updated SMT certificates
authorboehmes
Sun, 05 Jun 2011 15:00:52 +0200
changeset 43155 f4f27123daef
parent 43154 72e4753a6677
child 43156 04aaac80183f
updated SMT certificates
src/HOL/Boogie/Examples/Boogie_Dijkstra.certs
src/HOL/SMT_Examples/SMT_Examples.certs
src/HOL/SMT_Examples/SMT_Tests.certs
--- a/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Sun Jun 05 15:00:17 2011 +0200
+++ b/src/HOL/Boogie/Examples/Boogie_Dijkstra.certs	Sun Jun 05 15:00:52 2011 +0200
@@ -1,6772 +1,6836 @@
-9404399607250187a35291f0e20ac6b62142fe20 6771 0
+bb58c98b1c1f10bf4f2103c003d8f48ec713787b 6835 0
 #2 := false
 #8 := 0::Int
+decl f13 :: (-> S5 S2 Int)
+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)
+decl f1 :: S1
+#4 := f1
+#19472 := (= f1 #19471)
+#19473 := (not #19472)
 decl f4 :: (-> S3 Int)
 decl f5 :: (-> S2 S2 S3)
-decl ?v0!20 :: S2
-#2313 := ?v0!20
-decl f22 :: S2
-#170 := f22
-#14159 := (f5 f22 ?v0!20)
-#14160 := (f4 #14159)
-#1175 := -1::Int
-#14164 := (* -1::Int #14160)
+#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)
 decl f3 :: Int
 #9 := f3
-#14168 := (+ f3 #14164)
-#14169 := (<= #14168 0::Int)
-#12854 := (not #14169)
-decl f13 :: (-> S5 S2 Int)
-decl f14 :: S5
-#98 := f14
-#14126 := (f13 f14 ?v0!20)
-#14143 := (* -1::Int #14126)
-#14178 := (+ #14143 #14160)
-#174 := (f13 f14 f22)
-#14179 := (+ #174 #14178)
-#14180 := (>= #14179 0::Int)
-#14215 := (or #14169 #14180)
-#14218 := (not #14215)
+#19476 := (+ f3 #19047)
+#19477 := (<= #19476 0::Int)
+#34297 := (not #19477)
 decl f24 :: (-> S2 Int)
-#2314 := (f24 ?v0!20)
-#14212 := (= #2314 #14126)
-#22951 := (not #14212)
-#14144 := (+ #2314 #14143)
-#19137 := (>= #14144 0::Int)
-#22448 := (not #19137)
-decl f8 :: (-> S4 S2 S1)
-decl ?v1!7 :: (-> S2 S2)
-#14273 := (?v1!7 ?v0!20)
-decl f15 :: S4
-#104 := f15
-#14285 := (f8 f15 #14273)
-decl f1 :: S1
-#4 := f1
-#14286 := (= f1 #14285)
-decl f9 :: (-> S4 S2 S1 S4)
-#180 := (f9 f15 f22 f1)
-#5830 := (f8 #180 f22)
-#5831 := (= f1 #5830)
-decl f6 :: (-> S3 S2)
+#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
-#5873 := (f5 f22 f10)
-#6386 := (f6 #5873)
-#22127 := (= #6386 #14273)
-#22119 := (ite #22127 #5831 #14286)
-#22149 := (not #22119)
-#7238 := (f9 f15 #6386 #5830)
-#22125 := (f8 #7238 #14273)
-#22126 := (= f1 #22125)
-#22140 := (iff #22119 #22126)
-#12 := (:var 0 S2)
+#2894 := (= f10 ?v0!20)
+#4431 := (or #2327 #2894 #4419 #4428)
+#4434 := (not #4431)
+decl ?v0!19 :: S2
+#2284 := ?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)
-#4178 := (pattern #47)
+#4179 := (pattern #47)
 #51 := (f8 #43 #12)
-#387 := (= f1 #51)
-#384 := (= f1 #45)
+#388 := (= f1 #51)
+#385 := (= f1 #45)
 #49 := (= #12 #44)
-#390 := (ite #49 #384 #387)
-#380 := (= f1 #47)
-#393 := (iff #380 #390)
-#4179 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #4178) #393)
-#396 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) #393)
-#4182 := (iff #396 #4179)
-#4180 := (iff #393 #393)
-#4181 := [refl]: #4180
-#4183 := [quant-intro #4181]: #4182
-#1821 := (~ #396 #396)
-#1849 := (~ #393 #393)
-#1850 := [refl]: #1849
-#1822 := [nnf-pos #1850]: #1821
+#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)
-#397 := (iff #55 #396)
-#394 := (iff #54 #393)
-#391 := (iff #53 #390)
-#388 := (iff #52 #387)
-#389 := [rewrite]: #388
-#385 := (iff #50 #384)
-#386 := [rewrite]: #385
-#392 := [monotonicity #386 #389]: #391
-#382 := (iff #48 #380)
-#383 := [rewrite]: #382
-#395 := [monotonicity #383 #392]: #394
-#398 := [quant-intro #395]: #397
-#379 := [asserted]: #55
-#401 := [mp #379 #398]: #396
-#1851 := [mp~ #401 #1822]: #396
-#4184 := [mp #1851 #4183]: #4179
-#6238 := (not #4179)
-#22056 := (or #6238 #22140)
-#22120 := (= #14273 #6386)
-#22122 := (ite #22120 #5831 #14286)
-#22124 := (iff #22126 #22122)
-#22094 := (or #6238 #22124)
-#22055 := (iff #22094 #22056)
-#22097 := (iff #22056 #22056)
-#22093 := [rewrite]: #22097
-#22057 := (iff #22124 #22140)
-#22130 := (iff #22126 #22119)
-#22141 := (iff #22130 #22140)
-#22139 := [rewrite]: #22141
-#22131 := (iff #22124 #22130)
-#22123 := (iff #22122 #22119)
-#22121 := (iff #22120 #22127)
-#22128 := [rewrite]: #22121
-#22129 := [monotonicity #22128]: #22123
-#22118 := [monotonicity #22129]: #22131
-#22088 := [trans #22118 #22139]: #22057
-#22096 := [monotonicity #22088]: #22055
-#22144 := [trans #22096 #22093]: #22055
-#22095 := [quant-inst #104 #6386 #5830 #14273]: #22094
-#22148 := [mp #22095 #22144]: #22056
-#22563 := [unit-resolution #22148 #4184]: #22140
-#22266 := (not #22126)
-decl f23 :: S4
-#179 := f23
-#19072 := (f8 f23 #14273)
-#19073 := (= f1 #19072)
-#19080 := (not #19073)
-#22994 := (iff #19080 #22266)
-#22987 := (iff #19073 #22126)
-#23020 := (iff #22126 #19073)
-#23000 := (= #22125 #19072)
-#8697 := (= #7238 f23)
-#8695 := (= #180 f23)
-#181 := (= f23 #180)
-#2317 := (f5 #12 ?v0!20)
-#4421 := (pattern #2317)
-#188 := (f24 #12)
-#4361 := (pattern #188)
-#198 := (f8 f23 #12)
-#4387 := (pattern #198)
-#2318 := (f4 #2317)
-#2315 := (* -1::Int #2314)
-#2917 := (+ #2315 #2318)
-#2918 := (+ #188 #2917)
-#2921 := (= #2918 0::Int)
-#3483 := (not #2921)
-#2316 := (+ #188 #2315)
-#2321 := (>= #2316 0::Int)
-#774 := (= f1 #198)
-#780 := (not #774)
-#3484 := (or #780 #2321 #3483)
-#4422 := (forall (vars (?v1 S2)) (:pat #4387 #4361 #4421) #3484)
-#4427 := (not #4422)
-#11 := (:var 1 S2)
-#81 := (f5 #12 #11)
-#4216 := (pattern #81)
-#210 := (f24 #11)
-#1470 := (* -1::Int #210)
-#1471 := (+ #188 #1470)
-#82 := (f4 #81)
-#1501 := (+ #82 #1471)
-#1499 := (>= #1501 0::Int)
-#1198 := (* -1::Int #82)
-#1201 := (+ f3 #1198)
-#1202 := (<= #1201 0::Int)
-#3475 := (or #780 #1202 #1499)
-#4413 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4216) #3475)
-#4418 := (not #4413)
