src/HOL/Boogie/Examples/Boogie_Dijkstra.certs

merged

a7dbe4783d45017a8218697dc955b8483ad44034 7163 0
#2 := false
decl f11 :: (-> S7 S2 S1)
decl ?v1!7 :: (-> S2 S2)
decl ?v0!20 :: S2
#2334 := ?v0!20
#14575 := (?v1!7 ?v0!20)
decl f29 :: S7
#191 := f29
#21476 := (f11 f29 #14575)
decl f1 :: S1
#4 := f1
#21477 := (= f1 #21476)
decl f8 :: (-> S6 S3 S2)
decl f5 :: (-> S4 S2 S3)
decl f6 :: (-> S5 S2 S4)
decl f7 :: S5
#14 := f7
#14580 := (f6 f7 #14575)
#14581 := (f5 #14580 ?v0!20)
decl f9 :: S6
#25 := f9
#21962 := (f8 f9 #14581)
decl f12 :: (-> S8 S1 S7)
decl f28 :: S2
#182 := f28
decl f13 :: (-> S9 S2 S8)
decl f14 :: (-> S10 S7 S9)
decl f21 :: S7
#116 := f21
decl f15 :: S10
#40 := f15
#192 := (f14 f15 f21)
#193 := (f13 #192 f28)
#194 := (f12 #193 f1)
#6256 := (f11 #194 f28)
decl f16 :: S2
#66 := f16
#196 := (f6 f7 f28)
#6329 := (f5 #196 f16)
#7092 := (f8 f9 #6329)
#7451 := (f13 #192 #7092)
#7452 := (f12 #7451 #6256)
#27860 := (f11 #7452 #21962)
#24145 := (= #27860 #21476)
#24148 := (= #21476 #27860)
#21963 := (= #14575 #21962)
#12 := (:var 0 S2)
#11 := (:var 1 S2)
#15 := (f6 f7 #11)
#16 := (f5 #15 #12)
#4159 := (pattern #16)
#26 := (f8 f9 #16)
#358 := (= #11 #26)
#4172 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4159) #358)
#361 := (forall (vars (?v0 S2) (?v1 S2)) #358)
#4175 := (iff #361 #4172)
#4173 := (iff #358 #358)
#4174 := [refl]: #4173
#4176 := [quant-intro #4174]: #4175
#1828 := (~ #361 #361)
#1852 := (~ #358 #358)
#1853 := [refl]: #1852
#1829 := [nnf-pos #1853]: #1828
#27 := (= #26 #11)
#28 := (forall (vars (?v0 S2) (?v1 S2)) #27)
#362 := (iff #28 #361)
#359 := (iff #27 #358)
#360 := [rewrite]: #359
#363 := [quant-intro #360]: #362
#357 := [asserted]: #28
#366 := [mp #357 #363]: #361
#1854 := [mp~ #366 #1829]: #361
#4177 := [mp #1854 #4176]: #4172
#7209 := (not #4172)
#21231 := (or #7209 #21963)
#21190 := [quant-inst #14575 #2334]: #21231
#27911 := [unit-resolution #21190 #4177]: #21963
#21352 := (= f29 #7452)
#21373 := (= #194 #7452)
#9639 := (= #7452 #194)
#9698 := (= #6256 f1)
#6251 := (= f1 #6256)
#44 := (:var 0 S1)
#41 := (:var 2 S7)
#42 := (f14 f15 #41)
#43 := (f13 #42 #11)
#45 := (f12 #43 #44)
#4192 := (pattern #45)
#385 := (= f1 #44)
#46 := (f11 #45 #11)
#381 := (= f1 #46)
#388 := (iff #381 #385)
#4193 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) (:pat #4192) #388)
#391 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) #388)
#4196 := (iff #391 #4193)
#4194 := (iff #388 #388)
#4195 := [refl]: #4194
#4197 := [quant-intro #4195]: #4196
#1834 := (~ #391 #391)
#1861 := (~ #388 #388)
#1862 := [refl]: #1861
#1835 := [nnf-pos #1862]: #1834
#48 := (= #44 f1)
#47 := (= #46 f1)
#49 := (iff #47 #48)
#50 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1)) #49)
#392 := (iff #50 #391)
#389 := (iff #49 #388)
#386 := (iff #48 #385)
#387 := [rewrite]: #386
#383 := (iff #47 #381)
#384 := [rewrite]: #383
#390 := [monotonicity #384 #387]: #389
#393 := [quant-intro #390]: #392
#380 := [asserted]: #50
#396 := [mp #380 #393]: #391
#1863 := [mp~ #396 #1835]: #391
#4198 := [mp #1863 #4197]: #4193
#6302 := (not #4193)
#6303 := (or #6302 #6251)
#6237 := (= f1 f1)
#6257 := (iff #6251 #6237)
#6002 := (or #6302 #6257)
#6321 := (iff #6002 #6303)
#6323 := (iff #6303 #6303)
#6324 := [rewrite]: #6323
#6289 := (iff #6257 #6251)
#1 := true
#6290 := (iff #6251 true)
#6300 := (iff #6290 #6251)
#6298 := [rewrite]: #6300
#6297 := (iff #6257 #6290)
#6258 := (iff #6237 true)
#6259 := [rewrite]: #6258
#6299 := [monotonicity #6259]: #6297
#6301 := [trans #6299 #6298]: #6289
#6322 := [monotonicity #6301]: #6321
#6325 := [trans #6322 #6324]: #6321
#6003 := [quant-inst #116 #182 #4]: #6002
#6320 := [mp #6003 #6325]: #6303
#9703 := [unit-resolution #6320 #4198]: #6251
#9662 := [symm #9703]: #9698
#9663 := (= #7451 #193)
#8145 := (= #7092 f28)
#7093 := (= f28 #7092)
#7096 := (or #7209 #7093)
#7097 := [quant-inst #182 #66]: #7096
#8144 := [unit-resolution #7097 #4177]: #7093
#8146 := [symm #8144]: #8145
#9638 := [monotonicity #8146]: #9663
#9640 := [monotonicity #9638 #9662]: #9639
#21376 := [symm #9640]: #21373
#195 := (= f29 #194)
#92 := (f6 f7 #12)
#4246 := (pattern #92)
decl f30 :: (-> S2 Int)
#203 := (f30 #12)
#4381 := (pattern #203)
#213 := (f11 f29 #12)
#4407 := (pattern #213)
#8 := 0::Int
decl f4 :: (-> S3 Int)
#2338 := (f5 #92 ?v0!20)
#2339 := (f4 #2338)
#2335 := (f30 ?v0!20)
#1190 := -1::Int
#2336 := (* -1::Int #2335)
#2938 := (+ #2336 #2339)
#2939 := (+ #203 #2938)
#2942 := (= #2939 0::Int)
#3504 := (not #2942)
#2337 := (+ #203 #2336)
#2342 := (>= #2337 0::Int)
#789 := (= f1 #213)
#795 := (not #789)
#3505 := (or #795 #2342 #3504)
#4441 := (forall (vars (?v1 S2)) (:pat #4407 #4381 #4246) #3505)
#4446 := (not #4441)
#93 := (f5 #92 #11)
#4237 := (pattern #93)
#225 := (f30 #11)
#1485 := (* -1::Int #225)
#1486 := (+ #203 #1485)
#94 := (f4 #93)
#1516 := (+ #94 #1486)
#1514 := (>= #1516 0::Int)
#1213 := (* -1::Int #94)
decl f3 :: Int
#9 := f3
#1216 := (+ f3 #1213)
#1217 := (<= #1216 0::Int)
#3496 := (or #795 #1217 #1514)
#4433 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4237) #3496)
#4438 := (not #4433)
#2914 := (= f16 ?v0!20)
#2346 := (+ f3 #2336)
#2347 := (<= #2346 0::Int)
#4449 := (or #2347 #2914 #4438 #4446)
#4452 := (not #4449)
decl ?v0!19 :: S2
#2303 := ?v0!19
decl ?v1!18 :: S2
#2302 := ?v1!18
#2308 := (f6 f7 ?v1!18)
#2309 := (f5 #2308 ?v0!19)
#2310 := (f4 #2309)
#2313 := (* -1::Int #2310)
#2306 := (f30 ?v1!18)
#2900 := (* -1::Int #2306)
#2901 := (+ #2900 #2313)
#2304 := (f30 ?v0!19)
#2902 := (+ #2304 #2901)
#2903 := (<= #2902 0::Int)
#2317 := (f11 f29 ?v1!18)
#2318 := (= f1 #2317)
#3459 := (not #2318)
#2314 := (+ f3 #2313)
#2315 := (<= #2314 0::Int)
#3474 := (or #2315 #3459 #2903)
#3479 := (not #3474)
#4455 := (or #3479 #4452)
#4458 := (not #4455)
#4424 := (pattern #203 #225)
#1484 := (>= #1486 0::Int)
#222 := (f11 f29 #11)
#809 := (= f1 #222)
#3436 := (not #809)
#3451 := (or #789 #3436 #1484)
#4425 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4424) #3451)
#4430 := (not #4425)
#4461 := (or #4430 #4458)
#4464 := (not #4461)
decl ?v1!16 :: S2
#2275 := ?v1!16
#2279 := (f30 ?v1!16)
#2874 := (* -1::Int #2279)
decl ?v0!17 :: S2
#2276 := ?v0!17
#2277 := (f30 ?v0!17)
#2875 := (+ #2277 #2874)
#2876 := (<= #2875 0::Int)
#2284 := (f11 f29 ?v1!16)
#2285 := (= f1 #2284)
#2282 := (f11 f29 ?v0!17)
#2283 := (= f1 #2282)
#3413 := (not #2283)
#3428 := (or #3413 #2285 #2876)
#3433 := (not #3428)
#4467 := (or #3433 #4464)
#4470 := (not #4467)
#1475 := (>= #203 0::Int)
#4416 := (forall (vars (?v0 S2)) (:pat #4381) #1475)
#4421 := (not #4416)
#4473 := (or #4421 #4470)
#4476 := (not #4473)
decl ?v0!15 :: S2
#2260 := ?v0!15
#2261 := (f30 ?v0!15)
#2262 := (>= #2261 0::Int)
#2263 := (not #2262)
#4479 := (or #2263 #4476)
#4482 := (not #4479)
#217 := (f30 f16)
#218 := (= #217 0::Int)
#1472 := (not #218)
#4485 := (or #1472 #4482)
#4488 := (not #4485)
#4491 := (or #1472 #4488)
#4494 := (not #4491)
decl f19 :: (-> S11 S2 Int)
decl f20 :: S11
#110 := f20
#113 := (f19 f20 #12)
#4261 := (pattern #113)
#775 := (= #113 #203)
#796 := (or #775 #795)
#4408 := (forall (vars (?v0 S2)) (:pat #4261 #4381 #4407) #796)
#4413 := (not #4408)
#4497 := (or #4413 #4494)
#4500 := (not #4497)
decl ?v0!14 :: S2
#2235 := ?v0!14
#2240 := (f19 f20 ?v0!14)
#2239 := (f30 ?v0!14)
#2846 := (= #2239 #2240)
#2236 := (f11 f29 ?v0!14)
#2237 := (= f1 #2236)
#2238 := (not #2237)
#2852 := (or #2238 #2846)
#2857 := (not #2852)
#4503 := (or #2857 #4500)
#4506 := (not #4503)
#1460 := (* -1::Int #203)
#1461 := (+ #113 #1460)
#1459 := (>= #1461 0::Int)
#4399 := (forall (vars (?v0 S2)) (:pat #4261 #4381) #1459)
#4404 := (not #4399)
#4509 := (or #4404 #4506)
#4512 := (not #4509)
decl ?v0!13 :: S2
#2217 := ?v0!13
#2220 := (f19 f20 ?v0!13)
#2836 := (* -1::Int #2220)
#2218 := (f30 ?v0!13)
#2837 := (+ #2218 #2836)
#2838 := (<= #2837 0::Int)
#2843 := (not #2838)
#4515 := (or #2843 #4512)
#4518 := (not #4515)
#197 := (f5 #196 #12)
#4382 := (pattern #197)
#198 := (f4 #197)
#1603 := (+ #198 #1460)
#186 := (f19 f20 f28)
#1604 := (+ #186 #1603)
#1605 := (= #1604 0::Int)
#1429 := (* -1::Int #198)
#1435 := (* -1::Int #186)
#1436 := (+ #1435 #1429)
#1437 := (+ #113 #1436)
#1438 := (<= #1437 0::Int)
#1430 := (+ f3 #1429)
#1431 := (<= #1430 0::Int)
#3405 := (or #1431 #1438 #1605)
#4391 := (forall (vars (?v0 S2)) (:pat #4382 #4261 #4381) #3405)
#4396 := (not #4391)
#3385 := (or #1431 #1438)
#3386 := (not #3385)
#3389 := (or #775 #3386)
#4383 := (forall (vars (?v0 S2)) (:pat #4261 #4381 #4382) #3389)
#4388 := (not #4383)
decl ?v0!12 :: S2
#2193 := ?v0!12
#2199 := (f11 f21 ?v0!12)
#2200 := (= f1 #2199)
#2194 := (f19 f20 ?v0!12)
#2195 := (* -1::Int #2194)
#2196 := (+ f3 #2195)
#2197 := (<= #2196 0::Int)
#1635 := (+ f3 #1435)
#1636 := (<= #1635 0::Int)
#117 := (f11 f21 #12)
#4303 := (pattern #117)
#1618 := (+ #113 #1435)
#1617 := (>= #1618 0::Int)
#523 := (= f1 #117)
#1624 := (or #523 #1617)
#4373 := (forall (vars (?v0 S2)) (:pat #4303 #4261) #1624)
#4378 := (not #4373)
#183 := (f11 f21 f28)
#744 := (= f1 #183)
#977 := (not #195)
#4521 := (or #977 #744 #4378 #1636 #2197 #2200 #4388 #4396 #4518)
#4524 := (not #4521)
decl ?v0!11 :: S2
#2126 := ?v0!11
decl ?v1!10 :: S2
#2125 := ?v1!10
#2131 := (f6 f7 ?v1!10)
#2132 := (f5 #2131 ?v0!11)
#2133 := (f4 #2132)
#2140 := (* -1::Int #2133)
decl f25 :: S11
#149 := f25
#2129 := (f19 f25 ?v1!10)
#2136 := (* -1::Int #2129)
#2793 := (+ #2136 #2140)
#2127 := (f19 f25 ?v0!11)
#2794 := (+ #2127 #2793)
#2795 := (<= #2794 0::Int)
#2141 := (+ f3 #2140)
#2142 := (<= #2141 0::Int)
#2137 := (+ f3 #2136)
#2138 := (<= #2137 0::Int)
#3349 := (or #2138 #2142 #2795)
#3354 := (not #3349)
#157 := (f19 f25 #11)
#1337 := (* -1::Int #157)
#154 := (f19 f25 #12)
#1338 := (+ #154 #1337)
#1344 := (+ #94 #1338)
#1367 := (>= #1344 0::Int)
#1324 := (* -1::Int #154)
#1325 := (+ f3 #1324)
#1326 := (<= #1325 0::Int)
#3317 := (or #1217 #1326 #1367)
#4335 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4237) #3317)
#4340 := (not #4335)
#169 := (f19 f25 f16)
#170 := (= #169 0::Int)
#4343 := (or #170 #4340)
#4346 := (not #4343)
#4349 := (or #4346 #3354)
#4352 := (not #4349)
#4312 := (pattern #154)
decl ?v1!9 :: (-> S2 S2)
#2101 := (?v1!9 #12)
#2104 := (f6 f7 #2101)
#2105 := (f5 #2104 #12)
#2106 := (f4 #2105)
#2763 := (* -1::Int #2106)
#2102 := (f19 f25 #2101)
#2746 := (* -1::Int #2102)
#2764 := (+ #2746 #2763)
#2765 := (+ #154 #2764)
#2766 := (= #2765 0::Int)
#3287 := (not #2766)
#2747 := (+ #154 #2746)
#2748 := (<= #2747 0::Int)
#3288 := (or #2748 #3287)
#3289 := (not #3288)
#67 := (= #12 f16)
#3295 := (or #67 #1326 #3289)
#4327 := (forall (vars (?v0 S2)) (:pat #4312) #3295)
#4332 := (not #4327)
#4355 := (or #4332 #4352)
#4358 := (not #4355)
decl ?v0!8 :: S2
#2061 := ?v0!8
#2065 := (f5 #92 ?v0!8)
#2066 := (f4 #2065)
#2062 := (f19 f25 ?v0!8)
#2063 := (* -1::Int #2062)
#2716 := (+ #2063 #2066)
#2717 := (+ #154 #2716)
#2720 := (= #2717 0::Int)
#3251 := (not #2720)
#2064 := (+ #154 #2063)
#2069 := (>= #2064 0::Int)
#3252 := (or #2069 #3251)
#4313 := (forall (vars (?v1 S2)) (:pat #4312 #4246) #3252)
#4318 := (not #4313)
#2692 := (= f16 ?v0!8)
#2073 := (+ f3 #2063)
#2074 := (<= #2073 0::Int)
#4321 := (or #2074 #2692 #4318)
#4324 := (not #4321)
#4361 := (or #4324 #4358)
#4364 := (not #4361)
#1279 := (* -1::Int #113)
#1280 := (+ f3 #1279)
#1281 := (<= #1280 0::Int)
#3237 := (or #523 #1281)
#4304 := (forall (vars (?v0 S2)) (:pat #4303 #4261) #3237)
#4309 := (not #4304)
#614 := (= f20 f25)
#705 := (not #614)
decl f22 :: S7
#144 := f22
#611 := (= f21 f22)
#723 := (not #611)
decl f27 :: S11
#152 := f27
decl f26 :: S11
#151 := f26
#153 := (= f26 f27)
#696 := (not #153)
decl f24 :: S2
#147 := f24
decl f23 :: S2
#146 := f23
#148 := (= f23 f24)
#714 := (not #148)
#4367 := (or #714 #696 #723 #705 #4309 #4364)
#4370 := (not #4367)
#4527 := (or #4370 #4524)
#4530 := (not #4527)
#2023 := (?v1!7 #12)
#2024 := (f19 f20 #2023)
#2651 := (* -1::Int #2024)
#2666 := (+ #113 #2651)
#2667 := (<= #2666 0::Int)
#2028 := (f6 f7 #2023)
#2029 := (f5 #2028 #12)
#2030 := (f4 #2029)
#2652 := (* -1::Int #2030)
#2653 := (+ #2651 #2652)
#2654 := (+ #113 #2653)
#2655 := (= #2654 0::Int)
#3221 := (not #2655)
#2033 := (f11 f21 #2023)
#2034 := (= f1 #2033)
#3220 := (not #2034)
#3222 := (or #3220 #3221 #2667)
#3223 := (not #3222)
#3229 := (or #67 #1281 #3223)
#4295 := (forall (vars (?v0 S2)) (:pat #4261) #3229)
#4300 := (not #4295)
decl f17 :: (-> S2 Int)
#68 := (f17 #12)
#4206 := (pattern #68)
decl ?v1!6 :: (-> S2 S2)
#1994 := (?v1!6 #12)
#1999 := (f17 #1994)
#2610 := (* -1::Int #1999)
#1995 := (f6 f7 #1994)
#1996 := (f5 #1995 #12)
#1997 := (f4 #1996)
#2627 := (* -1::Int #1997)
#2628 := (+ #2627 #2610)
#2629 := (+ #68 #2628)
#2630 := (= #2629 0::Int)
#3193 := (not #2630)
#2611 := (+ #68 #2610)
#2612 := (<= #2611 0::Int)
decl f18 :: S7
#76 := f18
#2005 := (f11 f18 #1994)
#2006 := (= f1 #2005)
#3192 := (not #2006)
#3194 := (or #3192 #2612 #3193)
#3195 := (not #3194)
#1241 := (* -1::Int #68)
#1242 := (+ f3 #1241)
#1243 := (<= #1242 0::Int)
#3201 := (or #67 #1243 #3195)
#4287 := (forall (vars (?v0 S2)) (:pat #4206) #3201)
#4292 := (not #4287)
#120 := (f11 f21 #11)
#4278 := (pattern #117 #120)
#123 := (f19 f20 #11)
#1293 := (* -1::Int #123)
#1294 := (+ #113 #1293)
#1297 := (>= #1294 0::Int)
#529 := (= f1 #120)
#3158 := (not #529)
#3173 := (or #523 #3158 #1297)
#4279 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4278) #3173)
#4284 := (not #4279)
#1295 := (+ #94 #1294)
#1690 := (>= #1295 0::Int)
#526 := (not #523)
#3150 := (or #526 #1217 #1690)
#4270 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4237) #3150)
#4275 := (not #4270)
#1718 := (>= #113 0::Int)
#4262 := (forall (vars (?v0 S2)) (:pat #4261) #1718)
#4267 := (not #4262)
#111 := (f19 f20 f16)
#112 := (= #111 0::Int)
#1729 := (not #112)
#4533 := (or #1729 #4267 #4275 #4284 #4292 #4300 #4530)
#4536 := (not #4533)
#77 := (f11 f18 #12)
#4213 := (pattern #77)
decl ?v0!5 :: S2
#1950 := ?v0!5
#1953 := (f17 ?v0!5)
#1954 := (* -1::Int #1953)
#1951 := (f5 #92 ?v0!5)
#1952 := (f4 #1951)
#2578 := (+ #1952 #1954)
#2579 := (+ #68 #2578)
#2582 := (= #2579 0::Int)
#3111 := (not #2582)
#1958 := (+ #68 #1954)
#1959 := (>= #1958 0::Int)
#444 := (= f1 #77)
#447 := (not #444)
#3112 := (or #447 #1959 #3111)
#4247 := (forall (vars (?v1 S2)) (:pat #4213 #4206 #4246) #3112)
#4252 := (not #4247)
#2554 := (= f16 ?v0!5)
#1963 := (+ f3 #1954)
#1964 := (<= #1963 0::Int)
#4255 := (or #1964 #2554 #4252)
#4258 := (not #4255)
#4539 := (or #4258 #4536)
#4542 := (not #4539)
#88 := (f17 #11)
#1193 := (* -1::Int #88)
#1214 := (+ #1193 #94)
#1215 := (+ #68 #1214)
#1212 := (>= #1215 0::Int)
#3103 := (or #447 #1212 #1217)
#4238 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4237) #3103)
#4243 := (not #4238)
#4545 := (or #4243 #4542)
#4548 := (not #4545)
decl ?v1!3 :: S2
#1918 := ?v1!3
#1934 := (f17 ?v1!3)
decl ?v0!4 :: S2
#1919 := ?v0!4
#1931 := (f17 ?v0!4)
#1932 := (* -1::Int #1931)
#2535 := (+ #1932 #1934)
#1920 := (f6 f7 ?v1!3)
#1921 := (f5 #1920 ?v0!4)
#1922 := (f4 #1921)
#2536 := (+ #1922 #2535)
#2539 := (>= #2536 0::Int)
#1927 := (f11 f18 ?v1!3)
#1928 := (= f1 #1927)
#3066 := (not #1928)
#1923 := (* -1::Int #1922)
#1924 := (+ f3 #1923)
#1925 := (<= #1924 0::Int)
#3081 := (or #1925 #3066 #2539)
#6295 := [hypothesis]: #1928
#4214 := (forall (vars (?v0 S2)) (:pat #4213) #447)
#450 := (forall (vars (?v0 S2)) #447)
#4217 := (iff #450 #4214)
#4215 := (iff #447 #447)
#4216 := [refl]: #4215
#4218 := [quant-intro #4216]: #4217
#1840 := (~ #450 #450)
#1870 := (~ #447 #447)
#1871 := [refl]: #1870
#1841 := [nnf-pos #1871]: #1840
#69 := (= #68 0::Int)
#72 := (not #67)
#1787 := (or #72 #69)
#1790 := (forall (vars (?v0 S2)) #1787)
#1793 := (not #1790)
#1721 := (forall (vars (?v0 S2)) #1718)
#1724 := (not #1721)
#532 := (and #526 #529)
#538 := (not #532)
#1707 := (or #538 #1297)
#1712 := (forall (vars (?v0 S2) (?v1 S2)) #1707)
#1715 := (not #1712)
#1218 := (not #1217)
#1682 := (and #523 #1218)
#1687 := (not #1682)
#1693 := (or #1687 #1690)
#1696 := (forall (vars (?v0 S2) (?v1 S2)) #1693)
#1699 := (not #1696)
#1629 := (forall (vars (?v0 S2)) #1624)
#1632 := (not #1629)
#1439 := (not #1438)
#1432 := (not #1431)
#1442 := (and #1432 #1439)
#1600 := (not #1442)
#1608 := (or #1600 #1605)
#1611 := (forall (vars (?v0 S2)) #1608)
#1614 := (not #1611)
#1538 := (= #1516 0::Int)
#1541 := (not #1484)
#1550 := (and #789 #1541 #1538)
#1555 := (exists (vars (?v1 S2)) #1550)
#1527 := (+ f3 #1460)
#1528 := (<= #1527 0::Int)
#1529 := (not #1528)
#1532 := (and #72 #1529)
#1535 := (not #1532)
#1558 := (or #1535 #1555)
#1561 := (forall (vars (?v0 S2)) #1558)
#1506 := (and #789 #1218)
#1511 := (not #1506)
#1518 := (or #1511 #1514)
#1521 := (forall (vars (?v0 S2) (?v1 S2)) #1518)
#1524 := (not #1521)
#1564 := (or #1524 #1561)
#1567 := (and #1521 #1564)
#812 := (and #795 #809)
#818 := (not #812)
#1492 := (or #818 #1484)
#1497 := (forall (vars (?v0 S2) (?v1 S2)) #1492)
#1500 := (not #1497)
#1570 := (or #1500 #1567)
#1573 := (and #1497 #1570)
#1478 := (forall (vars (?v0 S2)) #1475)
#1481 := (not #1478)
#1576 := (or #1481 #1573)
#1579 := (and #1478 #1576)
#1582 := (or #1472 #1579)
#1585 := (and #218 #1582)
#801 := (forall (vars (?v0 S2)) #796)
#935 := (not #801)
#1588 := (or #935 #1585)
#1591 := (and #801 #1588)
#1464 := (forall (vars (?v0 S2)) #1459)
#1467 := (not #1464)
#1594 := (or #1467 #1591)
#1597 := (and #1464 #1594)
#1448 := (or #775 #1442)
#1453 := (forall (vars (?v0 S2)) #1448)
#1456 := (not #1453)
#1282 := (not #1281)
#1401 := (and #526 #1282)
#1406 := (exists (vars (?v0 S2)) #1401)
#1647 := (not #1406)
#1671 := (or #977 #744 #1647 #1456 #1597 #1614 #1632 #1636)
#1327 := (not #1326)
#1361 := (and #1218 #1327)
#1364 := (not #1361)
#1370 := (or #1364 #1367)
#1373 := (forall (vars (?v0 S2) (?v1 S2)) #1370)
#1376 := (not #1373)
#1384 := (or #170 #1376)
#1389 := (and #1373 #1384)
#1342 := (= #1344 0::Int)
#1336 := (>= #1338 0::Int)
#1339 := (not #1336)
#1346 := (and #1339 #1342)
#1349 := (exists (vars (?v1 S2)) #1346)
#1330 := (and #72 #1327)
#1333 := (not #1330)
#1352 := (or #1333 #1349)
#1355 := (forall (vars (?v0 S2)) #1352)
#1358 := (not #1355)
#1392 := (or #1358 #1389)
#1395 := (and #1355 #1392)
#1424 := (or #714 #696 #723 #705 #1395 #1406)
#1676 := (and #1424 #1671)
#1298 := (not #1297)
#1291 := (= #1295 0::Int)
#1307 := (and #523 #1291 #1298)
#1312 := (exists (vars (?v1 S2)) #1307)
#1285 := (and #72 #1282)
#1288 := (not #1285)
#1315 := (or #1288 #1312)
#1318 := (forall (vars (?v0 S2)) #1315)
#1321 := (not #1318)
#1253 := (= #1215 0::Int)
#1194 := (+ #68 #1193)
#1192 := (>= #1194 0::Int)
#1256 := (not #1192)
#1265 := (and #444 #1256 #1253)
#1270 := (exists (vars (?v1 S2)) #1265)
#1244 := (not #1243)
#1247 := (and #72 #1244)
#1250 := (not #1247)
#1273 := (or #1250 #1270)
#1276 := (forall (vars (?v0 S2)) #1273)
#1732 := (not #1276)
#1753 := (or #1729 #1732 #1321 #1676 #1699 #1715 #1724)
#1758 := (and #1276 #1753)
#1224 := (and #444 #1218)
#1229 := (not #1224)
#1232 := (or #1212 #1229)
#1235 := (forall (vars (?v0 S2) (?v1 S2)) #1232)
#1238 := (not #1235)
#1761 := (or #1238 #1758)
#1764 := (and #1235 #1761)
#85 := (f11 f18 #11)
#456 := (= f1 #85)
#459 := (and #447 #456)
#465 := (not #459)
#1199 := (or #465 #1192)
#1204 := (forall (vars (?v0 S2) (?v1 S2)) #1199)
#1207 := (not #1204)
#1767 := (or #1207 #1764)
#1770 := (and #1204 #1767)
#1183 := (>= #68 0::Int)
#1184 := (forall (vars (?v0 S2)) #1183)
#1187 := (not #1184)
#1773 := (or #1187 #1770)
#1776 := (and #1184 #1773)
#81 := (f17 f16)
#82 := (= #81 0::Int)
#1178 := (not #82)
#1779 := (or #1178 #1776)
#1782 := (and #82 #1779)
#1142 := (not #450)
#430 := (= f3 #68)
#436 := (or #67 #430)
#441 := (forall (vars (?v0 S2)) #436)
#1151 := (not #441)
#1805 := (or #1151 #1142 #1782 #1793)
#1810 := (not #1805)
#230 := (+ #203 #94)
#237 := (= #225 #230)
#214 := (= #213 f1)
#238 := (and #214 #237)
#236 := (< #203 #225)
#239 := (and #236 #238)
#240 := (exists (vars (?v1 S2)) #239)
#234 := (< #203 f3)
#235 := (and #72 #234)
#241 := (implies #235 #240)
#242 := (forall (vars (?v0 S2)) #241)
#243 := (and #242 true)
#231 := (<= #225 #230)
#95 := (< #94 f3)
#229 := (and #214 #95)
#232 := (implies #229 #231)
#233 := (forall (vars (?v0 S2) (?v1 S2)) #232)
#244 := (implies #233 #243)
#245 := (and #233 #244)
#226 := (<= #225 #203)
#223 := (= #222 f1)
#221 := (not #214)
#224 := (and #221 #223)
#227 := (implies #224 #226)
#228 := (forall (vars (?v0 S2) (?v1 S2)) #227)
#246 := (implies #228 #245)
#247 := (and #228 #246)
#219 := (<= 0::Int #203)
#220 := (forall (vars (?v0 S2)) #219)
#248 := (implies #220 #247)
#249 := (and #220 #248)
#250 := (implies #218 #249)
#251 := (and #218 #250)
#208 := (= #203 #113)
#215 := (implies #214 #208)
#216 := (forall (vars (?v0 S2)) #215)
#252 := (implies #216 #251)
#253 := (and #216 #252)
#211 := (<= #203 #113)
#212 := (forall (vars (?v0 S2)) #211)
#254 := (implies #212 #253)
#255 := (and #212 #254)
#200 := (+ #186 #198)
#201 := (< #200 #113)
#199 := (< #198 f3)
#202 := (and #199 #201)
#207 := (not #202)
#209 := (implies #207 #208)
#210 := (forall (vars (?v0 S2)) #209)
#256 := (implies #210 #255)
#204 := (= #203 #200)
#205 := (implies #202 #204)
#206 := (forall (vars (?v0 S2)) #205)
#257 := (implies #206 #256)
#258 := (implies #195 #257)
#188 := (<= #186 #113)
#118 := (= #117 f1)
#119 := (not #118)
#189 := (implies #119 #188)
#190 := (forall (vars (?v0 S2)) #189)
#259 := (implies #190 #258)
#187 := (< #186 f3)
#260 := (implies #187 #259)
#184 := (= #183 f1)
#185 := (not #184)
#261 := (implies #185 #260)
#132 := (< #113 f3)
#141 := (and #119 #132)
#142 := (exists (vars (?v0 S2)) #141)
#262 := (implies #142 #261)
#263 := (implies true #262)
#171 := (and #170 true)
#159 := (+ #154 #94)
#166 := (<= #157 #159)
#155 := (< #154 f3)
#165 := (and #155 #95)
#167 := (implies #165 #166)
#168 := (forall (vars (?v0 S2) (?v1 S2)) #167)
#172 := (implies #168 #171)
#173 := (and #168 #172)
#160 := (= #157 #159)
#158 := (< #154 #157)
#161 := (and #158 #160)
#162 := (exists (vars (?v1 S2)) #161)
#156 := (and #72 #155)
#163 := (implies #156 #162)
#164 := (forall (vars (?v0 S2)) #163)
#174 := (implies #164 #173)
#175 := (and #164 #174)
#176 := (implies #153 #175)
#150 := (= f25 f20)
#177 := (implies #150 #176)
#178 := (implies #148 #177)
#145 := (= f22 f21)
#179 := (implies #145 #178)
#143 := (not #142)
#180 := (implies #143 #179)
#181 := (implies true #180)
#264 := (and #181 #263)
#128 := (+ #113 #94)
#135 := (= #123 #128)
#136 := (and #118 #135)
#134 := (< #113 #123)
#137 := (and #134 #136)
#138 := (exists (vars (?v1 S2)) #137)
#133 := (and #72 #132)
#139 := (implies #133 #138)
#140 := (forall (vars (?v0 S2)) #139)
#265 := (implies #140 #264)
#129 := (<= #123 #128)
#127 := (and #118 #95)
#130 := (implies #127 #129)
#131 := (forall (vars (?v0 S2) (?v1 S2)) #130)
#266 := (implies #131 #265)
#124 := (<= #123 #113)
#121 := (= #120 f1)
#122 := (and #119 #121)
#125 := (implies #122 #124)
#126 := (forall (vars (?v0 S2) (?v1 S2)) #125)
#267 := (implies #126 #266)
#114 := (<= 0::Int #113)
#115 := (forall (vars (?v0 S2)) #114)
#268 := (implies #115 #267)
#269 := (implies #112 #268)
#270 := (implies true #269)
#97 := (+ #68 #94)
#104 := (= #88 #97)
#78 := (= #77 f1)
#105 := (and #78 #104)
#103 := (< #68 #88)
#106 := (and #103 #105)
#107 := (exists (vars (?v1 S2)) #106)
#101 := (< #68 f3)
#102 := (and #72 #101)
#108 := (implies #102 #107)
#109 := (forall (vars (?v0 S2)) #108)
#271 := (implies #109 #270)
#272 := (and #109 #271)
#98 := (<= #88 #97)
#96 := (and #78 #95)
#99 := (implies #96 #98)
#100 := (forall (vars (?v0 S2) (?v1 S2)) #99)
#273 := (implies #100 #272)
#274 := (and #100 #273)
#89 := (<= #88 #68)
#86 := (= #85 f1)
#79 := (not #78)
#87 := (and #79 #86)
#90 := (implies #87 #89)
#91 := (forall (vars (?v0 S2) (?v1 S2)) #90)
#275 := (implies #91 #274)
#276 := (and #91 #275)
#83 := (<= 0::Int #68)
#84 := (forall (vars (?v0 S2)) #83)
#277 := (implies #84 #276)
#278 := (and #84 #277)
#279 := (implies #82 #278)
#280 := (and #82 #279)
#80 := (forall (vars (?v0 S2)) #79)
#281 := (implies #80 #280)
#73 := (= #68 f3)
#74 := (implies #72 #73)
#75 := (forall (vars (?v0 S2)) #74)
#282 := (implies #75 #281)
#70 := (implies #67 #69)
#71 := (forall (vars (?v0 S2)) #70)
#283 := (implies #71 #282)
#284 := (implies true #283)
#285 := (not #284)
#1813 := (iff #285 #1810)
#835 := (+ #94 #203)
#853 := (= #225 #835)
#856 := (and #789 #853)
#859 := (and #236 #856)
#862 := (exists (vars (?v1 S2)) #859)
#868 := (not #235)
#869 := (or #868 #862)
#874 := (forall (vars (?v0 S2)) #869)
#838 := (<= #225 #835)
#830 := (and #95 #789)
#844 := (not #830)
#845 := (or #844 #838)
#850 := (forall (vars (?v0 S2) (?v1 S2)) #845)
#887 := (not #850)
#888 := (or #887 #874)
#893 := (and #850 #888)
#819 := (or #226 #818)
#824 := (forall (vars (?v0 S2) (?v1 S2)) #819)
#899 := (not #824)
#900 := (or #899 #893)
#905 := (and #824 #900)
#911 := (not #220)
#912 := (or #911 #905)
#917 := (and #220 #912)
#804 := (= 0::Int #217)
#923 := (not #804)
#924 := (or #923 #917)
#929 := (and #804 #924)
#936 := (or #935 #929)
#941 := (and #801 #936)
#947 := (not #212)
#948 := (or #947 #941)
#953 := (and #212 #948)
#781 := (or #202 #775)
#786 := (forall (vars (?v0 S2)) #781)
#959 := (not #786)
#960 := (or #959 #953)
#761 := (= #200 #203)
#767 := (or #207 #761)
#772 := (forall (vars (?v0 S2)) #767)
#968 := (not #772)
#969 := (or #968 #960)
#978 := (or #977 #969)
#753 := (or #188 #523)
#758 := (forall (vars (?v0 S2)) #753)
#986 := (not #758)
#987 := (or #986 #978)
#995 := (not #187)
#996 := (or #995 #987)
#1004 := (or #744 #996)
#600 := (and #132 #526)
#605 := (exists (vars (?v0 S2)) #600)
#608 := (not #605)
#1012 := (or #608 #1004)
#659 := (= 0::Int #169)
#617 := (+ #94 #154)
#644 := (<= #157 #617)
#641 := (and #95 #155)
#650 := (not #641)
#651 := (or #650 #644)
#656 := (forall (vars (?v0 S2) (?v1 S2)) #651)
#672 := (not #656)
#673 := (or #672 #659)
#678 := (and #656 #673)
#620 := (= #157 #617)
#623 := (and #158 #620)
#626 := (exists (vars (?v1 S2)) #623)
#632 := (not #156)
#633 := (or #632 #626)
#638 := (forall (vars (?v0 S2)) #633)
#684 := (not #638)
#685 := (or #684 #678)
#690 := (and #638 #685)
#697 := (or #696 #690)
#706 := (or #705 #697)
#715 := (or #714 #706)
#724 := (or #723 #715)
#732 := (or #605 #724)
#1024 := (and #732 #1012)
#555 := (+ #94 #113)
