #331
-#339 := [symm #332]: #335
+#334 := [unit-resolution #338 #106]: #333
+#339 := [symm #334]: #335
 #342 := [monotonicity #339]: #341
 #344 := [symm #342]: #343
-#306 := (= #49 #303)
-#18 := (:var 0 S4)
-#17 := (:var 1 Int)
-#16 := (:var 2 Int)
-#25 := (:var 3 S2)
-#32 := (f3 #25 #16)
-#33 := (f6 #32 #17 #18)
-#211 := (pattern #33)
-#19 := (f6 #16 #17 #18)
-#31 := (f9 #25 #19)
-#210 := (pattern #31)
-#34 := (= #31 #33)
-#212 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #210 #211) #34)
-#35 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #34)
-#215 := (iff #35 #212)
-#213 := (iff #34 #34)
-#214 := [refl]: #213
-#216 := [quant-intro #214]: #215
-#119 := (~ #35 #35)
-#117 := (~ #34 #34)
-#118 := [refl]: #117
-#120 := [nnf-pos #118]: #119
-#75 := [asserted]: #35
-#121 := [mp~ #75 #120]: #35
-#217 := [mp #121 #216]: #212
-#309 := (not #212)
+#306 := (= #49 #305)
+#17 := (:var 0 S3)
+#16 := (:var 1 Int)
+#15 := (:var 2 Int)
+#28 := (:var 3 S2)
+#30 := (f3 #28 #15)
+#31 := (f6 #30 #16 #17)
+#214 := (pattern #31)
+#18 := (f6 #15 #16 #17)
+#29 := (f9 #28 #18)
+#213 := (pattern #29)
+#32 := (= #29 #31)
+#215 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #213 #214) #32)
+#33 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #32)
+#218 := (iff #33 #215)
+#216 := (iff #32 #32)
+#217 := [refl]: #216
+#219 := [quant-intro #217]: #218
+#124 := (~ #33 #33)
+#122 := (~ #32 #32)
+#123 := [refl]: #122
+#125 := [nnf-pos #123]: #124
+#96 := [asserted]: #33
+#126 := [mp~ #96 #125]: #33
+#220 := [mp #126 #219]: #215
+#309 := (not #215)
 #310 := (or #309 #306)
 #311 := [quant-inst #8 #45 #46 #47]: #310
-#340 := [unit-resolution #311 #217]: #306
+#340 := [unit-resolution #311 #220]: #306
 #345 := [trans #340 #344]: #51
 #52 := (not #51)
-#99 := [asserted]: #52
-[unit-resolution #99 #345]: false
-unsat
-5ea02bfc9534897f0d6e70c9e3473bb7ef10a30a 73 0
-#2 := false
-decl f6 :: (-> Int Int S4 S5)
-decl f13 :: S4
+#100 := [asserted]: #52
+[unit-resolution #100 #345]: false
+unsat
+a5cf3bd14553e66b05989b95f1712c3548d79c05 73 0
+#2 := false
+decl f6 :: (-> Int Int S3 S4)
+decl f13 :: S3
 #47 := f13
 #12 := 6::Int
 #45 := 3::Int
 #50 := (f6 3::Int 6::Int f13)
-decl f8 :: (-> S2 S5 S5)
+decl f10 :: (-> S2 S4 S4)
 #46 := 4::Int
 #48 := (f6 3::Int 4::Int f13)
 decl f4 :: S2
 #8 := f4
-#49 := (f8 f4 #48)
+#49 := (f10 f4 #48)
 #51 := (= #49 #50)
 decl f3 :: (-> S2 Int Int)
-#302 := (f3 f4 4::Int)
-#303 := (f6 3::Int #302 f13)
-#343 := (= #303 #50)
-#341 := (= #50 #303)
-#335 := (= 6::Int #302)
-#331 := (= #302 6::Int)
+#304 := (f3 f4 4::Int)
+#305 := (f6 3::Int #304 f13)
+#343 := (= #305 #50)
+#341 := (= #50 #305)
+#335 := (= 6::Int #304)
+#331 := (= #304 6::Int)
 #9 := (:var 0 Int)
 #10 := (f3 f4 #9)
 #11 := (pattern #10)
@@ -52215,132 +52610,132 @@
 #339 := [symm #332]: #335
 #342 := [monotonicity #339]: #341
 #344 := [symm #342]: #343
-#306 := (= #49 #303)
-#18 := (:var 0 S4)
-#17 := (:var 1 Int)
-#25 := (:var 3 S2)
-#27 := (f3 #25 #17)
-#16 := (:var 2 Int)
-#28 := (f6 #16 #27 #18)
-#203 := (pattern #28)
-#19 := (f6 #16 #17 #18)
-#26 := (f8 #25 #19)
-#202 := (pattern #26)
-#29 := (= #26 #28)
-#204 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #202 #203) #29)
-#30 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #29)
-#207 := (iff #30 #204)
-#205 := (iff #29 #29)
-#206 := [refl]: #205
-#208 := [quant-intro #206]: #207
-#114 := (~ #30 #30)
-#112 := (~ #29 #29)
-#113 := [refl]: #112
-#115 := [nnf-pos #113]: #114
-#74 := [asserted]: #30
-#116 := [mp~ #74 #115]: #30
-#209 := [mp #116 #208]: #204
-#309 := (not #204)
+#306 := (= #49 #305)
+#17 := (:var 0 S3)
+#16 := (:var 1 Int)
+#28 := (:var 3 S2)
+#35 := (f3 #28 #16)
+#15 := (:var 2 Int)
+#36 := (f6 #15 #35 #17)
+#222 := (pattern #36)
+#18 := (f6 #15 #16 #17)
+#34 := (f10 #28 #18)
+#221 := (pattern #34)
+#37 := (= #34 #36)
+#223 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #221 #222) #37)
+#38 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #37)
+#226 := (iff #38 #223)
+#224 := (iff #37 #37)
+#225 := [refl]: #224
+#227 := [quant-intro #225]: #226
+#129 := (~ #38 #38)
+#127 := (~ #37 #37)
+#128 := [refl]: #127
+#130 := [nnf-pos #128]: #129
+#97 := [asserted]: #38
+#131 := [mp~ #97 #130]: #38
+#228 := [mp #131 #227]: #223
+#309 := (not #223)
 #310 := (or #309 #306)
 #311 := [quant-inst #8 #45 #46 #47]: #310
-#340 := [unit-resolution #311 #209]: #306
+#340 := [unit-resolution #311 #228]: #306
 #345 := [trans #340 #344]: #51
 #52 := (not #51)
-#99 := [asserted]: #52
-[unit-resolution #99 #345]: false
-unsat
-0ea4cdefb3e3290c8d99d636ae708d57bfa0c66f 211 0
-#2 := false
-decl f9 :: (-> S2 S5 S5)
-decl f10 :: (-> S2 S5 S5)
-decl f14 :: S5
+#100 := [asserted]: #52
+[unit-resolution #100 #345]: false
+unsat
+b59ea79b3381bb3b8446dda45524f635379fcd3e 211 0
+#2 := false
+decl f11 :: (-> S2 S4 S4)
+decl f10 :: (-> S2 S4 S4)
+decl f14 :: S4
 #51 := f14
 decl f5 :: S2
 #15 := f5
 #55 := (f10 f5 f14)
 decl f4 :: S2
 #8 := f4
-#56 := (f9 f4 #55)
-#108 := (= f14 #56)
-decl f7 :: (-> Int Int S4 S5)
-decl f11 :: (-> S5 S4)
-decl f15 :: S4
+#56 := (f11 f4 #55)
+#109 := (= f14 #56)
+decl f7 :: (-> Int Int S3 S4)
+decl f9 :: (-> S4 S3)
+decl f15 :: S3
 #52 := f15
 #12 := 4::Int
 #18 := 3::Int
 #53 := (f7 3::Int 4::Int f15)
-#316 := (f11 #53)
+#286 := (f9 #53)
 decl f3 :: (-> S2 Int Int)
 #269 := (f3 f5 3::Int)
-#318 := (f7 #269 4::Int #316)
-#350 := (f9 f4 #318)
+#321 := (f7 #269 4::Int #286)
+#350 := (f11 f4 #321)
 #431 := (= #350 #56)
 #424 := (= #56 #350)
-#422 := (= #55 #318)
+#422 := (= #55 #321)
 #270 := (f7 #269 4::Int f15)
-#418 := (= #270 #318)
-#415 := (= #318 #270)
-#404 := (= #316 f15)
-#317 := (= f15 #316)
-#24 := (:var 0 S4)
-#23 := (:var 1 Int)
-#22 := (:var 2 Int)
-#25 := (f7 #22 #23 #24)
-#250 := (pattern #25)
-#42 := (f11 #25)
-#85 := (= #24 #42)
-#251 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) (:pat #250) #85)
-#88 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #85)
-#254 := (iff #88 #251)
-#252 := (iff #85 #85)
-#253 := [refl]: #252
-#255 := [quant-intro #253]: #254
-#156 := (~ #88 #88)
-#154 := (~ #85 #85)
-#155 := [refl]: #154
-#157 := [nnf-pos #155]: #156
-#43 := (= #42 #24)
-#44 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #43)
-#89 := (iff #44 #88)
-#86 := (iff #43 #85)
-#87 := [rewrite]: #86
-#90 := [quant-intro #87]: #89
-#84 := [asserted]: #44
-#93 := [mp #84 #90]: #88
-#158 := [mp~ #93 #157]: #88
-#256 := [mp #158 #255]: #251
-#320 := (not #251)
-#321 := (or #320 #317)
-#322 := [quant-inst #18 #12 #52]: #321
-#403 := [unit-resolution #322 #256]: #317
-#408 := [symm #403]: #404
+#418 := (= #270 #321)
+#415 := (= #321 #270)
+#404 := (= #286 f15)
+#287 := (= f15 #286)
+#23 := (:var 0 S3)
+#22 := (:var 1 Int)
+#21 := (:var 2 Int)
+#24 := (f7 #21 #22 #23)
+#226 := (pattern #24)
+#31 := (f9 #24)
+#97 := (= #23 #31)
+#239 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) (:pat #226) #97)
+#101 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #97)
+#242 := (iff #101 #239)
+#240 := (iff #97 #97)
+#241 := [refl]: #240
+#243 := [quant-intro #241]: #242
+#151 := (~ #101 #101)
+#149 := (~ #97 #97)
+#150 := [refl]: #149
+#152 := [nnf-pos #150]: #151
+#32 := (= #31 #23)
+#33 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #32)
+#102 := (iff #33 #101)
+#99 := (iff #32 #97)
+#100 := [rewrite]: #99
+#103 := [quant-intro #100]: #102
+#96 := [asserted]: #33
+#106 := [mp #96 #103]: #101
+#153 := [mp~ #106 #152]: #101
+#244 := [mp #153 #243]: #239
+#290 := (not #239)
+#291 := (or #290 #287)
+#292 := [quant-inst #18 #12 #52]: #291
+#401 := [unit-resolution #292 #244]: #287
+#408 := [symm #401]: #404
 #416 := [monotonicity #408]: #415
 #419 := [symm #416]: #418
 #420 := (= #55 #270)
 #271 := (f10 f5 #53)
 #272 := (= #271 #270)
 #273 := (= #270 #271)
-#31 := (:var 3 S2)
-#38 := (f3 #31 #22)
-#39 := (f7 #38 #23 #24)
-#243 := (pattern #39)
-#37 := (f10 #31 #25)
-#242 := (pattern #37)
-#40 := (= #37 #39)
-#244 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #242 #243) #40)
-#41 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #40)
-#247 := (iff #41 #244)
-#245 := (iff #40 #40)
-#246 := [refl]: #245
-#248 := [quant-intro #246]: #247
-#151 := (~ #41 #41)
-#149 := (~ #40 #40)
-#150 := [refl]: #149
-#152 := [nnf-pos #150]: #151
-#83 := [asserted]: #41
-#153 := [mp~ #83 #152]: #41
-#249 := [mp #153 #248]: #244
-#276 := (not #244)
+#34 := (:var 3 S2)
+#36 := (f3 #34 #21)
+#37 := (f7 #36 #22 #23)
+#246 := (pattern #37)
+#35 := (f10 #34 #24)
+#245 := (pattern #35)
+#38 := (= #35 #37)
+#247 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #245 #246) #38)
+#39 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #38)
+#250 := (iff #39 #247)
+#248 := (iff #38 #38)
+#249 := [refl]: #248
+#251 := [quant-intro #249]: #250
+#156 := (~ #39 #39)
+#154 := (~ #38 #38)
+#155 := [refl]: #154
+#157 := [nnf-pos #155]: #156
+#104 := [asserted]: #39
+#158 := [mp~ #104 #157]: #39
+#252 := [mp #158 #251]: #247
+#276 := (not #247)
 #277 := (or #276 #273)
 #278 := (or #276 #272)
 #280 := (iff #278 #277)
@@ -52352,29 +52747,29 @@
 #284 := [trans #281 #283]: #280
 #279 := [quant-inst #15 #18 #12 #52]: #278
 #285 := [mp #279 #284]: #277
-#412 := [unit-resolution #285 #249]: #273
+#412 := [unit-resolution #285 #252]: #273
 #417 := [symm #412]: #272
 #413 := (= #55 #271)
 #54 := (= f14 #53)
 #115 := (not #54)
-#116 := (or #115 #108)
+#116 := (or #115 #109)
 #121 := (not #116)
 #57 := (= #56 f14)
 #58 := (implies #54 #57)
 #59 := (not #58)
 #122 := (iff #59 #121)
 #119 := (iff #58 #116)
-#112 := (implies #54 #108)
+#112 := (implies #54 #109)
 #117 := (iff #112 #116)
 #118 := [rewrite]: #117
 #113 := (iff #58 #112)
-#110 := (iff #57 #108)
+#110 := (iff #57 #109)
 #111 := [rewrite]: #110
 #114 := [monotonicity #111]: #113
 #120 := [trans #114 #118]: #119
 #123 := [monotonicity #120]: #122
-#107 := [asserted]: #59
-#126 := [mp #107 #123]: #121
+#108 := [asserted]: #59
+#126 := [mp #108 #123]: #121
 #124 := [not-or-elim #126]: #54
 #414 := [monotonicity #124]: #413
 #421 := [trans #414 #417]: #420
@@ -52382,29 +52777,29 @@
 #425 := [monotonicity #423]: #424
 #432 := [symm #425]: #431
 #435 := (= f14 #350)
-#343 := (f3 f4 4::Int)
-#346 := (f7 #269 #343 #316)
+#345 := (f3 f4 4::Int)
+#346 := (f7 #269 #345 #286)
 #352 := (= #346 #350)
-#33 := (f3 #31 #23)
-#34 := (f7 #22 #33 #24)
-#235 := (pattern #34)
-#32 := (f9 #31 #25)
-#234 := (pattern #32)
-#35 := (= #32 #34)
-#236 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #234 #235) #35)
-#36 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #35)
-#239 := (iff #36 #236)
-#237 := (iff #35 #35)
-#238 := [refl]: #237
-#240 := [quant-intro #238]: #239
-#146 := (~ #36 #36)
-#144 := (~ #35 #35)
-#145 := [refl]: #144
-#147 := [nnf-pos #145]: #146
-#82 := [asserted]: #36
-#148 := [mp~ #82 #147]: #36
-#241 := [mp #148 #240]: #236
-#355 := (not #236)
+#41 := (f3 #34 #22)
+#42 := (f7 #21 #41 #23)
+#254 := (pattern #42)
+#40 := (f11 #34 #24)
+#253 := (pattern #40)
+#43 := (= #40 #42)
+#255 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #253 #254) #43)
+#44 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #43)
+#258 := (iff #44 #255)
+#256 := (iff #43 #43)
+#257 := [refl]: #256
+#259 := [quant-intro #257]: #258
+#161 := (~ #44 #44)
+#159 := (~ #43 #43)
+#160 := [refl]: #159
+#162 := [nnf-pos #160]: #161
+#105 := [asserted]: #44
+#163 := [mp~ #105 #162]: #44
+#260 := [mp #163 #259]: #255
+#355 := (not #255)
 #356 := (or #355 #352)
 #351 := (= #350 #346)
 #357 := (or #355 #351)
@@ -52415,13 +52810,13 @@
 #354 := [rewrite]: #353
 #360 := [monotonicity #354]: #359
 #363 := [trans #360 #362]: #359
-#358 := [quant-inst #8 #269 #12 #316]: #357
+#358 := [quant-inst #8 #269 #12 #286]: #357
 #364 := [mp #358 #363]: #356
-#411 := [unit-resolution #364 #241]: #352
+#411 := [unit-resolution #364 #260]: #352
 #433 := (= f14 #346)
 #429 := (= #53 #346)
 #427 := (= #346 #53)
-#402 := (= #343 4::Int)
+#400 := (= #345 4::Int)
 #9 := (:var 0 Int)
 #10 := (f3 f4 #9)
 #11 := (pattern #10)
@@ -52434,10 +52829,10 @@
 #79 := [asserted]: #14
 #133 := [mp~ #79 #132]: #14
 #405 := (not #14)
-#406 := (or #405 #402)
+#406 := (or #405 #400)
 #407 := [quant-inst #12]: #406
-#409 := [unit-resolution #407 #133]: #402
-#342 := (= #269 3::Int)
+#409 := [unit-resolution #407 #133]: #400
+#344 := (= #269 3::Int)
 #16 := (f3 f5 #9)
 #17 := (pattern #16)
 #19 := (= #16 3::Int)
@@ -52449,110 +52844,110 @@
 #80 := [asserted]: #20
 #138 := [mp~ #80 #137]: #20
 #347 := (not #20)
-#348 := (or #347 #342)
+#348 := (or #347 #344)
 #349 := [quant-inst #18]: #348
-#410 := [unit-resolution #349 #138]: #342
+#410 := [unit-resolution #349 #138]: #344
 #428 := [monotonicity #410 #409 #408]: #427
 #430 := [symm #428]: #429
 #434 := [trans #124 #430]: #433
 #436 := [trans #434 #411]: #435
-#437 := [trans #436 #432]: #108
-#125 := (not #108)
+#437 := [trans #436 #432]: #109
+#125 := (not #109)
 #127 := [not-or-elim #126]: #125
 [unit-resolution #127 #437]: false
 unsat
-18733e050cdd31352b0648b5596d94a4afc48033 211 0
-#2 := false
-decl f10 :: (-> S2 S5 S5)
-decl f9 :: (-> S2 S5 S5)
-decl f14 :: S5
+e55f9d76dda3b8c2c60cf7fba6ece493ac2093db 211 0
+#2 := false
+decl f10 :: (-> S2 S4 S4)
+decl f11 :: (-> S2 S4 S4)
+decl f14 :: S4
 #51 := f14
 decl f4 :: S2
 #8 := f4
-#55 := (f9 f4 f14)
+#55 := (f11 f4 f14)
 decl f5 :: S2
 #15 := f5
 #56 := (f10 f5 #55)
-#108 := (= f14 #56)
-decl f7 :: (-> Int Int S4 S5)
-decl f11 :: (-> S5 S4)
-decl f15 :: S4
+#109 := (= f14 #56)
+decl f7 :: (-> Int Int S3 S4)
+decl f9 :: (-> S4 S3)
+decl f15 :: S3
 #52 := f15
 #12 := 4::Int
 #18 := 3::Int
 #53 := (f7 3::Int 4::Int f15)
-#316 := (f11 #53)
+#286 := (f9 #53)
 decl f3 :: (-> S2 Int Int)
 #269 := (f3 f4 4::Int)
-#318 := (f7 3::Int #269 #316)
-#350 := (f10 f5 #318)
+#321 := (f7 3::Int #269 #286)
+#350 := (f10 f5 #321)
 #431 := (= #350 #56)
 #424 := (= #56 #350)
-#422 := (= #55 #318)
+#422 := (= #55 #321)
 #270 := (f7 3::Int #269 f15)
-#418 := (= #270 #318)
-#415 := (= #318 #270)
-#404 := (= #316 f15)
-#317 := (= f15 #316)
-#24 := (:var 0 S4)
-#23 := (:var 1 Int)
-#22 := (:var 2 Int)
-#25 := (f7 #22 #23 #24)
-#250 := (pattern #25)
-#42 := (f11 #25)
-#85 := (= #24 #42)
-#251 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) (:pat #250) #85)
-#88 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #85)
-#254 := (iff #88 #251)
-#252 := (iff #85 #85)
-#253 := [refl]: #252
-#255 := [quant-intro #253]: #254
-#156 := (~ #88 #88)
-#154 := (~ #85 #85)
-#155 := [refl]: #154
-#157 := [nnf-pos #155]: #156
-#43 := (= #42 #24)
-#44 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #43)
-#89 := (iff #44 #88)
-#86 := (iff #43 #85)
-#87 := [rewrite]: #86
-#90 := [quant-intro #87]: #89
-#84 := [asserted]: #44
-#93 := [mp #84 #90]: #88
-#158 := [mp~ #93 #157]: #88
-#256 := [mp #158 #255]: #251
-#320 := (not #251)
-#321 := (or #320 #317)
-#322 := [quant-inst #18 #12 #52]: #321
-#403 := [unit-resolution #322 #256]: #317
+#418 := (= #270 #321)
+#415 := (= #321 #270)
+#404 := (= #286 f15)
+#287 := (= f15 #286)
+#23 := (:var 0 S3)
+#22 := (:var 1 Int)
+#21 := (:var 2 Int)
+#24 := (f7 #21 #22 #23)
+#226 := (pattern #24)
+#31 := (f9 #24)
+#97 := (= #23 #31)
+#239 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) (:pat #226) #97)
+#101 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #97)
+#242 := (iff #101 #239)
+#240 := (iff #97 #97)
+#241 := [refl]: #240
+#243 := [quant-intro #241]: #242
+#151 := (~ #101 #101)
+#149 := (~ #97 #97)
+#150 := [refl]: #149
+#152 := [nnf-pos #150]: #151
+#32 := (= #31 #23)
+#33 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S3)) #32)
+#102 := (iff #33 #101)
+#99 := (iff #32 #97)
+#100 := [rewrite]: #99
+#103 := [quant-intro #100]: #102
+#96 := [asserted]: #33
+#106 := [mp #96 #103]: #101
+#153 := [mp~ #106 #152]: #101
+#244 := [mp #153 #243]: #239
+#290 := (not #239)
+#291 := (or #290 #287)
+#292 := [quant-inst #18 #12 #52]: #291
+#403 := [unit-resolution #292 #244]: #287
 #408 := [symm #403]: #404
 #416 := [monotonicity #408]: #415
 #419 := [symm #416]: #418
 #420 := (= #55 #270)
-#271 := (f9 f4 #53)
+#271 := (f11 f4 #53)
 #272 := (= #271 #270)
 #273 := (= #270 #271)
-#31 := (:var 3 S2)
-#33 := (f3 #31 #23)
-#34 := (f7 #22 #33 #24)
-#235 := (pattern #34)
-#32 := (f9 #31 #25)
-#234 := (pattern #32)
-#35 := (= #32 #34)
-#236 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #234 #235) #35)
-#36 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #35)
-#239 := (iff #36 #236)
-#237 := (iff #35 #35)
-#238 := [refl]: #237
-#240 := [quant-intro #238]: #239
-#146 := (~ #36 #36)
-#144 := (~ #35 #35)
-#145 := [refl]: #144
-#147 := [nnf-pos #145]: #146
-#82 := [asserted]: #36
-#148 := [mp~ #82 #147]: #36
-#241 := [mp #148 #240]: #236
-#276 := (not #236)
+#34 := (:var 3 S2)
+#41 := (f3 #34 #22)
+#42 := (f7 #21 #41 #23)
+#254 := (pattern #42)
+#40 := (f11 #34 #24)
+#253 := (pattern #40)
+#43 := (= #40 #42)
+#255 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #253 #254) #43)
+#44 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #43)
+#258 := (iff #44 #255)
+#256 := (iff #43 #43)
+#257 := [refl]: #256
+#259 := [quant-intro #257]: #258
+#161 := (~ #44 #44)
+#159 := (~ #43 #43)
+#160 := [refl]: #159
+#162 := [nnf-pos #160]: #161
+#105 := [asserted]: #44
+#163 := [mp~ #105 #162]: #44
+#260 := [mp #163 #259]: #255
+#276 := (not #255)
 #277 := (or #276 #273)
 #278 := (or #276 #272)
 #280 := (iff #278 #277)
@@ -52564,29 +52959,29 @@
 #284 := [trans #281 #283]: #280
 #279 := [quant-inst #8 #18 #12 #52]: #278
 #285 := [mp #279 #284]: #277
-#412 := [unit-resolution #285 #241]: #273
+#412 := [unit-resolution #285 #260]: #273
 #417 := [symm #412]: #272
 #413 := (= #55 #271)
 #54 := (= f14 #53)
 #115 := (not #54)
-#116 := (or #115 #108)
+#116 := (or #115 #109)
 #121 := (not #116)
 #57 := (= #56 f14)
 #58 := (implies #54 #57)
 #59 := (not #58)
 #122 := (iff #59 #121)
 #119 := (iff #58 #116)
-#112 := (implies #54 #108)
+#112 := (implies #54 #109)
 #117 := (iff #112 #116)
 #118 := [rewrite]: #117
 #113 := (iff #58 #112)
-#110 := (iff #57 #108)
+#110 := (iff #57 #109)
 #111 := [rewrite]: #110
 #114 := [monotonicity #111]: #113
 #120 := [trans #114 #118]: #119
 #123 := [monotonicity #120]: #122
-#107 := [asserted]: #59
-#126 := [mp #107 #123]: #121
+#108 := [asserted]: #59
+#126 := [mp #108 #123]: #121
 #124 := [not-or-elim #126]: #54
 #414 := [monotonicity #124]: #413
 #421 := [trans #414 #417]: #420
@@ -52595,28 +52990,28 @@
 #432 := [symm #425]: #431
 #435 := (= f14 #350)
 #343 := (f3 f5 3::Int)
-#346 := (f7 #343 #269 #316)
+#346 := (f7 #343 #269 #286)
 #352 := (= #346 #350)
-#38 := (f3 #31 #22)
-#39 := (f7 #38 #23 #24)
-#243 := (pattern #39)
-#37 := (f10 #31 #25)
-#242 := (pattern #37)
-#40 := (= #37 #39)
-#244 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #242 #243) #40)
-#41 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #40)
-#247 := (iff #41 #244)
-#245 := (iff #40 #40)
-#246 := [refl]: #245
-#248 := [quant-intro #246]: #247
-#151 := (~ #41 #41)
-#149 := (~ #40 #40)
-#150 := [refl]: #149
-#152 := [nnf-pos #150]: #151
-#83 := [asserted]: #41
-#153 := [mp~ #83 #152]: #41
-#249 := [mp #153 #248]: #244
-#355 := (not #244)
+#36 := (f3 #34 #21)
+#37 := (f7 #36 #22 #23)
+#246 := (pattern #37)
+#35 := (f10 #34 #24)
+#245 := (pattern #35)
+#38 := (= #35 #37)
+#247 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #245 #246) #38)
+#39 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #38)
+#250 := (iff #39 #247)
+#248 := (iff #38 #38)
+#249 := [refl]: #248
+#251 := [quant-intro #249]: #250
+#156 := (~ #39 #39)
+#154 := (~ #38 #38)
+#155 := [refl]: #154
+#157 := [nnf-pos #155]: #156
+#104 := [asserted]: #39
+#158 := [mp~ #104 #157]: #39
+#252 := [mp #158 #251]: #247
+#355 := (not #247)
 #356 := (or #355 #352)
 #351 := (= #350 #346)
 #357 := (or #355 #351)
@@ -52627,9 +53022,9 @@
 #354 := [rewrite]: #353
 #360 := [monotonicity #354]: #359
 #363 := [trans #360 #362]: #359
-#358 := [quant-inst #15 #18 #269 #316]: #357
+#358 := [quant-inst #15 #18 #269 #286]: #357
 #364 := [mp #358 #363]: #356
-#411 := [unit-resolution #364 #249]: #352
+#411 := [unit-resolution #364 #252]: #352
 #433 := (= f14 #346)
 #429 := (= #53 #346)
 #427 := (= #346 #53)
@@ -52668,24 +53063,24 @@
 #430 := [symm #428]: #429
 #434 := [trans #124 #430]: #433
 #436 := [trans #434 #411]: #435
-#437 := [trans #436 #432]: #108
-#125 := (not #108)
+#437 := [trans #436 #432]: #109
+#125 := (not #109)
 #127 := [not-or-elim #126]: #125
 [unit-resolution #127 #437]: false
 unsat
-034f1b430cea4d797df825ad65ed44ba0879f423 27 0
-#2 := false
-decl f18 :: (-> S4 Int)
-decl f20 :: S4
+0d6a71e26872f02629f4a4cbea96b7d7f942acef 27 0
+#2 := false
+decl f3 :: (-> S3 Int)
+decl f20 :: S3
 #66 := f20
-#69 := (f18 f20)
-decl f19 :: S4
+#69 := (f3 f20)
+decl f19 :: S3
 #65 := f19
-#68 := (f18 f19)
+#68 := (f3 f19)
 #70 := (= #68 #69)
 #67 := (= f19 f20)
-#143 := (not #67)
-#145 := (or #143 #70)
+#144 := (not #67)
+#145 := (or #144 #70)
 #148 := (not #145)
 #71 := (implies #67 #70)
 #72 := (not #71)
@@ -52693,27 +53088,27 @@
 #146 := (iff #71 #145)
 #147 := [rewrite]: #146
 #150 := [monotonicity #147]: #149
-#142 := [asserted]: #72
-#153 := [mp #142 #150]: #148
+#143 := [asserted]: #72
+#153 := [mp #143 #150]: #148
 #151 := [not-or-elim #153]: #67
 #347 := [monotonicity #151]: #70
 #152 := (not #70)
 #154 := [not-or-elim #153]: #152
 [unit-resolution #154 #347]: false
 unsat
-abd2ff3a1f4279c6df17226a8ab8bfa529a1ad2f 27 0
-#2 := false
-decl f17 :: (-> S4 Int)
-decl f20 :: S4
+273905a3679343c2bf9e12a208edeb3b140defd5 27 0
+#2 := false
+decl f5 :: (-> S3 Int)
+decl f20 :: S3
 #66 := f20
-#69 := (f17 f20)
-decl f19 :: S4
+#69 := (f5 f20)
+decl f19 :: S3
 #65 := f19
-#68 := (f17 f19)
+#68 := (f5 f19)
 #70 := (= #68 #69)
 #67 := (= f19 f20)
-#143 := (not #67)
-#145 := (or #143 #70)
+#144 := (not #67)
+#145 := (or #144 #70)
 #148 := (not #145)
 #71 := (implies #67 #70)
 #72 := (not #71)
@@ -52721,28 +53116,28 @@
 #146 := (iff #71 #145)
 #147 := [rewrite]: #146
 #150 := [monotonicity #147]: #149
-#142 := [asserted]: #72
-#153 := [mp #142 #150]: #148
+#143 := [asserted]: #72
+#153 := [mp #143 #150]: #148
 #151 := [not-or-elim #153]: #67
 #347 := [monotonicity #151]: #70
 #152 := (not #70)
 #154 := [not-or-elim #153]: #152
 [unit-resolution #154 #347]: false
 unsat
-bcb488b65c53b04f7a912c4badcb5fcbbb811c48 71 0
-#2 := false
-decl f10 :: (-> S4 S1)
-decl f20 :: S4
+1a1dbb36df0b0fe92eb18b671d63ad44f5ac7c76 71 0
+#2 := false
+decl f12 :: (-> S3 S1)
+decl f20 :: S3
 #66 := f20
-#70 := (f10 f20)
+#70 := (f12 f20)
 decl f1 :: S1
 #4 := f1
 #149 := (= f1 #70)
-decl f19 :: S4
+decl f19 :: S3
 #65 := f19
-#68 := (f10 f19)
-#145 := (= f1 #68)
-#152 := (iff #145 #149)
+#68 := (f12 f19)
+#146 := (= f1 #68)
+#152 := (iff #146 #149)
 #691 := (= #68 #70)
 #67 := (= f19 f20)
 #158 := (not #67)
@@ -52762,115 +53157,115 @@
 #153 := (iff #72 #152)
 #150 := (iff #71 #149)
 #151 := [rewrite]: #150
-#147 := (iff #69 #145)
+#147 := (iff #69 #146)
 #148 := [rewrite]: #147
 #154 := [monotonicity #148 #151]: #153
 #157 := [monotonicity #154]: #156
 #163 := [trans #157 #161]: #162
 #166 := [monotonicity #163]: #165
-#144 := [asserted]: #74
-#169 := [mp #144 #166]: #164
+#145 := [asserted]: #74
+#169 := [mp #145 #166]: #164
 #167 := [not-or-elim #169]: #67
 #693 := [monotonicity #167]: #691
 #348 := [monotonicity #693]: #152
 #372 := (not #149)
-#196 := (not #145)
-#480 := (iff #196 #372)
+#205 := (not #146)
+#480 := (iff #205 #372)
 #687 := [monotonicity #348]: #480
-#375 := [hypothesis]: #196
+#375 := [hypothesis]: #205
 #359 := [mp #375 #687]: #372
-#370 := (or #149 #145)
-#197 := (iff #149 #196)
+#370 := (or #149 #146)
+#206 := (iff #149 #205)
 #168 := (not #152)
-#198 := (iff #168 #197)
-#199 := [rewrite]: #198
+#207 := (iff #168 #206)
+#208 := [rewrite]: #207
 #170 := [not-or-elim #169]: #168
-#200 := [mp #170 #199]: #197
-#368 := (not #197)
-#369 := (or #149 #145 #368)
+#209 := [mp #170 #208]: #206
+#368 := (not #206)
+#369 := (or #149 #146 #368)
 #284 := [def-axiom]: #369
-#361 := [unit-resolution #284 #200]: #370
+#361 := [unit-resolution #284 #209]: #370
 #354 := [unit-resolution #361 #375]: #149
 #360 := [unit-resolution #354 #359]: false
-#694 := [lemma #360]: #145
+#694 := [lemma #360]: #146
 #696 := [mp #694 #348]: #149
-#374 := (or #372 #196)
-#373 := (or #372 #196 #368)
+#374 := (or #372 #205)
+#373 := (or #372 #205 #368)
 #301 := [def-axiom]: #373
-#371 := [unit-resolution #301 #200]: #374
+#371 := [unit-resolution #301 #209]: #374
 #695 := [unit-resolution #371 #694]: #372
 [unit-resolution #695 #696]: false
 unsat
-692be396fb86f21c3efb4c10b7720c21916ee57c 27 0
-#2 := false
-decl f18 :: (-> S4 Int)
-decl f20 :: S4
+1897084db6966355c13c4c1978569bc9dbb82d7e 27 0
+#2 := false
+decl f3 :: (-> S3 Int)
+decl f20 :: S3
 #67 := f20
-#68 := (f18 f20)
-decl f19 :: S4
+#68 := (f3 f20)
+decl f19 :: S3
 #65 := f19
-#66 := (f18 f19)
+#66 := (f3 f19)
 #69 := (= #66 #68)
 #71 := (= f19 f20)
 #72 := (not #71)
-#145 := (or #69 #72)
-#149 := (not #145)
+#146 := (or #69 #72)
+#149 := (not #146)
 #70 := (not #69)
 #73 := (implies #70 #72)
 #74 := (not #73)
 #150 := (iff #74 #149)
-#147 := (iff #73 #145)
+#147 := (iff #73 #146)
 #148 := [rewrite]: #147
 #151 := [monotonicity #148]: #150
-#144 := [asserted]: #74
-#154 := [mp #144 #151]: #149
+#145 := [asserted]: #74
+#154 := [mp #145 #151]: #149
 #153 := [not-or-elim #154]: #71
 #347 := [monotonicity #153]: #69
 #152 := [not-or-elim #154]: #70
 [unit-resolution #152 #347]: false
 unsat
-8c59e0b3bbed886482ee7c694f7985c4332c80bd 27 0
-#2 := false
-decl f17 :: (-> S4 Int)
-decl f20 :: S4
+84719c2fbfcecc692590cbd6c6776ee233f49981 27 0
+#2 := false
+decl f5 :: (-> S3 Int)
+decl f20 :: S3
 #67 := f20
-#68 := (f17 f20)
-decl f19 :: S4
+#68 := (f5 f20)
+decl f19 :: S3
 #65 := f19
-#66 := (f17 f19)
+#66 := (f5 f19)
 #69 := (= #66 #68)
 #71 := (= f19 f20)
 #72 := (not #71)
-#145 := (or #69 #72)
-#149 := (not #145)
+#146 := (or #69 #72)
+#149 := (not #146)
 #70 := (not #69)
 #73 := (implies #70 #72)
 #74 := (not #73)
 #150 := (iff #74 #149)
-#147 := (iff #73 #145)
+#147 := (iff #73 #146)
 #148 := [rewrite]: #147
 #151 := [monotonicity #148]: #150
-#144 := [asserted]: #74
-#154 := [mp #144 #151]: #149
+#145 := [asserted]: #74
+#154 := [mp #145 #151]: #149
 #153 := [not-or-elim #154]: #71
 #347 := [monotonicity #153]: #69
 #152 := [not-or-elim #154]: #70
 [unit-resolution #152 #347]: false
 unsat
-ec34ee7bf3443acccceee16793505089997d4233 87 0
-#2 := false
-decl f10 :: (-> S4 S1)
-decl f20 :: S4
+3c5eeec3f72704eac255d0f1e9284d0d20ab0722 87 0
+#2 := false
+decl f12 :: (-> S3 S1)
+decl f20 :: S3
 #68 := f20
-#69 := (f10 f20)
+#69 := (f12 f20)
 decl f1 :: S1
 #4 := f1
 #151 := (= f1 #69)
-decl f19 :: S4
+decl f19 :: S3
 #65 := f19
-#66 := (f10 f19)
-#147 := (= f1 #66)
-#154 := (iff #147 #151)
+#66 := (f12 f19)
+#148 := (= f1 #66)
+#154 := (iff #148 #151)
 #707 := (= #66 #69)
 #73 := (= f19 f20)
 #74 := (not #73)
@@ -52883,7 +53278,7 @@
 #75 := (implies #72 #74)
 #76 := (not #75)
 #186 := (iff #76 #183)
-#170 := (iff #151 #147)
+#170 := (iff #151 #148)
 #169 := (or #74 #170)
 #175 := (not #169)
 #184 := (iff #175 #183)
@@ -52894,7 +53289,7 @@
 #185 := [monotonicity #182]: #184
 #176 := (iff #76 #175)
 #173 := (iff #75 #169)
-#160 := (not #147)
+#160 := (not #148)
 #161 := (iff #151 #160)
 #166 := (implies #161 #74)
 #171 := (iff #166 #169)
@@ -52908,7 +53303,7 @@
 #155 := (iff #71 #154)
 #152 := (iff #70 #151)
 #153 := [rewrite]: #152
-#149 := (iff #67 #147)
+#149 := (iff #67 #148)
 #150 := [rewrite]: #149
 #156 := [monotonicity #150 #153]: #155
 #159 := [monotonicity #156]: #158
@@ -52917,8 +53312,8 @@
 #174 := [trans #168 #172]: #173
 #177 := [monotonicity #174]: #176
 #187 := [trans #177 #185]: #186
-#146 := [asserted]: #76
-#190 := [mp #146 #187]: #183
+#147 := [asserted]: #76
+#190 := [mp #147 #187]: #183
 #188 := [not-or-elim #190]: #73
 #709 := [monotonicity #188]: #707
 #364 := [monotonicity #709]: #154
@@ -52927,170 +53322,170 @@
 #703 := [monotonicity #364]: #496
 #391 := [hypothesis]: #160
 #375 := [mp #391 #703]: #388
-#386 := (or #151 #147)
+#386 := (or #151 #148)
 #189 := [not-or-elim #190]: #157
-#216 := [mp #189 #163]: #161
+#225 := [mp #189 #163]: #161
 #384 := (not #161)
-#385 := (or #151 #147 #384)
+#385 := (or #151 #148 #384)
 #300 := [def-axiom]: #385
-#377 := [unit-resolution #300 #216]: #386
+#377 := [unit-resolution #300 #225]: #386
 #370 := [unit-resolution #377 #391]: #151
 #376 := [unit-resolution #370 #375]: false
-#710 := [lemma #376]: #147
+#710 := [lemma #376]: #148
 #712 := [mp #710 #364]: #151
 #390 := (or #388 #160)
 #389 := (or #388 #160 #384)
 #317 := [def-axiom]: #389
-#387 := [unit-resolution #317 #216]: #390
+#387 := [unit-resolution #317 #225]: #390
 #711 := [unit-resolution #387 #710]: #388
 [unit-resolution #711 #712]: false
 unsat
-c2545d9068e0d6accd875f4379ed4317f0c0b477 58 0
+60180a7beca4718d4b909f1bb0ce2c0b84139dea 58 0
 #2 := false
 #65 := 3::Int
-decl f18 :: (-> S4 Int)
-decl f4 :: (-> Int Int S5 S4)
-decl f5 :: (-> S1 S3 S5)
-decl f20 :: S3
+decl f3 :: (-> S3 Int)
+decl f4 :: (-> Int Int S2 S3)
+decl f13 :: (-> S1 S6 S2)
+decl f20 :: S6
 #68 := f20
 decl f19 :: S1
 #67 := f19
-#69 := (f5 f19 f20)
+#69 := (f13 f19 f20)
 #66 := 4::Int
 #70 := (f4 3::Int 4::Int #69)
-#71 := (f18 #70)
+#71 := (f3 #70)
 #72 := (= #71 3::Int)
 #73 := (not #72)
-#143 := [asserted]: #73
-#38 := (:var 0 S5)
-#37 := (:var 1 Int)
-#10 := (:var 2 Int)
-#39 := (f4 #10 #37 #38)
-#316 := (pattern #39)
-#62 := (f18 #39)
-#136 := (= #10 #62)
-#329 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) (:pat #316) #136)
-#140 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) #136)
-#332 := (iff #140 #329)
-#330 := (iff #136 #136)
-#331 := [refl]: #330
-#333 := [quant-intro #331]: #332
-#203 := (~ #140 #140)
-#201 := (~ #136 #136)
-#202 := [refl]: #201
-#204 := [nnf-pos #202]: #203
-#63 := (= #62 #10)
-#64 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) #63)
-#141 := (iff #64 #140)
-#138 := (iff #63 #136)
-#139 := [rewrite]: #138
-#142 := [quant-intro #139]: #141
-#135 := [asserted]: #64
-#145 := [mp #135 #142]: #140
-#205 := [mp~ #145 #204]: #140
-#334 := [mp #205 #333]: #329
-#335 := (not #329)
-#336 := (or #335 #72)
-#144 := (= 3::Int #71)
-#337 := (or #335 #144)
-#339 := (iff #337 #336)
-#341 := (iff #336 #336)
-#342 := [rewrite]: #341
-#151 := (iff #144 #72)
+#144 := [asserted]: #73
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f4 #8 #9 #10)
+#263 := (pattern #11)
+#12 := (f3 #11)
+#94 := (= #8 #12)
+#264 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #263) #94)
+#97 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #94)
+#267 := (iff #97 #264)
+#265 := (iff #94 #94)
+#266 := [refl]: #265
+#268 := [quant-intro #266]: #267
+#158 := (~ #97 #97)
+#156 := (~ #94 #94)
+#157 := [refl]: #156
+#159 := [nnf-pos #157]: #158
+#13 := (= #12 #8)
+#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
+#98 := (iff #14 #97)
+#95 := (iff #13 #94)
+#96 := [rewrite]: #95
+#99 := [quant-intro #96]: #98
+#93 := [asserted]: #14
+#102 := [mp #93 #99]: #97
+#160 := [mp~ #102 #159]: #97
+#269 := [mp #160 #268]: #264
