updated SMT certificates
authorboehmes
Sun, 26 Jun 2011 19:10:03 +0200
changeset 43555 93c1fc6ac527
parent 43554 9bece8cbb5be
child 43556 0d78c8d31d0d
updated SMT certificates
src/HOL/Boogie/Examples/Boogie_Dijkstra.certs
src/HOL/Boogie/Examples/Boogie_Max.certs
src/HOL/Boogie/Examples/VCC_Max.certs
src/HOL/Multivariate_Analysis/Integration.certs
src/HOL/SMT_Examples/SMT_Examples.certs
src/HOL/SMT_Examples/SMT_Tests.certs
src/HOL/SMT_Examples/SMT_Word_Examples.certs
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Sun Jun 26 19:10:02 2011 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Sun Jun 26 19:10:03 2011 +0200
@@ -1,6836 +1,7164 @@
-bb58c98b1c1f10bf4f2103c003d8f48ec713787b 6835 0
+a7dbe4783d45017a8218697dc955b8483ad44034 7163 0
 #2 := false
-#8 := 0::Int
-decl f13 :: (-> S5 S2 Int)
+decl f11 :: (-> S7 S2 S1)
 decl ?v1!7 :: (-> S2 S2)
 decl ?v0!20 :: S2
-#2314 := ?v0!20
-#19459 := (?v1!7 ?v0!20)
-decl f14 :: S5
-#99 := f14
-#19460 := (f13 f14 #19459)
-#1176 := -1::Int
-#19461 := (* -1::Int #19460)
-#19006 := (f13 f14 ?v0!20)
-#19462 := (+ #19006 #19461)
-#19463 := (<= #19462 0::Int)
-#24892 := (not #19463)
-decl f8 :: (-> S4 S2 S1)
-decl f15 :: S4
-#105 := f15
-#19471 := (f8 f15 #19459)
+#2334 := ?v0!20
+#14575 := (?v1!7 ?v0!20)
+decl f29 :: S7
+#191 := f29
+#21476 := (f11 f29 #14575)
 decl f1 :: S1
 #4 := f1
-#19472 := (= f1 #19471)
-#19473 := (not #19472)
+#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)
-decl f5 :: (-> S2 S2 S3)
-#19464 := (f5 #19459 ?v0!20)
-#19465 := (f4 #19464)
-#19466 := (* -1::Int #19465)
-#19467 := (+ #19461 #19466)
-#19468 := (+ #19006 #19467)
-#19469 := (= #19468 0::Int)
-#19470 := (not #19469)
-#19479 := (or #19463 #19470 #19473)
-#19482 := (not #19479)
-#19047 := (* -1::Int #19006)
+#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
-#19476 := (+ f3 #19047)
-#19477 := (<= #19476 0::Int)
-#34297 := (not #19477)
-decl f24 :: (-> S2 Int)
-#2315 := (f24 ?v0!20)
-#2316 := (* -1::Int #2315)
-#2326 := (+ f3 #2316)
-#2327 := (<= #2326 0::Int)
-#2328 := (not #2327)
-#12 := (:var 0 S2)
-#2318 := (f5 #12 ?v0!20)
-#4422 := (pattern #2318)
-#189 := (f24 #12)
-#4362 := (pattern #189)
-decl f23 :: S4
-#180 := f23
-#199 := (f8 f23 #12)
-#4388 := (pattern #199)
-#2319 := (f4 #2318)
-#2918 := (+ #2316 #2319)
-#2919 := (+ #189 #2918)
-#2922 := (= #2919 0::Int)
-#3484 := (not #2922)
-#2317 := (+ #189 #2316)
-#2322 := (>= #2317 0::Int)
-#775 := (= f1 #199)
-#781 := (not #775)
-#3485 := (or #781 #2322 #3484)
-#4423 := (forall (vars (?v1 S2)) (:pat #4388 #4362 #4422) #3485)
-#4428 := (not #4423)
-#11 := (:var 1 S2)
-#82 := (f5 #12 #11)
-#4217 := (pattern #82)
-#211 := (f24 #11)
-#1471 := (* -1::Int #211)
-#1472 := (+ #189 #1471)
-#83 := (f4 #82)
-#1502 := (+ #83 #1472)
-#1500 := (>= #1502 0::Int)
-#1199 := (* -1::Int #83)
-#1202 := (+ f3 #1199)
-#1203 := (<= #1202 0::Int)
-#3476 := (or #781 #1203 #1500)
-#4414 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4217) #3476)
-#4419 := (not #4414)
-decl f10 :: S2
-#56 := f10
-#2894 := (= f10 ?v0!20)
-#4431 := (or #2327 #2894 #4419 #4428)
-#4434 := (not #4431)
+#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
-#2284 := ?v0!19
+#2303 := ?v0!19
 decl ?v1!18 :: S2
-#2283 := ?v1!18
-#2289 := (f5 ?v1!18 ?v0!19)
-#2290 := (f4 #2289)
-#2293 := (* -1::Int #2290)
-#2287 := (f24 ?v1!18)
-#2880 := (* -1::Int #2287)
-#2881 := (+ #2880 #2293)
-#2285 := (f24 ?v0!19)
-#2882 := (+ #2285 #2881)
-#2883 := (<= #2882 0::Int)
-#2297 := (f8 f23 ?v1!18)
-#2298 := (= f1 #2297)
-#3439 := (not #2298)
-#2294 := (+ f3 #2293)
-#2295 := (<= #2294 0::Int)
-#3454 := (or #2295 #3439 #2883)
-#2296 := (not #2295)
-#3459 := (not #3454)
-#26093 := [hypothesis]: #3459
-#4082 := (or #3454 #2296)
-#4088 := [def-axiom]: #4082
-#26260 := [unit-resolution #4088 #26093]: #2296
-#4089 := (or #3454 #2298)
-#4083 := [def-axiom]: #4089
-#26253 := [unit-resolution #4083 #26093]: #2298
-#4090 := (not #2883)
-#3919 := (or #3454 #4090)
-#3921 := [def-axiom]: #3919
-#24467 := [unit-resolution #3921 #26093]: #4090
-#23366 := (or #3439 #2295 #2883)
-decl f22 :: S2
-#171 := f22
-#7763 := (f5 f22 ?v0!19)
-#7764 := (f4 #7763)
-#7706 := (f13 f14 ?v0!19)
-#7747 := (* -1::Int #7706)
-#7782 := (+ #7747 #7764)
-#175 := (f13 f14 f22)
-#7783 := (+ #175 #7782)
-#7784 := (>= #7783 0::Int)
-#22698 := (not #7784)
-#7768 := (* -1::Int #7764)
-#23161 := (+ #2290 #7768)
-#23171 := (>= #23161 0::Int)
-#23160 := (= #2290 #7764)
-#22435 := (= #2289 #7763)
-#23292 := (= ?v1!18 f22)
-decl f7 :: (-> S3 S2)
-#6107 := (f5 f22 f22)
-#6633 := (f7 #6107)
-#10520 := (= #6633 f22)
-#6642 := (= f22 #6633)
-#13768 := (not #6642)
-#13791 := [hypothesis]: #13768
-#14 := (f5 #11 #12)
-#4139 := (pattern #14)
-#26 := (f7 #14)
-#351 := (= #12 #26)
-#4158 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4139) #351)
-#355 := (forall (vars (?v0 S2) (?v1 S2)) #351)
-#4161 := (iff #355 #4158)
-#4159 := (iff #351 #351)
-#4160 := [refl]: #4159
-#4162 := [quant-intro #4160]: #4161
-#1816 := (~ #355 #355)
-#1841 := (~ #351 #351)
-#1842 := [refl]: #1841
-#1817 := [nnf-pos #1842]: #1816
-#27 := (= #26 #12)
-#28 := (forall (vars (?v0 S2) (?v1 S2)) #27)
-#356 := (iff #28 #355)
-#353 := (iff #27 #351)
-#354 := [rewrite]: #353
-#357 := [quant-intro #354]: #356
-#350 := [asserted]: #28
-#360 := [mp #350 #357]: #355
-#1843 := [mp~ #360 #1817]: #355
-#4163 := [mp #1843 #4162]: #4158
-#6483 := (not #4158)
-#6645 := (or #6483 #6642)
-#6646 := [quant-inst #171 #171]: #6645
-#13794 := [unit-resolution #6646 #4163 #13791]: false
-#13795 := [lemma #13794]: #6642
-#16510 := [symm #13795]: #10520
-#13580 := (= ?v1!18 #6633)
-#8146 := (f8 f15 ?v1!18)
-#8147 := (= f1 #8146)
-decl f9 :: (-> S4 S2 S1 S4)
-#181 := (f9 f15 f22 f1)
-#5797 := (f8 #181 f22)
-#5798 := (= f1 #5797)
-#13581 := (ite #13580 #5798 #8147)
-#8578 := (f9 f15 #6633 #5797)
-#13582 := (f8 #8578 ?v1!18)
-#13583 := (= f1 #13582)
-#13585 := (iff #13581 #13583)
-#45 := (:var 1 S1)
-#44 := (:var 2 S2)
-#43 := (:var 3 S4)
-#46 := (f9 #43 #44 #45)
-#47 := (f8 #46 #12)
-#4179 := (pattern #47)
-#51 := (f8 #43 #12)
-#388 := (= f1 #51)
-#385 := (= f1 #45)
-#49 := (= #12 #44)
-#391 := (ite #49 #385 #388)
-#381 := (= f1 #47)
-#394 := (iff #381 #391)
-#4180 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #4179) #394)
-#397 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) #394)
-#4183 := (iff #397 #4180)
-#4181 := (iff #394 #394)
-#4182 := [refl]: #4181
-#4184 := [quant-intro #4182]: #4183
-#1822 := (~ #397 #397)
-#1850 := (~ #394 #394)
-#1851 := [refl]: #1850
-#1823 := [nnf-pos #1851]: #1822
-#52 := (= #51 f1)
-#50 := (= #45 f1)
-#53 := (ite #49 #50 #52)
-#48 := (= #47 f1)
-#54 := (iff #48 #53)
-#55 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) #54)
-#398 := (iff #55 #397)
-#395 := (iff #54 #394)
-#392 := (iff #53 #391)
-#389 := (iff #52 #388)
-#390 := [rewrite]: #389
-#386 := (iff #50 #385)
-#387 := [rewrite]: #386
-#393 := [monotonicity #387 #390]: #392
-#383 := (iff #48 #381)
-#384 := [rewrite]: #383
-#396 := [monotonicity #384 #393]: #395
-#399 := [quant-intro #396]: #398
-#380 := [asserted]: #55
-#402 := [mp #380 #399]: #397
-#1852 := [mp~ #402 #1823]: #397
-#4185 := [mp #1852 #4184]: #4180
-#6350 := (not #4180)
-#22066 := (or #6350 #13585)
-#13584 := (iff #13583 #13581)
-#22070 := (or #6350 #13584)
-#22072 := (iff #22070 #22066)
-#22073 := (iff #22066 #22066)
-#22074 := [rewrite]: #22073
-#13586 := (iff #13584 #13585)
-#13587 := [rewrite]: #13586
-#22067 := [monotonicity #13587]: #22072
-#22076 := [trans #22067 #22074]: #22072
-#22071 := [quant-inst #105 #6633 #5797 #2283]: #22070
-#22077 := [mp #22071 #22076]: #22066
-#23294 := [unit-resolution #22077 #4185]: #13585
-#23299 := (= #2297 #13582)
-#23295 := (= #13582 #2297)
-#10524 := (= #8578 f23)
-#6551 := (= #181 f23)
-#182 := (= f23 #181)
-#4437 := (or #3459 #4434)
-#4440 := (not #4437)
-#4405 := (pattern #189 #211)
-#1470 := (>= #1472 0::Int)
-#208 := (f8 f23 #11)
-#795 := (= f1 #208)
-#3416 := (not #795)
-#3431 := (or #775 #3416 #1470)
-#4406 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4405) #3431)
-#4411 := (not #4406)
-#4443 := (or #4411 #4440)
-#4446 := (not #4443)
+#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
-#2256 := ?v1!16
-#2260 := (f24 ?v1!16)
-#2854 := (* -1::Int #2260)
+#2275 := ?v1!16
+#2279 := (f30 ?v1!16)
+#2874 := (* -1::Int #2279)
 decl ?v0!17 :: S2
-#2257 := ?v0!17
-#2258 := (f24 ?v0!17)
-#2855 := (+ #2258 #2854)
-#2856 := (<= #2855 0::Int)
-#2265 := (f8 f23 ?v1!16)
-#2266 := (= f1 #2265)
-#2263 := (f8 f23 ?v0!17)
-#2264 := (= f1 #2263)
-#3393 := (not #2264)
-#3408 := (or #3393 #2266 #2856)
-#3413 := (not #3408)
-#4449 := (or #3413 #4446)
-#4452 := (not #4449)
-#1461 := (>= #189 0::Int)
-#4397 := (forall (vars (?v0 S2)) (:pat #4362) #1461)
-#4402 := (not #4397)
-#4455 := (or #4402 #4452)
-#4458 := (not #4455)
-decl ?v0!15 :: S2
-#2241 := ?v0!15
-#2242 := (f24 ?v0!15)
-#2243 := (>= #2242 0::Int)
-#2244 := (not #2243)
-#4461 := (or #2244 #4458)
-#4464 := (not #4461)
-#203 := (f24 f10)
-#204 := (= #203 0::Int)
-#1458 := (not #204)
-#4467 := (or #1458 #4464)
+#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)
-#4473 := (or #1458 #4470)
+#1475 := (>= #203 0::Int)
+#4416 := (forall (vars (?v0 S2)) (:pat #4381) #1475)
+#4421 := (not #4416)
+#4473 := (or #4421 #4470)
 #4476 := (not #4473)
-#102 := (f13 f14 #12)
-#4241 := (pattern #102)
-#761 := (= #102 #189)
-#782 := (or #761 #781)
-#4389 := (forall (vars (?v0 S2)) (:pat #4241 #4362 #4388) #782)
-#4394 := (not #4389)
-#4479 := (or #4394 #4476)
+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)
-decl ?v0!14 :: S2
-#2216 := ?v0!14
-#2221 := (f13 f14 ?v0!14)
-#2220 := (f24 ?v0!14)
-#2826 := (= #2220 #2221)
-#2217 := (f8 f23 ?v0!14)
-#2218 := (= f1 #2217)
-#2219 := (not #2218)
-#2832 := (or #2219 #2826)
-#2837 := (not #2832)
-#4485 := (or #2837 #4482)
+#217 := (f30 f16)
+#218 := (= #217 0::Int)
+#1472 := (not #218)
+#4485 := (or #1472 #4482)
 #4488 := (not #4485)
-#1446 := (* -1::Int #189)
-#1447 := (+ #102 #1446)
-#1445 := (>= #1447 0::Int)
-#4380 := (forall (vars (?v0 S2)) (:pat #4241 #4362) #1445)
-#4385 := (not #4380)
-#4491 := (or #4385 #4488)
+#4491 := (or #1472 #4488)
 #4494 := (not #4491)
-decl ?v0!13 :: S2
-#2198 := ?v0!13
-#2201 := (f13 f14 ?v0!13)
-#2816 := (* -1::Int #2201)
-#2199 := (f24 ?v0!13)
-#2817 := (+ #2199 #2816)
-#2818 := (<= #2817 0::Int)
-#2823 := (not #2818)
-#4497 := (or #2823 #4494)
+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)
-#183 := (f5 f22 #12)
-#4363 := (pattern #183)
-#184 := (f4 #183)
-#1589 := (+ #184 #1446)
-#1590 := (+ #175 #1589)
-#1591 := (= #1590 0::Int)
-#1415 := (* -1::Int #184)
-#1421 := (* -1::Int #175)
-#1422 := (+ #1421 #1415)
-#1423 := (+ #102 #1422)
-#1424 := (<= #1423 0::Int)
-#1416 := (+ f3 #1415)
-#1417 := (<= #1416 0::Int)
-#3385 := (or #1417 #1424 #1591)
-#4372 := (forall (vars (?v0 S2)) (:pat #4363 #4241 #4362) #3385)
-#4377 := (not #4372)
-#3365 := (or #1417 #1424)
-#3366 := (not #3365)
-#3369 := (or #761 #3366)
-#4364 := (forall (vars (?v0 S2)) (:pat #4241 #4362 #4363) #3369)
-#4369 := (not #4364)
+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
-#2174 := ?v0!12
-#2180 := (f8 f15 ?v0!12)
-#2181 := (= f1 #2180)
-#2175 := (f13 f14 ?v0!12)
-#2176 := (* -1::Int #2175)
-#2177 := (+ f3 #2176)
-#2178 := (<= #2177 0::Int)
-#1621 := (+ f3 #1421)
-#1622 := (<= #1621 0::Int)
-#106 := (f8 f15 #12)
-#4283 := (pattern #106)
-#1604 := (+ #102 #1421)
-#1603 := (>= #1604 0::Int)
-#509 := (= f1 #106)
-#1610 := (or #509 #1603)
-#4354 := (forall (vars (?v0 S2)) (:pat #4283 #4241) #1610)
-#4359 := (not #4354)
-#172 := (f8 f15 f22)
-#730 := (= f1 #172)
-#963 := (not #182)
-#4503 := (or #963 #730 #4359 #1622 #2178 #2181 #4369 #4377 #4500)
-#4506 := (not #4503)
+#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
-#2108 := ?v0!11
+#2126 := ?v0!11
 decl ?v1!10 :: S2
-#2107 := ?v1!10
-#2113 := (f5 ?v1!10 ?v0!11)
-#2114 := (f4 #2113)
-#2121 := (* -1::Int #2114)
-decl f19 :: S5
-#138 := f19
-#2111 := (f13 f19 ?v1!10)
-#2117 := (* -1::Int #2111)
-#2773 := (+ #2117 #2121)
-#2109 := (f13 f19 ?v0!11)
-#2774 := (+ #2109 #2773)
-#2775 := (<= #2774 0::Int)
-#2122 := (+ f3 #2121)
-#2123 := (<= #2122 0::Int)
-#2118 := (+ f3 #2117)
-#2119 := (<= #2118 0::Int)
-#3329 := (or #2119 #2123 #2775)
-#3334 := (not #3329)
-#146 := (f13 f19 #11)
-#1323 := (* -1::Int #146)
-#143 := (f13 f19 #12)
-#1324 := (+ #143 #1323)
-#1330 := (+ #83 #1324)
-#1353 := (>= #1330 0::Int)
-#1310 := (* -1::Int #143)
-#1311 := (+ f3 #1310)
-#1312 := (<= #1311 0::Int)
-#3297 := (or #1203 #1312 #1353)
-#4316 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4217) #3297)
-#4321 := (not #4316)
-#158 := (f13 f19 f10)
-#159 := (= #158 0::Int)
-#4324 := (or #159 #4321)
-#4327 := (not #4324)
-#4330 := (or #4327 #3334)
-#4333 := (not #4330)
-#4292 := (pattern #143)
+#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)
-#2084 := (?v1!9 #12)
-#2087 := (f5 #2084 #12)
-#2088 := (f4 #2087)
-#2743 := (* -1::Int #2088)
-#2085 := (f13 f19 #2084)
-#2726 := (* -1::Int #2085)
-#2744 := (+ #2726 #2743)
-#2745 := (+ #143 #2744)
-#2746 := (= #2745 0::Int)
-#3267 := (not #2746)
-#2727 := (+ #143 #2726)
-#2728 := (<= #2727 0::Int)
-#3268 := (or #2728 #3267)
-#3269 := (not #3268)
-#57 := (= #12 f10)
-#3275 := (or #57 #1312 #3269)
-#4308 := (forall (vars (?v0 S2)) (:pat #4292) #3275)
-#4313 := (not #4308)
-#4336 := (or #4313 #4333)
-#4339 := (not #4336)
+#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
-#2044 := ?v0!8
-#2048 := (f5 #12 ?v0!8)
-#4293 := (pattern #2048)
-#2049 := (f4 #2048)
-#2045 := (f13 f19 ?v0!8)
-#2046 := (* -1::Int #2045)
-#2696 := (+ #2046 #2049)
-#2697 := (+ #143 #2696)
-#2700 := (= #2697 0::Int)
-#3231 := (not #2700)
-#2047 := (+ #143 #2046)
-#2052 := (>= #2047 0::Int)
-#3232 := (or #2052 #3231)
-#4294 := (forall (vars (?v1 S2)) (:pat #4292 #4293) #3232)
-#4299 := (not #4294)
-#2672 := (= f10 ?v0!8)
-#2056 := (+ f3 #2046)
-#2057 := (<= #2056 0::Int)
-#4302 := (or #2057 #2672 #4299)
-#4305 := (not #4302)
-#4342 := (or #4305 #4339)
-#4345 := (not #4342)
-#1265 := (* -1::Int #102)
-#1266 := (+ f3 #1265)
-#1267 := (<= #1266 0::Int)
-#3217 := (or #509 #1267)
-#4284 := (forall (vars (?v0 S2)) (:pat #4283 #4241) #3217)
-#4289 := (not #4284)
-#600 := (= f14 f19)
-#691 := (not #600)
-decl f16 :: S4
-#133 := f16
-#597 := (= f15 f16)
-#709 := (not #597)
-decl f21 :: S5
-#141 := f21
-decl f20 :: S5
-#140 := f20
-#142 := (= f20 f21)
-#682 := (not #142)
-decl f18 :: S2
-#136 := f18
-decl f17 :: S2
-#135 := f17
-#137 := (= f17 f18)
-#700 := (not #137)
-#4348 := (or #700 #682 #709 #691 #4289 #4345)
-#4796 := (?v1!7 ?v0!8)
-#5111 := (f13 f19 #4796)
-#5157 := (* -1::Int #5111)
-#4797 := (f13 f14 #4796)
-#6353 := (+ #4797 #5157)
-#6357 := (<= #6353 0::Int)
-#6352 := (= #4797 #5111)
-#9885 := (= #5111 #4797)
-#139 := (= f19 f14)
-#4351 := (not #4348)
-#9784 := [hypothesis]: #4351
-#4102 := (or #4348 #600)
-#4103 := [def-axiom]: #4102
-#9853 := [unit-resolution #4103 #9784]: #600
-#9854 := [symm #9853]: #139
-#9886 := [monotonicity #9854]: #9885
-#9783 := [symm #9886]: #6352
-#9887 := (not #6352)
-#9815 := (or #9887 #6357)
-#9719 := [th-lemma arith triangle-eq]: #9815
-#9720 := [unit-resolution #9719 #9783]: #6357
-#4729 := (f13 f14 ?v0!8)
-#4730 := (* -1::Int #4729)
-#5068 := (+ #2045 #4730)
-#6038 := (<= #5068 0::Int)
-#6037 := (= #2045 #4729)
-#9773 := (= #4729 #2045)
-#10654 := [monotonicity #9853]: #9773
-#10651 := [symm #10654]: #6037
-#10657 := (not #6037)
-#10656 := (or #10657 #6038)
-#10658 := [th-lemma arith triangle-eq]: #10656
-#10659 := [unit-resolution #10658 #10651]: #6038
-#4798 := (* -1::Int #4797)
-#4782 := (f5 #4796 ?v0!8)
-#4783 := (f4 #4782)
-#4784 := (* -1::Int #4783)
-#4864 := (+ #4784 #4798)
-#4865 := (+ #4729 #4864)
-#4951 := (<= #4865 0::Int)
-#4868 := (= #4865 0::Int)
-#4850 := (not #4868)
-#4799 := (+ #4729 #4798)
-#4800 := (<= #4799 0::Int)
-#4788 := (f8 f15 #4796)
-#4789 := (= f1 #4788)
-#4790 := (not #4789)
-#4855 := (or #4790 #4800 #4850)
-#4874 := (not #4855)
-#4731 := (+ f3 #4730)
-#4732 := (<= #4731 0::Int)
-#10943 := (not #4732)
-#5109 := (>= #5068 0::Int)
-#10709 := (or #10657 #5109)
-#10829 := [th-lemma arith triangle-eq]: #10709
-#10802 := [unit-resolution #10829 #10651]: #5109
-#2058 := (not #2057)
-#4104 := (or #4348 #4342)
-#4101 := [def-axiom]: #4104
-#10253 := [unit-resolution #4101 #9784]: #4342
-#3818 := (or #4348 #4284)
-#4100 := [def-axiom]: #3818
-#10315 := [unit-resolution #4100 #9784]: #4284
-#10697 := (or #3329 #4289 #691)
-#112 := (f13 f14 #11)
-#1279 := (* -1::Int #112)
-#1280 := (+ #102 #1279)
-#1281 := (+ #83 #1280)
-#1676 := (>= #1281 0::Int)
-#512 := (not #509)
-#3130 := (or #512 #1203 #1676)
-#4250 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4217) #3130)
-#4509 := (or #4351 #4506)
-#4512 := (not #4509)
-#2007 := (?v1!7 #12)
-#2008 := (f13 f14 #2007)
-#2631 := (* -1::Int #2008)
-#2646 := (+ #102 #2631)
-#2647 := (<= #2646 0::Int)
-#2012 := (f5 #2007 #12)
-#2013 := (f4 #2012)
-#2632 := (* -1::Int #2013)
-#2633 := (+ #2631 #2632)
-#2634 := (+ #102 #2633)
-#2635 := (= #2634 0::Int)
-#3201 := (not #2635)
-#2016 := (f8 f15 #2007)
-#2017 := (= f1 #2016)
-#3200 := (not #2017)
-#3202 := (or #3200 #3201 #2647)
-#3203 := (not #3202)
-#3209 := (or #57 #1267 #3203)
-#4275 := (forall (vars (?v0 S2)) (:pat #4241) #3209)
-#4280 := (not #4275)
-decl f11 :: (-> S2 Int)
-#58 := (f11 #12)
-#4186 := (pattern #58)
+#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)
-#1979 := (?v1!6 #12)
-#1983 := (f11 #1979)
-#2590 := (* -1::Int #1983)
-#1980 := (f5 #1979 #12)
-#1981 := (f4 #1980)
-#2607 := (* -1::Int #1981)
-#2608 := (+ #2607 #2590)
-#2609 := (+ #58 #2608)
-#2610 := (= #2609 0::Int)
-#3173 := (not #2610)
-#2591 := (+ #58 #2590)
-#2592 := (<= #2591 0::Int)
-decl f12 :: S4
-#66 := f12
-#1989 := (f8 f12 #1979)
-#1990 := (= f1 #1989)
-#3172 := (not #1990)
-#3174 := (or #3172 #2592 #3173)
-#3175 := (not #3174)
-#1227 := (* -1::Int #58)
-#1228 := (+ f3 #1227)
-#1229 := (<= #1228 0::Int)
-#3181 := (or #57 #1229 #3175)
-#4267 := (forall (vars (?v0 S2)) (:pat #4186) #3181)
-#4272 := (not #4267)
-#109 := (f8 f15 #11)
-#4258 := (pattern #106 #109)
-#1283 := (>= #1280 0::Int)
-#515 := (= f1 #109)
-#3138 := (not #515)
-#3153 := (or #509 #3138 #1283)
-#4259 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4258) #3153)
-#4264 := (not #4259)
-#4255 := (not #4250)
-#1704 := (>= #102 0::Int)
-#4242 := (forall (vars (?v0 S2)) (:pat #4241) #1704)
-#4247 := (not #4242)
-#100 := (f13 f14 f10)
-#101 := (= #100 0::Int)
-#1715 := (not #101)
-#4515 := (or #1715 #4247 #4255 #4264 #4272 #4280 #4512)
-#4518 := (not #4515)
+#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
-#1935 := ?v0!5
-#1936 := (f5 #12 ?v0!5)
-#4226 := (pattern #1936)
-#67 := (f8 f12 #12)
-#4193 := (pattern #67)
-#1938 := (f11 ?v0!5)
-#1939 := (* -1::Int #1938)
-#1937 := (f4 #1936)
-#2558 := (+ #1937 #1939)
-#2559 := (+ #58 #2558)
-#2562 := (= #2559 0::Int)
-#3091 := (not #2562)
-#1943 := (+ #58 #1939)
-#1944 := (>= #1943 0::Int)
-#430 := (= f1 #67)
-#433 := (not #430)
-#3092 := (or #433 #1944 #3091)
-#4227 := (forall (vars (?v1 S2)) (:pat #4193 #4186 #4226) #3092)
-#4232 := (not #4227)
-#2534 := (= f10 ?v0!5)
-#1948 := (+ f3 #1939)
-#1949 := (<= #1948 0::Int)
-#4235 := (or #1949 #2534 #4232)
-#4238 := (not #4235)
-#4521 := (or #4238 #4518)
-#4524 := (not #4521)
-#78 := (f11 #11)
-#1179 := (* -1::Int #78)
-#1200 := (+ #1179 #83)
-#1201 := (+ #58 #1200)
-#1198 := (>= #1201 0::Int)
-#3083 := (or #433 #1198 #1203)
-#4218 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4217) #3083)
-#4223 := (not #4218)
-#4527 := (or #4223 #4524)
-#4530 := (not #4527)
+#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
-#1904 := ?v1!3
-#1919 := (f11 ?v1!3)
+#1918 := ?v1!3
+#1934 := (f17 ?v1!3)
 decl ?v0!4 :: S2
-#1905 := ?v0!4
-#1916 := (f11 ?v0!4)
-#1917 := (* -1::Int #1916)
-#2515 := (+ #1917 #1919)
-#1906 := (f5 ?v1!3 ?v0!4)
-#1907 := (f4 #1906)
-#2516 := (+ #1907 #2515)
-#2519 := (>= #2516 0::Int)
-#1912 := (f8 f12 ?v1!3)
-#1913 := (= f1 #1912)
-#3046 := (not #1913)
-#1908 := (* -1::Int #1907)
-#1909 := (+ f3 #1908)
-#1910 := (<= #1909 0::Int)
-#3061 := (or #1910 #3046 #2519)
-#3066 := (not #3061)
-#4533 := (or #3066 #4530)
-#4536 := (not #4533)
-#4208 := (pattern #58 #78)
-#1180 := (+ #58 #1179)
-#1178 := (>= #1180 0::Int)
-#75 := (f8 f12 #11)
-#442 := (= f1 #75)
-#2487 := (not #442)
-#3038 := (or #430 #2487 #1178)
-#4209 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4208) #3038)
-#4214 := (not #4209)
-#4539 := (or #4214 #4536)
-#4542 := (not #4539)
-decl ?v1!1 :: S2
-#1877 := ?v1!1
-#1881 := (f11 ?v1!1)
-#2502 := (* -1::Int #1881)
-decl ?v0!2 :: S2
-#1878 := ?v0!2
-#1879 := (f11 ?v0!2)
-#2503 := (+ #1879 #2502)
-#2504 := (<= #2503 0::Int)
-#1886 := (f8 f12 ?v1!1)
-#1887 := (= f1 #1886)
-#1884 := (f8 f12 ?v0!2)
-#1885 := (= f1 #1884)
-#2097 := (not #1885)
-#2305 := (or #2097 #1887 #2504)
-#2275 := (not #2305)
-#4545 := (or #2275 #4542)
-#4548 := (not #4545)
-#1169 := (>= #58 0::Int)
-#4200 := (forall (vars (?v0 S2)) (:pat #4186) #1169)
-#4205 := (not #4200)
-#4551 := (or #4205 #4548)
-#4554 := (not #4551)
-decl ?v0!0 :: S2
-#1862 := ?v0!0
-#1863 := (f11 ?v0!0)
-#1864 := (>= #1863 0::Int)
-#294 := (<= f3 0::Int)
-#295 := (not #294)
-#10 := (< 0::Int f3)
-#296 := (iff #10 #295)
-#297 := [rewrite]: #296
-#291 := [asserted]: #10
-#298 := [mp #291 #297]: #295
-#3875 := (* -1::Int #1863)
-#4599 := (+ f3 #3875)
-#4722 := (<= #4599 0::Int)
-#3791 := (= f3 #1863)
-#3785 := (= f10 ?v0!0)
-#4961 := (not #3785)
-#4723 := (= #1863 0::Int)
-#5298 := (not #4723)
-#1865 := (not #1864)
-#5292 := [hypothesis]: #1865
-#5299 := (or #5298 #1864)
-#5300 := [th-lemma arith triangle-eq]: #5299
-#5280 := [unit-resolution #5300 #5292]: #5298
-#59 := (= #58 0::Int)
-#62 := (not #57)
-#1773 := (or #62 #59)
-#4573 := (forall (vars (?v0 S2)) (:pat #4186) #1773)
-#1776 := (forall (vars (?v0 S2)) #1773)
-#4576 := (iff #1776 #4573)
-#4574 := (iff #1773 #1773)
-#4575 := [refl]: #4574