#573 := (= #123 #555)
#576 := (and #523 #573)
#579 := (and #134 #576)
#582 := (exists (vars (?v1 S2)) #579)
#588 := (not #133)
#589 := (or #588 #582)
#594 := (forall (vars (?v0 S2)) #589)
#1030 := (not #594)
#1031 := (or #1030 #1024)
#558 := (<= #123 #555)
#550 := (and #95 #523)
#564 := (not #550)
#565 := (or #564 #558)
#570 := (forall (vars (?v0 S2) (?v1 S2)) #565)
#1039 := (not #570)
#1040 := (or #1039 #1031)
#539 := (or #124 #538)
#544 := (forall (vars (?v0 S2) (?v1 S2)) #539)
#1048 := (not #544)
#1049 := (or #1048 #1040)
#1057 := (not #115)
#1058 := (or #1057 #1049)
#520 := (= 0::Int #111)
#1066 := (not #520)
#1067 := (or #1066 #1058)
#497 := (and #104 #444)
#502 := (and #103 #497)
#505 := (exists (vars (?v1 S2)) #502)
#511 := (not #102)
#512 := (or #511 #505)
#517 := (forall (vars (?v0 S2)) #512)
#1082 := (not #517)
#1083 := (or #1082 #1067)
#1088 := (and #517 #1083)
#477 := (and #95 #444)
#485 := (not #477)
#486 := (or #98 #485)
#491 := (forall (vars (?v0 S2) (?v1 S2)) #486)
#1094 := (not #491)
#1095 := (or #1094 #1088)
#1100 := (and #491 #1095)
#466 := (or #89 #465)
#471 := (forall (vars (?v0 S2) (?v1 S2)) #466)
#1106 := (not #471)
#1107 := (or #1106 #1100)
#1112 := (and #471 #1107)
#1118 := (not #84)
#1119 := (or #1118 #1112)
#1124 := (and #84 #1119)
#453 := (= 0::Int #81)
#1130 := (not #453)
#1131 := (or #1130 #1124)
#1136 := (and #453 #1131)
#1143 := (or #1142 #1136)
#1152 := (or #1151 #1143)
#415 := (= 0::Int #68)
#422 := (or #72 #415)
#427 := (forall (vars (?v0 S2)) #422)
#1160 := (not #427)
#1161 := (or #1160 #1152)
#1173 := (not #1161)
#1811 := (iff #1173 #1810)
#1808 := (iff #1161 #1805)
#1796 := (or #1142 #1782)
#1799 := (or #1151 #1796)
#1802 := (or #1793 #1799)
#1806 := (iff #1802 #1805)
#1807 := [rewrite]: #1806
#1803 := (iff #1161 #1802)
#1800 := (iff #1152 #1799)
#1797 := (iff #1143 #1796)
#1783 := (iff #1136 #1782)
#1780 := (iff #1131 #1779)
#1777 := (iff #1124 #1776)
#1774 := (iff #1119 #1773)
#1771 := (iff #1112 #1770)
#1768 := (iff #1107 #1767)
#1765 := (iff #1100 #1764)
#1762 := (iff #1095 #1761)
#1759 := (iff #1088 #1758)
#1756 := (iff #1083 #1753)
#1735 := (or #1321 #1676)
#1738 := (or #1699 #1735)
#1741 := (or #1715 #1738)
#1744 := (or #1724 #1741)
#1747 := (or #1729 #1744)
#1750 := (or #1732 #1747)
#1754 := (iff #1750 #1753)
#1755 := [rewrite]: #1754
#1751 := (iff #1083 #1750)
#1748 := (iff #1067 #1747)
#1745 := (iff #1058 #1744)
#1742 := (iff #1049 #1741)
#1739 := (iff #1040 #1738)
#1736 := (iff #1031 #1735)
#1677 := (iff #1024 #1676)
#1674 := (iff #1012 #1671)
#1650 := (or #1456 #1597)
#1653 := (or #1614 #1650)
#1656 := (or #977 #1653)
#1659 := (or #1632 #1656)
#1662 := (or #1636 #1659)
#1665 := (or #744 #1662)
#1668 := (or #1647 #1665)
#1672 := (iff #1668 #1671)
#1673 := [rewrite]: #1672
#1669 := (iff #1012 #1668)
#1666 := (iff #1004 #1665)
#1663 := (iff #996 #1662)
#1660 := (iff #987 #1659)
#1657 := (iff #978 #1656)
#1654 := (iff #969 #1653)
#1651 := (iff #960 #1650)
#1598 := (iff #953 #1597)
#1595 := (iff #948 #1594)
#1592 := (iff #941 #1591)
#1589 := (iff #936 #1588)
#1586 := (iff #929 #1585)
#1583 := (iff #924 #1582)
#1580 := (iff #917 #1579)
#1577 := (iff #912 #1576)
#1574 := (iff #905 #1573)
#1571 := (iff #900 #1570)
#1568 := (iff #893 #1567)
#1565 := (iff #888 #1564)
#1562 := (iff #874 #1561)
#1559 := (iff #869 #1558)
#1556 := (iff #862 #1555)
#1553 := (iff #859 #1550)
#1544 := (and #789 #1538)
#1547 := (and #1541 #1544)
#1551 := (iff #1547 #1550)
#1552 := [rewrite]: #1551
#1548 := (iff #859 #1547)
#1545 := (iff #856 #1544)
#1539 := (iff #853 #1538)
#1540 := [rewrite]: #1539
#1546 := [monotonicity #1540]: #1545
#1542 := (iff #236 #1541)
#1543 := [rewrite]: #1542
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#1554 := [trans #1549 #1552]: #1553
#1557 := [quant-intro #1554]: #1556
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#1533 := (iff #235 #1532)
#1530 := (iff #234 #1529)
#1531 := [rewrite]: #1530
#1534 := [monotonicity #1531]: #1533
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#1560 := [monotonicity #1537 #1557]: #1559
#1563 := [quant-intro #1560]: #1562
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#1522 := (iff #850 #1521)
#1519 := (iff #845 #1518)
#1515 := (iff #838 #1514)
#1517 := [rewrite]: #1515
#1512 := (iff #844 #1511)
#1509 := (iff #830 #1506)
#1503 := (and #1218 #789)
#1507 := (iff #1503 #1506)
#1508 := [rewrite]: #1507
#1504 := (iff #830 #1503)
#1219 := (iff #95 #1218)
#1220 := [rewrite]: #1219
#1505 := [monotonicity #1220]: #1504
#1510 := [trans #1505 #1508]: #1509
#1513 := [monotonicity #1510]: #1512
#1520 := [monotonicity #1513 #1517]: #1519
#1523 := [quant-intro #1520]: #1522
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#1566 := [monotonicity #1526 #1563]: #1565
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#1501 := (iff #899 #1500)
#1498 := (iff #824 #1497)
#1495 := (iff #819 #1492)
#1489 := (or #1484 #818)
#1493 := (iff #1489 #1492)
#1494 := [rewrite]: #1493
#1490 := (iff #819 #1489)
#1487 := (iff #226 #1484)
#1488 := [rewrite]: #1487
#1491 := [monotonicity #1488]: #1490
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#1499 := [quant-intro #1496]: #1498
#1502 := [monotonicity #1499]: #1501
#1572 := [monotonicity #1502 #1569]: #1571
#1575 := [monotonicity #1499 #1572]: #1574
#1482 := (iff #911 #1481)
#1479 := (iff #220 #1478)
#1476 := (iff #219 #1475)
#1477 := [rewrite]: #1476
#1480 := [quant-intro #1477]: #1479
#1483 := [monotonicity #1480]: #1482
#1578 := [monotonicity #1483 #1575]: #1577
#1581 := [monotonicity #1480 #1578]: #1580
#1473 := (iff #923 #1472)
#1470 := (iff #804 #218)
#1471 := [rewrite]: #1470
#1474 := [monotonicity #1471]: #1473
#1584 := [monotonicity #1474 #1581]: #1583
#1587 := [monotonicity #1471 #1584]: #1586
#1590 := [monotonicity #1587]: #1589
#1593 := [monotonicity #1590]: #1592
#1468 := (iff #947 #1467)
#1465 := (iff #212 #1464)
#1462 := (iff #211 #1459)
#1463 := [rewrite]: #1462
#1466 := [quant-intro #1463]: #1465
#1469 := [monotonicity #1466]: #1468
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#1599 := [monotonicity #1466 #1596]: #1598
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#1454 := (iff #786 #1453)
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#1445 := (or #1442 #775)
#1449 := (iff #1445 #1448)
#1450 := [rewrite]: #1449
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#1443 := (iff #202 #1442)
#1440 := (iff #201 #1439)
#1441 := [rewrite]: #1440
#1433 := (iff #199 #1432)
#1434 := [rewrite]: #1433
#1444 := [monotonicity #1434 #1441]: #1443
#1447 := [monotonicity #1444]: #1446
#1452 := [trans #1447 #1450]: #1451
#1455 := [quant-intro #1452]: #1454
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#1652 := [monotonicity #1458 #1599]: #1651
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#1612 := (iff #772 #1611)
#1609 := (iff #767 #1608)
#1606 := (iff #761 #1605)
#1607 := [rewrite]: #1606
#1601 := (iff #207 #1600)
#1602 := [monotonicity #1444]: #1601
#1610 := [monotonicity #1602 #1607]: #1609
#1613 := [quant-intro #1610]: #1612
#1616 := [monotonicity #1613]: #1615
#1655 := [monotonicity #1616 #1652]: #1654
#1658 := [monotonicity #1655]: #1657
#1633 := (iff #986 #1632)
#1630 := (iff #758 #1629)
#1627 := (iff #753 #1624)
#1621 := (or #1617 #523)
#1625 := (iff #1621 #1624)
#1626 := [rewrite]: #1625
#1622 := (iff #753 #1621)
#1619 := (iff #188 #1617)
#1620 := [rewrite]: #1619
#1623 := [monotonicity #1620]: #1622
#1628 := [trans #1623 #1626]: #1627
#1631 := [quant-intro #1628]: #1630
#1634 := [monotonicity #1631]: #1633
#1661 := [monotonicity #1634 #1658]: #1660
#1645 := (iff #995 #1636)
#1637 := (not #1636)
#1640 := (not #1637)
#1643 := (iff #1640 #1636)
#1644 := [rewrite]: #1643
#1641 := (iff #995 #1640)
#1638 := (iff #187 #1637)
#1639 := [rewrite]: #1638
#1642 := [monotonicity #1639]: #1641
#1646 := [trans #1642 #1644]: #1645
#1664 := [monotonicity #1646 #1661]: #1663
#1667 := [monotonicity #1664]: #1666
#1648 := (iff #608 #1647)
#1407 := (iff #605 #1406)
#1404 := (iff #600 #1401)
#1398 := (and #1282 #526)
#1402 := (iff #1398 #1401)
#1403 := [rewrite]: #1402
#1399 := (iff #600 #1398)
#1283 := (iff #132 #1282)
#1284 := [rewrite]: #1283
#1400 := [monotonicity #1284]: #1399
#1405 := [trans #1400 #1403]: #1404
#1408 := [quant-intro #1405]: #1407
#1649 := [monotonicity #1408]: #1648
#1670 := [monotonicity #1649 #1667]: #1669
#1675 := [trans #1670 #1673]: #1674
#1427 := (iff #732 #1424)
#1409 := (or #696 #1395)
#1412 := (or #705 #1409)
#1415 := (or #714 #1412)
#1418 := (or #723 #1415)
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#1425 := (iff #1421 #1424)
#1426 := [rewrite]: #1425
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#1393 := (iff #685 #1392)
#1390 := (iff #678 #1389)
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#1381 := (or #1376 #170)
#1385 := (iff #1381 #1384)
#1386 := [rewrite]: #1385
#1382 := (iff #673 #1381)
#1379 := (iff #659 #170)
#1380 := [rewrite]: #1379
#1377 := (iff #672 #1376)
#1374 := (iff #656 #1373)
#1371 := (iff #651 #1370)
#1368 := (iff #644 #1367)
#1369 := [rewrite]: #1368
#1365 := (iff #650 #1364)
#1362 := (iff #641 #1361)
#1328 := (iff #155 #1327)
#1329 := [rewrite]: #1328
#1363 := [monotonicity #1220 #1329]: #1362
#1366 := [monotonicity #1363]: #1365
#1372 := [monotonicity #1366 #1369]: #1371
#1375 := [quant-intro #1372]: #1374
#1378 := [monotonicity #1375]: #1377
#1383 := [monotonicity #1378 #1380]: #1382
#1388 := [trans #1383 #1386]: #1387
#1391 := [monotonicity #1375 #1388]: #1390
#1359 := (iff #684 #1358)
#1356 := (iff #638 #1355)
#1353 := (iff #633 #1352)
#1350 := (iff #626 #1349)
#1347 := (iff #623 #1346)
#1343 := (iff #620 #1342)
#1345 := [rewrite]: #1343
#1340 := (iff #158 #1339)
#1341 := [rewrite]: #1340
#1348 := [monotonicity #1341 #1345]: #1347
#1351 := [quant-intro #1348]: #1350
#1334 := (iff #632 #1333)
#1331 := (iff #156 #1330)
#1332 := [monotonicity #1329]: #1331
#1335 := [monotonicity #1332]: #1334
#1354 := [monotonicity #1335 #1351]: #1353
#1357 := [quant-intro #1354]: #1356
#1360 := [monotonicity #1357]: #1359
#1394 := [monotonicity #1360 #1391]: #1393
#1397 := [monotonicity #1357 #1394]: #1396
#1411 := [monotonicity #1397]: #1410
#1414 := [monotonicity #1411]: #1413
#1417 := [monotonicity #1414]: #1416
#1420 := [monotonicity #1417]: #1419
#1423 := [monotonicity #1408 #1420]: #1422
#1428 := [trans #1423 #1426]: #1427
#1678 := [monotonicity #1428 #1675]: #1677
#1322 := (iff #1030 #1321)
#1319 := (iff #594 #1318)
#1316 := (iff #589 #1315)
#1313 := (iff #582 #1312)
#1310 := (iff #579 #1307)
#1301 := (and #523 #1291)
#1304 := (and #1298 #1301)
#1308 := (iff #1304 #1307)
#1309 := [rewrite]: #1308
#1305 := (iff #579 #1304)
#1302 := (iff #576 #1301)
#1292 := (iff #573 #1291)
#1296 := [rewrite]: #1292
#1303 := [monotonicity #1296]: #1302
#1299 := (iff #134 #1298)
#1300 := [rewrite]: #1299
#1306 := [monotonicity #1300 #1303]: #1305
#1311 := [trans #1306 #1309]: #1310
#1314 := [quant-intro #1311]: #1313
#1289 := (iff #588 #1288)
#1286 := (iff #133 #1285)
#1287 := [monotonicity #1284]: #1286
#1290 := [monotonicity #1287]: #1289
#1317 := [monotonicity #1290 #1314]: #1316
#1320 := [quant-intro #1317]: #1319
#1323 := [monotonicity #1320]: #1322
#1737 := [monotonicity #1323 #1678]: #1736
#1700 := (iff #1039 #1699)
#1697 := (iff #570 #1696)
#1694 := (iff #565 #1693)
#1691 := (iff #558 #1690)
#1692 := [rewrite]: #1691
#1688 := (iff #564 #1687)
#1685 := (iff #550 #1682)
#1679 := (and #1218 #523)
#1683 := (iff #1679 #1682)
#1684 := [rewrite]: #1683
#1680 := (iff #550 #1679)
#1681 := [monotonicity #1220]: #1680
#1686 := [trans #1681 #1684]: #1685
#1689 := [monotonicity #1686]: #1688
#1695 := [monotonicity #1689 #1692]: #1694
#1698 := [quant-intro #1695]: #1697
#1701 := [monotonicity #1698]: #1700
#1740 := [monotonicity #1701 #1737]: #1739
#1716 := (iff #1048 #1715)
#1713 := (iff #544 #1712)
#1710 := (iff #539 #1707)
#1704 := (or #1297 #538)
#1708 := (iff #1704 #1707)
#1709 := [rewrite]: #1708
#1705 := (iff #539 #1704)
#1702 := (iff #124 #1297)
#1703 := [rewrite]: #1702
#1706 := [monotonicity #1703]: #1705
#1711 := [trans #1706 #1709]: #1710
#1714 := [quant-intro #1711]: #1713
#1717 := [monotonicity #1714]: #1716
#1743 := [monotonicity #1717 #1740]: #1742
#1725 := (iff #1057 #1724)
#1722 := (iff #115 #1721)
#1719 := (iff #114 #1718)
#1720 := [rewrite]: #1719
#1723 := [quant-intro #1720]: #1722
#1726 := [monotonicity #1723]: #1725
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#1730 := (iff #1066 #1729)
#1727 := (iff #520 #112)
#1728 := [rewrite]: #1727
#1731 := [monotonicity #1728]: #1730
#1749 := [monotonicity #1731 #1746]: #1748
#1733 := (iff #1082 #1732)
#1277 := (iff #517 #1276)
#1274 := (iff #512 #1273)
#1271 := (iff #505 #1270)
#1268 := (iff #502 #1265)
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#1266 := (iff #1262 #1265)
#1267 := [rewrite]: #1266
#1263 := (iff #502 #1262)
#1260 := (iff #497 #1259)
#1254 := (iff #104 #1253)
#1255 := [rewrite]: #1254
#1261 := [monotonicity #1255]: #1260
#1257 := (iff #103 #1256)
#1258 := [rewrite]: #1257
#1264 := [monotonicity #1258 #1261]: #1263
#1269 := [trans #1264 #1267]: #1268
#1272 := [quant-intro #1269]: #1271
#1251 := (iff #511 #1250)
#1248 := (iff #102 #1247)
#1245 := (iff #101 #1244)
#1246 := [rewrite]: #1245
#1249 := [monotonicity #1246]: #1248
#1252 := [monotonicity #1249]: #1251
#1275 := [monotonicity #1252 #1272]: #1274
#1278 := [quant-intro #1275]: #1277
#1734 := [monotonicity #1278]: #1733
#1752 := [monotonicity #1734 #1749]: #1751
#1757 := [trans #1752 #1755]: #1756
#1760 := [monotonicity #1278 #1757]: #1759
#1239 := (iff #1094 #1238)
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#1233 := (iff #486 #1232)
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#1221 := (and #1218 #444)
#1225 := (iff #1221 #1224)
#1226 := [rewrite]: #1225
#1222 := (iff #477 #1221)
#1223 := [monotonicity #1220]: #1222
#1228 := [trans #1223 #1226]: #1227
#1231 := [monotonicity #1228]: #1230
#1211 := (iff #98 #1212)
#1210 := [rewrite]: #1211
#1234 := [monotonicity #1210 #1231]: #1233
#1237 := [quant-intro #1234]: #1236
#1240 := [monotonicity #1237]: #1239
#1763 := [monotonicity #1240 #1760]: #1762
#1766 := [monotonicity #1237 #1763]: #1765
#1208 := (iff #1106 #1207)
#1205 := (iff #471 #1204)
#1202 := (iff #466 #1199)
#1196 := (or #1192 #465)
#1200 := (iff #1196 #1199)
#1201 := [rewrite]: #1200
#1197 := (iff #466 #1196)
#1191 := (iff #89 #1192)
#1195 := [rewrite]: #1191
#1198 := [monotonicity #1195]: #1197
#1203 := [trans #1198 #1201]: #1202
#1206 := [quant-intro #1203]: #1205
#1209 := [monotonicity #1206]: #1208
#1769 := [monotonicity #1209 #1766]: #1768
#1772 := [monotonicity #1206 #1769]: #1771
#1188 := (iff #1118 #1187)
#1185 := (iff #84 #1184)
#1181 := (iff #83 #1183)
#1182 := [rewrite]: #1181
#1186 := [quant-intro #1182]: #1185
#1189 := [monotonicity #1186]: #1188
#1775 := [monotonicity #1189 #1772]: #1774
#1778 := [monotonicity #1186 #1775]: #1777
#1179 := (iff #1130 #1178)
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#1177 := [rewrite]: #1176
#1180 := [monotonicity #1177]: #1179
#1781 := [monotonicity #1180 #1778]: #1780
#1784 := [monotonicity #1177 #1781]: #1783
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#1785 := (iff #415 #69)
#1786 := [rewrite]: #1785
#1789 := [monotonicity #1786]: #1788
#1792 := [quant-intro #1789]: #1791
#1795 := [monotonicity #1792]: #1794
#1804 := [monotonicity #1795 #1801]: #1803
#1809 := [trans #1804 #1807]: #1808
#1812 := [monotonicity #1809]: #1811
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#944 := (implies #212 #941)
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#914 := [rewrite]: #913
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#891 := (iff #244 #888)
#884 := (implies #850 #874)
#889 := (iff #884 #888)
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#882 := (iff #243 #874)
#877 := (and #874 true)
#880 := (iff #877 #874)
#881 := [rewrite]: #880
#878 := (iff #243 #877)
#875 := (iff #242 #874)
#872 := (iff #241 #869)
#865 := (implies #235 #862)
#870 := (iff #865 #869)
#871 := [rewrite]: #870
#866 := (iff #241 #865)
#863 := (iff #240 #862)
#860 := (iff #239 #859)
#857 := (iff #238 #856)
#854 := (iff #237 #853)
#836 := (= #230 #835)
#837 := [rewrite]: #836
#855 := [monotonicity #837]: #854
#790 := (iff #214 #789)
#791 := [rewrite]: #790
#858 := [monotonicity #791 #855]: #857
#861 := [monotonicity #858]: #860
#864 := [quant-intro #861]: #863
#867 := [monotonicity #864]: #866
#873 := [trans #867 #871]: #872
#876 := [quant-intro #873]: #875
#879 := [monotonicity #876]: #878
#883 := [trans #879 #881]: #882
#851 := (iff #233 #850)
#848 := (iff #232 #845)
#841 := (implies #830 #838)
#846 := (iff #841 #845)
#847 := [rewrite]: #846
#842 := (iff #232 #841)
#839 := (iff #231 #838)
#840 := [monotonicity #837]: #839
#833 := (iff #229 #830)
#827 := (and #789 #95)
#831 := (iff #827 #830)
#832 := [rewrite]: #831
#828 := (iff #229 #827)
#829 := [monotonicity #791]: #828
#834 := [trans #829 #832]: #833
#843 := [monotonicity #834 #840]: #842
#849 := [trans #843 #847]: #848
#852 := [quant-intro #849]: #851
#886 := [monotonicity #852 #883]: #885
#892 := [trans #886 #890]: #891
#895 := [monotonicity #852 #892]: #894
#825 := (iff #228 #824)
#822 := (iff #227 #819)
#815 := (implies #812 #226)
#820 := (iff #815 #819)
#821 := [rewrite]: #820
#816 := (iff #227 #815)
#813 := (iff #224 #812)
#810 := (iff #223 #809)
#811 := [rewrite]: #810
#807 := (iff #221 #795)
#808 := [monotonicity #791]: #807
#814 := [monotonicity #808 #811]: #813
#817 := [monotonicity #814]: #816
#823 := [trans #817 #821]: #822
#826 := [quant-intro #823]: #825
#898 := [monotonicity #826 #895]: #897
#904 := [trans #898 #902]: #903
#907 := [monotonicity #826 #904]: #906
#910 := [monotonicity #907]: #909
#916 := [trans #910 #914]: #915
#919 := [monotonicity #916]: #918
#805 := (iff #218 #804)
#806 := [rewrite]: #805
#922 := [monotonicity #806 #919]: #921
#928 := [trans #922 #926]: #927
#931 := [monotonicity #806 #928]: #930
#802 := (iff #216 #801)
#799 := (iff #215 #796)
#792 := (implies #789 #775)
#797 := (iff #792 #796)
#798 := [rewrite]: #797
#793 := (iff #215 #792)
#776 := (iff #208 #775)
#777 := [rewrite]: #776
#794 := [monotonicity #791 #777]: #793
#800 := [trans #794 #798]: #799
#803 := [quant-intro #800]: #802
#934 := [monotonicity #803 #931]: #933
#940 := [trans #934 #938]: #939
#943 := [monotonicity #803 #940]: #942
#946 := [monotonicity #943]: #945
#952 := [trans #946 #950]: #951
#955 := [monotonicity #952]: #954
#787 := (iff #210 #786)
#784 := (iff #209 #781)
#778 := (implies #207 #775)
#782 := (iff #778 #781)
#783 := [rewrite]: #782
#779 := (iff #209 #778)
#780 := [monotonicity #777]: #779
#785 := [trans #780 #783]: #784
#788 := [quant-intro #785]: #787
#958 := [monotonicity #788 #955]: #957
#964 := [trans #958 #962]: #963
#773 := (iff #206 #772)
#770 := (iff #205 #767)
#764 := (implies #202 #761)
#768 := (iff #764 #767)
#769 := [rewrite]: #768
#765 := (iff #205 #764)
#762 := (iff #204 #761)
#763 := [rewrite]: #762
#766 := [monotonicity #763]: #765
#771 := [trans #766 #769]: #770
#774 := [quant-intro #771]: #773
#967 := [monotonicity #774 #964]: #966
#973 := [trans #967 #971]: #972
#976 := [monotonicity #973]: #975
#982 := [trans #976 #980]: #981
#759 := (iff #190 #758)
#756 := (iff #189 #753)
#750 := (implies #526 #188)
#754 := (iff #750 #753)
#755 := [rewrite]: #754
#751 := (iff #189 #750)
#527 := (iff #119 #526)
#524 := (iff #118 #523)
#525 := [rewrite]: #524
#528 := [monotonicity #525]: #527
#752 := [monotonicity #528]: #751
#757 := [trans #752 #755]: #756
#760 := [quant-intro #757]: #759
#985 := [monotonicity #760 #982]: #984
#991 := [trans #985 #989]: #990
#994 := [monotonicity #991]: #993
#1000 := [trans #994 #998]: #999
#748 := (iff #185 #747)
#745 := (iff #184 #744)
#746 := [rewrite]: #745
#749 := [monotonicity #746]: #748
#1003 := [monotonicity #749 #1000]: #1002
#1008 := [trans #1003 #1006]: #1007
#606 := (iff #142 #605)
#603 := (iff #141 #600)
#597 := (and #526 #132)
#601 := (iff #597 #600)
#602 := [rewrite]: #601
#598 := (iff #141 #597)
#599 := [monotonicity #528]: #598
#604 := [trans #599 #602]: #603
#607 := [quant-intro #604]: #606
#1011 := [monotonicity #607 #1008]: #1010
#1016 := [trans #1011 #1014]: #1015
#1019 := [monotonicity #1016]: #1018
#1023 := [trans #1019 #1021]: #1022
#742 := (iff #181 #732)
#737 := (implies true #732)
#740 := (iff #737 #732)
#741 := [rewrite]: #740
#738 := (iff #181 #737)
#735 := (iff #180 #732)
#729 := (implies #608 #724)
#733 := (iff #729 #732)
#734 := [rewrite]: #733
#730 := (iff #180 #729)
#727 := (iff #179 #724)
#720 := (implies #611 #715)
#725 := (iff #720 #724)
#726 := [rewrite]: #725
#721 := (iff #179 #720)
#718 := (iff #178 #715)
#711 := (implies #148 #706)
#716 := (iff #711 #715)
#717 := [rewrite]: #716
#712 := (iff #178 #711)
#709 := (iff #177 #706)
#702 := (implies #614 #697)
#707 := (iff #702 #706)
#708 := [rewrite]: #707
#703 := (iff #177 #702)
#700 := (iff #176 #697)
#693 := (implies #153 #690)
#698 := (iff #693 #697)
#699 := [rewrite]: #698
#694 := (iff #176 #693)
#691 := (iff #175 #690)
#688 := (iff #174 #685)
#681 := (implies #638 #678)
#686 := (iff #681 #685)
#687 := [rewrite]: #686
#682 := (iff #174 #681)
#679 := (iff #173 #678)
#676 := (iff #172 #673)
#669 := (implies #656 #659)
#674 := (iff #669 #673)
#675 := [rewrite]: #674
#670 := (iff #172 #669)
#667 := (iff #171 #659)
#662 := (and #659 true)
#665 := (iff #662 #659)
#666 := [rewrite]: #665
#663 := (iff #171 #662)
#660 := (iff #170 #659)
#661 := [rewrite]: #660
#664 := [monotonicity #661]: #663
#668 := [trans #664 #666]: #667
#657 := (iff #168 #656)
#654 := (iff #167 #651)
#647 := (implies #641 #644)
#652 := (iff #647 #651)
#653 := [rewrite]: #652
#648 := (iff #167 #647)
#645 := (iff #166 #644)
#618 := (= #159 #617)
#619 := [rewrite]: #618
#646 := [monotonicity #619]: #645
#642 := (iff #165 #641)
#643 := [rewrite]: #642
#649 := [monotonicity #643 #646]: #648
#655 := [trans #649 #653]: #654
#658 := [quant-intro #655]: #657
#671 := [monotonicity #658 #668]: #670
#677 := [trans #671 #675]: #676
#680 := [monotonicity #658 #677]: #679
#639 := (iff #164 #638)
#636 := (iff #163 #633)
#629 := (implies #156 #626)
#634 := (iff #629 #633)
#635 := [rewrite]: #634
#630 := (iff #163 #629)
#627 := (iff #162 #626)
#624 := (iff #161 #623)
#621 := (iff #160 #620)
#622 := [monotonicity #619]: #621
#625 := [monotonicity #622]: #624
#628 := [quant-intro #625]: #627
#631 := [monotonicity #628]: #630
#637 := [trans #631 #635]: #636
#640 := [quant-intro #637]: #639
#683 := [monotonicity #640 #680]: #682
#689 := [trans #683 #687]: #688
#692 := [monotonicity #640 #689]: #691
#695 := [monotonicity #692]: #694
#701 := [trans #695 #699]: #700
#615 := (iff #150 #614)
#616 := [rewrite]: #615
#704 := [monotonicity #616 #701]: #703
#710 := [trans #704 #708]: #709
#713 := [monotonicity #710]: #712
#719 := [trans #713 #717]: #718
#612 := (iff #145 #611)
#613 := [rewrite]: #612
#722 := [monotonicity #613 #719]: #721
#728 := [trans #722 #726]: #727
#609 := (iff #143 #608)
#610 := [monotonicity #607]: #609
#731 := [monotonicity #610 #728]: #730
#736 := [trans #731 #734]: #735
#739 := [monotonicity #736]: #738
#743 := [trans #739 #741]: #742
#1026 := [monotonicity #743 #1023]: #1025
#595 := (iff #140 #594)
#592 := (iff #139 #589)
#585 := (implies #133 #582)
#590 := (iff #585 #589)
#591 := [rewrite]: #590
#586 := (iff #139 #585)
#583 := (iff #138 #582)
#580 := (iff #137 #579)
#577 := (iff #136 #576)
#574 := (iff #135 #573)
#556 := (= #128 #555)
#557 := [rewrite]: #556
#575 := [monotonicity #557]: #574
#578 := [monotonicity #525 #575]: #577
#581 := [monotonicity #578]: #580
#584 := [quant-intro #581]: #583
#587 := [monotonicity #584]: #586
#593 := [trans #587 #591]: #592
#596 := [quant-intro #593]: #595
#1029 := [monotonicity #596 #1026]: #1028
#1035 := [trans #1029 #1033]: #1034
#571 := (iff #131 #570)
#568 := (iff #130 #565)
#561 := (implies #550 #558)
#566 := (iff #561 #565)
#567 := [rewrite]: #566
#562 := (iff #130 #561)
#559 := (iff #129 #558)
#560 := [monotonicity #557]: #559
#553 := (iff #127 #550)
#547 := (and #523 #95)
#551 := (iff #547 #550)
#552 := [rewrite]: #551
#548 := (iff #127 #547)
#549 := [monotonicity #525]: #548
#554 := [trans #549 #552]: #553
#563 := [monotonicity #554 #560]: #562
#569 := [trans #563 #567]: #568
#572 := [quant-intro #569]: #571
#1038 := [monotonicity #572 #1035]: #1037
#1044 := [trans #1038 #1042]: #1043
#545 := (iff #126 #544)
#542 := (iff #125 #539)
#535 := (implies #532 #124)
#540 := (iff #535 #539)
#541 := [rewrite]: #540
#536 := (iff #125 #535)
#533 := (iff #122 #532)
#530 := (iff #121 #529)
#531 := [rewrite]: #530
#534 := [monotonicity #528 #531]: #533
#537 := [monotonicity #534]: #536
#543 := [trans #537 #541]: #542
#546 := [quant-intro #543]: #545
#1047 := [monotonicity #546 #1044]: #1046
#1053 := [trans #1047 #1051]: #1052
#1056 := [monotonicity #1053]: #1055
#1062 := [trans #1056 #1060]: #1061
#521 := (iff #112 #520)
#522 := [rewrite]: #521
#1065 := [monotonicity #522 #1062]: #1064
#1071 := [trans #1065 #1069]: #1070
#1074 := [monotonicity #1071]: #1073
#1078 := [trans #1074 #1076]: #1077
#518 := (iff #109 #517)
#515 := (iff #108 #512)
#508 := (implies #102 #505)
#513 := (iff #508 #512)
#514 := [rewrite]: #513
#509 := (iff #108 #508)
#506 := (iff #107 #505)
#503 := (iff #106 #502)
#500 := (iff #105 #497)
#494 := (and #444 #104)
#498 := (iff #494 #497)
#499 := [rewrite]: #498
#495 := (iff #105 #494)
#445 := (iff #78 #444)
#446 := [rewrite]: #445
#496 := [monotonicity #446]: #495
#501 := [trans #496 #499]: #500
#504 := [monotonicity #501]: #503
#507 := [quant-intro #504]: #506
#510 := [monotonicity #507]: #509
#516 := [trans #510 #514]: #515
#519 := [quant-intro #516]: #518
#1081 := [monotonicity #519 #1078]: #1080
#1087 := [trans #1081 #1085]: #1086
#1090 := [monotonicity #519 #1087]: #1089
#492 := (iff #100 #491)
#489 := (iff #99 #486)
#482 := (implies #477 #98)
#487 := (iff #482 #486)
#488 := [rewrite]: #487
#483 := (iff #99 #482)
#480 := (iff #96 #477)
#474 := (and #444 #95)
#478 := (iff #474 #477)
#479 := [rewrite]: #478
#475 := (iff #96 #474)
#476 := [monotonicity #446]: #475
#481 := [trans #476 #479]: #480
#484 := [monotonicity #481]: #483
#490 := [trans #484 #488]: #489
#493 := [quant-intro #490]: #492