+#370 := (not #264)
+#371 := (or #370 #72)
+#145 := (= 3::Int #71)
+#375 := (or #370 #145)
+#377 := (iff #375 #371)
+#379 := (iff #371 #371)
+#380 := [rewrite]: #379
+#151 := (iff #145 #72)
 #152 := [rewrite]: #151
-#340 := [monotonicity #152]: #339
-#343 := [trans #340 #342]: #339
-#338 := [quant-inst #65 #66 #69]: #337
-#344 := [mp #338 #343]: #336
-[unit-resolution #344 #334 #143]: false
-unsat
-e3bb9ab1eb53aa14b85baa6b04545cdb6811e412 58 0
+#378 := [monotonicity #152]: #377
+#381 := [trans #378 #380]: #377
+#376 := [quant-inst #65 #66 #69]: #375
+#382 := [mp #376 #381]: #371
+[unit-resolution #382 #269 #144]: false
+unsat
+4e405ea4a814758902eec1be5c3ffd542fdce183 58 0
 #2 := false
 #66 := 4::Int
-decl f17 :: (-> S4 Int)
-decl f4 :: (-> Int Int S5 S4)
-decl f5 :: (-> S1 S3 S5)
-decl f20 :: S3
+decl f5 :: (-> S3 Int)
+decl f4 :: (-> Int Int S2 S3)
+decl f13 :: (-> S1 S6 S2)
+decl f20 :: S6
 #68 := f20
 decl f19 :: S1
 #67 := f19
-#69 := (f5 f19 f20)
+#69 := (f13 f19 f20)
 #65 := 3::Int
 #70 := (f4 3::Int 4::Int #69)
-#71 := (f17 #70)
+#71 := (f5 #70)
 #72 := (= #71 4::Int)
 #73 := (not #72)
-#143 := [asserted]: #73
-#38 := (:var 0 S5)
-#37 := (:var 1 Int)
-#10 := (:var 2 Int)
-#39 := (f4 #10 #37 #38)
-#316 := (pattern #39)
-#59 := (f17 #39)
-#128 := (= #37 #59)
-#323 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) (:pat #316) #128)
-#132 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) #128)
-#326 := (iff #132 #323)
-#324 := (iff #128 #128)
-#325 := [refl]: #324
-#327 := [quant-intro #325]: #326
-#198 := (~ #132 #132)
-#196 := (~ #128 #128)
-#197 := [refl]: #196
-#199 := [nnf-pos #197]: #198
-#60 := (= #59 #37)
-#61 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) #60)
-#133 := (iff #61 #132)
-#130 := (iff #60 #128)
-#131 := [rewrite]: #130
-#134 := [quant-intro #131]: #133
-#127 := [asserted]: #61
-#137 := [mp #127 #134]: #132
-#200 := [mp~ #137 #199]: #132
-#328 := [mp #200 #327]: #323
-#350 := (not #323)
-#351 := (or #350 #72)
-#144 := (= 4::Int #71)
-#352 := (or #350 #144)
-#354 := (iff #352 #351)
-#356 := (iff #351 #351)
-#357 := [rewrite]: #356
-#151 := (iff #144 #72)
+#144 := [asserted]: #73
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f4 #8 #9 #10)
+#263 := (pattern #11)
+#15 := (f5 #11)
+#101 := (= #9 #15)
+#270 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #263) #101)
+#105 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #101)
+#273 := (iff #105 #270)
+#271 := (iff #101 #101)
+#272 := [refl]: #271
+#274 := [quant-intro #272]: #273
+#163 := (~ #105 #105)
+#161 := (~ #101 #101)
+#162 := [refl]: #161
+#164 := [nnf-pos #162]: #163
+#16 := (= #15 #9)
+#17 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #16)
+#106 := (iff #17 #105)
+#103 := (iff #16 #101)
+#104 := [rewrite]: #103
+#107 := [quant-intro #104]: #106
+#100 := [asserted]: #17
+#110 := [mp #100 #107]: #105
+#165 := [mp~ #110 #164]: #105
+#275 := [mp #165 #274]: #270
+#388 := (not #270)
+#389 := (or #388 #72)
+#145 := (= 4::Int #71)
+#390 := (or #388 #145)
+#392 := (iff #390 #389)
+#394 := (iff #389 #389)
+#395 := [rewrite]: #394
+#151 := (iff #145 #72)
 #152 := [rewrite]: #151
-#355 := [monotonicity #152]: #354
-#358 := [trans #355 #357]: #354
-#353 := [quant-inst #65 #66 #69]: #352
-#359 := [mp #353 #358]: #351
-[unit-resolution #359 #328 #143]: false
-unsat
-6296fe8461e452d749fb761ed56ebcfb1fc552d0 105 0
-#2 := false
-decl f10 :: (-> S4 S1)
-decl f4 :: (-> Int Int S5 S4)
-decl f5 :: (-> S1 S3 S5)
-decl f20 :: S3
+#393 := [monotonicity #152]: #392
+#396 := [trans #393 #395]: #392
+#391 := [quant-inst #65 #66 #69]: #390
+#397 := [mp #391 #396]: #389
+[unit-resolution #397 #275 #144]: false
+unsat
+4ed86aa1fa601dd0a3ec30f70fe5685baa4f141b 105 0
+#2 := false
+decl f12 :: (-> S3 S1)
+decl f4 :: (-> Int Int S2 S3)
+decl f13 :: (-> S1 S6 S2)
+decl f20 :: S6
 #68 := f20
 decl f19 :: S1
 #67 := f19
-#69 := (f5 f19 f20)
+#69 := (f13 f19 f20)
 #66 := 4::Int
 #65 := 3::Int
 #70 := (f4 3::Int 4::Int #69)
-#71 := (f10 #70)
-decl f1 :: S1
-#4 := f1
-#146 := (= f1 #71)
-#159 := (not #146)
-#404 := [hypothesis]: #159
+#71 := (f12 #70)
+decl f1 :: S1
+#4 := f1
+#147 := (= f1 #71)
+#159 := (not #147)
+#407 := [hypothesis]: #159
 #150 := (= f1 f19)
-#349 := (or #150 #146)
+#349 := (or #150 #147)
 #160 := (iff #150 #159)
 #73 := (= f19 f1)
 #72 := (= #71 f1)
 #74 := (iff #72 #73)
 #75 := (not #74)
 #163 := (iff #75 #160)
-#153 := (iff #146 #150)
+#153 := (iff #147 #150)
 #156 := (not #153)
 #161 := (iff #156 #160)
 #162 := [rewrite]: #161
@@ -53098,217 +53493,217 @@
 #154 := (iff #74 #153)
 #151 := (iff #73 #150)
 #152 := [rewrite]: #151
-#148 := (iff #72 #146)
+#148 := (iff #72 #147)
 #149 := [rewrite]: #148
 #155 := [monotonicity #149 #152]: #154
 #158 := [monotonicity #155]: #157
 #164 := [trans #158 #162]: #163
-#145 := [asserted]: #75
-#167 := [mp #145 #164]: #160
+#146 := [asserted]: #75
+#167 := [mp #146 #164]: #160
 #346 := (not #160)
-#347 := (or #150 #146 #346)
+#347 := (or #150 #147 #346)
 #348 := [def-axiom]: #347
 #350 := [unit-resolution #348 #167]: #349
-#405 := [unit-resolution #350 #404]: #150
+#408 := [unit-resolution #350 #407]: #150
 #351 := (not #150)
-#410 := (or #146 #351)
-#12 := (:var 0 S3)
-#11 := (:var 1 S1)
-#13 := (f5 #11 #12)
-#10 := (:var 2 Int)
-#9 := (:var 3 Int)
-#14 := (f4 #9 #10 #13)
-#290 := (pattern #14)
-#109 := (= f1 #11)
-#31 := (f10 #14)
-#105 := (= f1 #31)
-#112 := (iff #105 #109)
-#297 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S3)) (:pat #290) #112)
-#115 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S3)) #112)
-#300 := (iff #115 #297)
-#298 := (iff #112 #112)
-#299 := [refl]: #298
-#301 := [quant-intro #299]: #300
-#184 := (~ #115 #115)
-#182 := (~ #112 #112)
-#183 := [refl]: #182
-#185 := [nnf-pos #183]: #184
-#33 := (= #11 f1)
-#32 := (= #31 f1)
-#34 := (iff #32 #33)
-#35 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S3)) #34)
-#116 := (iff #35 #115)
-#113 := (iff #34 #112)
-#110 := (iff #33 #109)
-#111 := [rewrite]: #110
-#107 := (iff #32 #105)
-#108 := [rewrite]: #107
-#114 := [monotonicity #108 #111]: #113
-#117 := [quant-intro #114]: #116
-#104 := [asserted]: #35
-#120 := [mp #104 #117]: #115
-#186 := [mp~ #120 #185]: #115
-#302 := [mp #186 #301]: #297
-#393 := (not #297)
-#394 := (or #393 #153)
-#395 := [quant-inst #65 #66 #67 #68]: #394
-#409 := [unit-resolution #395 #302]: #153
-#396 := (or #156 #146 #351)
-#397 := [def-axiom]: #396
-#411 := [unit-resolution #397 #409]: #410
-#412 := [unit-resolution #411 #405 #404]: false
-#413 := [lemma #412]: #146
+#410 := (or #147 #351)
+#40 := (:var 0 S6)
+#39 := (:var 1 S1)
+#41 := (f13 #39 #40)
+#8 := (:var 2 Int)
+#38 := (:var 3 Int)
+#42 := (f4 #38 #8 #41)
+#317 := (pattern #42)
+#126 := (= f1 #39)
+#43 := (f12 #42)
+#123 := (= f1 #43)
+#129 := (iff #123 #126)
+#318 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S6)) (:pat #317) #129)
+#132 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S6)) #129)
+#321 := (iff #132 #318)
+#319 := (iff #129 #129)
+#320 := [refl]: #319
+#322 := [quant-intro #320]: #321
+#199 := (~ #132 #132)
+#197 := (~ #129 #129)
+#198 := [refl]: #197
+#200 := [nnf-pos #198]: #199
+#45 := (= #39 f1)
+#44 := (= #43 f1)
+#46 := (iff #44 #45)
+#47 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S6)) #46)
+#133 := (iff #47 #132)
+#130 := (iff #46 #129)
+#127 := (iff #45 #126)
+#128 := [rewrite]: #127
+#124 := (iff #44 #123)
+#125 := [rewrite]: #124
+#131 := [monotonicity #125 #128]: #130
+#134 := [quant-intro #131]: #133
+#122 := [asserted]: #47
+#137 := [mp #122 #134]: #132
+#201 := [mp~ #137 #200]: #132
+#323 := [mp #201 #322]: #318
+#358 := (not #318)
+#359 := (or #358 #153)
+#360 := [quant-inst #65 #66 #67 #68]: #359
+#409 := [unit-resolution #360 #323]: #153
+#361 := (or #156 #147 #351)
+#362 := [def-axiom]: #361
+#411 := [unit-resolution #362 #409]: #410
+#412 := [unit-resolution #411 #408 #407]: false
+#413 := [lemma #412]: #147
 #354 := (or #351 #159)
 #352 := (or #351 #159 #346)
 #353 := [def-axiom]: #352
 #355 := [unit-resolution #353 #167]: #354
 #414 := [unit-resolution #355 #413]: #351
 #415 := (or #159 #150)
-#398 := (or #156 #159 #150)
-#399 := [def-axiom]: #398
-#416 := [unit-resolution #399 #409]: #415
+#363 := (or #156 #159 #150)
+#364 := [def-axiom]: #363
+#416 := [unit-resolution #364 #409]: #415
 [unit-resolution #416 #414 #413]: false
 unsat
-da58db0437f12c2e8d1330c20990ed8cbae3b7f4 113 0
+1106827b733d83eccb037f282dd3b096b2abf8d0 113 0
 #2 := false
 #66 := 4::Int
 #65 := 3::Int
 #404 := (= 3::Int 4::Int)
 #406 := (iff #404 false)
 #407 := [rewrite]: #406
-decl f17 :: (-> S4 Int)
-decl f4 :: (-> Int Int S5 S4)
-decl f5 :: (-> S1 S3 S5)
-decl f20 :: S3
+decl f5 :: (-> S3 Int)
+decl f4 :: (-> Int Int S2 S3)
+decl f13 :: (-> S1 S6 S2)
+decl f20 :: S6
 #68 := f20
 decl f19 :: S1
 #67 := f19
-#69 := (f5 f19 f20)
+#69 := (f13 f19 f20)
 #70 := (f4 3::Int 4::Int #69)
-#72 := (f17 #70)
-#347 := (= #72 4::Int)
-#38 := (:var 0 S5)
-#37 := (:var 1 Int)
-#10 := (:var 2 Int)
-#39 := (f4 #10 #37 #38)
-#311 := (pattern #39)
-#59 := (f17 #39)
-#130 := (= #37 #59)
-#318 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) (:pat #311) #130)
-#134 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) #130)
-#321 := (iff #134 #318)
-#319 := (iff #130 #130)
-#320 := [refl]: #319
-#322 := [quant-intro #320]: #321
-#193 := (~ #134 #134)
-#191 := (~ #130 #130)
-#192 := [refl]: #191
-#194 := [nnf-pos #192]: #193
-#60 := (= #59 #37)
-#61 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) #60)
-#135 := (iff #61 #134)
-#132 := (iff #60 #130)
-#133 := [rewrite]: #132
-#136 := [quant-intro #133]: #135
-#129 := [asserted]: #61
-#139 := [mp #129 #136]: #134
-#195 := [mp~ #139 #194]: #134
-#323 := [mp #195 #322]: #318
-#348 := (not #318)
-#349 := (or #348 #347)
-#344 := (= 4::Int #72)
-#350 := (or #348 #344)
-#352 := (iff #350 #349)
-#354 := (iff #349 #349)
-#355 := [rewrite]: #354
-#345 := (iff #344 #347)
-#346 := [rewrite]: #345
-#353 := [monotonicity #346]: #352
-#356 := [trans #353 #355]: #352
-#351 := [quant-inst #65 #66 #69]: #350
-#357 := [mp #351 #356]: #349
-#393 := [unit-resolution #357 #323]: #347
+#72 := (f5 #70)
+#385 := (= #72 4::Int)
+#10 := (:var 0 S2)
+#9 := (:var 1 Int)
+#8 := (:var 2 Int)
+#11 := (f4 #8 #9 #10)
+#258 := (pattern #11)
+#15 := (f5 #11)
+#103 := (= #9 #15)
+#265 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #258) #103)
+#107 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #103)
+#268 := (iff #107 #265)
+#266 := (iff #103 #103)
+#267 := [refl]: #266
+#269 := [quant-intro #267]: #268
+#158 := (~ #107 #107)
+#156 := (~ #103 #103)
+#157 := [refl]: #156
+#159 := [nnf-pos #157]: #158
+#16 := (= #15 #9)
+#17 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #16)
+#108 := (iff #17 #107)
+#105 := (iff #16 #103)
+#106 := [rewrite]: #105
+#109 := [quant-intro #106]: #108
+#102 := [asserted]: #17
+#112 := [mp #102 #109]: #107
+#160 := [mp~ #112 #159]: #107
+#270 := [mp #160 #269]: #265
+#386 := (not #265)
+#387 := (or #386 #385)
+#382 := (= 4::Int #72)
+#388 := (or #386 #382)
+#390 := (iff #388 #387)
+#392 := (iff #387 #387)
+#393 := [rewrite]: #392
+#383 := (iff #382 #385)
+#384 := [rewrite]: #383
+#391 := [monotonicity #384]: #390
+#394 := [trans #391 #393]: #390
+#389 := [quant-inst #65 #66 #69]: #388
+#395 := [mp #389 #394]: #387
+#396 := [unit-resolution #395 #270]: #385
 #402 := (= 3::Int #72)
 #400 := (= #72 3::Int)
-decl f18 :: (-> S4 Int)
-#71 := (f18 #70)
-#333 := (= #71 3::Int)
-#62 := (f18 #39)
-#138 := (= #10 #62)
-#324 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) (:pat #311) #138)
-#142 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) #138)
-#327 := (iff #142 #324)
-#325 := (iff #138 #138)
-#326 := [refl]: #325
-#328 := [quant-intro #326]: #327
-#198 := (~ #142 #142)
-#196 := (~ #138 #138)
-#197 := [refl]: #196
-#199 := [nnf-pos #197]: #198
-#63 := (= #62 #10)
-#64 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S5)) #63)
-#143 := (iff #64 #142)
-#140 := (iff #63 #138)
-#141 := [rewrite]: #140
-#144 := [quant-intro #141]: #143
-#137 := [asserted]: #64
-#147 := [mp #137 #144]: #142
-#200 := [mp~ #147 #199]: #142
-#329 := [mp #200 #328]: #324
-#334 := (not #324)
-#335 := (or #334 #333)
-#330 := (= 3::Int #71)
-#336 := (or #334 #330)
-#338 := (iff #336 #335)
-#340 := (iff #335 #335)
-#341 := [rewrite]: #340
-#331 := (iff #330 #333)
-#332 := [rewrite]: #331
-#339 := [monotonicity #332]: #338
-#342 := [trans #339 #341]: #338
-#337 := [quant-inst #65 #66 #69]: #336
-#343 := [mp #337 #342]: #335
-#394 := [unit-resolution #343 #329]: #333
+decl f3 :: (-> S3 Int)
+#71 := (f3 #70)
+#371 := (= #71 3::Int)
+#12 := (f3 #11)
+#96 := (= #8 #12)
+#259 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) (:pat #258) #96)
+#99 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #96)
+#262 := (iff #99 #259)
+#260 := (iff #96 #96)
+#261 := [refl]: #260
+#263 := [quant-intro #261]: #262
+#153 := (~ #99 #99)
+#150 := (~ #96 #96)
+#152 := [refl]: #150
+#154 := [nnf-pos #152]: #153
+#13 := (= #12 #8)
+#14 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S2)) #13)
+#100 := (iff #14 #99)
+#97 := (iff #13 #96)
+#98 := [rewrite]: #97
+#101 := [quant-intro #98]: #100
+#95 := [asserted]: #14
+#104 := [mp #95 #101]: #99
+#155 := [mp~ #104 #154]: #99
+#264 := [mp #155 #263]: #259
+#372 := (not #259)
+#373 := (or #372 #371)
+#365 := (= 3::Int #71)
+#374 := (or #372 #365)
+#376 := (iff #374 #373)
+#378 := (iff #373 #373)
+#379 := [rewrite]: #378
+#366 := (iff #365 #371)
+#370 := [rewrite]: #366
+#377 := [monotonicity #370]: #376
+#380 := [trans #377 #379]: #376
+#375 := [quant-inst #65 #66 #69]: #374
+#381 := [mp #375 #380]: #373
+#397 := [unit-resolution #381 #264]: #371
 #398 := (= #72 #71)
 #73 := (= #71 #72)
 #74 := (not #73)
 #75 := (not #74)
-#146 := (iff #75 #73)
-#148 := [rewrite]: #146
-#145 := [asserted]: #75
-#151 := [mp #145 #148]: #73
+#147 := (iff #75 #73)
+#148 := [rewrite]: #147
+#146 := [asserted]: #75
+#151 := [mp #146 #148]: #73
 #399 := [symm #151]: #398
-#401 := [trans #399 #394]: #400
+#401 := [trans #399 #397]: #400
 #403 := [symm #401]: #402
-#405 := [trans #403 #393]: #404
+#405 := [trans #403 #396]: #404
 [mp #405 #407]: false
 unsat
-b782d188626a2e0381f5b576a0374250a8df82c5 77 0
-#2 := false
-decl f6 :: (-> Int Int S6 S5)
-decl f7 :: (-> S1 S4 S6)
-decl f21 :: S4
+df574a4365f54e674a55945a532b21aa0b2dc1f4 77 0
+#2 := false
+decl f6 :: (-> Int Int S3 S4)
+decl f14 :: (-> S1 S6 S3)
+decl f21 :: S6
 #75 := f21
 decl f20 :: S1
 #74 := f20
-#76 := (f7 f20 f21)
+#76 := (f14 f20 f21)
 #73 := 4::Int
 #12 := 5::Int
 #79 := (f6 5::Int 4::Int #76)
-decl f16 :: (-> S2 S5 S5)
+decl f9 :: (-> S2 S4 S4)
 #72 := 3::Int
 #77 := (f6 3::Int 4::Int #76)
 decl f4 :: S2
 #8 := f4
-#78 := (f16 f4 #77)
+#78 := (f9 f4 #77)
 #80 := (= #78 #79)
 decl f3 :: (-> S2 Int Int)
-#466 := (f3 f4 3::Int)
-#467 := (f6 #466 4::Int #76)
-#538 := (= #467 #79)
-#536 := (= #79 #467)
-#530 := (= 5::Int #466)
-#526 := (= #466 5::Int)
+#468 := (f3 f4 3::Int)
+#469 := (f6 #468 4::Int #76)
+#538 := (= #469 #79)
+#536 := (= #79 #469)
+#530 := (= 5::Int #468)
+#528 := (= #468 5::Int)
 #9 := (:var 0 Int)
 #10 := (f3 f4 #9)
 #11 := (pattern #10)
@@ -53321,72 +53716,72 @@
 #101 := [asserted]: #14
 #159 := [mp~ #101 #158]: #14
 #531 := (not #14)
-#532 := (or #531 #526)
+#532 := (or #531 #528)
 #533 := [quant-inst #72]: #532
-#527 := [unit-resolution #533 #159]: #526
-#534 := [symm #527]: #530
+#529 := [unit-resolution #533 #159]: #528
+#534 := [symm #529]: #530
 #537 := [monotonicity #534]: #536
 #539 := [symm #537]: #538
-#470 := (= #78 #467)
-#45 := (:var 0 S6)
-#44 := (:var 1 Int)
-#17 := (:var 2 Int)
-#52 := (:var 3 S2)
-#59 := (f3 #52 #17)
-#60 := (f6 #59 #44 #45)
-#313 := (pattern #60)
-#46 := (f6 #17 #44 #45)
-#58 := (f16 #52 #46)
-#312 := (pattern #58)
-#61 := (= #58 #60)
-#314 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S6)) (:pat #312 #313) #61)
-#62 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S6)) #61)
-#317 := (iff #62 #314)
-#315 := (iff #61 #61)
-#316 := [refl]: #315
-#318 := [quant-intro #316]: #317
-#192 := (~ #62 #62)
-#190 := (~ #61 #61)
-#191 := [refl]: #190
-#193 := [nnf-pos #191]: #192
-#128 := [asserted]: #62
-#194 := [mp~ #128 #193]: #62
-#319 := [mp #194 #318]: #314
-#473 := (not #314)
+#470 := (= #78 #469)
+#17 := (:var 0 S3)
+#16 := (:var 1 Int)
+#15 := (:var 2 Int)
+#28 := (:var 3 S2)
+#30 := (f3 #28 #15)
+#31 := (f6 #30 #16 #17)
+#287 := (pattern #31)
+#18 := (f6 #15 #16 #17)
+#29 := (f9 #28 #18)
+#286 := (pattern #29)
+#32 := (= #29 #31)
+#288 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #286 #287) #32)
+#33 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #32)
+#291 := (iff #33 #288)
+#289 := (iff #32 #32)
+#290 := [refl]: #289
+#292 := [quant-intro #290]: #291
+#177 := (~ #33 #33)
+#175 := (~ #32 #32)
+#176 := [refl]: #175
+#178 := [nnf-pos #176]: #177
+#125 := [asserted]: #33
+#179 := [mp~ #125 #178]: #33
+#293 := [mp #179 #292]: #288
+#473 := (not #288)
 #474 := (or #473 #470)
 #475 := [quant-inst #8 #72 #73 #76]: #474
-#535 := [unit-resolution #475 #319]: #470
+#535 := [unit-resolution #475 #293]: #470
 #540 := [trans #535 #539]: #80
 #81 := (not #80)
-#152 := [asserted]: #81
-[unit-resolution #152 #540]: false
-unsat
-a4d93eb089616c7c0d14a8c862a8b98919dd97bb 77 0
-#2 := false
-decl f6 :: (-> Int Int S6 S5)
-decl f7 :: (-> S1 S4 S6)
-decl f21 :: S4
+#153 := [asserted]: #81
+[unit-resolution #153 #540]: false
+unsat
+4e89c6fb18f25038439974fdc91cdb5ab18a8af0 77 0
+#2 := false
+decl f6 :: (-> Int Int S3 S4)
+decl f14 :: (-> S1 S6 S3)
+decl f21 :: S6
 #75 := f21
 decl f20 :: S1
 #74 := f20
-#76 := (f7 f20 f21)
+#76 := (f14 f20 f21)
 #12 := 6::Int
 #72 := 3::Int
 #79 := (f6 3::Int 6::Int #76)
-decl f15 :: (-> S2 S5 S5)
+decl f10 :: (-> S2 S4 S4)
 #73 := 4::Int
 #77 := (f6 3::Int 4::Int #76)
 decl f4 :: S2
 #8 := f4
-#78 := (f15 f4 #77)
+#78 := (f10 f4 #77)
 #80 := (= #78 #79)
 decl f3 :: (-> S2 Int Int)
-#466 := (f3 f4 4::Int)
-#467 := (f6 3::Int #466 #76)
-#538 := (= #467 #79)
-#536 := (= #79 #467)
-#530 := (= 6::Int #466)
-#526 := (= #466 6::Int)
+#468 := (f3 f4 4::Int)
+#469 := (f6 3::Int #468 #76)
+#538 := (= #469 #79)
+#536 := (= #79 #469)
+#530 := (= 6::Int #468)
+#526 := (= #468 6::Int)
 #9 := (:var 0 Int)
 #10 := (f3 f4 #9)
 #11 := (pattern #10)
@@ -53405,214 +53800,214 @@
 #534 := [symm #527]: #530
 #537 := [monotonicity #534]: #536
 #539 := [symm #537]: #538
-#470 := (= #78 #467)
-#45 := (:var 0 S6)
-#44 := (:var 1 Int)
-#52 := (:var 3 S2)
-#54 := (f3 #52 #44)
-#17 := (:var 2 Int)
-#55 := (f6 #17 #54 #45)
-#305 := (pattern #55)
-#46 := (f6 #17 #44 #45)
-#53 := (f15 #52 #46)
-#304 := (pattern #53)
-#56 := (= #53 #55)
-#306 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S6)) (:pat #304 #305) #56)
-#57 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S6)) #56)
-#309 := (iff #57 #306)
-#307 := (iff #56 #56)
-#308 := [refl]: #307
-#310 := [quant-intro #308]: #309
-#187 := (~ #57 #57)
-#185 := (~ #56 #56)
-#186 := [refl]: #185
-#188 := [nnf-pos #186]: #187
-#126 := [asserted]: #57
-#189 := [mp~ #126 #188]: #57
-#311 := [mp #189 #310]: #306
-#473 := (not #306)
+#470 := (= #78 #469)
+#17 := (:var 0 S3)
+#16 := (:var 1 Int)
+#28 := (:var 3 S2)
+#35 := (f3 #28 #16)
+#15 := (:var 2 Int)
+#36 := (f6 #15 #35 #17)
+#295 := (pattern #36)
+#18 := (f6 #15 #16 #17)
+#34 := (f10 #28 #18)
+#294 := (pattern #34)
+#37 := (= #34 #36)
+#296 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) (:pat #294 #295) #37)
+#38 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S3)) #37)
+#299 := (iff #38 #296)
+#297 := (iff #37 #37)
+#298 := [refl]: #297
+#300 := [quant-intro #298]: #299
+#182 := (~ #38 #38)
+#180 := (~ #37 #37)
+#181 := [refl]: #180
+#183 := [nnf-pos #181]: #182
+#126 := [asserted]: #38
+#184 := [mp~ #126 #183]: #38
+#301 := [mp #184 #300]: #296
+#473 := (not #296)
 #474 := (or #473 #470)
 #475 := [quant-inst #8 #72 #73 #76]: #474
-#535 := [unit-resolution #475 #311]: #470
+#535 := [unit-resolution #475 #301]: #470
 #540 := [trans #535 #539]: #80
 #81 := (not #80)
-#152 := [asserted]: #81
-[unit-resolution #152 #540]: false
-unsat
-9b928998cfefb8ac92745f24b207e3b96bdec398 409 0
-#2 := false
-decl f12 :: (-> S3 S6 S6)
-decl f17 :: (-> S2 S6 S6)
-decl f18 :: (-> S2 S6 S6)
-decl f22 :: S6
+#153 := [asserted]: #81
+[unit-resolution #153 #540]: false
+unsat
+68e99be1e87e8d0678d49d93a4e91b40c95b96ee 409 0
+#2 := false
+decl f19 :: (-> S3 S5 S5)
+decl f13 :: (-> S2 S5 S5)
+decl f12 :: (-> S2 S5 S5)
+decl f22 :: S5
 #85 := f22
 decl f5 :: S2
 #15 := f5
-#90 := (f18 f5 f22)
+#90 := (f12 f5 f22)
 decl f4 :: S2
 #8 := f4
-#91 := (f17 f4 #90)
+#91 := (f13 f4 #90)
 decl f7 :: S3
 #21 := f7
-#92 := (f12 f7 #91)
-#183 := (= f22 #92)
-decl f9 :: (-> Int Int S7 S6)
-decl f10 :: (-> S1 S5 S7)
-decl f13 :: (-> S6 S5)
-decl f23 :: S5
+#92 := (f19 f7 #91)
+#184 := (= f22 #92)
+decl f9 :: (-> Int Int S4 S5)
+decl f17 :: (-> S1 S7 S4)
+decl f18 :: (-> S5 S7)
+decl f23 :: S7
 #86 := f23
 decl f1 :: S1
 #4 := f1
-#87 := (f10 f1 f23)
+#87 := (f17 f1 f23)
 #12 := 4::Int
 #18 := 3::Int
 #88 := (f9 3::Int 4::Int #87)
-#473 := (f13 #88)
-decl f14 :: (-> S6 S1)
-#448 := (f14 #88)
-#499 := (f10 #448 #473)
+#438 := (f18 #88)
+decl f16 :: (-> S5 S1)
+#416 := (f16 #88)
+#478 := (f17 #416 #438)
 decl f3 :: (-> S2 Int Int)
-#532 := (f3 f4 4::Int)
-#591 := (f9 3::Int #532 #499)
-#628 := (f12 f7 #591)
+#534 := (f3 f4 4::Int)
+#554 := (f9 3::Int #534 #478)
+#628 := (f19 f7 #554)
 #793 := (= #628 #92)
 #786 := (= #92 #628)
-#784 := (= #91 #591)
-decl f19 :: (-> S6 S7)
-#445 := (f19 #88)
+#784 := (= #91 #554)
+decl f11 :: (-> S5 S4)
+#440 := (f11 #88)
 #398 := (f3 f5 3::Int)
-#535 := (f9 #398 #532 #445)
-#780 := (= #535 #591)
-#778 := (= #591 #535)
-#755 := (= #499 #445)
-#446 := (= #87 #445)
-#58 := (:var 0 S7)
-#57 := (:var 1 Int)
-#30 := (:var 2 Int)
-#59 := (f9 #30 #57 #58)
-#379 := (pattern #59)
-#76 := (f19 #59)
-#160 := (= #58 #76)
-#380 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S7)) (:pat #379) #160)
-#163 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S7)) #160)
-#383 := (iff #163 #380)
-#381 := (iff #160 #160)
-#382 := [refl]: #381
-#384 := [quant-intro #382]: #383
-#256 := (~ #163 #163)
-#254 := (~ #160 #160)
-#255 := [refl]: #254
-#257 := [nnf-pos #255]: #256
-#77 := (= #76 #58)
-#78 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S7)) #77)
-#164 := (iff #78 #163)
-#161 := (iff #77 #160)
-#162 := [rewrite]: #161
-#165 := [quant-intro #162]: #164
-#159 := [asserted]: #78
-#168 := [mp #159 #165]: #163
-#258 := [mp~ #168 #257]: #163
-#385 := [mp #258 #384]: #380
-#449 := (not #380)
-#450 := (or #449 #446)
-#451 := [quant-inst #18 #12 #87]: #450
-#749 := [unit-resolution #451 #385]: #446
-#753 := (= #499 #87)
-#737 := (= #473 f23)
-#474 := (= f23 #473)
-#32 := (:var 0 S5)
-#31 := (:var 1 S1)
-#33 := (f10 #31 #32)
-#29 := (:var 3 Int)
-#34 := (f9 #29 #30 #33)
-#342 := (pattern #34)
-#48 := (f13 #34)
-#135 := (= #32 #48)
-#343 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) (:pat #342) #135)
-#138 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #135)
-#346 := (iff #138 #343)
-#344 := (iff #135 #135)
-#345 := [refl]: #344
-#347 := [quant-intro #345]: #346
-#231 := (~ #138 #138)
-#229 := (~ #135 #135)
+#535 := (f9 #398 #534 #440)
+#780 := (= #535 #554)
+#778 := (= #554 #535)
+#755 := (= #478 #440)
+#441 := (= #87 #440)
+#30 := (:var 0 S4)
+#29 := (:var 1 Int)
+#28 := (:var 2 Int)
+#31 := (f9 #28 #29 #30)
+#326 := (pattern #31)
+#38 := (f11 #31)
+#148 := (= #30 #38)
+#339 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) (:pat #326) #148)
+#152 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #148)
+#342 := (iff #152 #339)
+#340 := (iff #148 #148)
+#341 := [refl]: #340
+#343 := [quant-intro #341]: #342
+#231 := (~ #152 #152)
+#229 := (~ #148 #148)
 #230 := [refl]: #229
 #232 := [nnf-pos #230]: #231
-#49 := (= #48 #32)
-#50 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #49)
-#139 := (iff #50 #138)
-#136 := (iff #49 #135)
-#137 := [rewrite]: #136
-#140 := [quant-intro #137]: #139
-#134 := [asserted]: #50
-#143 := [mp #134 #140]: #138
-#233 := [mp~ #143 #232]: #138
-#348 := [mp #233 #347]: #343
-#477 := (not #343)
-#478 := (or #477 #474)
-#479 := [quant-inst #18 #12 #4 #86]: #478
-#736 := [unit-resolution #479 #348]: #474
+#39 := (= #38 #30)
+#40 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #39)
+#153 := (iff #40 #152)
+#150 := (iff #39 #148)
+#151 := [rewrite]: #150
+#154 := [quant-intro #151]: #153
+#147 := [asserted]: #40
+#157 := [mp #147 #154]: #152
+#233 := [mp~ #157 #232]: #152
+#344 := [mp #233 #343]: #339
+#447 := (not #339)
+#448 := (or #447 #441)
+#449 := [quant-inst #18 #12 #87]: #448
+#749 := [unit-resolution #449 #344]: #441
+#753 := (= #478 #87)
+#737 := (= #438 f23)
+#439 := (= f23 #438)
+#60 := (:var 0 S7)
+#59 := (:var 1 S1)
+#61 := (f17 #59 #60)
+#58 := (:var 3 Int)
+#62 := (f9 #58 #28 #61)
+#369 := (pattern #62)
+#68 := (f18 #62)
+#173 := (= #60 #68)
+#376 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) (:pat #369) #173)
+#177 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #173)
+#379 := (iff #177 #376)
+#377 := (iff #173 #173)
+#378 := [refl]: #377
+#380 := [quant-intro #378]: #379
+#256 := (~ #177 #177)
+#254 := (~ #173 #173)
+#255 := [refl]: #254
+#257 := [nnf-pos #255]: #256
+#69 := (= #68 #60)
+#70 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #69)
+#178 := (iff #70 #177)
+#175 := (iff #69 #173)
+#176 := [rewrite]: #175
+#179 := [quant-intro #176]: #178
+#172 := [asserted]: #70
+#182 := [mp #172 #179]: #177
+#258 := [mp~ #182 #257]: #177
+#381 := [mp #258 #380]: #376
+#442 := (not #376)
+#443 := (or #442 #439)
+#444 := [quant-inst #18 #12 #4 #86]: #443
+#736 := [unit-resolution #444 #381]: #439
 #741 := [symm #736]: #737
-#751 := (= #448 f1)
-#452 := (= f1 #448)
-#146 := (= f1 #31)
-#51 := (f14 #34)
-#142 := (= f1 #51)
-#149 := (iff #142 #146)
-#349 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) (:pat #342) #149)
-#152 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #149)
-#352 := (iff #152 #349)
-#350 := (iff #149 #149)
-#351 := [refl]: #350
-#353 := [quant-intro #351]: #352
-#236 := (~ #152 #152)
-#234 := (~ #149 #149)
-#235 := [refl]: #234
-#237 := [nnf-pos #235]: #236
-#53 := (= #31 f1)
-#52 := (= #51 f1)
-#54 := (iff #52 #53)
-#55 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #54)
-#153 := (iff #55 #152)
-#150 := (iff #54 #149)
-#147 := (iff #53 #146)
-#148 := [rewrite]: #147
-#144 := (iff #52 #142)
-#145 := [rewrite]: #144
-#151 := [monotonicity #145 #148]: #150
-#154 := [quant-intro #151]: #153
-#141 := [asserted]: #55
-#157 := [mp #141 #154]: #152
-#238 := [mp~ #157 #237]: #152
-#354 := [mp #238 #353]: #349
-#463 := (not #349)
-#464 := (or #463 #452)
-#447 := (= f1 f1)
-#453 := (iff #452 #447)
-#465 := (or #463 #453)
-#467 := (iff #465 #464)
-#469 := (iff #464 #464)
-#470 := [rewrite]: #469
-#461 := (iff #453 #452)
-#1 := true
-#456 := (iff #452 true)
-#459 := (iff #456 #452)
-#460 := [rewrite]: #459
-#457 := (iff #453 #456)
-#454 := (iff #447 true)
-#455 := [rewrite]: #454
-#458 := [monotonicity #455]: #457
-#462 := [trans #458 #460]: #461
-#468 := [monotonicity #462]: #467
-#471 := [trans #468 #470]: #467
-#466 := [quant-inst #18 #12 #4 #86]: #465
-#472 := [mp #466 #471]: #464
-#750 := [unit-resolution #472 #354]: #452
+#751 := (= #416 f1)
+#417 := (= f1 #416)
+#163 := (= f1 #59)
+#63 := (f16 #62)
+#160 := (= f1 #63)
+#166 := (iff #160 #163)
+#370 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) (:pat #369) #166)
+#169 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #166)
+#373 := (iff #169 #370)
+#371 := (iff #166 #166)
+#372 := [refl]: #371
+#374 := [quant-intro #372]: #373
+#251 := (~ #169 #169)
+#249 := (~ #166 #166)
+#250 := [refl]: #249
+#252 := [nnf-pos #250]: #251
+#65 := (= #59 f1)
+#64 := (= #63 f1)
+#66 := (iff #64 #65)
+#67 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #66)
+#170 := (iff #67 #169)
+#167 := (iff #66 #166)
+#164 := (iff #65 #163)
+#165 := [rewrite]: #164
+#161 := (iff #64 #160)
+#162 := [rewrite]: #161
+#168 := [monotonicity #162 #165]: #167
+#171 := [quant-intro #168]: #170
+#159 := [asserted]: #67
+#174 := [mp #159 #171]: #169
+#253 := [mp~ #174 #252]: #169
+#375 := [mp #253 #374]: #370
+#428 := (not #370)
+#429 := (or #428 #417)
+#415 := (= f1 f1)
+#418 := (iff #417 #415)
+#430 := (or #428 #418)
+#432 := (iff #430 #429)
+#434 := (iff #429 #429)
+#435 := [rewrite]: #434
+#426 := (iff #418 #417)
+#1 := true
+#421 := (iff #417 true)
+#424 := (iff #421 #417)
+#425 := [rewrite]: #424
+#422 := (iff #418 #421)
+#419 := (iff #415 true)
+#420 := [rewrite]: #419
+#423 := [monotonicity #420]: #422
+#427 := [trans #423 #425]: #426
+#433 := [monotonicity #427]: #432
+#436 := [trans #433 #435]: #432
+#431 := [quant-inst #18 #12 #4 #86]: #430
+#437 := [mp #431 #436]: #429
+#750 := [unit-resolution #437 #375]: #417
 #752 := [symm #750]: #751
 #754 := [monotonicity #752 #741]: #753
 #756 := [trans #754 #749]: #755
 #758 := (= 3::Int #398)
-#531 := (= #398 3::Int)
+#533 := (= #398 3::Int)
 #9 := (:var 0 Int)
 #16 := (f3 f5 #9)
 #17 := (pattern #16)
@@ -53625,38 +54020,38 @@
 #116 := [asserted]: #20
 #213 := [mp~ #116 #212]: #20
 #536 := (not #20)
-#537 := (or #536 #531)
+#537 := (or #536 #533)
 #538 := [quant-inst #18]: #537
-#757 := [unit-resolution #538 #213]: #531
+#757 := [unit-resolution #538 #213]: #533
 #759 := [symm #757]: #758
 #779 := [monotonicity #759 #756]: #778
 #781 := [symm #779]: #780
 #782 := (= #91 #535)
-#475 := (f9 #398 4::Int #445)
-#539 := (f17 f4 #475)
+#508 := (f9 #398 4::Int #440)
+#539 := (f13 f4 #508)
 #540 := (= #539 #535)
 #541 := (= #535 #539)
-#65 := (:var 3 S2)
-#67 := (f3 #65 #57)
-#68 := (f9 #30 #67 #58)
-#364 := (pattern #68)
-#66 := (f17 #65 #59)
-#363 := (pattern #66)
-#69 := (= #66 #68)
-#365 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) (:pat #363 #364) #69)
-#70 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) #69)
-#368 := (iff #70 #365)
-#366 := (iff #69 #69)
-#367 := [refl]: #366
-#369 := [quant-intro #367]: #368
-#246 := (~ #70 #70)
-#244 := (~ #69 #69)
-#245 := [refl]: #244
-#247 := [nnf-pos #245]: #246
-#156 := [asserted]: #70
-#248 := [mp~ #156 #247]: #70
-#370 := [mp #248 #369]: #365
-#544 := (not #365)
+#41 := (:var 3 S2)
+#48 := (f3 #41 #29)
+#49 := (f9 #28 #48 #30)
+#354 := (pattern #49)
+#47 := (f13 #41 #31)
+#353 := (pattern #47)
+#50 := (= #47 #49)
+#355 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #353 #354) #50)
+#51 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #50)
+#358 := (iff #51 #355)
+#356 := (iff #50 #50)
+#357 := [refl]: #356
+#359 := [quant-intro #357]: #358
+#241 := (~ #51 #51)
+#239 := (~ #50 #50)
+#240 := [refl]: #239
+#242 := [nnf-pos #240]: #241
+#156 := [asserted]: #51
+#243 := [mp~ #156 #242]: #51
+#360 := [mp #243 #359]: #355
+#544 := (not #355)
 #545 := (or #544 #541)
 #546 := (or #544 #540)
 #548 := (iff #546 #545)
@@ -53666,43 +54061,43 @@
 #543 := [rewrite]: #542
 #549 := [monotonicity #543]: #548
 #552 := [trans #549 #551]: #548