-#4577 := [quant-intro #4575]: #4576
-#1868 := (~ #1776 #1776)
-#2207 := (~ #1773 #1773)
-#2208 := [refl]: #2207
-#1869 := [nnf-pos #2208]: #1868
-#1779 := (not #1776)
-#1707 := (forall (vars (?v0 S2)) #1704)
-#1710 := (not #1707)
-#518 := (and #512 #515)
-#524 := (not #518)
-#1693 := (or #524 #1283)
-#1698 := (forall (vars (?v0 S2) (?v1 S2)) #1693)
-#1701 := (not #1698)
-#1204 := (not #1203)
-#1668 := (and #509 #1204)
-#1673 := (not #1668)
-#1679 := (or #1673 #1676)
-#1682 := (forall (vars (?v0 S2) (?v1 S2)) #1679)
-#1685 := (not #1682)
-#1615 := (forall (vars (?v0 S2)) #1610)
-#1618 := (not #1615)
-#1425 := (not #1424)
-#1418 := (not #1417)
-#1428 := (and #1418 #1425)
-#1586 := (not #1428)
-#1594 := (or #1586 #1591)
-#1597 := (forall (vars (?v0 S2)) #1594)
-#1600 := (not #1597)
-#1524 := (= #1502 0::Int)
-#1527 := (not #1470)
-#1536 := (and #775 #1527 #1524)
-#1541 := (exists (vars (?v1 S2)) #1536)
-#1513 := (+ f3 #1446)
-#1514 := (<= #1513 0::Int)
-#1515 := (not #1514)
-#1518 := (and #62 #1515)
-#1521 := (not #1518)
-#1544 := (or #1521 #1541)
-#1547 := (forall (vars (?v0 S2)) #1544)
-#1492 := (and #775 #1204)
-#1497 := (not #1492)
-#1504 := (or #1497 #1500)
-#1507 := (forall (vars (?v0 S2) (?v1 S2)) #1504)
-#1510 := (not #1507)
-#1550 := (or #1510 #1547)
-#1553 := (and #1507 #1550)
-#798 := (and #781 #795)
-#804 := (not #798)
-#1478 := (or #804 #1470)
-#1483 := (forall (vars (?v0 S2) (?v1 S2)) #1478)
-#1486 := (not #1483)
-#1556 := (or #1486 #1553)
-#1559 := (and #1483 #1556)
-#1464 := (forall (vars (?v0 S2)) #1461)
+#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)
-#1562 := (or #1467 #1559)
-#1565 := (and #1464 #1562)
-#1568 := (or #1458 #1565)
-#1571 := (and #204 #1568)
-#787 := (forall (vars (?v0 S2)) #782)
-#921 := (not #787)
-#1574 := (or #921 #1571)
-#1577 := (and #787 #1574)
-#1450 := (forall (vars (?v0 S2)) #1445)
-#1453 := (not #1450)
-#1580 := (or #1453 #1577)
-#1583 := (and #1450 #1580)
-#1434 := (or #761 #1428)
-#1439 := (forall (vars (?v0 S2)) #1434)
-#1442 := (not #1439)
-#1268 := (not #1267)
-#1387 := (and #512 #1268)
-#1392 := (exists (vars (?v0 S2)) #1387)
-#1633 := (not #1392)
-#1657 := (or #963 #730 #1633 #1442 #1583 #1600 #1618 #1622)
-#1313 := (not #1312)
-#1347 := (and #1204 #1313)
-#1350 := (not #1347)
-#1356 := (or #1350 #1353)
-#1359 := (forall (vars (?v0 S2) (?v1 S2)) #1356)
-#1362 := (not #1359)
-#1370 := (or #159 #1362)
-#1375 := (and #1359 #1370)
-#1328 := (= #1330 0::Int)
-#1322 := (>= #1324 0::Int)
-#1325 := (not #1322)
-#1332 := (and #1325 #1328)
-#1335 := (exists (vars (?v1 S2)) #1332)
-#1316 := (and #62 #1313)
-#1319 := (not #1316)
-#1338 := (or #1319 #1335)
-#1341 := (forall (vars (?v0 S2)) #1338)
-#1344 := (not #1341)
-#1378 := (or #1344 #1375)
-#1381 := (and #1341 #1378)
-#1410 := (or #700 #682 #709 #691 #1381 #1392)
-#1662 := (and #1410 #1657)
-#1284 := (not #1283)
-#1277 := (= #1281 0::Int)
-#1293 := (and #509 #1277 #1284)
-#1298 := (exists (vars (?v1 S2)) #1293)
-#1271 := (and #62 #1268)
-#1274 := (not #1271)
-#1301 := (or #1274 #1298)
-#1304 := (forall (vars (?v0 S2)) #1301)
-#1307 := (not #1304)
-#1239 := (= #1201 0::Int)
-#1242 := (not #1178)
-#1251 := (and #430 #1242 #1239)
-#1256 := (exists (vars (?v1 S2)) #1251)
-#1230 := (not #1229)
-#1233 := (and #62 #1230)
-#1236 := (not #1233)
-#1259 := (or #1236 #1256)
-#1262 := (forall (vars (?v0 S2)) #1259)
-#1718 := (not #1262)
-#1739 := (or #1715 #1718 #1307 #1662 #1685 #1701 #1710)
-#1744 := (and #1262 #1739)
-#1210 := (and #430 #1204)
-#1215 := (not #1210)
-#1218 := (or #1198 #1215)
-#1221 := (forall (vars (?v0 S2) (?v1 S2)) #1218)
-#1224 := (not #1221)
-#1747 := (or #1224 #1744)
-#1750 := (and #1221 #1747)
-#445 := (and #433 #442)
-#451 := (not #445)
-#1185 := (or #451 #1178)
-#1190 := (forall (vars (?v0 S2) (?v1 S2)) #1185)
-#1193 := (not #1190)
-#1753 := (or #1193 #1750)
-#1756 := (and #1190 #1753)
-#1170 := (forall (vars (?v0 S2)) #1169)
-#1173 := (not #1170)
-#1759 := (or #1173 #1756)
-#1762 := (and #1170 #1759)
-#71 := (f11 f10)
-#72 := (= #71 0::Int)
-#1164 := (not #72)
-#1765 := (or #1164 #1762)
-#1768 := (and #72 #1765)
-#436 := (forall (vars (?v0 S2)) #433)
-#1128 := (not #436)
-#416 := (= f3 #58)
-#422 := (or #57 #416)
-#427 := (forall (vars (?v0 S2)) #422)
-#1137 := (not #427)
-#1791 := (or #1137 #1128 #1768 #1779)
-#1796 := (not #1791)
-#1 := true
-#216 := (+ #189 #83)
-#223 := (= #211 #216)
-#200 := (= #199 f1)
-#224 := (and #200 #223)
-#222 := (< #189 #211)
-#225 := (and #222 #224)
-#226 := (exists (vars (?v1 S2)) #225)
-#220 := (< #189 f3)
-#221 := (and #62 #220)
-#227 := (implies #221 #226)
-#228 := (forall (vars (?v0 S2)) #227)
-#229 := (and #228 true)
-#217 := (<= #211 #216)
-#84 := (< #83 f3)
-#215 := (and #200 #84)
-#218 := (implies #215 #217)
-#219 := (forall (vars (?v0 S2) (?v1 S2)) #218)
-#230 := (implies #219 #229)
-#231 := (and #219 #230)
-#212 := (<= #211 #189)
-#209 := (= #208 f1)
-#207 := (not #200)
-#210 := (and #207 #209)
-#213 := (implies #210 #212)
-#214 := (forall (vars (?v0 S2) (?v1 S2)) #213)
-#232 := (implies #214 #231)
-#233 := (and #214 #232)
-#205 := (<= 0::Int #189)
+#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)
-#234 := (implies #206 #233)
-#235 := (and #206 #234)
-#236 := (implies #204 #235)
-#237 := (and #204 #236)
-#194 := (= #189 #102)
-#201 := (implies #200 #194)
-#202 := (forall (vars (?v0 S2)) #201)
-#238 := (implies #202 #237)
-#239 := (and #202 #238)
-#197 := (<= #189 #102)
-#198 := (forall (vars (?v0 S2)) #197)
-#240 := (implies #198 #239)
-#241 := (and #198 #240)
-#186 := (+ #175 #184)
-#187 := (< #186 #102)
-#185 := (< #184 f3)
-#188 := (and #185 #187)
-#193 := (not #188)
-#195 := (implies #193 #194)
-#196 := (forall (vars (?v0 S2)) #195)
-#242 := (implies #196 #241)
-#190 := (= #189 #186)
-#191 := (implies #188 #190)
-#192 := (forall (vars (?v0 S2)) #191)
-#243 := (implies #192 #242)
-#244 := (implies #182 #243)
-#177 := (<= #175 #102)
-#107 := (= #106 f1)
-#108 := (not #107)
-#178 := (implies #108 #177)
-#179 := (forall (vars (?v0 S2)) #178)
-#245 := (implies #179 #244)
-#176 := (< #175 f3)
-#246 := (implies #176 #245)
-#173 := (= #172 f1)
-#174 := (not #173)
-#247 := (implies #174 #246)
-#121 := (< #102 f3)
-#130 := (and #108 #121)
-#131 := (exists (vars (?v0 S2)) #130)
-#248 := (implies #131 #247)
-#249 := (implies true #248)
-#160 := (and #159 true)
-#148 := (+ #143 #83)
-#155 := (<= #146 #148)
-#144 := (< #143 f3)
-#154 := (and #144 #84)
-#156 := (implies #154 #155)
-#157 := (forall (vars (?v0 S2) (?v1 S2)) #156)
-#161 := (implies #157 #160)
-#162 := (and #157 #161)
-#149 := (= #146 #148)
-#147 := (< #143 #146)
-#150 := (and #147 #149)
-#151 := (exists (vars (?v1 S2)) #150)
-#145 := (and #62 #144)
-#152 := (implies #145 #151)
-#153 := (forall (vars (?v0 S2)) #152)
-#163 := (implies #153 #162)
-#164 := (and #153 #163)
-#165 := (implies #142 #164)
-#166 := (implies #139 #165)
-#167 := (implies #137 #166)
-#134 := (= f16 f15)
-#168 := (implies #134 #167)
-#132 := (not #131)
-#169 := (implies #132 #168)
-#170 := (implies true #169)
-#250 := (and #170 #249)
-#117 := (+ #102 #83)
-#124 := (= #112 #117)
-#125 := (and #107 #124)
-#123 := (< #102 #112)
-#126 := (and #123 #125)
-#127 := (exists (vars (?v1 S2)) #126)
-#122 := (and #62 #121)
-#128 := (implies #122 #127)
-#129 := (forall (vars (?v0 S2)) #128)
-#251 := (implies #129 #250)
-#118 := (<= #112 #117)
-#116 := (and #107 #84)
-#119 := (implies #116 #118)
-#120 := (forall (vars (?v0 S2) (?v1 S2)) #119)
-#252 := (implies #120 #251)
-#113 := (<= #112 #102)
-#110 := (= #109 f1)
-#111 := (and #108 #110)
-#114 := (implies #111 #113)
-#115 := (forall (vars (?v0 S2) (?v1 S2)) #114)
-#253 := (implies #115 #252)
-#103 := (<= 0::Int #102)
-#104 := (forall (vars (?v0 S2)) #103)
-#254 := (implies #104 #253)
-#255 := (implies #101 #254)
-#256 := (implies true #255)
-#86 := (+ #58 #83)
-#93 := (= #78 #86)
-#68 := (= #67 f1)
-#94 := (and #68 #93)
-#92 := (< #58 #78)
-#95 := (and #92 #94)
-#96 := (exists (vars (?v1 S2)) #95)
-#90 := (< #58 f3)
-#91 := (and #62 #90)
-#97 := (implies #91 #96)
-#98 := (forall (vars (?v0 S2)) #97)
-#257 := (implies #98 #256)
-#258 := (and #98 #257)
-#87 := (<= #78 #86)
-#85 := (and #68 #84)
-#88 := (implies #85 #87)
-#89 := (forall (vars (?v0 S2) (?v1 S2)) #88)
-#259 := (implies #89 #258)
-#260 := (and #89 #259)
-#79 := (<= #78 #58)
-#76 := (= #75 f1)
-#69 := (not #68)
-#77 := (and #69 #76)
-#80 := (implies #77 #79)
-#81 := (forall (vars (?v0 S2) (?v1 S2)) #80)
-#261 := (implies #81 #260)
-#262 := (and #81 #261)
-#73 := (<= 0::Int #58)
-#74 := (forall (vars (?v0 S2)) #73)
-#263 := (implies #74 #262)
-#264 := (and #74 #263)
-#265 := (implies #72 #264)
-#266 := (and #72 #265)
-#70 := (forall (vars (?v0 S2)) #69)
-#267 := (implies #70 #266)
-#63 := (= #58 f3)
-#64 := (implies #62 #63)
-#65 := (forall (vars (?v0 S2)) #64)
-#268 := (implies #65 #267)
-#60 := (implies #57 #59)
-#61 := (forall (vars (?v0 S2)) #60)
-#269 := (implies #61 #268)
+#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)
-#271 := (not #270)
-#1799 := (iff #271 #1796)
-#821 := (+ #83 #189)
-#839 := (= #211 #821)
-#842 := (and #775 #839)
-#845 := (and #222 #842)
-#848 := (exists (vars (?v1 S2)) #845)
-#854 := (not #221)
-#855 := (or #854 #848)
-#860 := (forall (vars (?v0 S2)) #855)
-#824 := (<= #211 #821)
-#816 := (and #84 #775)
-#830 := (not #816)
-#831 := (or #830 #824)
-#836 := (forall (vars (?v0 S2) (?v1 S2)) #831)
-#873 := (not #836)
-#874 := (or #873 #860)
-#879 := (and #836 #874)
-#805 := (or #212 #804)
-#810 := (forall (vars (?v0 S2) (?v1 S2)) #805)
-#885 := (not #810)
-#886 := (or #885 #879)
-#891 := (and #810 #886)
-#897 := (not #206)
-#898 := (or #897 #891)
-#903 := (and #206 #898)
-#790 := (= 0::Int #203)
-#909 := (not #790)
-#910 := (or #909 #903)
-#915 := (and #790 #910)
-#922 := (or #921 #915)
-#927 := (and #787 #922)
-#933 := (not #198)
-#934 := (or #933 #927)
-#939 := (and #198 #934)
-#767 := (or #188 #761)
+#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)
-#945 := (not #772)
-#946 := (or #945 #939)
-#747 := (= #186 #189)
-#753 := (or #193 #747)
+#968 := (not #772)
+#969 := (or #968 #960)
+#978 := (or #977 #969)
+#753 := (or #188 #523)
 #758 := (forall (vars (?v0 S2)) #753)
-#954 := (not #758)
-#955 := (or #954 #946)
-#964 := (or #963 #955)
-#739 := (or #177 #509)
-#744 := (forall (vars (?v0 S2)) #739)
-#972 := (not #744)
-#973 := (or #972 #964)
-#981 := (not #176)
-#982 := (or #981 #973)
-#990 := (or #730 #982)
-#586 := (and #121 #512)
-#591 := (exists (vars (?v0 S2)) #586)
-#594 := (not #591)
-#998 := (or #594 #990)
-#645 := (= 0::Int #158)
-#603 := (+ #83 #143)
-#630 := (<= #146 #603)
-#627 := (and #84 #144)
-#636 := (not #627)
-#637 := (or #636 #630)
-#642 := (forall (vars (?v0 S2) (?v1 S2)) #637)
-#658 := (not #642)
-#659 := (or #658 #645)
-#664 := (and #642 #659)
-#606 := (= #146 #603)
-#609 := (and #147 #606)
-#612 := (exists (vars (?v1 S2)) #609)
-#618 := (not #145)
-#619 := (or #618 #612)
-#624 := (forall (vars (?v0 S2)) #619)
-#670 := (not #624)
-#671 := (or #670 #664)
-#676 := (and #624 #671)
-#683 := (or #682 #676)
-#692 := (or #691 #683)
-#701 := (or #700 #692)
-#710 := (or #709 #701)
-#718 := (or #591 #710)
-#1010 := (and #718 #998)
-#541 := (+ #83 #102)
-#559 := (= #112 #541)
-#562 := (and #509 #559)
-#565 := (and #123 #562)
-#568 := (exists (vars (?v1 S2)) #565)
-#574 := (not #122)
-#575 := (or #574 #568)
-#580 := (forall (vars (?v0 S2)) #575)
-#1016 := (not #580)
-#1017 := (or #1016 #1010)
-#544 := (<= #112 #541)
-#536 := (and #84 #509)
-#550 := (not #536)
-#551 := (or #550 #544)
-#556 := (forall (vars (?v0 S2) (?v1 S2)) #551)
-#1025 := (not #556)
-#1026 := (or #1025 #1017)
-#525 := (or #113 #524)
-#530 := (forall (vars (?v0 S2) (?v1 S2)) #525)
-#1034 := (not #530)
-#1035 := (or #1034 #1026)
-#1043 := (not #104)
-#1044 := (or #1043 #1035)
-#506 := (= 0::Int #100)
-#1052 := (not #506)
-#1053 := (or #1052 #1044)
-#483 := (and #93 #430)
-#488 := (and #92 #483)
-#491 := (exists (vars (?v1 S2)) #488)
-#497 := (not #91)
-#498 := (or #497 #491)
-#503 := (forall (vars (?v0 S2)) #498)
-#1068 := (not #503)
-#1069 := (or #1068 #1053)
-#1074 := (and #503 #1069)
-#463 := (and #84 #430)
-#471 := (not #463)
-#472 := (or #87 #471)
-#477 := (forall (vars (?v0 S2) (?v1 S2)) #472)
-#1080 := (not #477)
-#1081 := (or #1080 #1074)
-#1086 := (and #477 #1081)
-#452 := (or #79 #451)
-#457 := (forall (vars (?v0 S2) (?v1 S2)) #452)
-#1092 := (not #457)
-#1093 := (or #1092 #1086)
-#1098 := (and #457 #1093)
-#1104 := (not #74)
-#1105 := (or #1104 #1098)
-#1110 := (and #74 #1105)
-#439 := (= 0::Int #71)
-#1116 := (not #439)
-#1117 := (or #1116 #1110)
-#1122 := (and #439 #1117)
-#1129 := (or #1128 #1122)
-#1138 := (or #1137 #1129)
-#401 := (= 0::Int #58)
-#408 := (or #62 #401)
-#413 := (forall (vars (?v0 S2)) #408)
-#1146 := (not #413)
-#1147 := (or #1146 #1138)
-#1159 := (not #1147)
-#1797 := (iff #1159 #1796)
-#1794 := (iff #1147 #1791)
-#1782 := (or #1128 #1768)
-#1785 := (or #1137 #1782)
-#1788 := (or #1779 #1785)
-#1792 := (iff #1788 #1791)
-#1793 := [rewrite]: #1792
-#1789 := (iff #1147 #1788)
-#1786 := (iff #1138 #1785)
-#1783 := (iff #1129 #1782)
-#1769 := (iff #1122 #1768)
-#1766 := (iff #1117 #1765)
-#1763 := (iff #1110 #1762)
-#1760 := (iff #1105 #1759)
-#1757 := (iff #1098 #1756)
-#1754 := (iff #1093 #1753)
-#1751 := (iff #1086 #1750)
-#1748 := (iff #1081 #1747)
-#1745 := (iff #1074 #1744)
-#1742 := (iff #1069 #1739)
-#1721 := (or #1307 #1662)
-#1724 := (or #1685 #1721)
-#1727 := (or #1701 #1724)
-#1730 := (or #1710 #1727)
-#1733 := (or #1715 #1730)
-#1736 := (or #1718 #1733)
-#1740 := (iff #1736 #1739)
-#1741 := [rewrite]: #1740
-#1737 := (iff #1069 #1736)
-#1734 := (iff #1053 #1733)
-#1731 := (iff #1044 #1730)
-#1728 := (iff #1035 #1727)
-#1725 := (iff #1026 #1724)
-#1722 := (iff #1017 #1721)
-#1663 := (iff #1010 #1662)
-#1660 := (iff #998 #1657)
-#1636 := (or #1442 #1583)
-#1639 := (or #1600 #1636)
-#1642 := (or #963 #1639)
-#1645 := (or #1618 #1642)
-#1648 := (or #1622 #1645)
-#1651 := (or #730 #1648)
-#1654 := (or #1633 #1651)
-#1658 := (iff #1654 #1657)
-#1659 := [rewrite]: #1658
-#1655 := (iff #998 #1654)
-#1652 := (iff #990 #1651)
-#1649 := (iff #982 #1648)
-#1646 := (iff #973 #1645)
-#1643 := (iff #964 #1642)
-#1640 := (iff #955 #1639)
-#1637 := (iff #946 #1636)
-#1584 := (iff #939 #1583)
-#1581 := (iff #934 #1580)
-#1578 := (iff #927 #1577)
-#1575 := (iff #922 #1574)
-#1572 := (iff #915 #1571)
-#1569 := (iff #910 #1568)
-#1566 := (iff #903 #1565)
-#1563 := (iff #898 #1562)
-#1560 := (iff #891 #1559)
-#1557 := (iff #886 #1556)
-#1554 := (iff #879 #1553)
-#1551 := (iff #874 #1550)
-#1548 := (iff #860 #1547)
-#1545 := (iff #855 #1544)
-#1542 := (iff #848 #1541)
-#1539 := (iff #845 #1536)
-#1530 := (and #775 #1524)
-#1533 := (and #1527 #1530)
-#1537 := (iff #1533 #1536)
-#1538 := [rewrite]: #1537
-#1534 := (iff #845 #1533)
-#1531 := (iff #842 #1530)
-#1525 := (iff #839 #1524)
-#1526 := [rewrite]: #1525
-#1532 := [monotonicity #1526]: #1531
-#1528 := (iff #222 #1527)
-#1529 := [rewrite]: #1528
-#1535 := [monotonicity #1529 #1532]: #1534
-#1540 := [trans #1535 #1538]: #1539
-#1543 := [quant-intro #1540]: #1542
-#1522 := (iff #854 #1521)
-#1519 := (iff #221 #1518)
-#1516 := (iff #220 #1515)
-#1517 := [rewrite]: #1516
-#1520 := [monotonicity #1517]: #1519
-#1523 := [monotonicity #1520]: #1522
-#1546 := [monotonicity #1523 #1543]: #1545
-#1549 := [quant-intro #1546]: #1548
-#1511 := (iff #873 #1510)
-#1508 := (iff #836 #1507)
-#1505 := (iff #831 #1504)
-#1501 := (iff #824 #1500)
-#1503 := [rewrite]: #1501
-#1498 := (iff #830 #1497)
-#1495 := (iff #816 #1492)
-#1489 := (and #1204 #775)
+#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
+#1549 := [monotonicity #1543 #1546]: #1548
+#1554 := [trans #1549 #1552]: #1553
+#1557 := [quant-intro #1554]: #1556
+#1536 := (iff #868 #1535)
+#1533 := (iff #235 #1532)
+#1530 := (iff #234 #1529)
+#1531 := [rewrite]: #1530
+#1534 := [monotonicity #1531]: #1533
+#1537 := [monotonicity #1534]: #1536
+#1560 := [monotonicity #1537 #1557]: #1559
+#1563 := [quant-intro #1560]: #1562
+#1525 := (iff #887 #1524)
+#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
+#1526 := [monotonicity #1523]: #1525
+#1566 := [monotonicity #1526 #1563]: #1565
+#1569 := [monotonicity #1523 #1566]: #1568
+#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 #816 #1489)
-#1205 := (iff #84 #1204)
-#1206 := [rewrite]: #1205
-#1491 := [monotonicity #1206]: #1490
+#1490 := (iff #819 #1489)
+#1487 := (iff #226 #1484)
+#1488 := [rewrite]: #1487
+#1491 := [monotonicity #1488]: #1490
 #1496 := [trans #1491 #1494]: #1495
-#1499 := [monotonicity #1496]: #1498
-#1506 := [monotonicity #1499 #1503]: #1505
-#1509 := [quant-intro #1506]: #1508
-#1512 := [monotonicity #1509]: #1511
-#1552 := [monotonicity #1512 #1549]: #1551
-#1555 := [monotonicity #1509 #1552]: #1554
-#1487 := (iff #885 #1486)
-#1484 := (iff #810 #1483)
-#1481 := (iff #805 #1478)
-#1475 := (or #1470 #804)
-#1479 := (iff #1475 #1478)
-#1480 := [rewrite]: #1479
-#1476 := (iff #805 #1475)
-#1473 := (iff #212 #1470)
-#1474 := [rewrite]: #1473
-#1477 := [monotonicity #1474]: #1476
-#1482 := [trans #1477 #1480]: #1481
-#1485 := [quant-intro #1482]: #1484
-#1488 := [monotonicity #1485]: #1487
-#1558 := [monotonicity #1488 #1555]: #1557
-#1561 := [monotonicity #1485 #1558]: #1560
-#1468 := (iff #897 #1467)
-#1465 := (iff #206 #1464)
-#1462 := (iff #205 #1461)
+#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
-#1564 := [monotonicity #1469 #1561]: #1563
-#1567 := [monotonicity #1466 #1564]: #1566
-#1459 := (iff #909 #1458)
-#1456 := (iff #790 #204)
-#1457 := [rewrite]: #1456
-#1460 := [monotonicity #1457]: #1459
-#1570 := [monotonicity #1460 #1567]: #1569
-#1573 := [monotonicity #1457 #1570]: #1572
-#1576 := [monotonicity #1573]: #1575
-#1579 := [monotonicity #1576]: #1578
-#1454 := (iff #933 #1453)
-#1451 := (iff #198 #1450)
-#1448 := (iff #197 #1445)
-#1449 := [rewrite]: #1448
-#1452 := [quant-intro #1449]: #1451
-#1455 := [monotonicity #1452]: #1454
-#1582 := [monotonicity #1455 #1579]: #1581
-#1585 := [monotonicity #1452 #1582]: #1584
-#1443 := (iff #945 #1442)
-#1440 := (iff #772 #1439)
-#1437 := (iff #767 #1434)
-#1431 := (or #1428 #761)
-#1435 := (iff #1431 #1434)
-#1436 := [rewrite]: #1435
-#1432 := (iff #767 #1431)
-#1429 := (iff #188 #1428)
-#1426 := (iff #187 #1425)
-#1427 := [rewrite]: #1426
-#1419 := (iff #185 #1418)
-#1420 := [rewrite]: #1419
-#1430 := [monotonicity #1420 #1427]: #1429
-#1433 := [monotonicity #1430]: #1432
-#1438 := [trans #1433 #1436]: #1437
-#1441 := [quant-intro #1438]: #1440
-#1444 := [monotonicity #1441]: #1443
-#1638 := [monotonicity #1444 #1585]: #1637
-#1601 := (iff #954 #1600)
-#1598 := (iff #758 #1597)
-#1595 := (iff #753 #1594)
-#1592 := (iff #747 #1591)
-#1593 := [rewrite]: #1592
-#1587 := (iff #193 #1586)
-#1588 := [monotonicity #1430]: #1587
-#1596 := [monotonicity #1588 #1593]: #1595
-#1599 := [quant-intro #1596]: #1598
-#1602 := [monotonicity #1599]: #1601
-#1641 := [monotonicity #1602 #1638]: #1640
-#1644 := [monotonicity #1641]: #1643
-#1619 := (iff #972 #1618)
-#1616 := (iff #744 #1615)
-#1613 := (iff #739 #1610)
-#1607 := (or #1603 #509)
-#1611 := (iff #1607 #1610)
-#1612 := [rewrite]: #1611
-#1608 := (iff #739 #1607)
-#1605 := (iff #177 #1603)
-#1606 := [rewrite]: #1605
-#1609 := [monotonicity #1606]: #1608
-#1614 := [trans #1609 #1612]: #1613
-#1617 := [quant-intro #1614]: #1616
-#1620 := [monotonicity #1617]: #1619
-#1647 := [monotonicity #1620 #1644]: #1646
-#1631 := (iff #981 #1622)
-#1623 := (not #1622)
-#1626 := (not #1623)
-#1629 := (iff #1626 #1622)
-#1630 := [rewrite]: #1629
-#1627 := (iff #981 #1626)
-#1624 := (iff #176 #1623)
-#1625 := [rewrite]: #1624
-#1628 := [monotonicity #1625]: #1627
-#1632 := [trans #1628 #1630]: #1631
-#1650 := [monotonicity #1632 #1647]: #1649
-#1653 := [monotonicity #1650]: #1652
-#1634 := (iff #594 #1633)
-#1393 := (iff #591 #1392)
-#1390 := (iff #586 #1387)
-#1384 := (and #1268 #512)
-#1388 := (iff #1384 #1387)
-#1389 := [rewrite]: #1388
-#1385 := (iff #586 #1384)
-#1269 := (iff #121 #1268)
-#1270 := [rewrite]: #1269
-#1386 := [monotonicity #1270]: #1385
-#1391 := [trans #1386 #1389]: #1390
-#1394 := [quant-intro #1391]: #1393
-#1635 := [monotonicity #1394]: #1634
-#1656 := [monotonicity #1635 #1653]: #1655
-#1661 := [trans #1656 #1659]: #1660
-#1413 := (iff #718 #1410)
-#1395 := (or #682 #1381)
-#1398 := (or #691 #1395)
-#1401 := (or #700 #1398)
-#1404 := (or #709 #1401)
-#1407 := (or #1392 #1404)
-#1411 := (iff #1407 #1410)
-#1412 := [rewrite]: #1411
-#1408 := (iff #718 #1407)
-#1405 := (iff #710 #1404)
-#1402 := (iff #701 #1401)
-#1399 := (iff #692 #1398)
-#1396 := (iff #683 #1395)
-#1382 := (iff #676 #1381)
-#1379 := (iff #671 #1378)
-#1376 := (iff #664 #1375)
-#1373 := (iff #659 #1370)
-#1367 := (or #1362 #159)
-#1371 := (iff #1367 #1370)
-#1372 := [rewrite]: #1371
-#1368 := (iff #659 #1367)
-#1365 := (iff #645 #159)
-#1366 := [rewrite]: #1365
-#1363 := (iff #658 #1362)
-#1360 := (iff #642 #1359)
-#1357 := (iff #637 #1356)
-#1354 := (iff #630 #1353)
-#1355 := [rewrite]: #1354
-#1351 := (iff #636 #1350)
-#1348 := (iff #627 #1347)
-#1314 := (iff #144 #1313)
-#1315 := [rewrite]: #1314
-#1349 := [monotonicity #1206 #1315]: #1348
-#1352 := [monotonicity #1349]: #1351
-#1358 := [monotonicity #1352 #1355]: #1357
-#1361 := [quant-intro #1358]: #1360
-#1364 := [monotonicity #1361]: #1363
-#1369 := [monotonicity #1364 #1366]: #1368
-#1374 := [trans #1369 #1372]: #1373
-#1377 := [monotonicity #1361 #1374]: #1376
-#1345 := (iff #670 #1344)
-#1342 := (iff #624 #1341)
-#1339 := (iff #619 #1338)
-#1336 := (iff #612 #1335)
-#1333 := (iff #609 #1332)
-#1329 := (iff #606 #1328)
-#1331 := [rewrite]: #1329
-#1326 := (iff #147 #1325)
-#1327 := [rewrite]: #1326
-#1334 := [monotonicity #1327 #1331]: #1333
-#1337 := [quant-intro #1334]: #1336
-#1320 := (iff #618 #1319)
-#1317 := (iff #145 #1316)
-#1318 := [monotonicity #1315]: #1317
-#1321 := [monotonicity #1318]: #1320