#1093 := [monotonicity #493 #1090]: #1092
#1099 := [trans #1093 #1097]: #1098
#1102 := [monotonicity #493 #1099]: #1101
#472 := (iff #91 #471)
#469 := (iff #90 #466)
#462 := (implies #459 #89)
#467 := (iff #462 #466)
#468 := [rewrite]: #467
#463 := (iff #90 #462)
#460 := (iff #87 #459)
#457 := (iff #86 #456)
#458 := [rewrite]: #457
#448 := (iff #79 #447)
#449 := [monotonicity #446]: #448
#461 := [monotonicity #449 #458]: #460
#464 := [monotonicity #461]: #463
#470 := [trans #464 #468]: #469
#473 := [quant-intro #470]: #472
#1105 := [monotonicity #473 #1102]: #1104
#1111 := [trans #1105 #1109]: #1110
#1114 := [monotonicity #473 #1111]: #1113
#1117 := [monotonicity #1114]: #1116
#1123 := [trans #1117 #1121]: #1122
#1126 := [monotonicity #1123]: #1125
#454 := (iff #82 #453)
#455 := [rewrite]: #454
#1129 := [monotonicity #455 #1126]: #1128
#1135 := [trans #1129 #1133]: #1134
#1138 := [monotonicity #455 #1135]: #1137
#451 := (iff #80 #450)
#452 := [quant-intro #449]: #451
#1141 := [monotonicity #452 #1138]: #1140
#1147 := [trans #1141 #1145]: #1146
#442 := (iff #75 #441)
#439 := (iff #74 #436)
#433 := (implies #72 #430)
#437 := (iff #433 #436)
#438 := [rewrite]: #437
#434 := (iff #74 #433)
#431 := (iff #73 #430)
#432 := [rewrite]: #431
#435 := [monotonicity #432]: #434
#440 := [trans #435 #438]: #439
#443 := [quant-intro #440]: #442
#1150 := [monotonicity #443 #1147]: #1149
#1156 := [trans #1150 #1154]: #1155
#428 := (iff #71 #427)
#425 := (iff #70 #422)
#419 := (implies #67 #415)
#423 := (iff #419 #422)
#424 := [rewrite]: #423
#420 := (iff #70 #419)
#417 := (iff #69 #415)
#418 := [rewrite]: #417
#421 := [monotonicity #418]: #420
#426 := [trans #421 #424]: #425
#429 := [quant-intro #426]: #428
#1159 := [monotonicity #429 #1156]: #1158
#1165 := [trans #1159 #1163]: #1164
#1168 := [monotonicity #1165]: #1167
#1172 := [trans #1168 #1170]: #1171
#1175 := [monotonicity #1172]: #1174
#1814 := [trans #1175 #1812]: #1813
#414 := [asserted]: #285
#1815 := [mp #414 #1814]: #1810
#1817 := [not-or-elim #1815]: #450
#1872 := [mp~ #1817 #1841]: #450
#4219 := [mp #1872 #4218]: #4214
#5792 := (not #4214)
#5793 := (or #5792 #3066)
#5794 := [quant-inst #1918]: #5793
#6296 := [unit-resolution #5794 #4219 #6295]: false
#6304 := [lemma #6296]: #3066
#3833 := (or #3081 #1928)
#3837 := [def-axiom]: #3833
#6962 := [unit-resolution #3837 #6304]: #3081
#3086 := (not #3081)
#4551 := (or #3086 #4548)
#4554 := (not #4551)
#4228 := (pattern #68 #88)
#2507 := (not #456)
#3058 := (or #444 #2507 #1192)
#4229 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4228) #3058)
#4234 := (not #4229)
#4557 := (or #4234 #4554)
#4560 := (not #4557)
decl ?v1!1 :: S2
#1891 := ?v1!1
#1895 := (f17 ?v1!1)
#2522 := (* -1::Int #1895)
decl ?v0!2 :: S2
#1892 := ?v0!2
#1893 := (f17 ?v0!2)
#2523 := (+ #1893 #2522)
#2524 := (<= #2523 0::Int)
#1900 := (f11 f18 ?v1!1)
#1901 := (= f1 #1900)
#1898 := (f11 f18 ?v0!2)
#1899 := (= f1 #1898)
#2267 := (not #1899)
#1941 := (or #2267 #1901 #2524)
#2039 := (not #1941)
#4563 := (or #2039 #4560)
#4566 := (not #4563)
#4220 := (forall (vars (?v0 S2)) (:pat #4206) #1183)
#4225 := (not #4220)
#4569 := (or #4225 #4566)
#4572 := (not #4569)
decl ?v0!0 :: S2
#1876 := ?v0!0
#1877 := (f17 ?v0!0)
#1878 := (>= #1877 0::Int)
#308 := (<= f3 0::Int)
#309 := (not #308)
#10 := (< 0::Int f3)
#310 := (iff #10 #309)
#311 := [rewrite]: #310
#305 := [asserted]: #10
#312 := [mp #305 #311]: #309
#3895 := (* -1::Int #1877)
#3758 := (+ f3 #3895)
#3754 := (<= #3758 0::Int)
#3801 := (= f3 #1877)
#3815 := (= f16 ?v0!0)
#4605 := (not #3815)
#3746 := (= #1877 0::Int)
#5133 := (not #3746)
#1879 := (not #1878)
#4745 := [hypothesis]: #1879
#5134 := (or #5133 #1878)
#5135 := [th-lemma arith triangle-eq]: #5134
#5150 := [unit-resolution #5135 #4745]: #5133
#4591 := (forall (vars (?v0 S2)) (:pat #4206) #1787)
#4594 := (iff #1790 #4591)
#4592 := (iff #1787 #1787)
#4593 := [refl]: #4592
#4595 := [quant-intro #4593]: #4594
#2226 := (~ #1790 #1790)
#2205 := (~ #1787 #1787)
#2206 := [refl]: #2205
#2227 := [nnf-pos #2206]: #2226
#1820 := [not-or-elim #1815]: #1790
#2266 := [mp~ #1820 #2227]: #1790
#4596 := [mp #2266 #4595]: #4591
#3847 := (not #4591)
#4618 := (or #3847 #3746 #4605)
#3802 := (= ?v0!0 f16)
#3748 := (not #3802)
#4604 := (or #3748 #3746)
#4733 := (or #3847 #4604)
#4989 := (iff #4733 #4618)
#4610 := (or #3746 #4605)
#4738 := (or #3847 #4610)
#4742 := (iff #4738 #4618)
#4988 := [rewrite]: #4742
#4740 := (iff #4733 #4738)
#4613 := (iff #4604 #4610)
#4608 := (or #4605 #3746)
#4611 := (iff #4608 #4610)
#4612 := [rewrite]: #4611
#4603 := (iff #4604 #4608)
#4606 := (iff #3748 #4605)
#3804 := (iff #3802 #3815)
#3805 := [rewrite]: #3804
#4607 := [monotonicity #3805]: #4606
#4609 := [monotonicity #4607]: #4603
#4617 := [trans #4609 #4612]: #4613
#4741 := [monotonicity #4617]: #4740
#4999 := [trans #4741 #4988]: #4989
#4739 := [quant-inst #1876]: #4733
#5002 := [mp #4739 #4999]: #4618
#5151 := [unit-resolution #5002 #4596 #5150]: #4605
#3786 := (or #3801 #3815)
#4207 := (forall (vars (?v0 S2)) (:pat #4206) #436)
#4210 := (iff #441 #4207)
#4208 := (iff #436 #436)
#4209 := [refl]: #4208
#4211 := [quant-intro #4209]: #4210
#1838 := (~ #441 #441)
#1867 := (~ #436 #436)
#1868 := [refl]: #1867
#1839 := [nnf-pos #1868]: #1838
#1816 := [not-or-elim #1815]: #441
#1869 := [mp~ #1816 #1839]: #441
#4212 := [mp #1869 #4211]: #4207
#3783 := (not #4207)
#3767 := (or #3783 #3801 #3815)
#3803 := (or #3802 #3801)
#3772 := (or #3783 #3803)
#3756 := (iff #3772 #3767)
#3775 := (or #3783 #3786)
#3752 := (iff #3775 #3767)
#3753 := [rewrite]: #3752
#3777 := (iff #3772 #3775)
#3761 := (iff #3803 #3786)
#3806 := (or #3815 #3801)
#3781 := (iff #3806 #3786)
#3787 := [rewrite]: #3781
#3795 := (iff #3803 #3806)
#3807 := [monotonicity #3805]: #3795
#3766 := [trans #3807 #3787]: #3761
#3755 := [monotonicity #3766]: #3777
#3757 := [trans #3755 #3753]: #3756
#3774 := [quant-inst #1876]: #3772
#3771 := [mp #3774 #3757]: #3767
#5132 := [unit-resolution #3771 #4212]: #3786
#5172 := [unit-resolution #5132 #5151]: #3801
#5173 := (not #3801)
#5174 := (or #5173 #3754)
#5175 := [th-lemma arith triangle-eq]: #5174
#5176 := [unit-resolution #5175 #5172]: #3754
#4676 := (<= #1877 0::Int)
#3935 := (or #4676 #1878)
#4677 := [th-lemma arith farkas 1 1]: #3935
#4678 := [unit-resolution #4677 #4745]: #4676
#5334 := [th-lemma arith farkas 1 -1 1 #4678 #5176 #312]: false
#5403 := [lemma #5334]: #1878
#4575 := (or #1879 #4572)
#4578 := (not #4575)
#4581 := (or #1178 #4578)
#4584 := (not #4581)
#3811 := [hypothesis]: #1178
#3839 := (or #3847 #82)
#3891 := (= f16 f16)
#3892 := (not #3891)
#3887 := (or #3892 #82)
#3848 := (or #3847 #3887)
#3840 := (iff #3848 #3839)
#3850 := (iff #3839 #3839)
#3817 := [rewrite]: #3850
#3860 := (iff #3887 #82)
#3869 := (or false #82)
#3870 := (iff #3869 #82)
#3859 := [rewrite]: #3870
#3872 := (iff #3887 #3869)
#3866 := (iff #3892 false)
#3894 := (not true)
#3880 := (iff #3894 false)
#3865 := [rewrite]: #3880
#3871 := (iff #3892 #3894)
#3893 := (iff #3891 true)
#3882 := [rewrite]: #3893
#3873 := [monotonicity #3882]: #3871
#3867 := [trans #3873 #3865]: #3866
#3868 := [monotonicity #3867]: #3872
#3861 := [trans #3868 #3859]: #3860
#3846 := [monotonicity #3861]: #3840
#3819 := [trans #3846 #3817]: #3840
#3849 := [quant-inst #66]: #3848
#3820 := [mp #3849 #3819]: #3839
#3794 := [unit-resolution #3820 #3811 #4596]: false
#3796 := [lemma #3794]: #82
#4587 := (or #1178 #4584)
#3516 := (forall (vars (?v1 S2)) #3505)
#3523 := (not #3516)
#3501 := (forall (vars (?v0 S2) (?v1 S2)) #3496)
#3522 := (not #3501)
#3524 := (or #2347 #2914 #3522 #3523)
#3525 := (not #3524)
#3530 := (or #3479 #3525)
#3537 := (not #3530)
#3456 := (forall (vars (?v0 S2) (?v1 S2)) #3451)
#3536 := (not #3456)
#3538 := (or #3536 #3537)
#3539 := (not #3538)
#3544 := (or #3433 #3539)
#3550 := (not #3544)
#3551 := (or #1481 #3550)
#3552 := (not #3551)
#3557 := (or #2263 #3552)
#3563 := (not #3557)
#3564 := (or #1472 #3563)
#3565 := (not #3564)
#3570 := (or #1472 #3565)
#3576 := (not #3570)
#3577 := (or #935 #3576)
#3578 := (not #3577)
#3583 := (or #2857 #3578)
#3589 := (not #3583)
#3590 := (or #1467 #3589)
#3591 := (not #3590)
#3596 := (or #2843 #3591)
#3604 := (not #3596)
#3410 := (forall (vars (?v0 S2)) #3405)
#3603 := (not #3410)
#3392 := (forall (vars (?v0 S2)) #3389)
#3602 := (not #3392)
#3605 := (or #977 #744 #1632 #1636 #2197 #2200 #3602 #3603 #3604)
#3606 := (not #3605)
#3322 := (forall (vars (?v0 S2) (?v1 S2)) #3317)
#3328 := (not #3322)
#3329 := (or #170 #3328)
#3330 := (not #3329)
#3357 := (or #3330 #3354)
#3364 := (not #3357)
#3300 := (forall (vars (?v0 S2)) #3295)
#3363 := (not #3300)
#3365 := (or #3363 #3364)
#3366 := (not #3365)
#3263 := (forall (vars (?v1 S2)) #3252)
#3269 := (not #3263)
#3270 := (or #2074 #2692 #3269)
#3271 := (not #3270)
#3371 := (or #3271 #3366)
#3378 := (not #3371)
#3248 := (forall (vars (?v0 S2)) #3237)
#3377 := (not #3248)
#3379 := (or #714 #696 #723 #705 #3377 #3378)
#3380 := (not #3379)
#3611 := (or #3380 #3606)
#3621 := (not #3611)
#3234 := (forall (vars (?v0 S2)) #3229)
#3620 := (not #3234)
#3206 := (forall (vars (?v0 S2)) #3201)
#3619 := (not #3206)
#3178 := (forall (vars (?v0 S2) (?v1 S2)) #3173)
#3618 := (not #3178)
#3155 := (forall (vars (?v0 S2) (?v1 S2)) #3150)
#3617 := (not #3155)
#3622 := (or #1729 #1724 #3617 #3618 #3619 #3620 #3621)
#3623 := (not #3622)
#3123 := (forall (vars (?v1 S2)) #3112)
#3129 := (not #3123)
#3130 := (or #1964 #2554 #3129)
#3131 := (not #3130)
#3628 := (or #3131 #3623)
#3635 := (not #3628)
#3108 := (forall (vars (?v0 S2) (?v1 S2)) #3103)
#3634 := (not #3108)
#3636 := (or #3634 #3635)
#3637 := (not #3636)
#3642 := (or #3086 #3637)
#3649 := (not #3642)
#3063 := (forall (vars (?v0 S2) (?v1 S2)) #3058)
#3648 := (not #3063)
#3650 := (or #3648 #3649)
#3651 := (not #3650)
#3656 := (or #2039 #3651)
#3662 := (not #3656)
#3663 := (or #1187 #3662)
#3664 := (not #3663)
#3669 := (or #1879 #3664)
#3675 := (not #3669)
#3676 := (or #1178 #3675)
#3677 := (not #3676)
#3682 := (or #1178 #3677)
#4588 := (iff #3682 #4587)
#4585 := (iff #3677 #4584)
#4582 := (iff #3676 #4581)
#4579 := (iff #3675 #4578)
#4576 := (iff #3669 #4575)
#4573 := (iff #3664 #4572)
#4570 := (iff #3663 #4569)
#4567 := (iff #3662 #4566)
#4564 := (iff #3656 #4563)
#4561 := (iff #3651 #4560)
#4558 := (iff #3650 #4557)
#4555 := (iff #3649 #4554)
#4552 := (iff #3642 #4551)
#4549 := (iff #3637 #4548)
#4546 := (iff #3636 #4545)
#4543 := (iff #3635 #4542)
#4540 := (iff #3628 #4539)
#4537 := (iff #3623 #4536)
#4534 := (iff #3622 #4533)
#4531 := (iff #3621 #4530)
#4528 := (iff #3611 #4527)
#4525 := (iff #3606 #4524)
#4522 := (iff #3605 #4521)
#4519 := (iff #3604 #4518)
#4516 := (iff #3596 #4515)
#4513 := (iff #3591 #4512)
#4510 := (iff #3590 #4509)
#4507 := (iff #3589 #4506)
#4504 := (iff #3583 #4503)
#4501 := (iff #3578 #4500)
#4498 := (iff #3577 #4497)
#4495 := (iff #3576 #4494)
#4492 := (iff #3570 #4491)
#4489 := (iff #3565 #4488)
#4486 := (iff #3564 #4485)
#4483 := (iff #3563 #4482)
#4480 := (iff #3557 #4479)
#4477 := (iff #3552 #4476)
#4474 := (iff #3551 #4473)
#4471 := (iff #3550 #4470)
#4468 := (iff #3544 #4467)
#4465 := (iff #3539 #4464)
#4462 := (iff #3538 #4461)
#4459 := (iff #3537 #4458)
#4456 := (iff #3530 #4455)
#4453 := (iff #3525 #4452)
#4450 := (iff #3524 #4449)
#4447 := (iff #3523 #4446)
#4444 := (iff #3516 #4441)
#4442 := (iff #3505 #3505)
#4443 := [refl]: #4442
#4445 := [quant-intro #4443]: #4444
#4448 := [monotonicity #4445]: #4447
#4439 := (iff #3522 #4438)
#4436 := (iff #3501 #4433)
#4434 := (iff #3496 #3496)
#4435 := [refl]: #4434
#4437 := [quant-intro #4435]: #4436
#4440 := [monotonicity #4437]: #4439
#4451 := [monotonicity #4440 #4448]: #4450
#4454 := [monotonicity #4451]: #4453
#4457 := [monotonicity #4454]: #4456
#4460 := [monotonicity #4457]: #4459
#4431 := (iff #3536 #4430)
#4428 := (iff #3456 #4425)
#4426 := (iff #3451 #3451)
#4427 := [refl]: #4426
#4429 := [quant-intro #4427]: #4428
#4432 := [monotonicity #4429]: #4431
#4463 := [monotonicity #4432 #4460]: #4462
#4466 := [monotonicity #4463]: #4465
#4469 := [monotonicity #4466]: #4468
#4472 := [monotonicity #4469]: #4471
#4422 := (iff #1481 #4421)
#4419 := (iff #1478 #4416)
#4417 := (iff #1475 #1475)
#4418 := [refl]: #4417
#4420 := [quant-intro #4418]: #4419
#4423 := [monotonicity #4420]: #4422
#4475 := [monotonicity #4423 #4472]: #4474
#4478 := [monotonicity #4475]: #4477
#4481 := [monotonicity #4478]: #4480
#4484 := [monotonicity #4481]: #4483
#4487 := [monotonicity #4484]: #4486
#4490 := [monotonicity #4487]: #4489
#4493 := [monotonicity #4490]: #4492
#4496 := [monotonicity #4493]: #4495
#4414 := (iff #935 #4413)
#4411 := (iff #801 #4408)
#4409 := (iff #796 #796)
#4410 := [refl]: #4409
#4412 := [quant-intro #4410]: #4411
#4415 := [monotonicity #4412]: #4414
#4499 := [monotonicity #4415 #4496]: #4498
#4502 := [monotonicity #4499]: #4501
#4505 := [monotonicity #4502]: #4504
#4508 := [monotonicity #4505]: #4507
#4405 := (iff #1467 #4404)
#4402 := (iff #1464 #4399)
#4400 := (iff #1459 #1459)
#4401 := [refl]: #4400
#4403 := [quant-intro #4401]: #4402
#4406 := [monotonicity #4403]: #4405
#4511 := [monotonicity #4406 #4508]: #4510
#4514 := [monotonicity #4511]: #4513
#4517 := [monotonicity #4514]: #4516
#4520 := [monotonicity #4517]: #4519
#4397 := (iff #3603 #4396)
#4394 := (iff #3410 #4391)
#4392 := (iff #3405 #3405)
#4393 := [refl]: #4392
#4395 := [quant-intro #4393]: #4394
#4398 := [monotonicity #4395]: #4397
#4389 := (iff #3602 #4388)
#4386 := (iff #3392 #4383)
#4384 := (iff #3389 #3389)
#4385 := [refl]: #4384
#4387 := [quant-intro #4385]: #4386
#4390 := [monotonicity #4387]: #4389
#4379 := (iff #1632 #4378)
#4376 := (iff #1629 #4373)
#4374 := (iff #1624 #1624)
#4375 := [refl]: #4374
#4377 := [quant-intro #4375]: #4376
#4380 := [monotonicity #4377]: #4379
#4523 := [monotonicity #4380 #4390 #4398 #4520]: #4522
#4526 := [monotonicity #4523]: #4525
#4371 := (iff #3380 #4370)
#4368 := (iff #3379 #4367)
#4365 := (iff #3378 #4364)
#4362 := (iff #3371 #4361)
#4359 := (iff #3366 #4358)
#4356 := (iff #3365 #4355)
#4353 := (iff #3364 #4352)
#4350 := (iff #3357 #4349)
#4347 := (iff #3330 #4346)
#4344 := (iff #3329 #4343)
#4341 := (iff #3328 #4340)
#4338 := (iff #3322 #4335)
#4336 := (iff #3317 #3317)
#4337 := [refl]: #4336
#4339 := [quant-intro #4337]: #4338
#4342 := [monotonicity #4339]: #4341
#4345 := [monotonicity #4342]: #4344
#4348 := [monotonicity #4345]: #4347
#4351 := [monotonicity #4348]: #4350
#4354 := [monotonicity #4351]: #4353
#4333 := (iff #3363 #4332)
#4330 := (iff #3300 #4327)
#4328 := (iff #3295 #3295)
#4329 := [refl]: #4328
#4331 := [quant-intro #4329]: #4330
#4334 := [monotonicity #4331]: #4333
#4357 := [monotonicity #4334 #4354]: #4356
#4360 := [monotonicity #4357]: #4359
#4325 := (iff #3271 #4324)
#4322 := (iff #3270 #4321)
#4319 := (iff #3269 #4318)
#4316 := (iff #3263 #4313)
#4314 := (iff #3252 #3252)
#4315 := [refl]: #4314
#4317 := [quant-intro #4315]: #4316
#4320 := [monotonicity #4317]: #4319
#4323 := [monotonicity #4320]: #4322
#4326 := [monotonicity #4323]: #4325
#4363 := [monotonicity #4326 #4360]: #4362
#4366 := [monotonicity #4363]: #4365
#4310 := (iff #3377 #4309)
#4307 := (iff #3248 #4304)
#4305 := (iff #3237 #3237)
#4306 := [refl]: #4305
#4308 := [quant-intro #4306]: #4307
#4311 := [monotonicity #4308]: #4310
#4369 := [monotonicity #4311 #4366]: #4368
#4372 := [monotonicity #4369]: #4371
#4529 := [monotonicity #4372 #4526]: #4528
#4532 := [monotonicity #4529]: #4531
#4301 := (iff #3620 #4300)
#4298 := (iff #3234 #4295)
#4296 := (iff #3229 #3229)
#4297 := [refl]: #4296
#4299 := [quant-intro #4297]: #4298
#4302 := [monotonicity #4299]: #4301
#4293 := (iff #3619 #4292)
#4290 := (iff #3206 #4287)
#4288 := (iff #3201 #3201)
#4289 := [refl]: #4288
#4291 := [quant-intro #4289]: #4290
#4294 := [monotonicity #4291]: #4293
#4285 := (iff #3618 #4284)
#4282 := (iff #3178 #4279)
#4280 := (iff #3173 #3173)
#4281 := [refl]: #4280
#4283 := [quant-intro #4281]: #4282
#4286 := [monotonicity #4283]: #4285
#4276 := (iff #3617 #4275)
#4273 := (iff #3155 #4270)
#4271 := (iff #3150 #3150)
#4272 := [refl]: #4271
#4274 := [quant-intro #4272]: #4273
#4277 := [monotonicity #4274]: #4276
#4268 := (iff #1724 #4267)
#4265 := (iff #1721 #4262)
#4263 := (iff #1718 #1718)
#4264 := [refl]: #4263
#4266 := [quant-intro #4264]: #4265
#4269 := [monotonicity #4266]: #4268
#4535 := [monotonicity #4269 #4277 #4286 #4294 #4302 #4532]: #4534
#4538 := [monotonicity #4535]: #4537
#4259 := (iff #3131 #4258)
#4256 := (iff #3130 #4255)
#4253 := (iff #3129 #4252)
#4250 := (iff #3123 #4247)
#4248 := (iff #3112 #3112)
#4249 := [refl]: #4248
#4251 := [quant-intro #4249]: #4250
#4254 := [monotonicity #4251]: #4253
#4257 := [monotonicity #4254]: #4256
#4260 := [monotonicity #4257]: #4259
#4541 := [monotonicity #4260 #4538]: #4540
#4544 := [monotonicity #4541]: #4543
#4244 := (iff #3634 #4243)
#4241 := (iff #3108 #4238)
#4239 := (iff #3103 #3103)
#4240 := [refl]: #4239
#4242 := [quant-intro #4240]: #4241
#4245 := [monotonicity #4242]: #4244
#4547 := [monotonicity #4245 #4544]: #4546
#4550 := [monotonicity #4547]: #4549
#4553 := [monotonicity #4550]: #4552
#4556 := [monotonicity #4553]: #4555
#4235 := (iff #3648 #4234)
#4232 := (iff #3063 #4229)
#4230 := (iff #3058 #3058)
#4231 := [refl]: #4230
#4233 := [quant-intro #4231]: #4232
#4236 := [monotonicity #4233]: #4235
#4559 := [monotonicity #4236 #4556]: #4558
#4562 := [monotonicity #4559]: #4561
#4565 := [monotonicity #4562]: #4564
#4568 := [monotonicity #4565]: #4567
#4226 := (iff #1187 #4225)
#4223 := (iff #1184 #4220)
#4221 := (iff #1183 #1183)
#4222 := [refl]: #4221
#4224 := [quant-intro #4222]: #4223
#4227 := [monotonicity #4224]: #4226
#4571 := [monotonicity #4227 #4568]: #4570
#4574 := [monotonicity #4571]: #4573
#4577 := [monotonicity #4574]: #4576
#4580 := [monotonicity #4577]: #4579
#4583 := [monotonicity #4580]: #4582
#4586 := [monotonicity #4583]: #4585
#4589 := [monotonicity #4586]: #4588
#2343 := (not #2342)
#2945 := (and #789 #2343 #2942)
#2948 := (not #2945)
#2951 := (forall (vars (?v1 S2)) #2948)
#2917 := (not #2914)
#2348 := (not #2347)
#2960 := (and #1521 #2348 #2917 #2951)
#2316 := (not #2315)
#2887 := (and #2316 #2318)
#2890 := (not #2887)
#2908 := (or #2890 #2903)
#2911 := (not #2908)
#2965 := (or #2911 #2960)
#2968 := (and #1497 #2965)
#2286 := (not #2285)
#2862 := (and #2283 #2286)
#2865 := (not #2862)
#2881 := (or #2865 #2876)
#2884 := (not #2881)
#2971 := (or #2884 #2968)
#2974 := (and #1478 #2971)
#2977 := (or #2263 #2974)
#2980 := (and #218 #2977)
#2983 := (or #1472 #2980)
#2986 := (and #801 #2983)
#2989 := (or #2857 #2986)
#2992 := (and #1464 #2989)
#2995 := (or #2843 #2992)
#2201 := (not #2200)
#2198 := (not #2197)
#3001 := (and #195 #747 #1453 #1611 #1629 #1637 #2198 #2201 #2995)
#2143 := (not #2142)
#2139 := (not #2138)
#2780 := (and #2139 #2143)
#2783 := (not #2780)
#2800 := (or #2783 #2795)
#2803 := (not #2800)
#2152 := (not #170)
#2162 := (and #2152 #1373)
#2809 := (or #2162 #2803)
#2753 := (not #2748)
#2771 := (and #2753 #2766)
#2774 := (or #1333 #2771)
#2777 := (forall (vars (?v0 S2)) #2774)
#2814 := (and #2777 #2809)
#2070 := (not #2069)
#2723 := (and #2070 #2720)
#2726 := (not #2723)
#2729 := (forall (vars (?v1 S2)) #2726)
#2695 := (not #2692)
#2075 := (not #2074)
#2735 := (and #2075 #2695 #2729)
#2817 := (or #2735 #2814)
#2178 := (not #1401)
#2181 := (forall (vars (?v0 S2)) #2178)
#2823 := (and #148 #153 #611 #614 #2181 #2817)
#3006 := (or #2823 #3001)
#2672 := (not #2667)
#2675 := (and #2034 #2655 #2672)
#2678 := (or #1288 #2675)
#2681 := (forall (vars (?v0 S2)) #2678)
#2617 := (not #2612)
#2635 := (and #2006 #2617 #2630)
#2638 := (or #1250 #2635)
#2641 := (forall (vars (?v0 S2)) #2638)
#3012 := (and #112 #1696 #1712 #1721 #2641 #2681 #3006)
#1960 := (not #1959)
#2585 := (and #444 #1960 #2582)
#2588 := (not #2585)
#2591 := (forall (vars (?v1 S2)) #2588)
#2557 := (not #2554)
#1965 := (not #1964)
#2597 := (and #1965 #2557 #2591)
#3017 := (or #2597 #3012)
#3020 := (and #1235 #3017)
#1926 := (not #1925)
#2542 := (and #1926 #1928)
#2545 := (not #2542)
#2548 := (or #2539 #2545)
#2551 := (not #2548)
#3023 := (or #2551 #3020)
#3026 := (and #1204 #3023)
#1902 := (not #1901)
#2510 := (and #1899 #1902)
#2513 := (not #2510)
#2529 := (or #2513 #2524)
#2532 := (not #2529)
#3029 := (or #2532 #3026)
#3032 := (and #1184 #3029)
#3035 := (or #1879 #3032)
#3038 := (and #82 #3035)
#3041 := (or #1178 #3038)
#3683 := (iff #3041 #3682)
#3680 := (iff #3038 #3677)
#3672 := (and #82 #3669)
#3678 := (iff #3672 #3677)
#3679 := [rewrite]: #3678
#3673 := (iff #3038 #3672)
#3670 := (iff #3035 #3669)
#3667 := (iff #3032 #3664)
#3659 := (and #1184 #3656)
#3665 := (iff #3659 #3664)
#3666 := [rewrite]: #3665
#3660 := (iff #3032 #3659)
#3657 := (iff #3029 #3656)
#3654 := (iff #3026 #3651)
#3645 := (and #3063 #3642)
#3652 := (iff #3645 #3651)
#3653 := [rewrite]: #3652
#3646 := (iff #3026 #3645)
#3643 := (iff #3023 #3642)
#3640 := (iff #3020 #3637)
#3631 := (and #3108 #3628)
#3638 := (iff #3631 #3637)
#3639 := [rewrite]: #3638
#3632 := (iff #3020 #3631)
#3629 := (iff #3017 #3628)
#3626 := (iff #3012 #3623)
#3614 := (and #112 #3155 #3178 #1721 #3206 #3234 #3611)
#3624 := (iff #3614 #3623)
#3625 := [rewrite]: #3624
#3615 := (iff #3012 #3614)
#3612 := (iff #3006 #3611)
#3609 := (iff #3001 #3606)
#3599 := (and #195 #747 #3392 #3410 #1629 #1637 #2198 #2201 #3596)
#3607 := (iff #3599 #3606)
#3608 := [rewrite]: #3607
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#3558 := (iff #2977 #3557)
#3555 := (iff #2974 #3552)
#3547 := (and #1478 #3544)
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#3542 := (iff #2968 #3539)
#3533 := (and #3456 #3530)
#3540 := (iff #3533 #3539)
#3541 := [rewrite]: #3540
#3534 := (iff #2968 #3533)
#3531 := (iff #2965 #3530)
#3528 := (iff #2960 #3525)
#3519 := (and #3501 #2348 #2917 #3516)
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#3527 := [rewrite]: #3526
#3520 := (iff #2960 #3519)
#3517 := (iff #2951 #3516)
#3514 := (iff #2948 #3505)
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#3512 := (iff #3509 #3505)
#3513 := [rewrite]: #3512
#3510 := (iff #2948 #3509)
#3507 := (iff #2945 #3506)
#3508 := [rewrite]: #3507
#3511 := [monotonicity #3508]: #3510
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#3518 := [quant-intro #3515]: #3517
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#3495 := [monotonicity #3492]: #3494
#3500 := [trans #3495 #3498]: #3499
#3503 := [quant-intro #3500]: #3502
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#3477 := (iff #2908 #3474)
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#3469 := (iff #2890 #3460)
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#3465 := (iff #2890 #3464)
#3462 := (iff #2887 #3461)
#3463 := [rewrite]: #3462
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#3470 := [trans #3466 #3468]: #3469
#3473 := [monotonicity #3470]: #3472
#3478 := [trans #3473 #3476]: #3477
#3481 := [monotonicity #3478]: #3480
#3532 := [monotonicity #3481 #3529]: #3531
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#3454 := (iff #1492 #3451)
#3437 := (or #789 #3436)
#3448 := (or #3437 #1484)
#3452 := (iff #3448 #3451)
#3453 := [rewrite]: #3452
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#3446 := (iff #818 #3437)
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#3441 := (not #3438)
#3444 := (iff #3441 #3437)
#3445 := [rewrite]: #3444
#3442 := (iff #818 #3441)
#3439 := (iff #812 #3438)
#3440 := [rewrite]: #3439
#3443 := [monotonicity #3440]: #3442
#3447 := [trans #3443 #3445]: #3446
#3450 := [monotonicity #3447]: #3449
#3455 := [trans #3450 #3453]: #3454
#3458 := [quant-intro #3455]: #3457
#3535 := [monotonicity #3458 #3532]: #3534
#3543 := [trans #3535 #3541]: #3542
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#3431 := (iff #2881 #3428)
#3414 := (or #3413 #2285)
#3425 := (or #3414 #2876)
#3429 := (iff #3425 #3428)
#3430 := [rewrite]: #3429
#3426 := (iff #2881 #3425)
#3423 := (iff #2865 #3414)
#3415 := (not #3414)
#3418 := (not #3415)
#3421 := (iff #3418 #3414)
#3422 := [rewrite]: #3421
#3419 := (iff #2865 #3418)
#3416 := (iff #2862 #3415)
#3417 := [rewrite]: #3416
#3420 := [monotonicity #3417]: #3419
#3424 := [trans #3420 #3422]: #3423
#3427 := [monotonicity #3424]: #3426
#3432 := [trans #3427 #3430]: #3431
#3435 := [monotonicity #3432]: #3434
#3546 := [monotonicity #3435 #3543]: #3545
#3549 := [monotonicity #3546]: #3548
#3556 := [trans #3549 #3554]: #3555
#3559 := [monotonicity #3556]: #3558
#3562 := [monotonicity #3559]: #3561
#3569 := [trans #3562 #3567]: #3568
#3572 := [monotonicity #3569]: #3571
#3575 := [monotonicity #3572]: #3574
#3582 := [trans #3575 #3580]: #3581
#3585 := [monotonicity #3582]: #3584
#3588 := [monotonicity #3585]: #3587
#3595 := [trans #3588 #3593]: #3594
#3598 := [monotonicity #3595]: #3597
#3411 := (iff #1611 #3410)
#3408 := (iff #1608 #3405)
#3402 := (or #3385 #1605)
#3406 := (iff #3402 #3405)
#3407 := [rewrite]: #3406
#3403 := (iff #1608 #3402)
#3400 := (iff #1600 #3385)
#3395 := (not #3386)
#3398 := (iff #3395 #3385)
#3399 := [rewrite]: #3398
#3396 := (iff #1600 #3395)
#3387 := (iff #1442 #3386)
#3388 := [rewrite]: #3387
#3397 := [monotonicity #3388]: #3396
#3401 := [trans #3397 #3399]: #3400
#3404 := [monotonicity #3401]: #3403
#3409 := [trans #3404 #3407]: #3408
#3412 := [quant-intro #3409]: #3411
#3393 := (iff #1453 #3392)
#3390 := (iff #1448 #3389)
#3391 := [monotonicity #3388]: #3390
#3394 := [quant-intro #3391]: #3393
#3601 := [monotonicity #3394 #3412 #3598]: #3600
#3610 := [trans #3601 #3608]: #3609
#3383 := (iff #2823 #3380)
#3374 := (and #148 #153 #611 #614 #3248 #3371)
#3381 := (iff #3374 #3380)
#3382 := [rewrite]: #3381
#3375 := (iff #2823 #3374)
#3372 := (iff #2817 #3371)
#3369 := (iff #2814 #3366)
#3360 := (and #3300 #3357)
#3367 := (iff #3360 #3366)
#3368 := [rewrite]: #3367
#3361 := (iff #2814 #3360)
#3358 := (iff #2809 #3357)
#3355 := (iff #2803 #3354)
#3352 := (iff #2800 #3349)
#3335 := (or #2138 #2142)
#3346 := (or #3335 #2795)
#3350 := (iff #3346 #3349)
#3351 := [rewrite]: #3350
#3347 := (iff #2800 #3346)
#3344 := (iff #2783 #3335)
#3336 := (not #3335)
#3339 := (not #3336)
#3342 := (iff #3339 #3335)
#3343 := [rewrite]: #3342
#3340 := (iff #2783 #3339)
#3337 := (iff #2780 #3336)