-#547 := [quant-inst #8 #398 #12 #445]: #546
+#547 := [quant-inst #8 #398 #12 #440]: #546
 #553 := [mp #547 #552]: #545
-#760 := [unit-resolution #553 #370]: #541
+#760 := [unit-resolution #553 #360]: #541
 #777 := [symm #760]: #540
 #775 := (= #91 #539)
-#773 := (= #90 #475)
+#773 := (= #90 #508)
 #399 := (f9 #398 4::Int #87)
-#769 := (= #399 #475)
-#766 := (= #475 #399)
-#762 := (= #445 #87)
+#769 := (= #399 #508)
+#766 := (= #508 #399)
+#762 := (= #440 #87)
 #763 := [symm #749]: #762
 #767 := [monotonicity #763]: #766
 #770 := [symm #767]: #769
 #771 := (= #90 #399)
-#400 := (f18 f5 #88)
+#400 := (f12 f5 #88)
 #401 := (= #400 #399)
 #402 := (= #399 #400)
-#72 := (f3 #65 #30)
-#73 := (f9 #72 #57 #58)
-#372 := (pattern #73)
-#71 := (f18 #65 #59)
-#371 := (pattern #71)
-#74 := (= #71 #73)
-#373 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) (:pat #371 #372) #74)
-#75 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) #74)
-#376 := (iff #75 #373)
-#374 := (iff #74 #74)
-#375 := [refl]: #374
-#377 := [quant-intro #375]: #376
-#251 := (~ #75 #75)
-#249 := (~ #74 #74)
-#250 := [refl]: #249
-#252 := [nnf-pos #250]: #251
-#158 := [asserted]: #75
-#253 := [mp~ #158 #252]: #75
-#378 := [mp #253 #377]: #373
-#405 := (not #373)
+#43 := (f3 #41 #28)
+#44 := (f9 #43 #29 #30)
+#346 := (pattern #44)
+#42 := (f12 #41 #31)
+#345 := (pattern #42)
+#45 := (= #42 #44)
+#347 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #345 #346) #45)
+#46 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #45)
+#350 := (iff #46 #347)
+#348 := (iff #45 #45)
+#349 := [refl]: #348
+#351 := [quant-intro #349]: #350
+#236 := (~ #46 #46)
+#234 := (~ #45 #45)
+#235 := [refl]: #234
+#237 := [nnf-pos #235]: #236
+#155 := [asserted]: #46
+#238 := [mp~ #155 #237]: #46
+#352 := [mp #238 #351]: #347
+#405 := (not #347)
 #406 := (or #405 #402)
 #407 := (or #405 #401)
 #409 := (iff #407 #406)
@@ -53714,29 +54109,29 @@
 #413 := [trans #410 #412]: #409
 #408 := [quant-inst #15 #18 #12 #87]: #407
 #414 := [mp #408 #413]: #406
-#761 := [unit-resolution #414 #378]: #402
+#761 := [unit-resolution #414 #352]: #402
 #768 := [symm #761]: #401
 #764 := (= #90 #400)
 #89 := (= f22 #88)
 #190 := (not #89)
-#191 := (or #190 #183)
+#191 := (or #190 #184)
 #196 := (not #191)
 #93 := (= #92 f22)
 #94 := (implies #89 #93)
 #95 := (not #94)
 #197 := (iff #95 #196)
 #194 := (iff #94 #191)
-#187 := (implies #89 #183)
+#187 := (implies #89 #184)
 #192 := (iff #187 #191)
 #193 := [rewrite]: #192
 #188 := (iff #94 #187)
-#185 := (iff #93 #183)
+#185 := (iff #93 #184)
 #186 := [rewrite]: #185
 #189 := [monotonicity #186]: #188
 #195 := [trans #189 #193]: #194
 #198 := [monotonicity #195]: #197
-#182 := [asserted]: #95
-#201 := [mp #182 #198]: #196
+#183 := [asserted]: #95
+#201 := [mp #183 #198]: #196
 #199 := [not-or-elim #201]: #89
 #765 := [monotonicity #199]: #764
 #772 := [trans #765 #768]: #771
@@ -53748,32 +54143,32 @@
 #794 := [symm #787]: #793
 #797 := (= f22 #628)
 decl f6 :: (-> S3 S1 S1)
-#620 := (f6 f7 #448)
-#623 := (f10 #620 #473)
-#627 := (f9 3::Int #532 #623)
+#620 := (f6 f7 #416)
+#623 := (f17 #620 #438)
+#627 := (f9 3::Int #534 #623)
 #630 := (= #627 #628)
-#41 := (:var 4 S3)
-#43 := (f6 #41 #31)
-#44 := (f10 #43 #32)
-#45 := (f9 #29 #30 #44)
-#335 := (pattern #45)
-#42 := (f12 #41 #34)
-#334 := (pattern #42)
-#46 := (= #42 #45)
-#336 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S5)) (:pat #334 #335) #46)
-#47 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S5)) #46)
-#339 := (iff #47 #336)
-#337 := (iff #46 #46)
-#338 := [refl]: #337
-#340 := [quant-intro #338]: #339
-#226 := (~ #47 #47)
-#224 := (~ #46 #46)
-#225 := [refl]: #224
-#227 := [nnf-pos #225]: #226
-#132 := [asserted]: #47
-#228 := [mp~ #132 #227]: #47
-#341 := [mp #228 #340]: #336
-#633 := (not #336)
+#71 := (:var 4 S3)
+#73 := (f6 #71 #59)
+#74 := (f17 #73 #60)
+#75 := (f9 #58 #28 #74)
+#383 := (pattern #75)
+#72 := (f19 #71 #62)
+#382 := (pattern #72)
+#76 := (= #72 #75)
+#384 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S7)) (:pat #382 #383) #76)
+#77 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S7)) #76)
+#387 := (iff #77 #384)
+#385 := (iff #76 #76)
+#386 := [refl]: #385
+#388 := [quant-intro #386]: #387
+#261 := (~ #77 #77)
+#259 := (~ #76 #76)
+#260 := [refl]: #259
+#262 := [nnf-pos #260]: #261
+#180 := [asserted]: #77
+#263 := [mp~ #180 #262]: #77
+#389 := [mp #263 #388]: #384
+#633 := (not #384)
 #634 := (or #633 #630)
 #629 := (= #628 #627)
 #635 := (or #633 #629)
@@ -53784,15 +54179,15 @@
 #632 := [rewrite]: #631
 #638 := [monotonicity #632]: #637
 #641 := [trans #638 #640]: #637
-#636 := [quant-inst #21 #18 #532 #448 #473]: #635
+#636 := [quant-inst #21 #18 #534 #416 #438]: #635
 #642 := [mp #636 #641]: #634
-#748 := [unit-resolution #642 #341]: #630
+#748 := [unit-resolution #642 #389]: #630
 #795 := (= f22 #627)
 #791 := (= #88 #627)
 #789 := (= #627 #88)
 #745 := (= #623 #87)
 #743 := (= #620 f1)
-#691 := (= f1 #620)
+#643 := (= f1 #620)
 #22 := (:var 0 S1)
 #23 := (f6 f7 #22)
 #24 := (pattern #23)
@@ -53820,12 +54215,12 @@
 #133 := [mp #117 #130]: #128
 #218 := [mp~ #133 #217]: #128
 #738 := (not #128)
-#739 := (or #738 #691)
-#740 := [quant-inst #448]: #739
-#742 := [unit-resolution #740 #218]: #691
+#739 := (or #738 #643)
+#740 := [quant-inst #416]: #739
+#742 := [unit-resolution #740 #218]: #643
 #744 := [symm #742]: #743
 #746 := [monotonicity #744 #741]: #745
-#619 := (= #532 4::Int)
+#619 := (= #534 4::Int)
 #10 := (f3 f4 #9)
 #11 := (pattern #10)
 #13 := (= #10 4::Int)
@@ -53844,55 +54239,55 @@
 #792 := [symm #790]: #791
 #796 := [trans #199 #792]: #795
 #798 := [trans #796 #748]: #797
-#799 := [trans #798 #794]: #183
-#200 := (not #183)
+#799 := [trans #798 #794]: #184
+#200 := (not #184)
 #202 := [not-or-elim #201]: #200
 [unit-resolution #202 #799]: false
 unsat
-4e5bdb146605ddee0e865e055a144749744ef3dd 381 0
-#2 := false
-decl f18 :: (-> S2 S6 S6)
-decl f12 :: (-> S3 S6 S6)
-decl f17 :: (-> S2 S6 S6)
-decl f22 :: S6
+b772603aaba9792fa294ee48d2ae093633041197 381 0
+#2 := false
+decl f12 :: (-> S2 S5 S5)
+decl f19 :: (-> S3 S5 S5)
+decl f13 :: (-> S2 S5 S5)
+decl f22 :: S5
 #85 := f22
 decl f4 :: S2
 #8 := f4
-#90 := (f17 f4 f22)
+#90 := (f13 f4 f22)
 decl f7 :: S3
 #21 := f7
-#91 := (f12 f7 #90)
+#91 := (f19 f7 #90)
 decl f5 :: S2
 #15 := f5
-#92 := (f18 f5 #91)
-#183 := (= f22 #92)
-decl f9 :: (-> Int Int S7 S6)
-decl f10 :: (-> S1 S5 S7)
-decl f13 :: (-> S6 S5)
-decl f23 :: S5
+#92 := (f12 f5 #91)
+#184 := (= f22 #92)
+decl f9 :: (-> Int Int S4 S5)
+decl f17 :: (-> S1 S7 S4)
+decl f18 :: (-> S5 S7)
+decl f23 :: S7
 #86 := f23
 decl f1 :: S1
 #4 := f1
-#87 := (f10 f1 f23)
+#87 := (f17 f1 f23)
 #12 := 4::Int
 #18 := 3::Int
 #88 := (f9 3::Int 4::Int #87)
-#473 := (f13 #88)
+#438 := (f18 #88)
 decl f6 :: (-> S3 S1 S1)
-decl f14 :: (-> S6 S1)
-#448 := (f14 #88)
-#532 := (f6 f7 #448)
-#535 := (f10 #532 #473)
-#555 := (f9 3::Int 4::Int #535)
-#638 := (f18 f5 #555)
+decl f16 :: (-> S5 S1)
+#416 := (f16 #88)
+#532 := (f6 f7 #416)
+#535 := (f17 #532 #438)
+#556 := (f9 3::Int 4::Int #535)
+#638 := (f12 f5 #556)
 #794 := (= #638 #92)
 #787 := (= #92 #638)
-#785 := (= #91 #555)
+#785 := (= #91 #556)
 decl f3 :: (-> S2 Int Int)
 #398 := (f3 f4 4::Int)
 #539 := (f9 3::Int #398 #535)
-#781 := (= #539 #555)
-#779 := (= #555 #539)
+#781 := (= #539 #556)
+#779 := (= #556 #539)
 #750 := (= 4::Int #398)
 #531 := (= #398 4::Int)
 #9 := (:var 0 Int)
@@ -53914,39 +54309,39 @@
 #780 := [monotonicity #751]: #779
 #782 := [symm #780]: #781
 #783 := (= #91 #539)
-#499 := (f10 #448 #473)
-#500 := (f9 3::Int #398 #499)
-#540 := (f12 f7 #500)
+#478 := (f17 #416 #438)
+#479 := (f9 3::Int #398 #478)
+#540 := (f19 f7 #479)
 #541 := (= #540 #539)
 #542 := (= #539 #540)
-#32 := (:var 0 S5)
-#31 := (:var 1 S1)
-#41 := (:var 4 S3)
-#43 := (f6 #41 #31)
-#44 := (f10 #43 #32)
-#30 := (:var 2 Int)
-#29 := (:var 3 Int)
-#45 := (f9 #29 #30 #44)
-#335 := (pattern #45)
-#33 := (f10 #31 #32)
-#34 := (f9 #29 #30 #33)
-#42 := (f12 #41 #34)
-#334 := (pattern #42)
-#46 := (= #42 #45)
-#336 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S5)) (:pat #334 #335) #46)
-#47 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S5)) #46)
-#339 := (iff #47 #336)
-#337 := (iff #46 #46)
-#338 := [refl]: #337
-#340 := [quant-intro #338]: #339
-#226 := (~ #47 #47)
-#224 := (~ #46 #46)
-#225 := [refl]: #224
-#227 := [nnf-pos #225]: #226
-#132 := [asserted]: #47
-#228 := [mp~ #132 #227]: #47
-#341 := [mp #228 #340]: #336
-#545 := (not #336)
+#60 := (:var 0 S7)
+#59 := (:var 1 S1)
+#71 := (:var 4 S3)
+#73 := (f6 #71 #59)
+#74 := (f17 #73 #60)
+#28 := (:var 2 Int)
+#58 := (:var 3 Int)
+#75 := (f9 #58 #28 #74)
+#383 := (pattern #75)
+#61 := (f17 #59 #60)
+#62 := (f9 #58 #28 #61)
+#72 := (f19 #71 #62)
+#382 := (pattern #72)
+#76 := (= #72 #75)
+#384 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S7)) (:pat #382 #383) #76)
+#77 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S7)) #76)
+#387 := (iff #77 #384)
+#385 := (iff #76 #76)
+#386 := [refl]: #385
+#388 := [quant-intro #386]: #387
+#261 := (~ #77 #77)
+#259 := (~ #76 #76)
+#260 := [refl]: #259
+#262 := [nnf-pos #260]: #261
+#180 := [asserted]: #77
+#263 := [mp~ #180 #262]: #77
+#389 := [mp #263 #388]: #384
+#545 := (not #384)
 #546 := (or #545 #542)
 #547 := (or #545 #541)
 #549 := (iff #547 #546)
@@ -53956,100 +54351,100 @@
 #544 := [rewrite]: #543
 #550 := [monotonicity #544]: #549
 #553 := [trans #550 #552]: #549
-#548 := [quant-inst #21 #18 #398 #448 #473]: #547
+#548 := [quant-inst #21 #18 #398 #416 #438]: #547
 #554 := [mp #548 #553]: #546
-#752 := [unit-resolution #554 #341]: #542
+#752 := [unit-resolution #554 #389]: #542
 #778 := [symm #752]: #541
 #776 := (= #91 #540)
-#774 := (= #90 #500)
-#768 := (= #88 #500)
-#761 := (= #500 #88)
-#757 := (= #499 #87)
-#737 := (= #473 f23)
-#474 := (= f23 #473)
-#342 := (pattern #34)
-#48 := (f13 #34)
-#135 := (= #32 #48)
-#343 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) (:pat #342) #135)
-#138 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #135)
-#346 := (iff #138 #343)
-#344 := (iff #135 #135)
-#345 := [refl]: #344
-#347 := [quant-intro #345]: #346
-#231 := (~ #138 #138)
-#229 := (~ #135 #135)
-#230 := [refl]: #229
-#232 := [nnf-pos #230]: #231
-#49 := (= #48 #32)
-#50 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #49)
-#139 := (iff #50 #138)
-#136 := (iff #49 #135)
-#137 := [rewrite]: #136
-#140 := [quant-intro #137]: #139
-#134 := [asserted]: #50
-#143 := [mp #134 #140]: #138
-#233 := [mp~ #143 #232]: #138
-#348 := [mp #233 #347]: #343
-#477 := (not #343)
-#478 := (or #477 #474)
-#479 := [quant-inst #18 #12 #4 #86]: #478
-#736 := [unit-resolution #479 #348]: #474
+#774 := (= #90 #479)
+#768 := (= #88 #479)
+#761 := (= #479 #88)
+#757 := (= #478 #87)
+#737 := (= #438 f23)
+#439 := (= f23 #438)
+#369 := (pattern #62)
+#68 := (f18 #62)
+#173 := (= #60 #68)
+#376 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) (:pat #369) #173)
+#177 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #173)
+#379 := (iff #177 #376)
+#377 := (iff #173 #173)
+#378 := [refl]: #377
+#380 := [quant-intro #378]: #379
+#256 := (~ #177 #177)
+#254 := (~ #173 #173)
+#255 := [refl]: #254
+#257 := [nnf-pos #255]: #256
+#69 := (= #68 #60)
+#70 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #69)
+#178 := (iff #70 #177)
+#175 := (iff #69 #173)
+#176 := [rewrite]: #175
+#179 := [quant-intro #176]: #178
+#172 := [asserted]: #70
+#182 := [mp #172 #179]: #177
+#258 := [mp~ #182 #257]: #177
+#381 := [mp #258 #380]: #376
+#442 := (not #376)
+#443 := (or #442 #439)
+#444 := [quant-inst #18 #12 #4 #86]: #443
+#736 := [unit-resolution #444 #381]: #439
 #741 := [symm #736]: #737
-#755 := (= #448 f1)
-#452 := (= f1 #448)
-#146 := (= f1 #31)
-#51 := (f14 #34)
-#142 := (= f1 #51)
-#149 := (iff #142 #146)
-#349 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) (:pat #342) #149)
-#152 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #149)
-#352 := (iff #152 #349)
-#350 := (iff #149 #149)
-#351 := [refl]: #350
-#353 := [quant-intro #351]: #352
-#236 := (~ #152 #152)
-#234 := (~ #149 #149)
-#235 := [refl]: #234
-#237 := [nnf-pos #235]: #236
-#53 := (= #31 f1)
-#52 := (= #51 f1)
-#54 := (iff #52 #53)
-#55 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #54)
-#153 := (iff #55 #152)
-#150 := (iff #54 #149)
-#147 := (iff #53 #146)
-#148 := [rewrite]: #147
-#144 := (iff #52 #142)
-#145 := [rewrite]: #144
-#151 := [monotonicity #145 #148]: #150
-#154 := [quant-intro #151]: #153
-#141 := [asserted]: #55
-#157 := [mp #141 #154]: #152
-#238 := [mp~ #157 #237]: #152
-#354 := [mp #238 #353]: #349
-#463 := (not #349)
-#464 := (or #463 #452)
-#447 := (= f1 f1)
-#453 := (iff #452 #447)
-#465 := (or #463 #453)
-#467 := (iff #465 #464)
-#469 := (iff #464 #464)
-#470 := [rewrite]: #469
-#461 := (iff #453 #452)
-#1 := true
-#456 := (iff #452 true)
-#459 := (iff #456 #452)
-#460 := [rewrite]: #459
-#457 := (iff #453 #456)
-#454 := (iff #447 true)
-#455 := [rewrite]: #454
-#458 := [monotonicity #455]: #457
-#462 := [trans #458 #460]: #461
-#468 := [monotonicity #462]: #467
-#471 := [trans #468 #470]: #467
-#466 := [quant-inst #18 #12 #4 #86]: #465
-#472 := [mp #466 #471]: #464
-#754 := [unit-resolution #472 #354]: #452
+#755 := (= #416 f1)
+#417 := (= f1 #416)
+#163 := (= f1 #59)
+#63 := (f16 #62)
+#160 := (= f1 #63)
+#166 := (iff #160 #163)
+#370 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) (:pat #369) #166)
+#169 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #166)
+#373 := (iff #169 #370)
+#371 := (iff #166 #166)
+#372 := [refl]: #371
+#374 := [quant-intro #372]: #373
+#251 := (~ #169 #169)
+#249 := (~ #166 #166)
+#250 := [refl]: #249
+#252 := [nnf-pos #250]: #251
+#65 := (= #59 f1)
+#64 := (= #63 f1)
+#66 := (iff #64 #65)
+#67 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #66)
+#170 := (iff #67 #169)
+#167 := (iff #66 #166)
+#164 := (iff #65 #163)
+#165 := [rewrite]: #164
+#161 := (iff #64 #160)
+#162 := [rewrite]: #161
+#168 := [monotonicity #162 #165]: #167
+#171 := [quant-intro #168]: #170
+#159 := [asserted]: #67
+#174 := [mp #159 #171]: #169
+#253 := [mp~ #174 #252]: #169
+#375 := [mp #253 #374]: #370
+#428 := (not #370)
+#429 := (or #428 #417)
+#415 := (= f1 f1)
+#418 := (iff #417 #415)
+#430 := (or #428 #418)
+#432 := (iff #430 #429)
+#434 := (iff #429 #429)
+#435 := [rewrite]: #434
+#426 := (iff #418 #417)
+#1 := true
+#421 := (iff #417 true)
+#424 := (iff #421 #417)
+#425 := [rewrite]: #424
+#422 := (iff #418 #421)
+#419 := (iff #415 true)
+#420 := [rewrite]: #419
+#423 := [monotonicity #420]: #422
+#427 := [trans #423 #425]: #426
+#433 := [monotonicity #427]: #432
+#436 := [trans #433 #435]: #432
+#431 := [quant-inst #18 #12 #4 #86]: #430
+#437 := [mp #431 #436]: #429
+#754 := [unit-resolution #437 #375]: #417
 #756 := [symm #754]: #755
 #758 := [monotonicity #756 #741]: #757
 #762 := [monotonicity #749 #758]: #761
@@ -54061,33 +54456,33 @@
 #764 := [monotonicity #751]: #763
 #767 := [symm #764]: #766
 #770 := (= #90 #399)
-#400 := (f17 f4 #88)
+#400 := (f13 f4 #88)
 #401 := (= #400 #399)
 #402 := (= #399 #400)
-#58 := (:var 0 S7)
-#57 := (:var 1 Int)
-#65 := (:var 3 S2)
-#67 := (f3 #65 #57)
-#68 := (f9 #30 #67 #58)
-#364 := (pattern #68)
-#59 := (f9 #30 #57 #58)
-#66 := (f17 #65 #59)
-#363 := (pattern #66)
-#69 := (= #66 #68)
-#365 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) (:pat #363 #364) #69)
-#70 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) #69)
-#368 := (iff #70 #365)
-#366 := (iff #69 #69)
-#367 := [refl]: #366
-#369 := [quant-intro #367]: #368
-#246 := (~ #70 #70)
-#244 := (~ #69 #69)
-#245 := [refl]: #244
-#247 := [nnf-pos #245]: #246
-#156 := [asserted]: #70
-#248 := [mp~ #156 #247]: #70
-#370 := [mp #248 #369]: #365
-#405 := (not #365)
+#30 := (:var 0 S4)
+#29 := (:var 1 Int)
+#41 := (:var 3 S2)
+#48 := (f3 #41 #29)
+#49 := (f9 #28 #48 #30)
+#354 := (pattern #49)
+#31 := (f9 #28 #29 #30)
+#47 := (f13 #41 #31)
+#353 := (pattern #47)
+#50 := (= #47 #49)
+#355 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #353 #354) #50)
+#51 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #50)
+#358 := (iff #51 #355)
+#356 := (iff #50 #50)
+#357 := [refl]: #356
+#359 := [quant-intro #357]: #358
+#241 := (~ #51 #51)
+#239 := (~ #50 #50)
+#240 := [refl]: #239
+#242 := [nnf-pos #240]: #241
+#156 := [asserted]: #51
+#243 := [mp~ #156 #242]: #51
+#360 := [mp #243 #359]: #355
+#405 := (not #355)
 #406 := (or #405 #402)
 #407 := (or #405 #401)
 #409 := (iff #407 #406)
@@ -54099,29 +54494,29 @@
 #413 := [trans #410 #412]: #409
 #408 := [quant-inst #8 #18 #12 #87]: #407
 #414 := [mp #408 #413]: #406
-#753 := [unit-resolution #414 #370]: #402
+#753 := [unit-resolution #414 #360]: #402
 #765 := [symm #753]: #401
 #759 := (= #90 #400)
 #89 := (= f22 #88)
 #190 := (not #89)
-#191 := (or #190 #183)
+#191 := (or #190 #184)
 #196 := (not #191)
 #93 := (= #92 f22)
 #94 := (implies #89 #93)
 #95 := (not #94)
 #197 := (iff #95 #196)
 #194 := (iff #94 #191)
-#187 := (implies #89 #183)
+#187 := (implies #89 #184)
 #192 := (iff #187 #191)
 #193 := [rewrite]: #192
 #188 := (iff #94 #187)
-#185 := (iff #93 #183)
+#185 := (iff #93 #184)
 #186 := [rewrite]: #185
 #189 := [monotonicity #186]: #188
 #195 := [trans #189 #193]: #194
 #198 := [monotonicity #195]: #197
-#182 := [asserted]: #95
-#201 := [mp #182 #198]: #196
+#183 := [asserted]: #95
+#201 := [mp #183 #198]: #196
 #199 := [not-or-elim #201]: #89
 #760 := [monotonicity #199]: #759
 #771 := [trans #760 #765]: #770
@@ -54136,26 +54531,26 @@
 #633 := (f3 f5 3::Int)
 #634 := (f9 #633 4::Int #535)
 #640 := (= #634 #638)
-#72 := (f3 #65 #30)
-#73 := (f9 #72 #57 #58)
-#372 := (pattern #73)
-#71 := (f18 #65 #59)
-#371 := (pattern #71)
-#74 := (= #71 #73)
-#373 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) (:pat #371 #372) #74)
-#75 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) #74)
-#376 := (iff #75 #373)
-#374 := (iff #74 #74)
-#375 := [refl]: #374
-#377 := [quant-intro #375]: #376
-#251 := (~ #75 #75)
-#249 := (~ #74 #74)
-#250 := [refl]: #249
-#252 := [nnf-pos #250]: #251
-#158 := [asserted]: #75
-#253 := [mp~ #158 #252]: #75
-#378 := [mp #253 #377]: #373
-#643 := (not #373)
+#43 := (f3 #41 #28)
+#44 := (f9 #43 #29 #30)
+#346 := (pattern #44)
+#42 := (f12 #41 #31)
+#345 := (pattern #42)
+#45 := (= #42 #44)
+#347 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #345 #346) #45)
+#46 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #45)
+#350 := (iff #46 #347)
+#348 := (iff #45 #45)
+#349 := [refl]: #348
+#351 := [quant-intro #349]: #350
+#236 := (~ #46 #46)
+#234 := (~ #45 #45)
+#235 := [refl]: #234
+#237 := [nnf-pos #235]: #236
+#155 := [asserted]: #46
+#238 := [mp~ #155 #237]: #46
+#352 := [mp #238 #351]: #347
+#643 := (not #347)
 #644 := (or #643 #640)
 #639 := (= #638 #634)
 #645 := (or #643 #639)
@@ -54168,13 +54563,13 @@
 #651 := [trans #648 #650]: #647
 #646 := [quant-inst #15 #18 #12 #535]: #645
 #652 := [mp #646 #651]: #644
-#748 := [unit-resolution #652 #378]: #640
+#748 := [unit-resolution #652 #352]: #640
 #796 := (= f22 #634)
 #792 := (= #88 #634)
 #790 := (= #634 #88)
 #745 := (= #535 #87)
 #743 := (= #532 f1)
-#586 := (= f1 #532)
+#555 := (= f1 #532)
 #22 := (:var 0 S1)
 #23 := (f6 f7 #22)
 #24 := (pattern #23)
@@ -54202,9 +54597,9 @@
 #133 := [mp #117 #130]: #128
 #218 := [mp~ #133 #217]: #128
 #635 := (not #128)
-#636 := (or #635 #586)
-#637 := [quant-inst #448]: #636
-#742 := [unit-resolution #637 #218]: #586
+#636 := (or #635 #555)
+#637 := [quant-inst #416]: #636
+#742 := [unit-resolution #637 #218]: #555
 #744 := [symm #742]: #743
 #746 := [monotonicity #744 #741]: #745
 #735 := (= #633 3::Int)
@@ -54226,113 +54621,113 @@
 #793 := [symm #791]: #792
 #797 := [trans #199 #793]: #796
 #799 := [trans #797 #748]: #798
-#800 := [trans #799 #795]: #183
-#200 := (not #183)
+#800 := [trans #799 #795]: #184
+#200 := (not #184)
 #202 := [not-or-elim #201]: #200
 [unit-resolution #202 #800]: false
 unsat
-28647514baf56d812f754250e53a79198fbce4ff 371 0
-#2 := false
-decl f17 :: (-> S2 S6 S6)
-decl f18 :: (-> S2 S6 S6)
-decl f12 :: (-> S3 S6 S6)
-decl f22 :: S6
+4bea4bb3dde48b2c759327219b4fbf786808215a 371 0
+#2 := false
+decl f13 :: (-> S2 S5 S5)
+decl f12 :: (-> S2 S5 S5)
+decl f19 :: (-> S3 S5 S5)
+decl f22 :: S5
 #85 := f22
 decl f7 :: S3
 #21 := f7
-#90 := (f12 f7 f22)
+#90 := (f19 f7 f22)
 decl f5 :: S2
 #15 := f5
-#91 := (f18 f5 #90)
+#91 := (f12 f5 #90)
 decl f4 :: S2
 #8 := f4
-#92 := (f17 f4 #91)
-#183 := (= f22 #92)
-decl f9 :: (-> Int Int S7 S6)
-decl f19 :: (-> S6 S7)
-decl f10 :: (-> S1 S5 S7)
-decl f23 :: S5
+#92 := (f13 f4 #91)
+#184 := (= f22 #92)
+decl f9 :: (-> Int Int S4 S5)
+decl f11 :: (-> S5 S4)
+decl f17 :: (-> S1 S7 S4)
+decl f23 :: S7
 #86 := f23
 decl f6 :: (-> S3 S1 S1)
 decl f1 :: S1
 #4 := f1
 #398 := (f6 f7 f1)
-#399 := (f10 #398 f23)
+#399 := (f17 #398 f23)
 #12 := 4::Int
 #18 := 3::Int
 #400 := (f9 3::Int 4::Int #399)
-#507 := (f19 #400)
+#510 := (f11 #400)
 decl f3 :: (-> S2 Int Int)
 #546 := (f3 f5 3::Int)
-#566 := (f9 #546 4::Int #507)
-#643 := (f17 f4 #566)
+#612 := (f9 #546 4::Int #510)
+#643 := (f13 f4 #612)
 #788 := (= #643 #92)
 #781 := (= #92 #643)
-#766 := (= #91 #566)
+#766 := (= #91 #612)
 #547 := (f9 #546 4::Int #399)
-#762 := (= #547 #566)
-#760 := (= #566 #547)
-#742 := (= #507 #399)
-#508 := (= #399 #507)
-#58 := (:var 0 S7)
-#57 := (:var 1 Int)
-#30 := (:var 2 Int)
-#59 := (f9 #30 #57 #58)
-#379 := (pattern #59)
-#76 := (f19 #59)
-#160 := (= #58 #76)
-#380 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S7)) (:pat #379) #160)
-#163 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S7)) #160)
-#383 := (iff #163 #380)
-#381 := (iff #160 #160)
-#382 := [refl]: #381
-#384 := [quant-intro #382]: #383
-#256 := (~ #163 #163)
-#254 := (~ #160 #160)
-#255 := [refl]: #254
-#257 := [nnf-pos #255]: #256
-#77 := (= #76 #58)
-#78 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S7)) #77)
-#164 := (iff #78 #163)
-#161 := (iff #77 #160)
-#162 := [rewrite]: #161
-#165 := [quant-intro #162]: #164
-#159 := [asserted]: #78
-#168 := [mp #159 #165]: #163
-#258 := [mp~ #168 #257]: #163
-#385 := [mp #258 #384]: #380
-#450 := (not #380)
-#511 := (or #450 #508)
-#512 := [quant-inst #18 #12 #399]: #511
-#741 := [unit-resolution #512 #385]: #508
-#746 := [symm #741]: #742
+#762 := (= #547 #612)
+#760 := (= #612 #547)
+#742 := (= #510 #399)
+#511 := (= #399 #510)
+#30 := (:var 0 S4)
+#29 := (:var 1 Int)
+#28 := (:var 2 Int)
+#31 := (f9 #28 #29 #30)
+#326 := (pattern #31)
+#38 := (f11 #31)
+#148 := (= #30 #38)
+#339 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) (:pat #326) #148)
+#152 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #148)
+#342 := (iff #152 #339)
+#340 := (iff #148 #148)
+#341 := [refl]: #340
+#343 := [quant-intro #341]: #342
+#231 := (~ #152 #152)
+#229 := (~ #148 #148)
+#230 := [refl]: #229
+#232 := [nnf-pos #230]: #231
+#39 := (= #38 #30)
+#40 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S4)) #39)
+#153 := (iff #40 #152)
+#150 := (iff #39 #148)
+#151 := [rewrite]: #150
+#154 := [quant-intro #151]: #153
+#147 := [asserted]: #40
+#157 := [mp #147 #154]: #152
+#233 := [mp~ #157 #232]: #152
+#344 := [mp #233 #343]: #339
+#448 := (not #339)
+#516 := (or #448 #511)
+#517 := [quant-inst #18 #12 #399]: #516
+#739 := [unit-resolution #517 #344]: #511
+#746 := [symm #739]: #742
 #761 := [monotonicity #746]: #760
 #763 := [symm #761]: #762
 #764 := (= #91 #547)
-#551 := (f18 f5 #400)
+#551 := (f12 f5 #400)
 #552 := (= #551 #547)
 #553 := (= #547 #551)
-#65 := (:var 3 S2)
-#72 := (f3 #65 #30)
-#73 := (f9 #72 #57 #58)
-#372 := (pattern #73)
-#71 := (f18 #65 #59)
-#371 := (pattern #71)
-#74 := (= #71 #73)
-#373 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) (:pat #371 #372) #74)
-#75 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) #74)
-#376 := (iff #75 #373)
-#374 := (iff #74 #74)
-#375 := [refl]: #374
-#377 := [quant-intro #375]: #376
-#251 := (~ #75 #75)
-#249 := (~ #74 #74)
-#250 := [refl]: #249
-#252 := [nnf-pos #250]: #251
-#158 := [asserted]: #75
-#253 := [mp~ #158 #252]: #75
-#378 := [mp #253 #377]: #373
-#556 := (not #373)
+#41 := (:var 3 S2)
+#43 := (f3 #41 #28)
+#44 := (f9 #43 #29 #30)
+#346 := (pattern #44)
+#42 := (f12 #41 #31)
+#345 := (pattern #42)
+#45 := (= #42 #44)
+#347 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #345 #346) #45)
+#46 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #45)
+#350 := (iff #46 #347)
+#348 := (iff #45 #45)
+#349 := [refl]: #348
+#351 := [quant-intro #349]: #350
+#236 := (~ #46 #46)
+#234 := (~ #45 #45)
+#235 := [refl]: #234
+#237 := [nnf-pos #235]: #236
+#155 := [asserted]: #46
+#238 := [mp~ #155 #237]: #46
+#352 := [mp #238 #351]: #347
+#556 := (not #347)
 #557 := (or #556 #553)
 #558 := (or #556 #552)
 #560 := (iff #558 #557)
@@ -54344,42 +54739,42 @@
 #564 := [trans #561 #563]: #560
 #559 := [quant-inst #15 #18 #12 #399]: #558
 #565 := [mp #559 #564]: #557
-#750 := [unit-resolution #565 #378]: #553
+#750 := [unit-resolution #565 #352]: #553
 #759 := [symm #750]: #552
 #757 := (= #91 #551)
 #755 := (= #90 #400)
-#87 := (f10 f1 f23)
+#87 := (f17 f1 f23)
 #88 := (f9 3::Int 4::Int #87)
-#401 := (f12 f7 #88)
+#401 := (f19 f7 #88)
 #402 := (= #401 #400)
 #403 := (= #400 #401)
-#32 := (:var 0 S5)
-#31 := (:var 1 S1)
-#41 := (:var 4 S3)
-#43 := (f6 #41 #31)
-#44 := (f10 #43 #32)
-#29 := (:var 3 Int)
-#45 := (f9 #29 #30 #44)
-#335 := (pattern #45)
-#33 := (f10 #31 #32)
-#34 := (f9 #29 #30 #33)
-#42 := (f12 #41 #34)
-#334 := (pattern #42)
-#46 := (= #42 #45)
-#336 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S5)) (:pat #334 #335) #46)
-#47 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S5)) #46)
-#339 := (iff #47 #336)
-#337 := (iff #46 #46)
-#338 := [refl]: #337
-#340 := [quant-intro #338]: #339
-#226 := (~ #47 #47)
-#224 := (~ #46 #46)
-#225 := [refl]: #224
-#227 := [nnf-pos #225]: #226
-#132 := [asserted]: #47
-#228 := [mp~ #132 #227]: #47
-#341 := [mp #228 #340]: #336
-#406 := (not #336)
+#60 := (:var 0 S7)
+#59 := (:var 1 S1)
+#71 := (:var 4 S3)
+#73 := (f6 #71 #59)
+#74 := (f17 #73 #60)
+#58 := (:var 3 Int)
+#75 := (f9 #58 #28 #74)
+#383 := (pattern #75)
+#61 := (f17 #59 #60)
+#62 := (f9 #58 #28 #61)
+#72 := (f19 #71 #62)
+#382 := (pattern #72)
+#76 := (= #72 #75)
+#384 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S7)) (:pat #382 #383) #76)
+#77 := (forall (vars (?v0 S3) (?v1 Int) (?v2 Int) (?v3 S1) (?v4 S7)) #76)
+#387 := (iff #77 #384)
+#385 := (iff #76 #76)
+#386 := [refl]: #385
+#388 := [quant-intro #386]: #387
+#261 := (~ #77 #77)
+#259 := (~ #76 #76)
+#260 := [refl]: #259
+#262 := [nnf-pos #260]: #261
+#180 := [asserted]: #77
+#263 := [mp~ #180 #262]: #77
+#389 := [mp #263 #388]: #384
+#406 := (not #384)
 #407 := (or #406 #403)
 #408 := (or #406 #402)
 #410 := (iff #408 #407)
@@ -54391,29 +54786,29 @@
 #414 := [trans #411 #413]: #410
 #409 := [quant-inst #21 #18 #12 #4 #86]: #408
 #415 := [mp #409 #414]: #407
-#751 := [unit-resolution #415 #341]: #403
+#751 := [unit-resolution #415 #389]: #403
 #754 := [symm #751]: #402
 #752 := (= #90 #401)
 #89 := (= f22 #88)
 #190 := (not #89)
-#191 := (or #190 #183)
+#191 := (or #190 #184)
 #196 := (not #191)
 #93 := (= #92 f22)
 #94 := (implies #89 #93)
 #95 := (not #94)
 #197 := (iff #95 #196)
 #194 := (iff #94 #191)
-#187 := (implies #89 #183)
+#187 := (implies #89 #184)
 #192 := (iff #187 #191)
 #193 := [rewrite]: #192
 #188 := (iff #94 #187)
-#185 := (iff #93 #183)
+#185 := (iff #93 #184)
 #186 := [rewrite]: #185
 #189 := [monotonicity #186]: #188
 #195 := [trans #189 #193]: #194
 #198 := [monotonicity #195]: #197
-#182 := [asserted]: #95
-#201 := [mp #182 #198]: #196
+#183 := [asserted]: #95
+#201 := [mp #183 #198]: #196
 #199 := [not-or-elim #201]: #89
 #753 := [monotonicity #199]: #752
 #756 := [trans #753 #754]: #755
@@ -54424,28 +54819,28 @@
 #789 := [symm #782]: #788
 #794 := (= f22 #643)
 #638 := (f3 f4 4::Int)
-#639 := (f9 #546 #638 #507)
+#639 := (f9 #546 #638 #510)
 #645 := (= #639 #643)
-#67 := (f3 #65 #57)
-#68 := (f9 #30 #67 #58)
-#364 := (pattern #68)
-#66 := (f17 #65 #59)
-#363 := (pattern #66)
-#69 := (= #66 #68)
-#365 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) (:pat #363 #364) #69)
-#70 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S7)) #69)
-#368 := (iff #70 #365)
-#366 := (iff #69 #69)
-#367 := [refl]: #366
-#369 := [quant-intro #367]: #368
-#246 := (~ #70 #70)
-#244 := (~ #69 #69)
-#245 := [refl]: #244
-#247 := [nnf-pos #245]: #246
-#156 := [asserted]: #70
-#248 := [mp~ #156 #247]: #70
-#370 := [mp #248 #369]: #365
-#648 := (not #365)
+#48 := (f3 #41 #29)
+#49 := (f9 #28 #48 #30)
+#354 := (pattern #49)
+#47 := (f13 #41 #31)
+#353 := (pattern #47)
+#50 := (= #47 #49)
+#355 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) (:pat #353 #354) #50)
+#51 := (forall (vars (?v0 S2) (?v1 Int) (?v2 Int) (?v3 S4)) #50)
+#358 := (iff #51 #355)
+#356 := (iff #50 #50)
+#357 := [refl]: #356
+#359 := [quant-intro #357]: #358
+#241 := (~ #51 #51)
+#239 := (~ #50 #50)
+#240 := [refl]: #239
+#242 := [nnf-pos #240]: #241
+#156 := [asserted]: #51
+#243 := [mp~ #156 #242]: #51
+#360 := [mp #243 #359]: #355
+#648 := (not #355)
 #649 := (or #648 #645)
 #644 := (= #643 #639)
 #650 := (or #648 #644)
@@ -54456,13 +54851,13 @@
 #647 := [rewrite]: #646
 #653 := [monotonicity #647]: #652
 #656 := [trans #653 #655]: #652
-#651 := [quant-inst #8 #546 #12 #507]: #650
+#651 := [quant-inst #8 #546 #12 #510]: #650
 #657 := [mp #651 #656]: #649
-#749 := [unit-resolution #657 #370]: #645
+#749 := [unit-resolution #657 #360]: #645
 #792 := (= f22 #639)
 #786 := (= #400 #639)
 #784 := (= #639 #400)
-#740 := (= #638 4::Int)
+#738 := (= #638 4::Int)
 #9 := (:var 0 Int)
 #10 := (f3 f4 #9)
 #11 := (pattern #10)
@@ -54475,9 +54870,9 @@
 #115 := [asserted]: #14
 #208 := [mp~ #115 #207]: #14
 #743 := (not #14)
-#744 := (or #743 #740)
+#744 := (or #743 #738)
 #745 := [quant-inst #12]: #744
-#747 := [unit-resolution #745 #208]: #740
+#747 := [unit-resolution #745 #208]: #738
 #637 := (= #546 3::Int)
 #16 := (f3 f5 #9)
 #17 := (pattern #16)
@@ -54498,70 +54893,70 @@
 #790 := (= f22 #400)
 #779 := (= #88 #400)
 #777 := (= #87 #399)
-#509 := (= f1 #398)
-decl f14 :: (-> S6 S1)
-#449 := (f14 #88)
-#542 := (f6 f7 #449)
-#774 := (= #542 #398)
-#770 := (= #398 #542)
-#453 := (= f1 #449)
-#342 := (pattern #34)
-#146 := (= f1 #31)
-#51 := (f14 #34)
-#142 := (= f1 #51)
-#149 := (iff #142 #146)
-#349 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) (:pat #342) #149)
-#152 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #149)
-#352 := (iff #152 #349)
-#350 := (iff #149 #149)
-#351 := [refl]: #350
-#353 := [quant-intro #351]: #352
-#236 := (~ #152 #152)
-#234 := (~ #149 #149)
-#235 := [refl]: #234
-#237 := [nnf-pos #235]: #236
-#53 := (= #31 f1)
-#52 := (= #51 f1)
-#54 := (iff #52 #53)
-#55 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S5)) #54)
-#153 := (iff #55 #152)
-#150 := (iff #54 #149)
-#147 := (iff #53 #146)
-#148 := [rewrite]: #147
-#144 := (iff #52 #142)
-#145 := [rewrite]: #144
