src/HOL/Boogie/Examples/Boogie_Dijkstra.certs

updated SMT certificates

b9c818fc8db5c62ae4864b1c933f204656ce6c70 7184 0
#2 := false
decl f13 :: (-> S5 S3 Int)
decl f22 :: S3
#170 := f22
decl f14 :: S5
#98 := f14
#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
#104 := f15
#6072 := (f3 f15 #6060)
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
#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)
#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)
#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)
#4493 := (not #4490)
#4496 := (or #1481 #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)
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)
#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)
#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)
#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)
#4312 := (not #4307)
#623 := (= f14 f19)
#714 := (not #623)
decl f16 :: S2
#132 := f16
#620 := (= f15 f16)
#732 := (not #620)
decl f21 :: S5
#140 := f21
decl f20 :: S5
#139 := f20
#141 := (= f20 f21)
#705 := (not #141)
decl f18 :: S3
#135 := f18
decl f17 :: S3
#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)
#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)
#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)
#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
#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)
#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)
#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)
#1 := true
#215 := (+ #188 #82)
#222 := (= #210 #215)
#199 := (= #198 f1)
#223 := (and #199 #222)
#221 := (< #188 #210)
#224 := (and #221 #223)
#225 := (exists (vars (?v1 S3)) #224)
#219 := (< #188 f8)
#220 := (and #62 #219)
#226 := (implies #220 #225)
#227 := (forall (vars (?v0 S3)) #226)
#228 := (and #227 true)
#216 := (<= #210 #215)
#83 := (< #82 f8)
#214 := (and #199 #83)
#217 := (implies #214 #216)
#218 := (forall (vars (?v0 S3) (?v1 S3)) #217)
#229 := (implies #218 #228)
#230 := (and #218 #229)
#211 := (<= #210 #188)
#208 := (= #207 f1)
#206 := (not #199)
#209 := (and #206 #208)
#212 := (implies #209 #211)
#213 := (forall (vars (?v0 S3) (?v1 S3)) #212)
#231 := (implies #213 #230)
#232 := (and #213 #231)
#204 := (<= 0::Int #188)
#205 := (forall (vars (?v0 S3)) #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)
#237 := (implies #201 #236)
#238 := (and #201 #237)
#196 := (<= #188 #101)
#197 := (forall (vars (?v0 S3)) #196)
#239 := (implies #197 #238)
#240 := (and #197 #239)
#185 := (+ #174 #183)
#186 := (< #185 #101)
#184 := (< #183 f8)
#187 := (and #184 #186)
#192 := (not #187)
#194 := (implies #192 #193)
#195 := (forall (vars (?v0 S3)) #194)
#241 := (implies #195 #240)
#189 := (= #188 #185)
#190 := (implies #187 #189)
#191 := (forall (vars (?v0 S3)) #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)
#244 := (implies #178 #243)
#175 := (< #174 f8)
#245 := (implies #175 #244)
#172 := (= #171 f1)
#173 := (not #172)
#246 := (implies #173 #245)
#120 := (< #101 f8)
#129 := (and #107 #120)
#130 := (exists (vars (?v0 S3)) #129)
#247 := (implies #130 #246)
#248 := (implies true #247)
#159 := (and #158 true)
#147 := (+ #142 #82)
#154 := (<= #145 #147)
#143 := (< #142 f8)
#153 := (and #143 #83)
#155 := (implies #153 #154)
#156 := (forall (vars (?v0 S3) (?v1 S3)) #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)