#3338 := [rewrite]: #3337
#3341 := [monotonicity #3338]: #3340
#3345 := [trans #3341 #3343]: #3344
#3348 := [monotonicity #3345]: #3347
#3353 := [trans #3348 #3351]: #3352
#3356 := [monotonicity #3353]: #3355
#3333 := (iff #2162 #3330)
#3325 := (and #2152 #3322)
#3331 := (iff #3325 #3330)
#3332 := [rewrite]: #3331
#3326 := (iff #2162 #3325)
#3323 := (iff #1373 #3322)
#3320 := (iff #1370 #3317)
#3303 := (or #1217 #1326)
#3314 := (or #3303 #1367)
#3318 := (iff #3314 #3317)
#3319 := [rewrite]: #3318
#3315 := (iff #1370 #3314)
#3312 := (iff #1364 #3303)
#3304 := (not #3303)
#3307 := (not #3304)
#3310 := (iff #3307 #3303)
#3311 := [rewrite]: #3310
#3308 := (iff #1364 #3307)
#3305 := (iff #1361 #3304)
#3306 := [rewrite]: #3305
#3309 := [monotonicity #3306]: #3308
#3313 := [trans #3309 #3311]: #3312
#3316 := [monotonicity #3313]: #3315
#3321 := [trans #3316 #3319]: #3320
#3324 := [quant-intro #3321]: #3323
#3327 := [monotonicity #3324]: #3326
#3334 := [trans #3327 #3332]: #3333
#3359 := [monotonicity #3334 #3356]: #3358
#3301 := (iff #2777 #3300)
#3298 := (iff #2774 #3295)
#3276 := (or #67 #1326)
#3292 := (or #3276 #3289)
#3296 := (iff #3292 #3295)
#3297 := [rewrite]: #3296
#3293 := (iff #2774 #3292)
#3290 := (iff #2771 #3289)
#3291 := [rewrite]: #3290
#3285 := (iff #1333 #3276)
#3277 := (not #3276)
#3280 := (not #3277)
#3283 := (iff #3280 #3276)
#3284 := [rewrite]: #3283
#3281 := (iff #1333 #3280)
#3278 := (iff #1330 #3277)
#3279 := [rewrite]: #3278
#3282 := [monotonicity #3279]: #3281
#3286 := [trans #3282 #3284]: #3285
#3294 := [monotonicity #3286 #3291]: #3293
#3299 := [trans #3294 #3297]: #3298
#3302 := [quant-intro #3299]: #3301
#3362 := [monotonicity #3302 #3359]: #3361
#3370 := [trans #3362 #3368]: #3369
#3274 := (iff #2735 #3271)
#3266 := (and #2075 #2695 #3263)
#3272 := (iff #3266 #3271)
#3273 := [rewrite]: #3272
#3267 := (iff #2735 #3266)
#3264 := (iff #2729 #3263)
#3261 := (iff #2726 #3252)
#3253 := (not #3252)
#3256 := (not #3253)
#3259 := (iff #3256 #3252)
#3260 := [rewrite]: #3259
#3257 := (iff #2726 #3256)
#3254 := (iff #2723 #3253)
#3255 := [rewrite]: #3254
#3258 := [monotonicity #3255]: #3257
#3262 := [trans #3258 #3260]: #3261
#3265 := [quant-intro #3262]: #3264
#3268 := [monotonicity #3265]: #3267
#3275 := [trans #3268 #3273]: #3274
#3373 := [monotonicity #3275 #3370]: #3372
#3249 := (iff #2181 #3248)
#3246 := (iff #2178 #3237)
#3238 := (not #3237)
#3241 := (not #3238)
#3244 := (iff #3241 #3237)
#3245 := [rewrite]: #3244
#3242 := (iff #2178 #3241)
#3239 := (iff #1401 #3238)
#3240 := [rewrite]: #3239
#3243 := [monotonicity #3240]: #3242
#3247 := [trans #3243 #3245]: #3246
#3250 := [quant-intro #3247]: #3249
#3376 := [monotonicity #3250 #3373]: #3375
#3384 := [trans #3376 #3382]: #3383
#3613 := [monotonicity #3384 #3610]: #3612
#3235 := (iff #2681 #3234)
#3232 := (iff #2678 #3229)
#3209 := (or #67 #1281)
#3226 := (or #3209 #3223)
#3230 := (iff #3226 #3229)
#3231 := [rewrite]: #3230
#3227 := (iff #2678 #3226)
#3224 := (iff #2675 #3223)
#3225 := [rewrite]: #3224
#3218 := (iff #1288 #3209)
#3210 := (not #3209)
#3213 := (not #3210)
#3216 := (iff #3213 #3209)
#3217 := [rewrite]: #3216
#3214 := (iff #1288 #3213)
#3211 := (iff #1285 #3210)
#3212 := [rewrite]: #3211
#3215 := [monotonicity #3212]: #3214
#3219 := [trans #3215 #3217]: #3218
#3228 := [monotonicity #3219 #3225]: #3227
#3233 := [trans #3228 #3231]: #3232
#3236 := [quant-intro #3233]: #3235
#3207 := (iff #2641 #3206)
#3204 := (iff #2638 #3201)
#3181 := (or #67 #1243)
#3198 := (or #3181 #3195)
#3202 := (iff #3198 #3201)
#3203 := [rewrite]: #3202
#3199 := (iff #2638 #3198)
#3196 := (iff #2635 #3195)
#3197 := [rewrite]: #3196
#3190 := (iff #1250 #3181)
#3182 := (not #3181)
#3185 := (not #3182)
#3188 := (iff #3185 #3181)
#3189 := [rewrite]: #3188
#3186 := (iff #1250 #3185)
#3183 := (iff #1247 #3182)
#3184 := [rewrite]: #3183
#3187 := [monotonicity #3184]: #3186
#3191 := [trans #3187 #3189]: #3190
#3200 := [monotonicity #3191 #3197]: #3199
#3205 := [trans #3200 #3203]: #3204
#3208 := [quant-intro #3205]: #3207
#3179 := (iff #1712 #3178)
#3176 := (iff #1707 #3173)
#3159 := (or #523 #3158)
#3170 := (or #3159 #1297)
#3174 := (iff #3170 #3173)
#3175 := [rewrite]: #3174
#3171 := (iff #1707 #3170)
#3168 := (iff #538 #3159)
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#3163 := (not #3160)
#3166 := (iff #3163 #3159)
#3167 := [rewrite]: #3166
#3164 := (iff #538 #3163)
#3161 := (iff #532 #3160)
#3162 := [rewrite]: #3161
#3165 := [monotonicity #3162]: #3164
#3169 := [trans #3165 #3167]: #3168
#3172 := [monotonicity #3169]: #3171
#3177 := [trans #3172 #3175]: #3176
#3180 := [quant-intro #3177]: #3179
#3156 := (iff #1696 #3155)
#3153 := (iff #1693 #3150)
#3136 := (or #526 #1217)
#3147 := (or #3136 #1690)
#3151 := (iff #3147 #3150)
#3152 := [rewrite]: #3151
#3148 := (iff #1693 #3147)
#3145 := (iff #1687 #3136)
#3137 := (not #3136)
#3140 := (not #3137)
#3143 := (iff #3140 #3136)
#3144 := [rewrite]: #3143
#3141 := (iff #1687 #3140)
#3138 := (iff #1682 #3137)
#3139 := [rewrite]: #3138
#3142 := [monotonicity #3139]: #3141
#3146 := [trans #3142 #3144]: #3145
#3149 := [monotonicity #3146]: #3148
#3154 := [trans #3149 #3152]: #3153
#3157 := [quant-intro #3154]: #3156
#3616 := [monotonicity #3157 #3180 #3208 #3236 #3613]: #3615
#3627 := [trans #3616 #3625]: #3626
#3134 := (iff #2597 #3131)
#3126 := (and #1965 #2557 #3123)
#3132 := (iff #3126 #3131)
#3133 := [rewrite]: #3132
#3127 := (iff #2597 #3126)
#3124 := (iff #2591 #3123)
#3121 := (iff #2588 #3112)
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#3116 := (not #3113)
#3119 := (iff #3116 #3112)
#3120 := [rewrite]: #3119
#3117 := (iff #2588 #3116)
#3114 := (iff #2585 #3113)
#3115 := [rewrite]: #3114
#3118 := [monotonicity #3115]: #3117
#3122 := [trans #3118 #3120]: #3121
#3125 := [quant-intro #3122]: #3124
#3128 := [monotonicity #3125]: #3127
#3135 := [trans #3128 #3133]: #3134
#3630 := [monotonicity #3135 #3627]: #3629
#3109 := (iff #1235 #3108)
#3106 := (iff #1232 #3103)
#3089 := (or #447 #1217)
#3100 := (or #1212 #3089)
#3104 := (iff #3100 #3103)
#3105 := [rewrite]: #3104
#3101 := (iff #1232 #3100)
#3098 := (iff #1229 #3089)
#3090 := (not #3089)
#3093 := (not #3090)
#3096 := (iff #3093 #3089)
#3097 := [rewrite]: #3096
#3094 := (iff #1229 #3093)
#3091 := (iff #1224 #3090)
#3092 := [rewrite]: #3091
#3095 := [monotonicity #3092]: #3094
#3099 := [trans #3095 #3097]: #3098
#3102 := [monotonicity #3099]: #3101
#3107 := [trans #3102 #3105]: #3106
#3110 := [quant-intro #3107]: #3109
#3633 := [monotonicity #3110 #3630]: #3632
#3641 := [trans #3633 #3639]: #3640
#3087 := (iff #2551 #3086)
#3084 := (iff #2548 #3081)
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#3082 := (iff #3078 #3081)
#3083 := [rewrite]: #3082
#3079 := (iff #2548 #3078)
#3076 := (iff #2545 #3067)
#3068 := (not #3067)
#3071 := (not #3068)
#3074 := (iff #3071 #3067)
#3075 := [rewrite]: #3074
#3072 := (iff #2545 #3071)
#3069 := (iff #2542 #3068)
#3070 := [rewrite]: #3069
#3073 := [monotonicity #3070]: #3072
#3077 := [trans #3073 #3075]: #3076
#3080 := [monotonicity #3077]: #3079
#3085 := [trans #3080 #3083]: #3084
#3088 := [monotonicity #3085]: #3087
#3644 := [monotonicity #3088 #3641]: #3643
#3064 := (iff #1204 #3063)
#3061 := (iff #1199 #3058)
#3044 := (or #444 #2507)
#3055 := (or #3044 #1192)
#3059 := (iff #3055 #3058)
#3060 := [rewrite]: #3059
#3056 := (iff #1199 #3055)
#3053 := (iff #465 #3044)
#3045 := (not #3044)
#3048 := (not #3045)
#3051 := (iff #3048 #3044)
#3052 := [rewrite]: #3051
#3049 := (iff #465 #3048)
#3046 := (iff #459 #3045)
#3047 := [rewrite]: #3046
#3050 := [monotonicity #3047]: #3049
#3054 := [trans #3050 #3052]: #3053
#3057 := [monotonicity #3054]: #3056
#3062 := [trans #3057 #3060]: #3061
#3065 := [quant-intro #3062]: #3064
#3647 := [monotonicity #3065 #3644]: #3646
#3655 := [trans #3647 #3653]: #3654
#2246 := (iff #2532 #2039)
#1883 := (iff #2529 #1941)
#2293 := (or #2267 #1901)
#2011 := (or #2293 #2524)
#1942 := (iff #2011 #1941)
#1882 := [rewrite]: #1942
#2114 := (iff #2529 #2011)
#2151 := (iff #2513 #2293)
#1846 := (not #2293)
#2325 := (not #1846)
#1910 := (iff #2325 #2293)
#2150 := [rewrite]: #1910
#2326 := (iff #2513 #2325)
#1847 := (iff #2510 #1846)
#2294 := [rewrite]: #1847
#1909 := [monotonicity #2294]: #2326
#2010 := [trans #1909 #2150]: #2151
#2115 := [monotonicity #2010]: #2114
#2038 := [trans #2115 #1882]: #1883
#2247 := [monotonicity #2038]: #2246
#3658 := [monotonicity #2247 #3655]: #3657
#3661 := [monotonicity #3658]: #3660
#3668 := [trans #3661 #3666]: #3667
#3671 := [monotonicity #3668]: #3670
#3674 := [monotonicity #3671]: #3673
#3681 := [trans #3674 #3679]: #3680
#3684 := [monotonicity #3681]: #3683
#2340 := (+ #2339 #2337)
#2341 := (= #2340 0::Int)
#2344 := (and #789 #2343 #2341)
#2361 := (not #2344)
#2364 := (forall (vars (?v1 S2)) #2361)
#2349 := (= ?v0!20 f16)
#2350 := (not #2349)
#2351 := (and #2350 #2348)
#2352 := (not #2351)
#2358 := (not #2352)
#2368 := (and #2358 #2364)
#2373 := (and #1521 #2368)
#2305 := (* -1::Int #2304)
#2307 := (+ #2306 #2305)
#2311 := (+ #2310 #2307)
#2312 := (>= #2311 0::Int)
#2319 := (and #2318 #2316)
#2320 := (not #2319)
#2321 := (or #2320 #2312)
#2322 := (not #2321)
#2377 := (or #2322 #2373)
#2381 := (and #1497 #2377)
#2278 := (* -1::Int #2277)
#2280 := (+ #2279 #2278)
#2281 := (>= #2280 0::Int)
#2287 := (and #2286 #2283)
#2288 := (not #2287)
#2289 := (or #2288 #2281)
#2290 := (not #2289)
#2385 := (or #2290 #2381)
#2389 := (and #1478 #2385)
#2393 := (or #2263 #2389)
#2257 := (not #1472)
#2397 := (and #2257 #2393)
#2401 := (or #1472 #2397)
#2405 := (and #801 #2401)
#2241 := (= #2240 #2239)
#2242 := (or #2241 #2238)
#2243 := (not #2242)
#2409 := (or #2243 #2405)
#2413 := (and #1464 #2409)
#2219 := (* -1::Int #2218)
#2221 := (+ #2220 #2219)
#2222 := (>= #2221 0::Int)
#2223 := (not #2222)
#2417 := (or #2223 #2413)
#2202 := (and #2201 #2198)
#2188 := (not #977)
#2437 := (and #2188 #747 #2202 #1453 #2417 #1611 #1629 #1637)
#2128 := (* -1::Int #2127)
#2130 := (+ #2129 #2128)
#2134 := (+ #2133 #2130)
#2135 := (>= #2134 0::Int)
#2144 := (and #2143 #2139)
#2145 := (not #2144)
#2146 := (or #2145 #2135)
#2147 := (not #2146)
#2166 := (or #2147 #2162)
#2103 := (+ #2102 #1324)
#2107 := (+ #2106 #2103)
#2108 := (= #2107 0::Int)
#2109 := (>= #2103 0::Int)
#2110 := (not #2109)
#2111 := (and #2110 #2108)
#2116 := (or #1333 #2111)
#2119 := (forall (vars (?v0 S2)) #2116)
#2170 := (and #2119 #2166)
#2067 := (+ #2066 #2064)
#2068 := (= #2067 0::Int)
#2071 := (and #2070 #2068)
#2087 := (not #2071)
#2090 := (forall (vars (?v1 S2)) #2087)
#2076 := (= ?v0!8 f16)
#2077 := (not #2076)
#2078 := (and #2077 #2075)
#2079 := (not #2078)
#2084 := (not #2079)
#2094 := (and #2084 #2090)
#2174 := (or #2094 #2170)
#2058 := (not #705)
#2055 := (not #723)
#2052 := (not #696)
#2049 := (not #714)
#2184 := (and #2049 #2052 #2055 #2058 #2174 #2181)
#2441 := (or #2184 #2437)
#2025 := (+ #2024 #1279)
#2026 := (>= #2025 0::Int)
#2027 := (not #2026)
#2031 := (+ #2030 #2025)
#2032 := (= #2031 0::Int)
#2035 := (and #2034 #2032 #2027)
#2040 := (or #1288 #2035)
#2043 := (forall (vars (?v0 S2)) #2040)
#1998 := (+ #1241 #1997)
#2000 := (+ #1999 #1998)
#2001 := (= #2000 0::Int)
#2002 := (+ #1999 #1241)
#2003 := (>= #2002 0::Int)
#2004 := (not #2003)
#2007 := (and #2006 #2004 #2001)
#2012 := (or #1250 #2007)
#2015 := (forall (vars (?v0 S2)) #2012)
#1989 := (not #1729)
#2466 := (and #1989 #2015 #2043 #2441 #1696 #1712 #1721)
#1955 := (+ #1954 #1952)
#1956 := (+ #68 #1955)
#1957 := (= #1956 0::Int)
#1961 := (and #444 #1960 #1957)
#1977 := (not #1961)
#1980 := (forall (vars (?v1 S2)) #1977)
#1966 := (= ?v0!5 f16)
#1967 := (not #1966)
#1968 := (and #1967 #1965)
#1969 := (not #1968)
#1974 := (not #1969)
#1984 := (and #1974 #1980)
#2470 := (or #1984 #2466)
#2474 := (and #1235 #2470)
#1929 := (and #1928 #1926)
#1930 := (not #1929)
#1933 := (+ #1932 #1922)
#1935 := (+ #1934 #1933)
#1936 := (>= #1935 0::Int)
#1937 := (or #1936 #1930)
#1938 := (not #1937)
#2478 := (or #1938 #2474)
#2482 := (and #1204 #2478)
#1894 := (* -1::Int #1893)
#1896 := (+ #1895 #1894)
#1897 := (>= #1896 0::Int)
#1903 := (and #1902 #1899)
#1904 := (not #1903)
#1905 := (or #1904 #1897)
#1906 := (not #1905)
#2486 := (or #1906 #2482)
#2490 := (and #1184 #2486)
#2494 := (or #1879 #2490)
#1842 := (not #1178)
#2498 := (and #1842 #2494)
#2502 := (or #1178 #2498)
#3042 := (iff #2502 #3041)
#3039 := (iff #2498 #3038)
#3036 := (iff #2494 #3035)
#3033 := (iff #2490 #3032)
#3030 := (iff #2486 #3029)
#3027 := (iff #2482 #3026)
#3024 := (iff #2478 #3023)
#3021 := (iff #2474 #3020)
#3018 := (iff #2470 #3017)
#3015 := (iff #2466 #3012)
#3009 := (and #112 #2641 #2681 #3006 #1696 #1712 #1721)
#3013 := (iff #3009 #3012)
#3014 := [rewrite]: #3013
#3010 := (iff #2466 #3009)
#3007 := (iff #2441 #3006)
#3004 := (iff #2437 #3001)
#2998 := (and #195 #747 #2202 #1453 #2995 #1611 #1629 #1637)
#3002 := (iff #2998 #3001)
#3003 := [rewrite]: #3002
#2999 := (iff #2437 #2998)
#2996 := (iff #2417 #2995)
#2993 := (iff #2413 #2992)
#2990 := (iff #2409 #2989)
#2987 := (iff #2405 #2986)
#2984 := (iff #2401 #2983)
#2981 := (iff #2397 #2980)
#2978 := (iff #2393 #2977)
#2975 := (iff #2389 #2974)
#2972 := (iff #2385 #2971)
#2969 := (iff #2381 #2968)
#2966 := (iff #2377 #2965)
#2963 := (iff #2373 #2960)
#2923 := (and #2348 #2917)
#2954 := (and #2923 #2951)
#2957 := (and #1521 #2954)
#2961 := (iff #2957 #2960)
#2962 := [rewrite]: #2961
#2958 := (iff #2373 #2957)
#2955 := (iff #2368 #2954)
#2952 := (iff #2364 #2951)
#2949 := (iff #2361 #2948)
#2946 := (iff #2344 #2945)
#2943 := (iff #2341 #2942)
#2940 := (= #2340 #2939)
#2941 := [rewrite]: #2940
#2944 := [monotonicity #2941]: #2943
#2947 := [monotonicity #2944]: #2946
#2950 := [monotonicity #2947]: #2949
#2953 := [quant-intro #2950]: #2952
#2936 := (iff #2358 #2923)
#2928 := (not #2923)
#2931 := (not #2928)
#2934 := (iff #2931 #2923)
#2935 := [rewrite]: #2934
#2932 := (iff #2358 #2931)
#2929 := (iff #2352 #2928)
#2926 := (iff #2351 #2923)
#2920 := (and #2917 #2348)
#2924 := (iff #2920 #2923)
#2925 := [rewrite]: #2924
#2921 := (iff #2351 #2920)
#2918 := (iff #2350 #2917)
#2915 := (iff #2349 #2914)
#2916 := [rewrite]: #2915
#2919 := [monotonicity #2916]: #2918
#2922 := [monotonicity #2919]: #2921
#2927 := [trans #2922 #2925]: #2926
#2930 := [monotonicity #2927]: #2929
#2933 := [monotonicity #2930]: #2932
#2937 := [trans #2933 #2935]: #2936
#2956 := [monotonicity #2937 #2953]: #2955
#2959 := [monotonicity #2956]: #2958
#2964 := [trans #2959 #2962]: #2963
#2912 := (iff #2322 #2911)
#2909 := (iff #2321 #2908)
#2906 := (iff #2312 #2903)
#2893 := (+ #2306 #2310)
#2894 := (+ #2305 #2893)
#2897 := (>= #2894 0::Int)
#2904 := (iff #2897 #2903)
#2905 := [rewrite]: #2904
#2898 := (iff #2312 #2897)
#2895 := (= #2311 #2894)
#2896 := [rewrite]: #2895
#2899 := [monotonicity #2896]: #2898
#2907 := [trans #2899 #2905]: #2906
#2891 := (iff #2320 #2890)
#2888 := (iff #2319 #2887)
#2889 := [rewrite]: #2888
#2892 := [monotonicity #2889]: #2891
#2910 := [monotonicity #2892 #2907]: #2909
#2913 := [monotonicity #2910]: #2912
#2967 := [monotonicity #2913 #2964]: #2966
#2970 := [monotonicity #2967]: #2969
#2885 := (iff #2290 #2884)
#2882 := (iff #2289 #2881)
#2879 := (iff #2281 #2876)
#2868 := (+ #2278 #2279)
#2871 := (>= #2868 0::Int)
#2877 := (iff #2871 #2876)
#2878 := [rewrite]: #2877
#2872 := (iff #2281 #2871)
#2869 := (= #2280 #2868)
#2870 := [rewrite]: #2869
#2873 := [monotonicity #2870]: #2872
#2880 := [trans #2873 #2878]: #2879
#2866 := (iff #2288 #2865)
#2863 := (iff #2287 #2862)
#2864 := [rewrite]: #2863
#2867 := [monotonicity #2864]: #2866
#2883 := [monotonicity #2867 #2880]: #2882
#2886 := [monotonicity #2883]: #2885
#2973 := [monotonicity #2886 #2970]: #2972
#2976 := [monotonicity #2973]: #2975
#2979 := [monotonicity #2976]: #2978
#2860 := (iff #2257 #218)
#2861 := [rewrite]: #2860
#2982 := [monotonicity #2861 #2979]: #2981
#2985 := [monotonicity #2982]: #2984
#2988 := [monotonicity #2985]: #2987
#2858 := (iff #2243 #2857)
#2855 := (iff #2242 #2852)
#2849 := (or #2846 #2238)
#2853 := (iff #2849 #2852)
#2854 := [rewrite]: #2853
#2850 := (iff #2242 #2849)
#2847 := (iff #2241 #2846)
#2848 := [rewrite]: #2847
#2851 := [monotonicity #2848]: #2850
#2856 := [trans #2851 #2854]: #2855
#2859 := [monotonicity #2856]: #2858
#2991 := [monotonicity #2859 #2988]: #2990
#2994 := [monotonicity #2991]: #2993
#2844 := (iff #2223 #2843)
#2841 := (iff #2222 #2838)
#2830 := (+ #2219 #2220)
#2833 := (>= #2830 0::Int)
#2839 := (iff #2833 #2838)
#2840 := [rewrite]: #2839
#2834 := (iff #2222 #2833)
#2831 := (= #2221 #2830)
#2832 := [rewrite]: #2831
#2835 := [monotonicity #2832]: #2834
#2842 := [trans #2835 #2840]: #2841
#2845 := [monotonicity #2842]: #2844
#2997 := [monotonicity #2845 #2994]: #2996
#2828 := (iff #2188 #195)
#2829 := [rewrite]: #2828
#3000 := [monotonicity #2829 #2997]: #2999
#3005 := [trans #3000 #3003]: #3004
#2826 := (iff #2184 #2823)
#2820 := (and #148 #153 #611 #614 #2817 #2181)
#2824 := (iff #2820 #2823)
#2825 := [rewrite]: #2824
#2821 := (iff #2184 #2820)
#2818 := (iff #2174 #2817)
#2815 := (iff #2170 #2814)
#2812 := (iff #2166 #2809)
#2806 := (or #2803 #2162)
#2810 := (iff #2806 #2809)
#2811 := [rewrite]: #2810
#2807 := (iff #2166 #2806)
#2804 := (iff #2147 #2803)
#2801 := (iff #2146 #2800)
#2798 := (iff #2135 #2795)
#2786 := (+ #2129 #2133)
#2787 := (+ #2128 #2786)
#2790 := (>= #2787 0::Int)
#2796 := (iff #2790 #2795)
#2797 := [rewrite]: #2796
#2791 := (iff #2135 #2790)
#2788 := (= #2134 #2787)
#2789 := [rewrite]: #2788
#2792 := [monotonicity #2789]: #2791
#2799 := [trans #2792 #2797]: #2798
#2784 := (iff #2145 #2783)
#2781 := (iff #2144 #2780)
#2782 := [rewrite]: #2781
#2785 := [monotonicity #2782]: #2784
#2802 := [monotonicity #2785 #2799]: #2801
#2805 := [monotonicity #2802]: #2804
#2808 := [monotonicity #2805]: #2807
#2813 := [trans #2808 #2811]: #2812
#2778 := (iff #2119 #2777)
#2775 := (iff #2116 #2774)
#2772 := (iff #2111 #2771)
#2769 := (iff #2108 #2766)
#2756 := (+ #2102 #2106)
#2757 := (+ #1324 #2756)
#2760 := (= #2757 0::Int)
#2767 := (iff #2760 #2766)
#2768 := [rewrite]: #2767
#2761 := (iff #2108 #2760)
#2758 := (= #2107 #2757)
#2759 := [rewrite]: #2758
#2762 := [monotonicity #2759]: #2761
#2770 := [trans #2762 #2768]: #2769
#2754 := (iff #2110 #2753)
#2751 := (iff #2109 #2748)
#2740 := (+ #1324 #2102)
#2743 := (>= #2740 0::Int)
#2749 := (iff #2743 #2748)
#2750 := [rewrite]: #2749
#2744 := (iff #2109 #2743)
#2741 := (= #2103 #2740)
#2742 := [rewrite]: #2741
#2745 := [monotonicity #2742]: #2744
#2752 := [trans #2745 #2750]: #2751
#2755 := [monotonicity #2752]: #2754
#2773 := [monotonicity #2755 #2770]: #2772
#2776 := [monotonicity #2773]: #2775
#2779 := [quant-intro #2776]: #2778
#2816 := [monotonicity #2779 #2813]: #2815
#2738 := (iff #2094 #2735)
#2701 := (and #2075 #2695)
#2732 := (and #2701 #2729)
#2736 := (iff #2732 #2735)
#2737 := [rewrite]: #2736
#2733 := (iff #2094 #2732)
#2730 := (iff #2090 #2729)
#2727 := (iff #2087 #2726)
#2724 := (iff #2071 #2723)
#2721 := (iff #2068 #2720)
#2718 := (= #2067 #2717)
#2719 := [rewrite]: #2718
#2722 := [monotonicity #2719]: #2721
#2725 := [monotonicity #2722]: #2724
#2728 := [monotonicity #2725]: #2727
#2731 := [quant-intro #2728]: #2730
#2714 := (iff #2084 #2701)
#2706 := (not #2701)
#2709 := (not #2706)
#2712 := (iff #2709 #2701)
#2713 := [rewrite]: #2712
#2710 := (iff #2084 #2709)
#2707 := (iff #2079 #2706)
#2704 := (iff #2078 #2701)
#2698 := (and #2695 #2075)
#2702 := (iff #2698 #2701)
#2703 := [rewrite]: #2702
#2699 := (iff #2078 #2698)
#2696 := (iff #2077 #2695)
#2693 := (iff #2076 #2692)
#2694 := [rewrite]: #2693
#2697 := [monotonicity #2694]: #2696
#2700 := [monotonicity #2697]: #2699
#2705 := [trans #2700 #2703]: #2704
#2708 := [monotonicity #2705]: #2707
#2711 := [monotonicity #2708]: #2710
#2715 := [trans #2711 #2713]: #2714
#2734 := [monotonicity #2715 #2731]: #2733
#2739 := [trans #2734 #2737]: #2738
#2819 := [monotonicity #2739 #2816]: #2818
#2690 := (iff #2058 #614)
#2691 := [rewrite]: #2690
#2688 := (iff #2055 #611)
#2689 := [rewrite]: #2688
#2686 := (iff #2052 #153)
#2687 := [rewrite]: #2686
#2684 := (iff #2049 #148)
#2685 := [rewrite]: #2684
#2822 := [monotonicity #2685 #2687 #2689 #2691 #2819]: #2821
#2827 := [trans #2822 #2825]: #2826
#3008 := [monotonicity #2827 #3005]: #3007
#2682 := (iff #2043 #2681)
#2679 := (iff #2040 #2678)
#2676 := (iff #2035 #2675)
#2673 := (iff #2027 #2672)
#2670 := (iff #2026 #2667)
#2660 := (+ #1279 #2024)
#2663 := (>= #2660 0::Int)
#2668 := (iff #2663 #2667)
#2669 := [rewrite]: #2668
#2664 := (iff #2026 #2663)
#2661 := (= #2025 #2660)
#2662 := [rewrite]: #2661
#2665 := [monotonicity #2662]: #2664
#2671 := [trans #2665 #2669]: #2670
#2674 := [monotonicity #2671]: #2673
#2658 := (iff #2032 #2655)
#2644 := (+ #2024 #2030)
#2645 := (+ #1279 #2644)
#2648 := (= #2645 0::Int)
#2656 := (iff #2648 #2655)
#2657 := [rewrite]: #2656
#2649 := (iff #2032 #2648)
#2646 := (= #2031 #2645)
#2647 := [rewrite]: #2646
#2650 := [monotonicity #2647]: #2649
#2659 := [trans #2650 #2657]: #2658
#2677 := [monotonicity #2659 #2674]: #2676
#2680 := [monotonicity #2677]: #2679
#2683 := [quant-intro #2680]: #2682
#2642 := (iff #2015 #2641)
#2639 := (iff #2012 #2638)
#2636 := (iff #2007 #2635)
#2633 := (iff #2001 #2630)
#2620 := (+ #1997 #1999)
#2621 := (+ #1241 #2620)
#2624 := (= #2621 0::Int)
#2631 := (iff #2624 #2630)
#2632 := [rewrite]: #2631
#2625 := (iff #2001 #2624)
#2622 := (= #2000 #2621)
#2623 := [rewrite]: #2622
#2626 := [monotonicity #2623]: #2625
#2634 := [trans #2626 #2632]: #2633
#2618 := (iff #2004 #2617)
#2615 := (iff #2003 #2612)
#2604 := (+ #1241 #1999)
#2607 := (>= #2604 0::Int)
#2613 := (iff #2607 #2612)
#2614 := [rewrite]: #2613
#2608 := (iff #2003 #2607)
#2605 := (= #2002 #2604)
#2606 := [rewrite]: #2605
#2609 := [monotonicity #2606]: #2608
#2616 := [trans #2609 #2614]: #2615
#2619 := [monotonicity #2616]: #2618
#2637 := [monotonicity #2619 #2634]: #2636
#2640 := [monotonicity #2637]: #2639
#2643 := [quant-intro #2640]: #2642
#2602 := (iff #1989 #112)
#2603 := [rewrite]: #2602
#3011 := [monotonicity #2603 #2643 #2683 #3008]: #3010
#3016 := [trans #3011 #3014]: #3015
#2600 := (iff #1984 #2597)
#2563 := (and #1965 #2557)
#2594 := (and #2563 #2591)
#2598 := (iff #2594 #2597)
#2599 := [rewrite]: #2598
#2595 := (iff #1984 #2594)
#2592 := (iff #1980 #2591)
#2589 := (iff #1977 #2588)
#2586 := (iff #1961 #2585)
#2583 := (iff #1957 #2582)
#2580 := (= #1956 #2579)
#2581 := [rewrite]: #2580
#2584 := [monotonicity #2581]: #2583
#2587 := [monotonicity #2584]: #2586
#2590 := [monotonicity #2587]: #2589
#2593 := [quant-intro #2590]: #2592
#2576 := (iff #1974 #2563)
#2568 := (not #2563)
#2571 := (not #2568)
#2574 := (iff #2571 #2563)
#2575 := [rewrite]: #2574
#2572 := (iff #1974 #2571)
#2569 := (iff #1969 #2568)
#2566 := (iff #1968 #2563)
#2560 := (and #2557 #1965)
#2564 := (iff #2560 #2563)
#2565 := [rewrite]: #2564
#2561 := (iff #1968 #2560)
#2558 := (iff #1967 #2557)
#2555 := (iff #1966 #2554)
#2556 := [rewrite]: #2555
#2559 := [monotonicity #2556]: #2558
#2562 := [monotonicity #2559]: #2561
#2567 := [trans #2562 #2565]: #2566
#2570 := [monotonicity #2567]: #2569
#2573 := [monotonicity #2570]: #2572
#2577 := [trans #2573 #2575]: #2576
#2596 := [monotonicity #2577 #2593]: #2595
#2601 := [trans #2596 #2599]: #2600
#3019 := [monotonicity #2601 #3016]: #3018
#3022 := [monotonicity #3019]: #3021
#2552 := (iff #1938 #2551)
#2549 := (iff #1937 #2548)
#2546 := (iff #1930 #2545)
#2543 := (iff #1929 #2542)
#2544 := [rewrite]: #2543
#2547 := [monotonicity #2544]: #2546
#2540 := (iff #1936 #2539)
#2537 := (= #1935 #2536)
#2538 := [rewrite]: #2537
#2541 := [monotonicity #2538]: #2540
#2550 := [monotonicity #2541 #2547]: #2549
#2553 := [monotonicity #2550]: #2552
#3025 := [monotonicity #2553 #3022]: #3024
#3028 := [monotonicity #3025]: #3027
#2533 := (iff #1906 #2532)
#2530 := (iff #1905 #2529)
#2527 := (iff #1897 #2524)
#2516 := (+ #1894 #1895)
#2519 := (>= #2516 0::Int)
#2525 := (iff #2519 #2524)
#2526 := [rewrite]: #2525
#2520 := (iff #1897 #2519)
#2517 := (= #1896 #2516)
#2518 := [rewrite]: #2517
#2521 := [monotonicity #2518]: #2520
#2528 := [trans #2521 #2526]: #2527
#2514 := (iff #1904 #2513)
#2511 := (iff #1903 #2510)
#2512 := [rewrite]: #2511
#2515 := [monotonicity #2512]: #2514
#2531 := [monotonicity #2515 #2528]: #2530
#2534 := [monotonicity #2531]: #2533
#3031 := [monotonicity #2534 #3028]: #3030
#3034 := [monotonicity #3031]: #3033
#3037 := [monotonicity #3034]: #3036
#2508 := (iff #1842 #82)
#2509 := [rewrite]: #2508
#3040 := [monotonicity #2509 #3037]: #3039
#3043 := [monotonicity #3040]: #3042
#1818 := (not #1782)
#2503 := (~ #1818 #2502)
#2499 := (not #1779)
#2500 := (~ #2499 #2498)
#2495 := (not #1776)
#2496 := (~ #2495 #2494)
#2491 := (not #1773)
#2492 := (~ #2491 #2490)
#2487 := (not #1770)
#2488 := (~ #2487 #2486)
#2483 := (not #1767)
#2484 := (~ #2483 #2482)
#2479 := (not #1764)
#2480 := (~ #2479 #2478)
#2475 := (not #1761)
#2476 := (~ #2475 #2474)
#2471 := (not #1758)
#2472 := (~ #2471 #2470)
#2467 := (not #1753)
#2468 := (~ #2467 #2466)
#2463 := (not #1724)
#2464 := (~ #2463 #1721)
#2461 := (~ #1721 #1721)
#2459 := (~ #1718 #1718)
#2460 := [refl]: #2459
#2462 := [nnf-pos #2460]: #2461
#2465 := [nnf-neg #2462]: #2464
#2456 := (not #1715)
#2457 := (~ #2456 #1712)
#2454 := (~ #1712 #1712)
#2452 := (~ #1707 #1707)
#2453 := [refl]: #2452
#2455 := [nnf-pos #2453]: #2454
#2458 := [nnf-neg #2455]: #2457
#2449 := (not #1699)
#2450 := (~ #2449 #1696)
#2447 := (~ #1696 #1696)
#2445 := (~ #1693 #1693)
#2446 := [refl]: #2445
#2448 := [nnf-pos #2446]: #2447
#2451 := [nnf-neg #2448]: #2450
#2442 := (not #1676)
#2443 := (~ #2442 #2441)
#2438 := (not #1671)
#2439 := (~ #2438 #2437)
#2435 := (~ #1637 #1637)
#2436 := [refl]: #2435
#2432 := (not #1632)
#2433 := (~ #2432 #1629)
#2430 := (~ #1629 #1629)
#2428 := (~ #1624 #1624)
#2429 := [refl]: #2428
#2431 := [nnf-pos #2429]: #2430
#2434 := [nnf-neg #2431]: #2433
#2425 := (not #1614)
#2426 := (~ #2425 #1611)
#2423 := (~ #1611 #1611)
#2421 := (~ #1608 #1608)
#2422 := [refl]: #2421
#2424 := [nnf-pos #2422]: #2423
#2427 := [nnf-neg #2424]: #2426
#2418 := (not #1597)
#2419 := (~ #2418 #2417)
#2414 := (not #1594)
#2415 := (~ #2414 #2413)
#2410 := (not #1591)