-#151 := [monotonicity #145 #148]: #150
-#154 := [quant-intro #151]: #153
-#141 := [asserted]: #55
-#157 := [mp #141 #154]: #152
-#238 := [mp~ #157 #237]: #152
-#354 := [mp #238 #353]: #349
-#464 := (not #349)
-#465 := (or #464 #453)
-#448 := (= f1 f1)
-#454 := (iff #453 #448)
-#466 := (or #464 #454)
-#468 := (iff #466 #465)
-#470 := (iff #465 #465)
-#471 := [rewrite]: #470
-#462 := (iff #454 #453)
-#1 := true
-#457 := (iff #453 true)
-#460 := (iff #457 #453)
-#461 := [rewrite]: #460
-#458 := (iff #454 #457)
-#455 := (iff #448 true)
-#456 := [rewrite]: #455
-#459 := [monotonicity #456]: #458
-#463 := [trans #459 #461]: #462
-#469 := [monotonicity #463]: #468
-#472 := [trans #469 #471]: #468
-#467 := [quant-inst #18 #12 #4 #86]: #466
-#473 := [mp #467 #472]: #465
-#769 := [unit-resolution #473 #354]: #453
+#479 := (= f1 #398)
+decl f16 :: (-> S5 S1)
+#417 := (f16 #88)
+#544 := (f6 f7 #417)
+#774 := (= #544 #398)
+#770 := (= #398 #544)
+#418 := (= f1 #417)
+#369 := (pattern #62)
+#163 := (= f1 #59)
+#63 := (f16 #62)
+#160 := (= f1 #63)
+#166 := (iff #160 #163)
+#370 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) (:pat #369) #166)
+#169 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #166)
+#373 := (iff #169 #370)
+#371 := (iff #166 #166)
+#372 := [refl]: #371
+#374 := [quant-intro #372]: #373
+#251 := (~ #169 #169)
+#249 := (~ #166 #166)
+#250 := [refl]: #249
+#252 := [nnf-pos #250]: #251
+#65 := (= #59 f1)
+#64 := (= #63 f1)
+#66 := (iff #64 #65)
+#67 := (forall (vars (?v0 Int) (?v1 Int) (?v2 S1) (?v3 S7)) #66)
+#170 := (iff #67 #169)
+#167 := (iff #66 #166)
+#164 := (iff #65 #163)
+#165 := [rewrite]: #164
+#161 := (iff #64 #160)
+#162 := [rewrite]: #161
+#168 := [monotonicity #162 #165]: #167
+#171 := [quant-intro #168]: #170
+#159 := [asserted]: #67
+#174 := [mp #159 #171]: #169
+#253 := [mp~ #174 #252]: #169
+#375 := [mp #253 #374]: #370
+#429 := (not #370)
+#430 := (or #429 #418)
+#416 := (= f1 f1)
+#419 := (iff #418 #416)
+#431 := (or #429 #419)
+#433 := (iff #431 #430)
+#435 := (iff #430 #430)
+#436 := [rewrite]: #435
+#427 := (iff #419 #418)
+#1 := true
+#422 := (iff #418 true)
+#425 := (iff #422 #418)
+#426 := [rewrite]: #425
+#423 := (iff #419 #422)
+#420 := (iff #416 true)
+#421 := [rewrite]: #420
+#424 := [monotonicity #421]: #423
+#428 := [trans #424 #426]: #427
+#434 := [monotonicity #428]: #433
+#437 := [trans #434 #436]: #433
+#432 := [quant-inst #18 #12 #4 #86]: #431
+#438 := [mp #432 #437]: #430
+#769 := [unit-resolution #438 #375]: #418
 #771 := [monotonicity #769]: #770
 #775 := [symm #771]: #774
-#543 := (= f1 #542)
+#545 := (= f1 #544)
 #22 := (:var 0 S1)
 #23 := (f6 f7 #22)
 #24 := (pattern #23)
@@ -54589,17 +54984,17 @@
 #133 := [mp #117 #130]: #128
 #218 := [mp~ #133 #217]: #128
 #548 := (not #128)
-#549 := (or #548 #543)
-#550 := [quant-inst #449]: #549
-#768 := [unit-resolution #550 #218]: #543
-#776 := [trans #768 #775]: #509
+#549 := (or #548 #545)
+#550 := [quant-inst #417]: #549
+#768 := [unit-resolution #550 #218]: #545
+#776 := [trans #768 #775]: #479
 #778 := [monotonicity #776]: #777
 #780 := [monotonicity #778]: #779
 #791 := [trans #199 #780]: #790
 #793 := [trans #791 #787]: #792
 #795 := [trans #793 #749]: #794
-#796 := [trans #795 #789]: #183
-#200 := (not #183)
+#796 := [trans #795 #789]: #184
+#200 := (not #184)
 #202 := [not-or-elim #201]: #200
 [unit-resolution #202 #796]: false
 unsat
@@ -55633,109 +56028,109 @@
 #157 := [mp #147 #154]: #152
 [unit-resolution #157 #592]: false
 unsat
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+unsat
+1bb4f3696612274f0ada059e663e5df3e8c1753c 1 0
+unsat
+623fc7125ec95a195982348a426ec1bce1689250 1 0
+unsat
+99a4b89024a5ade20a17839e46c3c800a839dc73 1 0
+unsat
+25d7cafeec4877bd332c7a84d48d1e1bba149730 1 0
+unsat
+46cecad9c27ddd660a32c43da02fbc077e4d2653 1 0
+unsat
+9985536f3adcfa82b82611a2e3c65c48234903b7 1 0
+unsat
+650e66124ceb469142418bdf9b727f4eb46000d3 1 0
+unsat
+ad845af29980d8f1b8f9106555beea4a0787e50b 1 0
+unsat
+1226a39ae26fb124fa2784c01feeda2fa8b7f164 1 0
+unsat
+aeed0548e98a49111c97d9c505f2ddcc25a8f0a0 1 0
+unsat
+6937351f88cbcd4ce38d156d36ca3f3b7400b010 1 0
+unsat
+660ffa7d21617f3d9be770c0a37b4fe52fc41f63 1 0
+unsat
+1ed7927ce715bf3dc565062fba9fbc3b84987ef9 1 0
+unsat
+6532a71dc82cca7c8160ba5c854a2f0362cd0410 1 0
+unsat
+990af511d3a0b46205abbd2ddd25c459f6e66c5a 1 0
+unsat
+cf85ae43503909529635475e22a3bb7409c56a5c 1 0
+unsat
+fb00d7a0af114cd80f8efb9453ee0baf42d58298 1 0
+unsat
+ea112adb690b675025a205ff95598c0e1bacd1b3 1 0
+unsat
+cde5d9f95f561892bc84c1a943338cf0d427920f 1 0
+unsat
+848677eef79eb7cb4fb3573c0d5c5fca34811251 1 0
+unsat
+0e0faa00af41d5f14b5cb0a291dc7001b6276b81 1 0
+unsat
+3ec23529e810aeac05c8d7c95856e437cc15481a 1 0
+unsat
+991d721d9af19456ad333e832e6e1ff105598a2a 1 0
+unsat
+c6d7a69a2fdeee85db63627aecd087b63d4f1c1c 1 0
+unsat
+f67f5ba5a69d007092f7dd70dc2dbb1215926e11 1 0
+unsat
+1839415a04580c458d9a54c09162d0c394cad86c 1 0
+unsat
+595084d6acf7cb9e727b2d71c11dcd5adfd678ca 1 0
+unsat
+ce8e551a982c6290b1be8781429cefd4f9165293 1 0
+unsat
+c271fe52291540adaf545c617359ed457de173b1 1 0
+unsat
+d040cce0ec356b71ba4556c265407ab2f545e54c 1 0
+unsat
+674646d69af329d3589eeca7a6f731cbd7aabfb5 1 0
+unsat
+789139e6d5722962adae903c7c6f741a024ed141 1 0
+unsat
[phone]c654e6dbfb3153a9601c28877a3114 1 0
+unsat
+16408e8543328af45ac16df15c0d63f3fc509499 1 0
+unsat
+0cbacef48453639efbd9117592087fa963979a9a 1 0
+unsat
+4f76e31263dc24919943a2ac6835f5ab5cbb885d 1 0
+unsat
+a76f56105de0da9e78f9f1ecf4de50bfa08478b8 1 0
+unsat
+fb3320cb741f8a5fec9b3b50a2caeab3ab35af68 1 0
+unsat
+4236ba058a6f6c1bacb0db47f2f621769329ff77 1 0
+unsat
+fe15efedfaad3ad3884dcd453f022326a429c99f 1 0
+unsat
+0adc18b99c93cda1aa22c7bd01d4133c76309534 1 0
 unsat
 49462927b92e2fe852e19ddabb722de885a6169e 1 0
 unsat
@@ -55747,7 +56142,7 @@
 unsat
 67cb8659b90bbf301d02aab19df117412048c996 1 0
 unsat
-f647fab40fc301b72eb10ef98660c1294aab2896 91 0
+ec3ebf7405b892e3e8aa681f42fd689c0fcd9783 50 0
 #2 := false
 decl f3 :: (-> S2 S3 S4 S3 S4)
 decl f6 :: S3
@@ -55767,79 +56162,38 @@
 #77 := [monotonicity #74]: #76
 #70 := [asserted]: #29
 #80 := [mp #70 #77]: #75
-#11 := (:var 0 S3)
-#10 := (:var 1 S4)
-#9 := (:var 2 S3)
-#8 := (:var 3 S2)
-#12 := (f3 #8 #9 #10 #11)
-#574 := (pattern #12)
-decl f4 :: (-> S2 S3 S4)
-#14 := (f4 #8 #11)
-#95 := (= #12 #14)
-#94 := (= #10 #12)
-#50 := (= #9 #11)
-#84 := (ite #50 #94 #95)
-#575 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #574) #84)
-#87 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #84)
-#578 := (iff #87 #575)
-#576 := (iff #84 #84)
+#9 := (:var 1 S3)
+#10 := (:var 0 S4)
+#8 := (:var 2 S2)
+#11 := (f3 #8 #9 #10 #9)
+#574 := (pattern #11)
+#50 := (= #10 #11)
+#575 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #574) #50)
+#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #50)
+#578 := (iff #53 #575)
+#576 := (iff #50 #50)
 #577 := [refl]: #576
 #579 := [quant-intro #577]: #578
-#53 := (ite #50 #10 #14)
-#56 := (= #12 #53)
-#59 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #56)
-#96 := (iff #59 #87)
-#85 := (iff #56 #84)
-#86 := [rewrite]: #85
-#97 := [quant-intro #86]: #96
-#90 := (~ #59 #59)
-#88 := (~ #56 #56)
+#90 := (~ #53 #53)
+#88 := (~ #50 #50)
 #89 := [refl]: #88
 #91 := [nnf-pos #89]: #90
-#13 := (= #11 #9)
-#15 := (ite #13 #10 #14)
-#16 := (= #12 #15)
-#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #16)
-#60 := (iff #17 #59)
-#57 := (iff #16 #56)
-#54 := (= #15 #53)
-#51 := (iff #13 #50)
+#12 := (= #11 #10)
+#13 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #12)
+#54 := (iff #13 #53)
+#51 := (iff #12 #50)
 #52 := [rewrite]: #51
-#55 := [monotonicity #52]: #54
-#58 := [monotonicity #55]: #57
-#61 := [quant-intro #58]: #60
-#49 := [asserted]: #17
-#64 := [mp #49 #61]: #59
-#79 := [mp~ #64 #91]: #59
-#98 := [mp #79 #97]: #87
-#580 := [mp #98 #579]: #575
-#229 := (not #575)
-#566 := (or #229 #71)
-#156 := (f4 f5 f6)
-#243 := (= #27 #156)
-#157 := (= f6 f6)
-#244 := (ite #157 #71 #243)
-#568 := (or #229 #244)
-#355 := (iff #568 #566)
-#234 := (iff #566 #566)
-#235 := [rewrite]: #234
-#246 := (iff #244 #71)
-#1 := true
-#236 := (ite true #71 #243)
-#176 := (iff #236 #71)
-#249 := [rewrite]: #176
-#247 := (iff #244 #236)
-#158 := (iff #157 true)
-#245 := [rewrite]: #158
-#248 := [monotonicity #245]: #247
-#250 := [trans #248 #249]: #246
-#562 := [monotonicity #250]: #355
-#569 := [trans #562 #235]: #355
-#223 := [quant-inst #24 #25 #26 #25]: #568
-#570 := [mp #223 #569]: #566
-[unit-resolution #570 #580 #80]: false
-unsat
-af1534012c3020b480c853afaac6d90a71a2c734 85 0
+#55 := [quant-intro #52]: #54
+#49 := [asserted]: #13
+#58 := [mp #49 #55]: #53
+#79 := [mp~ #58 #91]: #53
+#580 := [mp #79 #579]: #575
+#157 := (not #575)
+#244 := (or #157 #71)
+#158 := [quant-inst #24 #25 #26]: #244
+[unit-resolution #158 #580 #80]: false
+unsat
+563b862cbf86c0992768ce09950fbd8d9a1a7821 85 0
 #2 := false
 decl f4 :: (-> S2 S3 S4)
 decl f6 :: S3
@@ -55875,57 +56229,57 @@
 #257 := (or #255 #26 #32)
 #254 := [def-axiom]: #257
 #165 := [unit-resolution #254 #83 #86]: #255
-#11 := (:var 0 S3)
-#10 := (:var 1 S4)
-#9 := (:var 2 S3)
-#8 := (:var 3 S2)
-#12 := (f3 #8 #9 #10 #11)
-#582 := (pattern #12)
-#14 := (f4 #8 #11)
-#105 := (= #12 #14)
-#104 := (= #10 #12)
-#55 := (= #9 #11)
-#92 := (ite #55 #104 #105)
-#583 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #582) #92)
+#17 := (:var 0 S3)
+#16 := (:var 1 S4)
+#15 := (:var 2 S3)
+#14 := (:var 3 S2)
+#18 := (f3 #14 #15 #16 #17)
+#589 := (pattern #18)
+#20 := (f4 #14 #17)
+#105 := (= #18 #20)
+#104 := (= #16 #18)
+#62 := (= #15 #17)
+#92 := (ite #62 #104 #105)
+#590 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #589) #92)
 #97 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #92)
-#586 := (iff #97 #583)
-#584 := (iff #92 #92)
-#585 := [refl]: #584
-#587 := [quant-intro #585]: #586
-#58 := (ite #55 #10 #14)
-#61 := (= #12 #58)
-#64 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #61)
-#94 := (iff #64 #97)
-#93 := (iff #61 #92)
+#593 := (iff #97 #590)
+#591 := (iff #92 #92)
+#592 := [refl]: #591
+#594 := [quant-intro #592]: #593
+#66 := (ite #62 #16 #20)
+#69 := (= #18 #66)
+#72 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #69)
+#94 := (iff #72 #97)
+#93 := (iff #69 #92)
 #96 := [rewrite]: #93
 #95 := [quant-intro #96]: #94
-#100 := (~ #64 #64)
-#98 := (~ #61 #61)
-#99 := [refl]: #98
-#101 := [nnf-pos #99]: #100
-#13 := (= #11 #9)
-#15 := (ite #13 #10 #14)
-#16 := (= #12 #15)
-#17 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #16)
-#65 := (iff #17 #64)
-#62 := (iff #16 #61)
-#59 := (= #15 #58)
-#56 := (iff #13 #55)
-#57 := [rewrite]: #56
-#60 := [monotonicity #57]: #59
-#63 := [monotonicity #60]: #62
-#66 := [quant-intro #63]: #65
-#54 := [asserted]: #17
-#69 := [mp #54 #66]: #64
-#88 := [mp~ #69 #101]: #64
-#106 := [mp #88 #95]: #97
-#588 := [mp #106 #587]: #583
-#166 := (not #583)
+#90 := (~ #72 #72)
+#89 := (~ #69 #69)
+#102 := [refl]: #89
+#91 := [nnf-pos #102]: #90
+#19 := (= #17 #15)
+#21 := (ite #19 #16 #20)
+#22 := (= #18 #21)
+#23 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #22)
+#73 := (iff #23 #72)
+#70 := (iff #22 #69)
+#67 := (= #21 #66)
+#64 := (iff #19 #62)
+#65 := [rewrite]: #64
+#68 := [monotonicity #65]: #67
+#71 := [monotonicity #68]: #70
+#74 := [quant-intro #71]: #73
+#61 := [asserted]: #23
+#77 := [mp #61 #74]: #72
+#103 := [mp~ #77 #91]: #72
+#106 := [mp #103 #95]: #97
+#595 := [mp #106 #594]: #590
+#166 := (not #590)
 #253 := (or #166 #251)
 #244 := [quant-inst #28 #24 #29 #25]: #253
-[unit-resolution #244 #588 #165]: false
-unsat
-57b1778e367cf6f6921505d440f3fc4fb8332587 158 0
+[unit-resolution #244 #595 #165]: false
+unsat
+8826b7841dfa8381482acc731f64e6e3046897f2 158 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f5 :: S3
@@ -55944,117 +56298,117 @@
 #35 := (f3 #34 f5)
 #80 := (= f8 #35)
 #176 := (f3 #32 f5)
-#263 := (= #35 #176)
-#580 := (iff #263 #80)
-#217 := (iff #80 #263)
+#267 := (= #35 #176)
+#580 := (iff #267 #80)
+#217 := (iff #80 #267)
 #570 := (= #176 #35)
-#577 := (iff #570 #263)
+#577 := (iff #570 #267)
 #579 := [commutativity]: #577
 #576 := (iff #80 #570)
-#242 := (= f8 #176)
-#21 := (:var 0 S4)
-#20 := (:var 1 S3)
-#19 := (:var 2 S2)
-#22 := (f4 #19 #20 #21)
-#601 := (pattern #22)
-#23 := (f3 #22 #20)
-#72 := (= #21 #23)
-#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #601) #72)
-#76 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #72)
-#602 := (iff #76 #603)
-#605 := (iff #603 #603)
-#606 := [rewrite]: #605
-#604 := [rewrite]: #602
-#607 := [trans #604 #606]: #602
-#102 := (~ #76 #76)
-#101 := (~ #72 #72)
-#114 := [refl]: #101
-#103 := [nnf-pos #114]: #102
-#24 := (= #23 #21)
-#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
-#77 := (iff #25 #76)
-#74 := (iff #24 #72)
-#75 := [rewrite]: #74
-#78 := [quant-intro #75]: #77
-#71 := [asserted]: #25
-#81 := [mp #71 #78]: #76
-#115 := [mp~ #81 #103]: #76
-#608 := [mp #115 #607]: #603
-#569 := (not #603)
-#230 := (or #569 #242)
-#231 := [quant-inst #30 #26 #31]: #230
-#575 := [unit-resolution #231 #608]: #242
+#263 := (= f8 #176)
+#10 := (:var 0 S4)
+#9 := (:var 1 S3)
+#8 := (:var 2 S2)
+#11 := (f4 #8 #9 #10)
+#594 := (pattern #11)
+#12 := (f3 #11 #9)
+#59 := (= #10 #12)
+#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #594) #59)
+#62 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #59)
+#595 := (iff #62 #596)
+#598 := (iff #596 #596)
+#599 := [rewrite]: #598
+#597 := [rewrite]: #595
+#600 := [trans #597 #599]: #595
+#112 := (~ #62 #62)
+#110 := (~ #59 #59)
+#111 := [refl]: #110
+#113 := [nnf-pos #111]: #112
+#13 := (= #12 #10)
+#14 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #13)
+#63 := (iff #14 #62)
+#60 := (iff #13 #59)
+#61 := [rewrite]: #60
+#64 := [quant-intro #61]: #63
+#58 := [asserted]: #14
+#67 := [mp #58 #64]: #62
+#100 := [mp~ #67 #113]: #62
+#601 := [mp #100 #600]: #596
+#178 := (not #596)
+#265 := (or #178 #263)
+#256 := [quant-inst #30 #26 #31]: #265
+#575 := [unit-resolution #256 #601]: #263
 #212 := [monotonicity #575]: #576
 #218 := [trans #212 #579]: #217
 #578 := [symm #218]: #580
-#177 := (= f9 #35)
+#268 := (= f9 #35)
 #28 := (= f5 f6)
-#267 := (ite #28 #177 #263)
-#12 := (:var 0 S3)
-#10 := (:var 1 S4)
-#9 := (:var 2 S3)
-#8 := (:var 3 S2)
-#11 := (f4 #8 #9 #10)
-#13 := (f3 #11 #12)
-#594 := (pattern #13)
-#15 := (f3 #8 #12)
-#117 := (= #13 #15)
-#116 := (= #10 #13)
-#59 := (= #9 #12)
-#104 := (ite #59 #116 #117)
-#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104)
+#588 := (ite #28 #268 #267)
+#19 := (:var 0 S3)
+#17 := (:var 1 S4)
+#16 := (:var 2 S3)
+#15 := (:var 3 S2)
+#18 := (f4 #15 #16 #17)
+#20 := (f3 #18 #19)
+#602 := (pattern #20)
+#22 := (f3 #15 #19)
+#117 := (= #20 #22)
+#116 := (= #17 #20)
+#66 := (= #16 #19)
+#104 := (ite #66 #116 #117)
+#603 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #602) #104)
 #109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104)
-#598 := (iff #109 #595)
-#596 := (iff #104 #104)
-#597 := [refl]: #596
-#599 := [quant-intro #597]: #598
-#62 := (ite #59 #10 #15)
-#65 := (= #13 #62)
-#68 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #65)
-#106 := (iff #68 #109)
-#105 := (iff #65 #104)
+#606 := (iff #109 #603)
+#604 := (iff #104 #104)
+#605 := [refl]: #604
+#607 := [quant-intro #605]: #606
+#70 := (ite #66 #17 #22)
+#73 := (= #20 #70)
+#76 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #73)
+#106 := (iff #76 #109)
+#105 := (iff #73 #104)
 #108 := [rewrite]: #105
 #107 := [quant-intro #108]: #106
-#112 := (~ #68 #68)
-#110 := (~ #65 #65)
-#111 := [refl]: #110
-#113 := [nnf-pos #111]: #112
-#14 := (= #12 #9)
-#16 := (ite #14 #10 #15)
-#17 := (= #13 #16)
-#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
-#69 := (iff #18 #68)
-#66 := (iff #17 #65)
-#63 := (= #16 #62)
-#60 := (iff #14 #59)
-#61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#70 := [quant-intro #67]: #69
-#58 := [asserted]: #18
-#73 := [mp #58 #70]: #68
-#100 := [mp~ #73 #113]: #68
-#118 := [mp #100 #107]: #109
-#600 := [mp #118 #599]: #595
-#269 := (not #595)
-#266 := (or #269 #267)
-#264 := (= f6 f5)
-#178 := (ite #264 #177 #263)
-#270 := (or #269 #178)
-#586 := (iff #270 #266)
-#243 := (iff #266 #266)
-#375 := [rewrite]: #243
-#268 := (iff #178 #267)
-#265 := (iff #264 #28)
-#256 := [rewrite]: #265
-#196 := [monotonicity #256]: #268
-#588 := [monotonicity #196]: #586
-#582 := [trans #588 #375]: #586
-#249 := [quant-inst #32 #27 #33 #26]: #270
-#254 := [mp #249 #582]: #266
-#232 := [unit-resolution #254 #600]: #267
-#255 := (not #267)
-#233 := (or #255 #263)
+#102 := (~ #76 #76)
+#101 := (~ #73 #73)
+#114 := [refl]: #101
+#103 := [nnf-pos #114]: #102
+#21 := (= #19 #16)
+#23 := (ite #21 #17 #22)
+#24 := (= #20 #23)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #24)
+#77 := (iff #25 #76)
+#74 := (iff #24 #73)
+#71 := (= #23 #70)
+#68 := (iff #21 #66)
+#69 := [rewrite]: #68
+#72 := [monotonicity #69]: #71
+#75 := [monotonicity #72]: #74
+#78 := [quant-intro #75]: #77
+#65 := [asserted]: #25
+#81 := [mp #65 #78]: #76
+#115 := [mp~ #81 #103]: #76
+#118 := [mp #115 #107]: #109
+#608 := [mp #118 #607]: #603
+#582 := (not #603)
+#254 := (or #582 #588)
+#266 := (= f6 f5)
+#270 := (ite #266 #268 #267)
+#255 := (or #582 #270)
+#590 := (iff #255 #254)
+#592 := (iff #254 #254)
+#587 := [rewrite]: #592
+#243 := (iff #270 #588)
+#249 := (iff #266 #28)
+#586 := [rewrite]: #249
+#375 := [monotonicity #586]: #243
+#591 := [monotonicity #375]: #590
+#593 := [trans #591 #587]: #590
+#589 := [quant-inst #32 #27 #33 #26]: #255
+#583 := [mp #589 #593]: #254
+#571 := [unit-resolution #583 #608]: #588
+#241 := (not #588)
+#572 := (or #241 #267)
 #29 := (not #28)
 #87 := (or #28 #80)
 #92 := (not #87)
@@ -56075,16 +56429,16 @@
 #79 := [asserted]: #38
 #97 := [mp #79 #94]: #92
 #95 := [not-or-elim #97]: #29
-#591 := (or #255 #28 #263)
-#592 := [def-axiom]: #591
-#573 := [unit-resolution #592 #95]: #233
-#574 := [unit-resolution #573 #232]: #263
+#242 := (or #241 #28 #267)
+#585 := [def-axiom]: #242
+#573 := [unit-resolution #585 #95]: #572
+#574 := [unit-resolution #573 #571]: #267
 #581 := [mp #574 #578]: #80
 #96 := (not #80)
 #98 := [not-or-elim #97]: #96
 [unit-resolution #98 #581]: false
 unsat
-c5924477e9186eb5df53c29cfb676c83a60e811c 111 0
+37f65501bb80435fad7d7311ecb517c648328aa9 72 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f6 :: S3
@@ -56124,79 +56478,40 @@
 #79 := [asserted]: #38
 #97 := [mp #79 #94]: #92
 #98 := [not-or-elim #97]: #96
-#12 := (:var 0 S3)
-#10 := (:var 1 S4)
-#9 := (:var 2 S3)
-#8 := (:var 3 S2)
+#10 := (:var 0 S4)
+#9 := (:var 1 S3)
+#8 := (:var 2 S2)
 #11 := (f4 #8 #9 #10)
-#13 := (f3 #11 #12)
-#594 := (pattern #13)
-#15 := (f3 #8 #12)
-#117 := (= #13 #15)
-#116 := (= #10 #13)
-#59 := (= #9 #12)
-#104 := (ite #59 #116 #117)
-#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104)
-#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104)
-#598 := (iff #109 #595)
-#596 := (iff #104 #104)
-#597 := [refl]: #596
-#599 := [quant-intro #597]: #598
-#62 := (ite #59 #10 #15)
-#65 := (= #13 #62)
-#68 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #65)
-#106 := (iff #68 #109)
-#105 := (iff #65 #104)
-#108 := [rewrite]: #105
-#107 := [quant-intro #108]: #106
-#112 := (~ #68 #68)
-#110 := (~ #65 #65)
+#594 := (pattern #11)
+#12 := (f3 #11 #9)
+#59 := (= #10 #12)
+#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #594) #59)
+#62 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #59)
+#595 := (iff #62 #596)
+#598 := (iff #596 #596)
+#599 := [rewrite]: #598
+#597 := [rewrite]: #595
+#600 := [trans #597 #599]: #595
+#112 := (~ #62 #62)
+#110 := (~ #59 #59)
 #111 := [refl]: #110
 #113 := [nnf-pos #111]: #112
-#14 := (= #12 #9)
-#16 := (ite #14 #10 #15)
-#17 := (= #13 #16)
-#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
-#69 := (iff #18 #68)
-#66 := (iff #17 #65)
-#63 := (= #16 #62)
-#60 := (iff #14 #59)
+#13 := (= #12 #10)
+#14 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #13)
+#63 := (iff #14 #62)
+#60 := (iff #13 #59)
 #61 := [rewrite]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#70 := [quant-intro #67]: #69
-#58 := [asserted]: #18
-#73 := [mp #58 #70]: #68
-#100 := [mp~ #73 #113]: #68
-#118 := [mp #100 #107]: #109
-#600 := [mp #118 #599]: #595
-#249 := (not #595)
-#586 := (or #249 #80)
-#176 := (f3 #32 f6)
-#263 := (= #35 #176)
-#177 := (= f6 f6)
-#264 := (ite #177 #80 #263)
-#588 := (or #249 #264)
-#375 := (iff #588 #586)
-#254 := (iff #586 #586)
-#255 := [rewrite]: #254
-#266 := (iff #264 #80)
-#1 := true
-#256 := (ite true #80 #263)
-#196 := (iff #256 #80)
-#269 := [rewrite]: #196
-#267 := (iff #264 #256)
-#178 := (iff #177 true)
-#265 := [rewrite]: #178
-#268 := [monotonicity #265]: #267
-#270 := [trans #268 #269]: #266
-#582 := [monotonicity #270]: #375
-#589 := [trans #582 #255]: #375
-#243 := [quant-inst #32 #27 #33 #27]: #588
-#590 := [mp #243 #589]: #586
-[unit-resolution #590 #600 #98]: false
-unsat
-7e28540fd0d4f5814439be9d6e362d0c1457f76e 123 0
+#64 := [quant-intro #61]: #63
+#58 := [asserted]: #14
+#67 := [mp #58 #64]: #62
+#100 := [mp~ #67 #113]: #62
+#601 := [mp #100 #600]: #596
+#178 := (not #596)
+#267 := (or #178 #80)
+#268 := [quant-inst #32 #27 #33]: #267
+[unit-resolution #268 #601 #98]: false
+unsat
+3acfd8a90a5c7edc1c996502faf6eb147578b0cd 81 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f5 :: S3
@@ -56214,9 +56529,9 @@
 #33 := (f4 #31 f6 f9)
 #34 := (f3 #33 f5)
 #79 := (= f9 #34)
-#263 := (f3 #33 f6)
-#571 := (= #263 #34)
-#585 := (= #34 #263)
+#264 := (f3 #33 f6)
+#231 := (= #264 #34)
+#569 := (= #34 #264)
 #28 := (= f5 f6)
 #86 := (not #28)
 #87 := (or #86 #79)
@@ -56238,89 +56553,47 @@
 #78 := [asserted]: #37
 #97 := [mp #78 #94]: #92
 #95 := [not-or-elim #97]: #28
-#233 := [monotonicity #95]: #585
-#572 := [symm #233]: #571
-#264 := (= f9 #263)
-#12 := (:var 0 S3)
-#10 := (:var 1 S4)
-#9 := (:var 2 S3)
-#8 := (:var 3 S2)
+#230 := [monotonicity #95]: #569
+#232 := [symm #230]: #231
+#178 := (= f9 #264)
+#10 := (:var 0 S4)
+#9 := (:var 1 S3)
+#8 := (:var 2 S2)
 #11 := (f4 #8 #9 #10)
-#13 := (f3 #11 #12)
-#594 := (pattern #13)
-#15 := (f3 #8 #12)
-#117 := (= #13 #15)
-#116 := (= #10 #13)
-#58 := (= #9 #12)
-#104 := (ite #58 #116 #117)
-#595 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #594) #104)
-#109 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #104)
-#598 := (iff #109 #595)
-#596 := (iff #104 #104)
-#597 := [refl]: #596
-#599 := [quant-intro #597]: #598
-#61 := (ite #58 #10 #15)
-#64 := (= #13 #61)
-#67 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #64)
-#106 := (iff #67 #109)
-#105 := (iff #64 #104)
-#108 := [rewrite]: #105
-#107 := [quant-intro #108]: #106
-#112 := (~ #67 #67)
-#110 := (~ #64 #64)
+#594 := (pattern #11)
+#12 := (f3 #11 #9)
+#58 := (= #10 #12)
+#596 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #594) #58)
+#61 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #58)
+#595 := (iff #61 #596)
+#598 := (iff #596 #596)
+#599 := [rewrite]: #598
+#597 := [rewrite]: #595
+#600 := [trans #597 #599]: #595
+#112 := (~ #61 #61)
+#110 := (~ #58 #58)
 #111 := [refl]: #110
 #113 := [nnf-pos #111]: #112
-#14 := (= #12 #9)
-#16 := (ite #14 #10 #15)
-#17 := (= #13 #16)
-#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
-#68 := (iff #18 #67)
-#65 := (iff #17 #64)
-#62 := (= #16 #61)
-#59 := (iff #14 #58)
+#13 := (= #12 #10)
+#14 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #13)
+#62 := (iff #14 #61)
+#59 := (iff #13 #58)
 #60 := [rewrite]: #59
-#63 := [monotonicity #60]: #62
-#66 := [monotonicity #63]: #65
-#69 := [quant-intro #66]: #68
-#57 := [asserted]: #18
-#72 := [mp #57 #69]: #67
-#100 := [mp~ #72 #113]: #67
-#118 := [mp #100 #107]: #109
-#600 := [mp #118 #599]: #595
-#582 := (not #595)
-#254 := (or #582 #264)
-#176 := (f3 #31 f6)
-#177 := (= #263 #176)
-#178 := (= f6 f6)
-#265 := (ite #178 #264 #177)
-#255 := (or #582 #265)
-#590 := (iff #255 #254)
-#592 := (iff #254 #254)
-#587 := [rewrite]: #592
-#243 := (iff #265 #264)
-#268 := (= #176 #263)
-#1 := true
-#266 := (ite true #264 #268)
-#586 := (iff #266 #264)
-#588 := [rewrite]: #586
-#270 := (iff #265 #266)
-#196 := (iff #177 #268)
-#269 := [rewrite]: #196
-#256 := (iff #178 true)
-#267 := [rewrite]: #256
-#249 := [monotonicity #267 #269]: #270
-#375 := [trans #249 #588]: #243
-#591 := [monotonicity #375]: #590
-#593 := [trans #591 #587]: #590
-#589 := [quant-inst #31 #27 #32 #27]: #255
-#583 := [mp #589 #593]: #254
-#242 := [unit-resolution #583 #600]: #264
-#573 := [trans #242 #572]: #79
+#63 := [quant-intro #60]: #62
+#57 := [asserted]: #14
+#66 := [mp #57 #63]: #61
+#100 := [mp~ #66 #113]: #61
+#601 := [mp #100 #600]: #596
+#265 := (not #596)
+#269 := (or #265 #178)
+#266 := [quant-inst #31 #27 #32]: #269
+#226 := [unit-resolution #266 #601]: #178
+#233 := [trans #226 #232]: #79
 #96 := (not #79)
 #98 := [not-or-elim #97]: #96
-[unit-resolution #98 #573]: false
-unsat
-6e80c9c78d8fedc6d33345078567183b7c70457d 190 0
+[unit-resolution #98 #233]: false
+unsat
+05ec36c56f52768389406748046bb67a1d15c59a 187 0
 #2 := false
 decl f3 :: (-> S2 S3 S4)
 decl f7 :: S3
@@ -56341,81 +56614,78 @@
 #34 := (f4 #32 f6 f10)
 #35 := (f3 #34 f7)
 #37 := (= #35 #36)
-#586 := (f3 #32 f5)
-#570 := (f4 f8 f5 #586)
-#206 := (f3 #570 f7)
-#211 := (= #206 #36)
-#562 := (= #36 #206)
-#572 := (= #206 #586)
+#249 := (f3 #32 f5)
+#563 := (f4 f8 f5 #249)
+#539 := (f3 #563 f7)
+#368 := (= #539 #36)
+#524 := (= #36 #539)
+#370 := (= #249 #539)
 #171 := (= f5 f7)
-#285 := (ite #171 #572 #562)
-#12 := (:var 0 S3)
-#10 := (:var 1 S4)
-#9 := (:var 2 S3)
-#8 := (:var 3 S2)
-#11 := (f4 #8 #9 #10)
-#13 := (f3 #11 #12)
-#588 := (pattern #13)
-#15 := (f3 #8 #12)
-#111 := (= #13 #15)
-#110 := (= #10 #13)
-#60 := (= #9 #12)
-#98 := (ite #60 #110 #111)
-#589 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #588) #98)
+#528 := (ite #171 #370 #524)
+#19 := (:var 0 S3)
+#17 := (:var 1 S4)
+#16 := (:var 2 S3)
+#15 := (:var 3 S2)
+#18 := (f4 #15 #16 #17)
+#20 := (f3 #18 #19)
+#596 := (pattern #20)
+#22 := (f3 #15 #19)
+#111 := (= #20 #22)
+#110 := (= #17 #20)
+#67 := (= #16 #19)
+#98 := (ite #67 #110 #111)
+#597 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) (:pat #596) #98)
 #103 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #98)
-#592 := (iff #103 #589)
-#590 := (iff #98 #98)
-#591 := [refl]: #590
-#593 := [quant-intro #591]: #592
-#63 := (ite #60 #10 #15)
-#66 := (= #13 #63)
-#69 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #66)
-#100 := (iff #69 #103)
-#99 := (iff #66 #98)
+#600 := (iff #103 #597)
+#598 := (iff #98 #98)
+#599 := [refl]: #598
+#601 := [quant-intro #599]: #600
+#71 := (ite #67 #17 #22)
+#74 := (= #20 #71)
+#77 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #74)
+#100 := (iff #77 #103)
+#99 := (iff #74 #98)
 #102 := [rewrite]: #99
 #101 := [quant-intro #102]: #100
-#106 := (~ #69 #69)
-#104 := (~ #66 #66)
-#105 := [refl]: #104
-#107 := [nnf-pos #105]: #106
-#14 := (= #12 #9)
-#16 := (ite #14 #10 #15)
-#17 := (= #13 #16)
-#18 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #17)
-#70 := (iff #18 #69)
-#67 := (iff #17 #66)
-#64 := (= #16 #63)
-#61 := (iff #14 #60)
-#62 := [rewrite]: #61
-#65 := [monotonicity #62]: #64
-#68 := [monotonicity #65]: #67
-#71 := [quant-intro #68]: #70
-#59 := [asserted]: #18
-#74 := [mp #59 #71]: #69
-#94 := [mp~ #74 #107]: #69
-#112 := [mp #94 #101]: #103
-#594 := [mp #112 #593]: #589
-#587 := (not #589)
-#287 := (or #587 #285)
-#212 := (= #586 #206)
-#574 := (ite #171 #212 #211)
-#178 := (or #587 #574)
-#558 := (iff #178 #287)
-#281 := (iff #287 #287)
-#555 := [rewrite]: #281
-#286 := (iff #574 #285)
-#268 := (iff #211 #562)
-#284 := [rewrite]: #268
-#575 := (iff #212 #572)
-#561 := [rewrite]: #575
-#272 := [monotonicity #561 #284]: #286
-#280 := [monotonicity #272]: #558
-#559 := [trans #280 #555]: #558
-#557 := [quant-inst #30 #26 #586 #28]: #178
-#556 := [mp #557 #559]: #287
-#516 := [unit-resolution #556 #594]: #285
-#560 := (not #285)
-#507 := (or #560 #562)
+#96 := (~ #77 #77)
+#95 := (~ #74 #74)
+#108 := [refl]: #95
+#97 := [nnf-pos #108]: #96
+#21 := (= #19 #16)
+#23 := (ite #21 #17 #22)
+#24 := (= #20 #23)
+#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4) (?v3 S3)) #24)
+#78 := (iff #25 #77)
+#75 := (iff #24 #74)
+#72 := (= #23 #71)
+#69 := (iff #21 #67)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#76 := [monotonicity #73]: #75
+#79 := [quant-intro #76]: #78
+#66 := [asserted]: #25
+#82 := [mp #66 #79]: #77
+#109 := [mp~ #82 #97]: #77
+#112 := [mp #109 #101]: #103
+#602 := [mp #112 #601]: #597
+#224 := (not #597)
+#411 := (or #224 #528)
+#371 := (ite #171 #370 #368)
+#412 := (or #224 #371)
+#372 := (iff #412 #411)
+#422 := (iff #411 #411)
+#517 := [rewrite]: #422
+#526 := (iff #371 #528)
+#525 := (iff #368 #524)
+#527 := [rewrite]: #525
+#529 := [monotonicity #527]: #526
+#520 := [monotonicity #529]: #372
+#518 := [trans #520 #517]: #372
+#413 := [quant-inst #30 #26 #249 #28]: #412
+#521 := [mp #413 #518]: #411
+#501 := [unit-resolution #521 #602]: #528
+#406 := (not #528)
+#514 := (or #406 #524)
 #258 := (not #171)
 #172 := (= f6 f7)
 #259 := (not #172)
@@ -56437,121 +56707,1391 @@
 #89 := [not-or-elim #91]: #29
 #237 := (or #81 #250)
 #369 := [def-axiom]: #237
-#505 := [unit-resolution #369 #89]: #250
+#503 := [unit-resolution #369 #89]: #250
 #261 := (not #250)
 #263 := (or #261 #258)
 #260 := [def-axiom]: #263
-#506 := [unit-resolution #260 #505]: #258
-#271 := (or #560 #171 #562)
-#273 := [def-axiom]: #271
-#508 := [unit-resolution #273 #506]: #507
-#502 := [unit-resolution #508 #516]: #562
-#486 := [symm #502]: #211
-#487 := (= #35 #206)
-#249 := (f3 #32 f7)
-#495 := (= #249 #206)
-#498 := (= #206 #249)
-#515 := (= #570 #32)
-#513 := (= #586 f9)
-#581 := (= f9 #586)
-#21 := (:var 0 S4)
-#20 := (:var 1 S3)
-#19 := (:var 2 S2)
-#22 := (f4 #19 #20 #21)
-#595 := (pattern #22)
-#23 := (f3 #22 #20)
-#73 := (= #21 #23)
-#597 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #595) #73)
-#77 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #73)
-#596 := (iff #77 #597)
-#599 := (iff #597 #597)
-#600 := [rewrite]: #599
-#598 := [rewrite]: #596
-#601 := [trans #598 #600]: #596
-#96 := (~ #77 #77)
-#95 := (~ #73 #73)
-#108 := [refl]: #95
-#97 := [nnf-pos #108]: #96
-#24 := (= #23 #21)
-#25 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #24)
-#78 := (iff #25 #77)
-#75 := (iff #24 #73)
-#76 := [rewrite]: #75
-#79 := [quant-intro #76]: #78
-#72 := [asserted]: #25
-#82 := [mp #72 #79]: #77
-#109 := [mp~ #82 #97]: #77
-#602 := [mp #109 #601]: #597
-#568 := (not #597)
-#569 := (or #568 #581)
-#564 := [quant-inst #30 #26 #31]: #569
-#503 := [unit-resolution #564 #602]: #581
-#514 := [symm #503]: #513
-#511 := [monotonicity #514]: #515
-#499 := [monotonicity #511]: #498
-#500 := [symm #499]: #495
-#583 := (= #35 #249)
-#584 := (= f10 #35)
-#585 := (ite #172 #584 #583)
-#577 := (or #587 #585)
-#235 := [quant-inst #32 #27 #33 #28]: #577
-#509 := [unit-resolution #235 #594]: #585
-#240 := (not #585)
-#494 := (or #240 #583)
+#513 := [unit-resolution #260 #503]: #258