#144 := (and #62 #143)
#151 := (implies #144 #150)
#152 := (forall (vars (?v0 S3)) #151)
#162 := (implies #152 #161)
#163 := (and #152 #162)
#164 := (implies #141 #163)
#138 := (= f19 f14)
#165 := (implies #138 #164)
#166 := (implies #136 #165)
#133 := (= f16 f15)
#167 := (implies #133 #166)
#131 := (not #130)
#168 := (implies #131 #167)
#169 := (implies true #168)
#249 := (and #169 #248)
#116 := (+ #101 #82)
#123 := (= #111 #116)
#124 := (and #106 #123)
#122 := (< #101 #111)
#125 := (and #122 #124)
#126 := (exists (vars (?v1 S3)) #125)
#121 := (and #62 #120)
#127 := (implies #121 #126)
#128 := (forall (vars (?v0 S3)) #127)
#250 := (implies #128 #249)
#117 := (<= #111 #116)
#115 := (and #106 #83)
#118 := (implies #115 #117)
#119 := (forall (vars (?v0 S3) (?v1 S3)) #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)
#252 := (implies #114 #251)
#102 := (<= 0::Int #101)
#103 := (forall (vars (?v0 S3)) #102)
#253 := (implies #103 #252)
#254 := (implies #100 #253)
#255 := (implies true #254)
#85 := (+ #58 #82)
#92 := (= #77 #85)
#67 := (= #66 f1)
#93 := (and #67 #92)
#91 := (< #58 #77)
#94 := (and #91 #93)
#95 := (exists (vars (?v1 S3)) #94)
#89 := (< #58 f8)
#90 := (and #62 #89)
#96 := (implies #90 #95)
#97 := (forall (vars (?v0 S3)) #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)
#258 := (implies #88 #257)
#259 := (and #88 #258)
#78 := (<= #77 #58)
#75 := (= #74 f1)
#68 := (not #67)
#76 := (and #68 #75)
#79 := (implies #76 #78)
#80 := (forall (vars (?v0 S3) (?v1 S3)) #79)
#260 := (implies #80 #259)
#261 := (and #80 #260)
#72 := (<= 0::Int #58)
#73 := (forall (vars (?v0 S3)) #72)
#262 := (implies #73 #261)
#263 := (and #73 #262)
#264 := (implies #71 #263)
#265 := (and #71 #264)
#69 := (forall (vars (?v0 S3)) #68)
#266 := (implies #69 #265)
#63 := (= #58 f8)
#64 := (implies #62 #63)
#65 := (forall (vars (?v0 S3)) #64)
#267 := (implies #65 #266)
#60 := (implies #57 #59)
#61 := (forall (vars (?v0 S3)) #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)
#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)
#909 := (or #908 #902)
#914 := (and #833 #909)
#920 := (not #205)
#921 := (or #920 #914)
#926 := (and #205 #921)
#813 := (= 0::Int #202)
#932 := (not #813)
#933 := (or #932 #926)
#938 := (and #813 #933)
#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)
#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)
#1104 := (or #1103 #1097)
#1109 := (and #500 #1104)
#475 := (or #78 #474)
#480 := (forall (vars (?v0 S3) (?v1 S3)) #475)
#1115 := (not #480)
#1116 := (or #1115 #1109)
#1121 := (and #480 #1116)
#1127 := (not #73)
#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
#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
#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
#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)
#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
#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)
#1186 := [rewrite]: #1185
#1189 := [monotonicity #1186]: #1188
#1790 := [monotonicity #1189 #1787]: #1789
#1793 := [monotonicity #1186 #1790]: #1792
#1807 := [monotonicity #1793]: #1806
#1810 := [monotonicity #1807]: #1809
#1803 := (iff #1169 #1802)
#1800 := (iff #436 #1799)
#1797 := (iff #431 #1796)
#1794 := (iff #425 #59)
#1795 := [rewrite]: #1794
#1798 := [monotonicity #1795]: #1797
#1801 := [quant-intro #1798]: #1800