#2411 := (~ #2410 #2409)
#2406 := (not #1588)
#2407 := (~ #2406 #2405)
#2402 := (not #1585)
#2403 := (~ #2402 #2401)
#2398 := (not #1582)
#2399 := (~ #2398 #2397)
#2394 := (not #1579)
#2395 := (~ #2394 #2393)
#2390 := (not #1576)
#2391 := (~ #2390 #2389)
#2386 := (not #1573)
#2387 := (~ #2386 #2385)
#2382 := (not #1570)
#2383 := (~ #2382 #2381)
#2378 := (not #1567)
#2379 := (~ #2378 #2377)
#2374 := (not #1564)
#2375 := (~ #2374 #2373)
#2355 := (not #1561)
#2371 := (~ #2355 #2368)
#2345 := (exists (vars (?v1 S2)) #2344)
#2353 := (or #2352 #2345)
#2354 := (not #2353)
#2369 := (~ #2354 #2368)
#2365 := (not #2345)
#2366 := (~ #2365 #2364)
#2362 := (~ #2361 #2361)
#2363 := [refl]: #2362
#2367 := [nnf-neg #2363]: #2366
#2359 := (~ #2358 #2358)
#2360 := [refl]: #2359
#2370 := [nnf-neg #2360 #2367]: #2369
#2356 := (~ #2355 #2354)
#2357 := [sk]: #2356
#2372 := [trans #2357 #2370]: #2371
#2331 := (not #1524)
#2332 := (~ #2331 #1521)
#2329 := (~ #1521 #1521)
#2327 := (~ #1518 #1518)
#2328 := [refl]: #2327
#2330 := [nnf-pos #2328]: #2329
#2333 := [nnf-neg #2330]: #2332
#2376 := [nnf-neg #2333 #2372]: #2375
#2323 := (~ #1524 #2322)
#2324 := [sk]: #2323
#2380 := [nnf-neg #2324 #2376]: #2379
#2299 := (not #1500)
#2300 := (~ #2299 #1497)
#2297 := (~ #1497 #1497)
#2295 := (~ #1492 #1492)
#2296 := [refl]: #2295
#2298 := [nnf-pos #2296]: #2297
#2301 := [nnf-neg #2298]: #2300
#2384 := [nnf-neg #2301 #2380]: #2383
#2291 := (~ #1500 #2290)
#2292 := [sk]: #2291
#2388 := [nnf-neg #2292 #2384]: #2387
#2272 := (not #1481)
#2273 := (~ #2272 #1478)
#2270 := (~ #1478 #1478)
#2268 := (~ #1475 #1475)
#2269 := [refl]: #2268
#2271 := [nnf-pos #2269]: #2270
#2274 := [nnf-neg #2271]: #2273
#2392 := [nnf-neg #2274 #2388]: #2391
#2264 := (~ #1481 #2263)
#2265 := [sk]: #2264
#2396 := [nnf-neg #2265 #2392]: #2395
#2258 := (~ #2257 #2257)
#2259 := [refl]: #2258
#2400 := [nnf-neg #2259 #2396]: #2399
#2255 := (~ #1472 #1472)
#2256 := [refl]: #2255
#2404 := [nnf-neg #2256 #2400]: #2403
#2252 := (not #935)
#2253 := (~ #2252 #801)
#2250 := (~ #801 #801)
#2248 := (~ #796 #796)
#2249 := [refl]: #2248
#2251 := [nnf-pos #2249]: #2250
#2254 := [nnf-neg #2251]: #2253
#2408 := [nnf-neg #2254 #2404]: #2407
#2244 := (~ #935 #2243)
#2245 := [sk]: #2244
#2412 := [nnf-neg #2245 #2408]: #2411
#2232 := (not #1467)
#2233 := (~ #2232 #1464)
#2230 := (~ #1464 #1464)
#2228 := (~ #1459 #1459)
#2229 := [refl]: #2228
#2231 := [nnf-pos #2229]: #2230
#2234 := [nnf-neg #2231]: #2233
#2416 := [nnf-neg #2234 #2412]: #2415
#2224 := (~ #1467 #2223)
#2225 := [sk]: #2224
#2420 := [nnf-neg #2225 #2416]: #2419
#2214 := (not #1456)
#2215 := (~ #2214 #1453)
#2212 := (~ #1453 #1453)
#2210 := (~ #1448 #1448)
#2211 := [refl]: #2210
#2213 := [nnf-pos #2211]: #2212
#2216 := [nnf-neg #2213]: #2215
#2207 := (not #1647)
#2208 := (~ #2207 #2202)
#2203 := (~ #1406 #2202)
#2204 := [sk]: #2203
#2209 := [nnf-neg #2204]: #2208
#2191 := (~ #747 #747)
#2192 := [refl]: #2191
#2189 := (~ #2188 #2188)
#2190 := [refl]: #2189
#2440 := [nnf-neg #2190 #2192 #2209 #2216 #2420 #2427 #2434 #2436]: #2439
#2185 := (not #1424)
#2186 := (~ #2185 #2184)
#2182 := (~ #1647 #2181)
#2179 := (~ #2178 #2178)
#2180 := [refl]: #2179
#2183 := [nnf-neg #2180]: #2182
#2175 := (not #1395)
#2176 := (~ #2175 #2174)
#2171 := (not #1392)
#2172 := (~ #2171 #2170)
#2167 := (not #1389)
#2168 := (~ #2167 #2166)
#2163 := (not #1384)
#2164 := (~ #2163 #2162)
#2159 := (not #1376)
#2160 := (~ #2159 #1373)
#2157 := (~ #1373 #1373)
#2155 := (~ #1370 #1370)
#2156 := [refl]: #2155
#2158 := [nnf-pos #2156]: #2157
#2161 := [nnf-neg #2158]: #2160
#2153 := (~ #2152 #2152)
#2154 := [refl]: #2153
#2165 := [nnf-neg #2154 #2161]: #2164
#2148 := (~ #1376 #2147)
#2149 := [sk]: #2148
#2169 := [nnf-neg #2149 #2165]: #2168
#2122 := (not #1358)
#2123 := (~ #2122 #2119)
#2120 := (~ #1355 #2119)
#2117 := (~ #1352 #2116)
#2112 := (~ #1349 #2111)
#2113 := [sk]: #2112
#2099 := (~ #1333 #1333)
#2100 := [refl]: #2099
#2118 := [monotonicity #2100 #2113]: #2117
#2121 := [nnf-pos #2118]: #2120
#2124 := [nnf-neg #2121]: #2123
#2173 := [nnf-neg #2124 #2169]: #2172
#2097 := (~ #1358 #2094)
#2072 := (exists (vars (?v1 S2)) #2071)
#2080 := (or #2079 #2072)
#2081 := (not #2080)
#2095 := (~ #2081 #2094)
#2091 := (not #2072)
#2092 := (~ #2091 #2090)
#2088 := (~ #2087 #2087)
#2089 := [refl]: #2088
#2093 := [nnf-neg #2089]: #2092
#2085 := (~ #2084 #2084)
#2086 := [refl]: #2085
#2096 := [nnf-neg #2086 #2093]: #2095
#2082 := (~ #1358 #2081)
#2083 := [sk]: #2082
#2098 := [trans #2083 #2096]: #2097
#2177 := [nnf-neg #2098 #2173]: #2176
#2059 := (~ #2058 #2058)
#2060 := [refl]: #2059
#2056 := (~ #2055 #2055)
#2057 := [refl]: #2056
#2053 := (~ #2052 #2052)
#2054 := [refl]: #2053
#2050 := (~ #2049 #2049)
#2051 := [refl]: #2050
#2187 := [nnf-neg #2051 #2054 #2057 #2060 #2177 #2183]: #2186
#2444 := [nnf-neg #2187 #2440]: #2443
#2046 := (not #1321)
#2047 := (~ #2046 #2043)
#2044 := (~ #1318 #2043)
#2041 := (~ #1315 #2040)
#2036 := (~ #1312 #2035)
#2037 := [sk]: #2036
#2021 := (~ #1288 #1288)
#2022 := [refl]: #2021
#2042 := [monotonicity #2022 #2037]: #2041
#2045 := [nnf-pos #2042]: #2044
#2048 := [nnf-neg #2045]: #2047
#2018 := (not #1732)
#2019 := (~ #2018 #2015)
#2016 := (~ #1276 #2015)
#2013 := (~ #1273 #2012)
#2008 := (~ #1270 #2007)
#2009 := [sk]: #2008
#1992 := (~ #1250 #1250)
#1993 := [refl]: #1992
#2014 := [monotonicity #1993 #2009]: #2013
#2017 := [nnf-pos #2014]: #2016
#2020 := [nnf-neg #2017]: #2019
#1990 := (~ #1989 #1989)
#1991 := [refl]: #1990
#2469 := [nnf-neg #1991 #2020 #2048 #2444 #2451 #2458 #2465]: #2468
#1987 := (~ #1732 #1984)
#1962 := (exists (vars (?v1 S2)) #1961)
#1970 := (or #1969 #1962)
#1971 := (not #1970)
#1985 := (~ #1971 #1984)
#1981 := (not #1962)
#1982 := (~ #1981 #1980)
#1978 := (~ #1977 #1977)
#1979 := [refl]: #1978
#1983 := [nnf-neg #1979]: #1982
#1975 := (~ #1974 #1974)
#1976 := [refl]: #1975
#1986 := [nnf-neg #1976 #1983]: #1985
#1972 := (~ #1732 #1971)
#1973 := [sk]: #1972
#1988 := [trans #1973 #1986]: #1987
#2473 := [nnf-neg #1988 #2469]: #2472
#1947 := (not #1238)
#1948 := (~ #1947 #1235)
#1945 := (~ #1235 #1235)
#1943 := (~ #1232 #1232)
#1944 := [refl]: #1943
#1946 := [nnf-pos #1944]: #1945
#1949 := [nnf-neg #1946]: #1948
#2477 := [nnf-neg #1949 #2473]: #2476
#1939 := (~ #1238 #1938)
#1940 := [sk]: #1939
#2481 := [nnf-neg #1940 #2477]: #2480
#1915 := (not #1207)
#1916 := (~ #1915 #1204)
#1913 := (~ #1204 #1204)
#1911 := (~ #1199 #1199)
#1912 := [refl]: #1911
#1914 := [nnf-pos #1912]: #1913
#1917 := [nnf-neg #1914]: #1916
#2485 := [nnf-neg #1917 #2481]: #2484
#1907 := (~ #1207 #1906)
#1908 := [sk]: #1907
#2489 := [nnf-neg #1908 #2485]: #2488
#1888 := (not #1187)
#1889 := (~ #1888 #1184)
#1886 := (~ #1184 #1184)
#1884 := (~ #1183 #1183)
#1885 := [refl]: #1884
#1887 := [nnf-pos #1885]: #1886
#1890 := [nnf-neg #1887]: #1889
#2493 := [nnf-neg #1890 #2489]: #2492
#1880 := (~ #1187 #1879)
#1881 := [sk]: #1880
#2497 := [nnf-neg #1881 #2493]: #2496
#1843 := (~ #1842 #1842)
#1875 := [refl]: #1843
#2501 := [nnf-neg #1875 #2497]: #2500
#1873 := (~ #1178 #1178)
#1874 := [refl]: #1873
#2504 := [nnf-neg #1874 #2501]: #2503
#1819 := [not-or-elim #1815]: #1818
#2505 := [mp~ #1819 #2504]: #2502
#2506 := [mp #2505 #3043]: #3041
#3685 := [mp #2506 #3684]: #3682
#4590 := [mp #3685 #4589]: #4587
#6963 := [unit-resolution #4590 #3796]: #4584
#3931 := (or #4581 #4575)
#3932 := [def-axiom]: #3931
#6964 := [unit-resolution #3932 #6963]: #4575
#3926 := (or #4578 #1879 #4572)
#3927 := [def-axiom]: #3926
#6965 := [unit-resolution #3927 #6964]: #4575
#6966 := [unit-resolution #6965 #5403]: #4572
#3950 := (or #4569 #4563)
#3951 := [def-axiom]: #3950
#6967 := [unit-resolution #3951 #6966]: #4563
#5911 := [hypothesis]: #1899
#5408 := (or #5792 #2267)
#5409 := [quant-inst #1892]: #5408
#5912 := [unit-resolution #5409 #4219 #5911]: false
#5913 := [lemma #5912]: #2267
#3743 := (or #1941 #1899)
#3830 := [def-axiom]: #3743
#6968 := [unit-resolution #3830 #5913]: #1941
#3944 := (or #4566 #2039 #4560)
#3946 := [def-axiom]: #3944
#6969 := [unit-resolution #3946 #6968 #6967]: #4560
#3971 := (or #4557 #4551)
#3972 := [def-axiom]: #3971
#6970 := [unit-resolution #3972 #6969]: #4551
#3967 := (or #4554 #3086 #4548)
#3968 := [def-axiom]: #3967
#6971 := [unit-resolution #3968 #6970 #6962]: #4548
#3981 := (or #4545 #4539)
#4002 := [def-axiom]: #3981
#6972 := [unit-resolution #4002 #6971]: #4539
#6343 := (= f3 #1953)
#6402 := (not #6343)
#6400 := [hypothesis]: #4258
#4147 := (or #4255 #1965)
#3821 := [def-axiom]: #4147
#6401 := [unit-resolution #3821 #6400]: #1965
#6403 := (or #6402 #1964)
#6404 := [th-lemma arith triangle-eq]: #6403
#6405 := [unit-resolution #6404 #6401]: #6402
#3822 := (or #4255 #2557)
#4154 := [def-axiom]: #3822
#6406 := [unit-resolution #4154 #6400]: #2557
#6350 := (or #3783 #2554 #6343)
#6344 := (or #1966 #6343)
#6351 := (or #3783 #6344)
#6358 := (iff #6351 #6350)
#6347 := (or #2554 #6343)
#6353 := (or #3783 #6347)
#6356 := (iff #6353 #6350)
#6357 := [rewrite]: #6356
#6354 := (iff #6351 #6353)
#6348 := (iff #6344 #6347)
#6349 := [monotonicity #2556]: #6348
#6355 := [monotonicity #6349]: #6354
#6359 := [trans #6355 #6357]: #6358
#6352 := [quant-inst #1950]: #6351
#6360 := [mp #6352 #6359]: #6350
#6407 := [unit-resolution #6360 #4212 #6406 #6405]: false
#6408 := [lemma #6407]: #4255
#3989 := (or #4542 #4258 #4536)
#3990 := [def-axiom]: #3989
#6973 := [unit-resolution #3990 #6408 #6972]: #4536
#5401 := (or #4533 #4524)
#4750 := (f19 f20 ?v0!8)
#4751 := (* -1::Int #4750)
#4752 := (+ f3 #4751)
#4753 := (<= #4752 0::Int)
#5365 := (not #4753)
#5181 := (+ #2062 #4751)
#5209 := (>= #5181 0::Int)
#5180 := (= #2062 #4750)
#5926 := (= #4750 #2062)
#5335 := [hypothesis]: #4521
#5336 := [hypothesis]: #4536
#4011 := (or #4533 #4527)
#3979 := [def-axiom]: #4011
#5337 := [unit-resolution #3979 #5336]: #4527
#4016 := (or #4530 #4370 #4524)
#4017 := [def-axiom]: #4016
#5338 := [unit-resolution #4017 #5337 #5335]: #4370
#4122 := (or #4367 #614)
#4123 := [def-axiom]: #4122
#5339 := [unit-resolution #4123 #5338]: #614
#5340 := [monotonicity #5339]: #5926
#5341 := [symm #5340]: #5180
#5929 := (not #5180)
#5930 := (or #5929 #5209)
#5931 := [th-lemma arith triangle-eq]: #5930
#5342 := [unit-resolution #5931 #5341]: #5209
#4124 := (or #4367 #4361)
#4121 := [def-axiom]: #4124
#5322 := [unit-resolution #4121 #5338]: #4361
#4020 := (or #4533 #112)
#4021 := [def-axiom]: #4020
#5323 := [unit-resolution #4021 #5336]: #112
#5325 := (= #169 #111)
#5324 := [symm #5339]: #150
#5326 := [monotonicity #5324]: #5325
#5321 := [trans #5326 #5323]: #170
#4134 := (or #4343 #2152)
#3797 := [def-axiom]: #4134
#5327 := [unit-resolution #3797 #5321]: #4343
#3838 := (or #4367 #4304)
#4120 := [def-axiom]: #3838
#5328 := [unit-resolution #4120 #5338]: #4304
#4023 := (or #4533 #4270)
#4003 := [def-axiom]: #4023
#5329 := [unit-resolution #4003 #5336]: #4270
#5125 := (or #3349 #4275 #4309 #705)
#4822 := (f19 f20 ?v1!10)
#4684 := (f19 f20 ?v0!11)
#4685 := (* -1::Int #4684)
#4901 := (+ #4685 #4822)
#4902 := (+ #2133 #4901)
#4905 := (>= #4902 0::Int)
#4826 := (f11 f21 ?v1!10)
#4827 := (= f1 #4826)
#4823 := (* -1::Int #4822)
#4824 := (+ f3 #4823)
#4825 := (<= #4824 0::Int)
#5266 := (not #4825)
#5092 := [hypothesis]: #3354
#4137 := (or #3349 #2139)
#4138 := [def-axiom]: #4137
#5093 := [unit-resolution #4138 #5092]: #2139
#5008 := (+ #2129 #4823)
#5010 := (>= #5008 0::Int)
#5007 := (= #2129 #4822)
#5076 := (= #4822 #2129)
#5094 := [hypothesis]: #614
#5077 := [monotonicity #5094]: #5076
#5078 := [symm #5077]: #5007
#5079 := (not #5007)
#5080 := (or #5079 #5010)
#5075 := [th-lemma arith triangle-eq]: #5080
#5081 := [unit-resolution #5075 #5078]: #5010
#5267 := (not #5010)
#5268 := (or #5266 #5267 #2138)
#5262 := [hypothesis]: #2139
#5263 := [hypothesis]: #4825
#5264 := [hypothesis]: #5010
#5265 := [th-lemma arith farkas 1 -1 1 #5264 #5263 #5262]: false
#5269 := [lemma #5265]: #5268
#5082 := [unit-resolution #5269 #5081 #5093]: #5266
#4829 := (or #4825 #4827)
#5083 := [hypothesis]: #4304
#4832 := (or #4309 #4825 #4827)
#4828 := (or #4827 #4825)
#4833 := (or #4309 #4828)
#4840 := (iff #4833 #4832)
#4835 := (or #4309 #4829)
#4838 := (iff #4835 #4832)
#4839 := [rewrite]: #4838
#4836 := (iff #4833 #4835)
#4830 := (iff #4828 #4829)
#4831 := [rewrite]: #4830
#4837 := [monotonicity #4831]: #4836
#4841 := [trans #4837 #4839]: #4840
#4834 := [quant-inst #2125]: #4833
#4842 := [mp #4834 #4841]: #4832
#5084 := [unit-resolution #4842 #5083]: #4829
#5085 := [unit-resolution #5084 #5082]: #4827
#4899 := (not #4827)
#5140 := (or #4899 #4905)
#4139 := (or #3349 #2143)
#4140 := [def-axiom]: #4139
#5138 := [unit-resolution #4140 #5092]: #2143
#5139 := [hypothesis]: #4270
#4916 := (or #4275 #2142 #4899 #4905)
#4894 := (+ #4822 #4685)
#4895 := (+ #2133 #4894)
#4898 := (>= #4895 0::Int)
#4900 := (or #4899 #2142 #4898)
#4917 := (or #4275 #4900)
#4924 := (iff #4917 #4916)
#4911 := (or #2142 #4899 #4905)
#4919 := (or #4275 #4911)
#4922 := (iff #4919 #4916)
#4923 := [rewrite]: #4922
#4920 := (iff #4917 #4919)
#4914 := (iff #4900 #4911)
#4908 := (or #4899 #2142 #4905)
#4912 := (iff #4908 #4911)
#4913 := [rewrite]: #4912
#4909 := (iff #4900 #4908)
#4906 := (iff #4898 #4905)
#4903 := (= #4895 #4902)
#4904 := [rewrite]: #4903
#4907 := [monotonicity #4904]: #4906
#4910 := [monotonicity #4907]: #4909
#4915 := [trans #4910 #4913]: #4914
#4921 := [monotonicity #4915]: #4920
#4925 := [trans #4921 #4923]: #4924
#4918 := [quant-inst #2126 #2125]: #4917
#4926 := [mp #4918 #4925]: #4916
#5141 := [unit-resolution #4926 #5139 #5138]: #5140
#5142 := [unit-resolution #5141 #5085]: #4905
#4135 := (not #2795)
#4141 := (or #3349 #4135)
#3779 := [def-axiom]: #4141
#5143 := [unit-resolution #3779 #5092]: #4135
#4997 := (+ #2127 #4685)
#5005 := (<= #4997 0::Int)
#4996 := (= #2127 #4684)
#5144 := (= #4684 #2127)
#5145 := [monotonicity #5094]: #5144
#5146 := [symm #5145]: #4996
#5126 := (not #4996)
#5127 := (or #5126 #5005)
#5128 := [th-lemma arith triangle-eq]: #5127
#5129 := [unit-resolution #5128 #5146]: #5005
#5130 := [th-lemma arith farkas -1 1 1 1 #5129 #5143 #5081 #5142]: false
#5131 := [lemma #5130]: #5125
#5330 := [unit-resolution #5131 #5329 #5328 #5339]: #3349
#4146 := (or #4352 #4346 #3354)
#4132 := [def-axiom]: #4146
#5331 := [unit-resolution #4132 #5330 #5327]: #4352
#3856 := (or #4355 #4349)
#3857 := [def-axiom]: #3856
#5346 := [unit-resolution #3857 #5331]: #4355
#4126 := (or #4364 #4324 #4358)
#4130 := [def-axiom]: #4126
#5347 := [unit-resolution #4130 #5346 #5322]: #4324
#4158 := (or #4321 #2075)
#4148 := [def-axiom]: #4158
#5364 := [unit-resolution #4148 #5347]: #2075
#5678 := (not #5209)
#5366 := (or #5365 #2074 #5678)
#5367 := [th-lemma arith assign-bounds -1 -1]: #5366
#5368 := [unit-resolution #5367 #5364 #5342]: #5365
#4736 := (?v1!7 ?v0!8)
#4737 := (f19 f20 #4736)
#4881 := (+ #4737 #4751)
#4896 := (>= #4881 0::Int)
#4815 := (f6 f7 #4736)
#4816 := (f5 #4815 ?v0!8)
#4817 := (f4 #4816)
#4887 := (+ #4751 #4817)
#4888 := (+ #4737 #4887)
#4889 := (= #4888 0::Int)
#4873 := (not #4889)
#4804 := (f11 f21 #4736)
#4805 := (= f1 #4804)
#4806 := (not #4805)
#4956 := (or #4806 #4873 #4896)
#4149 := (or #4321 #4313)
#3809 := [def-axiom]: #4149
#5363 := [unit-resolution #3809 #5347]: #4313
#5970 := (or #4956 #4318 #705)
#5211 := (f19 f25 #4736)
#5234 := (* -1::Int #5211)
#5232 := (+ #2062 #5234)
#5235 := (<= #5232 0::Int)
#5935 := (not #5235)
#5470 := (+ #4737 #5234)
#5472 := (>= #5470 0::Int)
#5469 := (= #4737 #5211)
#5919 := (= #5211 #4737)
#5918 := [symm #5094]: #150
#5920 := [monotonicity #5918]: #5919
#5921 := [symm #5920]: #5469
#5922 := (not #5469)
#5923 := (or #5922 #5472)
#5924 := [th-lemma arith triangle-eq]: #5923
#5925 := [unit-resolution #5924 #5921]: #5472
#5927 := [monotonicity #5094]: #5926
#5928 := [symm #5927]: #5180
#5932 := [unit-resolution #5931 #5928]: #5209
#4998 := (not #4896)
#4958 := (not #4956)
#5933 := [hypothesis]: #4958
#5000 := (or #4956 #4998)
#5001 := [def-axiom]: #5000
#5934 := [unit-resolution #5001 #5933]: #4998
#5936 := (not #5472)
#5937 := (or #5935 #5678 #4896 #5936)
#5938 := [th-lemma arith assign-bounds -1 1 -1]: #5937
#5939 := [unit-resolution #5938 #5934 #5932 #5925]: #5935
#4818 := (* -1::Int #4817)
#5137 := (+ #4818 #5234)
#5239 := (+ #2062 #5137)
#5240 := (= #5239 0::Int)
#5281 := (>= #5239 0::Int)
#4981 := (<= #4888 0::Int)
#4990 := (or #4956 #4889)
#4991 := [def-axiom]: #4990
#5940 := [unit-resolution #4991 #5933]: #4889
#5941 := (or #4873 #4981)
#5942 := [th-lemma arith triangle-eq]: #5941
#5943 := [unit-resolution #5942 #5940]: #4981
#5680 := (not #4981)
#5944 := (or #5281 #5680 #5678 #5936)
#5945 := [th-lemma arith assign-bounds 1 -1 -1]: #5944
#5946 := [unit-resolution #5945 #5943 #5932 #5925]: #5281
#5280 := (<= #5239 0::Int)
#5471 := (<= #5470 0::Int)
#5947 := (or #5922 #5471)
#5948 := [th-lemma arith triangle-eq]: #5947
#5949 := [unit-resolution #5948 #5921]: #5471
#5208 := (<= #5181 0::Int)
#5950 := (or #5929 #5208)
#5951 := [th-lemma arith triangle-eq]: #5950
#5952 := [unit-resolution #5951 #5928]: #5208
#4987 := (>= #4888 0::Int)
#5953 := (or #4873 #4987)
#5954 := [th-lemma arith triangle-eq]: #5953
#5955 := [unit-resolution #5954 #5940]: #4987
#5958 := (not #5471)
#5957 := (not #5208)
#5956 := (not #4987)
#5959 := (or #5280 #5956 #5957 #5958)
#5960 := [th-lemma arith assign-bounds 1 -1 -1]: #5959
#5961 := [unit-resolution #5960 #5955 #5952 #5949]: #5280
#5963 := (not #5281)
#5962 := (not #5280)
#5964 := (or #5240 #5962 #5963)
#5965 := [th-lemma arith triangle-eq]: #5964
#5966 := [unit-resolution #5965 #5961 #5946]: #5240
#5252 := (not #5240)
#5256 := (or #5235 #5252)
#5967 := [hypothesis]: #4313
#5261 := (or #4318 #5235 #5252)
#5210 := (+ #2063 #4817)
#5212 := (+ #5211 #5210)
#5207 := (= #5212 0::Int)
#5213 := (not #5207)
#5214 := (+ #5211 #2063)
#5215 := (>= #5214 0::Int)
#5216 := (or #5215 #5213)
#5270 := (or #4318 #5216)
#5277 := (iff #5270 #5261)
#5272 := (or #4318 #5256)
#5275 := (iff #5272 #5261)
#5276 := [rewrite]: #5275
#5273 := (iff #5270 #5272)
#5257 := (iff #5216 #5256)
#5254 := (iff #5213 #5252)
#5249 := (iff #5207 #5240)
#5242 := (+ #4817 #5211)
#5245 := (+ #2063 #5242)
#5086 := (= #5245 0::Int)
#5241 := (iff #5086 #5240)
#5248 := [rewrite]: #5241
#5087 := (iff #5207 #5086)
#5246 := (= #5212 #5245)
#5247 := [rewrite]: #5246
#5136 := [monotonicity #5247]: #5087
#5250 := [trans #5136 #5248]: #5249
#5255 := [monotonicity #5250]: #5254
#5243 := (iff #5215 #5235)
#5217 := (+ #2063 #5211)
#5226 := (>= #5217 0::Int)
#5236 := (iff #5226 #5235)
#5237 := [rewrite]: #5236
#5227 := (iff #5215 #5226)
#5222 := (= #5214 #5217)
#5223 := [rewrite]: #5222
#5233 := [monotonicity #5223]: #5227
#5244 := [trans #5233 #5237]: #5243
#5258 := [monotonicity #5244 #5255]: #5257
#5274 := [monotonicity #5258]: #5273
#5278 := [trans #5274 #5276]: #5277
#5271 := [quant-inst #4736]: #5270
#5279 := [mp #5271 #5278]: #5261
#5968 := [unit-resolution #5279 #5967]: #5256
#5969 := [unit-resolution #5968 #5966 #5939]: false
#5971 := [lemma #5969]: #5970
#5369 := [unit-resolution #5971 #5363 #5339]: #4956
#5372 := (or #4753 #4958)
#3808 := (or #4321 #2695)
#3813 := [def-axiom]: #3808
#5370 := [unit-resolution #3813 #5347]: #2695
#4010 := (or #4533 #4295)
#4005 := [def-axiom]: #4010
#5371 := [unit-resolution #4005 #5336]: #4295
#4968 := (or #4300 #2692 #4753 #4958)
#4743 := (* -1::Int #4737)
#4758 := (+ #4750 #4743)
#4759 := (<= #4758 0::Int)
#4819 := (+ #4743 #4818)
#4820 := (+ #4750 #4819)
#4821 := (= #4820 0::Int)
#4803 := (not #4821)
#4807 := (or #4806 #4803 #4759)
#4802 := (not #4807)
#4808 := (or #2076 #4753 #4802)
#4969 := (or #4300 #4808)
#4984 := (iff #4969 #4968)
#4961 := (or #2692 #4753 #4958)
#4973 := (or #4300 #4961)
#4982 := (iff #4973 #4968)
#4983 := [rewrite]: #4982
#4974 := (iff #4969 #4973)
#4962 := (iff #4808 #4961)
#4959 := (iff #4802 #4958)
#4957 := (iff #4807 #4956)
#4954 := (iff #4759 #4896)
#4876 := (+ #4743 #4750)
#4878 := (<= #4876 0::Int)
#4897 := (iff #4878 #4896)
#4953 := [rewrite]: #4897
#4879 := (iff #4759 #4878)
#4871 := (= #4758 #4876)
#4877 := [rewrite]: #4871
#4880 := [monotonicity #4877]: #4879
#4955 := [trans #4880 #4953]: #4954
#4874 := (iff #4803 #4873)
#4892 := (iff #4821 #4889)
#4809 := (+ #4750 #4818)
#4810 := (+ #4743 #4809)
#4884 := (= #4810 0::Int)
#4890 := (iff #4884 #4889)
#4891 := [rewrite]: #4890
#4885 := (iff #4821 #4884)
#4811 := (= #4820 #4810)
#4812 := [rewrite]: #4811
#4886 := [monotonicity #4812]: #4885
#4872 := [trans #4886 #4891]: #4892
#4875 := [monotonicity #4872]: #4874
#4952 := [monotonicity #4875 #4955]: #4957
#4960 := [monotonicity #4952]: #4959
#4967 := [monotonicity #2694 #4960]: #4962
#4980 := [monotonicity #4967]: #4974
#4985 := [trans #4980 #4983]: #4984
#4972 := [quant-inst #2061]: #4969
#4986 := [mp #4972 #4985]: #4968
#5373 := [unit-resolution #4986 #5371 #5370]: #5372
#5400 := [unit-resolution #5373 #5369 #5368]: false
#5402 := [lemma #5400]: #5401
#6974 := [unit-resolution #5402 #6973]: #4524
#4039 := (or #4521 #195)
#4040 := [def-axiom]: #4039
#9702 := [unit-resolution #4040 #6974]: #195
#21377 := [trans #9702 #21376]: #21352
#24141 := [monotonicity #21377 #27911]: #24148
#24150 := [symm #24141]: #24145
#27861 := (= f1 #27860)
#22707 := (f11 f21 #21962)
#22708 := (= f1 #22707)
#27863 := (= #7092 #21962)
#27866 := (ite #27863 #6251 #22708)
#27869 := (iff #27861 #27866)
#55 := (:var 1 S1)
#53 := (:var 2 S2)
#51 := (:var 3 S7)
#52 := (f14 f15 #51)
#54 := (f13 #52 #53)
#56 := (f12 #54 #55)
#57 := (f11 #56 #12)
#4199 := (pattern #57)
#61 := (f11 #51 #12)
#402 := (= f1 #61)
#399 := (= f1 #55)
#59 := (= #12 #53)
#405 := (ite #59 #399 #402)
#395 := (= f1 #57)
#408 := (iff #395 #405)
#4200 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #4199) #408)
#411 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) #408)
#4203 := (iff #411 #4200)
#4201 := (iff #408 #408)
#4202 := [refl]: #4201
#4204 := [quant-intro #4202]: #4203
#1836 := (~ #411 #411)
#1864 := (~ #408 #408)
#1865 := [refl]: #1864
#1837 := [nnf-pos #1865]: #1836
#62 := (= #61 f1)
#60 := (= #55 f1)
#63 := (ite #59 #60 #62)
#58 := (= #57 f1)
#64 := (iff #58 #63)
#65 := (forall (vars (?v0 S7) (?v1 S2) (?v2 S1) (?v3 S2)) #64)
#412 := (iff #65 #411)
#409 := (iff #64 #408)
#406 := (iff #63 #405)
#403 := (iff #62 #402)
#404 := [rewrite]: #403
#400 := (iff #60 #399)
#401 := [rewrite]: #400
#407 := [monotonicity #401 #404]: #406
#397 := (iff #58 #395)
#398 := [rewrite]: #397
#410 := [monotonicity #398 #407]: #409
#413 := [quant-intro #410]: #412
#394 := [asserted]: #65
#416 := [mp #394 #413]: #411
#1866 := [mp~ #416 #1837]: #411
#4205 := [mp #1866 #4204]: #4200
#6756 := (not #4200)
#23189 := (or #6756 #27869)
#27856 := (= #21962 #7092)
#27857 := (ite #27856 #6251 #22708)
#27862 := (iff #27861 #27857)
#26170 := (or #6756 #27862)
#23236 := (iff #26170 #23189)
#27901 := (iff #23189 #23189)
#23219 := [rewrite]: #27901
#27870 := (iff #27862 #27869)
#27867 := (iff #27857 #27866)
#27864 := (iff #27856 #27863)
#27865 := [rewrite]: #27864
#27868 := [monotonicity #27865]: #27867
#27871 := [monotonicity #27868]: #27870
#23238 := [monotonicity #27871]: #23236
#23223 := [trans #23238 #23219]: #23236
#23190 := [quant-inst #116 #7092 #6256 #21962]: #26170
#23228 := [mp #23190 #23223]: #23189
#24138 := [unit-resolution #23228 #4205]: #27869
#23191 := (not #27869)
#24142 := (or #23191 #27861)
#27881 := (not #27866)
#27902 := [hypothesis]: #27881
#27882 := (not #27863)
#27903 := (or #27866 #27882)
#6770 := (not #6251)
#27887 := (or #27866 #27882 #6770)
#27888 := [def-axiom]: #27887
#27904 := [unit-resolution #27888 #9703]: #27903
#27905 := [unit-resolution #27904 #27902]: #27882
#27921 := (or #27866 #27863)
#14588 := (f11 f21 #14575)
#27918 := (= #14588 #22707)
#27914 := (= #22707 #14588)
#27912 := (= #21962 #14575)
#27913 := [symm #27911]: #27912
#27915 := [monotonicity #27913]: #27914
#27919 := [symm #27915]: #27918
#14589 := (= f1 #14588)
#14590 := (not #14589)
#14582 := (f4 #14581)
#14583 := (* -1::Int #14582)
#14576 := (f19 f20 #14575)
#14577 := (* -1::Int #14576)
#14584 := (+ #14577 #14583)
#14434 := (f19 f20 ?v0!20)
#14585 := (+ #14434 #14584)
#14586 := (= #14585 0::Int)
#14587 := (not #14586)
#14578 := (+ #14434 #14577)
#14579 := (<= #14578 0::Int)
#14596 := (or #14579 #14587 #14590)
#14599 := (not #14596)
#14445 := (* -1::Int #14434)
#14593 := (+ f3 #14445)
#14594 := (<= #14593 0::Int)
#23218 := (not #14594)
#8533 := (f19 f20 ?v0!15)
#8748 := (* -1::Int #8533)
#8749 := (+ #2261 #8748)
#9849 := (>= #8749 0::Int)
#8543 := (= #2261 #8533)
#10935 := [hypothesis]: #2263
#12213 := (or #8543 #2262)
#8928 := (f5 #196 ?v0!15)
#8930 := (f4 #8928)
#8733 := (* -1::Int #2261)
#8932 := (+ #8733 #8930)
#8933 := (+ #186 #8932)
#9973 := (<= #8933 0::Int)
#9115 := (= #8933 0::Int)
#8694 := (+ #8748 #8930)
#8695 := (+ #186 #8694)
#8696 := (>= #8695 0::Int)
#9764 := (not #8696)
#8497 := (* -1::Int #8930)
#8914 := (+ f3 #8497)
#8917 := (<= #8914 0::Int)
#9189 := (or #8696 #8917)
#9294 := (not #9189)
#10923 := (not #8543)
#10924 := [hypothesis]: #10923
#9293 := (or #8543 #9294)
#4032 := (or #4521 #4383)
#4027 := [def-axiom]: #4032
#6975 := [unit-resolution #4027 #6974]: #4383
#10206 := (or #4388 #8543 #9294)
#8498 := (+ #1435 #8497)
#8915 := (+ #8533 #8498)
#8916 := (<= #8915 0::Int)
#9205 := (or #8917 #8916)
#9206 := (not #9205)
#8538 := (= #8533 #2261)
#9201 := (or #8538 #9206)
#8256 := (or #4388 #9201)
#9985 := (iff #8256 #10206)
#9693 := (or #4388 #9293)
#9691 := (iff #9693 #10206)
#9980 := [rewrite]: #9691
#9694 := (iff #8256 #9693)
#9296 := (iff #9201 #9293)
#9295 := (iff #9206 #9294)
#9287 := (iff #9205 #9189)
#9207 := (or #8917 #8696)
#9190 := (iff #9207 #9189)
#9284 := [rewrite]: #9190
#9187 := (iff #9205 #9207)
#8698 := (iff #8916 #8696)
#8908 := (+ #8533 #8497)
#8919 := (+ #1435 #8908)
#8923 := (<= #8919 0::Int)
#8697 := (iff #8923 #8696)
#8692 := [rewrite]: #8697
#8926 := (iff #8916 #8923)
#8924 := (= #8915 #8919)
#8925 := [rewrite]: #8924
#8693 := [monotonicity #8925]: #8926
#8929 := [trans #8693 #8692]: #8698
#9188 := [monotonicity #8929]: #9187
#9288 := [trans #9188 #9284]: #9287
#9283 := [monotonicity #9288]: #9295
#8532 := (iff #8538 #8543)
#8544 := [rewrite]: #8532
#9297 := [monotonicity #8544 #9283]: #9296
#9695 := [monotonicity #9297]: #9694