+#424 := (or #406 #171 #524)
+#417 := [def-axiom]: #424
+#515 := [unit-resolution #417 #513]: #514
+#511 := [unit-resolution #515 #501]: #524
+#496 := [symm #511]: #368
+#497 := (= #35 #539)
+#577 := (f3 #32 f7)
+#493 := (= #577 #539)
+#502 := (= #539 #577)
+#512 := (= #563 #32)
+#523 := (= #249 f9)
+#583 := (= f9 #249)
+#10 := (:var 0 S4)
+#9 := (:var 1 S3)
+#8 := (:var 2 S2)
+#11 := (f4 #8 #9 #10)
+#588 := (pattern #11)
+#12 := (f3 #11 #9)
+#60 := (= #10 #12)
+#590 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) (:pat #588) #60)
+#63 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #60)
+#589 := (iff #63 #590)
+#592 := (iff #590 #590)
+#593 := [rewrite]: #592
+#591 := [rewrite]: #589
+#594 := [trans #591 #593]: #589
+#106 := (~ #63 #63)
+#104 := (~ #60 #60)
+#105 := [refl]: #104
+#107 := [nnf-pos #105]: #106
+#13 := (= #12 #10)
+#14 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S4)) #13)
+#64 := (iff #14 #63)
+#61 := (iff #13 #60)
+#62 := [rewrite]: #61
+#65 := [quant-intro #62]: #64
+#59 := [asserted]: #14
+#68 := [mp #59 #65]: #63
+#94 := [mp~ #68 #107]: #63
+#595 := [mp #94 #594]: #590
+#586 := (not #590)
+#581 := (or #586 #583)
+#587 := [quant-inst #30 #26 #31]: #581
+#519 := [unit-resolution #587 #595]: #583
+#510 := [symm #519]: #523
+#504 := [monotonicity #510]: #512
+#509 := [monotonicity #504]: #502
+#494 := [symm #509]: #493
+#235 := (= #35 #577)
+#236 := (= f10 #35)
+#579 := (ite #172 #236 #235)
+#225 := (or #224 #579)
+#226 := [quant-inst #32 #27 #33 #28]: #225
+#516 := [unit-resolution #226 #602]: #579
+#227 := (not #579)
+#506 := (or #227 #235)
 #264 := (or #261 #259)
 #243 := [def-axiom]: #264
-#493 := [unit-resolution #243 #505]: #259
-#579 := (or #240 #172 #583)
-#220 := [def-axiom]: #579
-#496 := [unit-resolution #220 #493]: #494
-#497 := [unit-resolution #496 #509]: #583
-#489 := [trans #497 #500]: #487
-#490 := [trans #489 #486]: #37
+#505 := [unit-resolution #243 #503]: #259
+#567 := (or #227 #172 #235)
+#568 := [def-axiom]: #567
+#507 := [unit-resolution #568 #505]: #506
+#508 := [unit-resolution #507 #516]: #235
+#498 := [trans #508 #494]: #497
+#499 := [trans #498 #496]: #37
 #90 := (not #37)
 #92 := [not-or-elim #91]: #90
-[unit-resolution #92 #490]: false
-unsat
-a8479ddc219a8a1f70834d2e3bfa9595c2e54d48 31 0
-#2 := false
-decl f1 :: S1
-#4 := f1
-decl f9 :: (-> S8 S1)
-decl f10 :: S8
+[unit-resolution #92 #499]: false
+unsat
+3ab56ce3ce9ea17007c9ef9659d24c1591a2f1dc 31 0
+#2 := false
+decl f1 :: S1
+#4 := f1
+decl f8 :: (-> S4 S1)
+decl f9 :: S4
+#32 := f9
+#33 := (f8 f9)
+#34 := (= #33 f1)
+#35 := (iff #34 #34)
+#36 := (not #35)
+#125 := (iff #36 false)
+#1 := true
+#120 := (not true)
+#123 := (iff #120 false)
+#124 := [rewrite]: #123
+#121 := (iff #36 #120)
+#118 := (iff #35 true)
+#109 := (= f1 #33)
+#113 := (iff #109 #109)
+#116 := (iff #113 true)
+#117 := [rewrite]: #116
+#114 := (iff #35 #113)
+#111 := (iff #34 #109)
+#112 := [rewrite]: #111
+#115 := [monotonicity #112 #112]: #114
+#119 := [trans #115 #117]: #118
+#122 := [monotonicity #119]: #121
+#126 := [trans #122 #124]: #125
+#108 := [asserted]: #36
+[mp #108 #126]: false
+unsat
+99e99593c1b6e7784dba4d3a0aca41c7272cf4c1 58 0
+#2 := false
+decl f3 :: (-> S2 S1)
+decl f8 :: S2
+#33 := f8
+#34 := (f3 f8)
+decl f1 :: S1
+#4 := f1
+#110 := (= f1 #34)
+#35 := (= #34 f1)
+#36 := (not #35)
+#37 := (not #36)
+#122 := (iff #37 #110)
+#114 := (not #110)
+#117 := (not #114)
+#120 := (iff #117 #110)
+#121 := [rewrite]: #120
+#118 := (iff #37 #117)
+#115 := (iff #36 #114)
+#112 := (iff #35 #110)
+#113 := [rewrite]: #112
+#116 := [monotonicity #113]: #115
+#119 := [monotonicity #116]: #118
+#123 := [trans #119 #121]: #122
+#109 := [asserted]: #37
+#126 := [mp #109 #123]: #110
+#8 := (:var 0 S2)
+#9 := (f3 #8)
+#634 := (pattern #9)
+#58 := (= f1 #9)
+#61 := (not #58)
+#635 := (forall (vars (?v0 S2)) (:pat #634) #61)
+#64 := (forall (vars (?v0 S2)) #61)
+#638 := (iff #64 #635)
+#636 := (iff #61 #61)
+#637 := [refl]: #636
+#639 := [quant-intro #637]: #638
+#140 := (~ #64 #64)
+#138 := (~ #61 #61)
+#139 := [refl]: #138
+#141 := [nnf-pos #139]: #140
+#10 := (= #9 f1)
+#11 := (not #10)
+#12 := (forall (vars (?v0 S2)) #11)
+#65 := (iff #12 #64)
+#62 := (iff #11 #61)
+#59 := (iff #10 #58)
+#60 := [rewrite]: #59
+#63 := [monotonicity #60]: #62
+#66 := [quant-intro #63]: #65
+#57 := [asserted]: #12
+#69 := [mp #57 #66]: #64
+#125 := [mp~ #69 #141]: #64
+#640 := [mp #125 #639]: #635
+#217 := (not #635)
+#304 := (or #217 #114)
+#218 := [quant-inst #33]: #304
+[unit-resolution #218 #640 #126]: false
+unsat
+d9322750c44c3fbc7422a30bcad6e401e2be0930 46 0
+#2 := false
+decl f4 :: (-> S3 S1)
+decl f8 :: S3
+#33 := f8
+#34 := (f4 f8)
+decl f1 :: S1
+#4 := f1
+#109 := (= f1 #34)
+#113 := (not #109)
+#35 := (= #34 f1)
+#36 := (not #35)
+#114 := (iff #36 #113)
+#111 := (iff #35 #109)
+#112 := [rewrite]: #111
+#115 := [monotonicity #112]: #114
+#108 := [asserted]: #36
+#118 := [mp #108 #115]: #113
+#13 := (:var 0 S3)
+#14 := (f4 #13)
+#633 := (pattern #14)
+#67 := (= f1 #14)
+#634 := (forall (vars (?v0 S3)) (:pat #633) #67)
+#71 := (forall (vars (?v0 S3)) #67)
+#637 := (iff #71 #634)
+#635 := (iff #67 #67)
+#636 := [refl]: #635
+#638 := [quant-intro #636]: #637
+#120 := (~ #71 #71)
+#119 := (~ #67 #67)
+#134 := [refl]: #119
+#121 := [nnf-pos #134]: #120
+#15 := (= #14 f1)
+#16 := (forall (vars (?v0 S3)) #15)
+#72 := (iff #16 #71)
+#69 := (iff #15 #67)
+#70 := [rewrite]: #69
+#73 := [quant-intro #70]: #72
+#66 := [asserted]: #16
+#76 := [mp #66 #73]: #71
+#135 := [mp~ #76 #121]: #71
+#639 := [mp #135 #638]: #634
+#209 := (not #634)
+#296 := (or #209 #109)
+#210 := [quant-inst #33]: #296
+[unit-resolution #210 #639 #118]: false
+unsat
+b2f7b9c42d68e0ecab24c1bc7abe7e061806dd00 119 0
+#2 := false
+decl f5 :: (-> S3 S3 S4 S1)
+decl f11 :: S4
+#41 := f11
+decl f10 :: S3
+#40 := f10
+decl f9 :: S3
+#39 := f9
+#42 := (f5 f9 f10 f11)
+decl f1 :: S1
+#4 := f1
+#129 := (= f1 #42)
+#148 := (not #129)
+#652 := [hypothesis]: #148
+decl f6 :: (-> S3 S4 S1)
+#46 := (f6 f10 f11)
+#136 := (= f1 #46)
+#44 := (f6 f9 f11)
+#133 := (= f1 #44)
+#139 := (or #133 #136)
+#340 := (or #139 #129)
+#149 := (iff #139 #148)
+#47 := (= #46 f1)
+#45 := (= #44 f1)
+#48 := (or #45 #47)
+#43 := (= #42 f1)
+#49 := (iff #43 #48)
+#50 := (not #49)
+#152 := (iff #50 #149)
+#142 := (iff #129 #139)
+#145 := (not #142)
+#150 := (iff #145 #149)
+#151 := [rewrite]: #150
+#146 := (iff #50 #145)
+#143 := (iff #49 #142)
+#140 := (iff #48 #139)
+#137 := (iff #47 #136)
+#138 := [rewrite]: #137
+#134 := (iff #45 #133)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#131 := (iff #43 #129)
+#132 := [rewrite]: #131
+#144 := [monotonicity #132 #141]: #143
+#147 := [monotonicity #144]: #146
+#153 := [trans #147 #151]: #152
+#128 := [asserted]: #50
+#156 := [mp #128 #153]: #149
+#266 := (not #149)
+#339 := (or #139 #129 #266)
+#336 := [def-axiom]: #339
+#319 := [unit-resolution #336 #156]: #340
+#324 := [unit-resolution #319 #652]: #139
+#326 := (not #139)
+#655 := (or #129 #326)
+#18 := (:var 0 S4)
+#17 := (:var 1 S3)
+#16 := (:var 2 S3)
+#19 := (f5 #16 #17 #18)
+#678 := (pattern #19)
+#23 := (f6 #17 #18)
+#96 := (= f1 #23)
+#21 := (f6 #16 #18)
+#93 := (= f1 #21)
+#99 := (or #93 #96)
+#89 := (= f1 #19)
+#102 := (iff #89 #99)
+#679 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) (:pat #678) #102)
+#105 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #102)
+#682 := (iff #105 #679)
+#680 := (iff #102 #102)
+#681 := [refl]: #680
+#683 := [quant-intro #681]: #682
+#160 := (~ #105 #105)
+#174 := (~ #102 #102)
+#175 := [refl]: #174
+#161 := [nnf-pos #175]: #160
+#24 := (= #23 f1)
+#22 := (= #21 f1)
+#25 := (or #22 #24)
+#20 := (= #19 f1)
+#26 := (iff #20 #25)
+#27 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #26)
+#106 := (iff #27 #105)
+#103 := (iff #26 #102)
+#100 := (iff #25 #99)
+#97 := (iff #24 #96)
+#98 := [rewrite]: #97
+#94 := (iff #22 #93)
+#95 := [rewrite]: #94
+#101 := [monotonicity #95 #98]: #100
+#91 := (iff #20 #89)
+#92 := [rewrite]: #91
+#104 := [monotonicity #92 #101]: #103
+#107 := [quant-intro #104]: #106
+#88 := [asserted]: #27
+#110 := [mp #88 #107]: #105
+#176 := [mp~ #110 #161]: #105
+#684 := [mp #176 #683]: #679
+#325 := (not #679)
+#659 := (or #325 #142)
+#660 := [quant-inst #39 #40 #41]: #659
+#312 := [unit-resolution #660 #684]: #142
+#661 := (or #145 #129 #326)
+#662 := [def-axiom]: #661
+#296 := [unit-resolution #662 #312]: #655
+#639 := [unit-resolution #296 #324 #652]: false
+#300 := [lemma #639]: #129
+#313 := (or #326 #148)
+#656 := (or #326 #148 #266)
+#658 := [def-axiom]: #656
+#445 := [unit-resolution #658 #156]: #313
+#301 := [unit-resolution #445 #300]: #326
+#302 := (or #148 #139)
+#657 := (or #145 #148 #139)
+#663 := [def-axiom]: #657
+#303 := [unit-resolution #663 #312]: #302
+[unit-resolution #303 #301 #300]: false
+unsat
+b364582b466f46f7d7a33b311dc9888a3ab60e44 154 0
+#2 := false
+decl f3 :: (-> S3 S2 S1)
+decl f10 :: S2
+#41 := f10
+decl f4 :: S3
+#8 := f4
+#330 := (f3 f4 f10)
+decl f1 :: S1
+#4 := f1
+#327 := (= f1 #330)
+decl f9 :: S3
+#40 := f9
+#44 := (f3 f9 f10)
+#130 := (= f1 #44)
+#331 := (or #130 #327)
+decl f6 :: (-> S3 S3 S2 S1)
+#42 := (f6 f9 f4 f10)
+#126 := (= f1 #42)
+#139 := (not #126)
+#647 := [hypothesis]: #139
+#325 := (or #130 #126)
+#140 := (iff #130 #139)
+#45 := (= #44 f1)
+#43 := (= #42 f1)
+#46 := (iff #43 #45)
+#47 := (not #46)
+#143 := (iff #47 #140)
+#133 := (iff #126 #130)
+#136 := (not #133)
+#141 := (iff #136 #140)
+#142 := [rewrite]: #141
+#137 := (iff #47 #136)
+#134 := (iff #46 #133)
+#131 := (iff #45 #130)
+#132 := [rewrite]: #131
+#128 := (iff #43 #126)
+#129 := [rewrite]: #128
+#135 := [monotonicity #129 #132]: #134
+#138 := [monotonicity #135]: #137
+#144 := [trans #138 #142]: #143
+#125 := [asserted]: #47
+#147 := [mp #125 #144]: #140
+#237 := (not #140)
+#324 := (or #130 #126 #237)
+#238 := [def-axiom]: #324
+#239 := [unit-resolution #238 #147]: #325
+#649 := [unit-resolution #239 #647]: #130
+#653 := (not #331)
+#293 := (or #126 #653)
+#310 := (iff #126 #331)
+#9 := (:var 0 S2)
+#19 := (:var 1 S3)
+#18 := (:var 2 S3)
+#20 := (f6 #18 #19 #9)
+#669 := (pattern #20)
+#24 := (f3 #19 #9)
+#93 := (= f1 #24)
+#22 := (f3 #18 #9)
+#90 := (= f1 #22)
+#96 := (or #90 #93)
+#86 := (= f1 #20)
+#99 := (iff #86 #96)
+#670 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) (:pat #669) #99)
+#102 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #99)
+#673 := (iff #102 #670)
+#671 := (iff #99 #99)
+#672 := [refl]: #671
+#674 := [quant-intro #672]: #673
+#151 := (~ #102 #102)
+#165 := (~ #99 #99)
+#166 := [refl]: #165
+#152 := [nnf-pos #166]: #151
+#25 := (= #24 f1)
+#23 := (= #22 f1)
+#26 := (or #23 #25)
+#21 := (= #20 f1)
+#27 := (iff #21 #26)
+#28 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #27)
+#103 := (iff #28 #102)
+#100 := (iff #27 #99)
+#97 := (iff #26 #96)
+#94 := (iff #25 #93)
+#95 := [rewrite]: #94
+#91 := (iff #23 #90)
+#92 := [rewrite]: #91
+#98 := [monotonicity #92 #95]: #97
+#88 := (iff #21 #86)
+#89 := [rewrite]: #88
+#101 := [monotonicity #89 #98]: #100
+#104 := [quant-intro #101]: #103
+#85 := [asserted]: #28
+#107 := [mp #85 #104]: #102
+#167 := [mp~ #107 #152]: #102
+#675 := [mp #167 #674]: #670
+#304 := (not #670)
+#436 := (or #304 #310)
+#643 := [quant-inst #40 #8 #41]: #436
+#292 := [unit-resolution #643 #675]: #310
+#644 := (not #310)
+#302 := (or #644 #126 #653)
+#307 := [def-axiom]: #302
+#294 := [unit-resolution #307 #292]: #293
+#632 := [unit-resolution #294 #647]: #653
+#326 := (not #130)
+#315 := (or #331 #326)
+#316 := [def-axiom]: #315
+#633 := [unit-resolution #316 #632 #649]: false
+#634 := [lemma #633]: #126
+#635 := (or #139 #331)
+#645 := (or #644 #139 #331)
+#303 := [def-axiom]: #645
+#636 := [unit-resolution #303 #292]: #635
+#638 := [unit-resolution #636 #634]: #331
+#329 := (or #326 #139)
+#317 := (or #326 #139 #237)
+#328 := [def-axiom]: #317
+#257 := [unit-resolution #328 #147]: #329
+#640 := [unit-resolution #257 #634]: #326
+#648 := (or #653 #130 #327)
+#654 := [def-axiom]: #648
+#278 := [unit-resolution #654 #640 #638]: #327
+#10 := (f3 f4 #9)
+#655 := (pattern #10)
+#68 := (= f1 #10)
+#71 := (not #68)
+#656 := (forall (vars (?v0 S2)) (:pat #655) #71)
+#74 := (forall (vars (?v0 S2)) #71)
+#659 := (iff #74 #656)
+#657 := (iff #71 #71)
+#658 := [refl]: #657
+#660 := [quant-intro #658]: #659
+#161 := (~ #74 #74)
+#159 := (~ #71 #71)
+#160 := [refl]: #159
+#162 := [nnf-pos #160]: #161
+#11 := (= #10 f1)
+#12 := (not #11)
+#13 := (forall (vars (?v0 S2)) #12)
+#75 := (iff #13 #74)
+#72 := (iff #12 #71)
+#69 := (iff #11 #68)
+#70 := [rewrite]: #69
+#73 := [monotonicity #70]: #72
+#76 := [quant-intro #73]: #75
+#67 := [asserted]: #13
+#79 := [mp #67 #76]: #74
+#146 := [mp~ #79 #162]: #74
+#661 := [mp #146 #660]: #656
+#650 := (not #327)
+#631 := (not #656)
+#637 := (or #631 #650)
+#273 := [quant-inst #41]: #637
+[unit-resolution #273 #661 #278]: false
+unsat
+7d907ff63da540f87f38f6be518dd4d79ce5f3db 128 0
+#2 := false
+decl f4 :: (-> S4 S3 S1)
+decl f10 :: S3
 #41 := f10
-#42 := (f9 f10)
+decl f5 :: S4
+#13 := f5
+#222 := (f4 f5 f10)
+decl f1 :: S1
+#4 := f1
+#309 := (= f1 #222)
+#636 := (not #309)
+decl f9 :: S4
+#40 := f9
+#223 := (f4 f9 f10)
+#310 := (= f1 #223)
+#302 := (or #309 #310)
+#287 := (not #302)
+decl f6 :: (-> S4 S4 S3 S1)
+#42 := (f6 f9 f5 f10)
+#123 := (= f1 #42)
+#242 := (iff #123 #302)
+#14 := (:var 0 S3)
+#19 := (:var 1 S4)
+#18 := (:var 2 S4)
+#20 := (f6 #18 #19 #14)
+#654 := (pattern #20)
+#24 := (f4 #19 #14)
+#90 := (= f1 #24)
+#22 := (f4 #18 #14)
+#87 := (= f1 #22)
+#93 := (or #87 #90)
+#83 := (= f1 #20)
+#96 := (iff #83 #93)
+#655 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) (:pat #654) #96)
+#99 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #96)
+#658 := (iff #99 #655)
+#656 := (iff #96 #96)
+#657 := [refl]: #656
+#659 := [quant-intro #657]: #658
+#136 := (~ #99 #99)
+#150 := (~ #96 #96)
+#151 := [refl]: #150
+#137 := [nnf-pos #151]: #136
+#25 := (= #24 f1)
+#23 := (= #22 f1)
+#26 := (or #23 #25)
+#21 := (= #20 f1)
+#27 := (iff #21 #26)
+#28 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #27)
+#100 := (iff #28 #99)
+#97 := (iff #27 #96)
+#94 := (iff #26 #93)
+#91 := (iff #25 #90)
+#92 := [rewrite]: #91
+#88 := (iff #23 #87)
+#89 := [rewrite]: #88
+#95 := [monotonicity #89 #92]: #94
+#85 := (iff #21 #83)
+#86 := [rewrite]: #85
+#98 := [monotonicity #86 #95]: #97
+#101 := [quant-intro #98]: #100
+#82 := [asserted]: #28
+#104 := [mp #82 #101]: #99
+#152 := [mp~ #104 #137]: #99
+#660 := [mp #152 #659]: #655
+#316 := (not #655)
+#295 := (or #316 #242)
+#224 := (or #310 #309)
+#311 := (iff #123 #224)
+#632 := (or #316 #311)
+#289 := (iff #632 #295)
+#628 := (iff #295 #295)
+#300 := [rewrite]: #628
+#315 := (iff #311 #242)
+#313 := (iff #224 #302)
+#314 := [rewrite]: #313
+#312 := [monotonicity #314]: #315
+#421 := [monotonicity #312]: #289
+#301 := [trans #421 #300]: #289
+#634 := [quant-inst #40 #13 #41]: #632
+#635 := [mp #634 #301]: #295
+#618 := [unit-resolution #635 #660]: #242
+#288 := (not #242)
+#619 := (or #288 #287)
+#127 := (not #123)
+#43 := (= #42 f1)
+#44 := (not #43)
+#128 := (iff #44 #127)
+#125 := (iff #43 #123)
+#126 := [rewrite]: #125
+#129 := [monotonicity #126]: #128
+#122 := [asserted]: #44
+#132 := [mp #122 #129]: #127
+#631 := (or #288 #123 #287)
+#272 := [def-axiom]: #631
+#622 := [unit-resolution #272 #132]: #619
+#258 := [unit-resolution #622 #618]: #287
+#637 := (or #302 #636)
+#638 := [def-axiom]: #637
+#623 := [unit-resolution #638 #258]: #636
+#15 := (f4 f5 #14)
+#647 := (pattern #15)
+#75 := (= f1 #15)
+#648 := (forall (vars (?v0 S3)) (:pat #647) #75)
+#79 := (forall (vars (?v0 S3)) #75)
+#651 := (iff #79 #648)
+#649 := (iff #75 #75)
+#650 := [refl]: #649
+#652 := [quant-intro #650]: #651
+#134 := (~ #79 #79)
+#133 := (~ #75 #75)
+#148 := [refl]: #133
+#135 := [nnf-pos #148]: #134
+#16 := (= #15 f1)
+#17 := (forall (vars (?v0 S3)) #16)
+#80 := (iff #17 #79)
+#77 := (iff #16 #75)
+#78 := [rewrite]: #77
+#81 := [quant-intro #78]: #80
+#74 := [asserted]: #17
+#84 := [mp #74 #81]: #79
+#149 := [mp~ #84 #135]: #79
+#653 := [mp #149 #652]: #648
+#620 := (not #648)
+#621 := (or #620 #309)
+#616 := [quant-inst #41]: #621
+[unit-resolution #616 #653 #623]: false
+unsat
+5cdc991e87f691c3b3a175ff2ede8c62635b20a0 146 0
+#2 := false
+decl f5 :: (-> S3 S3 S4 S1)
+decl f11 :: S4
+#41 := f11
+decl f9 :: S3
+#39 := f9
+decl f10 :: S3
+#40 := f10
+#44 := (f5 f10 f9 f11)
+decl f1 :: S1
+#4 := f1
+#130 := (= f1 #44)
+#326 := (not #130)
+#42 := (f5 f9 f10 f11)
+#126 := (= f1 #42)
+#139 := (not #126)
+#245 := [hypothesis]: #139
+#325 := (or #130 #126)
+#140 := (iff #130 #139)
+#45 := (= #44 f1)
 #43 := (= #42 f1)
-#44 := (iff #43 #43)
-#45 := (not #44)
-#140 := (iff #45 false)
-#1 := true
-#135 := (not true)
-#138 := (iff #135 false)
-#139 := [rewrite]: #138
-#136 := (iff #45 #135)
-#133 := (iff #44 true)
+#46 := (iff #43 #45)
+#47 := (not #46)
+#143 := (iff #47 #140)
+#133 := (iff #126 #130)
+#136 := (not #133)
+#141 := (iff #136 #140)
+#142 := [rewrite]: #141
+#137 := (iff #47 #136)
+#134 := (iff #46 #133)
+#131 := (iff #45 #130)
+#132 := [rewrite]: #131
+#128 := (iff #43 #126)
+#129 := [rewrite]: #128
+#135 := [monotonicity #129 #132]: #134
+#138 := [monotonicity #135]: #137
+#144 := [trans #138 #142]: #143
+#125 := [asserted]: #47
+#147 := [mp #125 #144]: #140
+#237 := (not #140)
+#324 := (or #130 #126 #237)
+#238 := [def-axiom]: #324
+#239 := [unit-resolution #238 #147]: #325
+#624 := [unit-resolution #239 #245]: #130
+decl f6 :: (-> S3 S4 S1)
+#330 := (f6 f9 f11)
+#327 := (= f1 #330)
+#331 := (f6 f10 f11)
+#310 := (= f1 #331)
+#647 := (or #310 #327)
+#644 := (not #647)
+#347 := (or #126 #644)
+#634 := (iff #126 #647)
+#18 := (:var 0 S4)
+#17 := (:var 1 S3)
+#16 := (:var 2 S3)
+#19 := (f5 #16 #17 #18)
+#669 := (pattern #19)
+#23 := (f6 #17 #18)
+#93 := (= f1 #23)
+#21 := (f6 #16 #18)
+#90 := (= f1 #21)
+#96 := (or #90 #93)
+#86 := (= f1 #19)
+#99 := (iff #86 #96)
+#670 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) (:pat #669) #99)
+#102 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #99)
+#673 := (iff #102 #670)
+#671 := (iff #99 #99)
+#672 := [refl]: #671
+#674 := [quant-intro #672]: #673
+#151 := (~ #102 #102)
+#165 := (~ #99 #99)
+#166 := [refl]: #165
+#152 := [nnf-pos #166]: #151
+#24 := (= #23 f1)
+#22 := (= #21 f1)
+#25 := (or #22 #24)
+#20 := (= #19 f1)
+#26 := (iff #20 #25)
+#27 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #26)
+#103 := (iff #27 #102)
+#100 := (iff #26 #99)
+#97 := (iff #25 #96)
+#94 := (iff #24 #93)
+#95 := [rewrite]: #94
+#91 := (iff #22 #90)
+#92 := [rewrite]: #91
+#98 := [monotonicity #92 #95]: #97
+#88 := (iff #20 #86)
+#89 := [rewrite]: #88
+#101 := [monotonicity #89 #98]: #100
+#104 := [quant-intro #101]: #103
+#85 := [asserted]: #27
+#107 := [mp #85 #104]: #102
+#167 := [mp~ #107 #152]: #102
+#675 := [mp #167 #674]: #670
+#643 := (not #670)
+#631 := (or #643 #634)
+#304 := (or #327 #310)
+#436 := (iff #126 #304)
+#637 := (or #643 #436)
+#638 := (iff #637 #631)
+#278 := (iff #631 #631)
+#279 := [rewrite]: #278
+#635 := (iff #436 #634)
+#632 := (iff #304 #647)
+#633 := [rewrite]: #632
+#636 := [monotonicity #633]: #635
+#640 := [monotonicity #636]: #638
+#641 := [trans #640 #279]: #638
+#273 := [quant-inst #39 #40 #41]: #637
+#639 := [mp #273 #641]: #631
+#625 := [unit-resolution #639 #675]: #634
+#642 := (not #634)
+#628 := (or #642 #126 #644)
+#629 := [def-axiom]: #628
+#348 := [unit-resolution #629 #625]: #347
+#622 := [unit-resolution #348 #245]: #644
+#623 := (or #326 #647)
+#649 := (iff #130 #647)
+#315 := (or #643 #649)
+#316 := [quant-inst #40 #39 #41]: #315
+#626 := [unit-resolution #316 #675]: #649
+#645 := (not #649)
+#287 := (or #645 #326 #647)
+#630 := [def-axiom]: #287
+#627 := [unit-resolution #630 #626]: #623
+#336 := [unit-resolution #627 #622 #624]: false
+#337 := [lemma #336]: #126
+#329 := (or #326 #139)
+#317 := (or #326 #139 #237)
+#328 := [def-axiom]: #317
+#257 := [unit-resolution #328 #147]: #329
+#338 := [unit-resolution #257 #337]: #326
+#340 := (or #139 #647)
+#335 := (or #642 #139 #647)
+#351 := [def-axiom]: #335
+#618 := [unit-resolution #351 #625]: #340
+#619 := [unit-resolution #618 #337]: #647
+#332 := (or #130 #644)
+#303 := (or #645 #130 #644)
+#646 := [def-axiom]: #303
+#616 := [unit-resolution #646 #626]: #332
+[unit-resolution #616 #619 #338]: false
+unsat
+fa2f9bd8c428cc56374865b6337a9b9b3979db13 121 0
+#2 := false
+decl f5 :: (-> S3 S3 S4 S1)
+decl f10 :: S4
+#40 := f10
+decl f9 :: S3
+#39 := f9
+#41 := (f5 f9 f9 f10)
+decl f1 :: S1
+#4 := f1
+#125 := (= f1 #41)
+#138 := (not #125)
+#629 := [hypothesis]: #138
+decl f6 :: (-> S3 S4 S1)
+#43 := (f6 f9 f10)
+#129 := (= f1 #43)
+#324 := (or #129 #125)
+#139 := (iff #129 #138)
+#44 := (= #43 f1)
+#42 := (= #41 f1)
+#45 := (iff #42 #44)
+#46 := (not #45)
+#142 := (iff #46 #139)
+#132 := (iff #125 #129)
+#135 := (not #132)
+#140 := (iff #135 #139)
+#141 := [rewrite]: #140
+#136 := (iff #46 #135)
+#133 := (iff #45 #132)
+#130 := (iff #44 #129)
+#131 := [rewrite]: #130
+#127 := (iff #42 #125)
+#128 := [rewrite]: #127
+#134 := [monotonicity #128 #131]: #133
+#137 := [monotonicity #134]: #136
+#143 := [trans #137 #141]: #142
+#124 := [asserted]: #46
+#146 := [mp #124 #143]: #139
+#236 := (not #139)
+#323 := (or #129 #125 #236)
+#237 := [def-axiom]: #323
+#238 := [unit-resolution #237 #146]: #324
+#290 := [unit-resolution #238 #629]: #129
+#325 := (not #129)
+#292 := (or #125 #325)
+#18 := (:var 0 S4)
+#17 := (:var 1 S3)
+#16 := (:var 2 S3)
+#19 := (f5 #16 #17 #18)
+#668 := (pattern #19)
+#23 := (f6 #17 #18)
+#92 := (= f1 #23)
+#21 := (f6 #16 #18)
+#89 := (= f1 #21)
+#95 := (or #89 #92)
+#85 := (= f1 #19)
+#98 := (iff #85 #95)
+#669 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) (:pat #668) #98)
+#101 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #98)
+#672 := (iff #101 #669)
+#670 := (iff #98 #98)
+#671 := [refl]: #670
+#673 := [quant-intro #671]: #672
+#150 := (~ #101 #101)
+#164 := (~ #98 #98)
+#165 := [refl]: #164
+#151 := [nnf-pos #165]: #150
+#24 := (= #23 f1)
+#22 := (= #21 f1)
+#25 := (or #22 #24)
+#20 := (= #19 f1)
+#26 := (iff #20 #25)
+#27 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #26)
+#102 := (iff #27 #101)
+#99 := (iff #26 #98)
+#96 := (iff #25 #95)
+#93 := (iff #24 #92)
+#94 := [rewrite]: #93
+#90 := (iff #22 #89)
+#91 := [rewrite]: #90
+#97 := [monotonicity #91 #94]: #96
+#87 := (iff #20 #85)
+#88 := [rewrite]: #87
+#100 := [monotonicity #88 #97]: #99
+#103 := [quant-intro #100]: #102
+#84 := [asserted]: #27
+#106 := [mp #84 #103]: #101
+#166 := [mp~ #106 #151]: #101
+#674 := [mp #166 #673]: #669
+#303 := (not #669)
+#435 := (or #303 #132)
+#329 := (or #129 #129)
+#326 := (iff #125 #329)
+#642 := (or #303 #326)
+#315 := (iff #642 #435)
+#650 := (iff #435 #435)
+#651 := [rewrite]: #650
+#646 := (iff #326 #132)
+#330 := (iff #329 #129)
+#309 := [rewrite]: #330
+#648 := [monotonicity #309]: #646
+#649 := [monotonicity #648]: #315
+#652 := [trans #649 #651]: #315
+#314 := [quant-inst #39 #39 #40]: #642
+#647 := [mp #314 #652]: #435
+#291 := [unit-resolution #647 #674]: #132
+#653 := (or #135 #125 #325)
+#643 := [def-axiom]: #653
+#293 := [unit-resolution #643 #291]: #292
+#631 := [unit-resolution #293 #290 #629]: false
+#632 := [lemma #631]: #125
+#328 := (or #325 #138)
+#316 := (or #325 #138 #236)
+#327 := [def-axiom]: #316
+#256 := [unit-resolution #327 #146]: #328
+#633 := [unit-resolution #256 #632]: #325
+#634 := (or #138 #129)
+#301 := (or #135 #138 #129)
+#306 := [def-axiom]: #301
+#635 := [unit-resolution #306 #291]: #634
+[unit-resolution #635 #633 #632]: false
+unsat
+63dfbec334f0b24e14d14e8841f417fc16248602 259 0
+#2 := false
+decl f5 :: (-> S3 S4 S1)
+decl f12 :: S4
+#45 := f12
+decl f10 :: S3
+#41 := f10
+#625 := (f5 f10 f12)
+decl f1 :: S1
+#4 := f1
+#338 := (= f1 #625)
+decl f11 :: S3
+#42 := f11
+#336 := (f5 f11 f12)
+#333 := (= f1 #336)
+#623 := (or #333 #338)
+decl f6 :: (-> S3 S3 S3)
+#43 := (f6 f10 f11)
+#310 := (f5 #43 f12)
+#442 := (= f1 #310)
+#617 := (iff #442 #623)
+#583 := (not #617)
+#595 := (not #623)
+#607 := (not #338)
+decl f9 :: S3
+#40 := f9
+#638 := (f5 f9 f12)
+#639 := (= f1 #638)
+#485 := (or #338 #639)
+#610 := (not #485)
+#48 := (f6 f9 f10)
+#337 := (f5 #48 f12)
+#316 := (= f1 #337)
+#593 := (iff #316 #485)
+#585 := (not #593)
+#578 := [hypothesis]: #585
+#19 := (:var 0 S4)
+#17 := (:var 1 S3)
+#16 := (:var 2 S3)
+#18 := (f6 #16 #17)
+#20 := (f5 #18 #19)
+#675 := (pattern #20)
+#24 := (f5 #17 #19)
+#99 := (= f1 #24)
+#22 := (f5 #16 #19)
+#96 := (= f1 #22)
+#102 := (or #96 #99)
+#92 := (= f1 #20)
+#105 := (iff #92 #102)
+#676 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) (:pat #675) #105)
+#108 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #105)
+#679 := (iff #108 #676)
+#677 := (iff #105 #105)
+#678 := [refl]: #677
+#680 := [quant-intro #678]: #679
+#157 := (~ #108 #108)
+#171 := (~ #105 #105)
+#172 := [refl]: #171
+#158 := [nnf-pos #172]: #157
+#25 := (= #24 f1)
+#23 := (= #22 f1)
+#26 := (or #23 #25)
+#21 := (= #20 f1)
+#27 := (iff #21 #26)
+#28 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S4)) #27)
+#109 := (iff #28 #108)
+#106 := (iff #27 #105)
+#103 := (iff #26 #102)
+#100 := (iff #25 #99)
+#101 := [rewrite]: #100
+#97 := (iff #23 #96)
+#98 := [rewrite]: #97
+#104 := [monotonicity #98 #101]: #103
+#94 := (iff #21 #92)
+#95 := [rewrite]: #94
+#107 := [monotonicity #95 #104]: #106
+#110 := [quant-intro #107]: #109
+#91 := [asserted]: #28
+#113 := [mp #91 #110]: #108
+#173 := [mp~ #113 #158]: #108
+#681 := [mp #173 #680]: #676
+#649 := (not #676)
+#591 := (or #649 #593)
+#602 := (or #639 #338)
+#484 := (iff #316 #602)
+#594 := (or #649 #484)
+#494 := (iff #594 #591)
+#497 := (iff #591 #591)
+#490 := [rewrite]: #497
+#495 := (iff #484 #593)
+#486 := (iff #602 #485)
+#445 := [rewrite]: #486
+#590 := [monotonicity #445]: #495
+#496 := [monotonicity #590]: #494
+#498 := [trans #496 #490]: #494
+#479 := [quant-inst #40 #41 #45]: #594
+#499 := [mp #479 #498]: #591
+#579 := [unit-resolution #499 #681 #578]: false
+#580 := [lemma #579]: #593
+#656 := (not #316)
+#653 := (or #316 #333)
+#650 := (not #653)
+#49 := (f6 #48 f11)
+#50 := (f5 #49 f12)
+#136 := (= f1 #50)
+#332 := (not #136)
+#44 := (f6 f9 #43)
+#46 := (f5 #44 f12)
+#132 := (= f1 #46)
+#145 := (not #132)
+#581 := [hypothesis]: #145
+#331 := (or #136 #132)
+#146 := (iff #136 #145)
+#51 := (= #50 f1)
+#47 := (= #46 f1)
+#52 := (iff #47 #51)
+#53 := (not #52)
+#149 := (iff #53 #146)
+#139 := (iff #132 #136)
+#142 := (not #139)
+#147 := (iff #142 #146)
+#148 := [rewrite]: #147
+#143 := (iff #53 #142)
+#140 := (iff #52 #139)
+#137 := (iff #51 #136)
+#138 := [rewrite]: #137
+#134 := (iff #47 #132)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#144 := [monotonicity #141]: #143
+#150 := [trans #144 #148]: #149
+#131 := [asserted]: #53
+#153 := [mp #131 #150]: #146
+#243 := (not #146)
+#330 := (or #136 #132 #243)
+#244 := [def-axiom]: #330
+#245 := [unit-resolution #244 #153]: #331
+#575 := [unit-resolution #245 #581]: #136
+#566 := (or #332 #653)
+#655 := (iff #136 #653)
+#321 := (or #649 #655)
+#322 := [quant-inst #48 #42 #45]: #321
+#582 := [unit-resolution #322 #681]: #655
+#651 := (not #655)
+#293 := (or #651 #332 #653)
+#636 := [def-axiom]: #293
+#567 := [unit-resolution #636 #582]: #566
+#569 := [unit-resolution #567 #575]: #653
+#659 := (not #333)
+#599 := (or #649 #617)
+#622 := (or #338 #333)
+#626 := (iff #442 #622)
+#619 := (or #649 #626)
+#614 := (iff #619 #599)
+#621 := (iff #599 #599)
+#462 := [rewrite]: #621
+#618 := (iff #626 #617)
+#627 := (iff #622 #623)
+#616 := [rewrite]: #627
+#613 := [monotonicity #616]: #618
+#615 := [monotonicity #613]: #614
+#463 := [trans #615 #462]: #614
+#620 := [quant-inst #41 #42 #45]: #619
+#464 := [mp #620 #463]: #599
+#570 := [unit-resolution #464 #681]: #617
+#560 := (or #583 #595)
+#358 := (not #442)
+#642 := (or #442 #639)
+#631 := (not #642)
+#572 := (or #132 #631)
+#279 := (iff #132 #642)
+#284 := (or #649 #279)
+#640 := (or #639 #442)
+#641 := (iff #132 #640)
+#285 := (or #649 #641)
+#645 := (iff #285 #284)
+#634 := (iff #284 #284)
+#635 := [rewrite]: #634
+#644 := (iff #641 #279)
+#637 := (iff #640 #642)
+#643 := [rewrite]: #637
+#646 := [monotonicity #643]: #644
+#648 := [monotonicity #646]: #645
+#341 := [trans #648 #635]: #645
+#647 := [quant-inst #40 #43 #45]: #285
+#357 := [mp #647 #341]: #284
+#571 := [unit-resolution #357 #681]: #279
+#628 := (not #279)
+#632 := (or #628 #132 #631)
+#629 := [def-axiom]: #632
+#568 := [unit-resolution #629 #571]: #572
+#573 := [unit-resolution #568 #581]: #631
+#359 := (or #642 #358)
+#345 := [def-axiom]: #359
+#559 := [unit-resolution #345 #573]: #358
+#577 := (or #583 #442 #595)
+#574 := [def-axiom]: #577
+#562 := [unit-resolution #574 #559]: #560
+#563 := [unit-resolution #562 #570]: #595
+#606 := (or #623 #659)
+#500 := [def-axiom]: #606
+#564 := [unit-resolution #500 #563]: #659
+#308 := (or #650 #316 #333)
+#313 := [def-axiom]: #308
+#561 := [unit-resolution #313 #564 #569]: #316
+#360 := (not #639)
+#251 := (or #642 #360)
+#630 := [def-axiom]: #251
+#565 := [unit-resolution #630 #573]: #360
+#501 := (or #623 #607)
+#502 := [def-axiom]: #501
+#545 := [unit-resolution #502 #563]: #607
+#611 := (or #610 #338 #639)
+#605 := [def-axiom]: #611
+#546 := [unit-resolution #605 #545 #565]: #610
+#443 := (or #585 #656 #485)
+#444 := [def-axiom]: #443
+#548 := [unit-resolution #444 #546 #561 #580]: false
+#549 := [lemma #548]: #132
+#335 := (or #332 #145)
+#323 := (or #332 #145 #243)
+#334 := [def-axiom]: #323
+#263 := [unit-resolution #334 #153]: #335
+#550 := [unit-resolution #263 #549]: #332
+#551 := (or #136 #650)
+#309 := (or #651 #136 #650)
+#652 := [def-axiom]: #309
+#552 := [unit-resolution #652 #582]: #551
+#553 := [unit-resolution #552 #550]: #650
+#657 := (or #653 #656)
+#658 := [def-axiom]: #657
+#554 := [unit-resolution #658 #553]: #656
+#612 := (or #585 #316 #610)
+#441 := [def-axiom]: #612
+#555 := [unit-resolution #441 #554 #580]: #610
+#608 := (or #485 #607)
+#609 := [def-axiom]: #608
+#556 := [unit-resolution #609 #555]: #607
+#654 := (or #653 #659)
+#660 := [def-axiom]: #654
+#557 := [unit-resolution #660 #553]: #659
+#592 := (or #595 #333 #338)
+#596 := [def-axiom]: #592
+#547 := [unit-resolution #596 #557 #556]: #595
+#558 := (or #145 #642)
+#633 := (or #628 #145 #642)
+#342 := [def-axiom]: #633
+#536 := [unit-resolution #342 #571]: #558
+#537 := [unit-resolution #536 #549]: #642
+#603 := (or #485 #360)
+#604 := [def-axiom]: #603
+#539 := [unit-resolution #604 #555]: #360
+#353 := (or #631 #442 #639)
+#354 := [def-axiom]: #353
+#540 := [unit-resolution #354 #539 #537]: #442
+#576 := (or #583 #358 #623)
+#586 := [def-axiom]: #576
+#541 := [unit-resolution #586 #540 #547]: #583
+[unit-resolution #464 #681 #541]: false
+unsat
+b9a56cfd9dd84219baf29a97bb74d87de1fcb3ba 153 0
+#2 := false
+decl f8 :: (-> S4 S5 S1)
+decl f11 :: S5
+#41 := f11
+decl f10 :: S4
+#40 := f10
+#46 := (f8 f10 f11)
+decl f1 :: S1