-#1340 := [monotonicity #1321 #1337]: #1339
-#1343 := [quant-intro #1340]: #1342
-#1346 := [monotonicity #1343]: #1345
-#1380 := [monotonicity #1346 #1377]: #1379
-#1383 := [monotonicity #1343 #1380]: #1382
-#1397 := [monotonicity #1383]: #1396
-#1400 := [monotonicity #1397]: #1399
-#1403 := [monotonicity #1400]: #1402
-#1406 := [monotonicity #1403]: #1405
-#1409 := [monotonicity #1394 #1406]: #1408
-#1414 := [trans #1409 #1412]: #1413
-#1664 := [monotonicity #1414 #1661]: #1663
-#1308 := (iff #1016 #1307)
-#1305 := (iff #580 #1304)
-#1302 := (iff #575 #1301)
-#1299 := (iff #568 #1298)
-#1296 := (iff #565 #1293)
-#1287 := (and #509 #1277)
-#1290 := (and #1284 #1287)
-#1294 := (iff #1290 #1293)
-#1295 := [rewrite]: #1294
-#1291 := (iff #565 #1290)
-#1288 := (iff #562 #1287)
-#1278 := (iff #559 #1277)
-#1282 := [rewrite]: #1278
-#1289 := [monotonicity #1282]: #1288
-#1285 := (iff #123 #1284)
-#1286 := [rewrite]: #1285
-#1292 := [monotonicity #1286 #1289]: #1291
-#1297 := [trans #1292 #1295]: #1296
-#1300 := [quant-intro #1297]: #1299
-#1275 := (iff #574 #1274)
-#1272 := (iff #122 #1271)
-#1273 := [monotonicity #1270]: #1272
-#1276 := [monotonicity #1273]: #1275
-#1303 := [monotonicity #1276 #1300]: #1302
-#1306 := [quant-intro #1303]: #1305
-#1309 := [monotonicity #1306]: #1308
-#1723 := [monotonicity #1309 #1664]: #1722
-#1686 := (iff #1025 #1685)
-#1683 := (iff #556 #1682)
-#1680 := (iff #551 #1679)
-#1677 := (iff #544 #1676)
-#1678 := [rewrite]: #1677
-#1674 := (iff #550 #1673)
-#1671 := (iff #536 #1668)
-#1665 := (and #1204 #509)
-#1669 := (iff #1665 #1668)
-#1670 := [rewrite]: #1669
-#1666 := (iff #536 #1665)
-#1667 := [monotonicity #1206]: #1666
-#1672 := [trans #1667 #1670]: #1671
-#1675 := [monotonicity #1672]: #1674
-#1681 := [monotonicity #1675 #1678]: #1680
-#1684 := [quant-intro #1681]: #1683
-#1687 := [monotonicity #1684]: #1686
-#1726 := [monotonicity #1687 #1723]: #1725
-#1702 := (iff #1034 #1701)
-#1699 := (iff #530 #1698)
-#1696 := (iff #525 #1693)
-#1690 := (or #1283 #524)
-#1694 := (iff #1690 #1693)
-#1695 := [rewrite]: #1694
-#1691 := (iff #525 #1690)
-#1688 := (iff #113 #1283)
-#1689 := [rewrite]: #1688
-#1692 := [monotonicity #1689]: #1691
-#1697 := [trans #1692 #1695]: #1696
-#1700 := [quant-intro #1697]: #1699
-#1703 := [monotonicity #1700]: #1702
-#1729 := [monotonicity #1703 #1726]: #1728
-#1711 := (iff #1043 #1710)
-#1708 := (iff #104 #1707)
-#1705 := (iff #103 #1704)
-#1706 := [rewrite]: #1705
-#1709 := [quant-intro #1706]: #1708
-#1712 := [monotonicity #1709]: #1711
-#1732 := [monotonicity #1712 #1729]: #1731
-#1716 := (iff #1052 #1715)
-#1713 := (iff #506 #101)
-#1714 := [rewrite]: #1713
+#1596 := [monotonicity #1469 #1593]: #1595
+#1599 := [monotonicity #1466 #1596]: #1598
+#1457 := (iff #959 #1456)
+#1454 := (iff #786 #1453)
+#1451 := (iff #781 #1448)
+#1445 := (or #1442 #775)
+#1449 := (iff #1445 #1448)
+#1450 := [rewrite]: #1449
+#1446 := (iff #781 #1445)
+#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
+#1458 := [monotonicity #1455]: #1457
+#1652 := [monotonicity #1458 #1599]: #1651
+#1615 := (iff #968 #1614)
+#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)
+#1421 := (or #1406 #1418)
+#1425 := (iff #1421 #1424)
+#1426 := [rewrite]: #1425
+#1422 := (iff #732 #1421)
+#1419 := (iff #724 #1418)
+#1416 := (iff #715 #1415)
+#1413 := (iff #706 #1412)
+#1410 := (iff #697 #1409)
+#1396 := (iff #690 #1395)
+#1393 := (iff #685 #1392)
+#1390 := (iff #678 #1389)
+#1387 := (iff #673 #1384)
+#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
-#1735 := [monotonicity #1717 #1732]: #1734
-#1719 := (iff #1068 #1718)
-#1263 := (iff #503 #1262)
-#1260 := (iff #498 #1259)
-#1257 := (iff #491 #1256)
-#1254 := (iff #488 #1251)
-#1245 := (and #1239 #430)
-#1248 := (and #1242 #1245)
-#1252 := (iff #1248 #1251)
-#1253 := [rewrite]: #1252
-#1249 := (iff #488 #1248)
-#1246 := (iff #483 #1245)
-#1240 := (iff #93 #1239)
-#1241 := [rewrite]: #1240
-#1247 := [monotonicity #1241]: #1246
-#1243 := (iff #92 #1242)
-#1244 := [rewrite]: #1243
-#1250 := [monotonicity #1244 #1247]: #1249
-#1255 := [trans #1250 #1253]: #1254
-#1258 := [quant-intro #1255]: #1257
-#1237 := (iff #497 #1236)
-#1234 := (iff #91 #1233)
-#1231 := (iff #90 #1230)
-#1232 := [rewrite]: #1231
-#1235 := [monotonicity #1232]: #1234
-#1238 := [monotonicity #1235]: #1237
-#1261 := [monotonicity #1238 #1258]: #1260
-#1264 := [quant-intro #1261]: #1263
-#1720 := [monotonicity #1264]: #1719
-#1738 := [monotonicity #1720 #1735]: #1737
-#1743 := [trans #1738 #1741]: #1742
-#1746 := [monotonicity #1264 #1743]: #1745
-#1225 := (iff #1080 #1224)
+#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
+#1746 := [monotonicity #1726 #1743]: #1745
+#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)
+#1259 := (and #1253 #444)
+#1262 := (and #1256 #1259)
+#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)
+#1236 := (iff #491 #1235)
+#1233 := (iff #486 #1232)
+#1230 := (iff #485 #1229)
+#1227 := (iff #477 #1224)
+#1221 := (and #1218 #444)
+#1225 := (iff #1221 #1224)
+#1226 := [rewrite]: #1225
 #1222 := (iff #477 #1221)
-#1219 := (iff #472 #1218)
-#1216 := (iff #471 #1215)
-#1213 := (iff #463 #1210)
-#1207 := (and #1204 #430)
-#1211 := (iff #1207 #1210)
-#1212 := [rewrite]: #1211
-#1208 := (iff #463 #1207)
+#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
-#1214 := [trans #1209 #1212]: #1213
-#1217 := [monotonicity #1214]: #1216
-#1197 := (iff #87 #1198)
-#1196 := [rewrite]: #1197
-#1220 := [monotonicity #1196 #1217]: #1219
-#1223 := [quant-intro #1220]: #1222
-#1226 := [monotonicity #1223]: #1225
-#1749 := [monotonicity #1226 #1746]: #1748
-#1752 := [monotonicity #1223 #1749]: #1751
-#1194 := (iff #1092 #1193)
-#1191 := (iff #457 #1190)
-#1188 := (iff #452 #1185)
-#1182 := (or #1178 #451)
-#1186 := (iff #1182 #1185)
-#1187 := [rewrite]: #1186
-#1183 := (iff #452 #1182)
-#1177 := (iff #79 #1178)
-#1181 := [rewrite]: #1177
-#1184 := [monotonicity #1181]: #1183
-#1189 := [trans #1184 #1187]: #1188
-#1192 := [quant-intro #1189]: #1191
-#1195 := [monotonicity #1192]: #1194
-#1755 := [monotonicity #1195 #1752]: #1754
-#1758 := [monotonicity #1192 #1755]: #1757
-#1174 := (iff #1104 #1173)
-#1171 := (iff #74 #1170)
-#1167 := (iff #73 #1169)
-#1168 := [rewrite]: #1167
-#1172 := [quant-intro #1168]: #1171
-#1175 := [monotonicity #1172]: #1174
-#1761 := [monotonicity #1175 #1758]: #1760
-#1764 := [monotonicity #1172 #1761]: #1763
-#1165 := (iff #1116 #1164)
-#1162 := (iff #439 #72)
+#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)
+#1176 := (iff #453 #82)
+#1177 := [rewrite]: #1176
+#1180 := [monotonicity #1177]: #1179
+#1781 := [monotonicity #1180 #1778]: #1780
+#1784 := [monotonicity #1177 #1781]: #1783
+#1798 := [monotonicity #1784]: #1797
+#1801 := [monotonicity #1798]: #1800
+#1794 := (iff #1160 #1793)
+#1791 := (iff #427 #1790)
+#1788 := (iff #422 #1787)
+#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
+#1174 := (iff #285 #1173)
+#1171 := (iff #284 #1161)
+#1166 := (implies true #1161)
+#1169 := (iff #1166 #1161)
+#1170 := [rewrite]: #1169
+#1167 := (iff #284 #1166)
+#1164 := (iff #283 #1161)
+#1157 := (implies #427 #1152)
+#1162 := (iff #1157 #1161)
 #1163 := [rewrite]: #1162
-#1166 := [monotonicity #1163]: #1165
-#1767 := [monotonicity #1166 #1764]: #1766
-#1770 := [monotonicity #1163 #1767]: #1769
-#1784 := [monotonicity #1770]: #1783
-#1787 := [monotonicity #1784]: #1786
-#1780 := (iff #1146 #1779)
-#1777 := (iff #413 #1776)
-#1774 := (iff #408 #1773)
-#1771 := (iff #401 #59)
-#1772 := [rewrite]: #1771
-#1775 := [monotonicity #1772]: #1774
-#1778 := [quant-intro #1775]: #1777
-#1781 := [monotonicity #1778]: #1780
-#1790 := [monotonicity #1781 #1787]: #1789
-#1795 := [trans #1790 #1793]: #1794
-#1798 := [monotonicity #1795]: #1797
-#1160 := (iff #271 #1159)
-#1157 := (iff #270 #1147)
-#1152 := (implies true #1147)
-#1155 := (iff #1152 #1147)
-#1156 := [rewrite]: #1155
-#1153 := (iff #270 #1152)
-#1150 := (iff #269 #1147)
-#1143 := (implies #413 #1138)
-#1148 := (iff #1143 #1147)
-#1149 := [rewrite]: #1148
-#1144 := (iff #269 #1143)
-#1141 := (iff #268 #1138)
-#1134 := (implies #427 #1129)
-#1139 := (iff #1134 #1138)
-#1140 := [rewrite]: #1139
-#1135 := (iff #268 #1134)
-#1132 := (iff #267 #1129)
-#1125 := (implies #436 #1122)
-#1130 := (iff #1125 #1129)
-#1131 := [rewrite]: #1130
-#1126 := (iff #267 #1125)
-#1123 := (iff #266 #1122)
-#1120 := (iff #265 #1117)
-#1113 := (implies #439 #1110)
-#1118 := (iff #1113 #1117)
-#1119 := [rewrite]: #1118
-#1114 := (iff #265 #1113)
-#1111 := (iff #264 #1110)
-#1108 := (iff #263 #1105)
-#1101 := (implies #74 #1098)
-#1106 := (iff #1101 #1105)
-#1107 := [rewrite]: #1106
-#1102 := (iff #263 #1101)
-#1099 := (iff #262 #1098)
-#1096 := (iff #261 #1093)
-#1089 := (implies #457 #1086)
-#1094 := (iff #1089 #1093)
-#1095 := [rewrite]: #1094
-#1090 := (iff #261 #1089)
-#1087 := (iff #260 #1086)
-#1084 := (iff #259 #1081)
-#1077 := (implies #477 #1074)
-#1082 := (iff #1077 #1081)
-#1083 := [rewrite]: #1082
-#1078 := (iff #259 #1077)
-#1075 := (iff #258 #1074)
-#1072 := (iff #257 #1069)
-#1065 := (implies #503 #1053)
-#1070 := (iff #1065 #1069)
-#1071 := [rewrite]: #1070
-#1066 := (iff #257 #1065)
-#1063 := (iff #256 #1053)
-#1058 := (implies true #1053)
-#1061 := (iff #1058 #1053)
-#1062 := [rewrite]: #1061
-#1059 := (iff #256 #1058)
-#1056 := (iff #255 #1053)
-#1049 := (implies #506 #1044)
-#1054 := (iff #1049 #1053)
-#1055 := [rewrite]: #1054
-#1050 := (iff #255 #1049)
-#1047 := (iff #254 #1044)
-#1040 := (implies #104 #1035)
-#1045 := (iff #1040 #1044)
-#1046 := [rewrite]: #1045
-#1041 := (iff #254 #1040)
-#1038 := (iff #253 #1035)
-#1031 := (implies #530 #1026)
-#1036 := (iff #1031 #1035)
-#1037 := [rewrite]: #1036
-#1032 := (iff #253 #1031)
-#1029 := (iff #252 #1026)
-#1022 := (implies #556 #1017)
-#1027 := (iff #1022 #1026)
-#1028 := [rewrite]: #1027
-#1023 := (iff #252 #1022)
-#1020 := (iff #251 #1017)
-#1013 := (implies #580 #1010)
-#1018 := (iff #1013 #1017)
-#1019 := [rewrite]: #1018
-#1014 := (iff #251 #1013)
-#1011 := (iff #250 #1010)
-#1008 := (iff #249 #998)
-#1003 := (implies true #998)
-#1006 := (iff #1003 #998)
-#1007 := [rewrite]: #1006
-#1004 := (iff #249 #1003)
-#1001 := (iff #248 #998)
-#995 := (implies #591 #990)
-#999 := (iff #995 #998)
-#1000 := [rewrite]: #999
-#996 := (iff #248 #995)
-#993 := (iff #247 #990)
-#733 := (not #730)
-#987 := (implies #733 #982)
-#991 := (iff #987 #990)
-#992 := [rewrite]: #991
-#988 := (iff #247 #987)
-#985 := (iff #246 #982)
-#978 := (implies #176 #973)
-#983 := (iff #978 #982)
-#984 := [rewrite]: #983
-#979 := (iff #246 #978)
-#976 := (iff #245 #973)
-#969 := (implies #744 #964)
-#974 := (iff #969 #973)
-#975 := [rewrite]: #974
-#970 := (iff #245 #969)
-#967 := (iff #244 #964)
-#960 := (implies #182 #955)
-#965 := (iff #960 #964)
-#966 := [rewrite]: #965
-#961 := (iff #244 #960)
-#958 := (iff #243 #955)
-#951 := (implies #758 #946)
-#956 := (iff #951 #955)
-#957 := [rewrite]: #956
-#952 := (iff #243 #951)
-#949 := (iff #242 #946)
-#942 := (implies #772 #939)
-#947 := (iff #942 #946)
-#948 := [rewrite]: #947
-#943 := (iff #242 #942)
-#940 := (iff #241 #939)
-#937 := (iff #240 #934)
-#930 := (implies #198 #927)
-#935 := (iff #930 #934)
-#936 := [rewrite]: #935
-#931 := (iff #240 #930)
-#928 := (iff #239 #927)
-#925 := (iff #238 #922)
-#918 := (implies #787 #915)
-#923 := (iff #918 #922)
-#924 := [rewrite]: #923
-#919 := (iff #238 #918)
-#916 := (iff #237 #915)
-#913 := (iff #236 #910)
-#906 := (implies #790 #903)
-#911 := (iff #906 #910)
-#912 := [rewrite]: #911
-#907 := (iff #236 #906)
-#904 := (iff #235 #903)
-#901 := (iff #234 #898)
-#894 := (implies #206 #891)
-#899 := (iff #894 #898)
-#900 := [rewrite]: #899
-#895 := (iff #234 #894)
-#892 := (iff #233 #891)
-#889 := (iff #232 #886)
-#882 := (implies #810 #879)
-#887 := (iff #882 #886)
-#888 := [rewrite]: #887
-#883 := (iff #232 #882)
-#880 := (iff #231 #879)
-#877 := (iff #230 #874)
-#870 := (implies #836 #860)
-#875 := (iff #870 #874)
-#876 := [rewrite]: #875
-#871 := (iff #230 #870)
-#868 := (iff #229 #860)
-#863 := (and #860 true)
-#866 := (iff #863 #860)
-#867 := [rewrite]: #866
-#864 := (iff #229 #863)
-#861 := (iff #228 #860)
-#858 := (iff #227 #855)
-#851 := (implies #221 #848)
-#856 := (iff #851 #855)
-#857 := [rewrite]: #856
-#852 := (iff #227 #851)
-#849 := (iff #226 #848)
-#846 := (iff #225 #845)
-#843 := (iff #224 #842)
-#840 := (iff #223 #839)
-#822 := (= #216 #821)
-#823 := [rewrite]: #822
-#841 := [monotonicity #823]: #840
-#776 := (iff #200 #775)
+#1158 := (iff #283 #1157)
+#1155 := (iff #282 #1152)
+#1148 := (implies #441 #1143)
+#1153 := (iff #1148 #1152)
+#1154 := [rewrite]: #1153
+#1149 := (iff #282 #1148)
+#1146 := (iff #281 #1143)
+#1139 := (implies #450 #1136)
+#1144 := (iff #1139 #1143)
+#1145 := [rewrite]: #1144
+#1140 := (iff #281 #1139)
+#1137 := (iff #280 #1136)
+#1134 := (iff #279 #1131)
+#1127 := (implies #453 #1124)
+#1132 := (iff #1127 #1131)
+#1133 := [rewrite]: #1132
+#1128 := (iff #279 #1127)
+#1125 := (iff #278 #1124)
+#1122 := (iff #277 #1119)
+#1115 := (implies #84 #1112)
+#1120 := (iff #1115 #1119)
+#1121 := [rewrite]: #1120
+#1116 := (iff #277 #1115)
+#1113 := (iff #276 #1112)
+#1110 := (iff #275 #1107)
+#1103 := (implies #471 #1100)
+#1108 := (iff #1103 #1107)
+#1109 := [rewrite]: #1108
+#1104 := (iff #275 #1103)
+#1101 := (iff #274 #1100)
+#1098 := (iff #273 #1095)
+#1091 := (implies #491 #1088)
+#1096 := (iff #1091 #1095)
+#1097 := [rewrite]: #1096
+#1092 := (iff #273 #1091)
+#1089 := (iff #272 #1088)
+#1086 := (iff #271 #1083)
+#1079 := (implies #517 #1067)
+#1084 := (iff #1079 #1083)
+#1085 := [rewrite]: #1084
+#1080 := (iff #271 #1079)
+#1077 := (iff #270 #1067)
+#1072 := (implies true #1067)
+#1075 := (iff #1072 #1067)
+#1076 := [rewrite]: #1075
+#1073 := (iff #270 #1072)
+#1070 := (iff #269 #1067)
+#1063 := (implies #520 #1058)
+#1068 := (iff #1063 #1067)
+#1069 := [rewrite]: #1068
+#1064 := (iff #269 #1063)
+#1061 := (iff #268 #1058)
+#1054 := (implies #115 #1049)
+#1059 := (iff #1054 #1058)
+#1060 := [rewrite]: #1059
+#1055 := (iff #268 #1054)
+#1052 := (iff #267 #1049)
+#1045 := (implies #544 #1040)
+#1050 := (iff #1045 #1049)
+#1051 := [rewrite]: #1050
+#1046 := (iff #267 #1045)
+#1043 := (iff #266 #1040)
+#1036 := (implies #570 #1031)
+#1041 := (iff #1036 #1040)
+#1042 := [rewrite]: #1041
+#1037 := (iff #266 #1036)
+#1034 := (iff #265 #1031)
+#1027 := (implies #594 #1024)
+#1032 := (iff #1027 #1031)
+#1033 := [rewrite]: #1032
+#1028 := (iff #265 #1027)
+#1025 := (iff #264 #1024)
+#1022 := (iff #263 #1012)
+#1017 := (implies true #1012)
+#1020 := (iff #1017 #1012)
+#1021 := [rewrite]: #1020
+#1018 := (iff #263 #1017)
+#1015 := (iff #262 #1012)
+#1009 := (implies #605 #1004)
+#1013 := (iff #1009 #1012)
+#1014 := [rewrite]: #1013
+#1010 := (iff #262 #1009)
+#1007 := (iff #261 #1004)
+#747 := (not #744)
+#1001 := (implies #747 #996)
+#1005 := (iff #1001 #1004)
+#1006 := [rewrite]: #1005
+#1002 := (iff #261 #1001)
+#999 := (iff #260 #996)
+#992 := (implies #187 #987)
+#997 := (iff #992 #996)
+#998 := [rewrite]: #997
+#993 := (iff #260 #992)
+#990 := (iff #259 #987)
+#983 := (implies #758 #978)
+#988 := (iff #983 #987)
+#989 := [rewrite]: #988
+#984 := (iff #259 #983)
+#981 := (iff #258 #978)
+#974 := (implies #195 #969)
+#979 := (iff #974 #978)
+#980 := [rewrite]: #979
+#975 := (iff #258 #974)
+#972 := (iff #257 #969)
+#965 := (implies #772 #960)
+#970 := (iff #965 #969)
+#971 := [rewrite]: #970
+#966 := (iff #257 #965)
+#963 := (iff #256 #960)
+#956 := (implies #786 #953)
+#961 := (iff #956 #960)
+#962 := [rewrite]: #961
+#957 := (iff #256 #956)
+#954 := (iff #255 #953)
+#951 := (iff #254 #948)
+#944 := (implies #212 #941)
+#949 := (iff #944 #948)
+#950 := [rewrite]: #949
+#945 := (iff #254 #944)
+#942 := (iff #253 #941)
+#939 := (iff #252 #936)
+#932 := (implies #801 #929)
+#937 := (iff #932 #936)
+#938 := [rewrite]: #937
+#933 := (iff #252 #932)
+#930 := (iff #251 #929)
+#927 := (iff #250 #924)
+#920 := (implies #804 #917)
+#925 := (iff #920 #924)
+#926 := [rewrite]: #925
+#921 := (iff #250 #920)
+#918 := (iff #249 #917)
+#915 := (iff #248 #912)
+#908 := (implies #220 #905)
+#913 := (iff #908 #912)
+#914 := [rewrite]: #913
+#909 := (iff #248 #908)
+#906 := (iff #247 #905)
+#903 := (iff #246 #900)
+#896 := (implies #824 #893)
+#901 := (iff #896 #900)
+#902 := [rewrite]: #901
+#897 := (iff #246 #896)
+#894 := (iff #245 #893)
+#891 := (iff #244 #888)
+#884 := (implies #850 #874)
+#889 := (iff #884 #888)
+#890 := [rewrite]: #889
+#885 := (iff #244 #884)
+#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
-#844 := [monotonicity #777 #841]: #843
-#847 := [monotonicity #844]: #846
-#850 := [quant-intro #847]: #849
-#853 := [monotonicity #850]: #852
-#859 := [trans #853 #857]: #858
-#862 := [quant-intro #859]: #861
-#865 := [monotonicity #862]: #864
-#869 := [trans #865 #867]: #868
-#837 := (iff #219 #836)
-#834 := (iff #218 #831)
-#827 := (implies #816 #824)
-#832 := (iff #827 #831)
-#833 := [rewrite]: #832
-#828 := (iff #218 #827)
-#825 := (iff #217 #824)
-#826 := [monotonicity #823]: #825
-#819 := (iff #215 #816)
-#813 := (and #775 #84)
-#817 := (iff #813 #816)
-#818 := [rewrite]: #817
-#814 := (iff #215 #813)
-#815 := [monotonicity #777]: #814
-#820 := [trans #815 #818]: #819
-#829 := [monotonicity #820 #826]: #828
-#835 := [trans #829 #833]: #834
-#838 := [quant-intro #835]: #837
-#872 := [monotonicity #838 #869]: #871
-#878 := [trans #872 #876]: #877
-#881 := [monotonicity #838 #878]: #880
-#811 := (iff #214 #810)
-#808 := (iff #213 #805)
-#801 := (implies #798 #212)
-#806 := (iff #801 #805)
-#807 := [rewrite]: #806
-#802 := (iff #213 #801)
-#799 := (iff #210 #798)
-#796 := (iff #209 #795)
-#797 := [rewrite]: #796
-#793 := (iff #207 #781)
-#794 := [monotonicity #777]: #793
-#800 := [monotonicity #794 #797]: #799
-#803 := [monotonicity #800]: #802
-#809 := [trans #803 #807]: #808
-#812 := [quant-intro #809]: #811
-#884 := [monotonicity #812 #881]: #883
-#890 := [trans #884 #888]: #889
-#893 := [monotonicity #812 #890]: #892
-#896 := [monotonicity #893]: #895
-#902 := [trans #896 #900]: #901
-#905 := [monotonicity #902]: #904
-#791 := (iff #204 #790)
-#792 := [rewrite]: #791
-#908 := [monotonicity #792 #905]: #907
-#914 := [trans #908 #912]: #913
-#917 := [monotonicity #792 #914]: #916
-#788 := (iff #202 #787)
-#785 := (iff #201 #782)
-#778 := (implies #775 #761)
-#783 := (iff #778 #782)
-#784 := [rewrite]: #783
-#779 := (iff #201 #778)
-#762 := (iff #194 #761)
-#763 := [rewrite]: #762
-#780 := [monotonicity #777 #763]: #779
-#786 := [trans #780 #784]: #785
-#789 := [quant-intro #786]: #788
-#920 := [monotonicity #789 #917]: #919
-#926 := [trans #920 #924]: #925
-#929 := [monotonicity #789 #926]: #928
-#932 := [monotonicity #929]: #931
-#938 := [trans #932 #936]: #937
-#941 := [monotonicity #938]: #940
-#773 := (iff #196 #772)
-#770 := (iff #195 #767)
-#764 := (implies #193 #761)
+#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 #195 #764)
+#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
-#944 := [monotonicity #774 #941]: #943
-#950 := [trans #944 #948]: #949
-#759 := (iff #192 #758)
-#756 := (iff #191 #753)
-#750 := (implies #188 #747)
+#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 #191 #750)
-#748 := (iff #190 #747)
-#749 := [rewrite]: #748
-#752 := [monotonicity #749]: #751
+#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
-#953 := [monotonicity #760 #950]: #952
-#959 := [trans #953 #957]: #958
-#962 := [monotonicity #959]: #961
-#968 := [trans #962 #966]: #967
-#745 := (iff #179 #744)
-#742 := (iff #178 #739)
-#736 := (implies #512 #177)
-#740 := (iff #736 #739)
-#741 := [rewrite]: #740
-#737 := (iff #178 #736)
-#513 := (iff #108 #512)
-#510 := (iff #107 #509)
-#511 := [rewrite]: #510
-#514 := [monotonicity #511]: #513
-#738 := [monotonicity #514]: #737
-#743 := [trans #738 #741]: #742
-#746 := [quant-intro #743]: #745
-#971 := [monotonicity #746 #968]: #970
-#977 := [trans #971 #975]: #976
-#980 := [monotonicity #977]: #979
-#986 := [trans #980 #984]: #985
-#734 := (iff #174 #733)
-#731 := (iff #173 #730)
-#732 := [rewrite]: #731
-#735 := [monotonicity #732]: #734
-#989 := [monotonicity #735 #986]: #988
-#994 := [trans #989 #992]: #993
-#592 := (iff #131 #591)
-#589 := (iff #130 #586)
-#583 := (and #512 #121)
-#587 := (iff #583 #586)
-#588 := [rewrite]: #587
-#584 := (iff #130 #583)
-#585 := [monotonicity #514]: #584
-#590 := [trans #585 #588]: #589
-#593 := [quant-intro #590]: #592
-#997 := [monotonicity #593 #994]: #996
-#1002 := [trans #997 #1000]: #1001
-#1005 := [monotonicity #1002]: #1004
-#1009 := [trans #1005 #1007]: #1008
-#728 := (iff #170 #718)
-#723 := (implies true #718)
-#726 := (iff #723 #718)
-#727 := [rewrite]: #726
-#724 := (iff #170 #723)
-#721 := (iff #169 #718)
-#715 := (implies #594 #710)
-#719 := (iff #715 #718)
-#720 := [rewrite]: #719
-#716 := (iff #169 #715)
-#713 := (iff #168 #710)
-#706 := (implies #597 #701)
-#711 := (iff #706 #710)
-#712 := [rewrite]: #711
-#707 := (iff #168 #706)
-#704 := (iff #167 #701)
-#697 := (implies #137 #692)
-#702 := (iff #697 #701)
-#703 := [rewrite]: #702
-#698 := (iff #167 #697)
-#695 := (iff #166 #692)
-#688 := (implies #600 #683)
-#693 := (iff #688 #692)
-#694 := [rewrite]: #693
-#689 := (iff #166 #688)
-#686 := (iff #165 #683)
-#679 := (implies #142 #676)
-#684 := (iff #679 #683)
-#685 := [rewrite]: #684
-#680 := (iff #165 #679)
-#677 := (iff #164 #676)
-#674 := (iff #163 #671)
-#667 := (implies #624 #664)
-#672 := (iff #667 #671)
-#673 := [rewrite]: #672
-#668 := (iff #163 #667)
-#665 := (iff #162 #664)
-#662 := (iff #161 #659)
-#655 := (implies #642 #645)
-#660 := (iff #655 #659)
-#661 := [rewrite]: #660
-#656 := (iff #161 #655)
-#653 := (iff #160 #645)
-#648 := (and #645 true)
-#651 := (iff #648 #645)
-#652 := [rewrite]: #651
-#649 := (iff #160 #648)
-#646 := (iff #159 #645)
-#647 := [rewrite]: #646
-#650 := [monotonicity #647]: #649
-#654 := [trans #650 #652]: #653