#9977 := [trans #9695 #9980]: #9985
#8362 := [quant-inst #2260]: #8256
#9983 := [mp #8362 #9977]: #10206
#10925 := [unit-resolution #9983 #6975]: #9293
#10926 := [unit-resolution #10925 #10924]: #9294
#9765 := (or #9189 #9764)
#10317 := [def-axiom]: #9765
#10927 := [unit-resolution #10317 #10926]: #9764
#9315 := (not #8917)
#10228 := (or #9189 #9315)
#9873 := [def-axiom]: #10228
#10928 := [unit-resolution #9873 #10926]: #9315
#9103 := (or #8696 #8917 #9115)
#4033 := (or #4521 #4391)
#4006 := [def-axiom]: #4033
#6979 := [unit-resolution #4006 #6974]: #4391
#9853 := (or #4396 #8696 #8917 #9115)
#8931 := (+ #8930 #8733)
#8484 := (+ #186 #8931)
#8485 := (= #8484 0::Int)
#8918 := (or #8917 #8916 #8485)
#9902 := (or #4396 #8918)
#9890 := (iff #9902 #9853)
#9586 := (or #4396 #9103)
#9668 := (iff #9586 #9853)
#9669 := [rewrite]: #9668
#9589 := (iff #9902 #9586)
#9056 := (iff #8918 #9103)
#9118 := (or #8917 #8696 #9115)
#9104 := (iff #9118 #9103)
#9055 := [rewrite]: #9104
#9119 := (iff #8918 #9118)
#9116 := (iff #8485 #9115)
#8934 := (= #8484 #8933)
#9114 := [rewrite]: #8934
#9117 := [monotonicity #9114]: #9116
#9102 := [monotonicity #8929 #9117]: #9119
#9051 := [trans #9102 #9055]: #9056
#9637 := [monotonicity #9051]: #9589
#9670 := [trans #9637 #9669]: #9890
#9921 := [quant-inst #2260]: #9902
#9664 := [mp #9921 #9670]: #9853
#10929 := [unit-resolution #9664 #6979]: #9103
#10930 := [unit-resolution #10929 #10928 #10927]: #9115
#10931 := (not #9115)
#10932 := (or #10931 #9973)
#10933 := [th-lemma arith triangle-eq]: #10932
#10934 := [unit-resolution #10933 #10930]: #9973
#6326 := (+ #111 #1435)
#10868 := (<= #6326 0::Int)
#8354 := (= #111 #186)
#12134 := (= #186 #111)
#6551 := (= f28 f16)
#6553 := (= f16 f28)
#6533 := (?v1!7 f28)
#6546 := (f11 f21 #6533)
#6547 := (= f1 #6546)
#6548 := (not #6547)
#6538 := (f6 f7 #6533)
#6539 := (f5 #6538 f28)
#6540 := (f4 #6539)
#6541 := (* -1::Int #6540)
#6534 := (f19 f20 #6533)
#6535 := (* -1::Int #6534)
#6542 := (+ #6535 #6541)
#6543 := (+ #186 #6542)
#6544 := (= #6543 0::Int)
#6545 := (not #6544)
#6536 := (+ #186 #6535)
#6537 := (<= #6536 0::Int)
#6556 := (or #6537 #6545 #6548)
#9745 := (or #2262 #6537)
#9841 := (>= #8533 0::Int)
#4022 := (or #4533 #4262)
#4018 := [def-axiom]: #4022
#7483 := [unit-resolution #4018 #6973]: #4262
#9916 := (or #4267 #9841)
#9895 := [quant-inst #2260]: #9916
#9883 := [unit-resolution #9895 #7483]: #9841
#6583 := (not #6537)
#10359 := [hypothesis]: #6583
#10959 := (or #8543 #2262 #6537)
#7535 := (f6 f7 #7092)
#10859 := (f5 #7535 ?v0!15)
#10867 := (f4 #10859)
#10909 := (* -1::Int #10867)
#10910 := (+ #8930 #10909)
#10912 := (>= #10910 0::Int)
#10908 := (= #8930 #10867)
#10915 := (= #10867 #8930)
#10913 := (= #10859 #8928)
#8147 := (= #7535 #196)
#8148 := [monotonicity #8146]: #8147
#10914 := [monotonicity #8148]: #10913
#10916 := [monotonicity #10914]: #10915
#10917 := [symm #10916]: #10908
#10918 := (not #10908)
#10919 := (or #10918 #10912)
#10920 := [th-lemma arith triangle-eq]: #10919
#10921 := [unit-resolution #10920 #10917]: #10912
#9105 := (>= #6534 0::Int)
#8377 := (or #4267 #9105)
#8383 := [quant-inst #6533]: #8377
#10922 := [unit-resolution #8383 #7483]: #9105
#10891 := (<= #10867 0::Int)
#10892 := (not #10891)
#10494 := (= ?v0!15 #7092)
#10839 := (not #10494)
#8266 := (f11 f21 ?v0!15)
#8358 := (= f1 #8266)
#10495 := (ite #10494 #6251 #8358)
#10838 := (not #10495)
#10809 := (f11 #7452 ?v0!15)
#10810 := (= f1 #10809)
#10812 := (iff #10495 #10810)
#10815 := (or #6756 #10812)
#10811 := (iff #10810 #10495)
#10816 := (or #6756 #10811)
#10818 := (iff #10816 #10815)
#10820 := (iff #10815 #10815)
#10835 := [rewrite]: #10820
#10813 := (iff #10811 #10812)
#10814 := [rewrite]: #10813
#10819 := [monotonicity #10814]: #10818
#10836 := [trans #10819 #10835]: #10818
#10817 := [quant-inst #116 #7092 #6256 #2260]: #10816
#10837 := [mp #10817 #10836]: #10815
#10936 := [unit-resolution #10837 #4205]: #10812
#10850 := (not #10810)
#8536 := (f11 f29 ?v0!15)
#8534 := (= f1 #8536)
#8537 := (not #8534)
#10949 := (iff #8537 #10850)
#10947 := (iff #8534 #10810)
#10945 := (iff #10810 #8534)
#10943 := (= #10809 #8536)
#9642 := (= #7452 f29)
#9661 := (= #194 f29)
#9641 := [symm #9702]: #9661
#9632 := [trans #9640 #9641]: #9642
#10944 := [monotonicity #9632]: #10943
#10946 := [monotonicity #10944]: #10945
#10948 := [symm #10946]: #10947
#10950 := [monotonicity #10948]: #10949
#8592 := (or #8537 #8543)
#9054 := (= #186 #2240)
#9880 := (= #2240 #186)
#7163 := (= ?v0!14 f28)
#7394 := (= ?v0!14 #7092)
#6992 := (f11 f21 ?v0!14)
#6993 := (= f1 #6992)
#7395 := (ite #7394 #6251 #6993)
#7459 := (f11 #7452 ?v0!14)
#7460 := (= f1 #7459)
#7462 := (iff #7395 #7460)
#10283 := (or #6756 #7462)
#7461 := (iff #7460 #7395)
#10260 := (or #6756 #7461)
#10263 := (iff #10260 #10283)
#10183 := (iff #10283 #10283)
#8172 := [rewrite]: #10183
#7463 := (iff #7461 #7462)
#7464 := [rewrite]: #7463
#10172 := [monotonicity #7464]: #10263
#8264 := [trans #10172 #8172]: #10263
#10261 := [quant-inst #116 #7092 #6256 #2235]: #10260
#8796 := [mp #10261 #8264]: #10283
#8272 := [unit-resolution #8796 #4205]: #7462
#8804 := (= #2236 #7459)
#8394 := (= #7459 #2236)
#9834 := [monotonicity #9632]: #8394
#8927 := [symm #9834]: #8804
#7945 := [hypothesis]: #2857
#4115 := (or #2852 #2237)
#4116 := [def-axiom]: #4115
#8392 := [unit-resolution #4116 #7945]: #2237
#9884 := [trans #8392 #8927]: #7460
#10319 := (not #7460)
#10324 := (not #7462)
#9827 := (or #10324 #7395 #10319)
#9839 := [def-axiom]: #9827
#10076 := [unit-resolution #9839 #9884 #8272]: #7395
#10323 := (not #6993)
#7536 := (f5 #7535 ?v0!14)
decl f10 :: S6
#29 := f10
#7583 := (f8 f10 #7536)
#10662 := (f11 f21 #7583)
#10663 := (= f1 #10662)
#10687 := (not #10663)
#9829 := (iff #10687 #10323)
#9659 := (iff #10663 #6993)
#9986 := (= #10662 #6992)
#10754 := (= #7583 ?v0!14)
#7584 := (= ?v0!14 #7583)
#30 := (f8 f10 #16)
#365 := (= #12 #30)
#4178 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4159) #365)
#369 := (forall (vars (?v0 S2) (?v1 S2)) #365)
#4181 := (iff #369 #4178)
#4179 := (iff #365 #365)
#4180 := [refl]: #4179
#4182 := [quant-intro #4180]: #4181
#1830 := (~ #369 #369)
#1855 := (~ #365 #365)
#1856 := [refl]: #1855
#1831 := [nnf-pos #1856]: #1830
#31 := (= #30 #12)
#32 := (forall (vars (?v0 S2) (?v1 S2)) #31)
#370 := (iff #32 #369)
#367 := (iff #31 #365)
#368 := [rewrite]: #367
#371 := [quant-intro #368]: #370
#364 := [asserted]: #32
#374 := [mp #364 #371]: #369
#1857 := [mp~ #374 #1831]: #369
#4183 := [mp #1857 #4182]: #4178
#5414 := (not #4178)
#7973 := (or #5414 #7584)
#10253 := [quant-inst #7092 #2235]: #7973
#10753 := [unit-resolution #10253 #4183]: #7584
#10782 := [symm #10753]: #10754
#10038 := [monotonicity #10782]: #9986
#9660 := [monotonicity #10038]: #9659
#9830 := [monotonicity #9660]: #9829
#7021 := (f5 #196 ?v0!14)
#7022 := (f4 #7021)
#6953 := (* -1::Int #2240)
#7039 := (+ #6953 #7022)
#7040 := (+ #186 #7039)
#7041 := (>= #7040 0::Int)
#10214 := (not #7041)
#7023 := (* -1::Int #7022)
#7027 := (+ f3 #7023)
#7028 := (<= #7027 0::Int)
#7046 := (or #7028 #7041)
#7049 := (not #7046)
#4111 := (not #2846)
#4112 := (or #2852 #4111)
#4117 := [def-axiom]: #4112
#8271 := [unit-resolution #4117 #7945]: #4111
#9899 := (or #4388 #2846 #7049)
#7024 := (+ #1435 #7023)
#7025 := (+ #2240 #7024)
#7026 := (<= #7025 0::Int)
#7029 := (or #7028 #7026)
#7030 := (not #7029)
#7031 := (or #2241 #7030)
#10178 := (or #4388 #7031)
#10209 := (iff #10178 #9899)
#7052 := (or #2846 #7049)
#10179 := (or #4388 #7052)
#10208 := (iff #10179 #9899)
#10119 := [rewrite]: #10208
#10207 := (iff #10178 #10179)
#7053 := (iff #7031 #7052)
#7050 := (iff #7030 #7049)
#7047 := (iff #7029 #7046)
#7044 := (iff #7026 #7041)
#7032 := (+ #2240 #7023)
#7033 := (+ #1435 #7032)
#7036 := (<= #7033 0::Int)
#7042 := (iff #7036 #7041)
#7043 := [rewrite]: #7042
#7037 := (iff #7026 #7036)
#7034 := (= #7025 #7033)
#7035 := [rewrite]: #7034
#7038 := [monotonicity #7035]: #7037
#7045 := [trans #7038 #7043]: #7044
#7048 := [monotonicity #7045]: #7047
#7051 := [monotonicity #7048]: #7050
#7054 := [monotonicity #2848 #7051]: #7053
#10120 := [monotonicity #7054]: #10207
#10210 := [trans #10120 #10119]: #10209
#10221 := [quant-inst #2235]: #10178
#10220 := [mp #10221 #10210]: #9899
#9861 := [unit-resolution #10220 #6975 #8271]: #7049
#10212 := (or #7046 #10214)
#10225 := [def-axiom]: #10212
#9988 := [unit-resolution #10225 #9861]: #10214
#10073 := (or #10687 #7041)
#10655 := (f19 f20 #7583)
#10656 := (* -1::Int #10655)
#7748 := (f19 f20 #7092)
#10660 := (+ #7748 #10656)
#10661 := (>= #10660 0::Int)
#10744 := [hypothesis]: #10663
#10750 := (or #10661 #10687)
#7631 := (f11 f21 #7092)
#7632 := (= f1 #7631)
#9432 := (not #7632)
#9433 := (iff #747 #9432)
#9430 := (iff #744 #7632)
#9428 := (iff #7632 #744)
#9426 := (= #7631 #183)
#9427 := [monotonicity #8146]: #9426
#9429 := [monotonicity #9427]: #9428
#9431 := [symm #9429]: #9430
#9434 := [monotonicity #9431]: #9433
#4041 := (or #4521 #747)
#4036 := [def-axiom]: #4041
#9399 := [unit-resolution #4036 #6974]: #747
#9435 := [mp #9399 #9434]: #9432
#3949 := (or #4533 #4279)
#4004 := [def-axiom]: #3949
#9436 := [unit-resolution #4004 #6973]: #4279
#10686 := (or #4284 #7632 #10661 #10687)
#10688 := (or #7632 #10687 #10661)
#10692 := (or #4284 #10688)
#10705 := (iff #10692 #10686)
#10689 := (or #7632 #10661 #10687)
#10694 := (or #4284 #10689)
#10703 := (iff #10694 #10686)
#10704 := [rewrite]: #10703
#10695 := (iff #10692 #10694)
#10690 := (iff #10688 #10689)
#10691 := [rewrite]: #10690
#10696 := [monotonicity #10691]: #10695
#10706 := [trans #10696 #10704]: #10705
#10693 := [quant-inst #7583 #7092]: #10692
#10707 := [mp #10693 #10706]: #10686
#10751 := [unit-resolution #10707 #9436 #9435]: #10750
#10752 := [unit-resolution #10751 #10744]: #10661
#7683 := (f5 #7535 #7583)
#7684 := (f4 #7683)
#7685 := (* -1::Int #7684)
#9108 := (+ #7022 #7685)
#8524 := (>= #9108 0::Int)
#9107 := (= #7022 #7684)
#10785 := (= #7684 #7022)
#10783 := (= #7683 #7021)
#10784 := [monotonicity #8148 #10782]: #10783
#10786 := [monotonicity #10784]: #10785
#10781 := [symm #10786]: #9107
#10787 := (not #9107)
#10788 := (or #10787 #8524)
#10789 := [th-lemma arith triangle-eq]: #10788
#10790 := [unit-resolution #10789 #10781]: #8524
#10333 := (>= #7684 0::Int)
#7537 := (f4 #7536)
#7538 := (* -1::Int #7537)
#9591 := (+ #7022 #7538)
#9735 := (>= #9591 0::Int)
#10186 := (= #7022 #7537)
#10800 := (= #7537 #7022)
#10791 := (= #7536 #7021)
#10799 := [monotonicity #8148]: #10791
#10801 := [monotonicity #10799]: #10800
#10802 := [symm #10801]: #10186
#10803 := (not #10186)
#10798 := (or #10803 #9735)
#10804 := [th-lemma arith triangle-eq]: #10798
#10805 := [unit-resolution #10804 #10802]: #9735
#10346 := (>= #7537 0::Int)
#7590 := (= #7537 0::Int)
#10823 := (not #7590)
#10821 := (not #10346)
#10822 := [hypothesis]: #10821
#10824 := (or #10823 #10346)
#10825 := [th-lemma arith triangle-eq]: #10824
#10826 := [unit-resolution #10825 #10822]: #10823
#7613 := (<= #7537 0::Int)
#10827 := (or #10346 #7613)
#10828 := [th-lemma arith farkas 1 1]: #10827
#10829 := [unit-resolution #10828 #10822]: #7613
#7615 := (not #7613)
#7617 := (or #7394 #7615)
#17 := (f4 #16)
#344 := (<= #17 0::Int)
#345 := (not #344)
#13 := (= #11 #12)
#348 := (or #13 #345)
#4166 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4159) #348)
#351 := (forall (vars (?v0 S2) (?v1 S2)) #348)
#4169 := (iff #351 #4166)
#4167 := (iff #348 #348)
#4168 := [refl]: #4167
#4170 := [quant-intro #4168]: #4169
#1826 := (~ #351 #351)
#1825 := (~ #348 #348)
#1822 := [refl]: #1825
#1827 := [nnf-pos #1822]: #1826
#22 := (< 0::Int #17)
#21 := (not #13)
#23 := (implies #21 #22)
#24 := (forall (vars (?v0 S2) (?v1 S2)) #23)
#354 := (iff #24 #351)
#338 := (or #13 #22)
#341 := (forall (vars (?v0 S2) (?v1 S2)) #338)
#352 := (iff #341 #351)
#349 := (iff #338 #348)
#346 := (iff #22 #345)
#347 := [rewrite]: #346
#350 := [monotonicity #347]: #349
#353 := [quant-intro #350]: #352
#342 := (iff #24 #341)
#339 := (iff #23 #338)
#340 := [rewrite]: #339
#343 := [quant-intro #340]: #342
#355 := [trans #343 #353]: #354
#337 := [asserted]: #24
#356 := [mp #337 #355]: #351
#1823 := [mp~ #356 #1827]: #351
#4171 := [mp #1823 #4170]: #4166
#7270 := (not #4166)
#10329 := (or #7270 #7394 #7615)
#7589 := (= #7092 ?v0!14)
#7616 := (or #7589 #7615)
#10342 := (or #7270 #7616)
#10321 := (iff #10342 #10329)
#10330 := (or #7270 #7617)
#9204 := (iff #10330 #10329)
#9755 := [rewrite]: #9204
#10331 := (iff #10342 #10330)
#7618 := (iff #7616 #7617)
#7595 := (iff #7589 #7394)
#7596 := [rewrite]: #7595
#7619 := [monotonicity #7596]: #7618
#10328 := [monotonicity #7619]: #10331
#10322 := [trans #10328 #9755]: #10321
#10344 := [quant-inst #7092 #2235]: #10342
#10336 := [mp #10344 #10322]: #10329
#10830 := [unit-resolution #10336 #4171]: #7617
#10831 := [unit-resolution #10830 #10829]: #7394
#7514 := (not #7394)
#7599 := (or #7514 #7590)
#18 := (= #17 0::Int)
#328 := (or #21 #18)
#4160 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4159) #328)
#331 := (forall (vars (?v0 S2) (?v1 S2)) #328)
#4163 := (iff #331 #4160)
#4161 := (iff #328 #328)
#4162 := [refl]: #4161
#4164 := [quant-intro #4162]: #4163
#1850 := (~ #331 #331)
#1848 := (~ #328 #328)
#1849 := [refl]: #1848
#1851 := [nnf-pos #1849]: #1850
#19 := (implies #13 #18)
#20 := (forall (vars (?v0 S2) (?v1 S2)) #19)
#334 := (iff #20 #331)
#307 := (= 0::Int #17)
#318 := (or #21 #307)
#323 := (forall (vars (?v0 S2) (?v1 S2)) #318)
#332 := (iff #323 #331)
#329 := (iff #318 #328)
#326 := (iff #307 #18)
#327 := [rewrite]: #326
#330 := [monotonicity #327]: #329
#333 := [quant-intro #330]: #332
#324 := (iff #20 #323)
#321 := (iff #19 #318)
#315 := (implies #13 #307)
#319 := (iff #315 #318)
#320 := [rewrite]: #319
#316 := (iff #19 #315)
#313 := (iff #18 #307)
#314 := [rewrite]: #313
#317 := [monotonicity #314]: #316
#322 := [trans #317 #320]: #321
#325 := [quant-intro #322]: #324
#335 := [trans #325 #333]: #334
#306 := [asserted]: #20
#336 := [mp #306 #335]: #331
#1824 := [mp~ #336 #1851]: #331
#4165 := [mp #1824 #4164]: #4160
#7259 := (not #4160)
#10247 := (or #7259 #7514 #7590)
#7593 := (not #7589)
#7594 := (or #7593 #7590)
#10259 := (or #7259 #7594)
#10338 := (iff #10259 #10247)
#10187 := (or #7259 #7599)
#10189 := (iff #10187 #10247)
#10337 := [rewrite]: #10189
#10332 := (iff #10259 #10187)
#7600 := (iff #7594 #7599)
#7597 := (iff #7593 #7514)
#7598 := [monotonicity #7596]: #7597
#7601 := [monotonicity #7598]: #7600
#10188 := [monotonicity #7601]: #10332
#10345 := [trans #10188 #10337]: #10338
#10184 := [quant-inst #7092 #2235]: #10259
#10262 := [mp #10184 #10345]: #10247
#10832 := [unit-resolution #10262 #4165]: #7599
#10833 := [unit-resolution #10832 #10831 #10826]: false
#10834 := [lemma #10833]: #10346
#9202 := (<= #9108 0::Int)
#10806 := (or #10787 #9202)
#10807 := [th-lemma arith triangle-eq]: #10806
#10808 := [unit-resolution #10807 #10781]: #9202
#8262 := (not #9735)
#8168 := (not #9202)
#8348 := (or #10333 #8168 #10821 #8262)
#8510 := [th-lemma arith assign-bounds 1 -1 -1]: #8348
#9067 := [unit-resolution #8510 #10808 #10834 #10805]: #10333
#9862 := [hypothesis]: #10214
#10711 := (+ #2240 #10656)
#10748 := (<= #10711 0::Int)
#10710 := (= #2240 #10655)
#9863 := (= #10655 #2240)
#9885 := [monotonicity #10782]: #9863
#9881 := [symm #9885]: #10710
#9872 := (not #10710)
#9888 := (or #9872 #10748)
#9896 := [th-lemma arith triangle-eq]: #9888
#10039 := [unit-resolution #9896 #9881]: #10748
#7758 := (* -1::Int #7748)
#8560 := (+ #186 #7758)
#8562 := (>= #8560 0::Int)
#8559 := (= #186 #7748)
#9410 := (= #7748 #186)
#9411 := [monotonicity #8146]: #9410
#9412 := [symm #9411]: #8559
#9413 := (not #8559)
#9414 := (or #9413 #8562)
#9415 := [th-lemma arith triangle-eq]: #9414
#9416 := [unit-resolution #9415 #9412]: #8562
#9968 := [th-lemma arith farkas 1 1 1 1 1 1 #9416 #10039 #9862 #9067 #10790 #10752]: false
#10074 := [lemma #9968]: #10073
#10032 := [unit-resolution #10074 #9988]: #10687
#9819 := [mp #10032 #9830]: #10323
#8797 := (not #7395)
#8263 := (or #8797 #7394 #6993)
#9322 := [def-axiom]: #8263
#9847 := [unit-resolution #9322 #9819 #10076]: #7394
#9868 := [trans #9847 #8146]: #7163
#9987 := [monotonicity #9868]: #9880
#9833 := [symm #9987]: #9054
#9984 := (= #2239 #186)
#6471 := (f30 f28)
#9061 := (= #6471 #186)
#6472 := (= #186 #6471)
#6459 := (f5 #196 f28)
#6460 := (f4 #6459)
#6479 := (>= #6460 0::Int)
#6463 := (* -1::Int #6460)
#6467 := (+ f3 #6463)
#6468 := (<= #6467 0::Int)
#6484 := (or #6468 #6479)
#8075 := (f5 #7535 #7092)
#8076 := (f4 #8075)
#8077 := (* -1::Int #8076)
#8141 := (+ #6460 #8077)
#8143 := (>= #8141 0::Int)
#8140 := (= #6460 #8076)
#8151 := (= #6459 #8075)
#8149 := (= #8075 #6459)
#8150 := [monotonicity #8148 #8146]: #8149
#8152 := [symm #8150]: #8151
#8153 := [monotonicity #8152]: #8140
#8154 := (not #8140)
#8155 := (or #8154 #8143)
#8156 := [th-lemma arith triangle-eq]: #8155
#8157 := [unit-resolution #8156 #8153]: #8143
#8086 := (>= #8076 0::Int)
#8114 := (= #8076 0::Int)
#8130 := (or #7259 #8114)
#7633 := (= #7092 #7092)
#8115 := (not #7633)
#8118 := (or #8115 #8114)
#8131 := (or #7259 #8118)
#8133 := (iff #8131 #8130)
#8135 := (iff #8130 #8130)
#8136 := [rewrite]: #8135
#8128 := (iff #8118 #8114)
#8123 := (or false #8114)
#8126 := (iff #8123 #8114)
#8127 := [rewrite]: #8126
#8124 := (iff #8118 #8123)
#8121 := (iff #8115 false)
#8119 := (iff #8115 #3894)
#7638 := (iff #7633 true)
#7639 := [rewrite]: #7638
#8120 := [monotonicity #7639]: #8119
#8122 := [trans #8120 #3865]: #8121
#8125 := [monotonicity #8122]: #8124
#8129 := [trans #8125 #8127]: #8128
#8134 := [monotonicity #8129]: #8133
#8137 := [trans #8134 #8136]: #8133
#8132 := [quant-inst #7092 #7092]: #8131
#8138 := [mp #8132 #8137]: #8130
#8158 := [unit-resolution #8138 #4165]: #8114
#8159 := (not #8114)
#8160 := (or #8159 #8086)
#8161 := [th-lemma arith triangle-eq]: #8160
#8162 := [unit-resolution #8161 #8158]: #8086
#6507 := (not #6479)
#8163 := [hypothesis]: #6507
#8164 := [th-lemma arith farkas -1 1 1 #8163 #8162 #8157]: false
#8165 := [lemma #8164]: #6479
#6508 := (or #6484 #6507)
#6509 := [def-axiom]: #6508
#9643 := [unit-resolution #6509 #8165]: #6484
#6487 := (not #6484)
#6490 := (or #6472 #6487)
#6493 := (or #4388 #6472 #6487)
#6464 := (+ #1435 #6463)
#6465 := (+ #186 #6464)
#6466 := (<= #6465 0::Int)
#6469 := (or #6468 #6466)
#6470 := (not #6469)
#6473 := (or #6472 #6470)
#6494 := (or #4388 #6473)
#6501 := (iff #6494 #6493)
#6496 := (or #4388 #6490)
#6499 := (iff #6496 #6493)
#6500 := [rewrite]: #6499
#6497 := (iff #6494 #6496)
#6491 := (iff #6473 #6490)
#6488 := (iff #6470 #6487)
#6485 := (iff #6469 #6484)
#6482 := (iff #6466 #6479)
#6476 := (<= #6463 0::Int)
#6480 := (iff #6476 #6479)
#6481 := [rewrite]: #6480
#6477 := (iff #6466 #6476)
#6474 := (= #6465 #6463)
#6475 := [rewrite]: #6474
#6478 := [monotonicity #6475]: #6477
#6483 := [trans #6478 #6481]: #6482
#6486 := [monotonicity #6483]: #6485
#6489 := [monotonicity #6486]: #6488
#6492 := [monotonicity #6489]: #6491
#6498 := [monotonicity #6492]: #6497
#6502 := [trans #6498 #6500]: #6501
#6495 := [quant-inst #182]: #6494
#6503 := [mp #6495 #6502]: #6493
#9644 := [unit-resolution #6503 #6975]: #6490
#9655 := [unit-resolution #9644 #9643]: #6472
#9837 := [symm #9655]: #9061
#9878 := (= #2239 #6471)
#9879 := [monotonicity #9868]: #9878
#9838 := [trans #9879 #9837]: #9984
#9824 := [trans #9838 #9833]: #2846
#9825 := [unit-resolution #8271 #9824]: false
#9058 := [lemma #9825]: #2852
#4007 := (or #4521 #4515)
#4008 := [def-axiom]: #4007
#9404 := [unit-resolution #4008 #6974]: #4515
#6777 := (f5 #196 ?v0!13)
#6778 := (f4 #6777)
#6803 := (+ #2219 #6778)
#6804 := (+ #186 #6803)
#6825 := (>= #6804 0::Int)
#6807 := (= #6804 0::Int)
#6782 := (* -1::Int #6778)
#6786 := (+ f3 #6782)
#6787 := (<= #6786 0::Int)
#6854 := (not #6787)
#6796 := (+ #2836 #6778)
#6797 := (+ #186 #6796)
#6798 := (>= #6797 0::Int)
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#6830 := (= #2218 #2220)
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#6783 := (+ #1435 #6782)
#6784 := (+ #2220 #6783)
#6785 := (<= #6784 0::Int)
#6826 := (or #6787 #6785)
#6827 := (not #6826)
#6828 := (= #2220 #2218)
#6829 := (or #6828 #6827)
#6843 := (or #4388 #6829)
#6850 := (iff #6843 #6842)
#6839 := (or #6830 #6836)
#6845 := (or #4388 #6839)
#6848 := (iff #6845 #6842)
#6849 := [rewrite]: #6848
#6846 := (iff #6843 #6845)
#6840 := (iff #6829 #6839)
#6837 := (iff #6827 #6836)
#6834 := (iff #6826 #6833)
#6801 := (iff #6785 #6798)
#6789 := (+ #2220 #6782)
#6790 := (+ #1435 #6789)
#6793 := (<= #6790 0::Int)
#6799 := (iff #6793 #6798)
#6800 := [rewrite]: #6799
#6794 := (iff #6785 #6793)
#6791 := (= #6784 #6790)
#6792 := [rewrite]: #6791
#6795 := [monotonicity #6792]: #6794
#6802 := [trans #6795 #6800]: #6801
#6835 := [monotonicity #6802]: #6834
#6838 := [monotonicity #6835]: #6837
#6831 := (iff #6828 #6830)
#6832 := [rewrite]: #6831
#6841 := [monotonicity #6832 #6838]: #6840
#6847 := [monotonicity #6841]: #6846
#6851 := [trans #6847 #6849]: #6850
#6844 := [quant-inst #2217]: #6843
#6852 := [mp #6844 #6851]: #6842
#6976 := [unit-resolution #6852 #6975 #6961]: #6836
#6855 := (or #6833 #6854)
#6856 := [def-axiom]: #6855
#6977 := [unit-resolution #6856 #6976]: #6854
#6857 := (not #6798)
#6858 := (or #6833 #6857)
#6859 := [def-axiom]: #6858
#6978 := [unit-resolution #6859 #6976]: #6857
#6810 := (or #6787 #6798 #6807)
#6813 := (or #4396 #6787 #6798 #6807)
#6779 := (+ #6778 #2219)
#6780 := (+ #186 #6779)
#6781 := (= #6780 0::Int)
#6788 := (or #6787 #6785 #6781)
#6814 := (or #4396 #6788)
#6821 := (iff #6814 #6813)
#6816 := (or #4396 #6810)
#6819 := (iff #6816 #6813)
#6820 := [rewrite]: #6819
#6817 := (iff #6814 #6816)
#6811 := (iff #6788 #6810)
#6808 := (iff #6781 #6807)
#6805 := (= #6780 #6804)
#6806 := [rewrite]: #6805
#6809 := [monotonicity #6806]: #6808
#6812 := [monotonicity #6802 #6809]: #6811
#6818 := [monotonicity #6812]: #6817
#6822 := [trans #6818 #6820]: #6821
#6815 := [quant-inst #2217]: #6814
#6823 := [mp #6815 #6822]: #6813
#6980 := [unit-resolution #6823 #6979]: #6810
#6981 := [unit-resolution #6980 #6978 #6977]: #6807
#6982 := (not #6807)
#6983 := (or #6982 #6825)
#6984 := [th-lemma arith triangle-eq]: #6983
#6985 := [unit-resolution #6984 #6981]: #6825
#6853 := (>= #2837 0::Int)
#6986 := (or #6853 #2838)
#6987 := [th-lemma arith farkas 1 1]: #6986
#6988 := [unit-resolution #6987 #6955]: #6853
#6989 := [th-lemma arith farkas 1 -1 1 #6988 #6978 #6985]: false
#6990 := [lemma #6989]: #2838
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#4038 := [def-axiom]: #4037
#9405 := [unit-resolution #4038 #6990 #9404]: #4512
#4052 := (or #4509 #4503)
#4053 := [def-axiom]: #4052
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#4049 := [def-axiom]: #4048
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#10939 := [unit-resolution #10938 #9058]: #4500
#4058 := (or #4497 #4408)
#4060 := [def-axiom]: #4058
#10940 := [unit-resolution #4060 #10939]: #4408
#10282 := (or #4413 #8537 #8543)
#8542 := (or #8538 #8537)
#10237 := (or #4413 #8542)
#10201 := (iff #10237 #10282)
#10224 := (or #4413 #8592)
#10167 := (iff #10224 #10282)
#10199 := [rewrite]: #10167
#10168 := (iff #10237 #10224)
#8595 := (iff #8542 #8592)
#8545 := (or #8543 #8537)
#8593 := (iff #8545 #8592)
#8594 := [rewrite]: #8593
#8546 := (iff #8542 #8545)
#8591 := [monotonicity #8544]: #8546
#8588 := [trans #8591 #8594]: #8595
#10222 := [monotonicity #8588]: #10168
#10341 := [trans #10222 #10199]: #10201
#10226 := [quant-inst #2260]: #10237
#10258 := [mp #10226 #10341]: #10282
#10941 := [unit-resolution #10258 #10940]: #8592
#10942 := [unit-resolution #10941 #10924]: #8537
#10951 := [mp #10942 #10950]: #10850
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#10853 := (or #10849 #10838 #10810)
#10854 := [def-axiom]: #10853
#10952 := [unit-resolution #10854 #10951 #10936]: #10838
#10953 := (or #10495 #10839)
#10844 := (or #10495 #10839 #6770)
#10845 := [def-axiom]: #10844
#10954 := [unit-resolution #10845 #9703]: #10953
#10955 := [unit-resolution #10954 #10952]: #10839
#10894 := (or #10494 #10892)
#10897 := (or #7270 #10494 #10892)
#10866 := (= #7092 ?v0!15)
#10893 := (or #10866 #10892)
#10898 := (or #7270 #10893)
#10905 := (iff #10898 #10897)
#10900 := (or #7270 #10894)
#10903 := (iff #10900 #10897)
#10904 := [rewrite]: #10903
#10901 := (iff #10898 #10900)
#10895 := (iff #10893 #10894)
#10873 := (iff #10866 #10494)
#10874 := [rewrite]: #10873
#10896 := [monotonicity #10874]: #10895
#10902 := [monotonicity #10896]: #10901
#10906 := [trans #10902 #10904]: #10905
#10899 := [quant-inst #7092 #2260]: #10898
#10907 := [mp #10899 #10906]: #10897
#10956 := [unit-resolution #10907 #4171]: #10894
#10957 := [unit-resolution #10956 #10955]: #10892
#10958 := [th-lemma arith farkas 1 1 1 1 1 1 #10957 #10935 #10934 #10922 #10359 #10921]: false
#10960 := [lemma #10958]: #10959
#9739 := [unit-resolution #10960 #10935 #10359]: #8543
#9736 := (or #10923 #9849)
#9726 := [th-lemma arith triangle-eq]: #9736
#9891 := [unit-resolution #9726 #9739]: #9849
#9740 := [th-lemma arith farkas -1 1 1 #10935 #9891 #9883]: false
#9738 := [lemma #9740]: #9745
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#6584 := (or #6556 #6583)
#6585 := [def-axiom]: #6584
#12181 := [unit-resolution #6585 #12106]: #6556
#6559 := (not #6556)
#12086 := (or #6553 #6559)
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#19440 := [unit-resolution #4025 #6974]: #1637
#12674 := [unit-resolution #4005 #6973]: #4295
#6570 := (or #4300 #1636 #6553 #6559)
#6549 := (or #6548 #6545 #6537)
#6550 := (not #6549)
#6552 := (or #6551 #1636 #6550)
#6571 := (or #4300 #6552)
#6578 := (iff #6571 #6570)
#6565 := (or #1636 #6553 #6559)
#6573 := (or #4300 #6565)
#6576 := (iff #6573 #6570)
#6577 := [rewrite]: #6576
#6574 := (iff #6571 #6573)
#6568 := (iff #6552 #6565)
#6562 := (or #6553 #1636 #6559)
#6566 := (iff #6562 #6565)
#6567 := [rewrite]: #6566
#6563 := (iff #6552 #6562)
#6560 := (iff #6550 #6559)
#6557 := (iff #6549 #6556)
#6558 := [rewrite]: #6557
#6561 := [monotonicity #6558]: #6560
#6554 := (iff #6551 #6553)
#6555 := [rewrite]: #6554
#6564 := [monotonicity #6555 #6561]: #6563
#6569 := [trans #6564 #6567]: #6568
#6575 := [monotonicity #6569]: #6574
#6579 := [trans #6575 #6577]: #6578