+#4 := f1
+#136 := (= f1 #46)
+#190 := (not #136)
+decl f9 :: S4
+#39 := f9
+#44 := (f8 f9 f11)
+#133 := (= f1 #44)
+#189 := (not #133)
+#191 := (or #189 #190)
+#192 := (not #191)
+#333 := [hypothesis]: #192
+decl f7 :: (-> S4 S4 S5 S1)
+#42 := (f7 f9 f10 f11)
+#129 := (= f1 #42)
+#148 := (not #129)
+#339 := (or #148 #191)
+#203 := (iff #129 #191)
+#139 := (and #133 #136)
+#149 := (iff #139 #148)
+#206 := (iff #149 #203)
+#198 := (iff #191 #129)
+#204 := (iff #198 #203)
+#205 := [rewrite]: #204
+#201 := (iff #149 #198)
+#195 := (iff #192 #148)
+#199 := (iff #195 #198)
+#200 := [rewrite]: #199
+#196 := (iff #149 #195)
+#193 := (iff #139 #192)
+#194 := [rewrite]: #193
+#197 := [monotonicity #194]: #196
+#202 := [trans #197 #200]: #201
+#207 := [trans #202 #205]: #206
+#47 := (= #46 f1)
+#45 := (= #44 f1)
+#48 := (and #45 #47)
+#43 := (= #42 f1)
+#49 := (iff #43 #48)
+#50 := (not #49)
+#152 := (iff #50 #149)
+#142 := (iff #129 #139)
+#145 := (not #142)
+#150 := (iff #145 #149)
+#151 := [rewrite]: #150
+#146 := (iff #50 #145)
+#143 := (iff #49 #142)
+#140 := (iff #48 #139)
+#137 := (iff #47 #136)
+#138 := [rewrite]: #137
+#134 := (iff #45 #133)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#131 := (iff #43 #129)
+#132 := [rewrite]: #131
+#144 := [monotonicity #132 #141]: #143
+#147 := [monotonicity #144]: #146
+#153 := [trans #147 #151]: #152
+#128 := [asserted]: #50
+#156 := [mp #128 #153]: #149
+#208 := [mp #156 #207]: #203
+#346 := (not #203)
+#356 := (or #148 #191 #346)
+#360 := [def-axiom]: #356
+#676 := [unit-resolution #360 #208]: #339
+#465 := [unit-resolution #676 #333]: #148
+#332 := (or #129 #191)
+#678 := (iff #129 #192)
+#29 := (:var 0 S5)
+#28 := (:var 1 S4)
+#27 := (:var 2 S4)
+#30 := (f7 #27 #28 #29)
+#705 := (pattern #30)
+#34 := (f8 #28 #29)
+#116 := (= f1 #34)
+#181 := (not #116)
+#32 := (f8 #27 #29)
+#113 := (= f1 #32)
+#180 := (not #113)
+#164 := (or #180 #181)
+#165 := (not #164)
+#109 := (= f1 #30)
+#182 := (iff #109 #165)
+#706 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #705) #182)
+#185 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #182)
+#709 := (iff #185 #706)
+#707 := (iff #182 #182)
+#708 := [refl]: #707
+#710 := [quant-intro #708]: #709
+#119 := (and #113 #116)
+#122 := (iff #109 #119)
+#125 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #122)
+#186 := (iff #125 #185)
+#183 := (iff #122 #182)
+#166 := (iff #119 #165)
+#167 := [rewrite]: #166
+#184 := [monotonicity #167]: #183
+#187 := [quant-intro #184]: #186
+#162 := (~ #125 #125)
+#177 := (~ #122 #122)
+#178 := [refl]: #177
+#163 := [nnf-pos #178]: #162
+#35 := (= #34 f1)
+#33 := (= #32 f1)
+#36 := (and #33 #35)
+#31 := (= #30 f1)
+#37 := (iff #31 #36)
+#38 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #37)
+#126 := (iff #38 #125)
+#123 := (iff #37 #122)
+#120 := (iff #36 #119)
+#117 := (iff #35 #116)
+#118 := [rewrite]: #117
+#114 := (iff #33 #113)
+#115 := [rewrite]: #114
+#121 := [monotonicity #115 #118]: #120
+#111 := (iff #31 #109)
+#112 := [rewrite]: #111
+#124 := [monotonicity #112 #121]: #123
+#127 := [quant-intro #124]: #126
+#108 := [asserted]: #38
+#130 := [mp #108 #127]: #125
+#179 := [mp~ #130 #163]: #125
+#188 := [mp #179 #187]: #185
+#711 := [mp #188 #710]: #706
+#672 := (not #706)
+#344 := (or #672 #678)
+#345 := [quant-inst #39 #40 #41]: #344
+#674 := [unit-resolution #345 #711]: #678
+#679 := (not #678)
+#680 := (or #679 #129 #191)
+#681 := [def-axiom]: #680
+#675 := [unit-resolution #681 #674]: #332
+#316 := [unit-resolution #675 #465 #333]: false
+#659 := [lemma #316]: #191
+#286 := (or #129 #192)
+#357 := (or #129 #192 #346)
+#358 := [def-axiom]: #357
+#359 := [unit-resolution #358 #208]: #286
+#320 := [unit-resolution #359 #659]: #129
+#321 := (or #148 #192)
+#682 := (or #679 #148 #192)
+#677 := [def-axiom]: #682
+#322 := [unit-resolution #677 #674]: #321
+[unit-resolution #322 #320 #659]: false
+unsat
+7f98a59af5916f5d5b5c30234aa00391b0645729 141 0
+#2 := false
+decl f3 :: (-> S3 S2 S1)
+decl f10 :: S2
+#41 := f10
+decl f4 :: S3
+#8 := f4
+#230 := (f3 f4 f10)
+decl f1 :: S1
+#4 := f1
+#317 := (= f1 #230)
+#231 := (not #317)
+decl f9 :: S3
+#40 := f9
+#318 := (f3 f9 f10)
+#232 := (= f1 #318)
+#319 := (not #232)
+#310 := (or #319 #231)
+#321 := (not #310)
+decl f8 :: (-> S3 S3 S2 S1)
+#42 := (f8 f9 f4 f10)
 #124 := (= f1 #42)
-#128 := (iff #124 #124)
-#131 := (iff #128 true)
-#132 := [rewrite]: #131
-#129 := (iff #44 #128)
-#126 := (iff #43 #124)
-#127 := [rewrite]: #126
-#130 := [monotonicity #127 #127]: #129
-#134 := [trans #130 #132]: #133
-#137 := [monotonicity #134]: #136
-#141 := [trans #137 #139]: #140
-#123 := [asserted]: #45
-[mp #123 #141]: false
-unsat
-4a8e2abc2ad72bd9865553c33c10577508b41462 58 0
-#2 := false
-decl f8 :: (-> S7 S1)
-decl f9 :: S7
-#41 := f9
-#42 := (f8 f9)
-decl f1 :: S1
-#4 := f1
-#124 := (= f1 #42)
+#322 := (iff #124 #321)
+#9 := (:var 0 S2)
+#30 := (:var 1 S3)
+#29 := (:var 2 S3)
+#31 := (f8 #29 #30 #9)
+#669 := (pattern #31)
+#35 := (f3 #30 #9)
+#111 := (= f1 #35)
+#165 := (not #111)
+#33 := (f3 #29 #9)
+#108 := (= f1 #33)
+#164 := (not #108)
+#148 := (or #164 #165)
+#149 := (not #148)
+#104 := (= f1 #31)
+#166 := (iff #104 #149)
+#670 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) (:pat #669) #166)
+#169 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #166)
+#673 := (iff #169 #670)
+#671 := (iff #166 #166)
+#672 := [refl]: #671
+#674 := [quant-intro #672]: #673
+#114 := (and #108 #111)
+#117 := (iff #104 #114)
+#120 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #117)
+#170 := (iff #120 #169)
+#167 := (iff #117 #166)
+#150 := (iff #114 #149)
+#151 := [rewrite]: #150
+#168 := [monotonicity #151]: #167
+#171 := [quant-intro #168]: #170
+#146 := (~ #120 #120)
+#161 := (~ #117 #117)
+#162 := [refl]: #161
+#147 := [nnf-pos #162]: #146
+#36 := (= #35 f1)
+#34 := (= #33 f1)
+#37 := (and #34 #36)
+#32 := (= #31 f1)
+#38 := (iff #32 #37)
+#39 := (forall (vars (?v0 S3) (?v1 S3) (?v2 S2)) #38)
+#121 := (iff #39 #120)
+#118 := (iff #38 #117)
+#115 := (iff #37 #114)
+#112 := (iff #36 #111)
+#113 := [rewrite]: #112
+#109 := (iff #34 #108)
+#110 := [rewrite]: #109
+#116 := [monotonicity #110 #113]: #115
+#106 := (iff #32 #104)
+#107 := [rewrite]: #106
+#119 := [monotonicity #107 #116]: #118
+#122 := [quant-intro #119]: #121
+#103 := [asserted]: #39
+#125 := [mp #103 #122]: #120
+#163 := [mp~ #125 #147]: #120
+#172 := [mp #163 #171]: #169
+#675 := [mp #172 #674]: #670
+#320 := (not #670)
+#324 := (or #320 #322)
+#303 := [quant-inst #40 #8 #41]: #324
+#250 := [unit-resolution #303 #675]: #322
+#309 := (not #322)
+#323 := (or #309 #321)
 #43 := (= #42 f1)
 #44 := (not #43)
 #45 := (not #44)
@@ -56569,2459 +58109,816 @@
 #137 := [trans #133 #135]: #136
 #123 := [asserted]: #45
 #140 := [mp #123 #137]: #124
-#36 := (:var 0 S7)
-#37 := (f8 #36)
-#669 := (pattern #37)
-#113 := (= f1 #37)
-#117 := (not #113)
-#670 := (forall (vars (?v0 S7)) (:pat #669) #117)
-#120 := (forall (vars (?v0 S7)) #117)
-#673 := (iff #120 #670)
-#671 := (iff #117 #117)
-#672 := [refl]: #671
-#674 := [quant-intro #672]: #673
-#146 := (~ #120 #120)
-#161 := (~ #117 #117)
-#162 := [refl]: #161
-#147 := [nnf-pos #162]: #146
-#38 := (= #37 f1)
-#39 := (not #38)
-#40 := (forall (vars (?v0 S7)) #39)
-#121 := (iff #40 #120)
-#118 := (iff #39 #117)
-#115 := (iff #38 #113)
-#116 := [rewrite]: #115
-#119 := [monotonicity #116]: #118
-#122 := [quant-intro #119]: #121
-#112 := [asserted]: #40
-#125 := [mp #112 #122]: #120
-#163 := [mp~ #125 #147]: #120
-#675 := [mp #163 #674]: #670
-#231 := (not #670)
-#318 := (or #231 #128)
-#232 := [quant-inst #41]: #318
-[unit-resolution #232 #675 #140]: false
-unsat
-091bf3e425fe9e8c8440218eb2682fa4e6096563 46 0
-#2 := false
-decl f7 :: (-> S6 S1)
-decl f9 :: S6
-#41 := f9
-#42 := (f7 f9)
-decl f1 :: S1
-#4 := f1
-#123 := (= f1 #42)
-#127 := (not #123)
-#43 := (= #42 f1)
-#44 := (not #43)
-#128 := (iff #44 #127)
-#125 := (iff #43 #123)
-#126 := [rewrite]: #125
-#129 := [monotonicity #126]: #128
-#122 := [asserted]: #44
-#132 := [mp #122 #129]: #127
-#32 := (:var 0 S6)
-#33 := (f7 #32)
-#654 := (pattern #33)
-#104 := (= f1 #33)
-#655 := (forall (vars (?v0 S6)) (:pat #654) #104)
-#108 := (forall (vars (?v0 S6)) #104)
-#658 := (iff #108 #655)
-#656 := (iff #104 #104)
-#657 := [refl]: #656
-#659 := [quant-intro #657]: #658
-#136 := (~ #108 #108)
-#150 := (~ #104 #104)
-#151 := [refl]: #150
-#137 := [nnf-pos #151]: #136
-#34 := (= #33 f1)
-#35 := (forall (vars (?v0 S6)) #34)
-#109 := (iff #35 #108)
-#106 := (iff #34 #104)
-#107 := [rewrite]: #106
-#110 := [quant-intro #107]: #109
-#103 := [asserted]: #35
-#113 := [mp #103 #110]: #108
-#152 := [mp~ #113 #137]: #108
-#660 := [mp #152 #659]: #655
-#223 := (not #655)
-#310 := (or #223 #123)
-#224 := [quant-inst #41]: #310
-[unit-resolution #224 #660 #132]: false
-unsat
-fd9a6405dcfcd8a8d48113910424b839f41afe7c 119 0
-#2 := false
-decl f5 :: (-> S4 S4 S5 S1)
-decl f11 :: S5
-#43 := f11
-decl f10 :: S4
-#42 := f10
-decl f9 :: S4
-#41 := f9
-#44 := (f5 f9 f10 f11)
-decl f1 :: S1
-#4 := f1
-#131 := (= f1 #44)
-#150 := (not #131)
-#654 := [hypothesis]: #150
-decl f6 :: (-> S4 S5 S1)
-#48 := (f6 f10 f11)
-#138 := (= f1 #48)
-#46 := (f6 f9 f11)
-#135 := (= f1 #46)
-#141 := (or #135 #138)
-#342 := (or #141 #131)
-#151 := (iff #141 #150)
-#49 := (= #48 f1)
-#47 := (= #46 f1)
-#50 := (or #47 #49)
-#45 := (= #44 f1)
-#51 := (iff #45 #50)
-#52 := (not #51)
-#154 := (iff #52 #151)
-#144 := (iff #131 #141)
-#147 := (not #144)
-#152 := (iff #147 #151)
-#153 := [rewrite]: #152
-#148 := (iff #52 #147)
-#145 := (iff #51 #144)
-#142 := (iff #50 #141)
-#139 := (iff #49 #138)
-#140 := [rewrite]: #139
-#136 := (iff #47 #135)
-#137 := [rewrite]: #136
-#143 := [monotonicity #137 #140]: #142
-#133 := (iff #45 #131)
-#134 := [rewrite]: #133
-#146 := [monotonicity #134 #143]: #145
-#149 := [monotonicity #146]: #148
-#155 := [trans #149 #153]: #154
-#130 := [asserted]: #52
-#158 := [mp #130 #155]: #151
-#268 := (not #151)
-#341 := (or #141 #131 #268)
-#338 := [def-axiom]: #341
-#321 := [unit-resolution #338 #158]: #342
-#326 := [unit-resolution #321 #654]: #141
-#328 := (not #141)
-#657 := (or #131 #328)
-#22 := (:var 0 S5)
-#21 := (:var 1 S4)
-#20 := (:var 2 S4)
-#23 := (f5 #20 #21 #22)
-#673 := (pattern #23)
-#27 := (f6 #21 #22)
-#99 := (= f1 #27)
-#25 := (f6 #20 #22)
-#96 := (= f1 #25)
-#102 := (or #96 #99)
-#92 := (= f1 #23)
-#105 := (iff #92 #102)
-#674 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #673) #105)
-#108 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #105)
-#677 := (iff #108 #674)
-#675 := (iff #105 #105)
-#676 := [refl]: #675
-#678 := [quant-intro #676]: #677
-#160 := (~ #108 #108)
-#159 := (~ #105 #105)
-#174 := [refl]: #159
-#161 := [nnf-pos #174]: #160
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
-#109 := (iff #31 #108)
-#106 := (iff #30 #105)
-#103 := (iff #29 #102)
-#100 := (iff #28 #99)
-#101 := [rewrite]: #100
-#97 := (iff #26 #96)
-#98 := [rewrite]: #97
-#104 := [monotonicity #98 #101]: #103
-#94 := (iff #24 #92)
-#95 := [rewrite]: #94
-#107 := [monotonicity #95 #104]: #106
-#110 := [quant-intro #107]: #109
-#91 := [asserted]: #31
-#113 := [mp #91 #110]: #108
-#175 := [mp~ #113 #161]: #108
-#679 := [mp #175 #678]: #674
-#327 := (not #674)
-#661 := (or #327 #144)
-#662 := [quant-inst #41 #42 #43]: #661
-#314 := [unit-resolution #662 #679]: #144
-#663 := (or #147 #131 #328)
-#664 := [def-axiom]: #663
-#298 := [unit-resolution #664 #314]: #657
-#641 := [unit-resolution #298 #326 #654]: false
-#302 := [lemma #641]: #131
-#315 := (or #328 #150)
-#658 := (or #328 #150 #268)
-#660 := [def-axiom]: #658
-#447 := [unit-resolution #660 #158]: #315
-#303 := [unit-resolution #447 #302]: #328
-#304 := (or #150 #141)
-#659 := (or #147 #150 #141)
-#665 := [def-axiom]: #659
-#305 := [unit-resolution #665 #314]: #304
-[unit-resolution #305 #303 #302]: false
-unsat
-1323dc787bd70f2161bb2e81688bf85b58b24887 154 0
-#2 := false
-decl f6 :: (-> S4 S5 S1)
-decl f10 :: S5
-#42 := f10
-decl f8 :: S4
-#36 := f8
-#331 := (f6 f8 f10)
-decl f1 :: S1
-#4 := f1
-#328 := (= f1 #331)
-decl f9 :: S4
-#41 := f9
-#45 := (f6 f9 f10)
-#131 := (= f1 #45)
-#332 := (or #131 #328)
-decl f5 :: (-> S4 S4 S5 S1)
-#43 := (f5 f9 f8 f10)
-#127 := (= f1 #43)
-#140 := (not #127)
-#648 := [hypothesis]: #140
-#326 := (or #131 #127)
-#141 := (iff #131 #140)
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (iff #44 #46)
-#48 := (not #47)
-#144 := (iff #48 #141)
-#134 := (iff #127 #131)
-#137 := (not #134)
-#142 := (iff #137 #141)
-#143 := [rewrite]: #142
-#138 := (iff #48 #137)
-#135 := (iff #47 #134)
-#132 := (iff #46 #131)
-#133 := [rewrite]: #132
-#129 := (iff #44 #127)
-#130 := [rewrite]: #129
-#136 := [monotonicity #130 #133]: #135
-#139 := [monotonicity #136]: #138
-#145 := [trans #139 #143]: #144
-#126 := [asserted]: #48
-#148 := [mp #126 #145]: #141
-#238 := (not #141)
-#325 := (or #131 #127 #238)
-#239 := [def-axiom]: #325
-#240 := [unit-resolution #239 #148]: #326
-#650 := [unit-resolution #240 #648]: #131
-#654 := (not #332)
-#294 := (or #127 #654)
-#311 := (iff #127 #332)
-#22 := (:var 0 S5)
-#21 := (:var 1 S4)
-#20 := (:var 2 S4)
-#23 := (f5 #20 #21 #22)
-#663 := (pattern #23)
-#27 := (f6 #21 #22)
-#95 := (= f1 #27)
-#25 := (f6 #20 #22)
-#92 := (= f1 #25)
-#98 := (or #92 #95)
-#88 := (= f1 #23)
-#101 := (iff #88 #98)
-#664 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #663) #101)
-#104 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #101)
-#667 := (iff #104 #664)
-#665 := (iff #101 #101)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#150 := (~ #104 #104)
-#149 := (~ #101 #101)
-#164 := [refl]: #149
-#151 := [nnf-pos #164]: #150
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
-#105 := (iff #31 #104)
-#102 := (iff #30 #101)
-#99 := (iff #29 #98)
-#96 := (iff #28 #95)
-#97 := [rewrite]: #96
-#93 := (iff #26 #92)
-#94 := [rewrite]: #93
-#100 := [monotonicity #94 #97]: #99
-#90 := (iff #24 #88)
-#91 := [rewrite]: #90
-#103 := [monotonicity #91 #100]: #102
-#106 := [quant-intro #103]: #105
-#87 := [asserted]: #31
-#109 := [mp #87 #106]: #104
-#165 := [mp~ #109 #151]: #104
-#669 := [mp #165 #668]: #664
-#305 := (not #664)
-#437 := (or #305 #311)
-#644 := [quant-inst #41 #36 #42]: #437
-#293 := [unit-resolution #644 #669]: #311
-#645 := (not #311)
-#303 := (or #645 #127 #654)
-#308 := [def-axiom]: #303
-#295 := [unit-resolution #308 #293]: #294
-#633 := [unit-resolution #295 #648]: #654
-#327 := (not #131)
-#316 := (or #332 #327)
-#317 := [def-axiom]: #316
-#634 := [unit-resolution #317 #633 #650]: false
-#635 := [lemma #634]: #127
-#636 := (or #140 #332)
-#646 := (or #645 #140 #332)
-#304 := [def-axiom]: #646
-#637 := [unit-resolution #304 #293]: #636
-#639 := [unit-resolution #637 #635]: #332
-#330 := (or #327 #140)
-#318 := (or #327 #140 #238)
-#329 := [def-axiom]: #318
-#258 := [unit-resolution #329 #148]: #330
-#641 := [unit-resolution #258 #635]: #327
-#649 := (or #654 #131 #328)
-#655 := [def-axiom]: #649
-#279 := [unit-resolution #655 #641 #639]: #328
-#37 := (f6 f8 #22)
-#677 := (pattern #37)
-#116 := (= f1 #37)
-#120 := (not #116)
-#678 := (forall (vars (?v0 S5)) (:pat #677) #120)
-#123 := (forall (vars (?v0 S5)) #120)
-#681 := (iff #123 #678)
-#679 := (iff #120 #120)
-#680 := [refl]: #679
-#682 := [quant-intro #680]: #681
-#154 := (~ #123 #123)
-#169 := (~ #120 #120)
-#170 := [refl]: #169
-#155 := [nnf-pos #170]: #154
-#38 := (= #37 f1)
-#39 := (not #38)
-#40 := (forall (vars (?v0 S5)) #39)
-#124 := (iff #40 #123)
-#121 := (iff #39 #120)
-#118 := (iff #38 #116)
-#119 := [rewrite]: #118
-#122 := [monotonicity #119]: #121
-#125 := [quant-intro #122]: #124
-#115 := [asserted]: #40
-#128 := [mp #115 #125]: #123
-#171 := [mp~ #128 #155]: #123
-#683 := [mp #171 #682]: #678
-#651 := (not #328)
-#632 := (not #678)
-#638 := (or #632 #651)
-#274 := [quant-inst #42]: #638
-[unit-resolution #274 #683 #279]: false
-unsat
-c8b1c55953a13602e2fa8c1b144b5f14c7db8217 128 0
-#2 := false
-decl f6 :: (-> S4 S5 S1)
-decl f10 :: S5
-#42 := f10
-decl f7 :: S4
-#32 := f7
-#223 := (f6 f7 f10)
-decl f1 :: S1
-#4 := f1
-#310 := (= f1 #223)
-#637 := (not #310)
-decl f9 :: S4
-#41 := f9
-#224 := (f6 f9 f10)
-#311 := (= f1 #224)
-#303 := (or #310 #311)
-#288 := (not #303)
-decl f5 :: (-> S4 S4 S5 S1)
-#43 := (f5 f9 f7 f10)
-#124 := (= f1 #43)
-#243 := (iff #124 #303)
-#22 := (:var 0 S5)
-#21 := (:var 1 S4)
-#20 := (:var 2 S4)
-#23 := (f5 #20 #21 #22)
-#648 := (pattern #23)
-#27 := (f6 #21 #22)
-#92 := (= f1 #27)
-#25 := (f6 #20 #22)
-#89 := (= f1 #25)
-#95 := (or #89 #92)
-#85 := (= f1 #23)
-#98 := (iff #85 #95)
-#649 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #648) #98)
-#101 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #98)
-#652 := (iff #101 #649)
-#650 := (iff #98 #98)
+#645 := (or #309 #128 #321)
+#646 := [def-axiom]: #645
+#639 := [unit-resolution #646 #140]: #323
+#280 := [unit-resolution #639 #250]: #321
+#297 := (or #310 #317)
+#429 := [def-axiom]: #297
+#623 := [unit-resolution #429 #280]: #317
+#10 := (f3 f4 #9)
+#648 := (pattern #10)
+#66 := (= f1 #10)
+#69 := (not #66)
+#649 := (forall (vars (?v0 S2)) (:pat #648) #69)
+#72 := (forall (vars (?v0 S2)) #69)
+#652 := (iff #72 #649)
+#650 := (iff #69 #69)
 #651 := [refl]: #650
 #653 := [quant-intro #651]: #652
-#135 := (~ #101 #101)
-#134 := (~ #98 #98)
-#149 := [refl]: #134
-#136 := [nnf-pos #149]: #135
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
-#102 := (iff #31 #101)
-#99 := (iff #30 #98)
-#96 := (iff #29 #95)
-#93 := (iff #28 #92)
-#94 := [rewrite]: #93
-#90 := (iff #26 #89)
-#91 := [rewrite]: #90
-#97 := [monotonicity #91 #94]: #96
-#87 := (iff #24 #85)
-#88 := [rewrite]: #87
-#100 := [monotonicity #88 #97]: #99
-#103 := [quant-intro #100]: #102
-#84 := [asserted]: #31
-#106 := [mp #84 #103]: #101
-#150 := [mp~ #106 #136]: #101
-#654 := [mp #150 #653]: #649
-#317 := (not #649)
-#296 := (or #317 #243)
-#225 := (or #311 #310)
-#312 := (iff #124 #225)
-#633 := (or #317 #312)
-#290 := (iff #633 #296)
-#629 := (iff #296 #296)
-#301 := [rewrite]: #629
-#316 := (iff #312 #243)
-#314 := (iff #225 #303)
-#315 := [rewrite]: #314
-#313 := [monotonicity #315]: #316
-#422 := [monotonicity #313]: #290
-#302 := [trans #422 #301]: #290
-#635 := [quant-inst #41 #32 #42]: #633
-#636 := [mp #635 #302]: #296
-#619 := [unit-resolution #636 #654]: #243
-#289 := (not #243)
-#620 := (or #289 #288)
-#128 := (not #124)
-#44 := (= #43 f1)
-#45 := (not #44)
-#129 := (iff #45 #128)
-#126 := (iff #44 #124)
-#127 := [rewrite]: #126
-#130 := [monotonicity #127]: #129
-#123 := [asserted]: #45
-#133 := [mp #123 #130]: #128
-#632 := (or #289 #124 #288)
-#273 := [def-axiom]: #632
-#623 := [unit-resolution #273 #133]: #620
-#259 := [unit-resolution #623 #619]: #288
-#638 := (or #303 #637)
-#639 := [def-axiom]: #638
-#624 := [unit-resolution #639 #259]: #637
-#33 := (f6 f7 #22)
-#655 := (pattern #33)
-#105 := (= f1 #33)
-#656 := (forall (vars (?v0 S5)) (:pat #655) #105)
-#109 := (forall (vars (?v0 S5)) #105)
-#659 := (iff #109 #656)
-#657 := (iff #105 #105)
-#658 := [refl]: #657
-#660 := [quant-intro #658]: #659
-#137 := (~ #109 #109)
-#151 := (~ #105 #105)
-#152 := [refl]: #151
-#138 := [nnf-pos #152]: #137
-#34 := (= #33 f1)
-#35 := (forall (vars (?v0 S5)) #34)
-#110 := (iff #35 #109)
-#107 := (iff #34 #105)
-#108 := [rewrite]: #107
-#111 := [quant-intro #108]: #110
-#104 := [asserted]: #35
-#114 := [mp #104 #111]: #109
-#153 := [mp~ #114 #138]: #109
-#661 := [mp #153 #660]: #656
-#621 := (not #656)
-#622 := (or #621 #310)
-#617 := [quant-inst #42]: #622
-[unit-resolution #617 #661 #624]: false
-unsat
-0fceb45afe271c647688273babe303962581fbf2 146 0
-#2 := false
-decl f5 :: (-> S4 S4 S5 S1)
-decl f11 :: S5
-#43 := f11
-decl f9 :: S4
-#41 := f9
-decl f10 :: S4
-#42 := f10
-#46 := (f5 f10 f9 f11)
-decl f1 :: S1
-#4 := f1
-#132 := (= f1 #46)
-#328 := (not #132)
-#44 := (f5 f9 f10 f11)
-#128 := (= f1 #44)
-#141 := (not #128)
-#247 := [hypothesis]: #141
-#327 := (or #132 #128)
-#142 := (iff #132 #141)
-#47 := (= #46 f1)
-#45 := (= #44 f1)
-#48 := (iff #45 #47)
-#49 := (not #48)
-#145 := (iff #49 #142)
-#135 := (iff #128 #132)
-#138 := (not #135)
-#143 := (iff #138 #142)
-#144 := [rewrite]: #143
-#139 := (iff #49 #138)
-#136 := (iff #48 #135)
-#133 := (iff #47 #132)
-#134 := [rewrite]: #133
-#130 := (iff #45 #128)
-#131 := [rewrite]: #130
-#137 := [monotonicity #131 #134]: #136
-#140 := [monotonicity #137]: #139
-#146 := [trans #140 #144]: #145
-#127 := [asserted]: #49
-#149 := [mp #127 #146]: #142
-#239 := (not #142)
-#326 := (or #132 #128 #239)
-#240 := [def-axiom]: #326
-#241 := [unit-resolution #240 #149]: #327
-#626 := [unit-resolution #241 #247]: #132
-decl f6 :: (-> S4 S5 S1)
-#332 := (f6 f9 f11)
-#329 := (= f1 #332)
-#333 := (f6 f10 f11)
-#312 := (= f1 #333)
-#649 := (or #312 #329)
-#646 := (not #649)
-#349 := (or #128 #646)
-#636 := (iff #128 #649)
-#22 := (:var 0 S5)
-#21 := (:var 1 S4)
-#20 := (:var 2 S4)
-#23 := (f5 #20 #21 #22)
-#664 := (pattern #23)
-#27 := (f6 #21 #22)
-#96 := (= f1 #27)
-#25 := (f6 #20 #22)
-#93 := (= f1 #25)
-#99 := (or #93 #96)
-#89 := (= f1 #23)
-#102 := (iff #89 #99)
-#665 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #664) #102)
-#105 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #102)
-#668 := (iff #105 #665)
-#666 := (iff #102 #102)
-#667 := [refl]: #666
-#669 := [quant-intro #667]: #668
-#151 := (~ #105 #105)
-#150 := (~ #102 #102)
-#165 := [refl]: #150
-#152 := [nnf-pos #165]: #151
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
-#106 := (iff #31 #105)
-#103 := (iff #30 #102)
-#100 := (iff #29 #99)
-#97 := (iff #28 #96)
-#98 := [rewrite]: #97
-#94 := (iff #26 #93)
-#95 := [rewrite]: #94
-#101 := [monotonicity #95 #98]: #100
-#91 := (iff #24 #89)
-#92 := [rewrite]: #91
-#104 := [monotonicity #92 #101]: #103
-#107 := [quant-intro #104]: #106
-#88 := [asserted]: #31
-#110 := [mp #88 #107]: #105
-#166 := [mp~ #110 #152]: #105
-#670 := [mp #166 #669]: #665
-#645 := (not #665)
-#633 := (or #645 #636)
-#306 := (or #329 #312)
-#438 := (iff #128 #306)
-#639 := (or #645 #438)
-#640 := (iff #639 #633)
-#280 := (iff #633 #633)
-#281 := [rewrite]: #280
-#637 := (iff #438 #636)
-#634 := (iff #306 #649)
-#635 := [rewrite]: #634
-#638 := [monotonicity #635]: #637
-#642 := [monotonicity #638]: #640
-#643 := [trans #642 #281]: #640
-#275 := [quant-inst #41 #42 #43]: #639
-#641 := [mp #275 #643]: #633
-#627 := [unit-resolution #641 #670]: #636
-#644 := (not #636)
-#630 := (or #644 #128 #646)
-#631 := [def-axiom]: #630
-#350 := [unit-resolution #631 #627]: #349
-#624 := [unit-resolution #350 #247]: #646
-#625 := (or #328 #649)
-#651 := (iff #132 #649)
-#317 := (or #645 #651)
-#318 := [quant-inst #42 #41 #43]: #317
-#628 := [unit-resolution #318 #670]: #651
-#647 := (not #651)
-#289 := (or #647 #328 #649)
-#632 := [def-axiom]: #289
-#629 := [unit-resolution #632 #628]: #625
-#338 := [unit-resolution #629 #624 #626]: false
-#339 := [lemma #338]: #128
-#331 := (or #328 #141)
-#319 := (or #328 #141 #239)
-#330 := [def-axiom]: #319
-#259 := [unit-resolution #330 #149]: #331
-#340 := [unit-resolution #259 #339]: #328
-#342 := (or #141 #649)
-#337 := (or #644 #141 #649)
-#353 := [def-axiom]: #337
-#620 := [unit-resolution #353 #627]: #342
-#621 := [unit-resolution #620 #339]: #649
-#334 := (or #132 #646)
-#305 := (or #647 #132 #646)
-#648 := [def-axiom]: #305
-#618 := [unit-resolution #648 #628]: #334
-[unit-resolution #618 #621 #340]: false
-unsat
-dd5a8039aacd6c3fcf9f486d31684a5899cfecfc 121 0
-#2 := false
-decl f5 :: (-> S4 S4 S5 S1)
-decl f10 :: S5
-#42 := f10
-decl f9 :: S4
-#41 := f9
-#43 := (f5 f9 f9 f10)
-decl f1 :: S1
-#4 := f1
-#127 := (= f1 #43)
-#140 := (not #127)
-#631 := [hypothesis]: #140
-decl f6 :: (-> S4 S5 S1)
-#45 := (f6 f9 f10)
-#131 := (= f1 #45)
-#326 := (or #131 #127)
-#141 := (iff #131 #140)
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (iff #44 #46)
-#48 := (not #47)
-#144 := (iff #48 #141)
-#134 := (iff #127 #131)
-#137 := (not #134)
-#142 := (iff #137 #141)
-#143 := [rewrite]: #142
-#138 := (iff #48 #137)
-#135 := (iff #47 #134)
-#132 := (iff #46 #131)
-#133 := [rewrite]: #132
-#129 := (iff #44 #127)
-#130 := [rewrite]: #129
-#136 := [monotonicity #130 #133]: #135
-#139 := [monotonicity #136]: #138
-#145 := [trans #139 #143]: #144
-#126 := [asserted]: #48
-#148 := [mp #126 #145]: #141
-#238 := (not #141)
-#325 := (or #131 #127 #238)
-#239 := [def-axiom]: #325
-#240 := [unit-resolution #239 #148]: #326
-#292 := [unit-resolution #240 #631]: #131
-#327 := (not #131)
-#294 := (or #127 #327)
-#22 := (:var 0 S5)
-#21 := (:var 1 S4)
-#20 := (:var 2 S4)
-#23 := (f5 #20 #21 #22)
-#663 := (pattern #23)
-#27 := (f6 #21 #22)
-#95 := (= f1 #27)
-#25 := (f6 #20 #22)
-#92 := (= f1 #25)
-#98 := (or #92 #95)
-#88 := (= f1 #23)
-#101 := (iff #88 #98)
-#664 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #663) #101)
-#104 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #101)
-#667 := (iff #104 #664)
-#665 := (iff #101 #101)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#150 := (~ #104 #104)
-#149 := (~ #101 #101)
-#164 := [refl]: #149
-#151 := [nnf-pos #164]: #150
-#28 := (= #27 f1)
-#26 := (= #25 f1)
-#29 := (or #26 #28)
-#24 := (= #23 f1)
-#30 := (iff #24 #29)
-#31 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #30)
-#105 := (iff #31 #104)
-#102 := (iff #30 #101)
-#99 := (iff #29 #98)
-#96 := (iff #28 #95)
-#97 := [rewrite]: #96
-#93 := (iff #26 #92)
-#94 := [rewrite]: #93
-#100 := [monotonicity #94 #97]: #99
-#90 := (iff #24 #88)
-#91 := [rewrite]: #90
-#103 := [monotonicity #91 #100]: #102
-#106 := [quant-intro #103]: #105
-#87 := [asserted]: #31
-#109 := [mp #87 #106]: #104
-#165 := [mp~ #109 #151]: #104
-#669 := [mp #165 #668]: #664
-#305 := (not #664)
-#437 := (or #305 #134)
-#331 := (or #131 #131)
-#328 := (iff #127 #331)
-#644 := (or #305 #328)
-#317 := (iff #644 #437)
-#652 := (iff #437 #437)
-#653 := [rewrite]: #652
-#648 := (iff #328 #134)
-#332 := (iff #331 #131)
-#311 := [rewrite]: #332
-#650 := [monotonicity #311]: #648
-#651 := [monotonicity #650]: #317
-#654 := [trans #651 #653]: #317
-#316 := [quant-inst #41 #41 #42]: #644
-#649 := [mp #316 #654]: #437
-#293 := [unit-resolution #649 #669]: #134
-#655 := (or #137 #127 #327)
-#645 := [def-axiom]: #655
-#295 := [unit-resolution #645 #293]: #294
-#633 := [unit-resolution #295 #292 #631]: false
-#634 := [lemma #633]: #127
-#330 := (or #327 #140)
-#318 := (or #327 #140 #238)
-#329 := [def-axiom]: #318
-#258 := [unit-resolution #329 #148]: #330
-#635 := [unit-resolution #258 #634]: #327
-#636 := (or #140 #131)
-#303 := (or #137 #140 #131)
-#308 := [def-axiom]: #303
-#637 := [unit-resolution #308 #293]: #636
-[unit-resolution #637 #635 #634]: false
-unsat
-8df9cadd28b79979ba76c3dfed467a1319648283 259 0
-#2 := false
-decl f5 :: (-> S4 S5 S1)
-decl f12 :: S5
-#47 := f12
-decl f10 :: S4
-#43 := f10
-#627 := (f5 f10 f12)
-decl f1 :: S1
-#4 := f1
-#340 := (= f1 #627)
-decl f11 :: S4
-#44 := f11
-#338 := (f5 f11 f12)
-#335 := (= f1 #338)
-#625 := (or #335 #340)
-decl f6 :: (-> S4 S4 S4)
-#45 := (f6 f10 f11)
-#312 := (f5 #45 f12)
-#444 := (= f1 #312)
-#619 := (iff #444 #625)
-#585 := (not #619)
-#597 := (not #625)
-#609 := (not #340)
+#154 := (~ #72 #72)
+#152 := (~ #69 #69)
+#153 := [refl]: #152
+#155 := [nnf-pos #153]: #154
+#11 := (= #10 f1)
+#12 := (not #11)
+#13 := (forall (vars (?v0 S2)) #12)
+#73 := (iff #13 #72)
+#70 := (iff #12 #69)
+#67 := (iff #11 #66)
+#68 := [rewrite]: #67
+#71 := [monotonicity #68]: #70
+#74 := [quant-intro #71]: #73
+#65 := [asserted]: #13
+#77 := [mp #65 #74]: #72
+#139 := [mp~ #77 #155]: #72
+#654 := [mp #139 #653]: #649
+#300 := (not #649)
+#638 := (or #300 #231)
+#296 := [quant-inst #41]: #638
+[unit-resolution #296 #654 #623]: false
+unsat
+b75cfd5dcf910762f51953bce5714d91441e0375 165 0
+#2 := false
+decl f4 :: (-> S4 S3 S1)
+decl f10 :: S3
+#41 := f10
 decl f9 :: S4
-#42 := f9
-#640 := (f5 f9 f12)
-#641 := (= f1 #640)
-#487 := (or #340 #641)
-#612 := (not #487)
-#50 := (f6 f9 f10)
-#339 := (f5 #50 f12)
-#318 := (= f1 #339)
-#595 := (iff #318 #487)
-#587 := (not #595)
-#580 := [hypothesis]: #587
-#23 := (:var 0 S5)
-#21 := (:var 1 S4)
-#20 := (:var 2 S4)
-#22 := (f6 #20 #21)
-#24 := (f5 #22 #23)
-#670 := (pattern #24)
-#28 := (f5 #21 #23)
-#102 := (= f1 #28)
-#26 := (f5 #20 #23)
-#99 := (= f1 #26)
-#105 := (or #99 #102)
-#95 := (= f1 #24)
-#108 := (iff #95 #105)
-#671 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #670) #108)
-#111 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #108)
-#674 := (iff #111 #671)
-#672 := (iff #108 #108)
-#673 := [refl]: #672
-#675 := [quant-intro #673]: #674
-#157 := (~ #111 #111)
-#156 := (~ #108 #108)
-#171 := [refl]: #156
-#158 := [nnf-pos #171]: #157
-#29 := (= #28 f1)
-#27 := (= #26 f1)
-#30 := (or #27 #29)
-#25 := (= #24 f1)
-#31 := (iff #25 #30)
-#32 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #31)
-#112 := (iff #32 #111)
-#109 := (iff #31 #108)
-#106 := (iff #30 #105)
-#103 := (iff #29 #102)
-#104 := [rewrite]: #103
-#100 := (iff #27 #99)
-#101 := [rewrite]: #100
-#107 := [monotonicity #101 #104]: #106
-#97 := (iff #25 #95)
-#98 := [rewrite]: #97
-#110 := [monotonicity #98 #107]: #109
-#113 := [quant-intro #110]: #112
-#94 := [asserted]: #32
-#116 := [mp #94 #113]: #111
-#172 := [mp~ #116 #158]: #111
-#676 := [mp #172 #675]: #671
-#651 := (not #671)
-#593 := (or #651 #595)
-#604 := (or #641 #340)
-#486 := (iff #318 #604)
-#596 := (or #651 #486)
-#496 := (iff #596 #593)
-#499 := (iff #593 #593)
-#492 := [rewrite]: #499
-#497 := (iff #486 #595)
-#488 := (iff #604 #487)
-#447 := [rewrite]: #488
-#592 := [monotonicity #447]: #497
-#498 := [monotonicity #592]: #496
-#500 := [trans #498 #492]: #496
-#481 := [quant-inst #42 #43 #47]: #596
-#501 := [mp #481 #500]: #593
-#581 := [unit-resolution #501 #676 #580]: false
-#582 := [lemma #581]: #595
-#658 := (not #318)
-#655 := (or #318 #335)
-#652 := (not #655)
-#51 := (f6 #50 f11)
-#52 := (f5 #51 f12)
-#138 := (= f1 #52)
-#334 := (not #138)
-#46 := (f6 f9 #45)
-#48 := (f5 #46 f12)
-#134 := (= f1 #48)
-#147 := (not #134)
-#583 := [hypothesis]: #147
-#333 := (or #138 #134)
-#148 := (iff #138 #147)
-#53 := (= #52 f1)
-#49 := (= #48 f1)
-#54 := (iff #49 #53)
-#55 := (not #54)
-#151 := (iff #55 #148)
-#141 := (iff #134 #138)
-#144 := (not #141)
-#149 := (iff #144 #148)
-#150 := [rewrite]: #149
-#145 := (iff #55 #144)
-#142 := (iff #54 #141)
-#139 := (iff #53 #138)
-#140 := [rewrite]: #139
-#136 := (iff #49 #134)
-#137 := [rewrite]: #136
-#143 := [monotonicity #137 #140]: #142
-#146 := [monotonicity #143]: #145
-#152 := [trans #146 #150]: #151
-#133 := [asserted]: #55
-#155 := [mp #133 #152]: #148
-#245 := (not #148)
-#332 := (or #138 #134 #245)
-#246 := [def-axiom]: #332
-#247 := [unit-resolution #246 #155]: #333
-#577 := [unit-resolution #247 #583]: #138
-#568 := (or #334 #655)
-#657 := (iff #138 #655)
-#323 := (or #651 #657)
-#324 := [quant-inst #50 #44 #47]: #323
-#584 := [unit-resolution #324 #676]: #657
-#653 := (not #657)
-#295 := (or #653 #334 #655)
-#638 := [def-axiom]: #295
-#569 := [unit-resolution #638 #584]: #568