-#2893 := (= f10 ?v0!20)
-#2325 := (+ f3 #2315)
-#2326 := (<= #2325 0::Int)
-#4430 := (or #2326 #2893 #4418 #4427)
-#4433 := (not #4430)
-decl ?v0!19 :: S2
-#2283 := ?v0!19
-decl ?v1!18 :: S2
-#2282 := ?v1!18
-#2288 := (f5 ?v1!18 ?v0!19)
-#2289 := (f4 #2288)
-#2292 := (* -1::Int #2289)
-#2286 := (f24 ?v1!18)
-#2879 := (* -1::Int #2286)
-#2880 := (+ #2879 #2292)
-#2284 := (f24 ?v0!19)
-#2881 := (+ #2284 #2880)
-#2882 := (<= #2881 0::Int)
-#2296 := (f8 f23 ?v1!18)
-#2297 := (= f1 #2296)
-#3438 := (not #2297)
-#2293 := (+ f3 #2292)
-#2294 := (<= #2293 0::Int)
-#3453 := (or #2294 #3438 #2882)
-#3458 := (not #3453)
-#4436 := (or #3458 #4433)
-#4439 := (not #4436)
-#4404 := (pattern #188 #210)
-#1469 := (>= #1471 0::Int)
-#207 := (f8 f23 #11)
-#794 := (= f1 #207)
-#3415 := (not #794)
-#3430 := (or #774 #3415 #1469)
-#4405 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4404) #3430)
-#4410 := (not #4405)
-#4442 := (or #4410 #4439)
-#4445 := (not #4442)
+#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)
 decl ?v1!16 :: S2
-#2255 := ?v1!16
-#2259 := (f24 ?v1!16)
-#2853 := (* -1::Int #2259)
+#2256 := ?v1!16
+#2260 := (f24 ?v1!16)
+#2854 := (* -1::Int #2260)
 decl ?v0!17 :: S2
-#2256 := ?v0!17
-#2257 := (f24 ?v0!17)
-#2854 := (+ #2257 #2853)
-#2855 := (<= #2854 0::Int)
-#2264 := (f8 f23 ?v1!16)
-#2265 := (= f1 #2264)
-#2262 := (f8 f23 ?v0!17)
-#2263 := (= f1 #2262)
-#3392 := (not #2263)
-#3407 := (or #3392 #2265 #2855)
-#3412 := (not #3407)
-#4448 := (or #3412 #4445)
-#4451 := (not #4448)
-#1460 := (>= #188 0::Int)
-#4396 := (forall (vars (?v0 S2)) (:pat #4361) #1460)
-#4401 := (not #4396)
-#4454 := (or #4401 #4451)
-#4457 := (not #4454)
+#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
-#2240 := ?v0!15
-#2241 := (f24 ?v0!15)
-#2242 := (>= #2241 0::Int)
-#2243 := (not #2242)
-#4460 := (or #2243 #4457)
-#4463 := (not #4460)
-#202 := (f24 f10)
-#203 := (= #202 0::Int)
-#1457 := (not #203)
-#4466 := (or #1457 #4463)
-#4469 := (not #4466)
-#4472 := (or #1457 #4469)
-#4475 := (not #4472)
-#101 := (f13 f14 #12)
-#4240 := (pattern #101)
-#760 := (= #101 #188)
-#781 := (or #760 #780)
-#4388 := (forall (vars (?v0 S2)) (:pat #4240 #4361 #4387) #781)
-#4393 := (not #4388)
-#4478 := (or #4393 #4475)
-#4481 := (not #4478)
+#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)
+#4470 := (not #4467)
+#4473 := (or #1458 #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)
+#4482 := (not #4479)
 decl ?v0!14 :: S2
-#2215 := ?v0!14
-#2220 := (f13 f14 ?v0!14)
-#2219 := (f24 ?v0!14)
-#2825 := (= #2219 #2220)
-#2216 := (f8 f23 ?v0!14)
-#2217 := (= f1 #2216)
-#2218 := (not #2217)
-#2831 := (or #2218 #2825)
-#2836 := (not #2831)
-#4484 := (or #2836 #4481)
-#4487 := (not #4484)
-#1445 := (* -1::Int #188)
-#1446 := (+ #101 #1445)
-#1444 := (>= #1446 0::Int)
-#4379 := (forall (vars (?v0 S2)) (:pat #4240 #4361) #1444)
-#4384 := (not #4379)
-#4490 := (or #4384 #4487)
-#4493 := (not #4490)
+#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)
+#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)
+#4494 := (not #4491)
 decl ?v0!13 :: S2
-#2197 := ?v0!13
-#2200 := (f13 f14 ?v0!13)
-#2815 := (* -1::Int #2200)
-#2198 := (f24 ?v0!13)
-#2816 := (+ #2198 #2815)
-#2817 := (<= #2816 0::Int)
-#2822 := (not #2817)
-#4496 := (or #2822 #4493)
-#4499 := (not #4496)
-#182 := (f5 f22 #12)
-#4362 := (pattern #182)
-#183 := (f4 #182)
-#1588 := (+ #183 #1445)
-#1589 := (+ #174 #1588)
-#1590 := (= #1589 0::Int)
-#1414 := (* -1::Int #183)
-#1420 := (* -1::Int #174)
-#1421 := (+ #1420 #1414)
-#1422 := (+ #101 #1421)
-#1423 := (<= #1422 0::Int)
-#1415 := (+ f3 #1414)
-#1416 := (<= #1415 0::Int)
-#3384 := (or #1416 #1423 #1590)
-#4371 := (forall (vars (?v0 S2)) (:pat #4362 #4240 #4361) #3384)
-#4376 := (not #4371)
-#3364 := (or #1416 #1423)
-#3365 := (not #3364)
-#3368 := (or #760 #3365)
-#4363 := (forall (vars (?v0 S2)) (:pat #4240 #4361 #4362) #3368)
-#4368 := (not #4363)
+#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)
+#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!12 :: S2
-#2173 := ?v0!12
-#2179 := (f8 f15 ?v0!12)
-#2180 := (= f1 #2179)
-#2174 := (f13 f14 ?v0!12)
-#2175 := (* -1::Int #2174)
-#2176 := (+ f3 #2175)
-#2177 := (<= #2176 0::Int)
-#1620 := (+ f3 #1420)
-#1621 := (<= #1620 0::Int)
-#105 := (f8 f15 #12)
-#4282 := (pattern #105)
-#1603 := (+ #101 #1420)
-#1602 := (>= #1603 0::Int)
-#508 := (= f1 #105)
-#1609 := (or #508 #1602)
-#4353 := (forall (vars (?v0 S2)) (:pat #4282 #4240) #1609)
-#4358 := (not #4353)
-#171 := (f8 f15 f22)
-#729 := (= f1 #171)
-#962 := (not #181)
-#4502 := (or #962 #729 #4358 #1621 #2177 #2180 #4368 #4376 #4499)
-#4505 := (not #4502)
+#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)
 decl ?v0!11 :: S2
-#2107 := ?v0!11
+#2108 := ?v0!11
 decl ?v1!10 :: S2
-#2106 := ?v1!10
-#2112 := (f5 ?v1!10 ?v0!11)
-#2113 := (f4 #2112)
-#2120 := (* -1::Int #2113)
+#2107 := ?v1!10
+#2113 := (f5 ?v1!10 ?v0!11)
+#2114 := (f4 #2113)
+#2121 := (* -1::Int #2114)
 decl f19 :: S5
-#137 := f19
-#2110 := (f13 f19 ?v1!10)
-#2116 := (* -1::Int #2110)
-#2772 := (+ #2116 #2120)
-#2108 := (f13 f19 ?v0!11)
-#2773 := (+ #2108 #2772)
-#2774 := (<= #2773 0::Int)
-#2121 := (+ f3 #2120)
-#2122 := (<= #2121 0::Int)
-#2117 := (+ f3 #2116)
-#2118 := (<= #2117 0::Int)
-#3328 := (or #2118 #2122 #2774)
-#3333 := (not #3328)
-#145 := (f13 f19 #11)
-#1322 := (* -1::Int #145)
-#142 := (f13 f19 #12)
-#1323 := (+ #142 #1322)
-#1329 := (+ #82 #1323)
-#1352 := (>= #1329 0::Int)
-#1309 := (* -1::Int #142)
-#1310 := (+ f3 #1309)
-#1311 := (<= #1310 0::Int)
-#3296 := (or #1202 #1311 #1352)
-#4315 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4216) #3296)
-#4320 := (not #4315)
-#157 := (f13 f19 f10)