#6572 := [quant-inst #182]: #6571
#6580 := [mp #6572 #6579]: #6570
#12091 := [unit-resolution #6580 #12674 #19440]: #12086
#12110 := [unit-resolution #12091 #12181]: #6553
#12118 := [symm #12110]: #6551
#12119 := [monotonicity #12118]: #12134
#12182 := [symm #12119]: #8354
#12180 := (not #8354)
#12185 := (or #12180 #10868)
#12132 := [th-lemma arith triangle-eq]: #12185
#12120 := [unit-resolution #12132 #12182]: #10868
#4614 := (>= #111 0::Int)
#7479 := [unit-resolution #4021 #6973]: #112
#21733 := (or #1729 #4614)
#21734 := [th-lemma arith triangle-eq]: #21733
#21735 := [unit-resolution #21734 #7479]: #4614
#11562 := (>= #10867 0::Int)
#19047 := [hypothesis]: #8534
#19048 := [unit-resolution #10258 #10940 #10924 #19047]: false
#19049 := [lemma #19048]: #8592
#12135 := [unit-resolution #19049 #10924]: #8537
#12117 := [mp #12135 #10950]: #10850
#12214 := [unit-resolution #10854 #12117 #10936]: #10838
#12215 := [unit-resolution #10954 #12214]: #10839
#12183 := [unit-resolution #10956 #12215]: #10892
#12210 := (or #11562 #10891)
#12133 := [th-lemma arith farkas 1 1]: #12210
#12211 := [unit-resolution #12133 #12183]: #11562
#12136 := [th-lemma arith farkas 1 1 -1 -1 1 1 #10935 #12211 #10921 #21735 #12120 #10934]: false
#12218 := [lemma #12136]: #12213
#8205 := [unit-resolution #12218 #10935]: #8543
#11190 := [unit-resolution #9726 #8205]: #9849
#11491 := [th-lemma arith farkas -1 1 1 #10935 #9883 #11190]: false
#11501 := [lemma #11491]: #2262
#4061 := (or #4497 #4491)
#4062 := [def-axiom]: #4061
#24108 := [unit-resolution #4062 #10939]: #4491
#24130 := (or #4494 #4488)
#6389 := (= #111 #217)
#24127 := (iff #6389 #218)
#24126 := [commutativity]: #1470
#24112 := (iff #6389 #804)
#24125 := [monotonicity #7479]: #24112
#24128 := [trans #24125 #24126]: #24127
#6330 := (f4 #6329)
#6337 := (* -1::Int #6330)
#6341 := (+ f3 #6337)
#6345 := (<= #6341 0::Int)
#6338 := (+ #1435 #6337)
#6339 := (+ #111 #6338)
#6340 := (<= #6339 0::Int)
#6391 := (or #6340 #6345)
#7248 := (f8 f9 #7021)
#7349 := (= f16 #7248)
#7099 := (f6 f7 #7248)
#7100 := (f5 #7099 f16)
#7291 := (f4 #7100)
#7374 := (<= #7291 0::Int)
#7292 := (* -1::Int #7291)
#7397 := (+ #6330 #7292)
#7399 := (>= #7397 0::Int)
#7396 := (= #6330 #7291)
#7472 := (= #7291 #6330)
#7470 := (= #7100 #6329)
#7468 := (= #7099 #196)
#7466 := (= #7248 f28)
#7249 := (= f28 #7248)
#7289 := (or #7209 #7249)
#7290 := [quant-inst #182 #2235]: #7289
#7465 := [unit-resolution #7290 #4177]: #7249
#7467 := [symm #7465]: #7466
#7469 := [monotonicity #7467]: #7468
#7471 := [monotonicity #7469]: #7470
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#7474 := [symm #7473]: #7396
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#7476 := (or #7475 #7399)
#7477 := [th-lemma arith triangle-eq]: #7476
#7478 := [unit-resolution #7477 #7474]: #7399
#4615 := (<= #111 0::Int)
#7480 := (or #1729 #4615)
#7481 := [th-lemma arith triangle-eq]: #7480
#7482 := [unit-resolution #7481 #7479]: #4615
#6592 := (>= #186 0::Int)
#6595 := (or #4267 #6592)
#6596 := [quant-inst #182]: #6595
#7484 := [unit-resolution #6596 #7483]: #6592
#6418 := (not #6340)
#7485 := [hypothesis]: #6418
#7487 := (not #6592)
#5597 := (not #4615)
#7486 := (not #7399)
#7488 := (or #7374 #7486 #5597 #7487 #6340)
#7489 := [th-lemma arith assign-bounds 1 1 1 1]: #7488
#7490 := [unit-resolution #7489 #7485 #7484 #7482 #7478]: #7374
#7376 := (not #7374)
#7378 := (or #7349 #7376)
#7381 := (or #7270 #7349 #7376)
#7343 := (= #7248 f16)
#7377 := (or #7343 #7376)
#7382 := (or #7270 #7377)
#7389 := (iff #7382 #7381)
#7384 := (or #7270 #7378)
#7387 := (iff #7384 #7381)
#7388 := [rewrite]: #7387
#7385 := (iff #7382 #7384)
#7379 := (iff #7377 #7378)
#7350 := (iff #7343 #7349)
#7351 := [rewrite]: #7350
#7380 := [monotonicity #7351]: #7379
#7386 := [monotonicity #7380]: #7385
#7390 := [trans #7386 #7388]: #7389
#7383 := [quant-inst #7248 #66]: #7382
#7391 := [mp #7383 #7390]: #7381
#7491 := [unit-resolution #7391 #4171]: #7378
#7492 := [unit-resolution #7491 #7490]: #7349
#7344 := (= #7291 0::Int)
#7497 := (not #7344)
#7375 := (>= #7291 0::Int)
#7493 := (not #7375)
#7494 := (or #7493 #7486 #5597 #7487 #6340)
#7495 := [th-lemma arith assign-bounds 1 -1 1 1]: #7494
#7496 := [unit-resolution #7495 #7485 #7484 #7482 #7478]: #7493
#7498 := (or #7497 #7375)
#7499 := [th-lemma arith triangle-eq]: #7498
#7500 := [unit-resolution #7499 #7496]: #7497
#7352 := (not #7349)
#7358 := (or #7344 #7352)
#7363 := (or #7259 #7344 #7352)
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#7348 := (or #7347 #7344)
#7364 := (or #7259 #7348)
#7371 := (iff #7364 #7363)
#7366 := (or #7259 #7358)
#7369 := (iff #7366 #7363)
#7370 := [rewrite]: #7369
#7367 := (iff #7364 #7366)
#7361 := (iff #7348 #7358)
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#7359 := (iff #7355 #7358)
#7360 := [rewrite]: #7359
#7356 := (iff #7348 #7355)
#7353 := (iff #7347 #7352)
#7354 := [monotonicity #7351]: #7353
#7357 := [monotonicity #7354]: #7356
#7362 := [trans #7357 #7360]: #7361
#7368 := [monotonicity #7362]: #7367
#7372 := [trans #7368 #7370]: #7371
#7365 := [quant-inst #7248 #66]: #7364
#7373 := [mp #7365 #7372]: #7363
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#7502 := [unit-resolution #7501 #7500 #7492]: false
#7503 := [lemma #7502]: #6340
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#6420 := [def-axiom]: #6419
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#6393 := (not #6391)
#6396 := (or #6389 #6393)
#6398 := (or #4388 #6389 #6393)
#6346 := (or #6345 #6340)
#6388 := (not #6346)
#6390 := (or #6389 #6388)
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#6415 := (iff #6399 #6398)
#6410 := (or #4388 #6396)
#6413 := (iff #6410 #6398)
#6414 := [rewrite]: #6413
#6411 := (iff #6399 #6410)
#6397 := (iff #6390 #6396)
#6394 := (iff #6388 #6393)
#6392 := (iff #6346 #6391)
#6387 := [rewrite]: #6392
#6395 := [monotonicity #6387]: #6394
#6361 := [monotonicity #6395]: #6397
#6412 := [monotonicity #6361]: #6411
#6416 := [trans #6412 #6414]: #6415
#6409 := [quant-inst #66]: #6399
#6417 := [mp #6409 #6416]: #6398
#24110 := [unit-resolution #6417 #6975]: #6396
#24111 := [unit-resolution #24110 #24109]: #6389
#24129 := [mp #24111 #24128]: #218
#4071 := (or #4494 #1472 #4488)
#4057 := [def-axiom]: #4071
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#24132 := [unit-resolution #24131 #24108]: #4488
#4080 := (or #4485 #4479)
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#24133 := [unit-resolution #4064 #24132]: #4479
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#24115 := [unit-resolution #24114 #11501]: #4476
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#4074 := [def-axiom]: #4072
#24116 := [unit-resolution #4074 #24115]: #4467
#24117 := (or #4470 #4464)
#7151 := (f19 f20 ?v0!17)
#8441 := (+ #7151 #7758)
#8449 := (<= #8441 0::Int)
#9760 := (not #8449)
#6512 := (* -1::Int #6471)
#6883 := (+ #186 #6512)
#7186 := (<= #6883 0::Int)
#9656 := (not #6472)
#9537 := (or #9656 #7186)
#9666 := [th-lemma arith triangle-eq]: #9537
#9667 := [unit-resolution #9666 #9655]: #7186
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#7628 := (+ #2277 #7627)
#7629 := (<= #7628 0::Int)
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#7610 := (+ #7151 #2278)
#7611 := (>= #7610 0::Int)
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#7670 := (iff #7668 #7667)
#7672 := (iff #7667 #7667)
#7673 := [rewrite]: #7672
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#7622 := (+ #2278 #7151)
#7625 := (>= #7622 0::Int)
#7630 := (iff #7625 #7629)
#7664 := [rewrite]: #7630
#7620 := (iff #7611 #7625)
#7623 := (= #7610 #7622)
#7624 := [rewrite]: #7623
#7626 := [monotonicity #7624]: #7620
#7666 := [trans #7626 #7664]: #7665
#7671 := [monotonicity #7666]: #7670
#7656 := [trans #7671 #7673]: #7670
#7669 := [quant-inst #2276]: #7668
#7657 := [mp #7669 #7656]: #7667
#9407 := [unit-resolution #7657 #9406]: #7629
#8944 := (+ #2277 #6512)
#8956 := (<= #8944 0::Int)
#8995 := (not #8956)
#7251 := (= ?v1!16 #7092)
#7342 := (not #7251)
#7331 := (f11 f21 ?v1!16)
#7326 := (= f1 #7331)
#7254 := (ite #7251 #6251 #7326)
#7341 := (not #7254)
#7255 := (f11 #7452 ?v1!16)
#7245 := (= f1 #7255)
#7256 := (iff #7245 #7254)
#7327 := (or #6756 #7256)
#7328 := [quant-inst #116 #7092 #6256 #2275]: #7327
#9699 := [unit-resolution #7328 #4205]: #7256
#7154 := (not #7245)
#9721 := (iff #2286 #7154)
#9720 := (iff #2285 #7245)
#9706 := (iff #7245 #2285)
#9657 := (= #7255 #2284)
#9658 := [monotonicity #9632]: #9657
#9707 := [monotonicity #9658]: #9706
#9709 := [symm #9707]: #9720
#9722 := [monotonicity #9709]: #9721
#9700 := [hypothesis]: #3433
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#3962 := [def-axiom]: #3961
#9701 := [unit-resolution #3962 #9700]: #2286
#9723 := [mp #9701 #9722]: #7154
#7457 := (not #7256)
#7458 := (or #7457 #7245 #7341)
#7153 := [def-axiom]: #7458
#9719 := [unit-resolution #7153 #9723 #9699]: #7341
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#7428 := (or #7254 #7342 #6770)
#7429 := [def-axiom]: #7428
#9725 := [unit-resolution #7429 #9703]: #9724
#9729 := [unit-resolution #9725 #9719]: #7342
#4104 := (not #2876)
#4105 := (or #3428 #4104)
#4106 := [def-axiom]: #4105
#9730 := [unit-resolution #4106 #9700]: #4104
#7934 := (f19 f20 ?v1!16)
#7924 := (* -1::Int #7934)
#8288 := (+ #186 #7924)
#8289 := (<= #8288 0::Int)
#7430 := (not #7326)
#7431 := (or #7254 #7251 #7430)
#7426 := [def-axiom]: #7431
#9728 := [unit-resolution #7426 #9729 #9719]: #7430
#8294 := (or #7326 #8289)
#4042 := (or #4521 #4373)
#4028 := [def-axiom]: #4042
#9747 := [unit-resolution #4028 #6974]: #4373
#8297 := (or #4378 #7326 #8289)
#8277 := (+ #7934 #1435)
#8278 := (>= #8277 0::Int)
#8281 := (or #7326 #8278)
#8298 := (or #4378 #8281)
#8305 := (iff #8298 #8297)
#8300 := (or #4378 #8294)
#8303 := (iff #8300 #8297)
#8304 := [rewrite]: #8303
#8301 := (iff #8298 #8300)
#8295 := (iff #8281 #8294)
#8292 := (iff #8278 #8289)
#8282 := (+ #1435 #7934)
#8285 := (>= #8282 0::Int)
#8290 := (iff #8285 #8289)
#8291 := [rewrite]: #8290
#8286 := (iff #8278 #8285)
#8283 := (= #8277 #8282)
#8284 := [rewrite]: #8283
#8287 := [monotonicity #8284]: #8286
#8293 := [trans #8287 #8291]: #8292
#8296 := [monotonicity #8293]: #8295
#8302 := [monotonicity #8296]: #8301
#8306 := [trans #8302 #8304]: #8305
#8299 := [quant-inst #2275]: #8298
#8307 := [mp #8299 #8306]: #8297
#9748 := [unit-resolution #8307 #9747]: #8294
#9746 := [unit-resolution #9748 #9728]: #8289
#10101 := (not #8289)
#9652 := (or #8995 #10101 #2876 #7251)
#7976 := (f5 #196 ?v1!16)
#7977 := (f4 #7976)
#8049 := (+ #2874 #7977)
#8050 := (+ #186 #8049)
#8061 := (= #8050 0::Int)
#9522 := (not #8061)
#8103 := (<= #8050 0::Int)
#9959 := (not #8103)
#9956 := [hypothesis]: #7342
#9396 := [hypothesis]: #4104
#8981 := [hypothesis]: #8956
#9960 := (or #9959 #2876 #8995 #7251)
#9946 := [hypothesis]: #8103
#9911 := (f5 #7535 ?v1!16)
#9919 := (f4 #9911)
#9942 := (* -1::Int #9919)
#9943 := (+ #7977 #9942)
#9945 := (>= #9943 0::Int)
#9941 := (= #7977 #9919)
#9949 := (= #9919 #7977)
#9947 := (= #9911 #7976)
#9948 := [monotonicity #8148]: #9947
#9950 := [monotonicity #9948]: #9949
#9951 := [symm #9950]: #9941
#9952 := (not #9941)
#9953 := (or #9952 #9945)
#9954 := [th-lemma arith triangle-eq]: #9953
#9955 := [unit-resolution #9954 #9951]: #9945
#9922 := (<= #9919 0::Int)
#9923 := (not #9922)
#9930 := (or #7270 #7251 #9923)
#9918 := (= #7092 ?v1!16)
#9924 := (or #9918 #9923)
#9931 := (or #7270 #9924)
#9938 := (iff #9931 #9930)
#9927 := (or #7251 #9923)
#9933 := (or #7270 #9927)
#9936 := (iff #9933 #9930)
#9937 := [rewrite]: #9936
#9934 := (iff #9931 #9933)
#9928 := (iff #9924 #9927)
#9925 := (iff #9918 #7251)
#9926 := [rewrite]: #9925
#9929 := [monotonicity #9926]: #9928
#9935 := [monotonicity #9929]: #9934
#9939 := [trans #9935 #9937]: #9938
#9932 := [quant-inst #7092 #2275]: #9931
#9940 := [mp #9932 #9939]: #9930
#9957 := [unit-resolution #9940 #4171 #9956]: #9923
#6884 := (>= #6883 0::Int)
#6888 := (or #4404 #6884)
#6889 := [quant-inst #182]: #6888
#8982 := [unit-resolution #6889 #9406]: #6884
#9958 := [th-lemma arith farkas 1 1 1 1 1 1 #8982 #9396 #9957 #9955 #9946 #8981]: false
#9961 := [lemma #9958]: #9960
#9521 := [unit-resolution #9961 #8981 #9396 #9956]: #9959
#9544 := (or #9522 #8103)
#9545 := [th-lemma arith triangle-eq]: #9544
#9517 := [unit-resolution #9545 #9521]: #9522
#8007 := (* -1::Int #7977)
#8005 := (+ f3 #8007)
#8011 := (<= #8005 0::Int)
#7878 := (not #8011)
#8043 := (+ #7924 #7977)
#8044 := (+ #186 #8043)
#8045 := (>= #8044 0::Int)
#7432 := (or #8011 #8045)
#7456 := (not #7432)
#8113 := (= #2279 #7934)
#9581 := (not #8113)
#7919 := (+ #2279 #7924)
#8074 := (>= #7919 0::Int)
#10100 := (not #8074)
#10098 := [hypothesis]: #8289
#10102 := (or #10100 #2876 #10101 #8995)
#10097 := [hypothesis]: #8074
#10099 := [th-lemma arith farkas -1 -1 1 -1 1 #8982 #9396 #10098 #10097 #8981]: false
#10103 := [lemma #10099]: #10102
#9518 := [unit-resolution #10103 #8981 #10098 #9396]: #10100
#9582 := (or #9581 #8074)
#9583 := [th-lemma arith triangle-eq]: #9582
#9584 := [unit-resolution #9583 #9518]: #9581
#7677 := (or #7456 #8113)
#7682 := (or #4388 #7456 #8113)
#8008 := (+ #1435 #8007)
#8009 := (+ #7934 #8008)
#8010 := (<= #8009 0::Int)
#8105 := (or #8011 #8010)
#8106 := (not #8105)
#8107 := (= #7934 #2279)
#8112 := (or #8107 #8106)
#7733 := (or #4388 #8112)
#7746 := (iff #7733 #7682)
#7735 := (or #4388 #7677)
#7744 := (iff #7735 #7682)
#7745 := [rewrite]: #7744
#7742 := (iff #7733 #7735)
#7680 := (iff #8112 #7677)
#7674 := (or #8113 #7456)
#7678 := (iff #7674 #7677)
#7679 := [rewrite]: #7678
#7675 := (iff #8112 #7674)
#7534 := (iff #8106 #7456)
#7433 := (iff #8105 #7432)
#8042 := (iff #8010 #8045)
#8013 := (+ #7934 #8007)
#8014 := (+ #1435 #8013)
#8021 := (<= #8014 0::Int)
#8046 := (iff #8021 #8045)
#8047 := [rewrite]: #8046
#8024 := (iff #8010 #8021)
#8015 := (= #8009 #8014)
#8020 := [rewrite]: #8015
#8025 := [monotonicity #8020]: #8024
#8048 := [trans #8025 #8047]: #8042
#7453 := [monotonicity #8048]: #7433
#7614 := [monotonicity #7453]: #7534
#8116 := (iff #8107 #8113)
#8117 := [rewrite]: #8116
#7676 := [monotonicity #8117 #7614]: #7675
#7681 := [trans #7676 #7679]: #7680
#7743 := [monotonicity #7681]: #7742
#7747 := [trans #7743 #7745]: #7746
#7734 := [quant-inst #2275]: #7733
#7844 := [mp #7734 #7747]: #7682
#9585 := [unit-resolution #7844 #6975]: #7677
#9646 := [unit-resolution #9585 #9584]: #7456
#7879 := (or #7432 #7878)
#7930 := [def-axiom]: #7879
#9647 := [unit-resolution #7930 #9646]: #7878
#7931 := (not #8045)
#8054 := (or #7432 #7931)
#8071 := [def-axiom]: #8054
#9651 := [unit-resolution #8071 #9646]: #7931
#8064 := (or #8011 #8045 #8061)
#8066 := (or #4396 #8011 #8045 #8061)
#7978 := (+ #7977 #2874)
#7979 := (+ #186 #7978)
#8006 := (= #7979 0::Int)
#8012 := (or #8011 #8010 #8006)
#8067 := (or #4396 #8012)
#8101 := (iff #8067 #8066)
#8069 := (or #4396 #8064)
#8099 := (iff #8069 #8066)
#8100 := [rewrite]: #8099
#8070 := (iff #8067 #8069)
#8065 := (iff #8012 #8064)
#8062 := (iff #8006 #8061)
#8051 := (= #7979 #8050)
#8052 := [rewrite]: #8051
#8063 := [monotonicity #8052]: #8062
#8060 := [monotonicity #8048 #8063]: #8065
#8098 := [monotonicity #8060]: #8070
#8102 := [trans #8098 #8100]: #8101
#8068 := [quant-inst #2275]: #8067
#8097 := [mp #8068 #8102]: #8066
#9590 := [unit-resolution #8097 #6979]: #8064
#9650 := [unit-resolution #9590 #9651 #9647 #9517]: false
#9653 := [lemma #9650]: #9652
#9749 := [unit-resolution #9653 #9746 #9730 #9729]: #8995
#9761 := (not #7629)
#9751 := (not #8562)
#9750 := (not #7186)
#9762 := (or #8956 #9750 #9751 #9760 #9761)
#9763 := [th-lemma arith assign-bounds -1 1 -1 -1]: #9762
#9779 := [unit-resolution #9763 #9749 #9407 #9416 #9667]: #9760
#7525 := (f11 f21 ?v0!17)
#7526 := (= f1 #7525)
#7527 := (= ?v0!17 #7092)
#7528 := (ite #7527 #6251 #7526)
#7529 := (f11 #7452 ?v0!17)
#7530 := (= f1 #7529)
#7532 := (iff #7528 #7530)
#7506 := (or #6756 #7532)
#7531 := (iff #7530 #7528)
#7504 := (or #6756 #7531)
#7508 := (iff #7504 #7506)
#7510 := (iff #7506 #7506)
#7511 := [rewrite]: #7510
#7533 := (iff #7531 #7532)
#7505 := [rewrite]: #7533
#7509 := [monotonicity #7505]: #7508
#7512 := [trans #7509 #7511]: #7508
#7507 := [quant-inst #116 #7092 #6256 #2276]: #7504
#7573 := [mp #7507 #7512]: #7506
#9759 := [unit-resolution #7573 #4205]: #7532
#9767 := (= #2282 #7529)
#9781 := (= #7529 #2282)
#9782 := [monotonicity #9632]: #9781
#9768 := [symm #9782]: #9767
#4119 := (or #3428 #2283)
#3960 := [def-axiom]: #4119
#9780 := [unit-resolution #3960 #9700]: #2283
#9787 := [trans #9780 #9768]: #7530
#7591 := (not #7530)
#7588 := (not #7532)
#7592 := (or #7588 #7528 #7591)
#7603 := [def-axiom]: #7592
#9769 := [unit-resolution #7603 #9787 #9759]: #7528
#7575 := (not #7527)
#8393 := (= #2277 #6471)
#8391 := (not #8393)
#8397 := (or #8391 #8956)
#8398 := [th-lemma arith triangle-eq]: #8397
#9770 := [unit-resolution #8398 #9749]: #8391
#8409 := (or #7575 #8393)
#8406 := (= ?v0!17 f28)
#8405 := [hypothesis]: #7527
#8404 := [trans #8405 #8146]: #8406
#8407 := [monotonicity #8404]: #8393
#8401 := [hypothesis]: #8391
#8408 := [unit-resolution #8401 #8407]: false
#8432 := [lemma #8408]: #8409
#9771 := [unit-resolution #8432 #9770]: #7575
#7574 := (not #7528)
#7572 := (or #7574 #7527 #7526)
#7578 := [def-axiom]: #7572
#9786 := [unit-resolution #7578 #9771 #9769]: #7526
#7581 := (not #7526)
#8470 := (or #4284 #7581 #7632 #8449)
#8433 := (+ #7748 #7627)
#8434 := (>= #8433 0::Int)
#8435 := (or #7632 #7581 #8434)
#8471 := (or #4284 #8435)
#8446 := (iff #8471 #8470)
#8465 := (or #7581 #7632 #8449)
#8447 := (or #4284 #8465)
#8458 := (iff #8447 #8470)
#8459 := [rewrite]: #8458
#8456 := (iff #8471 #8447)
#8468 := (iff #8435 #8465)
#8453 := (or #7632 #7581 #8449)
#8466 := (iff #8453 #8465)
#8467 := [rewrite]: #8466
#8454 := (iff #8435 #8453)
#8451 := (iff #8434 #8449)
#8436 := (+ #7627 #7748)
#8438 := (>= #8436 0::Int)
#8450 := (iff #8438 #8449)
#8448 := [rewrite]: #8450
#8439 := (iff #8434 #8438)
#8431 := (= #8433 #8436)
#8437 := [rewrite]: #8431
#8440 := [monotonicity #8437]: #8439
#8452 := [trans #8440 #8448]: #8451
#8455 := [monotonicity #8452]: #8454
#8469 := [trans #8455 #8467]: #8468
#8457 := [monotonicity #8469]: #8456
#8460 := [trans #8457 #8459]: #8446
#8472 := [quant-inst #2276 #7092]: #8471
#8461 := [mp #8472 #8460]: #8470
#9766 := [unit-resolution #8461 #9436 #9786 #9435 #9779]: false
#9772 := [lemma #9766]: #3428
#4094 := (or #4470 #3433 #4464)
#4081 := [def-axiom]: #4094
#24118 := [unit-resolution #4081 #9772]: #24117
#24113 := [unit-resolution #24118 #24116]: #4464
#3988 := (or #4461 #4455)
#3996 := [def-axiom]: #3988
#24119 := [unit-resolution #3996 #24113]: #4455
#24120 := (or #4458 #4452)
#17907 := [hypothesis]: #3479
#4102 := (or #3474 #2316)
#4108 := [def-axiom]: #4102
#17908 := [unit-resolution #4108 #17907]: #2316
#13474 := (f5 #196 ?v0!19)
#13475 := (f4 #13474)
#13479 := (* -1::Int #13475)
#13608 := (f8 f10 #2309)
#12640 := (f5 #196 #13608)
#12641 := (f4 #12640)
#14540 := (+ #12641 #13479)
#14541 := (>= #14540 0::Int)
#17541 := (= #12641 #13475)
#19277 := (= #13475 #12641)
#19275 := (= #13474 #12640)
#13609 := (= ?v0!19 #13608)
#17532 := (or #5414 #13609)
#17533 := [quant-inst #2302 #2303]: #17532
#19274 := [unit-resolution #17533 #4183]: #13609
#19276 := [monotonicity #19274]: #19275
#19278 := [monotonicity #19276]: #19277
#19279 := [symm #19278]: #17541
#19280 := (not #17541)
#19281 := (or #19280 #14541)
#19282 := [th-lemma arith triangle-eq]: #19281
#19283 := [unit-resolution #19282 #19279]: #14541
#12642 := (* -1::Int #12641)
#18095 := (+ #2310 #12642)
#18097 := (>= #18095 0::Int)
#18094 := (= #2310 #12641)
#18279 := (= #2309 #12640)
#18272 := (= #2308 #196)
#18270 := (= ?v1!18 f28)
#13068 := (= ?v1!18 #7092)
#13066 := (f11 f21 ?v1!18)
#13067 := (= f1 #13066)
#13069 := (ite #13068 #6251 #13067)
#13070 := (f11 #7452 ?v1!18)
#13071 := (= f1 #13070)
#13073 := (iff #13069 #13071)
#12561 := (or #6756 #13073)
#13072 := (iff #13071 #13069)
#12734 := (or #6756 #13072)
#12802 := (iff #12734 #12561)
#12800 := (iff #12561 #12561)
#12793 := [rewrite]: #12800
#13074 := (iff #13072 #13073)
#13075 := [rewrite]: #13074
#12746 := [monotonicity #13075]: #12802
#12803 := [trans #12746 #12793]: #12802
#12735 := [quant-inst #116 #7092 #6256 #2302]: #12734
#12828 := [mp #12735 #12803]: #12561
#17909 := [unit-resolution #12828 #4205]: #13073
#17914 := (= #2317 #13070)
#17910 := (= #13070 #2317)
#17911 := [monotonicity #9632]: #17910
#17928 := [symm #17911]: #17914
#4109 := (or #3474 #2318)
#4103 := [def-axiom]: #4109
#17904 := [unit-resolution #4103 #17907]: #2318
#17929 := [trans #17904 #17928]: #13071
#16530 := (not #13071)
#16532 := (not #13073)
#16533 := (or #16532 #13069 #16530)
#16534 := [def-axiom]: #16533
#17931 := [unit-resolution #16534 #17929 #17909]: #13069
#13093 := (not #13067)
#13423 := (f19 f20 ?v0!19)
#13458 := (* -1::Int #13423)
#13035 := (f19 f20 ?v1!18)
#13554 := (+ #13035 #13458)
#13555 := (+ #2310 #13554)
#13556 := (>= #13555 0::Int)
#19260 := (not #13556)
#4110 := (not #2903)
#3939 := (or #3474 #4110)
#3941 := [def-axiom]: #3939
#17932 := [unit-resolution #3941 #17907]: #4110
#13459 := (+ #2304 #13458)
#13460 := (<= #13459 0::Int)
#17488 := (or #4404 #13460)
#13450 := (+ #13423 #2305)
#13451 := (>= #13450 0::Int)
#17489 := (or #4404 #13451)
#17491 := (iff #17489 #17488)
#17493 := (iff #17488 #17488)
#17494 := [rewrite]: #17493
#13463 := (iff #13451 #13460)
#13452 := (+ #2305 #13423)
#13455 := (>= #13452 0::Int)
#13461 := (iff #13455 #13460)
#13462 := [rewrite]: #13461
#13456 := (iff #13451 #13455)
#13453 := (= #13450 #13452)
#13454 := [rewrite]: #13453
#13457 := [monotonicity #13454]: #13456
#13464 := [trans #13457 #13462]: #13463
#17492 := [monotonicity #13464]: #17491
#17495 := [trans #17492 #17494]: #17491
#17490 := [quant-inst #2303]: #17489
#17496 := [mp #17490 #17495]: #17488
#17930 := [unit-resolution #17496 #9406]: #13460
#13185 := (* -1::Int #13035)
#13186 := (+ #2306 #13185)
#12560 := (>= #13186 0::Int)
#13044 := (= #2306 #13035)
#11299 := (or #4413 #3459 #13044)
#13036 := (= #13035 #2306)
#13043 := (or #13036 #3459)
#11298 := (or #4413 #13043)
#11383 := (iff #11298 #11299)
#13050 := (or #3459 #13044)
#11324 := (or #4413 #13050)
#11362 := (iff #11324 #11299)
#11363 := [rewrite]: #11362
#11326 := (iff #11298 #11324)
#13053 := (iff #13043 #13050)
#13047 := (or #13044 #3459)
#13051 := (iff #13047 #13050)
#13052 := [rewrite]: #13051
#13048 := (iff #13043 #13047)
#13045 := (iff #13036 #13044)
#13046 := [rewrite]: #13045
#13049 := [monotonicity #13046]: #13048
#13054 := [trans #13049 #13052]: #13053
#11329 := [monotonicity #13054]: #11326
#11384 := [trans #11329 #11363]: #11383
#11322 := [quant-inst #2302]: #11298
#12500 := [mp #11322 #11384]: #11299
#17933 := [unit-resolution #12500 #10940 #17904]: #13044
#17934 := (not #13044)
#17935 := (or #17934 #12560)
#17951 := [th-lemma arith triangle-eq]: #17935
#17952 := [unit-resolution #17951 #17933]: #12560
#17953 := (not #13460)
#19264 := (not #12560)
#17954 := (or #19260 #2903 #19264 #17953)
#17955 := [th-lemma arith assign-bounds 1 1 -1]: #17954
#17956 := [unit-resolution #17955 #17952 #17930 #17932]: #19260
#18250 := (or #13093 #13556)
#18268 := [unit-resolution #4003 #6973]: #4270
#17508 := (or #4275 #2315 #13093 #13556)
#13557 := (or #13093 #2315 #13556)
#17509 := (or #4275 #13557)
#17516 := (iff #17509 #17508)
#13558 := (or #2315 #13093 #13556)
#17511 := (or #4275 #13558)
#17514 := (iff #17511 #17508)
#17515 := [rewrite]: #17514
#17512 := (iff #17509 #17511)
#13559 := (iff #13557 #13558)
#13560 := [rewrite]: #13559
#17513 := [monotonicity #13560]: #17512
#17517 := [trans #17513 #17515]: #17516
#17510 := [quant-inst #2303 #2302]: #17509
#17518 := [mp #17510 #17517]: #17508
#17957 := [unit-resolution #17518 #18268 #17908]: #18250
#17958 := [unit-resolution #17957 #17956]: #13093
#12829 := (not #13069)
#13468 := (or #12829 #13068 #13067)
#13540 := [def-axiom]: #13468
#17959 := [unit-resolution #13540 #17958 #17931]: #13068
#17960 := [trans #17959 #8146]: #18270
#17961 := [monotonicity #17960]: #18272
#17962 := [monotonicity #17961 #19274]: #18279
#17963 := [monotonicity #17962]: #18094
#18327 := (not #18094)
#18328 := (or #18327 #18097)
#18329 := [th-lemma arith triangle-eq]: #18328
#17964 := [unit-resolution #18329 #17963]: #18097
#13483 := (+ f3 #13479)
#13484 := (<= #13483 0::Int)
#13493 := (+ #13458 #13475)
#13494 := (+ #186 #13493)
#13495 := (>= #13494 0::Int)
#13526 := (or #13484 #13495)
#18413 := (or #13526 #2903 #19264 #12829 #2315)
#18210 := [hypothesis]: #13069
#19271 := [hypothesis]: #4110
#19272 := [hypothesis]: #12560
#13500 := (+ #2305 #13475)
#13501 := (+ #186 #13500)
#7577 := (>= #13501 0::Int)
#13504 := (= #13501 0::Int)
#13529 := (not #13526)
#15418 := [hypothesis]: #13529
#15423 := (or #13526 #13504)
#15416 := (not #13504)
#15417 := [hypothesis]: #15416
#13546 := (not #13484)
#13547 := (or #13526 #13546)
#13548 := [def-axiom]: #13547
#15419 := [unit-resolution #13548 #15418]: #13546
#13549 := (not #13495)
#13550 := (or #13526 #13549)
#13551 := [def-axiom]: #13550
#15420 := [unit-resolution #13551 #15418]: #13549
#13507 := (or #13484 #13495 #13504)
#13510 := (or #4396 #13484 #13495 #13504)
#13476 := (+ #13475 #2305)
#13477 := (+ #186 #13476)
#13478 := (= #13477 0::Int)
#13480 := (+ #1435 #13479)
#13481 := (+ #13423 #13480)
#13482 := (<= #13481 0::Int)
#13485 := (or #13484 #13482 #13478)
#13511 := (or #4396 #13485)
#13518 := (iff #13511 #13510)
#13513 := (or #4396 #13507)
#13516 := (iff #13513 #13510)
#13517 := [rewrite]: #13516
#13514 := (iff #13511 #13513)
#13508 := (iff #13485 #13507)
#13505 := (iff #13478 #13504)
#13502 := (= #13477 #13501)
#13503 := [rewrite]: #13502
#13506 := [monotonicity #13503]: #13505
#13498 := (iff #13482 #13495)
#13486 := (+ #13423 #13479)
#13487 := (+ #1435 #13486)
#13490 := (<= #13487 0::Int)
#13496 := (iff #13490 #13495)
#13497 := [rewrite]: #13496
#13491 := (iff #13482 #13490)
#13488 := (= #13481 #13487)
#13489 := [rewrite]: #13488
#13492 := [monotonicity #13489]: #13491
#13499 := [trans #13492 #13497]: #13498
#13509 := [monotonicity #13499 #13506]: #13508
#13515 := [monotonicity #13509]: #13514
#13519 := [trans #13515 #13517]: #13518
#13512 := [quant-inst #2303]: #13511