-#571 := [unit-resolution #569 #577]: #655
-#661 := (not #335)
-#601 := (or #651 #619)
-#624 := (or #340 #335)
-#628 := (iff #444 #624)
-#621 := (or #651 #628)
-#616 := (iff #621 #601)
-#623 := (iff #601 #601)
-#464 := [rewrite]: #623
-#620 := (iff #628 #619)
-#629 := (iff #624 #625)
-#618 := [rewrite]: #629
-#615 := [monotonicity #618]: #620
-#617 := [monotonicity #615]: #616
-#465 := [trans #617 #464]: #616
-#622 := [quant-inst #43 #44 #47]: #621
-#466 := [mp #622 #465]: #601
-#572 := [unit-resolution #466 #676]: #619
-#562 := (or #585 #597)
-#360 := (not #444)
-#644 := (or #444 #641)
-#633 := (not #644)
-#574 := (or #134 #633)
-#281 := (iff #134 #644)
-#286 := (or #651 #281)
-#642 := (or #641 #444)
-#643 := (iff #134 #642)
-#287 := (or #651 #643)
-#647 := (iff #287 #286)
-#636 := (iff #286 #286)
-#637 := [rewrite]: #636
-#646 := (iff #643 #281)
-#639 := (iff #642 #644)
-#645 := [rewrite]: #639
-#648 := [monotonicity #645]: #646
-#650 := [monotonicity #648]: #647
-#343 := [trans #650 #637]: #647
-#649 := [quant-inst #42 #45 #47]: #287
-#359 := [mp #649 #343]: #286
-#573 := [unit-resolution #359 #676]: #281
-#630 := (not #281)
-#634 := (or #630 #134 #633)
-#631 := [def-axiom]: #634
-#570 := [unit-resolution #631 #573]: #574
-#575 := [unit-resolution #570 #583]: #633
-#361 := (or #644 #360)
-#347 := [def-axiom]: #361
-#561 := [unit-resolution #347 #575]: #360
-#579 := (or #585 #444 #597)
-#576 := [def-axiom]: #579
-#564 := [unit-resolution #576 #561]: #562
-#565 := [unit-resolution #564 #572]: #597
-#608 := (or #625 #661)
-#502 := [def-axiom]: #608
-#566 := [unit-resolution #502 #565]: #661
-#310 := (or #652 #318 #335)
-#315 := [def-axiom]: #310
-#563 := [unit-resolution #315 #566 #571]: #318
-#362 := (not #641)
-#253 := (or #644 #362)
-#632 := [def-axiom]: #253
-#567 := [unit-resolution #632 #575]: #362
-#503 := (or #625 #609)
-#504 := [def-axiom]: #503
-#547 := [unit-resolution #504 #565]: #609
-#613 := (or #612 #340 #641)
-#607 := [def-axiom]: #613
-#548 := [unit-resolution #607 #547 #567]: #612
-#445 := (or #587 #658 #487)
-#446 := [def-axiom]: #445
-#550 := [unit-resolution #446 #548 #563 #582]: false
-#551 := [lemma #550]: #134
-#337 := (or #334 #147)
-#325 := (or #334 #147 #245)
-#336 := [def-axiom]: #325
-#265 := [unit-resolution #336 #155]: #337
-#552 := [unit-resolution #265 #551]: #334
-#553 := (or #138 #652)
-#311 := (or #653 #138 #652)
-#654 := [def-axiom]: #311
-#554 := [unit-resolution #654 #584]: #553
-#555 := [unit-resolution #554 #552]: #652
-#659 := (or #655 #658)
-#660 := [def-axiom]: #659
-#556 := [unit-resolution #660 #555]: #658
-#614 := (or #587 #318 #612)
-#443 := [def-axiom]: #614
-#557 := [unit-resolution #443 #556 #582]: #612
-#610 := (or #487 #609)
-#611 := [def-axiom]: #610
-#558 := [unit-resolution #611 #557]: #609
-#656 := (or #655 #661)
-#662 := [def-axiom]: #656
-#559 := [unit-resolution #662 #555]: #661
-#594 := (or #597 #335 #340)
-#598 := [def-axiom]: #594
-#549 := [unit-resolution #598 #559 #558]: #597
-#560 := (or #147 #644)
-#635 := (or #630 #147 #644)
-#344 := [def-axiom]: #635
-#538 := [unit-resolution #344 #573]: #560
-#539 := [unit-resolution #538 #551]: #644
-#605 := (or #487 #362)
-#606 := [def-axiom]: #605
-#541 := [unit-resolution #606 #557]: #362
-#355 := (or #633 #444 #641)
-#356 := [def-axiom]: #355
-#542 := [unit-resolution #356 #541 #539]: #444
-#578 := (or #585 #360 #625)
-#588 := [def-axiom]: #578
-#543 := [unit-resolution #588 #542 #549]: #585
-[unit-resolution #466 #676 #543]: false
-unsat
-e18331b7b676705a2856a4af405fce965b0fd82f 153 0
-#2 := false
-decl f4 :: (-> S2 S3 S1)
-decl f11 :: S3
-#43 := f11
-decl f10 :: S2
-#42 := f10
-#48 := (f4 f10 f11)
-decl f1 :: S1
-#4 := f1
-#138 := (= f1 #48)
-#192 := (not #138)
-decl f9 :: S2
-#41 := f9
-#46 := (f4 f9 f11)
-#135 := (= f1 #46)
-#191 := (not #135)
-#193 := (or #191 #192)
-#194 := (not #193)
-#335 := [hypothesis]: #194
-decl f3 :: (-> S2 S2 S3 S1)
-#44 := (f3 f9 f10 f11)
-#131 := (= f1 #44)
-#150 := (not #131)
-#341 := (or #150 #193)
-#205 := (iff #131 #193)
-#141 := (and #135 #138)
-#151 := (iff #141 #150)
-#208 := (iff #151 #205)
-#200 := (iff #193 #131)
-#206 := (iff #200 #205)
-#207 := [rewrite]: #206
-#203 := (iff #151 #200)
-#197 := (iff #194 #150)
-#201 := (iff #197 #200)
-#202 := [rewrite]: #201
-#198 := (iff #151 #197)
-#195 := (iff #141 #194)
-#196 := [rewrite]: #195
-#199 := [monotonicity #196]: #198
-#204 := [trans #199 #202]: #203
-#209 := [trans #204 #207]: #208
-#49 := (= #48 f1)
-#47 := (= #46 f1)
-#50 := (and #47 #49)
-#45 := (= #44 f1)
-#51 := (iff #45 #50)
-#52 := (not #51)
-#154 := (iff #52 #151)
-#144 := (iff #131 #141)
-#147 := (not #144)
-#152 := (iff #147 #151)
-#153 := [rewrite]: #152
-#148 := (iff #52 #147)
-#145 := (iff #51 #144)
-#142 := (iff #50 #141)
-#139 := (iff #49 #138)
-#140 := [rewrite]: #139
-#136 := (iff #47 #135)
-#137 := [rewrite]: #136
-#143 := [monotonicity #137 #140]: #142
-#133 := (iff #45 #131)
-#134 := [rewrite]: #133
-#146 := [monotonicity #134 #143]: #145
-#149 := [monotonicity #146]: #148
-#155 := [trans #149 #153]: #154
-#130 := [asserted]: #52
-#158 := [mp #130 #155]: #151
-#210 := [mp #158 #209]: #205
-#348 := (not #205)
-#358 := (or #150 #193 #348)
-#362 := [def-axiom]: #358
-#678 := [unit-resolution #362 #210]: #341
-#467 := [unit-resolution #678 #335]: #150
-#334 := (or #131 #193)
-#680 := (iff #131 #194)
-#10 := (:var 0 S3)
-#9 := (:var 1 S2)
-#8 := (:var 2 S2)
-#11 := (f3 #8 #9 #10)
-#686 := (pattern #11)
-#15 := (f4 #9 #10)
-#79 := (= f1 #15)
-#183 := (not #79)
-#13 := (f4 #8 #10)
-#76 := (= f1 #13)
-#182 := (not #76)
-#166 := (or #182 #183)
-#167 := (not #166)
-#73 := (= f1 #11)
-#184 := (iff #73 #167)
-#687 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #686) #184)
-#187 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #184)
-#690 := (iff #187 #687)
-#688 := (iff #184 #184)
-#689 := [refl]: #688
-#691 := [quant-intro #689]: #690
-#82 := (and #76 #79)
-#85 := (iff #73 #82)
-#88 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #85)
-#188 := (iff #88 #187)
-#185 := (iff #85 #184)
-#168 := (iff #82 #167)
-#169 := [rewrite]: #168
-#186 := [monotonicity #169]: #185
-#189 := [quant-intro #186]: #188
-#172 := (~ #88 #88)
-#170 := (~ #85 #85)
-#171 := [refl]: #170
-#173 := [nnf-pos #171]: #172
-#16 := (= #15 f1)
-#14 := (= #13 f1)
-#17 := (and #14 #16)
-#12 := (= #11 f1)
-#18 := (iff #12 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
-#89 := (iff #19 #88)
-#86 := (iff #18 #85)
-#83 := (iff #17 #82)
-#80 := (iff #16 #79)
-#81 := [rewrite]: #80
-#77 := (iff #14 #76)
-#78 := [rewrite]: #77
-#84 := [monotonicity #78 #81]: #83
-#74 := (iff #12 #73)
-#75 := [rewrite]: #74
-#87 := [monotonicity #75 #84]: #86
-#90 := [quant-intro #87]: #89
-#72 := [asserted]: #19
-#93 := [mp #72 #90]: #88
-#157 := [mp~ #93 #173]: #88
-#190 := [mp #157 #189]: #187
-#692 := [mp #190 #691]: #687
-#674 := (not #687)
-#346 := (or #674 #680)
-#347 := [quant-inst #41 #42 #43]: #346
-#676 := [unit-resolution #347 #692]: #680
-#681 := (not #680)
-#682 := (or #681 #131 #193)
-#683 := [def-axiom]: #682
-#677 := [unit-resolution #683 #676]: #334
-#318 := [unit-resolution #677 #467 #335]: false
-#661 := [lemma #318]: #193
-#288 := (or #131 #194)
-#359 := (or #131 #194 #348)
-#360 := [def-axiom]: #359
-#361 := [unit-resolution #360 #210]: #288
-#322 := [unit-resolution #361 #661]: #131
-#323 := (or #150 #194)
-#684 := (or #681 #150 #194)
-#679 := [def-axiom]: #684
-#324 := [unit-resolution #679 #676]: #323
-[unit-resolution #324 #322 #661]: false
-unsat
-2f40e8acf872d44aceb8e8d3d683e7b0a1b857ff 141 0
-#2 := false
-decl f4 :: (-> S2 S3 S1)
-decl f10 :: S3
-#42 := f10
-decl f8 :: S2
-#36 := f8
-#231 := (f4 f8 f10)
-decl f1 :: S1
-#4 := f1
-#318 := (= f1 #231)
-#232 := (not #318)
-decl f9 :: S2
-#41 := f9
-#319 := (f4 f9 f10)
-#233 := (= f1 #319)
-#320 := (not #233)
-#311 := (or #320 #232)
-#322 := (not #311)
-decl f3 :: (-> S2 S2 S3 S1)
-#43 := (f3 f9 f8 f10)
-#125 := (= f1 #43)
-#323 := (iff #125 #322)
-#10 := (:var 0 S3)
-#9 := (:var 1 S2)
-#8 := (:var 2 S2)
-#11 := (f3 #8 #9 #10)
-#649 := (pattern #11)
-#15 := (f4 #9 #10)
-#73 := (= f1 #15)
-#166 := (not #73)
-#13 := (f4 #8 #10)
-#70 := (= f1 #13)
-#165 := (not #70)
-#149 := (or #165 #166)
-#150 := (not #149)
-#67 := (= f1 #11)
-#167 := (iff #67 #150)
-#650 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #649) #167)
-#170 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #167)
-#653 := (iff #170 #650)
-#651 := (iff #167 #167)
-#652 := [refl]: #651
-#654 := [quant-intro #652]: #653
-#76 := (and #70 #73)
-#79 := (iff #67 #76)
-#82 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #79)
-#171 := (iff #82 #170)
-#168 := (iff #79 #167)
-#151 := (iff #76 #150)
-#152 := [rewrite]: #151
-#169 := [monotonicity #152]: #168
-#172 := [quant-intro #169]: #171
-#155 := (~ #82 #82)
-#153 := (~ #79 #79)
-#154 := [refl]: #153
-#156 := [nnf-pos #154]: #155
-#16 := (= #15 f1)
-#14 := (= #13 f1)
-#17 := (and #14 #16)
-#12 := (= #11 f1)
-#18 := (iff #12 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
-#83 := (iff #19 #82)
-#80 := (iff #18 #79)
-#77 := (iff #17 #76)
-#74 := (iff #16 #73)
-#75 := [rewrite]: #74
-#71 := (iff #14 #70)
-#72 := [rewrite]: #71
-#78 := [monotonicity #72 #75]: #77
-#68 := (iff #12 #67)
-#69 := [rewrite]: #68
-#81 := [monotonicity #69 #78]: #80
-#84 := [quant-intro #81]: #83
-#66 := [asserted]: #19
-#87 := [mp #66 #84]: #82
-#140 := [mp~ #87 #156]: #82
-#173 := [mp #140 #172]: #170
-#655 := [mp #173 #654]: #650
-#321 := (not #650)
-#325 := (or #321 #323)
-#304 := [quant-inst #41 #36 #42]: #325
-#251 := [unit-resolution #304 #655]: #323
-#310 := (not #323)
-#324 := (or #310 #322)
-#44 := (= #43 f1)
-#45 := (not #44)
-#46 := (not #45)
-#137 := (iff #46 #125)
-#129 := (not #125)
-#132 := (not #129)
-#135 := (iff #132 #125)
-#136 := [rewrite]: #135
-#133 := (iff #46 #132)
-#130 := (iff #45 #129)
-#127 := (iff #44 #125)
-#128 := [rewrite]: #127
-#131 := [monotonicity #128]: #130
-#134 := [monotonicity #131]: #133
-#138 := [trans #134 #136]: #137
-#124 := [asserted]: #46
-#141 := [mp #124 #138]: #125
-#646 := (or #310 #129 #322)
-#647 := [def-axiom]: #646
-#640 := [unit-resolution #647 #141]: #324
-#281 := [unit-resolution #640 #251]: #322
-#298 := (or #311 #318)
-#430 := [def-axiom]: #298
-#624 := [unit-resolution #430 #281]: #318
-#37 := (f4 f8 #10)
-#670 := (pattern #37)
-#114 := (= f1 #37)
-#118 := (not #114)
-#671 := (forall (vars (?v0 S3)) (:pat #670) #118)
-#121 := (forall (vars (?v0 S3)) #118)
-#674 := (iff #121 #671)
-#672 := (iff #118 #118)
-#673 := [refl]: #672
-#675 := [quant-intro #673]: #674
-#147 := (~ #121 #121)
-#162 := (~ #118 #118)
-#163 := [refl]: #162
-#148 := [nnf-pos #163]: #147
-#38 := (= #37 f1)
-#39 := (not #38)
-#40 := (forall (vars (?v0 S3)) #39)
-#122 := (iff #40 #121)
-#119 := (iff #39 #118)
-#116 := (iff #38 #114)
-#117 := [rewrite]: #116
-#120 := [monotonicity #117]: #119
-#123 := [quant-intro #120]: #122
-#113 := [asserted]: #40
-#126 := [mp #113 #123]: #121
-#164 := [mp~ #126 #148]: #121
-#676 := [mp #164 #675]: #671
-#301 := (not #671)
-#639 := (or #301 #232)
-#297 := [quant-inst #42]: #639
-[unit-resolution #297 #676 #624]: false
-unsat
-fc29248879b25eb4ac36871e75531b9c02a89803 165 0
-#2 := false
-decl f4 :: (-> S2 S3 S1)
-decl f10 :: S3
-#42 := f10
-decl f9 :: S2
-#41 := f9
-#45 := (f4 f9 f10)
-decl f1 :: S1
-#4 := f1
-#131 := (= f1 #45)
-#327 := (not #131)
-decl f3 :: (-> S2 S2 S3 S1)
-decl f7 :: S2
-#32 := f7
-#43 := (f3 f9 f7 f10)
-#127 := (= f1 #43)
-#331 := (f4 f7 f10)
-#328 := (= f1 #331)
-#332 := (not #328)
-#305 := [hypothesis]: #332
-#10 := (:var 0 S3)
-#33 := (f4 f7 #10)
-#670 := (pattern #33)
-#108 := (= f1 #33)
-#671 := (forall (vars (?v0 S3)) (:pat #670) #108)
-#112 := (forall (vars (?v0 S3)) #108)
-#674 := (iff #112 #671)
-#672 := (iff #108 #108)
-#673 := [refl]: #672
-#675 := [quant-intro #673]: #674
-#152 := (~ #112 #112)
-#166 := (~ #108 #108)
-#167 := [refl]: #166
-#153 := [nnf-pos #167]: #152
-#34 := (= #33 f1)
-#35 := (forall (vars (?v0 S3)) #34)
-#113 := (iff #35 #112)
-#110 := (iff #34 #108)
-#111 := [rewrite]: #110
-#114 := [quant-intro #111]: #113
-#107 := [asserted]: #35
-#117 := [mp #107 #114]: #112
-#168 := [mp~ #117 #153]: #112
-#676 := [mp #168 #675]: #671
-#293 := (not #671)
-#294 := (or #293 #328)
-#295 := [quant-inst #42]: #294
-#437 := [unit-resolution #295 #676 #305]: false
-#633 := [lemma #437]: #328
-#140 := (not #127)
-#634 := [hypothesis]: #140
-#326 := (or #131 #127)
-#141 := (iff #131 #140)
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (iff #44 #46)
-#48 := (not #47)
-#144 := (iff #48 #141)
-#134 := (iff #127 #131)
-#137 := (not #134)
-#142 := (iff #137 #141)
-#143 := [rewrite]: #142
-#138 := (iff #48 #137)
-#135 := (iff #47 #134)
-#132 := (iff #46 #131)
-#133 := [rewrite]: #132
-#129 := (iff #44 #127)
-#130 := [rewrite]: #129
-#136 := [monotonicity #130 #133]: #135
-#139 := [monotonicity #136]: #138
-#145 := [trans #139 #143]: #144
-#126 := [asserted]: #48
-#148 := [mp #126 #145]: #141
-#238 := (not #141)
-#325 := (or #131 #127 #238)
-#239 := [def-axiom]: #325
-#240 := [unit-resolution #239 #148]: #326
-#635 := [unit-resolution #240 #634]: #131
-#311 := (or #327 #332)
-#637 := (or #127 #311)
-#648 := (not #311)
-#650 := (iff #127 #648)
-#9 := (:var 1 S2)
-#8 := (:var 2 S2)
-#11 := (f3 #8 #9 #10)
-#656 := (pattern #11)
-#15 := (f4 #9 #10)
-#75 := (= f1 #15)
-#173 := (not #75)
-#13 := (f4 #8 #10)
-#72 := (= f1 #13)
-#172 := (not #72)
-#156 := (or #172 #173)
-#157 := (not #156)
-#69 := (= f1 #11)
-#174 := (iff #69 #157)
-#657 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #656) #174)
-#177 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #174)
-#660 := (iff #177 #657)
-#658 := (iff #174 #174)
-#659 := [refl]: #658
-#661 := [quant-intro #659]: #660
-#78 := (and #72 #75)
-#81 := (iff #69 #78)
-#84 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #81)
-#178 := (iff #84 #177)
-#175 := (iff #81 #174)
-#158 := (iff #78 #157)
-#159 := [rewrite]: #158
-#176 := [monotonicity #159]: #175
-#179 := [quant-intro #176]: #178
-#162 := (~ #84 #84)
-#160 := (~ #81 #81)
-#161 := [refl]: #160
-#163 := [nnf-pos #161]: #162
+#40 := f9
+#44 := (f4 f9 f10)
+decl f1 :: S1
+#4 := f1
+#130 := (= f1 #44)
+#326 := (not #130)
+decl f8 :: (-> S4 S4 S3 S1)
+decl f5 :: S4
+#13 := f5
+#42 := (f8 f9 f5 f10)
+#126 := (= f1 #42)
+#330 := (f4 f5 f10)
+#327 := (= f1 #330)
+#331 := (not #327)
+#304 := [hypothesis]: #331
+#14 := (:var 0 S3)
+#15 := (f4 f5 #14)
+#662 := (pattern #15)
+#78 := (= f1 #15)
+#663 := (forall (vars (?v0 S3)) (:pat #662) #78)
+#82 := (forall (vars (?v0 S3)) #78)
+#666 := (iff #82 #663)
+#664 := (iff #78 #78)
+#665 := [refl]: #664
+#667 := [quant-intro #665]: #666
+#149 := (~ #82 #82)
+#148 := (~ #78 #78)
+#163 := [refl]: #148
+#150 := [nnf-pos #163]: #149
 #16 := (= #15 f1)
-#14 := (= #13 f1)
-#17 := (and #14 #16)
-#12 := (= #11 f1)
-#18 := (iff #12 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
-#85 := (iff #19 #84)
-#82 := (iff #18 #81)
-#79 := (iff #17 #78)
-#76 := (iff #16 #75)
-#77 := [rewrite]: #76
-#73 := (iff #14 #72)
-#74 := [rewrite]: #73
-#80 := [monotonicity #74 #77]: #79
-#70 := (iff #12 #69)
-#71 := [rewrite]: #70
-#83 := [monotonicity #71 #80]: #82
-#86 := [quant-intro #83]: #85
-#68 := [asserted]: #19
-#89 := [mp #68 #86]: #84
-#147 := [mp~ #89 #163]: #84
-#180 := [mp #147 #179]: #177
-#662 := [mp #180 #661]: #657
-#644 := (not #657)
-#316 := (or #644 #650)
-#317 := [quant-inst #41 #32 #42]: #316
-#636 := [unit-resolution #317 #662]: #650
-#645 := (not #650)
-#303 := (or #645 #127 #311)
-#308 := [def-axiom]: #303
-#632 := [unit-resolution #308 #636]: #637
-#638 := [unit-resolution #632 #634]: #311
-#649 := (or #648 #327 #332)
-#655 := [def-axiom]: #649
-#274 := [unit-resolution #655 #638 #635 #633]: false
-#639 := [lemma #274]: #127
-#330 := (or #327 #140)
-#318 := (or #327 #140 #238)
-#329 := [def-axiom]: #318
-#258 := [unit-resolution #329 #148]: #330
-#641 := [unit-resolution #258 #639]: #327
-#279 := (or #140 #648)
-#646 := (or #645 #140 #648)
-#304 := [def-axiom]: #646
-#280 := [unit-resolution #304 #636]: #279
-#642 := [unit-resolution #280 #639]: #648
-#651 := (or #311 #131)
-#652 := [def-axiom]: #651
-[unit-resolution #652 #642 #641]: false
-unsat
-cde3f1655461765c0379419d9bc70392d3f61227 164 0
-#2 := false
-decl f3 :: (-> S2 S2 S3 S1)
-decl f11 :: S3
-#43 := f11
-decl f9 :: S2
-#41 := f9
-decl f10 :: S2
-#42 := f10
-#46 := (f3 f10 f9 f11)
-decl f1 :: S1
-#4 := f1
-#132 := (= f1 #46)
-#328 := (not #132)
-#44 := (f3 f9 f10 f11)
-#128 := (= f1 #44)
-#141 := (not #128)
-#630 := [hypothesis]: #141
-#327 := (or #132 #128)
-#142 := (iff #132 #141)
-#47 := (= #46 f1)
-#45 := (= #44 f1)
-#48 := (iff #45 #47)
-#49 := (not #48)
-#145 := (iff #49 #142)
-#135 := (iff #128 #132)
-#138 := (not #135)
-#143 := (iff #138 #142)
-#144 := [rewrite]: #143
-#139 := (iff #49 #138)
-#136 := (iff #48 #135)
-#133 := (iff #47 #132)
-#134 := [rewrite]: #133
-#130 := (iff #45 #128)
-#131 := [rewrite]: #130
-#137 := [monotonicity #131 #134]: #136
-#140 := [monotonicity #137]: #139
-#146 := [trans #140 #144]: #145
-#127 := [asserted]: #49
-#149 := [mp #127 #146]: #142
-#239 := (not #142)
-#326 := (or #132 #128 #239)
-#240 := [def-axiom]: #326
-#241 := [unit-resolution #240 #149]: #327
-#631 := [unit-resolution #241 #630]: #132
-decl f4 :: (-> S2 S3 S1)
-#312 := (f4 f10 f11)
-#649 := (= f1 #312)
-#651 := (not #649)
-#332 := (f4 f9 f11)
-#329 := (= f1 #332)
-#333 := (not #329)
-#317 := (or #333 #651)
-#628 := (or #128 #317)
-#653 := (not #317)
-#644 := (iff #128 #653)
-#10 := (:var 0 S3)
-#9 := (:var 1 S2)
-#8 := (:var 2 S2)
-#11 := (f3 #8 #9 #10)
-#657 := (pattern #11)
-#15 := (f4 #9 #10)
-#76 := (= f1 #15)
-#174 := (not #76)
-#13 := (f4 #8 #10)
-#73 := (= f1 #13)
-#173 := (not #73)
-#157 := (or #173 #174)
-#158 := (not #157)
-#70 := (= f1 #11)
-#175 := (iff #70 #158)
-#658 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #657) #175)
-#178 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #175)
-#661 := (iff #178 #658)
-#659 := (iff #175 #175)
-#660 := [refl]: #659
-#662 := [quant-intro #660]: #661
-#79 := (and #73 #76)
-#82 := (iff #70 #79)
-#85 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #82)
-#179 := (iff #85 #178)
-#176 := (iff #82 #175)
-#159 := (iff #79 #158)
-#160 := [rewrite]: #159
-#177 := [monotonicity #160]: #176
-#180 := [quant-intro #177]: #179
-#163 := (~ #85 #85)
-#161 := (~ #82 #82)
-#162 := [refl]: #161
-#164 := [nnf-pos #162]: #163
-#16 := (= #15 f1)
-#14 := (= #13 f1)
-#17 := (and #14 #16)
-#12 := (= #11 f1)
-#18 := (iff #12 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
-#86 := (iff #19 #85)
-#83 := (iff #18 #82)
-#80 := (iff #17 #79)
-#77 := (iff #16 #76)
-#78 := [rewrite]: #77
-#74 := (iff #14 #73)
-#75 := [rewrite]: #74
-#81 := [monotonicity #75 #78]: #80
-#71 := (iff #12 #70)
-#72 := [rewrite]: #71
-#84 := [monotonicity #72 #81]: #83
-#87 := [quant-intro #84]: #86
-#69 := [asserted]: #19
-#90 := [mp #69 #87]: #85
-#148 := [mp~ #90 #164]: #85
-#181 := [mp #148 #180]: #178
-#663 := [mp #181 #662]: #658
-#304 := (not #658)
-#337 := (or #304 #644)
-#353 := [quant-inst #41 #42 #43]: #337
-#624 := [unit-resolution #353 #663]: #644
-#354 := (not #644)
-#355 := (or #354 #128 #317)
-#341 := [def-axiom]: #355
-#625 := [unit-resolution #341 #624]: #628
-#629 := [unit-resolution #625 #630]: #317
-#339 := (or #328 #653)
-#650 := (iff #132 #653)
-#309 := (or #304 #650)
-#306 := (or #651 #333)
-#438 := (not #306)
-#645 := (iff #132 #438)
-#647 := (or #304 #645)
-#648 := (iff #647 #309)
-#632 := (iff #309 #309)
-#293 := [rewrite]: #632
-#656 := (iff #645 #650)
-#654 := (iff #438 #653)
-#318 := (iff #306 #317)
-#652 := [rewrite]: #318
-#655 := [monotonicity #652]: #654
-#646 := [monotonicity #655]: #656
-#289 := [monotonicity #646]: #648
-#294 := [trans #289 #293]: #648
-#305 := [quant-inst #42 #41 #43]: #647
-#295 := [mp #305 #294]: #309
-#338 := [unit-resolution #295 #663]: #650
-#633 := (not #650)
-#640 := (or #633 #328 #653)
-#642 := [def-axiom]: #640
-#340 := [unit-resolution #642 #338]: #339
-#342 := [unit-resolution #340 #629 #631]: false
-#620 := [lemma #342]: #128
-#331 := (or #328 #141)
-#319 := (or #328 #141 #239)
-#330 := [def-axiom]: #319
-#259 := [unit-resolution #330 #149]: #331
-#621 := [unit-resolution #259 #620]: #328
-#334 := (or #141 #653)
-#356 := (or #354 #141 #653)
-#247 := [def-axiom]: #356
-#618 := [unit-resolution #247 #624]: #334
-#622 := [unit-resolution #618 #620]: #653
-#619 := (or #132 #317)
-#639 := (or #633 #132 #317)
-#275 := [def-axiom]: #639
-#623 := [unit-resolution #275 #338]: #619
-[unit-resolution #623 #622 #621]: false
-unsat
-0602b5dc7726bda4b36d0dee5a2dbb8b5b433e1c 142 0
-#2 := false
-decl f3 :: (-> S2 S2 S3 S1)
-decl f10 :: S3
-#42 := f10
-decl f9 :: S2
-#41 := f9
-#43 := (f3 f9 f9 f10)
-decl f1 :: S1
-#4 := f1
-#127 := (= f1 #43)
-#140 := (not #127)
-#636 := [hypothesis]: #140
-decl f4 :: (-> S2 S3 S1)
-#45 := (f4 f9 f10)
-#131 := (= f1 #45)
-#326 := (or #131 #127)
-#141 := (iff #131 #140)
-#46 := (= #45 f1)
-#44 := (= #43 f1)
-#47 := (iff #44 #46)
-#48 := (not #47)
-#144 := (iff #48 #141)
-#134 := (iff #127 #131)
-#137 := (not #134)
-#142 := (iff #137 #141)
-#143 := [rewrite]: #142
-#138 := (iff #48 #137)
-#135 := (iff #47 #134)
-#132 := (iff #46 #131)
-#133 := [rewrite]: #132
-#129 := (iff #44 #127)
-#130 := [rewrite]: #129
-#136 := [monotonicity #130 #133]: #135
-#139 := [monotonicity #136]: #138
-#145 := [trans #139 #143]: #144
-#126 := [asserted]: #48
-#148 := [mp #126 #145]: #141
-#238 := (not #141)
-#325 := (or #131 #127 #238)
-#239 := [def-axiom]: #325
-#240 := [unit-resolution #239 #148]: #326
-#637 := [unit-resolution #240 #636]: #131
-#327 := (not #131)
-#638 := (or #127 #327)
-#10 := (:var 0 S3)
-#9 := (:var 1 S2)
-#8 := (:var 2 S2)
-#11 := (f3 #8 #9 #10)
-#656 := (pattern #11)
-#15 := (f4 #9 #10)
-#75 := (= f1 #15)
-#173 := (not #75)
-#13 := (f4 #8 #10)
-#72 := (= f1 #13)
-#172 := (not #72)
-#156 := (or #172 #173)
-#157 := (not #156)
-#69 := (= f1 #11)
-#174 := (iff #69 #157)
-#657 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #656) #174)
-#177 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #174)
-#660 := (iff #177 #657)
-#658 := (iff #174 #174)
-#659 := [refl]: #658
-#661 := [quant-intro #659]: #660
-#78 := (and #72 #75)
-#81 := (iff #69 #78)
-#84 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #81)
-#178 := (iff #84 #177)
-#175 := (iff #81 #174)
-#158 := (iff #78 #157)
-#159 := [rewrite]: #158
-#176 := [monotonicity #159]: #175
-#179 := [quant-intro #176]: #178
-#162 := (~ #84 #84)
-#160 := (~ #81 #81)
-#161 := [refl]: #160
-#163 := [nnf-pos #161]: #162
-#16 := (= #15 f1)
-#14 := (= #13 f1)
-#17 := (and #14 #16)
-#12 := (= #11 f1)
-#18 := (iff #12 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #18)
-#85 := (iff #19 #84)
-#82 := (iff #18 #81)
-#79 := (iff #17 #78)
-#76 := (iff #16 #75)
-#77 := [rewrite]: #76
-#73 := (iff #14 #72)
-#74 := [rewrite]: #73
-#80 := [monotonicity #74 #77]: #79
-#70 := (iff #12 #69)
-#71 := [rewrite]: #70
-#83 := [monotonicity #71 #80]: #82
-#86 := [quant-intro #83]: #85
-#68 := [asserted]: #19
-#89 := [mp #68 #86]: #84
-#147 := [mp~ #89 #163]: #84
-#180 := [mp #147 #179]: #177
-#662 := [mp #180 #661]: #657
-#654 := (not #657)
-#649 := (or #654 #134)
-#331 := (or #327 #327)
-#328 := (not #331)
-#332 := (iff #127 #328)
-#655 := (or #654 #332)
-#303 := (iff #655 #649)
-#646 := (iff #649 #649)
-#304 := [rewrite]: #646
-#652 := (iff #332 #134)
-#317 := (iff #328 #131)
-#650 := (not #327)
-#644 := (iff #650 #131)
-#316 := [rewrite]: #644
-#305 := (iff #328 #650)
-#311 := (iff #331 #327)
-#648 := [rewrite]: #311
-#437 := [monotonicity #648]: #305
-#651 := [trans #437 #316]: #317
-#653 := [monotonicity #651]: #652
-#308 := [monotonicity #653]: #303
-#647 := [trans #308 #304]: #303
-#645 := [quant-inst #41 #41 #42]: #655
-#288 := [mp #645 #647]: #649
-#632 := [unit-resolution #288 #662]: #134
-#631 := (or #137 #127 #327)
-#292 := [def-axiom]: #631
-#274 := [unit-resolution #292 #632]: #638
-#639 := [unit-resolution #274 #637 #636]: false
-#641 := [lemma #639]: #127
-#330 := (or #327 #140)
-#318 := (or #327 #140 #238)
-#329 := [def-axiom]: #318
-#258 := [unit-resolution #329 #148]: #330
-#279 := [unit-resolution #258 #641]: #327
-#280 := (or #140 #131)
-#293 := (or #137 #140 #131)
-#294 := [def-axiom]: #293
-#642 := [unit-resolution #294 #632]: #280
-[unit-resolution #642 #279 #641]: false
-unsat
-2197c1dae16f488eb4bfcbae6c35e5ab268a4235 280 0
-#2 := false
-decl f3 :: (-> S2 S3 S1)
-decl f12 :: S3
-#47 := f12
-decl f4 :: (-> S2 S2 S2)
-decl f10 :: S2
-#43 := f10
-decl f9 :: S2
-#42 := f9
-#50 := (f4 f9 f10)
-#318 := (f3 #50 f12)
-decl f1 :: S1
-#4 := f1
-#655 := (= f1 #318)
-#253 := (f3 f10 f12)
-#632 := (= f1 #253)
-#629 := (not #632)
-#343 := (f3 f9 f12)
-#359 := (= f1 #343)
-#360 := (not #359)
-#618 := (or #360 #629)
-#619 := (not #618)
-#615 := (iff #619 #655)
-#586 := (not #615)
-decl f11 :: S2
-#44 := f11
-#338 := (f3 f11 f12)
-#335 := (= f1 #338)
-#339 := (not #335)
-#488 := (or #339 #629)
-#497 := (not #488)
-#45 := (f4 f10 f11)
-#650 := (f3 #45 f12)
-#636 := (= f1 #650)
-#498 := (iff #497 #636)
-#591 := (not #498)
-#571 := [hypothesis]: #591
-#11 := (:var 0 S3)
-#9 := (:var 1 S2)
-#8 := (:var 2 S2)
-#10 := (f4 #8 #9)
-#12 := (f3 #10 #11)
-#663 := (pattern #12)
-#16 := (f3 #9 #11)
-#82 := (= f1 #16)
-#180 := (not #82)
-#14 := (f3 #8 #11)
-#79 := (= f1 #14)
-#179 := (not #79)
-#163 := (or #179 #180)
-#164 := (not #163)
-#76 := (= f1 #12)
-#181 := (iff #76 #164)
-#664 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) (:pat #663) #181)
-#184 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #181)
-#667 := (iff #184 #664)
-#665 := (iff #181 #181)
-#666 := [refl]: #665
-#668 := [quant-intro #666]: #667
-#85 := (and #79 #82)
-#88 := (iff #76 #85)
-#91 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #88)
-#185 := (iff #91 #184)
-#182 := (iff #88 #181)
-#165 := (iff #85 #164)
-#166 := [rewrite]: #165
-#183 := [monotonicity #166]: #182
-#186 := [quant-intro #183]: #185
-#169 := (~ #91 #91)
-#167 := (~ #88 #88)
-#168 := [refl]: #167
-#170 := [nnf-pos #168]: #169
-#17 := (= #16 f1)
-#15 := (= #14 f1)
-#18 := (and #15 #17)
-#13 := (= #12 f1)
-#19 := (iff #13 #18)
-#20 := (forall (vars (?v0 S2) (?v1 S2) (?v2 S3)) #19)
-#92 := (iff #20 #91)
-#89 := (iff #19 #88)
-#86 := (iff #18 #85)
+#17 := (forall (vars (?v0 S3)) #16)
 #83 := (iff #17 #82)
-#84 := [rewrite]: #83
-#80 := (iff #15 #79)
+#80 := (iff #16 #78)
 #81 := [rewrite]: #80
-#87 := [monotonicity #81 #84]: #86
-#77 := (iff #13 #76)
-#78 := [rewrite]: #77
-#90 := [monotonicity #78 #87]: #89
-#93 := [quant-intro #90]: #92
-#75 := [asserted]: #20
-#96 := [mp #75 #93]: #91
-#154 := [mp~ #96 #170]: #91
-#187 := [mp #154 #186]: #184
-#669 := [mp #187 #668]: #664
-#310 := (not #664)
-#502 := (or #310 #498)
-#604 := (or #629 #339)
-#486 := (not #604)
-#487 := (iff #636 #486)
-#503 := (or #310 #487)
-#597 := (iff #503 #502)
-#598 := (iff #502 #502)
-#585 := [rewrite]: #598
-#500 := (iff #487 #498)
-#596 := (iff #636 #497)
-#499 := (iff #596 #498)
-#492 := [rewrite]: #499
-#481 := (iff #487 #596)
-#592 := (iff #486 #497)
-#447 := (iff #604 #488)
-#595 := [rewrite]: #447
-#593 := [monotonicity #595]: #592
-#496 := [monotonicity #593]: #481
-#501 := [trans #496 #492]: #500
-#594 := [monotonicity #501]: #597
-#587 := [trans #594 #585]: #597
-#504 := [quant-inst #43 #44 #47]: #503
-#579 := [mp #504 #587]: #502
-#572 := [unit-resolution #579 #669 #571]: false
-#573 := [lemma #572]: #498
-#637 := (not #636)
-#361 := (or #360 #637)
-#347 := (not #361)
-#46 := (f4 f9 #45)
-#48 := (f3 #46 f12)
-#134 := (= f1 #48)
-#147 := (not #134)
-#574 := [hypothesis]: #147
-#575 := (or #134 #361)
-#362 := (iff #134 #347)
-#633 := (or #310 #362)
-#355 := [quant-inst #42 #45 #47]: #633
-#570 := [unit-resolution #355 #669]: #362
-#345 := (not #362)
-#346 := (or #345 #134 #361)
-#348 := [def-axiom]: #346
-#561 := [unit-resolution #348 #570]: #575
-#562 := [unit-resolution #561 #574]: #361
-#601 := (or #310 #615)
-#620 := (iff #655 #619)
-#617 := (or #310 #620)
-#622 := (iff #617 #601)
-#465 := (iff #601 #601)
-#466 := [rewrite]: #465
-#616 := (iff #620 #615)
-#621 := [rewrite]: #616
-#464 := [monotonicity #621]: #622
-#608 := [trans #464 #466]: #622
-#623 := [quant-inst #42 #43 #47]: #617
-#609 := [mp #623 #608]: #601
-#564 := [unit-resolution #609 #669]: #615
-#550 := (or #586 #619)
-#657 := (not #655)
-#323 := (or #339 #657)
-#659 := (not #323)
-#51 := (f4 #50 f11)
-#52 := (f3 #51 f12)
-#138 := (= f1 #52)
-#333 := (or #138 #134)
-#148 := (iff #138 #147)
-#53 := (= #52 f1)
-#49 := (= #48 f1)
-#54 := (iff #49 #53)
-#55 := (not #54)
-#151 := (iff #55 #148)
-#141 := (iff #134 #138)
-#144 := (not #141)
-#149 := (iff #144 #148)
-#150 := [rewrite]: #149
-#145 := (iff #55 #144)
-#142 := (iff #54 #141)
-#139 := (iff #53 #138)
-#140 := [rewrite]: #139
-#136 := (iff #49 #134)
-#137 := [rewrite]: #136
-#143 := [monotonicity #137 #140]: #142
-#146 := [monotonicity #143]: #145
-#152 := [trans #146 #150]: #151
-#133 := [asserted]: #55
-#155 := [mp #133 #152]: #148
-#245 := (not #148)
-#332 := (or #138 #134 #245)
-#246 := [def-axiom]: #332
-#247 := [unit-resolution #246 #155]: #333
-#565 := [unit-resolution #247 #574]: #138
-#334 := (not #138)
-#563 := (or #334 #659)
-#656 := (iff #138 #659)
-#315 := (or #310 #656)
-#312 := (or #657 #339)
-#444 := (not #312)
-#651 := (iff #138 #444)
-#653 := (or #310 #651)
-#654 := (iff #653 #315)
-#638 := (iff #315 #315)
-#299 := [rewrite]: #638
-#662 := (iff #651 #656)
-#660 := (iff #444 #659)
-#324 := (iff #312 #323)
-#658 := [rewrite]: #324
-#661 := [monotonicity #658]: #660
-#652 := [monotonicity #661]: #662
-#295 := [monotonicity #652]: #654
-#300 := [trans #295 #299]: #654
-#311 := [quant-inst #50 #44 #47]: #653
-#301 := [mp #311 #300]: #315
-#566 := [unit-resolution #301 #669]: #656
-#639 := (not #656)
-#646 := (or #639 #334 #659)
-#648 := [def-axiom]: #646
-#567 := [unit-resolution #648 #566]: #563
-#547 := [unit-resolution #567 #565]: #659
-#641 := (or #323 #655)
-#642 := [def-axiom]: #641
-#548 := [unit-resolution #642 #547]: #655
-#580 := (or #586 #619 #657)
-#581 := [def-axiom]: #580
-#551 := [unit-resolution #581 #548]: #550
-#552 := [unit-resolution #551 #564]: #619
-#610 := (or #618 #359)
-#576 := [def-axiom]: #610
-#553 := [unit-resolution #576 #552]: #359
-#635 := (or #347 #360 #637)
-#344 := [def-axiom]: #635
-#554 := [unit-resolution #344 #553 #562]: #637
-#302 := (or #323 #335)
-#640 := [def-axiom]: #302
-#555 := [unit-resolution #640 #547]: #335
-#578 := (or #618 #632)
-#588 := [def-axiom]: #578
-#556 := [unit-resolution #588 #552]: #632
-#613 := (or #497 #339 #629)
-#607 := [def-axiom]: #613
-#557 := [unit-resolution #607 #556 #555]: #497
-#445 := (or #591 #488 #636)
-#446 := [def-axiom]: #445
-#558 := [unit-resolution #446 #557 #554 #573]: false
-#559 := [lemma #558]: #134
-#549 := (or #147 #347)
-#626 := (or #345 #147 #347)
-#627 := [def-axiom]: #626
-#560 := [unit-resolution #627 #570]: #549