-#158 := (= #157 0::Int)
-#4323 := (or #158 #4320)
-#4326 := (not #4323)
-#4329 := (or #4326 #3333)
-#4332 := (not #4329)
-#4291 := (pattern #142)
+#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)
 decl ?v1!9 :: (-> S2 S2)
-#2083 := (?v1!9 #12)
-#2086 := (f5 #2083 #12)
-#2087 := (f4 #2086)
-#2742 := (* -1::Int #2087)
-#2084 := (f13 f19 #2083)
-#2725 := (* -1::Int #2084)
-#2743 := (+ #2725 #2742)
-#2744 := (+ #142 #2743)
-#2745 := (= #2744 0::Int)
-#3266 := (not #2745)
-#2726 := (+ #142 #2725)
-#2727 := (<= #2726 0::Int)
-#3267 := (or #2727 #3266)
-#3268 := (not #3267)
+#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)
-#3274 := (or #57 #1311 #3268)
-#4307 := (forall (vars (?v0 S2)) (:pat #4291) #3274)
-#4312 := (not #4307)
-#4335 := (or #4312 #4332)
-#4338 := (not #4335)
+#3275 := (or #57 #1312 #3269)
+#4308 := (forall (vars (?v0 S2)) (:pat #4292) #3275)
+#4313 := (not #4308)
+#4336 := (or #4313 #4333)
+#4339 := (not #4336)
 decl ?v0!8 :: S2
-#2043 := ?v0!8
-#2047 := (f5 #12 ?v0!8)
-#4292 := (pattern #2047)
-#2048 := (f4 #2047)
-#2044 := (f13 f19 ?v0!8)
-#2045 := (* -1::Int #2044)
-#2695 := (+ #2045 #2048)
-#2696 := (+ #142 #2695)
-#2699 := (= #2696 0::Int)
-#3230 := (not #2699)
-#2046 := (+ #142 #2045)
-#2051 := (>= #2046 0::Int)
-#3231 := (or #2051 #3230)
-#4293 := (forall (vars (?v1 S2)) (:pat #4291 #4292) #3231)
-#4298 := (not #4293)
-#2671 := (= f10 ?v0!8)
-#2055 := (+ f3 #2045)
-#2056 := (<= #2055 0::Int)
-#4301 := (or #2056 #2671 #4298)
-#4304 := (not #4301)
-#4341 := (or #4304 #4338)
-#4344 := (not #4341)
-#1264 := (* -1::Int #101)
-#1265 := (+ f3 #1264)
-#1266 := (<= #1265 0::Int)
-#3216 := (or #508 #1266)
-#4283 := (forall (vars (?v0 S2)) (:pat #4282 #4240) #3216)
-#4288 := (not #4283)
-#599 := (= f14 f19)
-#690 := (not #599)
+#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
-#132 := f16
-#596 := (= f15 f16)
-#708 := (not #596)
+#133 := f16
+#597 := (= f15 f16)
+#709 := (not #597)
 decl f21 :: S5
-#140 := f21
+#141 := f21
 decl f20 :: S5
-#139 := f20
-#141 := (= f20 f21)
-#681 := (not #141)
+#140 := f20
+#142 := (= f20 f21)
+#682 := (not #142)
 decl f18 :: S2
-#135 := f18
+#136 := f18
 decl f17 :: S2
-#134 := f17
-#136 := (= f17 f18)
-#699 := (not #136)
-#4347 := (or #699 #681 #708 #690 #4288 #4344)
-#4350 := (not #4347)
-#4508 := (or #4350 #4505)
-#4511 := (not #4508)
-#2006 := (?v1!7 #12)
-#2007 := (f13 f14 #2006)
-#2630 := (* -1::Int #2007)
-#2645 := (+ #101 #2630)
-#2646 := (<= #2645 0::Int)
-#2011 := (f5 #2006 #12)
-#2012 := (f4 #2011)
-#2631 := (* -1::Int #2012)
-#2632 := (+ #2630 #2631)
-#2633 := (+ #101 #2632)
-#2634 := (= #2633 0::Int)
-#3200 := (not #2634)
-#2015 := (f8 f15 #2006)
-#2016 := (= f1 #2015)
-#3199 := (not #2016)
-#3201 := (or #3199 #3200 #2646)
-#3202 := (not #3201)
-#3208 := (or #57 #1266 #3202)
-#4274 := (forall (vars (?v0 S2)) (:pat #4240) #3208)
-#4279 := (not #4274)
+#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)
-#4185 := (pattern #58)
+#4186 := (pattern #58)
 decl ?v1!6 :: (-> S2 S2)
-#1978 := (?v1!6 #12)
-#1982 := (f11 #1978)
-#2589 := (* -1::Int #1982)
-#1979 := (f5 #1978 #12)
-#1980 := (f4 #1979)
-#2606 := (* -1::Int #1980)
-#2607 := (+ #2606 #2589)
-#2608 := (+ #58 #2607)
-#2609 := (= #2608 0::Int)
-#3172 := (not #2609)
-#2590 := (+ #58 #2589)
-#2591 := (<= #2590 0::Int)
-decl f12 :: (-> S2 S1)
-#1988 := (f12 #1978)
-#1989 := (= f1 #1988)
-#3171 := (not #1989)
-#3173 := (or #3171 #2591 #3172)
-#3174 := (not #3173)
-#1226 := (* -1::Int #58)
-#1227 := (+ f3 #1226)
-#1228 := (<= #1227 0::Int)
-#3180 := (or #57 #1228 #3174)
-#4266 := (forall (vars (?v0 S2)) (:pat #4185) #3180)
-#4271 := (not #4266)
-#108 := (f8 f15 #11)
-#4257 := (pattern #105 #108)
-#111 := (f13 f14 #11)
-#1278 := (* -1::Int #111)
-#1279 := (+ #101 #1278)
-#1282 := (>= #1279 0::Int)
-#514 := (= f1 #108)
-#3137 := (not #514)
-#3152 := (or #508 #3137 #1282)
-#4258 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4257) #3152)
-#4263 := (not #4258)
-#1280 := (+ #82 #1279)
-#1675 := (>= #1280 0::Int)
-#511 := (not #508)
-#3129 := (or #511 #1202 #1675)
-#4249 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4216) #3129)
-#4254 := (not #4249)
-#1703 := (>= #101 0::Int)
-#4241 := (forall (vars (?v0 S2)) (:pat #4240) #1703)
-#4246 := (not #4241)
-#99 := (f13 f14 f10)
-#100 := (= #99 0::Int)
-#1714 := (not #100)
-#4514 := (or #1714 #4246 #4254 #4263 #4271 #4279 #4511)
-#4517 := (not #4514)
+#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)
 decl ?v0!5 :: S2
-#1934 := ?v0!5
-#1935 := (f5 #12 ?v0!5)
-#4225 := (pattern #1935)
-#66 := (f12 #12)
-#4192 := (pattern #66)
-#1937 := (f11 ?v0!5)
-#1938 := (* -1::Int #1937)
-#1936 := (f4 #1935)
-#2557 := (+ #1936 #1938)
-#2558 := (+ #58 #2557)
-#2561 := (= #2558 0::Int)
-#3090 := (not #2561)
-#1942 := (+ #58 #1938)
-#1943 := (>= #1942 0::Int)
-#429 := (= f1 #66)
-#432 := (not #429)
-#3091 := (or #432 #1943 #3090)
-#4226 := (forall (vars (?v1 S2)) (:pat #4192 #4185 #4225) #3091)
-#4231 := (not #4226)
-#2533 := (= f10 ?v0!5)
-#1947 := (+ f3 #1938)
-#1948 := (<= #1947 0::Int)
-#4234 := (or #1948 #2533 #4231)
-#5626 := (= f3 #1937)
-#5735 := (not #5626)
-#1949 := (not #1948)
-#4237 := (not #4234)
-#5733 := [hypothesis]: #4237
-#4126 := (or #4234 #1949)
-#3800 := [def-axiom]: #4126
-#5734 := [unit-resolution #3800 #5733]: #1949
-#5736 := (or #5735 #1948)
-#5737 := [th-lemma arith triangle-eq]: #5736
-#5738 := [unit-resolution #5737 #5734]: #5735
-#2536 := (not #2533)
-#3801 := (or #4234 #2536)
-#4133 := [def-axiom]: #3801
-#5739 := [unit-resolution #4133 #5733]: #2536
-#415 := (= f3 #58)
-#421 := (or #57 #415)
-#4186 := (forall (vars (?v0 S2)) (:pat #4185) #421)
-#426 := (forall (vars (?v0 S2)) #421)
-#4189 := (iff #426 #4186)