#1804 := [monotonicity #1801]: #1803
#1813 := [monotonicity #1804 #1810]: #1812
#1818 := [trans #1813 #1816]: #1817
#1821 := [monotonicity #1818]: #1820
#1183 := (iff #270 #1182)
#1180 := (iff #269 #1170)
#1175 := (implies true #1170)
#1178 := (iff #1175 #1170)
#1179 := [rewrite]: #1178
#1176 := (iff #269 #1175)
#1173 := (iff #268 #1170)
#1166 := (implies #436 #1161)
#1171 := (iff #1166 #1170)
#1172 := [rewrite]: #1171
#1167 := (iff #268 #1166)
#1164 := (iff #267 #1161)
#1157 := (implies #450 #1152)
#1162 := (iff #1157 #1161)
#1163 := [rewrite]: #1162
#1158 := (iff #267 #1157)
#1155 := (iff #266 #1152)
#1148 := (implies #459 #1145)
#1153 := (iff #1148 #1152)
#1154 := [rewrite]: #1153
#1149 := (iff #266 #1148)
#1146 := (iff #265 #1145)
#1143 := (iff #264 #1140)
#1136 := (implies #462 #1133)
#1141 := (iff #1136 #1140)
#1142 := [rewrite]: #1141
#1137 := (iff #264 #1136)
#1134 := (iff #263 #1133)
#1131 := (iff #262 #1128)
#1124 := (implies #73 #1121)
#1129 := (iff #1124 #1128)
#1130 := [rewrite]: #1129
#1125 := (iff #262 #1124)
#1122 := (iff #261 #1121)
#1119 := (iff #260 #1116)
#1112 := (implies #480 #1109)
#1117 := (iff #1112 #1116)
#1118 := [rewrite]: #1117
#1113 := (iff #260 #1112)
#1110 := (iff #259 #1109)
#1107 := (iff #258 #1104)
#1100 := (implies #500 #1097)
#1105 := (iff #1100 #1104)
#1106 := [rewrite]: #1105
#1101 := (iff #258 #1100)
#1098 := (iff #257 #1097)
#1095 := (iff #256 #1092)
#1088 := (implies #526 #1076)
#1093 := (iff #1088 #1092)
#1094 := [rewrite]: #1093
#1089 := (iff #256 #1088)
#1086 := (iff #255 #1076)
#1081 := (implies true #1076)
#1084 := (iff #1081 #1076)
#1085 := [rewrite]: #1084
#1082 := (iff #255 #1081)
#1079 := (iff #254 #1076)
#1072 := (implies #529 #1067)
#1077 := (iff #1072 #1076)
#1078 := [rewrite]: #1077
#1073 := (iff #254 #1072)
#1070 := (iff #253 #1067)
#1063 := (implies #103 #1058)
#1068 := (iff #1063 #1067)
#1069 := [rewrite]: #1068
#1064 := (iff #253 #1063)
#1061 := (iff #252 #1058)
#1054 := (implies #553 #1049)
#1059 := (iff #1054 #1058)
#1060 := [rewrite]: #1059
#1055 := (iff #252 #1054)
#1052 := (iff #251 #1049)
#1045 := (implies #579 #1040)
#1050 := (iff #1045 #1049)
#1051 := [rewrite]: #1050
#1046 := (iff #251 #1045)
#1043 := (iff #250 #1040)
#1036 := (implies #603 #1033)
#1041 := (iff #1036 #1040)
#1042 := [rewrite]: #1041
#1037 := (iff #250 #1036)
#1034 := (iff #249 #1033)
#1031 := (iff #248 #1021)
#1026 := (implies true #1021)
#1029 := (iff #1026 #1021)
#1030 := [rewrite]: #1029
#1027 := (iff #248 #1026)
#1024 := (iff #247 #1021)
#1018 := (implies #614 #1013)
#1022 := (iff #1018 #1021)
#1023 := [rewrite]: #1022
#1019 := (iff #247 #1018)
#1016 := (iff #246 #1013)
#756 := (not #753)
#1010 := (implies #756 #1005)
#1014 := (iff #1010 #1013)
#1015 := [rewrite]: #1014
#1011 := (iff #246 #1010)
#1008 := (iff #245 #1005)
#1001 := (implies #175 #996)
#1006 := (iff #1001 #1005)
#1007 := [rewrite]: #1006
#1002 := (iff #245 #1001)
#999 := (iff #244 #996)
#992 := (implies #767 #987)
#997 := (iff #992 #996)
#998 := [rewrite]: #997
#993 := (iff #244 #992)
#990 := (iff #243 #987)
#983 := (implies #181 #978)
#988 := (iff #983 #987)
#989 := [rewrite]: #988
#984 := (iff #243 #983)
#981 := (iff #242 #978)
#974 := (implies #781 #969)
#979 := (iff #974 #978)
#980 := [rewrite]: #979
#975 := (iff #242 #974)
#972 := (iff #241 #969)