-#538 := [unit-resolution #560 #559]: #347
-#634 := (or #361 #636)
-#631 := [def-axiom]: #634
-#539 := [unit-resolution #631 #538]: #636
-#614 := (or #591 #497 #637)
-#443 := [def-axiom]: #614
-#541 := [unit-resolution #443 #539 #573]: #497
-#606 := (or #488 #632)
-#612 := [def-axiom]: #606
-#542 := [unit-resolution #612 #541]: #632
-#356 := (or #361 #359)
-#630 := [def-axiom]: #356
-#543 := [unit-resolution #630 #538]: #359
-#589 := (or #619 #360 #629)
-#590 := [def-axiom]: #589
-#544 := [unit-resolution #590 #543 #542]: #619
-#337 := (or #334 #147)
-#325 := (or #334 #147 #245)
-#336 := [def-axiom]: #325
-#265 := [unit-resolution #336 #155]: #337
-#545 := [unit-resolution #265 #559]: #334
-#540 := (or #138 #323)
-#645 := (or #639 #138 #323)
-#281 := [def-axiom]: #645
-#546 := [unit-resolution #281 #566]: #540
-#532 := [unit-resolution #546 #545]: #323
-#611 := (or #488 #335)
-#605 := [def-axiom]: #611
-#528 := [unit-resolution #605 #541]: #335
-#643 := (or #659 #339 #657)
-#644 := [def-axiom]: #643
-#529 := [unit-resolution #644 #528 #532]: #657
-#582 := (or #586 #618 #655)
-#583 := [def-axiom]: #582
-#530 := [unit-resolution #583 #529 #544]: #586
-[unit-resolution #609 #669 #530]: false
-unsat
-2b2ce778241d0cd9017eb9658fd16ee31fe3f28e 18 0
-#2 := false
-decl f9 :: S8
-#41 := f9
-#42 := (= f9 f9)
-#43 := (not #42)
-#130 := (iff #43 false)
-#1 := true
-#125 := (not true)
-#128 := (iff #125 false)
+#84 := [quant-intro #81]: #83
+#77 := [asserted]: #17
+#87 := [mp #77 #84]: #82
+#164 := [mp~ #87 #150]: #82
+#668 := [mp #164 #667]: #663
+#292 := (not #663)
+#293 := (or #292 #327)
+#294 := [quant-inst #41]: #293
+#436 := [unit-resolution #294 #668 #304]: false
+#632 := [lemma #436]: #327
+#139 := (not #126)
+#633 := [hypothesis]: #139
+#325 := (or #130 #126)
+#140 := (iff #130 #139)
+#45 := (= #44 f1)
+#43 := (= #42 f1)
+#46 := (iff #43 #45)
+#47 := (not #46)
+#143 := (iff #47 #140)
+#133 := (iff #126 #130)
+#136 := (not #133)
+#141 := (iff #136 #140)
+#142 := [rewrite]: #141
+#137 := (iff #47 #136)
+#134 := (iff #46 #133)
+#131 := (iff #45 #130)
+#132 := [rewrite]: #131
+#128 := (iff #43 #126)
+#129 := [rewrite]: #128
+#135 := [monotonicity #129 #132]: #134
+#138 := [monotonicity #135]: #137
+#144 := [trans #138 #142]: #143
+#125 := [asserted]: #47
+#147 := [mp #125 #144]: #140
+#237 := (not #140)
+#324 := (or #130 #126 #237)
+#238 := [def-axiom]: #324
+#239 := [unit-resolution #238 #147]: #325
+#634 := [unit-resolution #239 #633]: #130
+#310 := (or #326 #331)
+#636 := (or #126 #310)
+#647 := (not #310)
+#649 := (iff #126 #647)
+#30 := (:var 1 S4)
+#29 := (:var 2 S4)
+#31 := (f8 #29 #30 #14)
+#676 := (pattern #31)
+#35 := (f4 #30 #14)
+#113 := (= f1 #35)
+#172 := (not #113)
+#33 := (f4 #29 #14)
+#110 := (= f1 #33)
+#171 := (not #110)
+#155 := (or #171 #172)
+#156 := (not #155)
+#106 := (= f1 #31)
+#173 := (iff #106 #156)
+#677 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) (:pat #676) #173)
+#176 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #173)
+#680 := (iff #176 #677)
+#678 := (iff #173 #173)
+#679 := [refl]: #678
+#681 := [quant-intro #679]: #680
+#116 := (and #110 #113)
+#119 := (iff #106 #116)
+#122 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #119)
+#177 := (iff #122 #176)
+#174 := (iff #119 #173)
+#157 := (iff #116 #156)
+#158 := [rewrite]: #157
+#175 := [monotonicity #158]: #174
+#178 := [quant-intro #175]: #177
+#153 := (~ #122 #122)
+#168 := (~ #119 #119)
+#169 := [refl]: #168
+#154 := [nnf-pos #169]: #153
+#36 := (= #35 f1)
+#34 := (= #33 f1)
+#37 := (and #34 #36)
+#32 := (= #31 f1)
+#38 := (iff #32 #37)
+#39 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S3)) #38)
+#123 := (iff #39 #122)
+#120 := (iff #38 #119)
+#117 := (iff #37 #116)
+#114 := (iff #36 #113)
+#115 := [rewrite]: #114
+#111 := (iff #34 #110)
+#112 := [rewrite]: #111
+#118 := [monotonicity #112 #115]: #117
+#108 := (iff #32 #106)
+#109 := [rewrite]: #108
+#121 := [monotonicity #109 #118]: #120
+#124 := [quant-intro #121]: #123
+#105 := [asserted]: #39
+#127 := [mp #105 #124]: #122
+#170 := [mp~ #127 #154]: #122
+#179 := [mp #170 #178]: #176
+#682 := [mp #179 #681]: #677
+#643 := (not #677)
+#315 := (or #643 #649)
+#316 := [quant-inst #40 #13 #41]: #315
+#635 := [unit-resolution #316 #682]: #649
+#644 := (not #649)
+#302 := (or #644 #126 #310)
+#307 := [def-axiom]: #302
+#631 := [unit-resolution #307 #635]: #636
+#637 := [unit-resolution #631 #633]: #310
+#648 := (or #647 #326 #331)
+#654 := [def-axiom]: #648
+#273 := [unit-resolution #654 #637 #634 #632]: false
+#638 := [lemma #273]: #126
+#329 := (or #326 #139)
+#317 := (or #326 #139 #237)
+#328 := [def-axiom]: #317
+#257 := [unit-resolution #328 #147]: #329
+#640 := [unit-resolution #257 #638]: #326
+#278 := (or #139 #647)
+#645 := (or #644 #139 #647)
+#303 := [def-axiom]: #645
+#279 := [unit-resolution #303 #635]: #278
+#641 := [unit-resolution #279 #638]: #647
+#650 := (or #310 #130)
+#651 := [def-axiom]: #650
+[unit-resolution #651 #641 #640]: false
+unsat
+600bc627f2a337ab9492b3414ff9a405597dcbc3 164 0
+#2 := false
+decl f7 :: (-> S4 S4 S5 S1)
+decl f11 :: S5
+#41 := f11
+decl f9 :: S4
+#39 := f9
+decl f10 :: S4
+#40 := f10
+#44 := (f7 f10 f9 f11)
+decl f1 :: S1
+#4 := f1
+#130 := (= f1 #44)
+#326 := (not #130)
+#42 := (f7 f9 f10 f11)
+#126 := (= f1 #42)
+#139 := (not #126)
+#628 := [hypothesis]: #139
+#325 := (or #130 #126)
+#140 := (iff #130 #139)
+#45 := (= #44 f1)
+#43 := (= #42 f1)
+#46 := (iff #43 #45)
+#47 := (not #46)
+#143 := (iff #47 #140)
+#133 := (iff #126 #130)
+#136 := (not #133)
+#141 := (iff #136 #140)
+#142 := [rewrite]: #141
+#137 := (iff #47 #136)
+#134 := (iff #46 #133)
+#131 := (iff #45 #130)
+#132 := [rewrite]: #131
+#128 := (iff #43 #126)
 #129 := [rewrite]: #128
-#126 := (iff #43 #125)
-#122 := (iff #42 true)
-#124 := [rewrite]: #122
-#127 := [monotonicity #124]: #126
-#131 := [trans #127 #129]: #130
-#121 := [asserted]: #43
-[mp #121 #131]: false
-unsat
-e82a6cc10c3ef4d2130dbd751caaaa2ceb41a37f 138 0
-#2 := false
-decl f4 :: S2
-#9 := f4
-decl f3 :: S2
-#8 := f3
-#152 := (= f3 f4)
-decl inj!0 :: (-> S3 S2)
-decl f6 :: (-> S2 S3)
-#22 := (f6 f4)
-#207 := (inj!0 #22)
-#208 := (= #207 f4)
-#209 := (= f4 #207)
-#14 := (:var 0 S2)
-#15 := (f6 #14)
-#89 := (pattern #15)
-#88 := (inj!0 #15)
-#85 := (= #88 #14)
-#570 := (forall (vars (k!0 S2)) (:pat #89) #85)
-#90 := (forall (vars (k!0 S2)) (:pat #89) #85)
-#571 := (iff #90 #570)
-#573 := (iff #570 #570)
-#574 := [rewrite]: #573
-#572 := [rewrite]: #571
-#575 := [trans #572 #574]: #571
-#12 := (:var 1 S2)
-#47 := (= #12 #14)
-#13 := (f6 #12)
-#16 := (= #13 #15)
-#53 := (not #16)
-#54 := (or #53 #47)
-#59 := (forall (vars (?v0 S2) (?v1 S2)) #54)
-#86 := (iff #59 #90)
-#83 := [rewrite]: #86
-#93 := (~ #59 #59)
-#91 := (~ #54 #54)
-#92 := [refl]: #91
-#94 := [nnf-pos #92]: #93
-decl f5 :: S2
-#10 := f5
-#11 := (distinct f3 f4 f5)
-#62 := (and #11 #59)
-#68 := (not #62)
-#21 := (f6 f3)
-#23 := (= #21 #22)
-#24 := (not #23)
-#69 := (or #24 #68)
-#74 := (not #69)
-#17 := (= #14 #12)
-#18 := (implies #16 #17)
-#19 := (forall (vars (?v0 S2) (?v1 S2)) #18)
-#20 := (and #11 #19)
-#25 := (implies #20 #24)
-#26 := (not #25)
-#75 := (iff #26 #74)
-#72 := (iff #25 #69)
-#65 := (implies #62 #24)
-#70 := (iff #65 #69)
-#71 := [rewrite]: #70
-#66 := (iff #25 #65)
-#63 := (iff #20 #62)
-#60 := (iff #19 #59)
-#57 := (iff #18 #54)
-#50 := (implies #16 #47)
-#55 := (iff #50 #54)
-#56 := [rewrite]: #55
-#51 := (iff #18 #50)
-#48 := (iff #17 #47)
-#49 := [rewrite]: #48
-#52 := [monotonicity #49]: #51
-#58 := [trans #52 #56]: #57
-#61 := [quant-intro #58]: #60
-#64 := [monotonicity #61]: #63
-#67 := [monotonicity #64]: #66
-#73 := [trans #67 #71]: #72
-#76 := [monotonicity #73]: #75
-#46 := [asserted]: #26
-#79 := [mp #46 #76]: #74
-#78 := [not-or-elim #79]: #62
-#81 := [and-elim #78]: #59
-#87 := [mp~ #81 #94]: #59
-#84 := [mp #87 #83]: #90
-#576 := [mp #84 #575]: #570
-#569 := (not #570)
-#549 := (or #569 #209)
-#550 := (or #569 #208)
-#546 := (iff #550 #549)
-#188 := (iff #549 #549)
-#553 := [rewrite]: #188
-#547 := (iff #208 #209)
-#548 := [rewrite]: #547
-#552 := [monotonicity #548]: #546
-#555 := [trans #552 #553]: #546
-#551 := [quant-inst #9]: #550
-#193 := [mp #551 #555]: #549
-#543 := [unit-resolution #193 #576]: #209
-#254 := [symm #543]: #208
-#269 := (= f3 #207)
-#565 := (inj!0 #21)
-#267 := (= #565 #207)
-#250 := (= #207 #565)
-#554 := (= #22 #21)
-#77 := [not-or-elim #79]: #23
-#557 := [symm #77]: #554
-#266 := [monotonicity #557]: #250
-#268 := [symm #266]: #267
-#567 := (= f3 #565)
-#559 := (or #569 #567)
-#566 := (= #565 f3)
-#217 := (or #569 #566)
-#560 := (iff #217 #559)
-#561 := (iff #559 #559)
-#202 := [rewrite]: #561
-#568 := (iff #566 #567)
-#563 := [rewrite]: #568
-#218 := [monotonicity #563]: #560
-#545 := [trans #218 #202]: #560
-#222 := [quant-inst #8]: #217
-#206 := [mp #222 #545]: #559
-#544 := [unit-resolution #206 #576]: #567
-#160 := [trans #544 #268]: #269
-#539 := [trans #160 #254]: #152
-#239 := (not #152)
-#154 := (= f4 f5)
-#241 := (not #154)
-#153 := (= f3 f5)
-#240 := (not #153)
-#232 := (and #239 #240 #241)
-#80 := [and-elim #78]: #11
-#219 := (not #11)
-#351 := (or #219 #232)
-#558 := [def-axiom]: #351
-#194 := [unit-resolution #558 #80]: #232
-#243 := (not #232)
-#244 := (or #243 #239)
-#172 := [def-axiom]: #244
-#556 := [unit-resolution #172 #194]: #239
-[unit-resolution #556 #539]: false
-unsat
-03a4fcd182047beb0b3be329b34440294749812c 117 0
-#2 := false
-decl f5 :: S3
-#18 := f5
-decl f4 :: S3
-#17 := f4
-#19 := (= f4 f5)
-decl inj!0 :: (-> S2 S4 S3)
-decl f3 :: (-> S2 S3 S4)
-decl f6 :: S2
-#22 := f6
-#24 := (f3 f6 f5)
-#565 := (inj!0 f6 #24)
-#220 := (= #565 f5)
-#352 := (= f5 #565)
-#9 := (:var 1 S3)
-#87 := (:var 0 S2)
-#84 := (f3 #87 #9)
-#85 := (pattern #84)
-#88 := (inj!0 #87 #84)
-#89 := (= #88 #9)
-#82 := (forall (vars (k!0 S2) (k!1 S3)) (:pat #85) #89)
-#11 := (:var 0 S3)
-#14 := (= #9 #11)
-#8 := (:var 2 S2)
-#12 := (f3 #8 #11)
-#10 := (f3 #8 #9)
-#13 := (= #10 #12)
-#49 := (not #13)
-#50 := (or #49 #14)
-#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #50)
-#83 := (iff #53 #82)
-#94 := [rewrite]: #83
-#92 := (~ #53 #53)
-#90 := (~ #50 #50)
-#91 := [refl]: #90
-#93 := [nnf-pos #91]: #92
-#20 := (not #19)
-#59 := (and #20 #53)
-#67 := (not #59)
-#23 := (f3 f6 f4)
-#25 := (= #23 #24)
-#26 := (not #25)
-#68 := (or #26 #67)
-#73 := (not #68)
-#15 := (implies #13 #14)
-#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S3)) #15)
-#21 := (and #16 #20)
-#27 := (implies #21 #26)
-#28 := (not #27)
-#74 := (iff #28 #73)
-#71 := (iff #27 #68)
-#64 := (implies #59 #26)
-#69 := (iff #64 #68)
-#70 := [rewrite]: #69
-#65 := (iff #27 #64)
-#62 := (iff #21 #59)
-#56 := (and #53 #20)
-#60 := (iff #56 #59)
-#61 := [rewrite]: #60
-#57 := (iff #21 #56)
-#54 := (iff #16 #53)
-#51 := (iff #15 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
-#58 := [monotonicity #55]: #57
-#63 := [trans #58 #61]: #62
-#66 := [monotonicity #63]: #65
-#72 := [trans #66 #70]: #71
-#75 := [monotonicity #72]: #74
-#48 := [asserted]: #28
-#78 := [mp #48 #75]: #73
-#77 := [not-or-elim #78]: #59
-#80 := [and-elim #77]: #53
-#86 := [mp~ #80 #93]: #53
-#95 := [mp #86 #94]: #82
-#242 := (not #82)
-#232 := (or #242 #352)
-#566 := (or #242 #220)
-#568 := (iff #566 #232)
-#564 := (iff #232 #232)
-#570 := [rewrite]: #564
-#559 := (iff #220 #352)
-#231 := [rewrite]: #559
-#569 := [monotonicity #231]: #568
-#560 := [trans #569 #570]: #568
-#567 := [quant-inst #18 #22]: #566
-#218 := [mp #567 #560]: #232
-#219 := [unit-resolution #218 #95]: #352
-#209 := [symm #219]: #220
-#210 := (= f4 #565)
-#153 := (inj!0 f6 #23)
-#207 := (= #153 #565)
-#203 := (= #565 #153)
-#223 := (= #24 #23)
-#76 := [not-or-elim #78]: #25
-#561 := [symm #76]: #223
-#546 := [monotonicity #561]: #203
-#208 := [symm #546]: #207
-#154 := (= f4 #153)
-#233 := (or #242 #154)
-#240 := (= #153 f4)
-#244 := (or #242 #240)
-#173 := (iff #244 #233)
-#243 := (iff #233 #233)
-#247 := [rewrite]: #243
-#241 := (iff #240 #154)
-#155 := [rewrite]: #241
-#246 := [monotonicity #155]: #173
-#226 := [trans #246 #247]: #173
-#245 := [quant-inst #17 #22]: #244
-#563 := [mp #245 #226]: #233
-#562 := [unit-resolution #563 #95]: #154
-#548 := [trans #562 #208]: #210
-#549 := [trans #548 #209]: #19
-#79 := [and-elim #77]: #20
-[unit-resolution #79 #549]: false
-unsat
-16237d3c6ed6b1b0d94625f503401c43285f9eec 115 0
-#2 := false
-decl f5 :: S2
-#18 := f5
-decl f4 :: S2
-#17 := f4
-#19 := (= f4 f5)
-decl inj!0 :: (-> S3 S4 S2)
-decl f3 :: (-> S2 S3 S4)
-decl f6 :: S3
-#22 := f6
-#24 := (f3 f5 f6)
-#563 := (inj!0 f6 #24)
-#218 := (= #563 f5)
-#350 := (= f5 #563)
-#9 := (:var 1 S3)
-#11 := (:var 0 S2)
-#12 := (f3 #11 #9)
-#88 := (pattern #12)
-#87 := (inj!0 #9 #12)
-#84 := (= #87 #11)
-#89 := (forall (vars (k!0 S2) (k!1 S3)) (:pat #88) #84)
-#8 := (:var 2 S2)
-#14 := (= #8 #11)
-#10 := (f3 #8 #9)
-#13 := (= #10 #12)
-#49 := (not #13)
-#50 := (or #49 #14)
-#53 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #50)
-#85 := (iff #53 #89)
-#82 := [rewrite]: #85
-#92 := (~ #53 #53)
-#90 := (~ #50 #50)
-#91 := [refl]: #90
-#93 := [nnf-pos #91]: #92
-#20 := (not #19)
-#59 := (and #20 #53)
-#67 := (not #59)
-#23 := (f3 f4 f6)
-#25 := (= #23 #24)
-#26 := (not #25)
-#68 := (or #26 #67)
-#73 := (not #68)
-#15 := (implies #13 #14)
-#16 := (forall (vars (?v0 S2) (?v1 S3) (?v2 S2)) #15)
-#21 := (and #16 #20)
-#27 := (implies #21 #26)
-#28 := (not #27)
-#74 := (iff #28 #73)
-#71 := (iff #27 #68)
-#64 := (implies #59 #26)
-#69 := (iff #64 #68)
-#70 := [rewrite]: #69
-#65 := (iff #27 #64)
-#62 := (iff #21 #59)
-#56 := (and #53 #20)
-#60 := (iff #56 #59)
-#61 := [rewrite]: #60
-#57 := (iff #21 #56)
-#54 := (iff #16 #53)
-#51 := (iff #15 #50)
-#52 := [rewrite]: #51
-#55 := [quant-intro #52]: #54
-#58 := [monotonicity #55]: #57
-#63 := [trans #58 #61]: #62
-#66 := [monotonicity #63]: #65
-#72 := [trans #66 #70]: #71
-#75 := [monotonicity #72]: #74
-#48 := [asserted]: #28
-#78 := [mp #48 #75]: #73
-#77 := [not-or-elim #78]: #59
-#80 := [and-elim #77]: #53
-#86 := [mp~ #80 #93]: #53
-#83 := [mp #86 #82]: #89
-#240 := (not #89)
-#230 := (or #240 #350)
-#564 := (or #240 #218)
-#566 := (iff #564 #230)
-#562 := (iff #230 #230)
-#568 := [rewrite]: #562
-#557 := (iff #218 #350)
-#229 := [rewrite]: #557
-#567 := [monotonicity #229]: #566
-#558 := [trans #567 #568]: #566
-#565 := [quant-inst #22 #18]: #564
-#216 := [mp #565 #558]: #230
-#217 := [unit-resolution #216 #83]: #350
-#207 := [symm #217]: #218
-#208 := (= f4 #563)
-#151 := (inj!0 f6 #23)
-#205 := (= #151 #563)
-#201 := (= #563 #151)
-#221 := (= #24 #23)
-#76 := [not-or-elim #78]: #25
-#559 := [symm #76]: #221
-#544 := [monotonicity #559]: #201
-#206 := [symm #544]: #205
-#152 := (= f4 #151)
-#231 := (or #240 #152)
-#238 := (= #151 f4)
-#242 := (or #240 #238)
-#171 := (iff #242 #231)
-#241 := (iff #231 #231)
-#245 := [rewrite]: #241
-#239 := (iff #238 #152)
-#153 := [rewrite]: #239
-#244 := [monotonicity #153]: #171
-#224 := [trans #244 #245]: #171
-#243 := [quant-inst #22 #17]: #242
-#561 := [mp #243 #224]: #231
-#560 := [unit-resolution #561 #83]: #152
-#546 := [trans #560 #206]: #208
-#547 := [trans #546 #207]: #19
-#79 := [and-elim #77]: #20
-[unit-resolution #79 #547]: false
-unsat
+#135 := [monotonicity #129 #132]: #134
+#138 := [monotonicity #135]: #137
+#144 := [trans #138 #142]: #143
+#125 := [asserted]: #47
+#147 := [mp #125 #144]: #140
+#237 := (not #140)
+#324 := (or #130 #126 #237)
+#238 := [def-axiom]: #324
+#239 := [unit-resolution #238 #147]: #325
+#629 := [unit-resolution #239 #628]: #130
+decl f8 :: (-> S4 S5 S1)
+#310 := (f8 f10 f11)
+#647 := (= f1 #310)
+#649 := (not #647)
+#330 := (f8 f9 f11)
+#327 := (= f1 #330)
+#331 := (not #327)
+#315 := (or #331 #649)
+#626 := (or #126 #315)
+#651 := (not #315)
+#642 := (iff #126 #651)
+#29 := (:var 0 S5)
+#28 := (:var 1 S4)
+#27 := (:var 2 S4)
+#30 := (f7 #27 #28 #29)
+#676 := (pattern #30)
+#34 := (f8 #28 #29)
+#113 := (= f1 #34)
+#172 := (not #113)
+#32 := (f8 #27 #29)
+#110 := (= f1 #32)
+#171 := (not #110)
+#155 := (or #171 #172)
+#156 := (not #155)
+#106 := (= f1 #30)
+#173 := (iff #106 #156)
+#677 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #676) #173)
+#176 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #173)
+#680 := (iff #176 #677)
+#678 := (iff #173 #173)
+#679 := [refl]: #678
+#681 := [quant-intro #679]: #680
+#116 := (and #110 #113)
+#119 := (iff #106 #116)
+#122 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #119)
+#177 := (iff #122 #176)
+#174 := (iff #119 #173)
+#157 := (iff #116 #156)
+#158 := [rewrite]: #157
+#175 := [monotonicity #158]: #174
+#178 := [quant-intro #175]: #177
+#153 := (~ #122 #122)
+#168 := (~ #119 #119)
+#169 := [refl]: #168
+#154 := [nnf-pos #169]: #153
+#35 := (= #34 f1)
+#33 := (= #32 f1)
+#36 := (and #33 #35)
+#31 := (= #30 f1)
+#37 := (iff #31 #36)
+#38 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #37)
+#123 := (iff #38 #122)
+#120 := (iff #37 #119)
+#117 := (iff #36 #116)
+#114 := (iff #35 #113)
+#115 := [rewrite]: #114
+#111 := (iff #33 #110)
+#112 := [rewrite]: #111
+#118 := [monotonicity #112 #115]: #117
+#108 := (iff #31 #106)
+#109 := [rewrite]: #108
+#121 := [monotonicity #109 #118]: #120
+#124 := [quant-intro #121]: #123
+#105 := [asserted]: #38
+#127 := [mp #105 #124]: #122
+#170 := [mp~ #127 #154]: #122
+#179 := [mp #170 #178]: #176
+#682 := [mp #179 #681]: #677
+#302 := (not #677)
+#335 := (or #302 #642)
+#351 := [quant-inst #39 #40 #41]: #335
+#622 := [unit-resolution #351 #682]: #642
+#352 := (not #642)
+#353 := (or #352 #126 #315)
+#339 := [def-axiom]: #353
+#623 := [unit-resolution #339 #622]: #626
+#627 := [unit-resolution #623 #628]: #315
+#337 := (or #326 #651)
+#648 := (iff #130 #651)
+#307 := (or #302 #648)
+#304 := (or #649 #331)
+#436 := (not #304)
+#643 := (iff #130 #436)
+#645 := (or #302 #643)
+#646 := (iff #645 #307)
+#630 := (iff #307 #307)
+#291 := [rewrite]: #630
+#654 := (iff #643 #648)
+#652 := (iff #436 #651)
+#316 := (iff #304 #315)
+#650 := [rewrite]: #316
+#653 := [monotonicity #650]: #652
+#644 := [monotonicity #653]: #654
+#287 := [monotonicity #644]: #646
+#292 := [trans #287 #291]: #646
+#303 := [quant-inst #40 #39 #41]: #645
+#293 := [mp #303 #292]: #307
+#336 := [unit-resolution #293 #682]: #648
+#631 := (not #648)
+#638 := (or #631 #326 #651)
+#640 := [def-axiom]: #638
+#338 := [unit-resolution #640 #336]: #337
+#340 := [unit-resolution #338 #627 #629]: false
+#618 := [lemma #340]: #126
+#329 := (or #326 #139)
+#317 := (or #326 #139 #237)
+#328 := [def-axiom]: #317
+#257 := [unit-resolution #328 #147]: #329
+#619 := [unit-resolution #257 #618]: #326
+#332 := (or #139 #651)
+#354 := (or #352 #139 #651)
+#245 := [def-axiom]: #354
+#616 := [unit-resolution #245 #622]: #332
+#620 := [unit-resolution #616 #618]: #651
+#617 := (or #130 #315)
+#637 := (or #631 #130 #315)
+#273 := [def-axiom]: #637
+#621 := [unit-resolution #273 #336]: #617
+[unit-resolution #621 #620 #619]: false
+unsat
+b05e302d276675d4c2c21abbf217592e2a23efc3 142 0
+#2 := false
+decl f7 :: (-> S4 S4 S5 S1)
+decl f10 :: S5
+#40 := f10
+decl f9 :: S4
+#39 := f9
+#41 := (f7 f9 f9 f10)
+decl f1 :: S1
+#4 := f1
+#125 := (= f1 #41)
+#138 := (not #125)
+#634 := [hypothesis]: #138
+decl f8 :: (-> S4 S5 S1)
+#43 := (f8 f9 f10)
+#129 := (= f1 #43)
+#324 := (or #129 #125)
+#139 := (iff #129 #138)
+#44 := (= #43 f1)
+#42 := (= #41 f1)
+#45 := (iff #42 #44)
+#46 := (not #45)
+#142 := (iff #46 #139)
+#132 := (iff #125 #129)
+#135 := (not #132)
+#140 := (iff #135 #139)
+#141 := [rewrite]: #140
+#136 := (iff #46 #135)
+#133 := (iff #45 #132)
+#130 := (iff #44 #129)
+#131 := [rewrite]: #130
+#127 := (iff #42 #125)
+#128 := [rewrite]: #127
+#134 := [monotonicity #128 #131]: #133
+#137 := [monotonicity #134]: #136
+#143 := [trans #137 #141]: #142
+#124 := [asserted]: #46
+#146 := [mp #124 #143]: #139
+#236 := (not #139)
+#323 := (or #129 #125 #236)
+#237 := [def-axiom]: #323
+#238 := [unit-resolution #237 #146]: #324
+#635 := [unit-resolution #238 #634]: #129
+#325 := (not #129)
+#636 := (or #125 #325)
+#29 := (:var 0 S5)
+#28 := (:var 1 S4)
+#27 := (:var 2 S4)
+#30 := (f7 #27 #28 #29)
+#675 := (pattern #30)
+#34 := (f8 #28 #29)
+#112 := (= f1 #34)
+#171 := (not #112)
+#32 := (f8 #27 #29)
+#109 := (= f1 #32)
+#170 := (not #109)
+#154 := (or #170 #171)
+#155 := (not #154)
+#105 := (= f1 #30)
+#172 := (iff #105 #155)
+#676 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #675) #172)
+#175 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #172)
+#679 := (iff #175 #676)
+#677 := (iff #172 #172)
+#678 := [refl]: #677
+#680 := [quant-intro #678]: #679
+#115 := (and #109 #112)
+#118 := (iff #105 #115)
+#121 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #118)
+#176 := (iff #121 #175)
+#173 := (iff #118 #172)
+#156 := (iff #115 #155)
+#157 := [rewrite]: #156
+#174 := [monotonicity #157]: #173
+#177 := [quant-intro #174]: #176
+#152 := (~ #121 #121)
+#167 := (~ #118 #118)
+#168 := [refl]: #167
+#153 := [nnf-pos #168]: #152
+#35 := (= #34 f1)
+#33 := (= #32 f1)
+#36 := (and #33 #35)
+#31 := (= #30 f1)
+#37 := (iff #31 #36)
+#38 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #37)
+#122 := (iff #38 #121)
+#119 := (iff #37 #118)
+#116 := (iff #36 #115)
+#113 := (iff #35 #112)
+#114 := [rewrite]: #113
+#110 := (iff #33 #109)
+#111 := [rewrite]: #110
+#117 := [monotonicity #111 #114]: #116
+#107 := (iff #31 #105)
+#108 := [rewrite]: #107
+#120 := [monotonicity #108 #117]: #119
+#123 := [quant-intro #120]: #122
+#104 := [asserted]: #38
+#126 := [mp #104 #123]: #121
+#169 := [mp~ #126 #153]: #121
+#178 := [mp #169 #177]: #175
+#681 := [mp #178 #680]: #676
+#652 := (not #676)
+#647 := (or #652 #132)
+#329 := (or #325 #325)
+#326 := (not #329)
+#330 := (iff #125 #326)
+#653 := (or #652 #330)
+#301 := (iff #653 #647)
+#644 := (iff #647 #647)
+#302 := [rewrite]: #644
+#650 := (iff #330 #132)
+#315 := (iff #326 #129)
+#648 := (not #325)
+#642 := (iff #648 #129)
+#314 := [rewrite]: #642
+#303 := (iff #326 #648)
+#309 := (iff #329 #325)
+#646 := [rewrite]: #309
+#435 := [monotonicity #646]: #303
+#649 := [trans #435 #314]: #315
+#651 := [monotonicity #649]: #650
+#306 := [monotonicity #651]: #301
+#645 := [trans #306 #302]: #301
+#643 := [quant-inst #39 #39 #40]: #653
+#286 := [mp #643 #645]: #647
+#630 := [unit-resolution #286 #681]: #132
+#629 := (or #135 #125 #325)
+#290 := [def-axiom]: #629
+#272 := [unit-resolution #290 #630]: #636
+#637 := [unit-resolution #272 #635 #634]: false
+#639 := [lemma #637]: #125
+#328 := (or #325 #138)
+#316 := (or #325 #138 #236)
+#327 := [def-axiom]: #316
+#256 := [unit-resolution #327 #146]: #328
+#277 := [unit-resolution #256 #639]: #325
+#278 := (or #138 #129)
+#291 := (or #135 #138 #129)
+#292 := [def-axiom]: #291
+#640 := [unit-resolution #292 #630]: #278
+[unit-resolution #640 #277 #639]: false
+unsat
+d8e9744832a91810c03cbef21eb26edf5cd1eec0 280 0
+#2 := false
+decl f7 :: (-> S4 S5 S1)
+decl f12 :: S5
+#45 := f12
+decl f8 :: (-> S4 S4 S4)
+decl f10 :: S4
+#41 := f10
+decl f9 :: S4
+#40 := f9
+#48 := (f8 f9 f10)
+#316 := (f7 #48 f12)
+decl f1 :: S1
+#4 := f1
+#653 := (= f1 #316)
+#251 := (f7 f10 f12)
+#630 := (= f1 #251)
+#627 := (not #630)
+#341 := (f7 f9 f12)
+#357 := (= f1 #341)
+#358 := (not #357)
+#616 := (or #358 #627)
+#617 := (not #616)
+#613 := (iff #617 #653)
+#584 := (not #613)
+decl f11 :: S4
+#42 := f11
+#336 := (f7 f11 f12)
+#333 := (= f1 #336)
+#337 := (not #333)
+#486 := (or #337 #627)
+#495 := (not #486)
+#43 := (f8 f10 f11)
+#648 := (f7 #43 f12)
+#634 := (= f1 #648)
+#496 := (iff #495 #634)
+#589 := (not #496)
+#569 := [hypothesis]: #589
+#30 := (:var 0 S5)
+#28 := (:var 1 S4)
+#27 := (:var 2 S4)
+#29 := (f8 #27 #28)
+#31 := (f7 #29 #30)
+#682 := (pattern #31)
+#35 := (f7 #28 #30)
+#119 := (= f1 #35)
+#178 := (not #119)
+#33 := (f7 #27 #30)
+#116 := (= f1 #33)
+#177 := (not #116)
+#161 := (or #177 #178)
+#162 := (not #161)
+#112 := (= f1 #31)
+#179 := (iff #112 #162)
+#683 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) (:pat #682) #179)
+#182 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #179)
+#686 := (iff #182 #683)
+#684 := (iff #179 #179)
+#685 := [refl]: #684
+#687 := [quant-intro #685]: #686
+#122 := (and #116 #119)
+#125 := (iff #112 #122)
+#128 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #125)
+#183 := (iff #128 #182)
+#180 := (iff #125 #179)
+#163 := (iff #122 #162)
+#164 := [rewrite]: #163
+#181 := [monotonicity #164]: #180
+#184 := [quant-intro #181]: #183
+#159 := (~ #128 #128)
+#174 := (~ #125 #125)
+#175 := [refl]: #174
+#160 := [nnf-pos #175]: #159
+#36 := (= #35 f1)
+#34 := (= #33 f1)
+#37 := (and #34 #36)
+#32 := (= #31 f1)
+#38 := (iff #32 #37)
+#39 := (forall (vars (?v0 S4) (?v1 S4) (?v2 S5)) #38)
+#129 := (iff #39 #128)
+#126 := (iff #38 #125)
+#123 := (iff #37 #122)
+#120 := (iff #36 #119)
+#121 := [rewrite]: #120
+#117 := (iff #34 #116)
+#118 := [rewrite]: #117
+#124 := [monotonicity #118 #121]: #123
+#114 := (iff #32 #112)
+#115 := [rewrite]: #114
+#127 := [monotonicity #115 #124]: #126
+#130 := [quant-intro #127]: #129
+#111 := [asserted]: #39
+#133 := [mp #111 #130]: #128
+#176 := [mp~ #133 #160]: #128
+#185 := [mp #176 #184]: #182
+#688 := [mp #185 #687]: #683
+#308 := (not #683)
+#500 := (or #308 #496)
+#602 := (or #627 #337)
+#484 := (not #602)
+#485 := (iff #634 #484)
+#501 := (or #308 #485)
+#595 := (iff #501 #500)
+#596 := (iff #500 #500)
+#583 := [rewrite]: #596
+#498 := (iff #485 #496)
+#594 := (iff #634 #495)
+#497 := (iff #594 #496)
+#490 := [rewrite]: #497
+#479 := (iff #485 #594)
+#590 := (iff #484 #495)
+#445 := (iff #602 #486)
+#593 := [rewrite]: #445
+#591 := [monotonicity #593]: #590
+#494 := [monotonicity #591]: #479
+#499 := [trans #494 #490]: #498
+#592 := [monotonicity #499]: #595
+#585 := [trans #592 #583]: #595
+#502 := [quant-inst #41 #42 #45]: #501
+#577 := [mp #502 #585]: #500
+#570 := [unit-resolution #577 #688 #569]: false
+#571 := [lemma #570]: #496
+#635 := (not #634)
+#359 := (or #358 #635)
+#345 := (not #359)
+#44 := (f8 f9 #43)
+#46 := (f7 #44 f12)
+#132 := (= f1 #46)
+#145 := (not #132)
+#572 := [hypothesis]: #145
+#573 := (or #132 #359)
+#360 := (iff #132 #345)
+#631 := (or #308 #360)
+#353 := [quant-inst #40 #43 #45]: #631
+#568 := [unit-resolution #353 #688]: #360
+#343 := (not #360)
+#344 := (or #343 #132 #359)
+#346 := [def-axiom]: #344
+#559 := [unit-resolution #346 #568]: #573
+#560 := [unit-resolution #559 #572]: #359
+#599 := (or #308 #613)
+#618 := (iff #653 #617)
+#615 := (or #308 #618)
+#620 := (iff #615 #599)
+#463 := (iff #599 #599)
+#464 := [rewrite]: #463
+#614 := (iff #618 #613)
+#619 := [rewrite]: #614
+#462 := [monotonicity #619]: #620
+#606 := [trans #462 #464]: #620
+#621 := [quant-inst #40 #41 #45]: #615
+#607 := [mp #621 #606]: #599
+#562 := [unit-resolution #607 #688]: #613
+#548 := (or #584 #617)
+#655 := (not #653)
+#321 := (or #337 #655)
+#657 := (not #321)
+#49 := (f8 #48 f11)
+#50 := (f7 #49 f12)
+#136 := (= f1 #50)
+#331 := (or #136 #132)
+#146 := (iff #136 #145)
+#51 := (= #50 f1)
+#47 := (= #46 f1)
+#52 := (iff #47 #51)
+#53 := (not #52)
+#149 := (iff #53 #146)
+#139 := (iff #132 #136)
+#142 := (not #139)
+#147 := (iff #142 #146)
+#148 := [rewrite]: #147
+#143 := (iff #53 #142)
+#140 := (iff #52 #139)
+#137 := (iff #51 #136)
+#138 := [rewrite]: #137
+#134 := (iff #47 #132)
+#135 := [rewrite]: #134
+#141 := [monotonicity #135 #138]: #140
+#144 := [monotonicity #141]: #143
+#150 := [trans #144 #148]: #149
+#131 := [asserted]: #53
+#153 := [mp #131 #150]: #146
+#243 := (not #146)
+#330 := (or #136 #132 #243)
+#244 := [def-axiom]: #330
+#245 := [unit-resolution #244 #153]: #331
+#563 := [unit-resolution #245 #572]: #136
+#332 := (not #136)
+#561 := (or #332 #657)
+#654 := (iff #136 #657)
+#313 := (or #308 #654)
+#310 := (or #655 #337)
+#442 := (not #310)
+#649 := (iff #136 #442)
+#651 := (or #308 #649)
+#652 := (iff #651 #313)
+#636 := (iff #313 #313)
+#297 := [rewrite]: #636
+#660 := (iff #649 #654)
+#658 := (iff #442 #657)
+#322 := (iff #310 #321)
+#656 := [rewrite]: #322
+#659 := [monotonicity #656]: #658
+#650 := [monotonicity #659]: #660
+#293 := [monotonicity #650]: #652
+#298 := [trans #293 #297]: #652
+#309 := [quant-inst #48 #42 #45]: #651
+#299 := [mp #309 #298]: #313
+#564 := [unit-resolution #299 #688]: #654
+#637 := (not #654)
+#644 := (or #637 #332 #657)
+#646 := [def-axiom]: #644
+#565 := [unit-resolution #646 #564]: #561
+#545 := [unit-resolution #565 #563]: #657
+#639 := (or #321 #653)
+#640 := [def-axiom]: #639
+#546 := [unit-resolution #640 #545]: #653
+#578 := (or #584 #617 #655)
+#579 := [def-axiom]: #578
+#549 := [unit-resolution #579 #546]: #548
+#550 := [unit-resolution #549 #562]: #617
+#608 := (or #616 #357)
+#574 := [def-axiom]: #608
+#551 := [unit-resolution #574 #550]: #357
+#633 := (or #345 #358 #635)
+#342 := [def-axiom]: #633
+#552 := [unit-resolution #342 #551 #560]: #635
+#300 := (or #321 #333)
+#638 := [def-axiom]: #300
+#553 := [unit-resolution #638 #545]: #333
+#576 := (or #616 #630)
+#586 := [def-axiom]: #576
+#554 := [unit-resolution #586 #550]: #630
+#611 := (or #495 #337 #627)
+#605 := [def-axiom]: #611
+#555 := [unit-resolution #605 #554 #553]: #495
+#443 := (or #589 #486 #634)
+#444 := [def-axiom]: #443
+#556 := [unit-resolution #444 #555 #552 #571]: false
+#557 := [lemma #556]: #132
+#547 := (or #145 #345)
+#624 := (or #343 #145 #345)
+#625 := [def-axiom]: #624
+#558 := [unit-resolution #625 #568]: #547
+#536 := [unit-resolution #558 #557]: #345
+#632 := (or #359 #634)
+#629 := [def-axiom]: #632
+#537 := [unit-resolution #629 #536]: #634
+#612 := (or #589 #495 #635)
+#441 := [def-axiom]: #612
+#539 := [unit-resolution #441 #537 #571]: #495
+#604 := (or #486 #630)
+#610 := [def-axiom]: #604
+#540 := [unit-resolution #610 #539]: #630
+#354 := (or #359 #357)
+#628 := [def-axiom]: #354
+#541 := [unit-resolution #628 #536]: #357
+#587 := (or #617 #358 #627)
+#588 := [def-axiom]: #587
+#542 := [unit-resolution #588 #541 #540]: #617
+#335 := (or #332 #145)
+#323 := (or #332 #145 #243)
+#334 := [def-axiom]: #323
+#263 := [unit-resolution #334 #153]: #335
+#543 := [unit-resolution #263 #557]: #332
+#538 := (or #136 #321)
+#643 := (or #637 #136 #321)
+#279 := [def-axiom]: #643
+#544 := [unit-resolution #279 #564]: #538
+#530 := [unit-resolution #544 #543]: #321
+#609 := (or #486 #333)
+#603 := [def-axiom]: #609
+#526 := [unit-resolution #603 #539]: #333
+#641 := (or #657 #337 #655)
+#642 := [def-axiom]: #641
+#527 := [unit-resolution #642 #526 #530]: #655
+#580 := (or #584 #616 #653)
+#581 := [def-axiom]: #580
+#528 := [unit-resolution #581 #527 #542]: #584
+[unit-resolution #607 #688 #528]: false
+unsat
+cdbf11c9465d749cfd2e9563f8fc0294f62a631c 18 0
+#2 := false
+decl f8 :: S4
+#32 := f8
+#33 := (= f8 f8)
+#34 := (not #33)
+#115 := (iff #34 false)
+#1 := true
+#110 := (not true)
+#113 := (iff #110 false)
+#114 := [rewrite]: #113
+#111 := (iff #34 #110)
+#107 := (iff #33 true)
+#109 := [rewrite]: #107
+#112 := [monotonicity #109]: #111
+#116 := [trans #112 #114]: #115
+#106 := [asserted]: #34
+[mp #106 #116]: false
+unsat