-#4187 := (iff #421 #421)
-#4188 := [refl]: #4187
-#4190 := [quant-intro #4188]: #4189
-#1823 := (~ #426 #426)
-#1852 := (~ #421 #421)
-#1853 := [refl]: #1852
-#1824 := [nnf-pos #1853]: #1823
+#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)
+decl ?v1!3 :: S2
+#1904 := ?v1!3
+#1919 := (f11 ?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)
-#1772 := (or #62 #59)
-#1775 := (forall (vars (?v0 S2)) #1772)
-#1778 := (not #1775)
-#1706 := (forall (vars (?v0 S2)) #1703)
-#1709 := (not #1706)
-#517 := (and #511 #514)
-#523 := (not #517)
-#1692 := (or #523 #1282)
-#1697 := (forall (vars (?v0 S2) (?v1 S2)) #1692)
-#1700 := (not #1697)
-#1203 := (not #1202)
-#1667 := (and #508 #1203)
-#1672 := (not #1667)
-#1678 := (or #1672 #1675)
-#1681 := (forall (vars (?v0 S2) (?v1 S2)) #1678)
-#1684 := (not #1681)
-#1614 := (forall (vars (?v0 S2)) #1609)
-#1617 := (not #1614)
-#1424 := (not #1423)
-#1417 := (not #1416)
-#1427 := (and #1417 #1424)
-#1585 := (not #1427)
-#1593 := (or #1585 #1590)
-#1596 := (forall (vars (?v0 S2)) #1593)
-#1599 := (not #1596)
-#1523 := (= #1501 0::Int)
-#1526 := (not #1469)
-#1535 := (and #774 #1526 #1523)
-#1540 := (exists (vars (?v1 S2)) #1535)
-#1512 := (+ f3 #1445)
-#1513 := (<= #1512 0::Int)
-#1514 := (not #1513)
-#1517 := (and #62 #1514)
-#1520 := (not #1517)
-#1543 := (or #1520 #1540)
-#1546 := (forall (vars (?v0 S2)) #1543)
-#1491 := (and #774 #1203)
-#1496 := (not #1491)
-#1503 := (or #1496 #1499)
-#1506 := (forall (vars (?v0 S2) (?v1 S2)) #1503)
-#1509 := (not #1506)
-#1549 := (or #1509 #1546)
-#1552 := (and #1506 #1549)
-#797 := (and #780 #794)
-#803 := (not #797)
-#1477 := (or #803 #1469)
-#1482 := (forall (vars (?v0 S2) (?v1 S2)) #1477)
-#1485 := (not #1482)
-#1555 := (or #1485 #1552)
-#1558 := (and #1482 #1555)
-#1463 := (forall (vars (?v0 S2)) #1460)
-#1466 := (not #1463)
-#1561 := (or #1466 #1558)
-#1564 := (and #1463 #1561)
-#1567 := (or #1457 #1564)
-#1570 := (and #203 #1567)
-#786 := (forall (vars (?v0 S2)) #781)
-#920 := (not #786)
-#1573 := (or #920 #1570)
-#1576 := (and #786 #1573)
-#1449 := (forall (vars (?v0 S2)) #1444)
-#1452 := (not #1449)
-#1579 := (or #1452 #1576)
-#1582 := (and #1449 #1579)
-#1433 := (or #760 #1427)
-#1438 := (forall (vars (?v0 S2)) #1433)
-#1441 := (not #1438)
-#1267 := (not #1266)
-#1386 := (and #511 #1267)
-#1391 := (exists (vars (?v0 S2)) #1386)
-#1632 := (not #1391)
-#1656 := (or #962 #729 #1632 #1441 #1582 #1599 #1617 #1621)
-#1312 := (not #1311)
-#1346 := (and #1203 #1312)
-#1349 := (not #1346)
-#1355 := (or #1349 #1352)
-#1358 := (forall (vars (?v0 S2) (?v1 S2)) #1355)
-#1361 := (not #1358)
-#1369 := (or #158 #1361)
-#1374 := (and #1358 #1369)
-#1327 := (= #1329 0::Int)
-#1321 := (>= #1323 0::Int)
-#1324 := (not #1321)
-#1331 := (and #1324 #1327)
-#1334 := (exists (vars (?v1 S2)) #1331)
-#1315 := (and #62 #1312)
-#1318 := (not #1315)
-#1337 := (or #1318 #1334)
-#1340 := (forall (vars (?v0 S2)) #1337)
-#1343 := (not #1340)
-#1377 := (or #1343 #1374)
-#1380 := (and #1340 #1377)
-#1409 := (or #699 #681 #708 #690 #1380 #1391)
-#1661 := (and #1409 #1656)
-#1283 := (not #1282)
-#1276 := (= #1280 0::Int)
-#1292 := (and #508 #1276 #1283)
-#1297 := (exists (vars (?v1 S2)) #1292)
-#1270 := (and #62 #1267)
-#1273 := (not #1270)
-#1300 := (or #1273 #1297)
-#1303 := (forall (vars (?v0 S2)) #1300)
-#1306 := (not #1303)
-#77 := (f11 #11)
-#1178 := (* -1::Int #77)
-#1199 := (+ #1178 #82)
-#1200 := (+ #58 #1199)
-#1238 := (= #1200 0::Int)
-#1179 := (+ #58 #1178)
-#1177 := (>= #1179 0::Int)
-#1241 := (not #1177)
-#1250 := (and #429 #1241 #1238)
-#1255 := (exists (vars (?v1 S2)) #1250)
-#1229 := (not #1228)
-#1232 := (and #62 #1229)
-#1235 := (not #1232)
-#1258 := (or #1235 #1255)
-#1261 := (forall (vars (?v0 S2)) #1258)
-#1717 := (not #1261)
-#1738 := (or #1714 #1717 #1306 #1661 #1684 #1700 #1709)
-#1743 := (and #1261 #1738)
-#1209 := (and #429 #1203)
-#1214 := (not #1209)
-#1197 := (>= #1200 0::Int)
-#1217 := (or #1197 #1214)
-#1220 := (forall (vars (?v0 S2) (?v1 S2)) #1217)
-#1223 := (not #1220)
-#1746 := (or #1223 #1743)
-#1749 := (and #1220 #1746)
-#74 := (f12 #11)
-#441 := (= f1 #74)
-#444 := (and #432 #441)
-#450 := (not #444)
-#1184 := (or #450 #1177)
-#1189 := (forall (vars (?v0 S2) (?v1 S2)) #1184)
-#1192 := (not #1189)
-#1752 := (or #1192 #1749)
-#1755 := (and #1189 #1752)
-#1168 := (>= #58 0::Int)
-#1169 := (forall (vars (?v0 S2)) #1168)
-#1172 := (not #1169)
-#1758 := (or #1172 #1755)
-#1761 := (and #1169 #1758)
-#70 := (f11 f10)
-#71 := (= #70 0::Int)
-#1163 := (not #71)
-#1764 := (or #1163 #1761)
-#1767 := (and #71 #1764)
-#435 := (forall (vars (?v0 S2)) #432)
-#1127 := (not #435)
-#1136 := (not #426)
-#1790 := (or #1136 #1127 #1767 #1778)
-#1795 := (not #1790)
+#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)
+#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
-#215 := (+ #188 #82)
-#222 := (= #210 #215)
-#199 := (= #198 f1)
-#223 := (and #199 #222)
-#221 := (< #188 #210)
-#224 := (and #221 #223)
-#225 := (exists (vars (?v1 S2)) #224)
-#219 := (< #188 f3)
-#220 := (and #62 #219)
-#226 := (implies #220 #225)
-#227 := (forall (vars (?v0 S2)) #226)
-#228 := (and #227 true)
-#216 := (<= #210 #215)
-#83 := (< #82 f3)
-#214 := (and #199 #83)
-#217 := (implies #214 #216)
-#218 := (forall (vars (?v0 S2) (?v1 S2)) #217)
-#229 := (implies #218 #228)
-#230 := (and #218 #229)
-#211 := (<= #210 #188)
-#208 := (= #207 f1)
-#206 := (not #199)
-#209 := (and #206 #208)
-#212 := (implies #209 #211)
-#213 := (forall (vars (?v0 S2) (?v1 S2)) #212)
-#231 := (implies #213 #230)
-#232 := (and #213 #231)
-#204 := (<= 0::Int #188)
-#205 := (forall (vars (?v0 S2)) #204)
-#233 := (implies #205 #232)
-#234 := (and #205 #233)