#965 := (implies #795 #962)
#970 := (iff #965 #969)
#971 := [rewrite]: #970
#966 := (iff #241 #965)
#963 := (iff #240 #962)
#960 := (iff #239 #957)
#953 := (implies #197 #950)
#958 := (iff #953 #957)
#959 := [rewrite]: #958
#954 := (iff #239 #953)
#951 := (iff #238 #950)
#948 := (iff #237 #945)
#941 := (implies #810 #938)
#946 := (iff #941 #945)
#947 := [rewrite]: #946
#942 := (iff #237 #941)
#939 := (iff #236 #938)
#936 := (iff #235 #933)
#929 := (implies #813 #926)
#934 := (iff #929 #933)
#935 := [rewrite]: #934
#930 := (iff #235 #929)
#927 := (iff #234 #926)
#924 := (iff #233 #921)
#917 := (implies #205 #914)
#922 := (iff #917 #921)
#923 := [rewrite]: #922
#918 := (iff #233 #917)
#915 := (iff #232 #914)
#912 := (iff #231 #909)
#905 := (implies #833 #902)
#910 := (iff #905 #909)
#911 := [rewrite]: #910
#906 := (iff #231 #905)
#903 := (iff #230 #902)
#900 := (iff #229 #897)
#893 := (implies #859 #883)
#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)
#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
#858 := [trans #852 #856]: #857
#861 := [quant-intro #858]: #860
#895 := [monotonicity #861 #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
#913 := [trans #907 #911]: #912
#916 := [monotonicity #835 #913]: #915
#919 := [monotonicity #916]: #918
#925 := [trans #919 #923]: #924
#928 := [monotonicity #925]: #927
#814 := (iff #203 #813)
#815 := [rewrite]: #814
#931 := [monotonicity #815 #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
#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)
#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)
#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)
#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
#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)
#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
#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
#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
#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
#1120 := [trans #1114 #1118]: #1119
#1123 := [monotonicity #482 #1120]: #1122
#1126 := [monotonicity #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)
#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)
#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
#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
#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
#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
#4483 := [monotonicity #4480]: #4482
#4486 := [monotonicity #4483]: #4485
#4489 := [monotonicity #4486]: #4488
#4492 := [monotonicity #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
#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)
#4357 := (iff #3367 #4356)
#4354 := (iff #3360 #4353)
#4351 := (iff #3333 #4350)
#4348 := (iff #3332 #4347)
#4345 := (iff #3331 #4344)
#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)
#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)
#4259 := (iff #3133 #4258)
#4256 := (iff #3132 #4255)
#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)
#4243 := [refl]: #4242
#4245 := [quant-intro #4243]: #4244
#4248 := [monotonicity #4245]: #4247
#4552 := [monotonicity #4248 #4549]: #4551
#4555 := [monotonicity #4552]: #4554
#4558 := [monotonicity #4555]: #4557
#4561 := [monotonicity #4558]: #4560
#4238 := (iff #3651 #4237)
#4235 := (iff #3066 #4232)
#4233 := (iff #3061 #3061)