#13520 := [mp #13512 #13519]: #13510
#15421 := [unit-resolution #13520 #6979]: #13507
#15422 := [unit-resolution #15421 #15420 #15419 #15417]: false
#15424 := [lemma #15422]: #15423
#18211 := [unit-resolution #15424 #15418]: #13504
#18213 := (or #15416 #7577)
#18214 := [th-lemma arith triangle-eq]: #18213
#18212 := [unit-resolution #18214 #18211]: #7577
#13732 := (f19 f20 #13608)
#13746 := (* -1::Int #13732)
#12701 := (+ #12641 #13746)
#12697 := (+ #186 #12701)
#12706 := (>= #12697 0::Int)
#17576 := (not #12706)
#10185 := (<= #13501 0::Int)
#18209 := (or #15416 #10185)
#18215 := [th-lemma arith triangle-eq]: #18209
#18216 := [unit-resolution #18215 #18211]: #10185
#14505 := (<= #14540 0::Int)
#18172 := (or #19280 #14505)
#18217 := [th-lemma arith triangle-eq]: #18172
#18218 := [unit-resolution #18217 #19279]: #14505
#12542 := (+ #13423 #13746)
#12543 := (<= #12542 0::Int)
#17531 := (= #13423 #13732)
#19284 := [monotonicity #19274]: #17531
#19285 := (not #17531)
#18219 := (or #19285 #12543)
#18244 := [th-lemma arith triangle-eq]: #18219
#18147 := [unit-resolution #18244 #19284]: #12543
#14171 := (>= #13459 0::Int)
#18245 := (not #14171)
#19263 := (not #7577)
#18246 := (or #18245 #13495 #19263)
#18247 := [th-lemma arith assign-bounds -1 1]: #18246
#18248 := [unit-resolution #18247 #18212 #15420]: #18245
#18253 := (not #10185)
#18252 := (not #14505)
#18243 := (not #12543)
#18251 := (or #17576 #14171 #18243 #18252 #18253)
#18264 := [th-lemma arith assign-bounds -1 -1 -1 -1]: #18251
#18265 := [unit-resolution #18264 #18248 #18147 #18218 #18216]: #17576
#19265 := (or #19260 #12706 #19263 #19264 #2903)
#19273 := [hypothesis]: #7577
#17536 := (>= #12542 0::Int)
#19286 := (or #19285 #17536)
#19287 := [th-lemma arith triangle-eq]: #19286
#19288 := [unit-resolution #19287 #19284]: #17536
#19289 := [hypothesis]: #17576
#19261 := [hypothesis]: #13556
#19262 := [th-lemma arith farkas 1 1 1 1 1 1 1 #19261 #19289 #19288 #19283 #19273 #19272 #19271]: false
#19266 := [lemma #19262]: #19265
#18266 := [unit-resolution #19266 #18265 #18212 #19272 #19271]: #19260
#18267 := [hypothesis]: #2316
#18263 := [unit-resolution #17518 #18268 #18267]: #18250
#18249 := [unit-resolution #18263 #18266]: #13093
#18269 := [unit-resolution #13540 #18249 #18210]: #13068
#18271 := [trans #18269 #8146]: #18270
#18273 := [monotonicity #18271]: #18272
#18324 := [monotonicity #18273 #19274]: #18279
#18325 := [monotonicity #18324]: #18094
#18330 := [unit-resolution #18329 #18325]: #18097
#13610 := (f8 f9 #2309)
#13631 := (f19 f20 #13610)
#13649 := (* -1::Int #13631)
#13650 := (+ #186 #13649)
#13651 := (<= #13650 0::Int)
#21052 := (= #186 #13631)
#21166 := (= #13631 #186)
#21154 := (= #13610 f28)
#14249 := (= #13610 #7092)
#21151 := (= #13610 ?v1!18)
#13611 := (= ?v1!18 #13610)
#17534 := (or #7209 #13611)
#17535 := [quant-inst #2302 #2303]: #17534
#21150 := [unit-resolution #17535 #4177]: #13611
#21152 := [symm #21150]: #21151
#18331 := [trans #21152 #18269]: #14249
#18326 := [trans #18331 #8146]: #21154
#18314 := [monotonicity #18326]: #21166
#18315 := [symm #18314]: #21052
#21169 := (not #21052)
#18316 := (or #21169 #13651)
#18317 := [th-lemma arith triangle-eq]: #18316
#18318 := [unit-resolution #18317 #18315]: #13651
#17538 := (+ #13035 #13649)
#17540 := (>= #17538 0::Int)
#17537 := (= #13035 #13631)
#18353 := [monotonicity #21150]: #17537
#18354 := (not #17537)
#18355 := (or #18354 #17540)
#18356 := [th-lemma arith triangle-eq]: #18355
#18411 := [unit-resolution #18356 #18353]: #17540
#18412 := [th-lemma arith farkas 1 1 1 1 1 -1 1 #19283 #18212 #19271 #19272 #18411 #18318 #18330]: false
#18414 := [lemma #18412]: #18413
#17965 := [unit-resolution #18414 #17932 #17952 #17931 #17908]: #13526
#17966 := [trans #21152 #17959]: #14249
#17967 := [trans #17966 #8146]: #21154
#17968 := [monotonicity #17967]: #21166
#17969 := [symm #17968]: #21052
#17970 := [unit-resolution #18317 #17969]: #13651
#17945 := (not #13651)
#17942 := (not #17540)
#17944 := (not #14541)
#17943 := (not #18097)
#17946 := (or #13549 #17953 #17943 #17944 #2903 #19264 #17942 #17945)
#17947 := [th-lemma arith assign-bounds -1 1 1 1 1 1 -1]: #17946
#17948 := [unit-resolution #17947 #17932 #17970 #19283 #17952 #17930 #18411 #17964]: #13549
#7522 := (or #13529 #13484 #13495)
#7580 := [def-axiom]: #7522
#17949 := [unit-resolution #7580 #17948 #17965]: #13484
#17950 := [th-lemma arith farkas -1 1 1 1 #17949 #17964 #19283 #17908]: false
#17973 := [lemma #17950]: #3474
#3977 := (or #4458 #3479 #4452)
#3992 := [def-axiom]: #3977
#24121 := [unit-resolution #3992 #17973]: #24120
#24122 := [unit-resolution #24121 #24119]: #4452
#4096 := (or #4449 #2348)
#4098 := [def-axiom]: #4096
#27906 := [unit-resolution #4098 #24122]: #2348
#3983 := (or #4449 #4441)
#3984 := [def-axiom]: #3983
#24123 := [unit-resolution #3984 #24122]: #4441
#23337 := (or #23218 #4446 #2347)
#8166 := (f30 #7092)
#10712 := (* -1::Int #8166)
#14416 := (+ #2335 #10712)
#14011 := (<= #14416 0::Int)
#9203 := (f11 f29 #7092)
#10442 := (= f1 #9203)
#23231 := (= #6256 #9203)
#23227 := (= #9203 #6256)
#23230 := [monotonicity #9702 #8146]: #23227
#23232 := [symm #23230]: #23231
#23234 := [trans #9703 #23232]: #10442
#13997 := (f5 #7535 ?v0!20)
#13998 := (f4 #13997)
#14026 := (* -1::Int #13998)
#14027 := (+ #10712 #14026)
#14023 := (+ #2335 #14027)
#14028 := (= #14023 0::Int)
#14461 := (f5 #196 ?v0!20)
#14462 := (f4 #14461)
#14487 := (+ #2336 #14462)
#14488 := (+ #186 #14487)
#14491 := (= #14488 0::Int)
#14480 := (+ #14445 #14462)
#14481 := (+ #186 #14480)
#14482 := (>= #14481 0::Int)
#14466 := (* -1::Int #14462)
#14470 := (+ f3 #14466)
#14471 := (<= #14470 0::Int)
#14517 := (or #14471 #14482)
#14520 := (not #14517)
#14514 := (= #2335 #14434)
#23226 := (not #14514)
#14446 := (+ #2335 #14445)
#12186 := (>= #14446 0::Int)
#23214 := (not #12186)
#23130 := [hypothesis]: #2348
#23188 := [hypothesis]: #14594
#23127 := (or #23214 #23218 #2347)
#23131 := [hypothesis]: #12186
#23132 := [th-lemma arith farkas -1 1 1 #23188 #23131 #23130]: false
#23133 := [lemma #23132]: #23127
#23196 := [unit-resolution #23133 #23188 #23130]: #23214
#23239 := (or #23226 #12186)
#23240 := [th-lemma arith triangle-eq]: #23239
#23170 := [unit-resolution #23240 #23196]: #23226
#14523 := (or #14514 #14520)
#12064 := (or #4388 #14514 #14520)
#14467 := (+ #1435 #14466)
#14468 := (+ #14434 #14467)
#14469 := (<= #14468 0::Int)
#14510 := (or #14471 #14469)
#14511 := (not #14510)
#14512 := (= #14434 #2335)
#14513 := (or #14512 #14511)
#12047 := (or #4388 #14513)
#12069 := (iff #12047 #12064)
#12074 := (or #4388 #14523)
#12045 := (iff #12074 #12064)
#12076 := [rewrite]: #12045
#12082 := (iff #12047 #12074)
#14524 := (iff #14513 #14523)
#14521 := (iff #14511 #14520)
#14518 := (iff #14510 #14517)
#14485 := (iff #14469 #14482)
#14473 := (+ #14434 #14466)
#14474 := (+ #1435 #14473)
#14477 := (<= #14474 0::Int)
#14483 := (iff #14477 #14482)
#14484 := [rewrite]: #14483
#14478 := (iff #14469 #14477)
#14475 := (= #14468 #14474)
#14476 := [rewrite]: #14475
#14479 := [monotonicity #14476]: #14478
#14486 := [trans #14479 #14484]: #14485
#14519 := [monotonicity #14486]: #14518
#14522 := [monotonicity #14519]: #14521
#14515 := (iff #14512 #14514)
#14516 := [rewrite]: #14515
#14525 := [monotonicity #14516 #14522]: #14524
#12087 := [monotonicity #14525]: #12082
#12073 := [trans #12087 #12076]: #12069
#12057 := [quant-inst #2334]: #12047
#12078 := [mp #12057 #12073]: #12064
#22728 := [unit-resolution #12078 #6975]: #14523
#22597 := [unit-resolution #22728 #23170]: #14520
#23129 := (or #14517 #14491)
#23297 := (not #14491)
#23123 := [hypothesis]: #23297
#12077 := (not #14471)
#23124 := [hypothesis]: #14520
#12063 := (or #14517 #12077)
#12061 := [def-axiom]: #12063
#23122 := [unit-resolution #12061 #23124]: #12077
#12065 := (not #14482)
#12068 := (or #14517 #12065)
#12048 := [def-axiom]: #12068
#23125 := [unit-resolution #12048 #23124]: #12065
#14494 := (or #14471 #14482 #14491)
#12026 := (or #4396 #14471 #14482 #14491)
#14463 := (+ #14462 #2336)
#14464 := (+ #186 #14463)
#14465 := (= #14464 0::Int)
#14472 := (or #14471 #14469 #14465)
#12043 := (or #4396 #14472)
#12041 := (iff #12043 #12026)
#12044 := (or #4396 #14494)
#12033 := (iff #12044 #12026)
#11996 := [rewrite]: #12033
#12042 := (iff #12043 #12044)
#14495 := (iff #14472 #14494)
#14492 := (iff #14465 #14491)
#14489 := (= #14464 #14488)
#14490 := [rewrite]: #14489
#14493 := [monotonicity #14490]: #14492
#14496 := [monotonicity #14486 #14493]: #14495
#11999 := [monotonicity #14496]: #12042
#12039 := [trans #11999 #11996]: #12041
#12025 := [quant-inst #2334]: #12043
#12059 := [mp #12025 #12039]: #12026
#23126 := [unit-resolution #12059 #6979]: #14494
#23128 := [unit-resolution #23126 #23125 #23122 #23123]: false
#23116 := [lemma #23128]: #23129
#23105 := [unit-resolution #23116 #22597]: #14491
#23312 := (or #23297 #14028)
#14035 := (not #14028)
#23276 := [hypothesis]: #14035
#13116 := (>= #14023 0::Int)
#15462 := (+ #13998 #14466)
#15580 := (<= #15462 0::Int)
#15463 := (= #13998 #14462)
#23277 := (= #13997 #14461)
#23278 := [monotonicity #8148]: #23277
#23273 := [monotonicity #23278]: #15463
#23279 := (not #15463)
#23280 := (or #23279 #15580)
#23281 := [th-lemma arith triangle-eq]: #23280
#23282 := [unit-resolution #23281 #23273]: #15580
#11485 := (+ #6471 #10712)
#7606 := (>= #11485 0::Int)
#7517 := (= #6471 #8166)
#18951 := (= #8166 #6471)
#18952 := [monotonicity #8146]: #18951
#18953 := [symm #18952]: #7517
#18954 := (not #7517)
#23215 := (or #18954 #7606)
#23216 := [th-lemma arith triangle-eq]: #23215
#23217 := [unit-resolution #23216 #18953]: #7606
#12055 := (<= #14488 0::Int)
#23283 := [hypothesis]: #14491
#23298 := (or #23297 #12055)
#23299 := [th-lemma arith triangle-eq]: #23298
#23300 := [unit-resolution #23299 #23283]: #12055
#23302 := (not #15580)
#21754 := (not #6884)
#23221 := (not #7606)
#23301 := (not #12055)
#23303 := (or #13116 #23301 #23221 #21754 #23302)
#23304 := [th-lemma arith assign-bounds 1 -1 -1 1]: #23303
#23305 := [unit-resolution #23304 #23300 #23217 #8982 #23282]: #13116
#13130 := (<= #14023 0::Int)
#16451 := (>= #15462 0::Int)
#23285 := (or #23279 #16451)
#23286 := [th-lemma arith triangle-eq]: #23285
#23287 := [unit-resolution #23286 #23273]: #16451
#11486 := (<= #11485 0::Int)
#18955 := (or #18954 #11486)
#18956 := [th-lemma arith triangle-eq]: #18955
#18957 := [unit-resolution #18956 #18953]: #11486
#12060 := (>= #14488 0::Int)
#23288 := (or #23297 #12060)
#23289 := [th-lemma arith triangle-eq]: #23288
#23284 := [unit-resolution #23289 #23283]: #12060
#23291 := (not #16451)
#21762 := (not #11486)
#23290 := (not #12060)
#23292 := (or #13130 #23290 #21762 #9750 #23291)
#23293 := [th-lemma arith assign-bounds 1 -1 -1 1]: #23292
#23294 := [unit-resolution #23293 #23284 #18957 #9667 #23287]: #13130
#23309 := (not #13116)
#23308 := (not #13130)
#23307 := (or #14028 #23308 #23309)
#23310 := [th-lemma arith triangle-eq]: #23307
#23311 := [unit-resolution #23310 #23294 #23305 #23276]: false
#23313 := [lemma #23311]: #23312
#23111 := [unit-resolution #23313 #23105]: #14028
#10446 := (not #10442)
#13975 := (or #10446 #14011 #14035)
#23147 := [hypothesis]: #4441
#13102 := (or #4446 #10446 #14011 #14035)
#14000 := (+ #2336 #13998)
#14001 := (+ #8166 #14000)
#13993 := (= #14001 0::Int)
#13999 := (not #13993)
#14002 := (+ #8166 #2336)
#14003 := (>= #14002 0::Int)
#14004 := (or #10446 #14003 #13999)
#13099 := (or #4446 #14004)
#13095 := (iff #13099 #13102)
#12963 := (or #4446 #13975)
#13104 := (iff #12963 #13102)
#13100 := [rewrite]: #13104
#13113 := (iff #13099 #12963)
#14066 := (iff #14004 #13975)
#14036 := (iff #13999 #14035)
#14033 := (iff #13993 #14028)
#14018 := (+ #8166 #13998)
#14007 := (+ #2336 #14018)
#14020 := (= #14007 0::Int)
#13976 := (iff #14020 #14028)
#14029 := [rewrite]: #13976
#14021 := (iff #13993 #14020)
#14019 := (= #14001 #14007)
#14017 := [rewrite]: #14019
#14022 := [monotonicity #14017]: #14021
#14034 := [trans #14022 #14029]: #14033
#14037 := [monotonicity #14034]: #14036
#14015 := (iff #14003 #14011)
#14006 := (+ #2336 #8166)
#14008 := (>= #14006 0::Int)
#14005 := (iff #14008 #14011)
#14014 := [rewrite]: #14005
#14012 := (iff #14003 #14008)
#14009 := (= #14002 #14006)
#14010 := [rewrite]: #14009
#14013 := [monotonicity #14010]: #14012
#14016 := [trans #14013 #14014]: #14015
#14067 := [monotonicity #14016 #14037]: #14066
#13084 := [monotonicity #14067]: #13113
#13083 := [trans #13084 #13100]: #13095
#13077 := [quant-inst #7092]: #13099
#13103 := [mp #13077 #13083]: #13102
#23213 := [unit-resolution #13103 #23147]: #13975
#23186 := [unit-resolution #23213 #23111 #23234]: #14011
#23266 := [unit-resolution #23299 #23105]: #12055
#9106 := (f5 #6538 #7092)
#9306 := (f8 f9 #9106)
#10715 := (f6 f7 #9306)
#15683 := (f5 #10715 ?v0!20)
#23013 := (f8 f10 #15683)
#23026 := (f5 #7535 #23013)
#23029 := (f4 #23026)
#23033 := (* -1::Int #23029)
#23093 := (+ #14462 #23033)
#23044 := (>= #23093 0::Int)
#23046 := (= #14462 #23029)
#23270 := (= #23029 #14462)
#23269 := (= #23026 #14461)
#23248 := (= #23013 ?v0!20)
#23014 := (= ?v0!20 #23013)
#19532 := (or #5414 #23014)
#19557 := [quant-inst #9306 #2334]: #19532
#23267 := [unit-resolution #19557 #4183]: #23014
#23268 := [symm #23267]: #23248
#23265 := [monotonicity #8148 #23268]: #23269
#23271 := [monotonicity #23265]: #23270
#23272 := [symm #23271]: #23046
#23274 := (not #23046)
#23275 := (or #23274 #23044)
#23306 := [th-lemma arith triangle-eq]: #23275
#23314 := [unit-resolution #23306 #23272]: #23044
#23072 := (<= #23029 0::Int)
#23080 := (not #23072)
#23061 := (= #7092 #23013)
#23062 := (not #23061)
#23096 := (f11 f21 #23013)
#23097 := (= f1 #23096)
#23118 := (ite #23061 #6251 #23097)
#23063 := (not #23118)
#23112 := (f11 #7452 #23013)
#23113 := (= f1 #23112)
#23121 := (iff #23113 #23118)
#23047 := (or #6756 #23121)
#23098 := (= #23013 #7092)
#23099 := (ite #23098 #6251 #23097)
#23114 := (iff #23113 #23099)
#23037 := (or #6756 #23114)
#23050 := (iff #23037 #23047)
#23053 := (iff #23047 #23047)
#23054 := [rewrite]: #23053
#23100 := (iff #23114 #23121)
#23119 := (iff #23099 #23118)
#23115 := (iff #23098 #23061)
#23117 := [rewrite]: #23115
#23120 := [monotonicity #23117]: #23119
#23101 := [monotonicity #23120]: #23100
#23051 := [monotonicity #23101]: #23050
#23059 := [trans #23051 #23054]: #23050
#23052 := [quant-inst #116 #7092 #6256 #23013]: #23037
#23060 := [mp #23052 #23059]: #23047
#23315 := [unit-resolution #23060 #4205]: #23121
#23085 := (not #23113)
#10595 := (f11 f29 ?v0!20)
#10596 := (= f1 #10595)
#10603 := (not #10596)
#23326 := (iff #10603 #23085)
#23320 := (iff #10596 #23113)
#23323 := (iff #23113 #10596)
#23317 := (= #23112 #10595)
#23318 := [monotonicity #9632 #23268]: #23317
#23324 := [monotonicity #23318]: #23323
#23325 := [symm #23324]: #23320
#23327 := [monotonicity #23325]: #23326
#14850 := (or #10603 #14514)
#11930 := (or #4413 #10603 #14514)
#14829 := (or #14512 #10603)
#11894 := (or #4413 #14829)
#11956 := (iff #11894 #11930)
#11890 := (or #4413 #14850)
#11959 := (iff #11890 #11930)
#11960 := [rewrite]: #11959
#11927 := (iff #11894 #11890)
#14853 := (iff #14829 #14850)
#14830 := (or #14514 #10603)
#14851 := (iff #14830 #14850)
#14852 := [rewrite]: #14851
#14848 := (iff #14829 #14830)
#14849 := [monotonicity #14516]: #14848
#14854 := [trans #14849 #14852]: #14853
#11929 := [monotonicity #14854]: #11927
#11896 := [trans #11929 #11960]: #11956
#11958 := [quant-inst #2334]: #11894
#11957 := [mp #11958 #11896]: #11930
#23237 := [unit-resolution #11957 #10940]: #14850
#23316 := [unit-resolution #23237 #23170]: #10603
#23328 := [mp #23316 #23327]: #23085
#23077 := (not #23121)
#23024 := (or #23077 #23113 #23063)
#23078 := [def-axiom]: #23024
#23319 := [unit-resolution #23078 #23328 #23315]: #23063
#23329 := (or #23118 #23062)
#23074 := (or #23118 #23062 #6770)
#23073 := [def-axiom]: #23074
#23330 := [unit-resolution #23073 #9703]: #23329
#23331 := [unit-resolution #23330 #23319]: #23062
#23081 := (or #23061 #23080)
#23197 := (or #7270 #23061 #23080)
#23198 := (or #7270 #23081)
#22725 := (iff #23198 #23197)
#22726 := [rewrite]: #22725
#22598 := [quant-inst #7092 #23013]: #23198
#22727 := [mp #22598 #22726]: #23197
#23332 := [unit-resolution #22727 #4171]: #23081
#23333 := [unit-resolution #23332 #23331]: #23080
#23336 := [th-lemma arith farkas -1 -1 -1 -1 1 1 #23217 #8982 #23333 #23314 #23266 #23186]: false
#23338 := [lemma #23336]: #23337
#27907 := [unit-resolution #23338 #24123 #27906]: #23218
#4099 := (or #4449 #2917)
#4097 := [def-axiom]: #4099
#27908 := [unit-resolution #4097 #24122]: #2917
#17129 := (or #4300 #2914 #14594 #14599)
#14591 := (or #14590 #14587 #14579)
#14592 := (not #14591)
#14595 := (or #2349 #14594 #14592)
#17130 := (or #4300 #14595)
#17097 := (iff #17130 #17129)
#14602 := (or #2914 #14594 #14599)
#17070 := (or #4300 #14602)
#17101 := (iff #17070 #17129)
#17099 := [rewrite]: #17101
#17115 := (iff #17130 #17070)
#14603 := (iff #14595 #14602)
#14600 := (iff #14592 #14599)
#14597 := (iff #14591 #14596)
#14598 := [rewrite]: #14597
#14601 := [monotonicity #14598]: #14600
#14604 := [monotonicity #2916 #14601]: #14603
#17104 := [monotonicity #14604]: #17115
#17105 := [trans #17104 #17099]: #17097
#17131 := [quant-inst #2334]: #17130
#17117 := [mp #17131 #17105]: #17129
#27909 := [unit-resolution #17117 #12674 #27908 #27907]: #14599
#17149 := (or #14596 #14589)
#17152 := [def-axiom]: #17149
#27910 := [unit-resolution #17152 #27909]: #14589
#27920 := [trans #27910 #27919]: #22708
#22709 := (not #22708)
#27889 := (or #27866 #27863 #22709)
#27890 := [def-axiom]: #27889
#27922 := [unit-resolution #27890 #27920]: #27921
#27923 := [unit-resolution #27922 #27905 #27902]: false
#27924 := [lemma #27923]: #27866
#23192 := (or #23191 #27861 #27881)
#23193 := [def-axiom]: #23192
#24146 := [unit-resolution #23193 #27924]: #24142
#24147 := [unit-resolution #24146 #24138]: #27861
#24153 := [trans #24147 #24150]: #21477
#21522 := (not #21477)
#21523 := (f30 #14575)
#21555 := (* -1::Int #21523)
#21869 := (+ #14583 #21555)
#21870 := (+ #2335 #21869)
#21714 := (>= #21870 0::Int)
#16926 := [hypothesis]: #23214
#23220 := (not #14011)
#17376 := (or #23220 #12186)
#14284 := (f11 f21 ?v0!20)
#14285 := (= f1 #14284)
#14286 := (= ?v0!20 #7092)
#14287 := (ite #14286 #6251 #14285)
#10864 := (not #14287)
#14292 := (f11 #7452 ?v0!20)
#14293 := (= f1 #14292)
#14297 := (iff #14287 #14293)
#17251 := (or #6756 #14297)
#14296 := (iff #14293 #14287)
#17242 := (or #6756 #14296)
#17255 := (iff #17242 #17251)
#17260 := (iff #17251 #17251)
#17261 := [rewrite]: #17260
#14304 := (iff #14296 #14297)
#14305 := [rewrite]: #14304
#17258 := [monotonicity #14305]: #17255
#17288 := [trans #17258 #17261]: #17255
#17243 := [quant-inst #116 #7092 #6256 #2334]: #17242
#17289 := [mp #17243 #17288]: #17251
#23539 := [unit-resolution #17289 #4205]: #14297
#17274 := (not #14293)
#23534 := (iff #10603 #17274)
#23538 := (iff #10596 #14293)
#23544 := (iff #14293 #10596)
#23543 := (= #14292 #10595)
#23535 := [monotonicity #9632]: #23543
#23545 := [monotonicity #23535]: #23544
#23546 := [symm #23545]: #23538
#23547 := [monotonicity #23546]: #23534
#16899 := [unit-resolution #23240 #16926]: #23226
#23542 := [unit-resolution #11957 #10940 #16899]: #10603
#23548 := [mp #23542 #23547]: #17274
#17277 := (not #14297)
#17262 := (or #17277 #10864 #14293)
#17281 := [def-axiom]: #17262
#23549 := [unit-resolution #17281 #23548 #23539]: #10864
#17148 := (<= #13998 0::Int)
#23550 := [hypothesis]: #14011
#16924 := [unit-resolution #12078 #6975 #16899]: #14520
#16905 := [unit-resolution #23116 #16924]: #14491
#23555 := [unit-resolution #23299 #16905]: #12055
#14868 := (or #13116 #23301)
#15581 := [unit-resolution #23304 #23282 #23217 #8982]: #14868
#14888 := [unit-resolution #15581 #23555]: #13116
#14896 := (or #17148 #23309 #23220)
#14897 := [th-lemma arith assign-bounds 1 -1]: #14896
#15478 := [unit-resolution #14897 #14888 #23550]: #17148
#17286 := (not #17148)
#17431 := (or #14286 #17286)
#17474 := (or #7270 #14286 #17286)
#15601 := (= #7092 ?v0!20)
#17282 := (or #15601 #17286)
#17284 := (or #7270 #17282)
#16929 := (iff #17284 #17474)
#17726 := (or #7270 #17431)
#17722 := (iff #17726 #17474)
#17865 := [rewrite]: #17722
#17727 := (iff #17284 #17726)
#17280 := (iff #17282 #17431)
#15603 := (iff #15601 #14286)
#15602 := [rewrite]: #15603
#17473 := [monotonicity #15602]: #17280
#17283 := [monotonicity #17473]: #17727
#17430 := [trans #17283 #17865]: #16929
#17725 := [quant-inst #7092 #2334]: #17284
#16934 := [mp #17725 #17430]: #17474
#16501 := [unit-resolution #16934 #4171]: #17431
#16503 := [unit-resolution #16501 #15478]: #14286
#11258 := (not #14286)
#17247 := (or #14287 #11258)
#17256 := (or #14287 #11258 #6770)
#17273 := [def-axiom]: #17256
#17250 := [unit-resolution #17273 #9703]: #17247
#17359 := [unit-resolution #17250 #16503 #23549]: false
#17381 := [lemma #17359]: #17376
#24136 := [unit-resolution #17381 #16926]: #23220
#16968 := (or #4446 #14011 #12186)
#16923 := [hypothesis]: #10446
#16913 := [unit-resolution #16923 #23234]: false
#16925 := [lemma #16913]: #10442
#16898 := [hypothesis]: #23220
#16922 := [unit-resolution #13103 #23147 #16898 #16925]: #14035
#16907 := [unit-resolution #23313 #16905 #16922]: false
#16969 := [lemma #16907]: #16968
#24137 := [unit-resolution #16969 #24136 #16926 #24123]: false
#24139 := [lemma #24137]: #12186
#21550 := (+ #14576 #21555)
#21556 := (>= #21550 0::Int)
#20281 := (or #4404 #21556)
#20363 := [quant-inst #14575]: #20281
#26093 := [unit-resolution #20363 #9406]: #21556
#17079 := (>= #14585 0::Int)
#17150 := (or #14596 #14586)
#17143 := [def-axiom]: #17150
#26068 := [unit-resolution #17143 #27909]: #14586
#26119 := (or #14587 #17079)
#26097 := [th-lemma arith triangle-eq]: #26119
#26123 := [unit-resolution #26097 #26068]: #17079
#26122 := (not #21556)
#26105 := (not #17079)
#24754 := (or #21714 #26105 #23214 #26122)
#24755 := [th-lemma arith assign-bounds -1 -1 -1]: #24754
#24756 := [unit-resolution #24755 #26123 #26093 #24139]: #21714
#21871 := (<= #21870 0::Int)
#24757 := [hypothesis]: #21477
#26111 := (or #21522 #21871)
#21859 := (+ f3 #14583)
#21860 := (<= #21859 0::Int)
#24751 := (not #21860)
#21853 := (>= #14576 0::Int)
#20809 := (or #4267 #21853)
#20971 := [quant-inst #14575]: #20809
#24758 := [unit-resolution #20971 #7483]: #21853
#24759 := (not #21853)
#26112 := (or #24751 #24759 #26105 #2347 #23214)
#26113 := [th-lemma arith assign-bounds -1 -1 -1 -1]: #26112
#26114 := [unit-resolution #26113 #24139 #26123 #24758 #27906]: #24751
#21876 := (or #21522 #21860 #21871)
#4100 := (or #4449 #4433)
#3982 := [def-axiom]: #4100
#26107 := [unit-resolution #3982 #24122]: #4433
#21086 := (or #4438 #21522 #21860 #21871)
#21854 := (+ #21523 #2336)
#21855 := (+ #14582 #21854)
#21858 := (>= #21855 0::Int)
#21861 := (or #21522 #21860 #21858)
#19355 := (or #4438 #21861)
#20727 := (iff #19355 #21086)
#21085 := (or #4438 #21876)
#20589 := (iff #21085 #21086)
#20710 := [rewrite]: #20589
#19663 := (iff #19355 #21085)
#21877 := (iff #21861 #21876)
#21874 := (iff #21858 #21871)
#21862 := (+ #14582 #21523)
#21863 := (+ #2336 #21862)
#21866 := (>= #21863 0::Int)
#21872 := (iff #21866 #21871)
#21873 := [rewrite]: #21872
#21867 := (iff #21858 #21866)
#21864 := (= #21855 #21863)
#21865 := [rewrite]: #21864
#21868 := [monotonicity #21865]: #21867
#21875 := [trans #21868 #21873]: #21874
#21878 := [monotonicity #21875]: #21877
#20934 := [monotonicity #21878]: #19663
#20115 := [trans #20934 #20710]: #20727
#19367 := [quant-inst #2334 #14575]: #19355
#20114 := [mp #19367 #20115]: #21086
#26110 := [unit-resolution #20114 #26107]: #21876
#26125 := [unit-resolution #26110 #26114]: #26111
#26126 := [unit-resolution #26125 #24757]: #21871
#22038 := (= #21870 0::Int)
#22043 := (not #22038)
#22027 := (+ #2335 #21555)
#22028 := (<= #22027 0::Int)
#25515 := (not #22028)
#21997 := (<= #14582 0::Int)
#21999 := (not #21997)
#17136 := (not #14579)
#17144 := (or #14596 #17136)
#17151 := [def-axiom]: #17144
#24752 := [unit-resolution #17151 #27909]: #17136
#17078 := (<= #14585 0::Int)
#24753 := (or #14587 #17078)
#26121 := [th-lemma arith triangle-eq]: #24753
#26098 := [unit-resolution #26121 #26068]: #17078
#26102 := (not #17078)
#25350 := (or #21999 #26102 #14579)
#25344 := [th-lemma arith assign-bounds 1 -1]: #25350
#25517 := [unit-resolution #25344 #26098 #24752]: #21999
#25326 := (or #25515 #21997 #26105 #23214 #26122)
#26104 := [th-lemma arith assign-bounds -1 -1 -1 -1]: #25326
#25720 := [unit-resolution #26104 #26123 #26093 #25517 #24139]: #25515
#22046 := (or #21522 #22028 #22043)
#21521 := (or #4446 #21522 #22028 #22043)
#22015 := (+ #2336 #14582)
#22016 := (+ #21523 #22015)
#22017 := (= #22016 0::Int)
#22018 := (not #22017)
#22019 := (>= #21854 0::Int)
#22020 := (or #21522 #22019 #22018)
#21529 := (or #4446 #22020)
#21679 := (iff #21529 #21521)
#21554 := (or #4446 #22046)
#21539 := (iff #21554 #21521)
#21682 := [rewrite]: #21539
#21688 := (iff #21529 #21554)
#22047 := (iff #22020 #22046)
#22044 := (iff #22018 #22043)
#22041 := (iff #22017 #22038)
#22035 := (= #21863 0::Int)
#22039 := (iff #22035 #22038)
#22040 := [rewrite]: #22039
#22036 := (iff #22017 #22035)
#22033 := (= #22016 #21863)
#22034 := [rewrite]: #22033
#22037 := [monotonicity #22034]: #22036
#22042 := [trans #22037 #22040]: #22041
#22045 := [monotonicity #22042]: #22044
#22031 := (iff #22019 #22028)
#22021 := (+ #2336 #21523)
#22024 := (>= #22021 0::Int)
#22029 := (iff #22024 #22028)
#22030 := [rewrite]: #22029
#22025 := (iff #22019 #22024)
#22022 := (= #21854 #22021)
#22023 := [rewrite]: #22022
#22026 := [monotonicity #22023]: #22025
#22032 := [trans #22026 #22030]: #22031
#22048 := [monotonicity #22032 #22045]: #22047
#21713 := [monotonicity #22048]: #21688
#21680 := [trans #21713 #21682]: #21679
#21559 := [quant-inst #14575]: #21529
#21717 := [mp #21559 #21680]: #21521
#26092 := [unit-resolution #21717 #24123]: #22046
#25743 := [unit-resolution #26092 #24757 #25720]: #22043
#25831 := (not #21714)
#25327 := (not #21871)
#25832 := (or #22038 #25327 #25831)
#26091 := [th-lemma arith triangle-eq]: #25832
#26003 := [unit-resolution #26091 #25743 #26126 #24756]: false
#26005 := [lemma #26003]: #21522
[unit-resolution #26005 #24153]: false
unsat