-#235 := (implies #203 #234)
-#236 := (and #203 #235)
-#193 := (= #188 #101)
-#200 := (implies #199 #193)
-#201 := (forall (vars (?v0 S2)) #200)
-#237 := (implies #201 #236)
-#238 := (and #201 #237)
-#196 := (<= #188 #101)
-#197 := (forall (vars (?v0 S2)) #196)
-#239 := (implies #197 #238)
-#240 := (and #197 #239)
-#185 := (+ #174 #183)
-#186 := (< #185 #101)
-#184 := (< #183 f3)
-#187 := (and #184 #186)
-#192 := (not #187)
-#194 := (implies #192 #193)
-#195 := (forall (vars (?v0 S2)) #194)
-#241 := (implies #195 #240)
-#189 := (= #188 #185)
-#190 := (implies #187 #189)
-#191 := (forall (vars (?v0 S2)) #190)
-#242 := (implies #191 #241)
-#243 := (implies #181 #242)
-#176 := (<= #174 #101)
-#106 := (= #105 f1)
-#107 := (not #106)
-#177 := (implies #107 #176)
-#178 := (forall (vars (?v0 S2)) #177)
-#244 := (implies #178 #243)
-#175 := (< #174 f3)
-#245 := (implies #175 #244)
-#172 := (= #171 f1)
-#173 := (not #172)
-#246 := (implies #173 #245)
-#120 := (< #101 f3)
-#129 := (and #107 #120)
-#130 := (exists (vars (?v0 S2)) #129)
-#247 := (implies #130 #246)
-#248 := (implies true #247)
-#159 := (and #158 true)
-#147 := (+ #142 #82)
-#154 := (<= #145 #147)
-#143 := (< #142 f3)
-#153 := (and #143 #83)
-#155 := (implies #153 #154)
-#156 := (forall (vars (?v0 S2) (?v1 S2)) #155)
-#160 := (implies #156 #159)
-#161 := (and #156 #160)
-#148 := (= #145 #147)
-#146 := (< #142 #145)
-#149 := (and #146 #148)
-#150 := (exists (vars (?v1 S2)) #149)
-#144 := (and #62 #143)
-#151 := (implies #144 #150)
-#152 := (forall (vars (?v0 S2)) #151)
-#162 := (implies #152 #161)
-#163 := (and #152 #162)
-#164 := (implies #141 #163)
-#138 := (= f19 f14)
-#165 := (implies #138 #164)
-#166 := (implies #136 #165)
-#133 := (= f16 f15)
-#167 := (implies #133 #166)
-#131 := (not #130)
-#168 := (implies #131 #167)
-#169 := (implies true #168)
-#249 := (and #169 #248)
-#116 := (+ #101 #82)
-#123 := (= #111 #116)
-#124 := (and #106 #123)
-#122 := (< #101 #111)
-#125 := (and #122 #124)
-#126 := (exists (vars (?v1 S2)) #125)
-#121 := (and #62 #120)
-#127 := (implies #121 #126)
-#128 := (forall (vars (?v0 S2)) #127)
-#250 := (implies #128 #249)
-#117 := (<= #111 #116)
-#115 := (and #106 #83)
-#118 := (implies #115 #117)
-#119 := (forall (vars (?v0 S2) (?v1 S2)) #118)
-#251 := (implies #119 #250)
-#112 := (<= #111 #101)
-#109 := (= #108 f1)
-#110 := (and #107 #109)
-#113 := (implies #110 #112)
-#114 := (forall (vars (?v0 S2) (?v1 S2)) #113)
-#252 := (implies #114 #251)
-#102 := (<= 0::Int #101)
-#103 := (forall (vars (?v0 S2)) #102)
-#253 := (implies #103 #252)
-#254 := (implies #100 #253)
-#255 := (implies true #254)
-#85 := (+ #58 #82)
-#92 := (= #77 #85)
-#67 := (= #66 f1)
-#93 := (and #67 #92)
-#91 := (< #58 #77)
-#94 := (and #91 #93)
-#95 := (exists (vars (?v1 S2)) #94)
-#89 := (< #58 f3)
-#90 := (and #62 #89)
-#96 := (implies #90 #95)
-#97 := (forall (vars (?v0 S2)) #96)
-#256 := (implies #97 #255)
-#257 := (and #97 #256)
-#86 := (<= #77 #85)
-#84 := (and #67 #83)
-#87 := (implies #84 #86)
-#88 := (forall (vars (?v0 S2) (?v1 S2)) #87)
-#258 := (implies #88 #257)
-#259 := (and #88 #258)
-#78 := (<= #77 #58)
-#75 := (= #74 f1)
-#68 := (not #67)
-#76 := (and #68 #75)
-#79 := (implies #76 #78)
-#80 := (forall (vars (?v0 S2) (?v1 S2)) #79)
-#260 := (implies #80 #259)
-#261 := (and #80 #260)
-#72 := (<= 0::Int #58)
-#73 := (forall (vars (?v0 S2)) #72)
-#262 := (implies #73 #261)
-#263 := (and #73 #262)
-#264 := (implies #71 #263)
-#265 := (and #71 #264)
-#69 := (forall (vars (?v0 S2)) #68)
-#266 := (implies #69 #265)
+#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)
+#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)
-#267 := (implies #65 #266)
+#268 := (implies #65 #267)
 #60 := (implies #57 #59)
 #61 := (forall (vars (?v0 S2)) #60)
-#268 := (implies #61 #267)
-#269 := (implies true #268)
-#270 := (not #269)
-#1798 := (iff #270 #1795)
-#820 := (+ #82 #188)
-#838 := (= #210 #820)
-#841 := (and #774 #838)
-#844 := (and #221 #841)
-#847 := (exists (vars (?v1 S2)) #844)
-#853 := (not #220)
-#854 := (or #853 #847)
-#859 := (forall (vars (?v0 S2)) #854)
-#823 := (<= #210 #820)
-#815 := (and #83 #774)
-#829 := (not #815)
-#830 := (or #829 #823)
-#835 := (forall (vars (?v0 S2) (?v1 S2)) #830)
-#872 := (not #835)
-#873 := (or #872 #859)
-#878 := (and #835 #873)
-#804 := (or #211 #803)
-#809 := (forall (vars (?v0 S2) (?v1 S2)) #804)
-#884 := (not #809)
-#885 := (or #884 #878)
-#890 := (and #809 #885)
-#896 := (not #205)
-#897 := (or #896 #890)
-#902 := (and #205 #897)
-#789 := (= 0::Int #202)
-#908 := (not #789)
-#909 := (or #908 #902)
-#914 := (and #789 #909)
-#921 := (or #920 #914)
-#926 := (and #786 #921)
-#932 := (not #197)
-#933 := (or #932 #926)
-#938 := (and #197 #933)
-#766 := (or #187 #760)
-#771 := (forall (vars (?v0 S2)) #766)
-#944 := (not #771)
-#945 := (or #944 #938)
-#746 := (= #185 #188)
-#752 := (or #192 #746)
-#757 := (forall (vars (?v0 S2)) #752)
-#953 := (not #757)
-#954 := (or #953 #945)
-#963 := (or #962 #954)
-#738 := (or #176 #508)
-#743 := (forall (vars (?v0 S2)) #738)
-#971 := (not #743)
-#972 := (or #971 #963)
-#980 := (not #175)
-#981 := (or #980 #972)
-#989 := (or #729 #981)
-#585 := (and #120 #511)
-#590 := (exists (vars (?v0 S2)) #585)
-#593 := (not #590)
-#997 := (or #593 #989)
-#644 := (= 0::Int #157)
-#602 := (+ #82 #142)
-#629 := (<= #145 #602)
-#626 := (and #83 #143)
-#635 := (not #626)
-#636 := (or #635 #629)
-#641 := (forall (vars (?v0 S2) (?v1 S2)) #636)
-#657 := (not #641)
-#658 := (or #657 #644)
-#663 := (and #641 #658)
-#605 := (= #145 #602)
-#608 := (and #146 #605)
-#611 := (exists (vars (?v1 S2)) #608)
-#617 := (not #144)
-#618 := (or #617 #611)
-#623 := (forall (vars (?v0 S2)) #618)