#4234 := [refl]: #4233
#4236 := [quant-intro #4234]: #4235
#4239 := [monotonicity #4236]: #4238
#4564 := [monotonicity #4239 #4561]: #4563
#4567 := [monotonicity #4564]: #4566
#4570 := [monotonicity #4567]: #4569
#4573 := [monotonicity #4570]: #4572
#4229 := (iff #1196 #4228)
#4226 := (iff #1193 #4223)
#4224 := (iff #1192 #1192)
#4225 := [refl]: #4224
#4227 := [quant-intro #4225]: #4226
#4230 := [monotonicity #4227]: #4229
#4576 := [monotonicity #4230 #4573]: #4575
#4579 := [monotonicity #4576]: #4578
#4582 := [monotonicity #4579]: #4581
#4585 := [monotonicity #4582]: #4584
#4588 := [monotonicity #4585]: #4587
#4591 := [monotonicity #4588]: #4590
#4594 := [monotonicity #4591]: #4593
#2346 := (not #2345)
#2948 := (and #798 #2346 #2945)
#2951 := (not #2948)
#2954 := (forall (vars (?v1 S3)) #2951)
#2920 := (not #2917)
#2963 := (and #1530 #2351 #2920 #2954)
#2319 := (not #2318)
#2890 := (and #2319 #2321)
#2893 := (not #2890)
#2911 := (or #2893 #2906)
#2914 := (not #2911)
#2968 := (or #2914 #2963)
#2971 := (and #1506 #2968)
#2290 := (not #2289)
#2865 := (and #2287 #2290)
#2868 := (not #2865)
#2884 := (or #2868 #2879)
#2887 := (not #2884)
#2974 := (or #2887 #2971)
#2977 := (and #1487 #2974)
#2980 := (or #2267 #2977)
#2983 := (and #203 #2980)
#2986 := (or #1481 #2983)
#2989 := (and #810 #2986)
#2992 := (or #2860 #2989)
#2995 := (and #1473 #2992)
#2998 := (or #2846 #2995)
#2205 := (not #2204)
#2202 := (not #2201)
#3004 := (and #181 #756 #1462 #1620 #1638 #1646 #2202 #2205 #2998)
#2147 := (not #2146)
#2143 := (not #2142)
#2783 := (and #2143 #2147)
#2786 := (not #2783)
#2803 := (or #2786 #2798)
#2806 := (not #2803)
#2156 := (not #158)
#2166 := (and #2156 #1382)
#2812 := (or #2166 #2806)
#2756 := (not #2751)
#2774 := (and #2756 #2769)
#2777 := (or #1342 #2774)
#2780 := (forall (vars (?v0 S3)) #2777)
#2817 := (and #2780 #2812)
#2076 := (not #2075)
#2726 := (and #2076 #2723)
#2729 := (not #2726)
#2732 := (forall (vars (?v1 S3)) #2729)
#2698 := (not #2695)
#2081 := (not #2080)
#2738 := (and #2081 #2698 #2732)
#2820 := (or #2738 #2817)
#2182 := (not #1410)
#2185 := (forall (vars (?v0 S3)) #2182)
#2826 := (and #136 #141 #620 #623 #2185 #2820)
#3009 := (or #2826 #3004)
#2675 := (not #2670)
#2678 := (and #2040 #2658 #2675)
#2681 := (or #1297 #2678)
#2684 := (forall (vars (?v0 S3)) #2681)
#2620 := (not #2615)
#2638 := (and #2013 #2620 #2633)
#2641 := (or #1259 #2638)
#2644 := (forall (vars (?v0 S3)) #2641)
#3015 := (and #100 #1705 #1721 #1730 #2644 #2684 #3009)
#1968 := (not #1967)
#2588 := (and #453 #1968 #2585)
#2591 := (not #2588)
#2594 := (forall (vars (?v1 S3)) #2591)
#2560 := (not #2557)
#1973 := (not #1972)
#2600 := (and #1973 #2560 #2594)
#3020 := (or #2600 #3015)
#3023 := (and #1244 #3020)
#1934 := (not #1933)
#2545 := (and #1934 #1936)
#2548 := (not #2545)
#2551 := (or #2542 #2548)
#2554 := (not #2551)
#3026 := (or #2554 #3023)
#3029 := (and #1213 #3026)
#1911 := (not #1910)
#2513 := (and #1908 #1911)
#2516 := (not #2513)
#2532 := (or #2516 #2527)
#2535 := (not #2532)
#3032 := (or #2535 #3029)
#3035 := (and #1193 #3032)
#3038 := (or #1888 #3035)
#3041 := (and #71 #3038)
#3044 := (or #1187 #3041)
#3686 := (iff #3044 #3685)
#3683 := (iff #3041 #3680)
#3675 := (and #71 #3672)
#3681 := (iff #3675 #3680)
#3682 := [rewrite]: #3681
#3676 := (iff #3041 #3675)
#3673 := (iff #3038 #3672)