-#643 := (iff #157 #642)
-#640 := (iff #156 #637)
-#633 := (implies #627 #630)
-#638 := (iff #633 #637)
-#639 := [rewrite]: #638
-#634 := (iff #156 #633)
-#631 := (iff #155 #630)
-#604 := (= #148 #603)
-#605 := [rewrite]: #604
-#632 := [monotonicity #605]: #631
-#628 := (iff #154 #627)
-#629 := [rewrite]: #628
-#635 := [monotonicity #629 #632]: #634
-#641 := [trans #635 #639]: #640
-#644 := [quant-intro #641]: #643
-#657 := [monotonicity #644 #654]: #656
-#663 := [trans #657 #661]: #662
-#666 := [monotonicity #644 #663]: #665
-#625 := (iff #153 #624)
-#622 := (iff #152 #619)
-#615 := (implies #145 #612)
-#620 := (iff #615 #619)
-#621 := [rewrite]: #620
-#616 := (iff #152 #615)
-#613 := (iff #151 #612)
-#610 := (iff #150 #609)
-#607 := (iff #149 #606)
-#608 := [monotonicity #605]: #607
-#611 := [monotonicity #608]: #610
-#614 := [quant-intro #611]: #613
-#617 := [monotonicity #614]: #616
-#623 := [trans #617 #621]: #622
-#626 := [quant-intro #623]: #625
-#669 := [monotonicity #626 #666]: #668
-#675 := [trans #669 #673]: #674
-#678 := [monotonicity #626 #675]: #677
-#681 := [monotonicity #678]: #680
-#687 := [trans #681 #685]: #686
-#601 := (iff #139 #600)
+#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
-#690 := [monotonicity #602 #687]: #689
-#696 := [trans #690 #694]: #695
-#699 := [monotonicity #696]: #698
-#705 := [trans #699 #703]: #704
-#598 := (iff #134 #597)
-#599 := [rewrite]: #598
-#708 := [monotonicity #599 #705]: #707
-#714 := [trans #708 #712]: #713
-#595 := (iff #132 #594)
-#596 := [monotonicity #593]: #595
-#717 := [monotonicity #596 #714]: #716
-#722 := [trans #717 #720]: #721
-#725 := [monotonicity #722]: #724
-#729 := [trans #725 #727]: #728
-#1012 := [monotonicity #729 #1009]: #1011
-#581 := (iff #129 #580)
-#578 := (iff #128 #575)
-#571 := (implies #122 #568)
-#576 := (iff #571 #575)
-#577 := [rewrite]: #576
-#572 := (iff #128 #571)
-#569 := (iff #127 #568)
-#566 := (iff #126 #565)
-#563 := (iff #125 #562)
-#560 := (iff #124 #559)
-#542 := (= #117 #541)
-#543 := [rewrite]: #542
-#561 := [monotonicity #543]: #560
-#564 := [monotonicity #511 #561]: #563
-#567 := [monotonicity #564]: #566
-#570 := [quant-intro #567]: #569
-#573 := [monotonicity #570]: #572
-#579 := [trans #573 #577]: #578
-#582 := [quant-intro #579]: #581
-#1015 := [monotonicity #582 #1012]: #1014
-#1021 := [trans #1015 #1019]: #1020
-#557 := (iff #120 #556)
-#554 := (iff #119 #551)
-#547 := (implies #536 #544)
-#552 := (iff #547 #551)
-#553 := [rewrite]: #552
-#548 := (iff #119 #547)
-#545 := (iff #118 #544)
-#546 := [monotonicity #543]: #545
-#539 := (iff #116 #536)
-#533 := (and #509 #84)
-#537 := (iff #533 #536)
-#538 := [rewrite]: #537
-#534 := (iff #116 #533)
-#535 := [monotonicity #511]: #534
-#540 := [trans #535 #538]: #539
-#549 := [monotonicity #540 #546]: #548
-#555 := [trans #549 #553]: #554
-#558 := [quant-intro #555]: #557
-#1024 := [monotonicity #558 #1021]: #1023
-#1030 := [trans #1024 #1028]: #1029
-#531 := (iff #115 #530)
-#528 := (iff #114 #525)
-#521 := (implies #518 #113)
-#526 := (iff #521 #525)
-#527 := [rewrite]: #526
-#522 := (iff #114 #521)
-#519 := (iff #111 #518)
-#516 := (iff #110 #515)
-#517 := [rewrite]: #516
-#520 := [monotonicity #514 #517]: #519
-#523 := [monotonicity #520]: #522
-#529 := [trans #523 #527]: #528
-#532 := [quant-intro #529]: #531
-#1033 := [monotonicity #532 #1030]: #1032
-#1039 := [trans #1033 #1037]: #1038
-#1042 := [monotonicity #1039]: #1041
-#1048 := [trans #1042 #1046]: #1047
-#507 := (iff #101 #506)
-#508 := [rewrite]: #507
-#1051 := [monotonicity #508 #1048]: #1050
-#1057 := [trans #1051 #1055]: #1056
-#1060 := [monotonicity #1057]: #1059
-#1064 := [trans #1060 #1062]: #1063
-#504 := (iff #98 #503)
-#501 := (iff #97 #498)
-#494 := (implies #91 #491)
-#499 := (iff #494 #498)
-#500 := [rewrite]: #499
-#495 := (iff #97 #494)
-#492 := (iff #96 #491)
-#489 := (iff #95 #488)
-#486 := (iff #94 #483)
-#480 := (and #430 #93)
-#484 := (iff #480 #483)
-#485 := [rewrite]: #484
-#481 := (iff #94 #480)
-#431 := (iff #68 #430)
+#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
-#482 := [monotonicity #432]: #481
-#487 := [trans #482 #485]: #486
-#490 := [monotonicity #487]: #489
-#493 := [quant-intro #490]: #492
-#496 := [monotonicity #493]: #495
-#502 := [trans #496 #500]: #501
-#505 := [quant-intro #502]: #504
-#1067 := [monotonicity #505 #1064]: #1066
-#1073 := [trans #1067 #1071]: #1072
-#1076 := [monotonicity #505 #1073]: #1075
-#478 := (iff #89 #477)
-#475 := (iff #88 #472)
-#468 := (implies #463 #87)
-#473 := (iff #468 #472)
-#474 := [rewrite]: #473
-#469 := (iff #88 #468)
-#466 := (iff #85 #463)
-#460 := (and #430 #84)
-#464 := (iff #460 #463)
-#465 := [rewrite]: #464
-#461 := (iff #85 #460)
-#462 := [monotonicity #432]: #461
-#467 := [trans #462 #465]: #466
-#470 := [monotonicity #467]: #469
-#476 := [trans #470 #474]: #475
-#479 := [quant-intro #476]: #478
-#1079 := [monotonicity #479 #1076]: #1078
-#1085 := [trans #1079 #1083]: #1084
-#1088 := [monotonicity #479 #1085]: #1087
-#458 := (iff #81 #457)
-#455 := (iff #80 #452)
-#448 := (implies #445 #79)
-#453 := (iff #448 #452)
-#454 := [rewrite]: #453
-#449 := (iff #80 #448)
-#446 := (iff #77 #445)
-#443 := (iff #76 #442)
-#444 := [rewrite]: #443
-#434 := (iff #69 #433)
 #435 := [monotonicity #432]: #434
-#447 := [monotonicity #435 #444]: #446
-#450 := [monotonicity #447]: #449
-#456 := [trans #450 #454]: #455
-#459 := [quant-intro #456]: #458
-#1091 := [monotonicity #459 #1088]: #1090
-#1097 := [trans #1091 #1095]: #1096
-#1100 := [monotonicity #459 #1097]: #1099
-#1103 := [monotonicity #1100]: #1102
-#1109 := [trans #1103 #1107]: #1108
-#1112 := [monotonicity #1109]: #1111
-#440 := (iff #72 #439)
-#441 := [rewrite]: #440
-#1115 := [monotonicity #441 #1112]: #1114
-#1121 := [trans #1115 #1119]: #1120
-#1124 := [monotonicity #441 #1121]: #1123
-#437 := (iff #70 #436)
-#438 := [quant-intro #435]: #437
-#1127 := [monotonicity #438 #1124]: #1126
-#1133 := [trans #1127 #1131]: #1132
-#428 := (iff #65 #427)
-#425 := (iff #64 #422)
-#419 := (implies #62 #416)
+#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 #64 #419)
-#417 := (iff #63 #416)
+#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
-#1136 := [monotonicity #429 #1133]: #1135
-#1142 := [trans #1136 #1140]: #1141
-#414 := (iff #61 #413)
-#411 := (iff #60 #408)
-#405 := (implies #57 #401)
-#409 := (iff #405 #408)
-#410 := [rewrite]: #409
-#406 := (iff #60 #405)
-#403 := (iff #59 #401)
-#404 := [rewrite]: #403
-#407 := [monotonicity #404]: #406
-#412 := [trans #407 #410]: #411
-#415 := [quant-intro #412]: #414
-#1145 := [monotonicity #415 #1142]: #1144
-#1151 := [trans #1145 #1149]: #1150
-#1154 := [monotonicity #1151]: #1153
-#1158 := [trans #1154 #1156]: #1157
-#1161 := [monotonicity #1158]: #1160
-#1800 := [trans #1161 #1798]: #1799
-#400 := [asserted]: #271
-#1801 := [mp #400 #1800]: #1796
-#1806 := [not-or-elim #1801]: #1776
-#2096 := [mp~ #1806 #1869]: #1776
-#4578 := [mp #2096 #4577]: #4573
-#3848 := (not #4573)
-#4978 := (or #3848 #4961 #4723)
-#3774 := (= ?v0!0 f10)
-#4738 := (not #3774)
-#4739 := (or #4738 #4723)
-#4945 := (or #3848 #4739)
-#5294 := (iff #4945 #4978)
-#4947 := (or #4961 #4723)
-#4861 := (or #3848 #4947)
-#4984 := (iff #4861 #4978)
-#5293 := [rewrite]: #4984
-#4793 := (iff #4945 #4861)
-#4950 := (iff #4739 #4947)
-#4962 := (iff #4738 #4961)
-#3746 := (iff #3774 #3785)
-#3747 := [rewrite]: #3746
-#4946 := [monotonicity #3747]: #4962
-#4976 := [monotonicity #4946]: #4950
-#4971 := [monotonicity #4976]: #4793
-#5295 := [trans #4971 #5293]: #5294
-#4860 := [quant-inst #1862]: #4945
-#5296 := [mp #4860 #5295]: #4978
-#5281 := [unit-resolution #5296 #4578 #5280]: #4961
-#3752 := (or #3785 #3791)
-#4187 := (forall (vars (?v0 S2)) (:pat #4186) #422)
-#4190 := (iff #427 #4187)
-#4188 := (iff #422 #422)
-#4189 := [refl]: #4188
-#4191 := [quant-intro #4189]: #4190
-#1824 := (~ #427 #427)
-#1853 := (~ #422 #422)
-#1854 := [refl]: #1853
-#1825 := [nnf-pos #1854]: #1824
-#1802 := [not-or-elim #1801]: #427
-#1855 := [mp~ #1802 #1825]: #427
-#4192 := [mp #1855 #4191]: #4187
-#3757 := (not #4187)
-#3763 := (or #3757 #3785 #3791)
-#3784 := (or #3774 #3791)
-#3735 := (or #3757 #3784)
-#4719 := (iff #3735 #3763)
-#3733 := (or #3757 #3752)
-#4600 := (iff #3733 #3763)
-#4713 := [rewrite]: #4600
-#3736 := (iff #3735 #3733)
-#3754 := (iff #3784 #3752)
-#3755 := [monotonicity #3747]: #3754
-#3737 := [monotonicity #3755]: #3736
-#4720 := [trans #3737 #4713]: #4719
-#3732 := [quant-inst #1862]: #3735
-#4721 := [mp #3732 #4720]: #3763
-#3799 := [unit-resolution #4721 #4192]: #3752
-#3751 := [unit-resolution #3799 #5281]: #3791
-#3738 := (not #3791)
-#3734 := (or #3738 #4722)
-#4794 := [th-lemma arith triangle-eq]: #3734
-#4987 := [unit-resolution #4794 #3751]: #4722
-#5297 := (<= #1863 0::Int)
-#5063 := (or #5297 #1864)
-#5064 := [th-lemma arith farkas 1 1]: #5063
-#5282 := [unit-resolution #5064 #5292]: #5297
-#5285 := [th-lemma arith farkas 1 -1 1 #5282 #4987 #298]: false
-#5286 := [lemma #5285]: #1864
-#4557 := (or #1865 #4554)
+#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)
-#4563 := (or #1164 #4560)
+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)
-#3826 := [hypothesis]: #1164
-#3850 := (or #3848 #72)
-#3897 := (= f10 f10)
-#3901 := (not #3897)
-#3868 := (or #3901 #72)
-#3839 := (or #3848 #3868)
-#3841 := (iff #3839 #3850)
-#3819 := (iff #3850 #3850)
-#3828 := [rewrite]: #3819
-#3849 := (iff #3868 #72)
-#3853 := (or false #72)
-#3846 := (iff #3853 #72)
-#3847 := [rewrite]: #3846
-#3860 := (iff #3868 #3853)
-#3874 := (iff #3901 false)
-#3871 := (not true)
-#3873 := (iff #3871 false)
-#3862 := [rewrite]: #3873
-#3872 := (iff #3901 #3871)
-#3869 := (iff #3897 true)
-#3870 := [rewrite]: #3869
-#3867 := [monotonicity #3870]: #3872
-#3851 := [trans #3867 #3862]: #3874
-#3845 := [monotonicity #3851]: #3860
-#3852 := [trans #3845 #3847]: #3849
-#3827 := [monotonicity #3852]: #3841
-#3829 := [trans #3827 #3828]: #3841
-#3840 := [quant-inst #56]: #3839
-#3820 := [mp #3840 #3829]: #3850
-#3830 := [unit-resolution #3820 #3826 #4578]: false
-#3797 := [lemma #3830]: #72
-#4569 := (or #1164 #4566)
-#3496 := (forall (vars (?v1 S2)) #3485)
-#3503 := (not #3496)
-#3481 := (forall (vars (?v0 S2) (?v1 S2)) #3476)
-#3502 := (not #3481)
-#3504 := (or #2327 #2894 #3502 #3503)
-#3505 := (not #3504)
-#3510 := (or #3459 #3505)
-#3517 := (not #3510)
-#3436 := (forall (vars (?v0 S2) (?v1 S2)) #3431)
-#3516 := (not #3436)
-#3518 := (or #3516 #3517)
-#3519 := (not #3518)
-#3524 := (or #3413 #3519)
-#3530 := (not #3524)
-#3531 := (or #1467 #3530)
-#3532 := (not #3531)
-#3537 := (or #2244 #3532)
-#3543 := (not #3537)
-#3544 := (or #1458 #3543)
-#3545 := (not #3544)
-#3550 := (or #1458 #3545)
-#3556 := (not #3550)
-#3557 := (or #921 #3556)
-#3558 := (not #3557)
-#3563 := (or #2837 #3558)
-#3569 := (not #3563)
-#3570 := (or #1453 #3569)
-#3571 := (not #3570)
-#3576 := (or #2823 #3571)
-#3584 := (not #3576)
-#3390 := (forall (vars (?v0 S2)) #3385)
-#3583 := (not #3390)
-#3372 := (forall (vars (?v0 S2)) #3369)
-#3582 := (not #3372)
-#3585 := (or #963 #730 #1618 #1622 #2178 #2181 #3582 #3583 #3584)
-#3586 := (not #3585)
-#3302 := (forall (vars (?v0 S2) (?v1 S2)) #3297)
-#3308 := (not #3302)
-#3309 := (or #159 #3308)
-#3310 := (not #3309)
-#3337 := (or #3310 #3334)
-#3344 := (not #3337)
-#3280 := (forall (vars (?v0 S2)) #3275)
-#3343 := (not #3280)
-#3345 := (or #3343 #3344)
-#3346 := (not #3345)
-#3243 := (forall (vars (?v1 S2)) #3232)
-#3249 := (not #3243)
-#3250 := (or #2057 #2672 #3249)
-#3251 := (not #3250)
-#3351 := (or #3251 #3346)
-#3358 := (not #3351)
-#3228 := (forall (vars (?v0 S2)) #3217)
-#3357 := (not #3228)
-#3359 := (or #700 #682 #709 #691 #3357 #3358)
-#3360 := (not #3359)
-#3591 := (or #3360 #3586)
-#3601 := (not #3591)
-#3214 := (forall (vars (?v0 S2)) #3209)
-#3600 := (not #3214)
-#3186 := (forall (vars (?v0 S2)) #3181)
-#3599 := (not #3186)
-#3158 := (forall (vars (?v0 S2) (?v1 S2)) #3153)
-#3598 := (not #3158)
-#3135 := (forall (vars (?v0 S2) (?v1 S2)) #3130)
-#3597 := (not #3135)
-#3602 := (or #1715 #1710 #3597 #3598 #3599 #3600 #3601)
-#3603 := (not #3602)
-#3103 := (forall (vars (?v1 S2)) #3092)
-#3109 := (not #3103)
-#3110 := (or #1949 #2534 #3109)
-#3111 := (not #3110)
-#3608 := (or #3111 #3603)
-#3615 := (not #3608)
-#3088 := (forall (vars (?v0 S2) (?v1 S2)) #3083)
-#3614 := (not #3088)
-#3616 := (or #3614 #3615)
-#3617 := (not #3616)
-#3622 := (or #3066 #3617)
-#3629 := (not #3622)
-#3043 := (forall (vars (?v0 S2) (?v1 S2)) #3038)
-#3628 := (not #3043)
-#3630 := (or #3628 #3629)
-#3631 := (not #3630)
-#3636 := (or #2275 #3631)
-#3642 := (not #3636)
-#3643 := (or #1173 #3642)
-#3644 := (not #3643)
-#3649 := (or #1865 #3644)
-#3655 := (not #3649)
-#3656 := (or #1164 #3655)
-#3657 := (not #3656)
-#3662 := (or #1164 #3657)
-#4570 := (iff #3662 #4569)
-#4567 := (iff #3657 #4566)
+#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 #3655 #4560)
-#4558 := (iff #3649 #4557)
-#4555 := (iff #3644 #4554)
-#4552 := (iff #3643 #4551)
-#4549 := (iff #3642 #4548)
+#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 #3631 #4542)
-#4540 := (iff #3630 #4539)
-#4537 := (iff #3629 #4536)
+#4543 := (iff #3635 #4542)
+#4540 := (iff #3628 #4539)
+#4537 := (iff #3623 #4536)
 #4534 := (iff #3622 #4533)
-#4531 := (iff #3617 #4530)
-#4528 := (iff #3616 #4527)
-#4525 := (iff #3615 #4524)
-#4522 := (iff #3608 #4521)
-#4519 := (iff #3603 #4518)
-#4516 := (iff #3602 #4515)
-#4513 := (iff #3601 #4512)
-#4510 := (iff #3591 #4509)
-#4507 := (iff #3586 #4506)
-#4504 := (iff #3585 #4503)
-#4501 := (iff #3584 #4500)
-#4498 := (iff #3576 #4497)
-#4495 := (iff #3571 #4494)
+#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 #3569 #4488)
-#4486 := (iff #3563 #4485)
-#4483 := (iff #3558 #4482)
+#4489 := (iff #3565 #4488)
+#4486 := (iff #3564 #4485)
+#4483 := (iff #3563 #4482)
 #4480 := (iff #3557 #4479)
-#4477 := (iff #3556 #4476)
-#4474 := (iff #3550 #4473)
-#4471 := (iff #3545 #4470)
+#4477 := (iff #3552 #4476)
+#4474 := (iff #3551 #4473)
+#4471 := (iff #3550 #4470)
 #4468 := (iff #3544 #4467)
-#4465 := (iff #3543 #4464)
-#4462 := (iff #3537 #4461)
-#4459 := (iff #3532 #4458)
-#4456 := (iff #3531 #4455)
-#4453 := (iff #3530 #4452)
+#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 #3519 #4446)
-#4444 := (iff #3518 #4443)
-#4441 := (iff #3517 #4440)
-#4438 := (iff #3510 #4437)
-#4435 := (iff #3505 #4434)
-#4432 := (iff #3504 #4431)
-#4429 := (iff #3503 #4428)
-#4426 := (iff #3496 #4423)
-#4424 := (iff #3485 #3485)
-#4425 := [refl]: #4424
-#4427 := [quant-intro #4425]: #4426
-#4430 := [monotonicity #4427]: #4429
-#4420 := (iff #3502 #4419)
-#4417 := (iff #3481 #4414)
-#4415 := (iff #3476 #3476)
-#4416 := [refl]: #4415
-#4418 := [quant-intro #4416]: #4417
-#4421 := [monotonicity #4418]: #4420
-#4433 := [monotonicity #4421 #4430]: #4432
-#4436 := [monotonicity #4433]: #4435
-#4439 := [monotonicity #4436]: #4438
-#4442 := [monotonicity #4439]: #4441
-#4412 := (iff #3516 #4411)
-#4409 := (iff #3436 #4406)
-#4407 := (iff #3431 #3431)
-#4408 := [refl]: #4407
-#4410 := [quant-intro #4408]: #4409
-#4413 := [monotonicity #4410]: #4412
-#4445 := [monotonicity #4413 #4442]: #4444
+#4447 := (iff #3523 #4446)
+#4444 := (iff #3516 #4441)
+#4442 := (iff #3505 #3505)
+#4443 := [refl]: #4442
+#4445 := [quant-intro #4443]: #4444
 #4448 := [monotonicity #4445]: #4447
-#4451 := [monotonicity #4448]: #4450
+#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
-#4403 := (iff #1467 #4402)
-#4400 := (iff #1464 #4397)
-#4398 := (iff #1461 #1461)
-#4399 := [refl]: #4398
-#4401 := [quant-intro #4399]: #4400
-#4404 := [monotonicity #4401]: #4403
-#4457 := [monotonicity #4404 #4454]: #4456
+#4457 := [monotonicity #4454]: #4456
 #4460 := [monotonicity #4457]: #4459
-#4463 := [monotonicity #4460]: #4462
+#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
-#4475 := [monotonicity #4472]: #4474
+#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
-#4395 := (iff #921 #4394)
-#4392 := (iff #787 #4389)
-#4390 := (iff #782 #782)
-#4391 := [refl]: #4390
-#4393 := [quant-intro #4391]: #4392
-#4396 := [monotonicity #4393]: #4395
-#4481 := [monotonicity #4396 #4478]: #4480
+#4481 := [monotonicity #4478]: #4480
 #4484 := [monotonicity #4481]: #4483
 #4487 := [monotonicity #4484]: #4486
 #4490 := [monotonicity #4487]: #4489
-#4386 := (iff #1453 #4385)
-#4383 := (iff #1450 #4380)
-#4381 := (iff #1445 #1445)
-#4382 := [refl]: #4381
-#4384 := [quant-intro #4382]: #4383
-#4387 := [monotonicity #4384]: #4386
-#4493 := [monotonicity #4387 #4490]: #4492
+#4493 := [monotonicity #4490]: #4492
 #4496 := [monotonicity #4493]: #4495
-#4499 := [monotonicity #4496]: #4498
+#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
-#4378 := (iff #3583 #4377)
-#4375 := (iff #3390 #4372)
-#4373 := (iff #3385 #3385)
-#4374 := [refl]: #4373
-#4376 := [quant-intro #4374]: #4375
-#4379 := [monotonicity #4376]: #4378
-#4370 := (iff #3582 #4369)
-#4367 := (iff #3372 #4364)
-#4365 := (iff #3369 #3369)
-#4366 := [refl]: #4365
-#4368 := [quant-intro #4366]: #4367
-#4371 := [monotonicity #4368]: #4370
-#4360 := (iff #1618 #4359)
-#4357 := (iff #1615 #4354)
-#4355 := (iff #1610 #1610)
-#4356 := [refl]: #4355
-#4358 := [quant-intro #4356]: #4357
-#4361 := [monotonicity #4358]: #4360
-#4505 := [monotonicity #4361 #4371 #4379 #4502]: #4504
+#4505 := [monotonicity #4502]: #4504
 #4508 := [monotonicity #4505]: #4507
-#4352 := (iff #3360 #4351)
-#4349 := (iff #3359 #4348)
-#4346 := (iff #3358 #4345)
-#4343 := (iff #3351 #4342)
-#4340 := (iff #3346 #4339)
-#4337 := (iff #3345 #4336)
-#4334 := (iff #3344 #4333)
-#4331 := (iff #3337 #4330)
-#4328 := (iff #3310 #4327)
-#4325 := (iff #3309 #4324)
-#4322 := (iff #3308 #4321)
-#4319 := (iff #3302 #4316)
-#4317 := (iff #3297 #3297)
-#4318 := [refl]: #4317
-#4320 := [quant-intro #4318]: #4319
+#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
-#4329 := [monotonicity #4326]: #4328
-#4332 := [monotonicity #4329]: #4331
-#4335 := [monotonicity #4332]: #4334
-#4314 := (iff #3343 #4313)
-#4311 := (iff #3280 #4308)
-#4309 := (iff #3275 #3275)
-#4310 := [refl]: #4309
-#4312 := [quant-intro #4310]: #4311
-#4315 := [monotonicity #4312]: #4314
-#4338 := [monotonicity #4315 #4335]: #4337
-#4341 := [monotonicity #4338]: #4340
-#4306 := (iff #3251 #4305)
-#4303 := (iff #3250 #4302)
-#4300 := (iff #3249 #4299)
-#4297 := (iff #3243 #4294)
-#4295 := (iff #3232 #3232)
-#4296 := [refl]: #4295
-#4298 := [quant-intro #4296]: #4297
-#4301 := [monotonicity #4298]: #4300
-#4304 := [monotonicity #4301]: #4303
-#4307 := [monotonicity #4304]: #4306
-#4344 := [monotonicity #4307 #4341]: #4343
-#4347 := [monotonicity #4344]: #4346
-#4290 := (iff #3357 #4289)
-#4287 := (iff #3228 #4284)
-#4285 := (iff #3217 #3217)
-#4286 := [refl]: #4285
-#4288 := [quant-intro #4286]: #4287
-#4291 := [monotonicity #4288]: #4290
-#4350 := [monotonicity #4291 #4347]: #4349
-#4353 := [monotonicity #4350]: #4352
-#4511 := [monotonicity #4353 #4508]: #4510
-#4514 := [monotonicity #4511]: #4513
-#4281 := (iff #3600 #4280)
-#4278 := (iff #3214 #4275)
-#4276 := (iff #3209 #3209)
-#4277 := [refl]: #4276
-#4279 := [quant-intro #4277]: #4278
-#4282 := [monotonicity #4279]: #4281
-#4273 := (iff #3599 #4272)
-#4270 := (iff #3186 #4267)
-#4268 := (iff #3181 #3181)
-#4269 := [refl]: #4268
-#4271 := [quant-intro #4269]: #4270
-#4274 := [monotonicity #4271]: #4273
-#4265 := (iff #3598 #4264)
-#4262 := (iff #3158 #4259)
-#4260 := (iff #3153 #3153)
-#4261 := [refl]: #4260
-#4263 := [quant-intro #4261]: #4262
-#4266 := [monotonicity #4263]: #4265
-#4256 := (iff #3597 #4255)
-#4253 := (iff #3135 #4250)
-#4251 := (iff #3130 #3130)
-#4252 := [refl]: #4251
-#4254 := [quant-intro #4252]: #4253
+#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
-#4248 := (iff #1710 #4247)
-#4245 := (iff #1707 #4242)
-#4243 := (iff #1704 #1704)
-#4244 := [refl]: #4243
-#4246 := [quant-intro #4244]: #4245
-#4249 := [monotonicity #4246]: #4248
-#4517 := [monotonicity #4249 #4257 #4266 #4274 #4282 #4514]: #4516
-#4520 := [monotonicity #4517]: #4519
-#4239 := (iff #3111 #4238)
-#4236 := (iff #3110 #4235)
-#4233 := (iff #3109 #4232)
-#4230 := (iff #3103 #4227)
-#4228 := (iff #3092 #3092)
-#4229 := [refl]: #4228
-#4231 := [quant-intro #4229]: #4230
-#4234 := [monotonicity #4231]: #4233
-#4237 := [monotonicity #4234]: #4236
-#4240 := [monotonicity #4237]: #4239
-#4523 := [monotonicity #4240 #4520]: #4522
-#4526 := [monotonicity #4523]: #4525
-#4224 := (iff #3614 #4223)
-#4221 := (iff #3088 #4218)
-#4219 := (iff #3083 #3083)
-#4220 := [refl]: #4219
-#4222 := [quant-intro #4220]: #4221
-#4225 := [monotonicity #4222]: #4224
-#4529 := [monotonicity #4225 #4526]: #4528
-#4532 := [monotonicity #4529]: #4531
-#4535 := [monotonicity #4532]: #4534
-#4538 := [monotonicity #4535]: #4537
-#4215 := (iff #3628 #4214)
-#4212 := (iff #3043 #4209)
-#4210 := (iff #3038 #3038)
-#4211 := [refl]: #4210
-#4213 := [quant-intro #4211]: #4212
-#4216 := [monotonicity #4213]: #4215
-#4541 := [monotonicity #4216 #4538]: #4540
+#4260 := [monotonicity #4257]: #4259
+#4541 := [monotonicity #4260 #4538]: #4540
 #4544 := [monotonicity #4541]: #4543
-#4547 := [monotonicity #4544]: #4546
+#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
-#4206 := (iff #1173 #4205)
-#4203 := (iff #1170 #4200)
-#4201 := (iff #1169 #1169)
-#4202 := [refl]: #4201
-#4204 := [quant-intro #4202]: #4203
-#4207 := [monotonicity #4204]: #4206
-#4553 := [monotonicity #4207 #4550]: #4552
+#4553 := [monotonicity #4550]: #4552
 #4556 := [monotonicity #4553]: #4555
-#4559 := [monotonicity #4556]: #4558
+#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
-#4571 := [monotonicity #4568]: #4570
-#2323 := (not #2322)
-#2925 := (and #775 #2323 #2922)
-#2928 := (not #2925)
-#2931 := (forall (vars (?v1 S2)) #2928)
-#2897 := (not #2894)
-#2940 := (and #1507 #2328 #2897 #2931)
-#2867 := (and #2296 #2298)
-#2870 := (not #2867)
-#2888 := (or #2870 #2883)