-#669 := (not #623)
-#670 := (or #669 #663)
-#675 := (and #623 #670)
-#682 := (or #681 #675)
-#691 := (or #690 #682)
-#700 := (or #699 #691)
-#709 := (or #708 #700)
-#717 := (or #590 #709)
-#1009 := (and #717 #997)
-#540 := (+ #82 #101)
-#558 := (= #111 #540)
-#561 := (and #508 #558)
-#564 := (and #122 #561)
-#567 := (exists (vars (?v1 S2)) #564)
-#573 := (not #121)
-#574 := (or #573 #567)
-#579 := (forall (vars (?v0 S2)) #574)
-#1015 := (not #579)
-#1016 := (or #1015 #1009)
-#543 := (<= #111 #540)
-#535 := (and #83 #508)
-#549 := (not #535)
-#550 := (or #549 #543)
-#555 := (forall (vars (?v0 S2) (?v1 S2)) #550)
-#1024 := (not #555)
-#1025 := (or #1024 #1016)
-#524 := (or #112 #523)
-#529 := (forall (vars (?v0 S2) (?v1 S2)) #524)
-#1033 := (not #529)
-#1034 := (or #1033 #1025)
-#1042 := (not #103)
-#1043 := (or #1042 #1034)
-#505 := (= 0::Int #99)
-#1051 := (not #505)
-#1052 := (or #1051 #1043)
-#482 := (and #92 #429)
-#487 := (and #91 #482)
-#490 := (exists (vars (?v1 S2)) #487)
-#496 := (not #90)
-#497 := (or #496 #490)
-#502 := (forall (vars (?v0 S2)) #497)
-#1067 := (not #502)
-#1068 := (or #1067 #1052)
-#1073 := (and #502 #1068)
-#462 := (and #83 #429)
-#470 := (not #462)
-#471 := (or #86 #470)
-#476 := (forall (vars (?v0 S2) (?v1 S2)) #471)
-#1079 := (not #476)
-#1080 := (or #1079 #1073)
-#1085 := (and #476 #1080)
-#451 := (or #78 #450)
-#456 := (forall (vars (?v0 S2) (?v1 S2)) #451)
-#1091 := (not #456)
-#1092 := (or #1091 #1085)
-#1097 := (and #456 #1092)
-#1103 := (not #73)
-#1104 := (or #1103 #1097)
-#1109 := (and #73 #1104)
-#438 := (= 0::Int #70)
-#1115 := (not #438)
-#1116 := (or #1115 #1109)
-#1121 := (and #438 #1116)
-#1128 := (or #1127 #1121)
-#1137 := (or #1136 #1128)
-#400 := (= 0::Int #58)
-#407 := (or #62 #400)
-#412 := (forall (vars (?v0 S2)) #407)
-#1145 := (not #412)
-#1146 := (or #1145 #1137)
-#1158 := (not #1146)
-#1796 := (iff #1158 #1795)
-#1793 := (iff #1146 #1790)
-#1781 := (or #1127 #1767)
-#1784 := (or #1136 #1781)
-#1787 := (or #1778 #1784)
-#1791 := (iff #1787 #1790)
-#1792 := [rewrite]: #1791
-#1788 := (iff #1146 #1787)
-#1785 := (iff #1137 #1784)
-#1782 := (iff #1128 #1781)
-#1768 := (iff #1121 #1767)
-#1765 := (iff #1116 #1764)
-#1762 := (iff #1109 #1761)
-#1759 := (iff #1104 #1758)
-#1756 := (iff #1097 #1755)
-#1753 := (iff #1092 #1752)
-#1750 := (iff #1085 #1749)
-#1747 := (iff #1080 #1746)
-#1744 := (iff #1073 #1743)
-#1741 := (iff #1068 #1738)
-#1720 := (or #1306 #1661)
-#1723 := (or #1684 #1720)
-#1726 := (or #1700 #1723)
-#1729 := (or #1709 #1726)
-#1732 := (or #1714 #1729)
-#1735 := (or #1717 #1732)
-#1739 := (iff #1735 #1738)
-#1740 := [rewrite]: #1739
-#1736 := (iff #1068 #1735)
-#1733 := (iff #1052 #1732)
-#1730 := (iff #1043 #1729)
-#1727 := (iff #1034 #1726)
-#1724 := (iff #1025 #1723)
-#1721 := (iff #1016 #1720)
-#1662 := (iff #1009 #1661)
-#1659 := (iff #997 #1656)
-#1635 := (or #1441 #1582)
-#1638 := (or #1599 #1635)
-#1641 := (or #962 #1638)
-#1644 := (or #1617 #1641)
-#1647 := (or #1621 #1644)
-#1650 := (or #729 #1647)
-#1653 := (or #1632 #1650)
-#1657 := (iff #1653 #1656)
-#1658 := [rewrite]: #1657
-#1654 := (iff #997 #1653)
-#1651 := (iff #989 #1650)
-#1648 := (iff #981 #1647)
-#1645 := (iff #972 #1644)
-#1642 := (iff #963 #1641)
-#1639 := (iff #954 #1638)
-#1636 := (iff #945 #1635)
-#1583 := (iff #938 #1582)
-#1580 := (iff #933 #1579)
-#1577 := (iff #926 #1576)
-#1574 := (iff #921 #1573)
-#1571 := (iff #914 #1570)
-#1568 := (iff #909 #1567)
-#1565 := (iff #902 #1564)
-#1562 := (iff #897 #1561)
-#1559 := (iff #890 #1558)
-#1556 := (iff #885 #1555)
-#1553 := (iff #878 #1552)
-#1550 := (iff #873 #1549)
-#1547 := (iff #859 #1546)
-#1544 := (iff #854 #1543)
-#1541 := (iff #847 #1540)
-#1538 := (iff #844 #1535)
-#1529 := (and #774 #1523)
-#1532 := (and #1526 #1529)
-#1536 := (iff #1532 #1535)
-#1537 := [rewrite]: #1536
-#1533 := (iff #844 #1532)
-#1530 := (iff #841 #1529)
-#1524 := (iff #838 #1523)
-#1525 := [rewrite]: #1524
-#1531 := [monotonicity #1525]: #1530
-#1527 := (iff #221 #1526)
-#1528 := [rewrite]: #1527
-#1534 := [monotonicity #1528 #1531]: #1533
-#1539 := [trans #1534 #1537]: #1538
-#1542 := [quant-intro #1539]: #1541
-#1521 := (iff #853 #1520)
-#1518 := (iff #220 #1517)
-#1515 := (iff #219 #1514)
-#1516 := [rewrite]: #1515
-#1519 := [monotonicity #1516]: #1518
-#1522 := [monotonicity #1519]: #1521
-#1545 := [monotonicity #1522 #1542]: #1544
-#1548 := [quant-intro #1545]: #1547
-#1510 := (iff #872 #1509)
-#1507 := (iff #835 #1506)
-#1504 := (iff #830 #1503)
-#1500 := (iff #823 #1499)
-#1502 := [rewrite]: #1500
-#1497 := (iff #829 #1496)
-#1494 := (iff #815 #1491)
-#1488 := (and #1203 #774)
-#1492 := (iff #1488 #1491)
-#1493 := [rewrite]: #1492
-#1489 := (iff #815 #1488)
-#1204 := (iff #83 #1203)
-#1205 := [rewrite]: #1204
-#1490 := [monotonicity #1205]: #1489
-#1495 := [trans #1490 #1493]: #1494
-#1498 := [monotonicity #1495]: #1497
-#1505 := [monotonicity #1498 #1502]: #1504
-#1508 := [quant-intro #1505]: #1507
-#1511 := [monotonicity #1508]: #1510
-#1551 := [monotonicity #1511 #1548]: #1550
-#1554 := [monotonicity #1508 #1551]: #1553
-#1486 := (iff #884 #1485)
-#1483 := (iff #809 #1482)
-#1480 := (iff #804 #1477)
-#1474 := (or #1469 #803)
-#1478 := (iff #1474 #1477)
-#1479 := [rewrite]: #1478
-#1475 := (iff #804 #1474)
-#1472 := (iff #211 #1469)
-#1473 := [rewrite]: #1472
-#1476 := [monotonicity #1473]: #1475
-#1481 := [trans #1476 #1479]: #1480
-#1484 := [quant-intro #1481]: #1483
-#1487 := [monotonicity #1484]: #1486
-#1557 := [monotonicity #1487 #1554]: #1556
-#1560 := [monotonicity #1484 #1557]: #1559
-#1467 := (iff #896 #1466)
-#1464 := (iff #205 #1463)
-#1461 := (iff #204 #1460)
-#1462 := [rewrite]: #1461
-#1465 := [quant-intro #1462]: #1464