#3670 := (iff #3035 #3667)
#3662 := (and #1193 #3659)
#3668 := (iff #3662 #3667)
#3669 := [rewrite]: #3668
#3663 := (iff #3035 #3662)
#3660 := (iff #3032 #3659)
#3657 := (iff #3029 #3654)
#3648 := (and #3066 #3645)
#3655 := (iff #3648 #3654)
#3656 := [rewrite]: #3655
#3649 := (iff #3029 #3648)
#3646 := (iff #3026 #3645)
#3643 := (iff #3023 #3640)
#3634 := (and #3111 #3631)
#3641 := (iff #3634 #3640)
#3642 := [rewrite]: #3641
#3635 := (iff #3023 #3634)
#3632 := (iff #3020 #3631)
#3629 := (iff #3015 #3626)
#3617 := (and #100 #3158 #3181 #1730 #3209 #3237 #3614)
#3627 := (iff #3617 #3626)
#3628 := [rewrite]: #3627
#3618 := (iff #3015 #3617)
#3615 := (iff #3009 #3614)
#3612 := (iff #3004 #3609)
#3602 := (and #181 #756 #3395 #3413 #1638 #1646 #2202 #2205 #3599)
#3610 := (iff #3602 #3609)
#3611 := [rewrite]: #3610
#3603 := (iff #3004 #3602)
#3600 := (iff #2998 #3599)
#3597 := (iff #2995 #3594)
#3589 := (and #1473 #3586)
#3595 := (iff #3589 #3594)
#3596 := [rewrite]: #3595
#3590 := (iff #2995 #3589)
#3587 := (iff #2992 #3586)
#3584 := (iff #2989 #3581)
#3576 := (and #810 #3573)
#3582 := (iff #3576 #3581)
#3583 := [rewrite]: #3582
#3577 := (iff #2989 #3576)
#3574 := (iff #2986 #3573)
#3571 := (iff #2983 #3568)
#3563 := (and #203 #3560)
#3569 := (iff #3563 #3568)
#3570 := [rewrite]: #3569
#3564 := (iff #2983 #3563)
#3561 := (iff #2980 #3560)
#3558 := (iff #2977 #3555)
#3550 := (and #1487 #3547)
#3556 := (iff #3550 #3555)
#3557 := [rewrite]: #3556
#3551 := (iff #2977 #3550)
#3548 := (iff #2974 #3547)
#3545 := (iff #2971 #3542)
#3536 := (and #3459 #3533)
#3543 := (iff #3536 #3542)
#3544 := [rewrite]: #3543
#3537 := (iff #2971 #3536)
#3534 := (iff #2968 #3533)
#3531 := (iff #2963 #3528)
#3522 := (and #3504 #2351 #2920 #3519)
#3529 := (iff #3522 #3528)
#3530 := [rewrite]: #3529
#3523 := (iff #2963 #3522)
#3520 := (iff #2954 #3519)
#3517 := (iff #2951 #3508)
#3509 := (not #3508)
#3512 := (not #3509)
#3515 := (iff #3512 #3508)
#3516 := [rewrite]: #3515
#3513 := (iff #2951 #3512)
#3510 := (iff #2948 #3509)
#3511 := [rewrite]: #3510
#3514 := [monotonicity #3511]: #3513
#3518 := [trans #3514 #3516]: #3517
#3521 := [quant-intro #3518]: #3520
#3505 := (iff #1530 #3504)
#3502 := (iff #1527 #3499)
#3485 := (or #804 #1226)
#3496 := (or #3485 #1523)
#3500 := (iff #3496 #3499)
#3501 := [rewrite]: #3500
#3497 := (iff #1527 #3496)
#3494 := (iff #1520 #3485)
#3486 := (not #3485)
#3489 := (not #3486)
#3492 := (iff #3489 #3485)
#3493 := [rewrite]: #3492
#3490 := (iff #1520 #3489)
#3487 := (iff #1515 #3486)
#3488 := [rewrite]: #3487
#3491 := [monotonicity #3488]: #3490
#3495 := [trans #3491 #3493]: #3494
#3498 := [monotonicity #3495]: #3497
#3503 := [trans #3498 #3501]: #3502
#3506 := [quant-intro #3503]: #3505
#3524 := [monotonicity #3506 #3521]: #3523
#3532 := [trans #3524 #3530]: #3531
#3483 := (iff #2914 #3482)
#3480 := (iff #2911 #3477)
#3463 := (or #2318 #3462)
#3474 := (or #3463 #2906)
#3478 := (iff #3474 #3477)
#3479 := [rewrite]: #3478
#3475 := (iff #2911 #3474)
#3472 := (iff #2893 #3463)
#3464 := (not #3463)
#3467 := (not #3464)
#3470 := (iff #3467 #3463)
#3471 := [rewrite]: #3470
#3468 := (iff #2893 #3467)
#3465 := (iff #2890 #3464)
#3466 := [rewrite]: #3465
#3469 := [monotonicity #3466]: #3468
#3473 := [trans #3469 #3471]: #3472
#3476 := [monotonicity #3473]: #3475
#3481 := [trans #3476 #3479]: #3480