-#2891 := (not #2888)
-#2945 := (or #2891 #2940)
-#2948 := (and #1483 #2945)
-#2267 := (not #2266)
-#2842 := (and #2264 #2267)
-#2845 := (not #2842)
-#2861 := (or #2845 #2856)
-#2864 := (not #2861)
-#2951 := (or #2864 #2948)
-#2954 := (and #1464 #2951)
-#2957 := (or #2244 #2954)
-#2960 := (and #204 #2957)
-#2963 := (or #1458 #2960)
-#2966 := (and #787 #2963)
-#2969 := (or #2837 #2966)
-#2972 := (and #1450 #2969)
-#2975 := (or #2823 #2972)
-#2182 := (not #2181)
-#2179 := (not #2178)
-#2981 := (and #182 #733 #1439 #1597 #1615 #1623 #2179 #2182 #2975)
-#2124 := (not #2123)
-#2120 := (not #2119)
-#2760 := (and #2120 #2124)
-#2763 := (not #2760)
-#2780 := (or #2763 #2775)
+#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)
-#2133 := (not #159)
-#2143 := (and #2133 #1359)
-#2789 := (or #2143 #2783)
-#2733 := (not #2728)
-#2751 := (and #2733 #2746)
-#2754 := (or #1319 #2751)
-#2757 := (forall (vars (?v0 S2)) #2754)
-#2794 := (and #2757 #2789)
-#2053 := (not #2052)
-#2703 := (and #2053 #2700)
-#2706 := (not #2703)
-#2709 := (forall (vars (?v1 S2)) #2706)
-#2675 := (not #2672)
-#2715 := (and #2058 #2675 #2709)
-#2797 := (or #2715 #2794)
-#2159 := (not #1387)
-#2162 := (forall (vars (?v0 S2)) #2159)
-#2803 := (and #137 #142 #597 #600 #2162 #2797)
-#2986 := (or #2803 #2981)
-#2652 := (not #2647)
-#2655 := (and #2017 #2635 #2652)
-#2658 := (or #1274 #2655)
-#2661 := (forall (vars (?v0 S2)) #2658)
-#2597 := (not #2592)
-#2615 := (and #1990 #2597 #2610)
-#2618 := (or #1236 #2615)
-#2621 := (forall (vars (?v0 S2)) #2618)
-#2992 := (and #101 #1682 #1698 #1707 #2621 #2661 #2986)
-#1945 := (not #1944)
-#2565 := (and #430 #1945 #2562)
-#2568 := (not #2565)
-#2571 := (forall (vars (?v1 S2)) #2568)
-#2537 := (not #2534)
-#1950 := (not #1949)
-#2577 := (and #1950 #2537 #2571)
-#2997 := (or #2577 #2992)
-#3000 := (and #1221 #2997)
-#1911 := (not #1910)
-#2522 := (and #1911 #1913)
-#2525 := (not #2522)
-#2528 := (or #2519 #2525)
-#2531 := (not #2528)
-#3003 := (or #2531 #3000)
-#3006 := (and #1190 #3003)
-#1888 := (not #1887)
-#2490 := (and #1885 #1888)
-#2493 := (not #2490)
-#2509 := (or #2493 #2504)
-#2512 := (not #2509)
-#3009 := (or #2512 #3006)
-#3012 := (and #1170 #3009)
-#3015 := (or #1865 #3012)
-#3018 := (and #72 #3015)
-#3021 := (or #1164 #3018)
-#3663 := (iff #3021 #3662)
-#3660 := (iff #3018 #3657)
-#3652 := (and #72 #3649)
-#3658 := (iff #3652 #3657)
-#3659 := [rewrite]: #3658
-#3653 := (iff #3018 #3652)
-#3650 := (iff #3015 #3649)
-#3647 := (iff #3012 #3644)
-#3639 := (and #1170 #3636)
-#3645 := (iff #3639 #3644)
-#3646 := [rewrite]: #3645
-#3640 := (iff #3012 #3639)
-#3637 := (iff #3009 #3636)
-#3634 := (iff #3006 #3631)
-#3625 := (and #3043 #3622)
-#3632 := (iff #3625 #3631)
-#3633 := [rewrite]: #3632
-#3626 := (iff #3006 #3625)
-#3623 := (iff #3003 #3622)
-#3620 := (iff #3000 #3617)
-#3611 := (and #3088 #3608)
-#3618 := (iff #3611 #3617)
-#3619 := [rewrite]: #3618
-#3612 := (iff #3000 #3611)
-#3609 := (iff #2997 #3608)
-#3606 := (iff #2992 #3603)
-#3594 := (and #101 #3135 #3158 #1707 #3186 #3214 #3591)
-#3604 := (iff #3594 #3603)
-#3605 := [rewrite]: #3604
-#3595 := (iff #2992 #3594)
-#3592 := (iff #2986 #3591)
-#3589 := (iff #2981 #3586)
-#3579 := (and #182 #733 #3372 #3390 #1615 #1623 #2179 #2182 #3576)
-#3587 := (iff #3579 #3586)
-#3588 := [rewrite]: #3587
-#3580 := (iff #2981 #3579)
-#3577 := (iff #2975 #3576)
-#3574 := (iff #2972 #3571)
-#3566 := (and #1450 #3563)
-#3572 := (iff #3566 #3571)
-#3573 := [rewrite]: #3572
-#3567 := (iff #2972 #3566)
-#3564 := (iff #2969 #3563)
-#3561 := (iff #2966 #3558)
-#3553 := (and #787 #3550)
-#3559 := (iff #3553 #3558)
-#3560 := [rewrite]: #3559
-#3554 := (iff #2966 #3553)
-#3551 := (iff #2963 #3550)
-#3548 := (iff #2960 #3545)
-#3540 := (and #204 #3537)
-#3546 := (iff #3540 #3545)
-#3547 := [rewrite]: #3546
-#3541 := (iff #2960 #3540)
-#3538 := (iff #2957 #3537)
-#3535 := (iff #2954 #3532)
-#3527 := (and #1464 #3524)
-#3533 := (iff #3527 #3532)
-#3534 := [rewrite]: #3533
-#3528 := (iff #2954 #3527)
-#3525 := (iff #2951 #3524)
-#3522 := (iff #2948 #3519)
-#3513 := (and #3436 #3510)
-#3520 := (iff #3513 #3519)
-#3521 := [rewrite]: #3520
-#3514 := (iff #2948 #3513)
-#3511 := (iff #2945 #3510)
-#3508 := (iff #2940 #3505)
-#3499 := (and #3481 #2328 #2897 #3496)
-#3506 := (iff #3499 #3505)
-#3507 := [rewrite]: #3506
-#3500 := (iff #2940 #3499)
-#3497 := (iff #2931 #3496)
-#3494 := (iff #2928 #3485)
-#3486 := (not #3485)
-#3489 := (not #3486)
-#3492 := (iff #3489 #3485)
-#3493 := [rewrite]: #3492
-#3490 := (iff #2928 #3489)
-#3487 := (iff #2925 #3486)
-#3488 := [rewrite]: #3487
-#3491 := [monotonicity #3488]: #3490
-#3495 := [trans #3491 #3493]: #3494
-#3498 := [quant-intro #3495]: #3497
-#3482 := (iff #1507 #3481)
-#3479 := (iff #1504 #3476)
-#3462 := (or #781 #1203)
-#3473 := (or #3462 #1500)
-#3477 := (iff #3473 #3476)
-#3478 := [rewrite]: #3477
-#3474 := (iff #1504 #3473)
-#3471 := (iff #1497 #3462)
-#3463 := (not #3462)
-#3466 := (not #3463)
-#3469 := (iff #3466 #3462)
-#3470 := [rewrite]: #3469
-#3467 := (iff #1497 #3466)
-#3464 := (iff #1492 #3463)
-#3465 := [rewrite]: #3464
-#3468 := [monotonicity #3465]: #3467
-#3472 := [trans #3468 #3470]: #3471
-#3475 := [monotonicity #3472]: #3474
-#3480 := [trans #3475 #3478]: #3479
-#3483 := [quant-intro #3480]: #3482
-#3501 := [monotonicity #3483 #3498]: #3500
-#3509 := [trans #3501 #3507]: #3508
-#3460 := (iff #2891 #3459)
-#3457 := (iff #2888 #3454)
-#3440 := (or #2295 #3439)
-#3451 := (or #3440 #2883)
-#3455 := (iff #3451 #3454)
-#3456 := [rewrite]: #3455
-#3452 := (iff #2888 #3451)
-#3449 := (iff #2870 #3440)
-#3441 := (not #3440)
-#3444 := (not #3441)
-#3447 := (iff #3444 #3440)
-#3448 := [rewrite]: #3447
-#3445 := (iff #2870 #3444)
-#3442 := (iff #2867 #3441)
-#3443 := [rewrite]: #3442
-#3446 := [monotonicity #3443]: #3445
-#3450 := [trans #3446 #3448]: #3449
-#3453 := [monotonicity #3450]: #3452
-#3458 := [trans #3453 #3456]: #3457
-#3461 := [monotonicity #3458]: #3460
-#3512 := [monotonicity #3461 #3509]: #3511
-#3437 := (iff #1483 #3436)
-#3434 := (iff #1478 #3431)
-#3417 := (or #775 #3416)
-#3428 := (or #3417 #1470)
-#3432 := (iff #3428 #3431)
-#3433 := [rewrite]: #3432
-#3429 := (iff #1478 #3428)
-#3426 := (iff #804 #3417)
-#3418 := (not #3417)
-#3421 := (not #3418)
-#3424 := (iff #3421 #3417)
-#3425 := [rewrite]: #3424
-#3422 := (iff #804 #3421)
-#3419 := (iff #798 #3418)
-#3420 := [rewrite]: #3419
-#3423 := [monotonicity #3420]: #3422
-#3427 := [trans #3423 #3425]: #3426
-#3430 := [monotonicity #3427]: #3429
-#3435 := [trans #3430 #3433]: #3434
-#3438 := [quant-intro #3435]: #3437
-#3515 := [monotonicity #3438 #3512]: #3514
-#3523 := [trans #3515 #3521]: #3522
-#3414 := (iff #2864 #3413)
-#3411 := (iff #2861 #3408)
-#3394 := (or #3393 #2266)
-#3405 := (or #3394 #2856)
-#3409 := (iff #3405 #3408)
-#3410 := [rewrite]: #3409
-#3406 := (iff #2861 #3405)
-#3403 := (iff #2845 #3394)
-#3395 := (not #3394)
-#3398 := (not #3395)
-#3401 := (iff #3398 #3394)
-#3402 := [rewrite]: #3401
-#3399 := (iff #2845 #3398)
-#3396 := (iff #2842 #3395)
-#3397 := [rewrite]: #3396
-#3400 := [monotonicity #3397]: #3399
-#3404 := [trans #3400 #3402]: #3403
-#3407 := [monotonicity #3404]: #3406
-#3412 := [trans #3407 #3410]: #3411
-#3415 := [monotonicity #3412]: #3414
-#3526 := [monotonicity #3415 #3523]: #3525
-#3529 := [monotonicity #3526]: #3528
-#3536 := [trans #3529 #3534]: #3535
-#3539 := [monotonicity #3536]: #3538
-#3542 := [monotonicity #3539]: #3541
-#3549 := [trans #3542 #3547]: #3548
-#3552 := [monotonicity #3549]: #3551
-#3555 := [monotonicity #3552]: #3554
-#3562 := [trans #3555 #3560]: #3561
-#3565 := [monotonicity #3562]: #3564
-#3568 := [monotonicity #3565]: #3567
-#3575 := [trans #3568 #3573]: #3574
-#3578 := [monotonicity #3575]: #3577
-#3391 := (iff #1597 #3390)
-#3388 := (iff #1594 #3385)
-#3382 := (or #3365 #1591)
-#3386 := (iff #3382 #3385)
-#3387 := [rewrite]: #3386
-#3383 := (iff #1594 #3382)
-#3380 := (iff #1586 #3365)
-#3375 := (not #3366)
-#3378 := (iff #3375 #3365)
-#3379 := [rewrite]: #3378
-#3376 := (iff #1586 #3375)
-#3367 := (iff #1428 #3366)
+#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
+#3600 := (iff #3001 #3599)
+#3597 := (iff #2995 #3596)
+#3594 := (iff #2992 #3591)
+#3586 := (and #1464 #3583)
+#3592 := (iff #3586 #3591)
+#3593 := [rewrite]: #3592
+#3587 := (iff #2992 #3586)
+#3584 := (iff #2989 #3583)
+#3581 := (iff #2986 #3578)
+#3573 := (and #801 #3570)
+#3579 := (iff #3573 #3578)
+#3580 := [rewrite]: #3579
+#3574 := (iff #2986 #3573)
+#3571 := (iff #2983 #3570)
+#3568 := (iff #2980 #3565)
+#3560 := (and #218 #3557)
+#3566 := (iff #3560 #3565)
+#3567 := [rewrite]: #3566
+#3561 := (iff #2980 #3560)
+#3558 := (iff #2977 #3557)
+#3555 := (iff #2974 #3552)
+#3547 := (and #1478 #3544)
+#3553 := (iff #3547 #3552)
+#3554 := [rewrite]: #3553
+#3548 := (iff #2974 #3547)
+#3545 := (iff #2971 #3544)
+#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)
+#3526 := (iff #3519 #3525)
+#3527 := [rewrite]: #3526
+#3520 := (iff #2960 #3519)
+#3517 := (iff #2951 #3516)
+#3514 := (iff #2948 #3505)
+#3506 := (not #3505)
+#3509 := (not #3506)
+#3512 := (iff #3509 #3505)
+#3513 := [rewrite]: #3512
+#3510 := (iff #2948 #3509)
+#3507 := (iff #2945 #3506)
+#3508 := [rewrite]: #3507
+#3511 := [monotonicity #3508]: #3510
+#3515 := [trans #3511 #3513]: #3514
+#3518 := [quant-intro #3515]: #3517
+#3502 := (iff #1521 #3501)
+#3499 := (iff #1518 #3496)
+#3482 := (or #795 #1217)
+#3493 := (or #3482 #1514)
+#3497 := (iff #3493 #3496)
+#3498 := [rewrite]: #3497
+#3494 := (iff #1518 #3493)
+#3491 := (iff #1511 #3482)
+#3483 := (not #3482)
+#3486 := (not #3483)
+#3489 := (iff #3486 #3482)
+#3490 := [rewrite]: #3489
+#3487 := (iff #1511 #3486)
+#3484 := (iff #1506 #3483)
+#3485 := [rewrite]: #3484
+#3488 := [monotonicity #3485]: #3487
+#3492 := [trans #3488 #3490]: #3491
+#3495 := [monotonicity #3492]: #3494
+#3500 := [trans #3495 #3498]: #3499
+#3503 := [quant-intro #3500]: #3502
+#3521 := [monotonicity #3503 #3518]: #3520
+#3529 := [trans #3521 #3527]: #3528
+#3480 := (iff #2911 #3479)
+#3477 := (iff #2908 #3474)
+#3460 := (or #2315 #3459)
+#3471 := (or #3460 #2903)
+#3475 := (iff #3471 #3474)
+#3476 := [rewrite]: #3475
+#3472 := (iff #2908 #3471)
+#3469 := (iff #2890 #3460)
+#3461 := (not #3460)
+#3464 := (not #3461)
+#3467 := (iff #3464 #3460)
+#3468 := [rewrite]: #3467
+#3465 := (iff #2890 #3464)
+#3462 := (iff #2887 #3461)
+#3463 := [rewrite]: #3462
+#3466 := [monotonicity #3463]: #3465
+#3470 := [trans #3466 #3468]: #3469
+#3473 := [monotonicity #3470]: #3472
+#3478 := [trans #3473 #3476]: #3477
+#3481 := [monotonicity #3478]: #3480
+#3532 := [monotonicity #3481 #3529]: #3531
+#3457 := (iff #1497 #3456)
+#3454 := (iff #1492 #3451)
+#3437 := (or #789 #3436)
+#3448 := (or #3437 #1484)
+#3452 := (iff #3448 #3451)
+#3453 := [rewrite]: #3452
+#3449 := (iff #1492 #3448)
+#3446 := (iff #818 #3437)
+#3438 := (not #3437)
+#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
+#3434 := (iff #2884 #3433)
+#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
-#3377 := [monotonicity #3368]: #3376
-#3381 := [trans #3377 #3379]: #3380
-#3384 := [monotonicity #3381]: #3383
-#3389 := [trans #3384 #3387]: #3388
-#3392 := [quant-intro #3389]: #3391
-#3373 := (iff #1439 #3372)
-#3370 := (iff #1434 #3369)
-#3371 := [monotonicity #3368]: #3370
-#3374 := [quant-intro #3371]: #3373
-#3581 := [monotonicity #3374 #3392 #3578]: #3580
-#3590 := [trans #3581 #3588]: #3589
-#3363 := (iff #2803 #3360)
-#3354 := (and #137 #142 #597 #600 #3228 #3351)
-#3361 := (iff #3354 #3360)
-#3362 := [rewrite]: #3361
+#3361 := (iff #2814 #3360)
+#3358 := (iff #2809 #3357)
 #3355 := (iff #2803 #3354)
-#3352 := (iff #2797 #3351)
-#3349 := (iff #2794 #3346)
-#3340 := (and #3280 #3337)
-#3347 := (iff #3340 #3346)
-#3348 := [rewrite]: #3347
-#3341 := (iff #2794 #3340)
-#3338 := (iff #2789 #3337)
-#3335 := (iff #2783 #3334)
-#3332 := (iff #2780 #3329)
-#3315 := (or #2119 #2123)
-#3326 := (or #3315 #2775)
-#3330 := (iff #3326 #3329)
-#3331 := [rewrite]: #3330
-#3327 := (iff #2780 #3326)
-#3324 := (iff #2763 #3315)
-#3316 := (not #3315)
-#3319 := (not #3316)
-#3322 := (iff #3319 #3315)
-#3323 := [rewrite]: #3322
-#3320 := (iff #2763 #3319)
-#3317 := (iff #2760 #3316)
-#3318 := [rewrite]: #3317
-#3321 := [monotonicity #3318]: #3320
-#3325 := [trans #3321 #3323]: #3324
-#3328 := [monotonicity #3325]: #3327
-#3333 := [trans #3328 #3331]: #3332
-#3336 := [monotonicity #3333]: #3335
-#3313 := (iff #2143 #3310)
-#3305 := (and #2133 #3302)
-#3311 := (iff #3305 #3310)
-#3312 := [rewrite]: #3311
-#3306 := (iff #2143 #3305)
-#3303 := (iff #1359 #3302)
-#3300 := (iff #1356 #3297)
-#3283 := (or #1203 #1312)
-#3294 := (or #3283 #1353)
-#3298 := (iff #3294 #3297)
-#3299 := [rewrite]: #3298
-#3295 := (iff #1356 #3294)
-#3292 := (iff #1350 #3283)
-#3284 := (not #3283)
-#3287 := (not #3284)
-#3290 := (iff #3287 #3283)
+#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
-#3288 := (iff #1350 #3287)
-#3285 := (iff #1347 #3284)
-#3286 := [rewrite]: #3285
-#3289 := [monotonicity #3286]: #3288
-#3293 := [trans #3289 #3291]: #3292
-#3296 := [monotonicity #3293]: #3295
-#3301 := [trans #3296 #3299]: #3300
-#3304 := [quant-intro #3301]: #3303
-#3307 := [monotonicity #3304]: #3306
-#3314 := [trans #3307 #3312]: #3313
-#3339 := [monotonicity #3314 #3336]: #3338
-#3281 := (iff #2757 #3280)
-#3278 := (iff #2754 #3275)
-#3256 := (or #57 #1312)
-#3272 := (or #3256 #3269)
-#3276 := (iff #3272 #3275)
-#3277 := [rewrite]: #3276
-#3273 := (iff #2754 #3272)
-#3270 := (iff #2751 #3269)
-#3271 := [rewrite]: #3270
-#3265 := (iff #1319 #3256)
-#3257 := (not #3256)
-#3260 := (not #3257)
-#3263 := (iff #3260 #3256)
-#3264 := [rewrite]: #3263
-#3261 := (iff #1319 #3260)
-#3258 := (iff #1316 #3257)
-#3259 := [rewrite]: #3258
-#3262 := [monotonicity #3259]: #3261
-#3266 := [trans #3262 #3264]: #3265
-#3274 := [monotonicity #3266 #3271]: #3273
-#3279 := [trans #3274 #3277]: #3278
-#3282 := [quant-intro #3279]: #3281
-#3342 := [monotonicity #3282 #3339]: #3341
-#3350 := [trans #3342 #3348]: #3349
-#3254 := (iff #2715 #3251)
-#3246 := (and #2058 #2675 #3243)
-#3252 := (iff #3246 #3251)
-#3253 := [rewrite]: #3252
-#3247 := (iff #2715 #3246)
-#3244 := (iff #2709 #3243)
-#3241 := (iff #2706 #3232)
-#3233 := (not #3232)
-#3236 := (not #3233)
-#3239 := (iff #3236 #3232)
+#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
-#3237 := (iff #2706 #3236)
-#3234 := (iff #2703 #3233)
-#3235 := [rewrite]: #3234
-#3238 := [monotonicity #3235]: #3237
-#3242 := [trans #3238 #3240]: #3241
-#3245 := [quant-intro #3242]: #3244
-#3248 := [monotonicity #3245]: #3247
-#3255 := [trans #3248 #3253]: #3254
-#3353 := [monotonicity #3255 #3350]: #3352
-#3229 := (iff #2162 #3228)
-#3226 := (iff #2159 #3217)
-#3218 := (not #3217)
-#3221 := (not #3218)
-#3224 := (iff #3221 #3217)
+#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
-#3222 := (iff #2159 #3221)
-#3219 := (iff #1387 #3218)
-#3220 := [rewrite]: #3219
-#3223 := [monotonicity #3220]: #3222
-#3227 := [trans #3223 #3225]: #3226
-#3230 := [quant-intro #3227]: #3229
-#3356 := [monotonicity #3230 #3353]: #3355
-#3364 := [trans #3356 #3362]: #3363
-#3593 := [monotonicity #3364 #3590]: #3592
-#3215 := (iff #2661 #3214)
-#3212 := (iff #2658 #3209)
-#3189 := (or #57 #1267)
-#3206 := (or #3189 #3203)
-#3210 := (iff #3206 #3209)
-#3211 := [rewrite]: #3210
-#3207 := (iff #2658 #3206)
-#3204 := (iff #2655 #3203)
-#3205 := [rewrite]: #3204
-#3198 := (iff #1274 #3189)
-#3190 := (not #3189)
-#3193 := (not #3190)
-#3196 := (iff #3193 #3189)
+#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
-#3194 := (iff #1274 #3193)
-#3191 := (iff #1271 #3190)
-#3192 := [rewrite]: #3191
-#3195 := [monotonicity #3192]: #3194
-#3199 := [trans #3195 #3197]: #3198
-#3208 := [monotonicity #3199 #3205]: #3207
-#3213 := [trans #3208 #3211]: #3212
-#3216 := [quant-intro #3213]: #3215
-#3187 := (iff #2621 #3186)
-#3184 := (iff #2618 #3181)
-#3161 := (or #57 #1229)
-#3178 := (or #3161 #3175)
-#3182 := (iff #3178 #3181)
-#3183 := [rewrite]: #3182
-#3179 := (iff #2618 #3178)
-#3176 := (iff #2615 #3175)
-#3177 := [rewrite]: #3176
-#3170 := (iff #1236 #3161)
-#3162 := (not #3161)
-#3165 := (not #3162)
-#3168 := (iff #3165 #3161)
-#3169 := [rewrite]: #3168
-#3166 := (iff #1236 #3165)
-#3163 := (iff #1233 #3162)
-#3164 := [rewrite]: #3163
-#3167 := [monotonicity #3164]: #3166
-#3171 := [trans #3167 #3169]: #3170
-#3180 := [monotonicity #3171 #3177]: #3179
-#3185 := [trans #3180 #3183]: #3184
-#3188 := [quant-intro #3185]: #3187
-#3159 := (iff #1698 #3158)
-#3156 := (iff #1693 #3153)
-#3139 := (or #509 #3138)
-#3150 := (or #3139 #1283)
-#3154 := (iff #3150 #3153)
-#3155 := [rewrite]: #3154
-#3151 := (iff #1693 #3150)
-#3148 := (iff #524 #3139)
-#3140 := (not #3139)
-#3143 := (not #3140)
-#3146 := (iff #3143 #3139)
-#3147 := [rewrite]: #3146
-#3144 := (iff #524 #3143)
-#3141 := (iff #518 #3140)
-#3142 := [rewrite]: #3141
-#3145 := [monotonicity #3142]: #3144
-#3149 := [trans #3145 #3147]: #3148
-#3152 := [monotonicity #3149]: #3151
-#3157 := [trans #3152 #3155]: #3156
-#3160 := [quant-intro #3157]: #3159
-#3136 := (iff #1682 #3135)
-#3133 := (iff #1679 #3130)
-#3116 := (or #512 #1203)
-#3127 := (or #3116 #1676)
-#3131 := (iff #3127 #3130)
-#3132 := [rewrite]: #3131
-#3128 := (iff #1679 #3127)
-#3125 := (iff #1673 #3116)
-#3117 := (not #3116)
-#3120 := (not #3117)
-#3123 := (iff #3120 #3116)
-#3124 := [rewrite]: #3123
-#3121 := (iff #1673 #3120)
-#3118 := (iff #1668 #3117)
-#3119 := [rewrite]: #3118
-#3122 := [monotonicity #3119]: #3121
-#3126 := [trans #3122 #3124]: #3125
-#3129 := [monotonicity #3126]: #3128
-#3134 := [trans #3129 #3132]: #3133
-#3137 := [quant-intro #3134]: #3136
-#3596 := [monotonicity #3137 #3160 #3188 #3216 #3593]: #3595
-#3607 := [trans #3596 #3605]: #3606
-#3114 := (iff #2577 #3111)
-#3106 := (and #1950 #2537 #3103)
-#3112 := (iff #3106 #3111)
-#3113 := [rewrite]: #3112
-#3107 := (iff #2577 #3106)
-#3104 := (iff #2571 #3103)
-#3101 := (iff #2568 #3092)
-#3093 := (not #3092)
-#3096 := (not #3093)
-#3099 := (iff #3096 #3092)
-#3100 := [rewrite]: #3099
-#3097 := (iff #2568 #3096)
-#3094 := (iff #2565 #3093)
-#3095 := [rewrite]: #3094
-#3098 := [monotonicity #3095]: #3097
-#3102 := [trans #3098 #3100]: #3101
-#3105 := [quant-intro #3102]: #3104
-#3108 := [monotonicity #3105]: #3107
-#3115 := [trans #3108 #3113]: #3114
-#3610 := [monotonicity #3115 #3607]: #3609
-#3089 := (iff #1221 #3088)
-#3086 := (iff #1218 #3083)
-#3069 := (or #433 #1203)
-#3080 := (or #1198 #3069)
-#3084 := (iff #3080 #3083)
-#3085 := [rewrite]: #3084
-#3081 := (iff #1218 #3080)
-#3078 := (iff #1215 #3069)
-#3070 := (not #3069)
-#3073 := (not #3070)
-#3076 := (iff #3073 #3069)
-#3077 := [rewrite]: #3076
-#3074 := (iff #1215 #3073)
-#3071 := (iff #1210 #3070)
-#3072 := [rewrite]: #3071
-#3075 := [monotonicity #3072]: #3074
-#3079 := [trans #3075 #3077]: #3078
-#3082 := [monotonicity #3079]: #3081
-#3087 := [trans #3082 #3085]: #3086
-#3090 := [quant-intro #3087]: #3089
-#3613 := [monotonicity #3090 #3610]: #3612
-#3621 := [trans #3613 #3619]: #3620
-#3067 := (iff #2531 #3066)
-#3064 := (iff #2528 #3061)
-#3047 := (or #1910 #3046)
-#3058 := (or #2519 #3047)
-#3062 := (iff #3058 #3061)
-#3063 := [rewrite]: #3062
-#3059 := (iff #2528 #3058)
-#3056 := (iff #2525 #3047)
-#3048 := (not #3047)
-#3051 := (not #3048)
-#3054 := (iff #3051 #3047)
-#3055 := [rewrite]: #3054
-#3052 := (iff #2525 #3051)
-#3049 := (iff #2522 #3048)
-#3050 := [rewrite]: #3049
-#3053 := [monotonicity #3050]: #3052
-#3057 := [trans #3053 #3055]: #3056
-#3060 := [monotonicity #3057]: #3059
-#3065 := [trans #3060 #3063]: #3064
-#3068 := [monotonicity #3065]: #3067
-#3624 := [monotonicity #3068 #3621]: #3623
-#3044 := (iff #1190 #3043)
-#3041 := (iff #1185 #3038)
-#3024 := (or #430 #2487)
-#3035 := (or #3024 #1178)
-#3039 := (iff #3035 #3038)
-#3040 := [rewrite]: #3039
-#3036 := (iff #1185 #3035)
-#3033 := (iff #451 #3024)
-#3025 := (not #3024)
-#3028 := (not #3025)
-#3031 := (iff #3028 #3024)
-#3032 := [rewrite]: #3031
-#3029 := (iff #451 #3028)
-#3026 := (iff #445 #3025)
-#3027 := [rewrite]: #3026
-#3030 := [monotonicity #3027]: #3029
-#3034 := [trans #3030 #3032]: #3033
-#3037 := [monotonicity #3034]: #3036
-#3042 := [trans #3037 #3040]: #3041
-#3045 := [quant-intro #3042]: #3044
-#3627 := [monotonicity #3045 #3624]: #3626
-#3635 := [trans #3627 #3633]: #3634
-#1895 := (iff #2512 #2275)
-#2022 := (iff #2509 #2305)
-#2186 := (or #2097 #1887)
-#1995 := (or #2186 #2504)
-#2306 := (iff #1995 #2305)
-#2021 := [rewrite]: #2306
-#2247 := (iff #2509 #1995)
-#1927 := (iff #2493 #2186)
-#1832 := (not #2186)
-#2131 := (not #1832)
-#2228 := (iff #2131 #2186)
-#1926 := [rewrite]: #2228
-#2132 := (iff #2493 #2131)
-#1833 := (iff #2490 #1832)
-#2187 := [rewrite]: #1833
-#2227 := [monotonicity #2187]: #2132
-#1994 := [trans #2227 #1926]: #1927
-#2248 := [monotonicity #1994]: #2247
-#2274 := [trans #2248 #2021]: #2022
-#1896 := [monotonicity #2274]: #1895
-#3638 := [monotonicity #1896 #3635]: #3637
-#3641 := [monotonicity #3638]: #3640
-#3648 := [trans #3641 #3646]: #3647
-#3651 := [monotonicity #3648]: #3650
-#3654 := [monotonicity #3651]: #3653
-#3661 := [trans #3654 #3659]: #3660
-#3664 := [monotonicity #3661]: #3663
-#2320 := (+ #2319 #2317)
-#2321 := (= #2320 0::Int)
-#2324 := (and #775 #2323 #2321)
-#2341 := (not #2324)
-#2344 := (forall (vars (?v1 S2)) #2341)
-#2329 := (= ?v0!20 f10)
-#2330 := (not #2329)
-#2331 := (and #2330 #2328)
-#2332 := (not #2331)
-#2338 := (not #2332)
-#2348 := (and #2338 #2344)
-#2353 := (and #1507 #2348)
-#2286 := (* -1::Int #2285)
-#2288 := (+ #2287 #2286)
-#2291 := (+ #2290 #2288)
-#2292 := (>= #2291 0::Int)
-#2299 := (and #2298 #2296)
-#2300 := (not #2299)
-#2301 := (or #2300 #2292)
-#2302 := (not #2301)
-#2357 := (or #2302 #2353)
-#2361 := (and #1483 #2357)
-#2259 := (* -1::Int #2258)
-#2261 := (+ #2260 #2259)
-#2262 := (>= #2261 0::Int)
-#2268 := (and #2267 #2264)