-#1468 := [monotonicity #1465]: #1467
-#1563 := [monotonicity #1468 #1560]: #1562
-#1566 := [monotonicity #1465 #1563]: #1565
-#1458 := (iff #908 #1457)
-#1455 := (iff #789 #203)
-#1456 := [rewrite]: #1455
-#1459 := [monotonicity #1456]: #1458
-#1569 := [monotonicity #1459 #1566]: #1568
-#1572 := [monotonicity #1456 #1569]: #1571
-#1575 := [monotonicity #1572]: #1574
-#1578 := [monotonicity #1575]: #1577
-#1453 := (iff #932 #1452)
-#1450 := (iff #197 #1449)
-#1447 := (iff #196 #1444)
-#1448 := [rewrite]: #1447
-#1451 := [quant-intro #1448]: #1450
-#1454 := [monotonicity #1451]: #1453
-#1581 := [monotonicity #1454 #1578]: #1580
-#1584 := [monotonicity #1451 #1581]: #1583
-#1442 := (iff #944 #1441)
-#1439 := (iff #771 #1438)
-#1436 := (iff #766 #1433)
-#1430 := (or #1427 #760)
-#1434 := (iff #1430 #1433)
-#1435 := [rewrite]: #1434
-#1431 := (iff #766 #1430)
-#1428 := (iff #187 #1427)
-#1425 := (iff #186 #1424)
-#1426 := [rewrite]: #1425
-#1418 := (iff #184 #1417)
-#1419 := [rewrite]: #1418
-#1429 := [monotonicity #1419 #1426]: #1428
-#1432 := [monotonicity #1429]: #1431
-#1437 := [trans #1432 #1435]: #1436
-#1440 := [quant-intro #1437]: #1439
-#1443 := [monotonicity #1440]: #1442
-#1637 := [monotonicity #1443 #1584]: #1636
-#1600 := (iff #953 #1599)
-#1597 := (iff #757 #1596)
-#1594 := (iff #752 #1593)
-#1591 := (iff #746 #1590)
-#1592 := [rewrite]: #1591
-#1586 := (iff #192 #1585)
-#1587 := [monotonicity #1429]: #1586
-#1595 := [monotonicity #1587 #1592]: #1594
-#1598 := [quant-intro #1595]: #1597
-#1601 := [monotonicity #1598]: #1600
-#1640 := [monotonicity #1601 #1637]: #1639
-#1643 := [monotonicity #1640]: #1642
-#1618 := (iff #971 #1617)
-#1615 := (iff #743 #1614)
-#1612 := (iff #738 #1609)
-#1606 := (or #1602 #508)
-#1610 := (iff #1606 #1609)
-#1611 := [rewrite]: #1610
-#1607 := (iff #738 #1606)
-#1604 := (iff #176 #1602)
-#1605 := [rewrite]: #1604
-#1608 := [monotonicity #1605]: #1607
-#1613 := [trans #1608 #1611]: #1612
-#1616 := [quant-intro #1613]: #1615
-#1619 := [monotonicity #1616]: #1618
-#1646 := [monotonicity #1619 #1643]: #1645
-#1630 := (iff #980 #1621)
-#1622 := (not #1621)
-#1625 := (not #1622)
-#1628 := (iff #1625 #1621)
-#1629 := [rewrite]: #1628
-#1626 := (iff #980 #1625)
-#1623 := (iff #175 #1622)
-#1624 := [rewrite]: #1623
-#1627 := [monotonicity #1624]: #1626
-#1631 := [trans #1627 #1629]: #1630
-#1649 := [monotonicity #1631 #1646]: #1648
-#1652 := [monotonicity #1649]: #1651
-#1633 := (iff #593 #1632)
-#1392 := (iff #590 #1391)
-#1389 := (iff #585 #1386)
-#1383 := (and #1267 #511)
-#1387 := (iff #1383 #1386)
-#1388 := [rewrite]: #1387
-#1384 := (iff #585 #1383)
-#1268 := (iff #120 #1267)
-#1269 := [rewrite]: #1268
-#1385 := [monotonicity #1269]: #1384
-#1390 := [trans #1385 #1388]: #1389
-#1393 := [quant-intro #1390]: #1392
-#1634 := [monotonicity #1393]: #1633
-#1655 := [monotonicity #1634 #1652]: #1654
-#1660 := [trans #1655 #1658]: #1659
-#1412 := (iff #717 #1409)
-#1394 := (or #681 #1380)
-#1397 := (or #690 #1394)
-#1400 := (or #699 #1397)
-#1403 := (or #708 #1400)
-#1406 := (or #1391 #1403)
-#1410 := (iff #1406 #1409)
-#1411 := [rewrite]: #1410
-#1407 := (iff #717 #1406)
-#1404 := (iff #709 #1403)
-#1401 := (iff #700 #1400)
-#1398 := (iff #691 #1397)
-#1395 := (iff #682 #1394)
-#1381 := (iff #675 #1380)
-#1378 := (iff #670 #1377)
-#1375 := (iff #663 #1374)
-#1372 := (iff #658 #1369)
-#1366 := (or #1361 #158)
-#1370 := (iff #1366 #1369)
-#1371 := [rewrite]: #1370
-#1367 := (iff #658 #1366)
-#1364 := (iff #644 #158)
-#1365 := [rewrite]: #1364
-#1362 := (iff #657 #1361)
-#1359 := (iff #641 #1358)
-#1356 := (iff #636 #1355)
-#1353 := (iff #629 #1352)
-#1354 := [rewrite]: #1353
-#1350 := (iff #635 #1349)
-#1347 := (iff #626 #1346)
-#1313 := (iff #143 #1312)
-#1314 := [rewrite]: #1313
-#1348 := [monotonicity #1205 #1314]: #1347
-#1351 := [monotonicity #1348]: #1350
-#1357 := [monotonicity #1351 #1354]: #1356
-#1360 := [quant-intro #1357]: #1359
-#1363 := [monotonicity #1360]: #1362
-#1368 := [monotonicity #1363 #1365]: #1367
-#1373 := [trans #1368 #1371]: #1372
-#1376 := [monotonicity #1360 #1373]: #1375
-#1344 := (iff #669 #1343)
-#1341 := (iff #623 #1340)
-#1338 := (iff #618 #1337)
-#1335 := (iff #611 #1334)
-#1332 := (iff #608 #1331)
-#1328 := (iff #605 #1327)
-#1330 := [rewrite]: #1328
-#1325 := (iff #146 #1324)
-#1326 := [rewrite]: #1325
-#1333 := [monotonicity #1326 #1330]: #1332
-#1336 := [quant-intro #1333]: #1335
-#1319 := (iff #617 #1318)
-#1316 := (iff #144 #1315)
-#1317 := [monotonicity #1314]: #1316
-#1320 := [monotonicity #1317]: #1319
-#1339 := [monotonicity #1320 #1336]: #1338
-#1342 := [quant-intro #1339]: #1341
-#1345 := [monotonicity #1342]: #1344
-#1379 := [monotonicity #1345 #1376]: #1378
-#1382 := [monotonicity #1342 #1379]: #1381
-#1396 := [monotonicity #1382]: #1395
-#1399 := [monotonicity #1396]: #1398
-#1402 := [monotonicity #1399]: #1401
-#1405 := [monotonicity #1402]: #1404
-#1408 := [monotonicity #1393 #1405]: #1407
-#1413 := [trans #1408 #1411]: #1412
-#1663 := [monotonicity #1413 #1660]: #1662
-#1307 := (iff #1015 #1306)
-#1304 := (iff #579 #1303)
-#1301 := (iff #574 #1300)
-#1298 := (iff #567 #1297)
-#1295 := (iff #564 #1292)
-#1286 := (and #508 #1276)
-#1289 := (and #1283 #1286)
-#1293 := (iff #1289 #1292)
-#1294 := [rewrite]: #1293
-#1290 := (iff #564 #1289)
-#1287 := (iff #561 #1286)
-#1277 := (iff #558 #1276)
-#1281 := [rewrite]: #1277
-#1288 := [monotonicity #1281]: #1287
-#1284 := (iff #122 #1283)
-#1285 := [rewrite]: #1284
-#1291 := [monotonicity #1285 #1288]: #1290
-#1296 := [trans #1291 #1294]: #1295
-#1299 := [quant-intro #1296]: #1298
-#1274 := (iff #573 #1273)
-#1271 := (iff #121 #1270)