#3484 := [monotonicity #3481]: #3483
#3535 := [monotonicity #3484 #3532]: #3534
#3460 := (iff #1506 #3459)
#3457 := (iff #1501 #3454)
#3440 := (or #798 #3439)
#3451 := (or #3440 #1493)
#3455 := (iff #3451 #3454)
#3456 := [rewrite]: #3455
#3452 := (iff #1501 #3451)
#3449 := (iff #827 #3440)
#3441 := (not #3440)
#3444 := (not #3441)
#3447 := (iff #3444 #3440)
#3448 := [rewrite]: #3447
#3445 := (iff #827 #3444)
#3442 := (iff #821 #3441)
#3443 := [rewrite]: #3442
#3446 := [monotonicity #3443]: #3445
#3450 := [trans #3446 #3448]: #3449
#3453 := [monotonicity #3450]: #3452
#3458 := [trans #3453 #3456]: #3457
#3461 := [quant-intro #3458]: #3460
#3538 := [monotonicity #3461 #3535]: #3537
#3546 := [trans #3538 #3544]: #3545
#3437 := (iff #2887 #3436)
#3434 := (iff #2884 #3431)
#3417 := (or #3416 #2289)
#3428 := (or #3417 #2879)
#3432 := (iff #3428 #3431)
#3433 := [rewrite]: #3432
#3429 := (iff #2884 #3428)
#3426 := (iff #2868 #3417)
#3418 := (not #3417)
#3421 := (not #3418)
#3424 := (iff #3421 #3417)
#3425 := [rewrite]: #3424
#3422 := (iff #2868 #3421)
#3419 := (iff #2865 #3418)
#3420 := [rewrite]: #3419
#3423 := [monotonicity #3420]: #3422
#3427 := [trans #3423 #3425]: #3426
#3430 := [monotonicity #3427]: #3429
#3435 := [trans #3430 #3433]: #3434
#3438 := [monotonicity #3435]: #3437
#3549 := [monotonicity #3438 #3546]: #3548
#3552 := [monotonicity #3549]: #3551
#3559 := [trans #3552 #3557]: #3558
#3562 := [monotonicity #3559]: #3561
#3565 := [monotonicity #3562]: #3564
#3572 := [trans #3565 #3570]: #3571
#3575 := [monotonicity #3572]: #3574
#3578 := [monotonicity #3575]: #3577
#3585 := [trans #3578 #3583]: #3584
#3588 := [monotonicity #3585]: #3587
#3591 := [monotonicity #3588]: #3590
#3598 := [trans #3591 #3596]: #3597
#3601 := [monotonicity #3598]: #3600
#3414 := (iff #1620 #3413)
#3411 := (iff #1617 #3408)
#3405 := (or #3388 #1614)
#3409 := (iff #3405 #3408)
#3410 := [rewrite]: #3409
#3406 := (iff #1617 #3405)
#3403 := (iff #1609 #3388)
#3398 := (not #3389)
#3401 := (iff #3398 #3388)
#3402 := [rewrite]: #3401
#3399 := (iff #1609 #3398)
#3390 := (iff #1451 #3389)
#3391 := [rewrite]: #3390
#3400 := [monotonicity #3391]: #3399
#3404 := [trans #3400 #3402]: #3403
#3407 := [monotonicity #3404]: #3406
#3412 := [trans #3407 #3410]: #3411
#3415 := [quant-intro #3412]: #3414
#3396 := (iff #1462 #3395)
#3393 := (iff #1457 #3392)
#3394 := [monotonicity #3391]: #3393
#3397 := [quant-intro #3394]: #3396
#3604 := [monotonicity #3397 #3415 #3601]: #3603
#3613 := [trans #3604 #3611]: #3612
#3386 := (iff #2826 #3383)
#3377 := (and #136 #141 #620 #623 #3251 #3374)
#3384 := (iff #3377 #3383)
#3385 := [rewrite]: #3384
#3378 := (iff #2826 #3377)
#3375 := (iff #2820 #3374)
#3372 := (iff #2817 #3369)
#3363 := (and #3303 #3360)
#3370 := (iff #3363 #3369)
#3371 := [rewrite]: #3370
#3364 := (iff #2817 #3363)
#3361 := (iff #2812 #3360)
#3358 := (iff #2806 #3357)
#3355 := (iff #2803 #3352)
#3338 := (or #2142 #2146)
#3349 := (or #3338 #2798)
#3353 := (iff #3349 #3352)
#3354 := [rewrite]: #3353
#3350 := (iff #2803 #3349)
#3347 := (iff #2786 #3338)
#3339 := (not #3338)
#3342 := (not #3339)
#3345 := (iff #3342 #3338)
#3346 := [rewrite]: #3345
#3343 := (iff #2786 #3342)
#3340 := (iff #2783 #3339)
#3341 := [rewrite]: #3340
#3344 := [monotonicity #3341]: #3343
#3348 := [trans #3344 #3346]: #3347
#3351 := [monotonicity #3348]: #3350