-#2269 := (not #2268)
-#2270 := (or #2269 #2262)
-#2271 := (not #2270)
-#2365 := (or #2271 #2361)
-#2369 := (and #1464 #2365)
-#2373 := (or #2244 #2369)
-#2238 := (not #1458)
-#2377 := (and #2238 #2373)
-#2381 := (or #1458 #2377)
-#2385 := (and #787 #2381)
-#2222 := (= #2221 #2220)
-#2223 := (or #2222 #2219)
-#2224 := (not #2223)
-#2389 := (or #2224 #2385)
-#2393 := (and #1450 #2389)
-#2200 := (* -1::Int #2199)
-#2202 := (+ #2201 #2200)
-#2203 := (>= #2202 0::Int)
-#2204 := (not #2203)
-#2397 := (or #2204 #2393)
-#2183 := (and #2182 #2179)
-#2169 := (not #963)
-#2417 := (and #2169 #733 #2183 #1439 #2397 #1597 #1615 #1623)
-#2110 := (* -1::Int #2109)
-#2112 := (+ #2111 #2110)
-#2115 := (+ #2114 #2112)
-#2116 := (>= #2115 0::Int)
-#2125 := (and #2124 #2120)
-#2126 := (not #2125)
-#2127 := (or #2126 #2116)
-#2128 := (not #2127)
-#2147 := (or #2128 #2143)
-#2086 := (+ #2085 #1310)
-#2089 := (+ #2088 #2086)
-#2090 := (= #2089 0::Int)
-#2091 := (>= #2086 0::Int)
-#2092 := (not #2091)
-#2093 := (and #2092 #2090)
-#2098 := (or #1319 #2093)
-#2101 := (forall (vars (?v0 S2)) #2098)
-#2151 := (and #2101 #2147)
-#2050 := (+ #2049 #2047)
-#2051 := (= #2050 0::Int)
-#2054 := (and #2053 #2051)
-#2070 := (not #2054)
-#2073 := (forall (vars (?v1 S2)) #2070)
-#2059 := (= ?v0!8 f10)
-#2060 := (not #2059)
-#2061 := (and #2060 #2058)
-#2062 := (not #2061)
-#2067 := (not #2062)
-#2077 := (and #2067 #2073)
-#2155 := (or #2077 #2151)
-#2041 := (not #691)
-#2038 := (not #709)
-#2035 := (not #682)
-#2032 := (not #700)
-#2165 := (and #2032 #2035 #2038 #2041 #2155 #2162)
-#2421 := (or #2165 #2417)
-#2009 := (+ #2008 #1265)
-#2010 := (>= #2009 0::Int)
-#2011 := (not #2010)
-#2014 := (+ #2013 #2009)
-#2015 := (= #2014 0::Int)
-#2018 := (and #2017 #2015 #2011)
-#2023 := (or #1274 #2018)
-#2026 := (forall (vars (?v0 S2)) #2023)
-#1982 := (+ #1227 #1981)
-#1984 := (+ #1983 #1982)
-#1985 := (= #1984 0::Int)
-#1986 := (+ #1983 #1227)
-#1987 := (>= #1986 0::Int)
-#1988 := (not #1987)
-#1991 := (and #1990 #1988 #1985)
-#1996 := (or #1236 #1991)
-#1999 := (forall (vars (?v0 S2)) #1996)
-#1974 := (not #1715)
-#2446 := (and #1974 #1999 #2026 #2421 #1682 #1698 #1707)
-#1940 := (+ #1939 #1937)
-#1941 := (+ #58 #1940)
-#1942 := (= #1941 0::Int)
-#1946 := (and #430 #1945 #1942)
-#1962 := (not #1946)
-#1965 := (forall (vars (?v1 S2)) #1962)
-#1951 := (= ?v0!5 f10)
-#1952 := (not #1951)
-#1953 := (and #1952 #1950)
-#1954 := (not #1953)
-#1959 := (not #1954)
-#1969 := (and #1959 #1965)
-#2450 := (or #1969 #2446)
-#2454 := (and #1221 #2450)
-#1914 := (and #1913 #1911)
-#1915 := (not #1914)
-#1918 := (+ #1917 #1907)
-#1920 := (+ #1919 #1918)
-#1921 := (>= #1920 0::Int)
-#1922 := (or #1921 #1915)
-#1923 := (not #1922)
-#2458 := (or #1923 #2454)
-#2462 := (and #1190 #2458)
-#1880 := (* -1::Int #1879)
-#1882 := (+ #1881 #1880)
-#1883 := (>= #1882 0::Int)
-#1889 := (and #1888 #1885)
-#1890 := (not #1889)
-#1891 := (or #1890 #1883)
-#1892 := (not #1891)
-#2466 := (or #1892 #2462)
-#2470 := (and #1170 #2466)
-#2474 := (or #1865 #2470)
-#1828 := (not #1164)
-#2478 := (and #1828 #2474)
-#2482 := (or #1164 #2478)
-#3022 := (iff #2482 #3021)
-#3019 := (iff #2478 #3018)
-#3016 := (iff #2474 #3015)
-#3013 := (iff #2470 #3012)
+#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)
+#3160 := (not #3159)
+#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)
+#3113 := (not #3112)
+#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)
+#3067 := (or #1925 #3066)
+#3078 := (or #2539 #3067)
+#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 #2462 #3006)
-#3004 := (iff #2458 #3003)
-#3001 := (iff #2454 #3000)
-#2998 := (iff #2450 #2997)
-#2995 := (iff #2446 #2992)
-#2989 := (and #101 #2621 #2661 #2986 #1682 #1698 #1707)
-#2993 := (iff #2989 #2992)
-#2994 := [rewrite]: #2993
-#2990 := (iff #2446 #2989)
-#2987 := (iff #2421 #2986)
-#2984 := (iff #2417 #2981)
-#2978 := (and #182 #733 #2183 #1439 #2975 #1597 #1615 #1623)
-#2982 := (iff #2978 #2981)
-#2983 := [rewrite]: #2982
-#2979 := (iff #2417 #2978)
-#2976 := (iff #2397 #2975)
-#2973 := (iff #2393 #2972)
-#2970 := (iff #2389 #2969)
-#2967 := (iff #2385 #2966)
-#2964 := (iff #2381 #2963)
-#2961 := (iff #2377 #2960)
+#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 #2369 #2954)
-#2952 := (iff #2365 #2951)
+#2955 := (iff #2368 #2954)
+#2952 := (iff #2364 #2951)
 #2949 := (iff #2361 #2948)
-#2946 := (iff #2357 #2945)
-#2943 := (iff #2353 #2940)
-#2903 := (and #2328 #2897)
-#2934 := (and #2903 #2931)
-#2937 := (and #1507 #2934)
-#2941 := (iff #2937 #2940)
-#2942 := [rewrite]: #2941
-#2938 := (iff #2353 #2937)
-#2935 := (iff #2348 #2934)
-#2932 := (iff #2344 #2931)
-#2929 := (iff #2341 #2928)
-#2926 := (iff #2324 #2925)
-#2923 := (iff #2321 #2922)
-#2920 := (= #2320 #2919)
-#2921 := [rewrite]: #2920
-#2924 := [monotonicity #2921]: #2923
-#2927 := [monotonicity #2924]: #2926
+#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 := [quant-intro #2930]: #2932
-#2916 := (iff #2338 #2903)
-#2908 := (not #2903)
-#2911 := (not #2908)
-#2914 := (iff #2911 #2903)
-#2915 := [rewrite]: #2914
-#2912 := (iff #2338 #2911)
-#2909 := (iff #2332 #2908)
-#2906 := (iff #2331 #2903)
-#2900 := (and #2897 #2328)
-#2904 := (iff #2900 #2903)
+#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
-#2901 := (iff #2331 #2900)
-#2898 := (iff #2330 #2897)
-#2895 := (iff #2329 #2894)
+#2898 := (iff #2312 #2897)
+#2895 := (= #2311 #2894)
 #2896 := [rewrite]: #2895
 #2899 := [monotonicity #2896]: #2898
-#2902 := [monotonicity #2899]: #2901
-#2907 := [trans #2902 #2905]: #2906
-#2910 := [monotonicity #2907]: #2909
+#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
-#2917 := [trans #2913 #2915]: #2916
-#2936 := [monotonicity #2917 #2933]: #2935
-#2939 := [monotonicity #2936]: #2938
-#2944 := [trans #2939 #2942]: #2943
-#2892 := (iff #2302 #2891)
-#2889 := (iff #2301 #2888)
-#2886 := (iff #2292 #2883)
-#2873 := (+ #2287 #2290)
-#2874 := (+ #2286 #2873)
-#2877 := (>= #2874 0::Int)
-#2884 := (iff #2877 #2883)
-#2885 := [rewrite]: #2884
-#2878 := (iff #2292 #2877)
-#2875 := (= #2291 #2874)
-#2876 := [rewrite]: #2875
-#2879 := [monotonicity #2876]: #2878
-#2887 := [trans #2879 #2885]: #2886
-#2871 := (iff #2300 #2870)
-#2868 := (iff #2299 #2867)
-#2869 := [rewrite]: #2868
-#2872 := [monotonicity #2869]: #2871
-#2890 := [monotonicity #2872 #2887]: #2889
-#2893 := [monotonicity #2890]: #2892
-#2947 := [monotonicity #2893 #2944]: #2946
-#2950 := [monotonicity #2947]: #2949
-#2865 := (iff #2271 #2864)
-#2862 := (iff #2270 #2861)
-#2859 := (iff #2262 #2856)
-#2848 := (+ #2259 #2260)
-#2851 := (>= #2848 0::Int)
-#2857 := (iff #2851 #2856)
-#2858 := [rewrite]: #2857
-#2852 := (iff #2262 #2851)
-#2849 := (= #2261 #2848)
-#2850 := [rewrite]: #2849
-#2853 := [monotonicity #2850]: #2852
-#2860 := [trans #2853 #2858]: #2859
-#2846 := (iff #2269 #2845)
-#2843 := (iff #2268 #2842)
-#2844 := [rewrite]: #2843
-#2847 := [monotonicity #2844]: #2846
-#2863 := [monotonicity #2847 #2860]: #2862
-#2866 := [monotonicity #2863]: #2865
-#2953 := [monotonicity #2866 #2950]: #2952
-#2956 := [monotonicity #2953]: #2955
-#2959 := [monotonicity #2956]: #2958
-#2840 := (iff #2238 #204)
-#2841 := [rewrite]: #2840
-#2962 := [monotonicity #2841 #2959]: #2961
-#2965 := [monotonicity #2962]: #2964
-#2968 := [monotonicity #2965]: #2967
-#2838 := (iff #2224 #2837)
-#2835 := (iff #2223 #2832)
-#2829 := (or #2826 #2219)
-#2833 := (iff #2829 #2832)
-#2834 := [rewrite]: #2833
-#2830 := (iff #2223 #2829)
-#2827 := (iff #2222 #2826)
-#2828 := [rewrite]: #2827
-#2831 := [monotonicity #2828]: #2830
-#2836 := [trans #2831 #2834]: #2835
-#2839 := [monotonicity #2836]: #2838
-#2971 := [monotonicity #2839 #2968]: #2970
-#2974 := [monotonicity #2971]: #2973
-#2824 := (iff #2204 #2823)
-#2821 := (iff #2203 #2818)
-#2810 := (+ #2200 #2201)
-#2813 := (>= #2810 0::Int)
-#2819 := (iff #2813 #2818)
-#2820 := [rewrite]: #2819
-#2814 := (iff #2203 #2813)
-#2811 := (= #2202 #2810)
-#2812 := [rewrite]: #2811
-#2815 := [monotonicity #2812]: #2814
-#2822 := [trans #2815 #2820]: #2821
-#2825 := [monotonicity #2822]: #2824
-#2977 := [monotonicity #2825 #2974]: #2976
-#2808 := (iff #2169 #182)
-#2809 := [rewrite]: #2808
-#2980 := [monotonicity #2809 #2977]: #2979
-#2985 := [trans #2980 #2983]: #2984
-#2806 := (iff #2165 #2803)
-#2800 := (and #137 #142 #597 #600 #2797 #2162)
-#2804 := (iff #2800 #2803)
-#2805 := [rewrite]: #2804
-#2801 := (iff #2165 #2800)
-#2798 := (iff #2155 #2797)
-#2795 := (iff #2151 #2794)
-#2792 := (iff #2147 #2789)
-#2786 := (or #2783 #2143)
-#2790 := (iff #2786 #2789)
-#2791 := [rewrite]: #2790
-#2787 := (iff #2147 #2786)
-#2784 := (iff #2128 #2783)
-#2781 := (iff #2127 #2780)
-#2778 := (iff #2116 #2775)
-#2766 := (+ #2111 #2114)
-#2767 := (+ #2110 #2766)
-#2770 := (>= #2767 0::Int)
-#2776 := (iff #2770 #2775)
-#2777 := [rewrite]: #2776
-#2771 := (iff #2116 #2770)
-#2768 := (= #2115 #2767)
-#2769 := [rewrite]: #2768
-#2772 := [monotonicity #2769]: #2771
-#2779 := [trans #2772 #2777]: #2778
-#2764 := (iff #2126 #2763)
-#2761 := (iff #2125 #2760)
-#2762 := [rewrite]: #2761
-#2765 := [monotonicity #2762]: #2764
-#2782 := [monotonicity #2765 #2779]: #2781
+#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
-#2788 := [monotonicity #2785]: #2787
-#2793 := [trans #2788 #2791]: #2792
-#2758 := (iff #2101 #2757)
-#2755 := (iff #2098 #2754)
-#2752 := (iff #2093 #2751)
-#2749 := (iff #2090 #2746)
-#2736 := (+ #2085 #2088)
-#2737 := (+ #1310 #2736)
-#2740 := (= #2737 0::Int)
-#2747 := (iff #2740 #2746)
-#2748 := [rewrite]: #2747
-#2741 := (iff #2090 #2740)
-#2738 := (= #2089 #2737)
-#2739 := [rewrite]: #2738
-#2742 := [monotonicity #2739]: #2741
-#2750 := [trans #2742 #2748]: #2749
-#2734 := (iff #2092 #2733)
-#2731 := (iff #2091 #2728)
-#2720 := (+ #1310 #2085)
-#2723 := (>= #2720 0::Int)
-#2729 := (iff #2723 #2728)
-#2730 := [rewrite]: #2729
-#2724 := (iff #2091 #2723)
-#2721 := (= #2086 #2720)
-#2722 := [rewrite]: #2721
+#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
-#2732 := [trans #2725 #2730]: #2731
-#2735 := [monotonicity #2732]: #2734
-#2753 := [monotonicity #2735 #2750]: #2752
-#2756 := [monotonicity #2753]: #2755
-#2759 := [quant-intro #2756]: #2758
-#2796 := [monotonicity #2759 #2793]: #2795
-#2718 := (iff #2077 #2715)
-#2681 := (and #2058 #2675)
-#2712 := (and #2681 #2709)
-#2716 := (iff #2712 #2715)
-#2717 := [rewrite]: #2716
-#2713 := (iff #2077 #2712)
-#2710 := (iff #2073 #2709)
-#2707 := (iff #2070 #2706)
-#2704 := (iff #2054 #2703)
-#2701 := (iff #2051 #2700)
-#2698 := (= #2050 #2697)
-#2699 := [rewrite]: #2698
-#2702 := [monotonicity #2699]: #2701
-#2705 := [monotonicity #2702]: #2704
+#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 := [quant-intro #2708]: #2710
-#2694 := (iff #2067 #2681)
-#2686 := (not #2681)
-#2689 := (not #2686)
-#2692 := (iff #2689 #2681)
-#2693 := [rewrite]: #2692
-#2690 := (iff #2067 #2689)
-#2687 := (iff #2062 #2686)
-#2684 := (iff #2061 #2681)
-#2678 := (and #2675 #2058)
-#2682 := (iff #2678 #2681)
-#2683 := [rewrite]: #2682
-#2679 := (iff #2061 #2678)
-#2676 := (iff #2060 #2675)
-#2673 := (iff #2059 #2672)
-#2674 := [rewrite]: #2673
-#2677 := [monotonicity #2674]: #2676
-#2680 := [monotonicity #2677]: #2679
-#2685 := [trans #2680 #2683]: #2684
-#2688 := [monotonicity #2685]: #2687
-#2691 := [monotonicity #2688]: #2690
-#2695 := [trans #2691 #2693]: #2694
-#2714 := [monotonicity #2695 #2711]: #2713
-#2719 := [trans #2714 #2717]: #2718
-#2799 := [monotonicity #2719 #2796]: #2798
-#2670 := (iff #2041 #600)
-#2671 := [rewrite]: #2670
-#2668 := (iff #2038 #597)
+#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
-#2666 := (iff #2035 #142)
-#2667 := [rewrite]: #2666
-#2664 := (iff #2032 #137)
-#2665 := [rewrite]: #2664
-#2802 := [monotonicity #2665 #2667 #2669 #2671 #2799]: #2801
-#2807 := [trans #2802 #2805]: #2806
-#2988 := [monotonicity #2807 #2985]: #2987
-#2662 := (iff #2026 #2661)
-#2659 := (iff #2023 #2658)
-#2656 := (iff #2018 #2655)
-#2653 := (iff #2011 #2652)
-#2650 := (iff #2010 #2647)
-#2640 := (+ #1265 #2008)
-#2643 := (>= #2640 0::Int)
-#2648 := (iff #2643 #2647)
-#2649 := [rewrite]: #2648
-#2644 := (iff #2010 #2643)
-#2641 := (= #2009 #2640)
-#2642 := [rewrite]: #2641
-#2645 := [monotonicity #2642]: #2644
-#2651 := [trans #2645 #2649]: #2650
-#2654 := [monotonicity #2651]: #2653
-#2638 := (iff #2015 #2635)
-#2624 := (+ #2008 #2013)
-#2625 := (+ #1265 #2624)
-#2628 := (= #2625 0::Int)
-#2636 := (iff #2628 #2635)
-#2637 := [rewrite]: #2636
-#2629 := (iff #2015 #2628)
-#2626 := (= #2014 #2625)
-#2627 := [rewrite]: #2626
-#2630 := [monotonicity #2627]: #2629
-#2639 := [trans #2630 #2637]: #2638
-#2657 := [monotonicity #2639 #2654]: #2656
-#2660 := [monotonicity #2657]: #2659
-#2663 := [quant-intro #2660]: #2662
-#2622 := (iff #1999 #2621)
-#2619 := (iff #1996 #2618)
-#2616 := (iff #1991 #2615)
-#2613 := (iff #1985 #2610)
-#2600 := (+ #1981 #1983)
-#2601 := (+ #1227 #2600)
-#2604 := (= #2601 0::Int)
-#2611 := (iff #2604 #2610)
-#2612 := [rewrite]: #2611
-#2605 := (iff #1985 #2604)
-#2602 := (= #1984 #2601)
+#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
-#2606 := [monotonicity #2603]: #2605
-#2614 := [trans #2606 #2612]: #2613
-#2598 := (iff #1988 #2597)
-#2595 := (iff #1987 #2592)
-#2584 := (+ #1227 #1983)
-#2587 := (>= #2584 0::Int)
-#2593 := (iff #2587 #2592)
-#2594 := [rewrite]: #2593
-#2588 := (iff #1987 #2587)
-#2585 := (= #1986 #2584)
-#2586 := [rewrite]: #2585
-#2589 := [monotonicity #2586]: #2588
-#2596 := [trans #2589 #2594]: #2595
-#2599 := [monotonicity #2596]: #2598
-#2617 := [monotonicity #2599 #2614]: #2616
-#2620 := [monotonicity #2617]: #2619
-#2623 := [quant-intro #2620]: #2622
-#2582 := (iff #1974 #101)
-#2583 := [rewrite]: #2582
-#2991 := [monotonicity #2583 #2623 #2663 #2988]: #2990
-#2996 := [trans #2991 #2994]: #2995
-#2580 := (iff #1969 #2577)
-#2543 := (and #1950 #2537)
-#2574 := (and #2543 #2571)
-#2578 := (iff #2574 #2577)
-#2579 := [rewrite]: #2578
-#2575 := (iff #1969 #2574)
-#2572 := (iff #1965 #2571)
-#2569 := (iff #1962 #2568)
-#2566 := (iff #1946 #2565)
-#2563 := (iff #1942 #2562)
-#2560 := (= #1941 #2559)
-#2561 := [rewrite]: #2560
-#2564 := [monotonicity #2561]: #2563
-#2567 := [monotonicity #2564]: #2566
+#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 := [quant-intro #2570]: #2572
-#2556 := (iff #1959 #2543)
-#2548 := (not #2543)
-#2551 := (not #2548)
-#2554 := (iff #2551 #2543)
-#2555 := [rewrite]: #2554
-#2552 := (iff #1959 #2551)
-#2549 := (iff #1954 #2548)
-#2546 := (iff #1953 #2543)
-#2540 := (and #2537 #1950)
-#2544 := (iff #2540 #2543)
-#2545 := [rewrite]: #2544
-#2541 := (iff #1953 #2540)
-#2538 := (iff #1952 #2537)
-#2535 := (iff #1951 #2534)
-#2536 := [rewrite]: #2535
-#2539 := [monotonicity #2536]: #2538
-#2542 := [monotonicity #2539]: #2541
-#2547 := [trans #2542 #2545]: #2546
-#2550 := [monotonicity #2547]: #2549
+#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
-#2557 := [trans #2553 #2555]: #2556
-#2576 := [monotonicity #2557 #2573]: #2575
-#2581 := [trans #2576 #2579]: #2580
-#2999 := [monotonicity #2581 #2996]: #2998
-#3002 := [monotonicity #2999]: #3001
-#2532 := (iff #1923 #2531)
-#2529 := (iff #1922 #2528)
-#2526 := (iff #1915 #2525)
-#2523 := (iff #1914 #2522)
-#2524 := [rewrite]: #2523
-#2527 := [monotonicity #2524]: #2526
-#2520 := (iff #1921 #2519)
-#2517 := (= #1920 #2516)
+#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
-#2530 := [monotonicity #2521 #2527]: #2529
-#2533 := [monotonicity #2530]: #2532
-#3005 := [monotonicity #2533 #3002]: #3004
-#3008 := [monotonicity #3005]: #3007
-#2513 := (iff #1892 #2512)
-#2510 := (iff #1891 #2509)
-#2507 := (iff #1883 #2504)
-#2496 := (+ #1880 #1881)
-#2499 := (>= #2496 0::Int)
-#2505 := (iff #2499 #2504)
-#2506 := [rewrite]: #2505
-#2500 := (iff #1883 #2499)
-#2497 := (= #1882 #2496)
-#2498 := [rewrite]: #2497
-#2501 := [monotonicity #2498]: #2500
-#2508 := [trans #2501 #2506]: #2507
-#2494 := (iff #1890 #2493)
-#2491 := (iff #1889 #2490)
-#2492 := [rewrite]: #2491
-#2495 := [monotonicity #2492]: #2494
-#2511 := [monotonicity #2495 #2508]: #2510
-#2514 := [monotonicity #2511]: #2513
-#3011 := [monotonicity #2514 #3008]: #3010
-#3014 := [monotonicity #3011]: #3013
-#3017 := [monotonicity #3014]: #3016
-#2488 := (iff #1828 #72)
-#2489 := [rewrite]: #2488
-#3020 := [monotonicity #2489 #3017]: #3019
-#3023 := [monotonicity #3020]: #3022
-#1804 := (not #1768)
-#2483 := (~ #1804 #2482)
-#2479 := (not #1765)
+#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 #1762)
+#2475 := (not #1761)
 #2476 := (~ #2475 #2474)
-#2471 := (not #1759)
+#2471 := (not #1758)
 #2472 := (~ #2471 #2470)
-#2467 := (not #1756)
+#2467 := (not #1753)
 #2468 := (~ #2467 #2466)
-#2463 := (not #1753)
-#2464 := (~ #2463 #2462)
-#2459 := (not #1750)
-#2460 := (~ #2459 #2458)
-#2455 := (not #1747)
-#2456 := (~ #2455 #2454)
-#2451 := (not #1744)
-#2452 := (~ #2451 #2450)
-#2447 := (not #1739)
-#2448 := (~ #2447 #2446)
-#2443 := (not #1710)
-#2444 := (~ #2443 #1707)
-#2441 := (~ #1707 #1707)
-#2439 := (~ #1704 #1704)
-#2440 := [refl]: #2439
-#2442 := [nnf-pos #2440]: #2441
-#2445 := [nnf-neg #2442]: #2444
-#2436 := (not #1701)
-#2437 := (~ #2436 #1698)
-#2434 := (~ #1698 #1698)
-#2432 := (~ #1693 #1693)
-#2433 := [refl]: #2432
-#2435 := [nnf-pos #2433]: #2434
-#2438 := [nnf-neg #2435]: #2437
-#2429 := (not #1685)
-#2430 := (~ #2429 #1682)
-#2427 := (~ #1682 #1682)
-#2425 := (~ #1679 #1679)
-#2426 := [refl]: #2425
-#2428 := [nnf-pos #2426]: #2427
-#2431 := [nnf-neg #2428]: #2430
-#2422 := (not #1662)
-#2423 := (~ #2422 #2421)
-#2418 := (not #1657)
+#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)
-#2415 := (~ #1623 #1623)
-#2416 := [refl]: #2415
-#2412 := (not #1618)
-#2413 := (~ #2412 #1615)
-#2410 := (~ #1615 #1615)
-#2408 := (~ #1610 #1610)
-#2409 := [refl]: #2408
-#2411 := [nnf-pos #2409]: #2410
-#2414 := [nnf-neg #2411]: #2413
-#2405 := (not #1600)
-#2406 := (~ #2405 #1597)
-#2403 := (~ #1597 #1597)
-#2401 := (~ #1594 #1594)
-#2402 := [refl]: #2401
-#2404 := [nnf-pos #2402]: #2403
-#2407 := [nnf-neg #2404]: #2406
-#2398 := (not #1583)
+#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 #1580)
+#2394 := (not #1579)
 #2395 := (~ #2394 #2393)
-#2390 := (not #1577)
+#2390 := (not #1576)
 #2391 := (~ #2390 #2389)
-#2386 := (not #1574)
+#2386 := (not #1573)
 #2387 := (~ #2386 #2385)
-#2382 := (not #1571)
+#2382 := (not #1570)
 #2383 := (~ #2382 #2381)
-#2378 := (not #1568)
+#2378 := (not #1567)
 #2379 := (~ #2378 #2377)
-#2374 := (not #1565)
+#2374 := (not #1564)
 #2375 := (~ #2374 #2373)
-#2370 := (not #1562)
-#2371 := (~ #2370 #2369)
-#2366 := (not #1559)
-#2367 := (~ #2366 #2365)
-#2362 := (not #1556)
-#2363 := (~ #2362 #2361)
-#2358 := (not #1553)
-#2359 := (~ #2358 #2357)
-#2354 := (not #1550)
-#2355 := (~ #2354 #2353)
-#2335 := (not #1547)
-#2351 := (~ #2335 #2348)
-#2325 := (exists (vars (?v1 S2)) #2324)
-#2333 := (or #2332 #2325)
-#2334 := (not #2333)
-#2349 := (~ #2334 #2348)
-#2345 := (not #2325)
-#2346 := (~ #2345 #2344)
-#2342 := (~ #2341 #2341)
-#2343 := [refl]: #2342
-#2347 := [nnf-neg #2343]: #2346
-#2339 := (~ #2338 #2338)
-#2340 := [refl]: #2339
-#2350 := [nnf-neg #2340 #2347]: #2349
-#2336 := (~ #2335 #2334)
-#2337 := [sk]: #2336
-#2352 := [trans #2337 #2350]: #2351
-#2311 := (not #1510)
-#2312 := (~ #2311 #1507)
-#2309 := (~ #1507 #1507)
-#2307 := (~ #1504 #1504)
-#2308 := [refl]: #2307
-#2310 := [nnf-pos #2308]: #2309
-#2313 := [nnf-neg #2310]: #2312
-#2356 := [nnf-neg #2313 #2352]: #2355
-#2303 := (~ #1510 #2302)
-#2304 := [sk]: #2303
-#2360 := [nnf-neg #2304 #2356]: #2359
-#2280 := (not #1486)
-#2281 := (~ #2280 #1483)
-#2278 := (~ #1483 #1483)
-#2276 := (~ #1478 #1478)
-#2277 := [refl]: #2276
-#2279 := [nnf-pos #2277]: #2278
-#2282 := [nnf-neg #2279]: #2281
-#2364 := [nnf-neg #2282 #2360]: #2363
-#2272 := (~ #1486 #2271)
-#2273 := [sk]: #2272
-#2368 := [nnf-neg #2273 #2364]: #2367
-#2253 := (not #1467)
-#2254 := (~ #2253 #1464)
-#2251 := (~ #1464 #1464)
-#2249 := (~ #1461 #1461)
-#2250 := [refl]: #2249
-#2252 := [nnf-pos #2250]: #2251
-#2255 := [nnf-neg #2252]: #2254
-#2372 := [nnf-neg #2255 #2368]: #2371
-#2245 := (~ #1467 #2244)
-#2246 := [sk]: #2245
-#2376 := [nnf-neg #2246 #2372]: #2375
-#2239 := (~ #2238 #2238)
-#2240 := [refl]: #2239
-#2380 := [nnf-neg #2240 #2376]: #2379
-#2236 := (~ #1458 #1458)
-#2237 := [refl]: #2236
-#2384 := [nnf-neg #2237 #2380]: #2383
-#2233 := (not #921)
-#2234 := (~ #2233 #787)
-#2231 := (~ #787 #787)
-#2229 := (~ #782 #782)
-#2230 := [refl]: #2229
-#2232 := [nnf-pos #2230]: #2231
-#2235 := [nnf-neg #2232]: #2234
-#2388 := [nnf-neg #2235 #2384]: #2387
-#2225 := (~ #921 #2224)
-#2226 := [sk]: #2225
-#2392 := [nnf-neg #2226 #2388]: #2391
-#2213 := (not #1453)
-#2214 := (~ #2213 #1450)
-#2211 := (~ #1450 #1450)
-#2209 := (~ #1445 #1445)
-#2210 := [refl]: #2209
-#2212 := [nnf-pos #2210]: #2211
-#2215 := [nnf-neg #2212]: #2214
-#2396 := [nnf-neg #2215 #2392]: #2395
-#2205 := (~ #1453 #2204)
-#2206 := [sk]: #2205
-#2400 := [nnf-neg #2206 #2396]: #2399
-#2195 := (not #1442)
-#2196 := (~ #2195 #1439)
-#2193 := (~ #1439 #1439)
-#2191 := (~ #1434 #1434)
+#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
-#2194 := [nnf-pos #2192]: #2193
-#2197 := [nnf-neg #2194]: #2196
-#2188 := (not #1633)
-#2189 := (~ #2188 #2183)
-#2184 := (~ #1392 #2183)
-#2185 := [sk]: #2184
-#2190 := [nnf-neg #2185]: #2189
-#2172 := (~ #733 #733)
-#2173 := [refl]: #2172
-#2170 := (~ #2169 #2169)
-#2171 := [refl]: #2170
-#2420 := [nnf-neg #2171 #2173 #2190 #2197 #2400 #2407 #2414 #2416]: #2419
-#2166 := (not #1410)
-#2167 := (~ #2166 #2165)
-#2163 := (~ #1633 #2162)
-#2160 := (~ #2159 #2159)
-#2161 := [refl]: #2160
-#2164 := [nnf-neg #2161]: #2163
-#2156 := (not #1381)
-#2157 := (~ #2156 #2155)
-#2152 := (not #1378)
-#2153 := (~ #2152 #2151)
-#2148 := (not #1375)
-#2149 := (~ #2148 #2147)
-#2144 := (not #1370)
-#2145 := (~ #2144 #2143)
-#2140 := (not #1362)
-#2141 := (~ #2140 #1359)
-#2138 := (~ #1359 #1359)
-#2136 := (~ #1356 #1356)