#3356 := [trans #3351 #3354]: #3355
#3359 := [monotonicity #3356]: #3358
#3336 := (iff #2166 #3333)
#3328 := (and #2156 #3325)
#3334 := (iff #3328 #3333)
#3335 := [rewrite]: #3334
#3329 := (iff #2166 #3328)
#3326 := (iff #1382 #3325)
#3323 := (iff #1379 #3320)
#3306 := (or #1226 #1335)
#3317 := (or #3306 #1376)
#3321 := (iff #3317 #3320)
#3322 := [rewrite]: #3321
#3318 := (iff #1379 #3317)
#3315 := (iff #1373 #3306)
#3307 := (not #3306)
#3310 := (not #3307)
#3313 := (iff #3310 #3306)
#3314 := [rewrite]: #3313
#3311 := (iff #1373 #3310)
#3308 := (iff #1370 #3307)
#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
#3304 := (iff #2780 #3303)
#3301 := (iff #2777 #3298)
#3279 := (or #57 #1335)
#3295 := (or #3279 #3292)
#3299 := (iff #3295 #3298)
#3300 := [rewrite]: #3299
#3296 := (iff #2777 #3295)
#3293 := (iff #2774 #3292)
#3294 := [rewrite]: #3293
#3288 := (iff #1342 #3279)
#3280 := (not #3279)
#3283 := (not #3280)
#3286 := (iff #3283 #3279)
#3287 := [rewrite]: #3286
#3284 := (iff #1342 #3283)
#3281 := (iff #1339 #3280)
#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)
#3276 := [rewrite]: #3275
#3270 := (iff #2738 #3269)
#3267 := (iff #2732 #3266)
#3264 := (iff #2729 #3255)
#3256 := (not #3255)
#3259 := (not #3256)
#3262 := (iff #3259 #3255)
#3263 := [rewrite]: #3262
#3260 := (iff #2729 #3259)
#3257 := (iff #2726 #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)
#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)
#3116 := (not #3115)
#3119 := (not #3116)
#3122 := (iff #3119 #3115)
#3123 := [rewrite]: #3122
#3120 := (iff #2591 #3119)
#3117 := (iff #2588 #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
#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)
#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)
#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
#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)
#2627 := (= #2624 0::Int)
#2634 := (iff #2627 #2633)
#2635 := [rewrite]: #2634
#2628 := (iff #2008 #2627)
#2625 := (= #2007 #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)
#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)
#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)
#2479 := (~ #2478 #2477)
#2474 := (not #1767)
#2475 := (~ #2474 #2473)
#2470 := (not #1762)
#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)
#2439 := [refl]: #2438
#2435 := (not #1641)
#2436 := (~ #2435 #1638)
#2433 := (~ #1638 #1638)
#2431 := (~ #1633 #1633)
#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)
#2425 := [refl]: #2424
#2427 := [nnf-pos #2425]: #2426
#2430 := [nnf-neg #2427]: #2429
#2421 := (not #1606)
#2422 := (~ #2421 #2420)
#2417 := (not #1603)
#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)
#2398 := (~ #2397 #2396)
#2393 := (not #1585)
#2394 := (~ #2393 #2392)
#2389 := (not #1582)
#2390 := (~ #2389 #2388)
#2385 := (not #1579)
#2386 := (~ #2385 #2384)
#2381 := (not #1576)
#2382 := (~ #2381 #2380)
#2377 := (not #1573)
#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)
#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)
#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)
#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
#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)
#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)
#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
unsat