-#2137 := [refl]: #2136
-#2139 := [nnf-pos #2137]: #2138
-#2142 := [nnf-neg #2139]: #2141
-#2134 := (~ #2133 #2133)
-#2135 := [refl]: #2134
-#2146 := [nnf-neg #2135 #2142]: #2145
-#2129 := (~ #1362 #2128)
-#2130 := [sk]: #2129
-#2150 := [nnf-neg #2130 #2146]: #2149
-#2104 := (not #1344)
-#2105 := (~ #2104 #2101)
-#2102 := (~ #1341 #2101)
-#2099 := (~ #1338 #2098)
-#2094 := (~ #1335 #2093)
-#2095 := [sk]: #2094
-#2082 := (~ #1319 #1319)
-#2083 := [refl]: #2082
-#2100 := [monotonicity #2083 #2095]: #2099
-#2103 := [nnf-pos #2100]: #2102
-#2106 := [nnf-neg #2103]: #2105
-#2154 := [nnf-neg #2106 #2150]: #2153
-#2080 := (~ #1344 #2077)
-#2055 := (exists (vars (?v1 S2)) #2054)
-#2063 := (or #2062 #2055)
-#2064 := (not #2063)
-#2078 := (~ #2064 #2077)
-#2074 := (not #2055)
-#2075 := (~ #2074 #2073)
-#2071 := (~ #2070 #2070)
-#2072 := [refl]: #2071
-#2076 := [nnf-neg #2072]: #2075
-#2068 := (~ #2067 #2067)
-#2069 := [refl]: #2068
-#2079 := [nnf-neg #2069 #2076]: #2078
-#2065 := (~ #1344 #2064)
-#2066 := [sk]: #2065
-#2081 := [trans #2066 #2079]: #2080
-#2158 := [nnf-neg #2081 #2154]: #2157
-#2042 := (~ #2041 #2041)
-#2043 := [refl]: #2042
-#2039 := (~ #2038 #2038)
-#2040 := [refl]: #2039
-#2036 := (~ #2035 #2035)
-#2037 := [refl]: #2036
-#2033 := (~ #2032 #2032)
-#2034 := [refl]: #2033
-#2168 := [nnf-neg #2034 #2037 #2040 #2043 #2158 #2164]: #2167
-#2424 := [nnf-neg #2168 #2420]: #2423
-#2029 := (not #1307)
-#2030 := (~ #2029 #2026)
-#2027 := (~ #1304 #2026)
-#2024 := (~ #1301 #2023)
-#2019 := (~ #1298 #2018)
-#2020 := [sk]: #2019
-#2005 := (~ #1274 #1274)
-#2006 := [refl]: #2005
-#2025 := [monotonicity #2006 #2020]: #2024
-#2028 := [nnf-pos #2025]: #2027
-#2031 := [nnf-neg #2028]: #2030
-#2002 := (not #1718)
-#2003 := (~ #2002 #1999)
-#2000 := (~ #1262 #1999)
-#1997 := (~ #1259 #1996)
-#1992 := (~ #1256 #1991)
-#1993 := [sk]: #1992
-#1977 := (~ #1236 #1236)
-#1978 := [refl]: #1977
-#1998 := [monotonicity #1978 #1993]: #1997
-#2001 := [nnf-pos #1998]: #2000
-#2004 := [nnf-neg #2001]: #2003
+#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
-#2449 := [nnf-neg #1976 #2004 #2031 #2424 #2431 #2438 #2445]: #2448
-#1972 := (~ #1718 #1969)
-#1947 := (exists (vars (?v1 S2)) #1946)
-#1955 := (or #1954 #1947)
-#1956 := (not #1955)
-#1970 := (~ #1956 #1969)
-#1966 := (not #1947)
-#1967 := (~ #1966 #1965)
-#1963 := (~ #1962 #1962)
-#1964 := [refl]: #1963
-#1968 := [nnf-neg #1964]: #1967
-#1960 := (~ #1959 #1959)
-#1961 := [refl]: #1960
-#1971 := [nnf-neg #1961 #1968]: #1970
-#1957 := (~ #1718 #1956)
-#1958 := [sk]: #1957
-#1973 := [trans #1958 #1971]: #1972
-#2453 := [nnf-neg #1973 #2449]: #2452
-#1932 := (not #1224)
-#1933 := (~ #1932 #1221)
-#1930 := (~ #1221 #1221)
-#1928 := (~ #1218 #1218)
-#1929 := [refl]: #1928
-#1931 := [nnf-pos #1929]: #1930
-#1934 := [nnf-neg #1931]: #1933
-#2457 := [nnf-neg #1934 #2453]: #2456
-#1924 := (~ #1224 #1923)
-#1925 := [sk]: #1924
-#2461 := [nnf-neg #1925 #2457]: #2460
-#1901 := (not #1193)
-#1902 := (~ #1901 #1190)
-#1899 := (~ #1190 #1190)
-#1897 := (~ #1185 #1185)
-#1898 := [refl]: #1897
-#1900 := [nnf-pos #1898]: #1899
-#1903 := [nnf-neg #1900]: #1902
-#2465 := [nnf-neg #1903 #2461]: #2464
-#1893 := (~ #1193 #1892)
-#1894 := [sk]: #1893
-#2469 := [nnf-neg #1894 #2465]: #2468
-#1874 := (not #1173)
-#1875 := (~ #1874 #1170)
-#1872 := (~ #1170 #1170)
-#1870 := (~ #1169 #1169)
-#1871 := [refl]: #1870
-#1873 := [nnf-pos #1871]: #1872
-#1876 := [nnf-neg #1873]: #1875
-#2473 := [nnf-neg #1876 #2469]: #2472
-#1866 := (~ #1173 #1865)
-#1867 := [sk]: #1866
-#2477 := [nnf-neg #1867 #2473]: #2476
-#1829 := (~ #1828 #1828)
-#1861 := [refl]: #1829
-#2481 := [nnf-neg #1861 #2477]: #2480
-#1859 := (~ #1164 #1164)
-#1860 := [refl]: #1859
-#2484 := [nnf-neg #1860 #2481]: #2483
-#1805 := [not-or-elim #1801]: #1804
-#2485 := [mp~ #1805 #2484]: #2482
-#2486 := [mp #2485 #3023]: #3021
-#3665 := [mp #2486 #3664]: #3662
-#4572 := [mp #3665 #4571]: #4569
-#6574 := [unit-resolution #4572 #3797]: #4566
-#3911 := (or #4563 #4557)
-#3912 := [def-axiom]: #3911
-#6575 := [unit-resolution #3912 #6574]: #4557
-#3906 := (or #4560 #1865 #4554)
-#3907 := [def-axiom]: #3906
-#6576 := [unit-resolution #3907 #6575]: #4557
-#6577 := [unit-resolution #6576 #5286]: #4554
-#3930 := (or #4551 #4545)
-#3931 := [def-axiom]: #3930
-#6578 := [unit-resolution #3931 #6577]: #4545
-#6580 := (or #4548 #4542)
-#5283 := [hypothesis]: #1885
-#4194 := (forall (vars (?v0 S2)) (:pat #4193) #433)
-#4197 := (iff #436 #4194)
-#4195 := (iff #433 #433)
-#4196 := [refl]: #4195
-#4198 := [quant-intro #4196]: #4197
-#1826 := (~ #436 #436)
-#1856 := (~ #433 #433)
-#1857 := [refl]: #1856
-#1827 := [nnf-pos #1857]: #1826
-#1803 := [not-or-elim #1801]: #436
-#1858 := [mp~ #1803 #1827]: #436
-#4199 := [mp #1858 #4198]: #4194
-#3781 := (not #4194)
-#3782 := (or #3781 #2097)
-#3783 := [quant-inst #1878]: #3782
-#5284 := [unit-resolution #3783 #4199 #5283]: false
-#5279 := [lemma #5284]: #2097
-#3723 := (or #2305 #1885)
-#3810 := [def-axiom]: #3723
-#6579 := [unit-resolution #3810 #5279]: #2305
-#3924 := (or #4548 #2275 #4542)
-#3926 := [def-axiom]: #3924
-#6581 := [unit-resolution #3926 #6579]: #6580
-#6582 := [unit-resolution #6581 #6578]: #4542
-#3951 := (or #4539 #4533)
-#3952 := [def-axiom]: #3951
-#6583 := [unit-resolution #3952 #6582]: #4533
-#5937 := [hypothesis]: #1913
-#5067 := (or #3781 #3046)
-#5108 := [quant-inst #1904]: #5067
-#5938 := [unit-resolution #5108 #4199 #5937]: false
-#5945 := [lemma #5938]: #3046
-#3813 := (or #3061 #1913)
-#3817 := [def-axiom]: #3813
-#6584 := [unit-resolution #3817 #5945]: #3061
-#3947 := (or #4536 #3066 #4530)
-#3948 := [def-axiom]: #3947
-#6585 := [unit-resolution #3948 #6584 #6583]: #4530
-#3961 := (or #4527 #4521)
-#3982 := [def-axiom]: #3961
-#6586 := [unit-resolution #3982 #6585]: #4521
-#5944 := (= f3 #1938)
-#5995 := (not #5944)
-#5993 := [hypothesis]: #4238
-#4127 := (or #4235 #1950)
-#3801 := [def-axiom]: #4127
-#5994 := [unit-resolution #3801 #5993]: #1950
-#5996 := (or #5995 #1949)
-#5997 := [th-lemma arith triangle-eq]: #5996
-#5998 := [unit-resolution #5997 #5994]: #5995
-#3802 := (or #4235 #2537)
-#4134 := [def-axiom]: #3802
-#5999 := [unit-resolution #4134 #5993]: #2537
-#5883 := (or #3757 #2534 #5944)
-#5644 := (or #1951 #5944)
-#5904 := (or #3757 #5644)
-#5951 := (iff #5904 #5883)
-#5667 := (or #2534 #5944)
-#5946 := (or #3757 #5667)
-#5949 := (iff #5946 #5883)
-#5950 := [rewrite]: #5949
-#5947 := (iff #5904 #5946)
-#5881 := (iff #5644 #5667)
-#5882 := [monotonicity #2536]: #5881
-#5948 := [monotonicity #5882]: #5947
-#5952 := [trans #5948 #5950]: #5951
-#5934 := [quant-inst #1935]: #5904
-#5953 := [mp #5934 #5952]: #5883
-#6000 := [unit-resolution #5953 #4192 #5999 #5998]: false
-#6001 := [lemma #6000]: #4235
-#3969 := (or #4524 #4238 #4518)
-#3970 := [def-axiom]: #3969
-#6587 := [unit-resolution #3970 #6001 #6586]: #4518
-#4003 := (or #4515 #4250)
-#3983 := [def-axiom]: #4003
-#9283 := [unit-resolution #3983 #6587]: #4250
-#5101 := (or #3329 #4255 #4289 #691)
-#4801 := (f13 f14 ?v1!10)
-#4665 := (f13 f14 ?v0!11)
-#4666 := (* -1::Int #4665)
-#4879 := (+ #4666 #4801)
-#4880 := (+ #2114 #4879)
-#4883 := (>= #4880 0::Int)
-#4805 := (f8 f15 ?v1!10)
-#4806 := (= f1 #4805)
-#4802 := (* -1::Int #4801)
-#4803 := (+ f3 #4802)
-#4804 := (<= #4803 0::Int)
-#5242 := (not #4804)
-#5069 := [hypothesis]: #3334
-#4117 := (or #3329 #2120)
-#4118 := [def-axiom]: #4117
-#5070 := [unit-resolution #4118 #5069]: #2120
-#4986 := (+ #2111 #4802)
-#4988 := (>= #4986 0::Int)
-#4985 := (= #2111 #4801)
-#5053 := (= #4801 #2111)
-#5071 := [hypothesis]: #600
-#5054 := [monotonicity #5071]: #5053
-#5055 := [symm #5054]: #4985
-#5056 := (not #4985)
-#5057 := (or #5056 #4988)
-#5052 := [th-lemma arith triangle-eq]: #5057
-#5058 := [unit-resolution #5052 #5055]: #4988
-#5243 := (not #4988)
-#5244 := (or #5242 #5243 #2119)
-#5238 := [hypothesis]: #2120
-#5239 := [hypothesis]: #4804
-#5240 := [hypothesis]: #4988
-#5241 := [th-lemma arith farkas 1 -1 1 #5240 #5239 #5238]: false
-#5245 := [lemma #5241]: #5244
-#5059 := [unit-resolution #5245 #5058 #5070]: #5242
-#4808 := (or #4804 #4806)
-#5060 := [hypothesis]: #4284
-#4811 := (or #4289 #4804 #4806)
-#4807 := (or #4806 #4804)
-#4812 := (or #4289 #4807)
-#4819 := (iff #4812 #4811)
-#4814 := (or #4289 #4808)
-#4817 := (iff #4814 #4811)
-#4818 := [rewrite]: #4817
-#4815 := (iff #4812 #4814)
-#4809 := (iff #4807 #4808)
-#4810 := [rewrite]: #4809
-#4816 := [monotonicity #4810]: #4815
-#4820 := [trans #4816 #4818]: #4819
-#4813 := [quant-inst #2107]: #4812
-#4821 := [mp #4813 #4820]: #4811
-#5061 := [unit-resolution #4821 #5060]: #4808
-#5062 := [unit-resolution #5061 #5059]: #4806
-#4877 := (not #4806)
-#5116 := (or #4877 #4883)
-#4119 := (or #3329 #2124)
-#4120 := [def-axiom]: #4119
-#5114 := [unit-resolution #4120 #5069]: #2124
-#5115 := [hypothesis]: #4250
-#4894 := (or #4255 #2123 #4877 #4883)
-#4872 := (+ #4801 #4666)
-#4873 := (+ #2114 #4872)
-#4876 := (>= #4873 0::Int)
-#4878 := (or #4877 #2123 #4876)
-#4895 := (or #4255 #4878)
-#4902 := (iff #4895 #4894)
-#4889 := (or #2123 #4877 #4883)
-#4897 := (or #4255 #4889)
-#4900 := (iff #4897 #4894)
-#4901 := [rewrite]: #4900
-#4898 := (iff #4895 #4897)
-#4892 := (iff #4878 #4889)
-#4886 := (or #4877 #2123 #4883)
-#4890 := (iff #4886 #4889)
+#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
-#4887 := (iff #4878 #4886)
-#4884 := (iff #4876 #4883)
-#4881 := (= #4873 #4880)
-#4882 := [rewrite]: #4881
-#4885 := [monotonicity #4882]: #4884
-#4888 := [monotonicity #4885]: #4887
-#4893 := [trans #4888 #4891]: #4892
-#4899 := [monotonicity #4893]: #4898
-#4903 := [trans #4899 #4901]: #4902
-#4896 := [quant-inst #2108 #2107]: #4895
-#4904 := [mp #4896 #4903]: #4894
-#5117 := [unit-resolution #4904 #5115 #5114]: #5116
-#5118 := [unit-resolution #5117 #5062]: #4883
-#4115 := (not #2775)
-#4121 := (or #3329 #4115)
-#3759 := [def-axiom]: #4121
-#5119 := [unit-resolution #3759 #5069]: #4115
-#4975 := (+ #2109 #4666)
-#4983 := (<= #4975 0::Int)
-#4974 := (= #2109 #4665)
-#5120 := (= #4665 #2109)
-#5121 := [monotonicity #5071]: #5120
-#5122 := [symm #5121]: #4974
-#5102 := (not #4974)
-#5103 := (or #5102 #4983)
-#5104 := [th-lemma arith triangle-eq]: #5103
-#5105 := [unit-resolution #5104 #5122]: #4983
-#5106 := [th-lemma arith farkas -1 1 1 1 #5105 #5119 #5058 #5118]: false
-#5107 := [lemma #5106]: #5101
-#10698 := [unit-resolution #5107 #9283]: #10697
-#10693 := [unit-resolution #10698 #10315 #9853]: #3329
-#4000 := (or #4515 #101)
-#4001 := [def-axiom]: #4000
-#6590 := [unit-resolution #4001 #6587]: #101
-#10155 := (= #158 #100)
-#10699 := [monotonicity #9854]: #10155
-#10700 := [trans #10699 #6590]: #159
-#4114 := (or #4324 #2133)
-#3777 := [def-axiom]: #4114
-#10696 := [unit-resolution #3777 #10700]: #4324
-#4126 := (or #4333 #4327 #3334)
-#4112 := [def-axiom]: #4126
-#10701 := [unit-resolution #4112 #10696 #10693]: #4333
-#3836 := (or #4336 #4330)
-#3837 := [def-axiom]: #3836
-#10631 := [unit-resolution #3837 #10701]: #4336
-#4106 := (or #4345 #4305 #4339)
-#4110 := [def-axiom]: #4106
-#10828 := [unit-resolution #4110 #10631 #10253]: #4305
-#4138 := (or #4302 #2058)
-#4128 := [def-axiom]: #4138
-#10827 := [unit-resolution #4128 #10828]: #2058
-#11387 := (not #5109)
-#10881 := (or #10943 #2057 #11387)
-#10936 := [th-lemma arith assign-bounds -1 -1]: #10881
-#10948 := [unit-resolution #10936 #10827 #10802]: #10943
-#3788 := (or #4302 #2675)
-#3793 := [def-axiom]: #3788
-#10890 := [unit-resolution #3793 #10828]: #2675
-#3990 := (or #4515 #4275)
-#3985 := [def-axiom]: #3990
-#9365 := [unit-resolution #3985 #6587]: #4275
-#6090 := (or #4280 #2672 #4732 #4874)
-#4785 := (+ #4798 #4784)
-#4786 := (+ #4729 #4785)
-#4781 := (= #4786 0::Int)
-#4787 := (not #4781)
-#4791 := (or #4790 #4787 #4800)
-#4862 := (not #4791)
-#4863 := (or #2059 #4732 #4862)
-#6091 := (or #4280 #4863)
-#6153 := (iff #6091 #6090)
-#4932 := (or #2672 #4732 #4874)
-#6093 := (or #4280 #4932)
-#6110 := (iff #6093 #6090)
-#6152 := [rewrite]: #6110
-#6094 := (iff #6091 #6093)
-#4933 := (iff #4863 #4932)
-#4875 := (iff #4862 #4874)
-#4858 := (iff #4791 #4855)
-#4853 := (or #4790 #4850 #4800)
-#4856 := (iff #4853 #4855)
-#4857 := [rewrite]: #4856
-#4854 := (iff #4791 #4853)
-#4851 := (iff #4787 #4850)
-#4869 := (iff #4781 #4868)
-#4866 := (= #4786 #4865)
-#4867 := [rewrite]: #4866
-#4870 := [monotonicity #4867]: #4869
-#4852 := [monotonicity #4870]: #4851
-#4849 := [monotonicity #4852]: #4854
-#4859 := [trans #4849 #4857]: #4858
-#4931 := [monotonicity #4859]: #4875
-#4934 := [monotonicity #2674 #4931]: #4933
-#6109 := [monotonicity #4934]: #6094
-#6154 := [trans #6109 #6152]: #6153
-#6092 := [quant-inst #2044]: #6091
-#6155 := [mp #6092 #6154]: #6090
-#10886 := [unit-resolution #6155 #9365 #10890 #10948]: #4874
-#6143 := (or #4855 #4868)
-#6144 := [def-axiom]: #6143
-#10800 := [unit-resolution #6144 #10886]: #4868
-#10931 := (or #4850 #4951)
-#10937 := [th-lemma arith triangle-eq]: #10931
-#10889 := [unit-resolution #10937 #10800]: #4951
-#6358 := (>= #6353 0::Int)
-#10897 := (or #9887 #6358)
-#11102 := [th-lemma arith triangle-eq]: #10897
-#11103 := [unit-resolution #11102 #9783]: #6358
-#6158 := (not #4800)
-#6159 := (or #4855 #6158)
-#6142 := [def-axiom]: #6159
-#11104 := [unit-resolution #6142 #10886]: #6158
-#4129 := (or #4302 #4294)
-#3789 := [def-axiom]: #4129
-#11095 := [unit-resolution #3789 #10828]: #4294
-#5202 := (+ #4784 #5157)
-#5203 := (+ #2045 #5202)
-#6235 := (>= #5203 0::Int)
-#4952 := (>= #4865 0::Int)
-#10898 := (or #4850 #4952)
-#11114 := [th-lemma arith triangle-eq]: #10898
-#11030 := [unit-resolution #11114 #10800]: #4952
-#11371 := (not #6358)
-#10968 := (not #4952)
-#10969 := (or #6235 #10968 #11387 #11371)
-#10964 := [th-lemma arith assign-bounds -1 -1 -1]: #10969
-#10970 := [unit-resolution #10964 #11030 #10802 #11103]: #6235
-#11548 := (not #6357)
-#11547 := (not #6038)
-#11544 := (not #4951)
-#11456 := (not #6235)
-#11474 := (or #11456 #4299 #11387 #4800 #11371 #11544 #11547 #11548)
-#5184 := (+ #2045 #5157)
-#5185 := (<= #5184 0::Int)
-#11370 := (not #5185)
-#11196 := [hypothesis]: #6358
-#11327 := [hypothesis]: #6158
-#11381 := [hypothesis]: #5109
-#11410 := (or #11370 #4800 #11387 #11371)
-#11336 := [th-lemma arith assign-bounds -1 -1 -1]: #11410
-#11374 := [unit-resolution #11336 #11381 #11327 #11196]: #11370
-#5209 := (= #5203 0::Int)
-#11308 := [hypothesis]: #6235
-#6234 := (<= #5203 0::Int)
-#11409 := [hypothesis]: #6357
-#11505 := [hypothesis]: #6038
-#11369 := [hypothesis]: #4951
-#11454 := (or #6234 #11544 #11547 #11548)
-#11543 := [th-lemma arith assign-bounds -1 -1 -1]: #11454
-#11478 := [unit-resolution #11543 #11369 #11505 #11409]: #6234
-#11455 := (not #6234)
-#11549 := (or #5209 #11455 #11456)
-#11329 := [th-lemma arith triangle-eq]: #11549
-#11457 := [unit-resolution #11329 #11478 #11308]: #5209
-#5213 := (not #5209)
-#5218 := (or #5185 #5213)
-#11508 := [hypothesis]: #4294
-#6141 := (or #4299 #5185 #5213)
-#5110 := (+ #2046 #4783)
-#5126 := (+ #5111 #5110)
-#5127 := (= #5126 0::Int)
-#5148 := (not #5127)
-#5149 := (+ #5111 #2046)
-#5150 := (>= #5149 0::Int)
-#5151 := (or #5150 #5148)
-#6147 := (or #4299 #5151)
-#6231 := (iff #6147 #6141)
-#6174 := (or #4299 #5218)
-#6177 := (iff #6174 #6141)
-#6178 := [rewrite]: #6177
-#6175 := (iff #6147 #6174)
-#5221 := (iff #5151 #5218)
-#5219 := (iff #5148 #5213)
-#5211 := (iff #5127 #5209)
-#5189 := (+ #4783 #5111)
-#5190 := (+ #2046 #5189)
-#5193 := (= #5190 0::Int)
-#5210 := (iff #5193 #5209)
-#5208 := [rewrite]: #5210
-#5198 := (iff #5127 #5193)
-#5191 := (= #5126 #5190)
-#5192 := [rewrite]: #5191
-#5199 := [monotonicity #5192]: #5198
-#5212 := [trans #5199 #5208]: #5211
-#5220 := [monotonicity #5212]: #5219
-#5188 := (iff #5150 #5185)
-#5152 := (+ #2046 #5111)
-#5154 := (>= #5152 0::Int)
-#5186 := (iff #5154 #5185)
-#5187 := [rewrite]: #5186
-#5155 := (iff #5150 #5154)
-#5147 := (= #5149 #5152)
-#5153 := [rewrite]: #5147
-#5156 := [monotonicity #5153]: #5155
-#5183 := [trans #5156 #5187]: #5188
-#5222 := [monotonicity #5183 #5220]: #5221
-#6176 := [monotonicity #5222]: #6175
-#6232 := [trans #6176 #6178]: #6231
-#6168 := [quant-inst #4796]: #6147
-#6233 := [mp #6168 #6232]: #6141
-#11458 := [unit-resolution #6233 #11508]: #5218
-#11504 := [unit-resolution #11458 #11457 #11374]: false
-#11466 := [lemma #11504]: #11474
-#11105 := [unit-resolution #11466 #10970 #11095 #10802 #11104 #11103 #10889 #10659 #9720]: false
-#11068 := [lemma #11105]: #4348
-#3991 := (or #4515 #4509)
-#3959 := [def-axiom]: #3991
-#12083 := [unit-resolution #3959 #6587]: #4509
-#3996 := (or #4512 #4351 #4506)
-#3997 := [def-axiom]: #3996
-#12174 := [unit-resolution #3997 #12083]: #4509
-#12180 := [unit-resolution #12174 #11068]: #4506
-#4019 := (or #4503 #182)
-#4020 := [def-axiom]: #4019
-#14384 := [unit-resolution #4020 #12180]: #182
-#14411 := [symm #14384]: #6551
-#10522 := (= #8578 #181)
-#6547 := (= #5797 f1)
-#36 := (:var 0 S1)
-#35 := (:var 2 S4)
-#37 := (f9 #35 #11 #36)
-#4172 := (pattern #37)
-#371 := (= f1 #36)
-#38 := (f8 #37 #11)
-#367 := (= f1 #38)
-#374 := (iff #367 #371)
-#4173 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) (:pat #4172) #374)
-#377 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) #374)
-#4176 := (iff #377 #4173)
-#4174 := (iff #374 #374)
-#4175 := [refl]: #4174
-#4177 := [quant-intro #4175]: #4176
-#1820 := (~ #377 #377)
-#1847 := (~ #374 #374)
-#1848 := [refl]: #1847
-#1821 := [nnf-pos #1848]: #1820
-#40 := (= #36 f1)
-#39 := (= #38 f1)
-#41 := (iff #39 #40)
-#42 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) #41)
-#378 := (iff #42 #377)
-#375 := (iff #41 #374)
-#372 := (iff #40 #371)
-#373 := [rewrite]: #372
-#369 := (iff #39 #367)
-#370 := [rewrite]: #369
-#376 := [monotonicity #370 #373]: #375
-#379 := [quant-intro #376]: #378
-#366 := [asserted]: #42
-#382 := [mp #366 #379]: #377
-#1849 := [mp~ #382 #1821]: #377
-#4178 := [mp #1849 #4177]: #4173
-#5852 := (not #4173)
-#5856 := (or #5852 #5798)
-#5796 := (= f1 f1)
-#5793 := (iff #5798 #5796)
-#5909 := (or #5852 #5793)
-#5911 := (iff #5909 #5856)
-#5915 := (iff #5856 #5856)
-#5903 := [rewrite]: #5915
-#5850 := (iff #5793 #5798)
-#5847 := (iff #5798 true)
-#5844 := (iff #5847 #5798)
-#5849 := [rewrite]: #5844
-#5842 := (iff #5793 #5847)
-#5845 := (iff #5796 true)
-#5846 := [rewrite]: #5845
-#5848 := [monotonicity #5846]: #5842
-#5851 := [trans #5848 #5849]: #5850
-#5914 := [monotonicity #5851]: #5911
-#5916 := [trans #5914 #5903]: #5911
-#5910 := [quant-inst #105 #171 #4]: #5909
-#5923 := [mp #5910 #5916]: #5856
-#6546 := [unit-resolution #5923 #4178]: #5798
-#6548 := [symm #6546]: #6547
-#16201 := [monotonicity #16510 #6548]: #10522
-#16227 := [trans #16201 #14411]: #10524
-#23296 := [monotonicity #16227]: #23295
-#23314 := [symm #23296]: #23299
-#23289 := [hypothesis]: #2298
-#23315 := [trans #23289 #23314]: #13583
-#22104 := (not #13583)
-#22103 := (not #13585)
-#22099 := (or #22103 #13581 #22104)
-#22105 := [def-axiom]: #22099
-#23316 := [unit-resolution #22105 #23315 #23294]: #13581
-#8173 := (not #8147)
-#8015 := (f13 f14 ?v1!18)
-#8190 := (+ #7747 #8015)
-#8191 := (+ #2290 #8190)
-#8194 := (>= #8191 0::Int)
-#23305 := (not #8194)
-#8050 := (* -1::Int #8015)
-#8051 := (+ #2287 #8050)
-#22802 := (>= #8051 0::Int)
-#8020 := (= #2287 #8015)
-#6858 := (f13 f14 #6633)
-#16281 := (= #6858 #2221)
-#16269 := (= #2221 #6858)
-#13976 := (= ?v0!14 #6633)
-#11546 := (f8 f15 ?v0!14)
-#11948 := (= f1 #11546)
-#13977 := (ite #13976 #5798 #11948)
-#13978 := (f8 #8578 ?v0!14)
-#13979 := (= f1 #13978)
-#13905 := (iff #13977 #13979)
-#13931 := (or #6350 #13905)
-#13974 := (iff #13979 #13977)
-#13932 := (or #6350 #13974)
-#13934 := (iff #13932 #13931)
-#13935 := (iff #13931 #13931)
-#14012 := [rewrite]: #13935
-#13930 := (iff #13974 #13905)
-#13904 := [rewrite]: #13930
-#13929 := [monotonicity #13904]: #13934
-#14013 := [trans #13929 #14012]: #13934
-#13933 := [quant-inst #105 #6633 #5797 #2216]: #13932
-#14008 := [mp #13933 #14013]: #13931
-#16192 := [unit-resolution #14008 #4185]: #13905
-#16230 := (= #2217 #13978)
-#16228 := (= #13978 #2217)
-#16229 := [monotonicity #16227]: #16228
-#16242 := [symm #16229]: #16230
-#16171 := [hypothesis]: #2837
-#4095 := (or #2832 #2218)
-#4096 := [def-axiom]: #4095
-#16198 := [unit-resolution #4096 #16171]: #2218
-#16243 := [trans #16198 #16242]: #13979
-#14767 := (not #13979)
-#14761 := (not #13905)
-#15396 := (or #14761 #13977 #14767)
-#15397 := [def-axiom]: #15396
-#16244 := [unit-resolution #15397 #16243 #16192]: #13977
-#12960 := (not #11948)
-#15863 := (f5 #6633 ?v0!14)
-#15893 := (f7 #15863)
-#16428 := (f8 f15 #15893)
-#16429 := (= f1 #16428)
-#16427 := (not #16429)
-#16237 := (iff #16427 #12960)
-#16232 := (iff #16429 #11948)
-#16200 := (= #16428 #11546)
-#16484 := (= #15893 ?v0!14)
-#15894 := (= ?v0!14 #15893)
-#15908 := (or #6483 #15894)
-#15909 := [quant-inst #6633 #2216]: #15908
-#16483 := [unit-resolution #15909 #4163]: #15894
-#16485 := [symm #16483]: #16484
-#16231 := [monotonicity #16485]: #16200
-#16235 := [monotonicity #16231]: #16232
-#16238 := [monotonicity #16235]: #16237
-#12883 := (f5 f22 ?v0!14)
-#12885 := (f4 #12883)
-#12411 := (* -1::Int #2221)
-#12914 := (+ #12411 #12885)
-#12958 := (+ #175 #12914)
-#12957 := (>= #12958 0::Int)
-#13532 := (not #12957)
-#12888 := (* -1::Int #12885)
-#12884 := (+ f3 #12888)
-#12924 := (<= #12884 0::Int)
-#12972 := (or #12924 #12957)
-#12977 := (not #12972)
-#4091 := (not #2826)
-#4092 := (or #2832 #4091)
-#4097 := [def-axiom]: #4092
-#16193 := [unit-resolution #4097 #16171]: #4091
-#4012 := (or #4503 #4364)
-#4007 := [def-axiom]: #4012
-#12183 := [unit-resolution #4007 #12180]: #4364
-#13228 := (or #4369 #2826 #12977)
-#12889 := (+ #1421 #12888)
-#12910 := (+ #2221 #12889)
-#12919 := (<= #12910 0::Int)
-#12918 := (or #12924 #12919)
-#12925 := (not #12918)
-#12909 := (or #2222 #12925)
-#13245 := (or #4369 #12909)
-#13539 := (iff #13245 #13228)
-#12979 := (or #2826 #12977)
-#13243 := (or #4369 #12979)
-#13545 := (iff #13243 #13228)
-#13546 := [rewrite]: #13545
-#13234 := (iff #13245 #13243)
-#12973 := (iff #12909 #12979)
-#12952 := (iff #12925 #12977)
-#12970 := (iff #12918 #12972)
-#12975 := (iff #12919 #12957)
-#12923 := (+ #2221 #12888)
-#12927 := (+ #1421 #12923)
-#12954 := (<= #12927 0::Int)
-#12959 := (iff #12954 #12957)
-#12974 := [rewrite]: #12959
-#12917 := (iff #12919 #12954)
-#12953 := (= #12910 #12927)
-#12951 := [rewrite]: #12953
-#12955 := [monotonicity #12951]: #12917
-#12956 := [trans #12955 #12974]: #12975
-#12976 := [monotonicity #12956]: #12970
-#12978 := [monotonicity #12976]: #12952
-#12980 := [monotonicity #2828 #12978]: #12973
-#13544 := [monotonicity #12980]: #13234
-#13547 := [trans #13544 #13546]: #13539
-#13248 := [quant-inst #2216]: #13245
-#13543 := [mp #13248 #13547]: #13228
-#16270 := [unit-resolution #13543 #12183 #16193]: #12977
-#13533 := (or #12972 #13532)
-#13611 := [def-axiom]: #13533
-#16271 := [unit-resolution #13611 #16270]: #13532
-#16584 := (or #16427 #12957)
-#15871 := (f4 #15863)
-#15935 := (<= #15871 0::Int)
-#16419 := (f13 f14 #15893)
-#16422 := (* -1::Int #16419)
-#16455 := (+ #2221 #16422)
-#16465 := (<= #16455 0::Int)
-#16454 := (= #2221 #16419)
-#16486 := (= #16419 #2221)
-#16481 := [monotonicity #16485]: #16486
-#16487 := [symm #16481]: #16454
-#16488 := (not #16454)
-#16489 := (or #16488 #16465)
-#16490 := [th-lemma arith triangle-eq]: #16489
-#16491 := [unit-resolution #16490 #16487]: #16465
-#15424 := [hypothesis]: #13532
-#15872 := (* -1::Int #15871)
-#16136 := (+ #12885 #15872)
-#16143 := (>= #16136 0::Int)
-#16133 := (= #12885 #15871)
-#16513 := (= #15871 #12885)
-#16511 := (= #15863 #12883)
-#16512 := [monotonicity #16510]: #16511
-#16514 := [monotonicity #16512]: #16513
-#16509 := [symm #16514]: #16133
-#16515 := (not #16133)
-#16516 := (or #16515 #16143)
-#16517 := [th-lemma arith triangle-eq]: #16516
-#16518 := [unit-resolution #16517 #16509]: #16143
-#6879 := (* -1::Int #6858)
-#7903 := (+ #175 #6879)
-#8012 := (>= #7903 0::Int)
-#7909 := (= #175 #6858)
-#12821 := (= #6858 #175)
-#16519 := [monotonicity #16510]: #12821
-#16523 := [symm #16519]: #7909
-#12824 := (not #7909)
-#12825 := (or #12824 #8012)
-#12826 := [th-lemma arith triangle-eq]: #12825
-#16524 := [unit-resolution #12826 #16523]: #8012
-#16452 := (+ #6858 #16422)
-#16453 := (>= #16452 0::Int)
-#16522 := [hypothesis]: #16429
-#16526 := (or #16427 #16453)
-#6860 := (f8 f15 #6633)
-#6861 := (= f1 #6860)
-#13390 := (not #6861)
-#13769 := (or #13768 #13390)
-#15494 := (iff #733 #13390)
-#15492 := (iff #730 #6861)
-#15490 := (iff #6861 #730)
-#15488 := (= #6860 #172)
-#13757 := [hypothesis]: #6642
-#13759 := [symm #13757]: #10520
-#13760 := [monotonicity #13759]: #15488
-#13765 := [monotonicity #13760]: #15490
-#13766 := [symm #13765]: #15492
-#13756 := [monotonicity #13766]: #15494
-#4021 := (or #4503 #733)
-#4016 := [def-axiom]: #4021
-#13758 := [unit-resolution #4016 #12180]: #733
-#13764 := [mp #13758 #13756]: #13390
-#13755 := [hypothesis]: #6861
-#13767 := [unit-resolution #13755 #13764]: false
-#13774 := [lemma #13767]: #13769
-#16525 := [unit-resolution #13774 #13795]: #13390
-#3929 := (or #4515 #4259)
-#3984 := [def-axiom]: #3929
-#13392 := [unit-resolution #3984 #6587]: #4259
-#16456 := (or #4264 #6861 #16427 #16453)
-#16451 := (or #6861 #16427 #16453)
-#16461 := (or #4264 #16451)
-#16460 := (iff #16461 #16456)
-#16463 := [rewrite]: #16460
-#16462 := [quant-inst #15893 #6633]: #16461
-#16464 := [mp #16462 #16463]: #16456
-#16527 := [unit-resolution #16464 #13392 #16525]: #16526
-#16528 := [unit-resolution #16527 #16522]: #16453
-#16546 := (not #16465)
-#13410 := (not #8012)
-#16545 := (not #16453)
-#16529 := (not #16143)
-#16547 := (or #15935 #16529 #12957 #16545 #13410 #16546)
-#16548 := [th-lemma arith assign-bounds 1 1 1 1 1]: #16547
-#16549 := [unit-resolution #16548 #16528 #16524 #16518 #15424 #16491]: #15935
-#15917 := (not #15935)
-#15919 := (or #13976 #15917)
-#15 := (f4 #14)
-#330 := (<= #15 0::Int)
-#331 := (not #330)
+#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)
-#334 := (or #13 #331)
-#4146 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4139) #334)
-#337 := (forall (vars (?v0 S2) (?v1 S2)) #334)
-#4149 := (iff #337 #4146)
-#4147 := (iff #334 #334)
-#4148 := [refl]: #4147
-#4150 := [quant-intro #4148]: #4149
-#1812 := (~ #337 #337)
-#1811 := (~ #334 #334)
-#1808 := [refl]: #1811
-#1813 := [nnf-pos #1808]: #1812
-#20 := (< 0::Int #15)
-#19 := (not #13)
-#21 := (implies #19 #20)
-#22 := (forall (vars (?v0 S2) (?v1 S2)) #21)
-#340 := (iff #22 #337)
-#324 := (or #13 #20)
-#327 := (forall (vars (?v0 S2) (?v1 S2)) #324)
-#338 := (iff #327 #337)
-#335 := (iff #324 #334)
-#332 := (iff #20 #331)
-#333 := [rewrite]: #332
-#336 := [monotonicity #333]: #335
-#339 := [quant-intro #336]: #338
-#328 := (iff #22 #327)
-#325 := (iff #21 #324)
-#326 := [rewrite]: #325
-#329 := [quant-intro #326]: #328
-#341 := [trans #329 #339]: #340
-#323 := [asserted]: #22
-#342 := [mp #323 #341]: #337
-#1809 := [mp~ #342 #1813]: #337
-#4151 := [mp #1809 #4150]: #4146
-#5423 := (not #4146)
-#15916 := (or #5423 #13976 #15917)
-#15910 := (= #6633 ?v0!14)
-#15918 := (or #15910 #15917)
-#15922 := (or #5423 #15918)
-#15938 := (iff #15922 #15916)
-#15924 := (or #5423 #15919)
-#15939 := (iff #15924 #15916)
-#15940 := [rewrite]: #15939
-#15925 := (iff #15922 #15924)
-#15920 := (iff #15918 #15919)
-#15898 := (iff #15910 #13976)
-#15899 := [rewrite]: #15898
-#15921 := [monotonicity #15899]: #15920
-#15926 := [monotonicity #15921]: #15925
-#15941 := [trans #15926 #15940]: #15938
-#15923 := [quant-inst #6633 #2216]: #15922
-#15942 := [mp #15923 #15941]: #15916
-#16544 := [unit-resolution #15942 #4151]: #15919
-#16550 := [unit-resolution #16544 #16549]: #13976
-#15911 := (= #15871 0::Int)
-#16579 := (not #15911)
-#15936 := (>= #15871 0::Int)
-#16551 := (not #15936)
-#16552 := (or #16551 #16529 #12957 #16545 #13410 #16546)
-#16553 := [th-lemma arith assign-bounds 1 -1 1 1 -1]: #16552
-#16554 := [unit-resolution #16553 #16528 #16524 #16518 #15424 #16491]: #16551
-#16580 := (or #16579 #15936)
-#16581 := [th-lemma arith triangle-eq]: #16580
-#16582 := [unit-resolution #16581 #16554]: #16579
-#14015 := (not #13976)
-#15902 := (or #14015 #15911)
-#16 := (= #15 0::Int)
-#314 := (or #19 #16)
-#4140 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4139) #314)
-#317 := (forall (vars (?v0 S2) (?v1 S2)) #314)
-#4143 := (iff #317 #4140)
-#4141 := (iff #314 #314)
-#4142 := [refl]: #4141
-#4144 := [quant-intro #4142]: #4143
-#1836 := (~ #317 #317)
-#1834 := (~ #314 #314)
-#1835 := [refl]: #1834
-#1837 := [nnf-pos #1835]: #1836
-#17 := (implies #13 #16)
-#18 := (forall (vars (?v0 S2) (?v1 S2)) #17)
-#320 := (iff #18 #317)
-#293 := (= 0::Int #15)
-#304 := (or #19 #293)
-#309 := (forall (vars (?v0 S2) (?v1 S2)) #304)
-#318 := (iff #309 #317)
-#315 := (iff #304 #314)
-#312 := (iff #293 #16)
-#313 := [rewrite]: #312
-#316 := [monotonicity #313]: #315
-#319 := [quant-intro #316]: #318
-#310 := (iff #18 #309)
-#307 := (iff #17 #304)
-#301 := (implies #13 #293)
-#305 := (iff #301 #304)
-#306 := [rewrite]: #305
-#302 := (iff #17 #301)
-#299 := (iff #16 #293)
-#300 := [rewrite]: #299
-#303 := [monotonicity #300]: #302
-#308 := [trans #303 #306]: #307
-#311 := [quant-intro #308]: #310
-#321 := [trans #311 #319]: #320
-#292 := [asserted]: #18
-#322 := [mp #292 #321]: #317
-#1810 := [mp~ #322 #1837]: #317
-#4145 := [mp #1810 #4144]: #4140
-#5404 := (not #4140)
-#15904 := (or #5404 #14015 #15911)
-#15914 := (not #15910)
-#15915 := (or #15914 #15911)
-#15905 := (or #5404 #15915)
-#15932 := (iff #15905 #15904)
-#15907 := (or #5404 #15902)
-#15930 := (iff #15907 #15904)
-#15931 := [rewrite]: #15930
-#15928 := (iff #15905 #15907)
-#15897 := (iff #15915 #15902)
-#15900 := (iff #15914 #14015)
-#15901 := [monotonicity #15899]: #15900
-#15903 := [monotonicity #15901]: #15897
-#15929 := [monotonicity #15903]: #15928
-#15933 := [trans #15929 #15931]: #15932
-#15906 := [quant-inst #6633 #2216]: #15905
-#15934 := [mp #15906 #15933]: #15904
-#16583 := [unit-resolution #15934 #4145]: #15902
-#16578 := [unit-resolution #16583 #16582 #16550]: false
-#16585 := [lemma #16578]: #16584
-#16246 := [unit-resolution #16585 #16271]: #16427
-#16239 := [mp #16246 #16238]: #12960
-#14014 := (not #13977)
-#14082 := (or #14014 #13976 #11948)
-#14083 := [def-axiom]: #14082
-#16240 := [unit-resolution #14083 #16239 #16244]: #13976
-#16275 := [monotonicity #16240]: #16269
-#16278 := [symm #16275]: #16281
-#16297 := (= #2220 #6858)
-#14771 := (= #2220 #175)
-#6119 := (f24 f22)
-#16276 := (= #6119 #175)
-#6120 := (= #175 #6119)
-#6108 := (f4 #6107)
-#6127 := (>= #6108 0::Int)
-#6111 := (* -1::Int #6108)
-#6115 := (+ f3 #6111)
-#6116 := (<= #6115 0::Int)
-#6132 := (or #6116 #6127)
-#6641 := (= #6108 0::Int)
-#14106 := (not #6641)
-#12532 := [hypothesis]: #14106
-#12874 := (or #5404 #6641)
-#6327 := (= f22 f22)
-#6647 := (not #6327)
-#6650 := (or #6647 #6641)
-#12896 := (or #5404 #6650)
-#13528 := (iff #12896 #12874)
-#13607 := (iff #12874 #12874)
-#13608 := [rewrite]: #13607
-#6692 := (iff #6650 #6641)
-#6704 := (or false #6641)
-#6708 := (iff #6704 #6641)
-#6709 := [rewrite]: #6708
-#6706 := (iff #6650 #6704)
-#6658 := (iff #6647 false)
-#6651 := (iff #6647 #3871)
-#6333 := (iff #6327 true)
-#6334 := [rewrite]: #6333
-#6657 := [monotonicity #6334]: #6651
-#6703 := [trans #6657 #3862]: #6658
-#6707 := [monotonicity #6703]: #6706
-#6693 := [trans #6707 #6709]: #6692
-#13526 := [monotonicity #6693]: #13528
-#13661 := [trans #13526 #13608]: #13528
-#12880 := [quant-inst #171 #171]: #12896
-#13751 := [mp #12880 #13661]: #12874
-#12426 := [unit-resolution #13751 #4145 #12532]: false
-#12190 := [lemma #12426]: #6641
-#16194 := (or #14106 #6127)
-#16166 := [th-lemma arith triangle-eq]: #16194
-#16169 := [unit-resolution #16166 #12190]: #6127
-#6370 := (not #6127)
-#6355 := (or #6132 #6370)
-#6356 := [def-axiom]: #6355
-#16195 := [unit-resolution #6356 #16169]: #6132
-#6135 := (not #6132)
-#6138 := (or #6120 #6135)
-#6282 := (or #4369 #6120 #6135)
-#6112 := (+ #1421 #6111)
-#6113 := (+ #175 #6112)
-#6114 := (<= #6113 0::Int)
-#6117 := (or #6116 #6114)
-#6118 := (not #6117)
-#6121 := (or #6120 #6118)
-#6289 := (or #4369 #6121)
-#6365 := (iff #6289 #6282)
-#6325 := (or #4369 #6138)
-#6362 := (iff #6325 #6282)
-#6363 := [rewrite]: #6362
-#6360 := (iff #6289 #6325)
-#6139 := (iff #6121 #6138)
-#6136 := (iff #6118 #6135)
-#6133 := (iff #6117 #6132)
-#6130 := (iff #6114 #6127)
-#6124 := (<= #6111 0::Int)
-#6128 := (iff #6124 #6127)
-#6129 := [rewrite]: #6128
-#6125 := (iff #6114 #6124)
-#6122 := (= #6113 #6111)
-#6123 := [rewrite]: #6122
-#6126 := [monotonicity #6123]: #6125
-#6131 := [trans #6126 #6129]: #6130
-#6134 := [monotonicity #6131]: #6133
-#6137 := [monotonicity #6134]: #6136
-#6140 := [monotonicity #6137]: #6139
-#6361 := [monotonicity #6140]: #6360
-#6326 := [trans #6361 #6363]: #6365
-#6324 := [quant-inst #171]: #6289
-#6366 := [mp #6324 #6326]: #6282
-#16196 := [unit-resolution #6366 #12183]: #6138
-#16197 := [unit-resolution #16196 #16195]: #6120
-#16279 := [symm #16197]: #16276
-#14379 := (= #2220 #6119)
-#6789 := (f24 #6633)
-#15473 := (= #6789 #6119)
-#16274 := [monotonicity #16510]: #15473
-#16199 := (= #2220 #6789)
-#16273 := [monotonicity #16240]: #16199
-#16282 := [trans #16273 #16274]: #14379
-#16291 := [trans #16282 #16279]: #14771
-#16298 := [trans #16291 #16523]: #16297
-#16299 := [trans #16298 #16278]: #2826
-#16285 := [unit-resolution #16193 #16299]: false
-#16290 := [lemma #16285]: #2832
-#3987 := (or #4503 #4497)
-#3988 := [def-axiom]: #3987
-#14163 := [unit-resolution #3988 #12180]: #4497
-#11130 := (f5 f22 ?v0!13)
-#11133 := (f4 #11130)
-#11305 := (+ #2200 #11133)
-#11302 := (+ #175 #11305)
-#11707 := (>= #11302 0::Int)
-#11263 := (= #11302 0::Int)
-#11186 := (* -1::Int #11133)
-#11215 := (+ f3 #11186)
-#11269 := (<= #11215 0::Int)
-#12311 := (not #11269)
-#11201 := (+ #2816 #11133)
-#11206 := (+ #175 #11201)
-#11195 := (>= #11206 0::Int)
-#12033 := (or #11195 #11269)
-#10743 := (not #12033)
-#11606 := (= #2199 #2201)
-#12673 := (not #11606)
-#12526 := [hypothesis]: #2823
-#11506 := (or #12673 #2818)
-#12181 := [th-lemma arith triangle-eq]: #11506
-#12182 := [unit-resolution #12181 #12526]: #12673
-#12297 := (or #4369 #11606 #10743)
-#11235 := (+ #1421 #11186)
-#11236 := (+ #2201 #11235)
-#11214 := (<= #11236 0::Int)
-#11708 := (or #11269 #11214)
-#11683 := (not #11708)
-#11616 := (= #2201 #2199)
-#11617 := (or #11616 #11683)
-#12257 := (or #4369 #11617)
-#12299 := (iff #12257 #12297)
-#11871 := (or #11606 #10743)
-#12301 := (or #4369 #11871)
-#12342 := (iff #12301 #12297)
-#12348 := [rewrite]: #12342
-#12303 := (iff #12257 #12301)
-#12204 := (iff #11617 #11871)
-#12253 := (iff #11683 #10743)
-#9994 := (iff #11708 #12033)
-#11702 := (or #11269 #11195)
-#12034 := (iff #11702 #12033)
-#11922 := [rewrite]: #12034
-#11924 := (iff #11708 #11702)
-#11218 := (iff #11214 #11195)
-#11191 := (+ #2201 #11186)
-#11270 := (+ #1421 #11191)
-#9774 := (<= #11270 0::Int)
-#11304 := (iff #9774 #11195)
-#11325 := [rewrite]: #11304
-#10652 := (iff #11214 #9774)
-#11303 := (= #11236 #11270)
-#9768 := [rewrite]: #11303
-#10653 := [monotonicity #9768]: #10652
-#11326 := [trans #10653 #11325]: #11218
-#11949 := [monotonicity #11326]: #11924
-#11854 := [trans #11949 #11922]: #9994
-#12198 := [monotonicity #11854]: #12253
-#11611 := (iff #11616 #11606)
-#11923 := [rewrite]: #11611
-#12197 := [monotonicity #11923 #12198]: #12204
-#12283 := [monotonicity #12197]: #12303
-#12349 := [trans #12283 #12348]: #12299
-#12295 := [quant-inst #2198]: #12257
-#12305 := [mp #12295 #12349]: #12297
-#12192 := [unit-resolution #12305 #12183 #12182]: #10743
-#12339 := (or #12033 #12311)
-#12392 := [def-axiom]: #12339
-#12678 := [unit-resolution #12392 #12192]: #12311
-#12347 := (not #11195)
-#12314 := (or #12033 #12347)
-#12329 := [def-axiom]: #12314
-#12413 := [unit-resolution #12329 #12192]: #12347
-#11408 := (or #11195 #11263 #11269)
-#4013 := (or #4503 #4372)
-#3986 := [def-axiom]: #4013
-#12414 := [unit-resolution #3986 #12180]: #4372
-#11620 := (or #4377 #11195 #11263 #11269)
-#11135 := (+ #11133 #2200)
-#11098 := (+ #175 #11135)
-#11120 := (= #11098 0::Int)
-#11202 := (or #11269 #11214 #11120)
-#11586 := (or #4377 #11202)
-#11674 := (iff #11586 #11620)
-#11621 := (or #4377 #11408)
-#11781 := (iff #11621 #11620)
-#11785 := [rewrite]: #11781
-#11650 := (iff #11586 #11621)
-#11402 := (iff #11202 #11408)
-#11328 := (or #11269 #11195 #11263)
-#11412 := (iff #11328 #11408)
-#11467 := [rewrite]: #11412
-#11380 := (iff #11202 #11328)
-#11239 := (iff #11120 #11263)
-#11301 := (= #11098 #11302)
-#11299 := [rewrite]: #11301
-#11264 := [monotonicity #11299]: #11239
-#11262 := [monotonicity #11326 #11264]: #11380
-#11619 := [trans #11262 #11467]: #11402
-#11784 := [monotonicity #11619]: #11650
-#11737 := [trans #11784 #11785]: #11674
-#11585 := [quant-inst #2198]: #11586
-#11672 := [mp #11585 #11737]: #11620
-#12415 := [unit-resolution #11672 #12414]: #11408
-#12405 := [unit-resolution #12415 #12413 #12678]: #11263
-#12036 := (not #11263)
-#12542 := (or #12036 #11707)
-#12499 := [th-lemma arith triangle-eq]: #12542
-#12543 := [unit-resolution #12499 #12405]: #11707
-#12312 := (>= #2817 0::Int)
-#12431 := (or #12312 #2818)
-#12530 := [th-lemma arith farkas 1 1]: #12431
-#11405 := [unit-resolution #12530 #12526]: #12312
-#12529 := [th-lemma arith farkas 1 -1 1 #11405 #12413 #12543]: false
-#11320 := [lemma #12529]: #2818
-#4017 := (or #4500 #2823 #4494)
-#4018 := [def-axiom]: #4017
-#14172 := [unit-resolution #4018 #11320 #14163]: #4494
-#4032 := (or #4491 #4485)
-#4033 := [def-axiom]: #4032
-#21229 := [unit-resolution #4033 #14172]: #4485
-#4028 := (or #4488 #2837 #4482)
-#4029 := [def-axiom]: #4028
-#21233 := [unit-resolution #4029 #21229]: #4485
-#21234 := [unit-resolution #21233 #16290]: #4482
-#4038 := (or #4479 #4389)
-#4040 := [def-axiom]: #4038
-#21235 := [unit-resolution #4040 #21234]: #4389
-#22059 := (or #4394 #3439 #8020)
-#8016 := (= #8015 #2287)
-#8019 := (or #8016 #3439)
-#22060 := (or #4394 #8019)
-#22065 := (iff #22060 #22059)
-#8026 := (or #3439 #8020)
-#22029 := (or #4394 #8026)
-#22063 := (iff #22029 #22059)
-#22064 := [rewrite]: #22063
-#22061 := (iff #22060 #22029)
-#8029 := (iff #8019 #8026)
-#8023 := (or #8020 #3439)
-#8027 := (iff #8023 #8026)
-#8028 := [rewrite]: #8027
-#8024 := (iff #8019 #8023)
-#8021 := (iff #8016 #8020)
-#8022 := [rewrite]: #8021
-#8025 := [monotonicity #8022]: #8024
-#8030 := [trans #8025 #8028]: #8029
-#22062 := [monotonicity #8030]: #22061
-#22068 := [trans #22062 #22064]: #22065
-#22058 := [quant-inst #2283]: #22060
-#22069 := [mp #22058 #22068]: #22059
-#23317 := [unit-resolution #22069 #21235 #23289]: #8020
-#23318 := (not #8020)
-#23319 := (or #23318 #22802)
-#23320 := [th-lemma arith triangle-eq]: #23319
-#23321 := [unit-resolution #23320 #23317]: #22802
-#23303 := [hypothesis]: #4090
-#7748 := (+ #2285 #7747)
-#7749 := (<= #7748 0::Int)
-#4030 := (or #4491 #4380)
-#4031 := [def-axiom]: #4030
-#16406 := [unit-resolution #4031 #14172]: #4380
-#22553 := (or #4385 #7749)
-#7739 := (+ #7706 #2286)
-#7740 := (>= #7739 0::Int)
-#22554 := (or #4385 #7740)
-#22578 := (iff #22554 #22553)
-#22580 := (iff #22553 #22553)
-#22581 := [rewrite]: #22580
-#7752 := (iff #7740 #7749)
-#7741 := (+ #2286 #7706)
-#7744 := (>= #7741 0::Int)
-#7750 := (iff #7744 #7749)
-#7751 := [rewrite]: #7750
-#7745 := (iff #7740 #7744)
-#7742 := (= #7739 #7741)
-#7743 := [rewrite]: #7742
-#7746 := [monotonicity #7743]: #7745
-#7753 := [trans #7746 #7751]: #7752
-#22579 := [monotonicity #7753]: #22578
-#22576 := [trans #22579 #22581]: #22578
-#22577 := [quant-inst #2284]: #22554
-#22582 := [mp #22577 #22576]: #22553
-#23304 := [unit-resolution #22582 #16406]: #7749
-#23307 := (not #7749)
-#23306 := (not #22802)
-#23285 := (or #23305 #2883 #23306 #23307)
-#23286 := [th-lemma arith assign-bounds 1 1 -1]: #23285
-#23284 := [unit-resolution #23286 #23304 #23303 #23321]: #23305
-#23287 := (or #8173 #8194)
-#23352 := [hypothesis]: #2296
-#22714 := (or #4255 #2295 #8173 #8194)
-#8186 := (+ #8015 #7747)
-#8187 := (+ #2290 #8186)
-#8188 := (>= #8187 0::Int)
-#8189 := (or #8173 #2295 #8188)
-#22715 := (or #4255 #8189)
-#22739 := (iff #22715 #22714)
-#8200 := (or #2295 #8173 #8194)
-#22720 := (or #4255 #8200)
-#22722 := (iff #22720 #22714)
-#22723 := [rewrite]: #22722
-#22713 := (iff #22715 #22720)
-#8203 := (iff #8189 #8200)
-#8197 := (or #8173 #2295 #8194)
-#8201 := (iff #8197 #8200)
-#8202 := [rewrite]: #8201
-#8198 := (iff #8189 #8197)
-#8195 := (iff #8188 #8194)
-#8192 := (= #8187 #8191)
-#8193 := [rewrite]: #8192
-#8196 := [monotonicity #8193]: #8195
-#8199 := [monotonicity #8196]: #8198
-#8204 := [trans #8199 #8202]: #8203
-#22721 := [monotonicity #8204]: #22713
-#22740 := [trans #22721 #22723]: #22739
-#22719 := [quant-inst #2284 #2283]: #22715
-#22738 := [mp #22719 #22740]: #22714
-#23288 := [unit-resolution #22738 #9283 #23352]: #23287
-#23290 := [unit-resolution #23288 #23284]: #8173
-#22091 := (not #13581)
-#22094 := (or #22091 #13580 #8147)
-#22095 := [def-axiom]: #22094
-#23291 := [unit-resolution #22095 #23290 #23316]: #13580
-#23293 := [trans #23291 #16510]: #23292
-#22436 := [monotonicity #23293]: #22435
-#22437 := [monotonicity #22436]: #23160
-#22438 := (not #23160)
-#22440 := (or #22438 #23171)
-#22434 := [th-lemma arith triangle-eq]: #22440
-#22442 := [unit-resolution #22434 #22437]: #23171
-decl f6 :: (-> S3 S2)
-#8254 := (f6 #2289)
-#8989 := (f13 f14 #8254)
-#9003 := (* -1::Int #8989)
-#23119 := (+ #8015 #9003)
-#23122 := (>= #23119 0::Int)
-#23118 := (= #8015 #8989)
-#22446 := (= #8989 #8015)
-#22444 := (= #8254 ?v1!18)
-#8255 := (= ?v1!18 #8254)
-#23 := (f6 #14)
-#344 := (= #11 #23)
-#4152 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4139) #344)
-#347 := (forall (vars (?v0 S2) (?v1 S2)) #344)
-#4155 := (iff #347 #4152)
-#4153 := (iff #344 #344)
-#4154 := [refl]: #4153
-#4156 := [quant-intro #4154]: #4155
-#1814 := (~ #347 #347)
-#1838 := (~ #344 #344)
-#1839 := [refl]: #1838
-#1815 := [nnf-pos #1839]: #1814
-#24 := (= #23 #11)
-#25 := (forall (vars (?v0 S2) (?v1 S2)) #24)
-#348 := (iff #25 #347)
-#345 := (iff #24 #344)
-#346 := [rewrite]: #345
-#349 := [quant-intro #346]: #348
-#343 := [asserted]: #25
-#352 := [mp #343 #349]: #347
-#1840 := [mp~ #352 #1815]: #347
-#4157 := [mp #1840 #4156]: #4152
-#6486 := (not #4152)
-#22889 := (or #6486 #8255)
-#22890 := [quant-inst #2283 #2284]: #22889
-#22443 := [unit-resolution #22890 #4157]: #8255
-#22445 := [symm #22443]: #22444
-#22512 := [monotonicity #22445]: #22446
-#22591 := [symm #22512]: #23118
-#22511 := (not #23118)
-#22592 := (or #22511 #23122)
-#22599 := [th-lemma arith triangle-eq]: #22592
-#22600 := [unit-resolution #22599 #22591]: #23122
-#9004 := (+ #175 #9003)
-#9005 := (<= #9004 0::Int)
-#8994 := (f8 f15 #8254)
-#8995 := (= f1 #8994)
-#23333 := (not #8995)
-#23334 := (iff #8173 #23333)
-#23332 := (iff #8147 #8995)
-#23330 := (iff #8995 #8147)
-#23328 := (= #8994 #8146)
-#23329 := [monotonicity #22445]: #23328
-#23331 := [monotonicity #23329]: #23330
-#23313 := [symm #23331]: #23332
-#23335 := [monotonicity #23313]: #23334
-#23336 := [mp #23290 #23335]: #23333
-#9010 := (or #8995 #9005)
-#4022 := (or #4503 #4354)
-#4008 := [def-axiom]: #4022
-#23337 := [unit-resolution #4008 #12180]: #4354
-#22808 := (or #4359 #8995 #9005)
-#8990 := (+ #8989 #1421)
-#8993 := (>= #8990 0::Int)
-#8996 := (or #8995 #8993)
-#22937 := (or #4359 #8996)
-#22977 := (iff #22937 #22808)
-#22944 := (or #4359 #9010)
-#22947 := (iff #22944 #22808)
-#22976 := [rewrite]: #22947
-#22945 := (iff #22937 #22944)
-#9011 := (iff #8996 #9010)
-#9008 := (iff #8993 #9005)
-#8997 := (+ #1421 #8989)
-#9000 := (>= #8997 0::Int)
-#9006 := (iff #9000 #9005)
-#9007 := [rewrite]: #9006
-#9001 := (iff #8993 #9000)