-#1272 := [monotonicity #1269]: #1271
-#1275 := [monotonicity #1272]: #1274
-#1302 := [monotonicity #1275 #1299]: #1301
-#1305 := [quant-intro #1302]: #1304
-#1308 := [monotonicity #1305]: #1307
-#1722 := [monotonicity #1308 #1663]: #1721
-#1685 := (iff #1024 #1684)
-#1682 := (iff #555 #1681)
-#1679 := (iff #550 #1678)
-#1676 := (iff #543 #1675)
-#1677 := [rewrite]: #1676
-#1673 := (iff #549 #1672)
-#1670 := (iff #535 #1667)
-#1664 := (and #1203 #508)
-#1668 := (iff #1664 #1667)
-#1669 := [rewrite]: #1668
-#1665 := (iff #535 #1664)
-#1666 := [monotonicity #1205]: #1665
-#1671 := [trans #1666 #1669]: #1670
-#1674 := [monotonicity #1671]: #1673
-#1680 := [monotonicity #1674 #1677]: #1679
-#1683 := [quant-intro #1680]: #1682
-#1686 := [monotonicity #1683]: #1685
-#1725 := [monotonicity #1686 #1722]: #1724
-#1701 := (iff #1033 #1700)
-#1698 := (iff #529 #1697)
-#1695 := (iff #524 #1692)
-#1689 := (or #1282 #523)
-#1693 := (iff #1689 #1692)
-#1694 := [rewrite]: #1693
-#1690 := (iff #524 #1689)
-#1687 := (iff #112 #1282)
-#1688 := [rewrite]: #1687
-#1691 := [monotonicity #1688]: #1690
-#1696 := [trans #1691 #1694]: #1695
-#1699 := [quant-intro #1696]: #1698
-#1702 := [monotonicity #1699]: #1701
-#1728 := [monotonicity #1702 #1725]: #1727
-#1710 := (iff #1042 #1709)
-#1707 := (iff #103 #1706)
-#1704 := (iff #102 #1703)
-#1705 := [rewrite]: #1704
-#1708 := [quant-intro #1705]: #1707
-#1711 := [monotonicity #1708]: #1710
-#1731 := [monotonicity #1711 #1728]: #1730
-#1715 := (iff #1051 #1714)
-#1712 := (iff #505 #100)
-#1713 := [rewrite]: #1712
-#1716 := [monotonicity #1713]: #1715
-#1734 := [monotonicity #1716 #1731]: #1733
-#1718 := (iff #1067 #1717)
-#1262 := (iff #502 #1261)
-#1259 := (iff #497 #1258)
-#1256 := (iff #490 #1255)
-#1253 := (iff #487 #1250)
-#1244 := (and #1238 #429)
-#1247 := (and #1241 #1244)
-#1251 := (iff #1247 #1250)
-#1252 := [rewrite]: #1251
-#1248 := (iff #487 #1247)
-#1245 := (iff #482 #1244)
-#1239 := (iff #92 #1238)
-#1240 := [rewrite]: #1239
-#1246 := [monotonicity #1240]: #1245
-#1242 := (iff #91 #1241)
-#1243 := [rewrite]: #1242
-#1249 := [monotonicity #1243 #1246]: #1248
-#1254 := [trans #1249 #1252]: #1253
-#1257 := [quant-intro #1254]: #1256
-#1236 := (iff #496 #1235)
-#1233 := (iff #90 #1232)
-#1230 := (iff #89 #1229)
-#1231 := [rewrite]: #1230
-#1234 := [monotonicity #1231]: #1233
-#1237 := [monotonicity #1234]: #1236
-#1260 := [monotonicity #1237 #1257]: #1259
-#1263 := [quant-intro #1260]: #1262
-#1719 := [monotonicity #1263]: #1718
-#1737 := [monotonicity #1719 #1734]: #1736
-#1742 := [trans #1737 #1740]: #1741
-#1745 := [monotonicity #1263 #1742]: #1744
-#1224 := (iff #1079 #1223)
-#1221 := (iff #476 #1220)
-#1218 := (iff #471 #1217)
-#1215 := (iff #470 #1214)
-#1212 := (iff #462 #1209)
-#1206 := (and #1203 #429)
-#1210 := (iff #1206 #1209)
-#1211 := [rewrite]: #1210
-#1207 := (iff #462 #1206)
-#1208 := [monotonicity #1205]: #1207
-#1213 := [trans #1208 #1211]: #1212
-#1216 := [monotonicity #1213]: #1215
-#1196 := (iff #86 #1197)
-#1195 := [rewrite]: #1196
-#1219 := [monotonicity #1195 #1216]: #1218
-#1222 := [quant-intro #1219]: #1221
-#1225 := [monotonicity #1222]: #1224
-#1748 := [monotonicity #1225 #1745]: #1747
-#1751 := [monotonicity #1222 #1748]: #1750
-#1193 := (iff #1091 #1192)
-#1190 := (iff #456 #1189)
-#1187 := (iff #451 #1184)
-#1181 := (or #1177 #450)
-#1185 := (iff #1181 #1184)
-#1186 := [rewrite]: #1185
-#1182 := (iff #451 #1181)
-#1176 := (iff #78 #1177)
-#1180 := [rewrite]: #1176
-#1183 := [monotonicity #1180]: #1182
-#1188 := [trans #1183 #1186]: #1187
-#1191 := [quant-intro #1188]: #1190
-#1194 := [monotonicity #1191]: #1193
-#1754 := [monotonicity #1194 #1751]: #1753
-#1757 := [monotonicity #1191 #1754]: #1756
-#1173 := (iff #1103 #1172)
-#1170 := (iff #73 #1169)
-#1166 := (iff #72 #1168)
-#1167 := [rewrite]: #1166
-#1171 := [quant-intro #1167]: #1170
-#1174 := [monotonicity #1171]: #1173
-#1760 := [monotonicity #1174 #1757]: #1759
-#1763 := [monotonicity #1171 #1760]: #1762
-#1164 := (iff #1115 #1163)
-#1161 := (iff #438 #71)
-#1162 := [rewrite]: #1161
-#1165 := [monotonicity #1162]: #1164
-#1766 := [monotonicity #1165 #1763]: #1765
-#1769 := [monotonicity #1162 #1766]: #1768
-#1783 := [monotonicity #1769]: #1782
-#1786 := [monotonicity #1783]: #1785
-#1779 := (iff #1145 #1778)
-#1776 := (iff #412 #1775)
-#1773 := (iff #407 #1772)
-#1770 := (iff #400 #59)
-#1771 := [rewrite]: #1770
-#1774 := [monotonicity #1771]: #1773
-#1777 := [quant-intro #1774]: #1776
-#1780 := [monotonicity #1777]: #1779
-#1789 := [monotonicity #1780 #1786]: #1788
-#1794 := [trans #1789 #1792]: #1793
-#1797 := [monotonicity #1794]: #1796
-#1159 := (iff #270 #1158)
-#1156 := (iff #269 #1146)
-#1151 := (implies true #1146)
-#1154 := (iff #1151 #1146)
-#1155 := [rewrite]: #1154
-#1152 := (iff #269 #1151)
-#1149 := (iff #268 #1146)
-#1142 := (implies #412 #1137)
-#1147 := (iff #1142 #1146)
-#1148 := [rewrite]: #1147
-#1143 := (iff #268 #1142)
-#1140 := (iff #267 #1137)
-#1133 := (implies #426 #1128)
-#1138 := (iff #1133 #1137)
-#1139 := [rewrite]: #1138
-#1134 := (iff #267 #1133)
-#1131 := (iff #266 #1128)
-#1124 := (implies #435 #1121)
-#1129 := (iff #1124 #1128)
-#1130 := [rewrite]: #1129
-#1125 := (iff #266 #1124)
-#1122 := (iff #265 #1121)
-#1119 := (iff #264 #1116)
-#1112 := (implies #438 #1109)
-#1117 := (iff #1112 #1116)
-#1118 := [rewrite]: #1117
-#1113 := (iff #264 #1112)
-#1110 := (iff #263 #1109)
-#1107 := (iff #262 #1104)
-#1100 := (implies #73 #1097)
-#1105 := (iff #1100 #1104)
-#1106 := [rewrite]: #1105
-#1101 := (iff #262 #1100)
-#1098 := (iff #261 #1097)
-#1095 := (iff #260 #1092)
-#1088 := (implies #456 #1085)
-#1093 := (iff #1088 #1092)
-#1094 := [rewrite]: #1093
-#1089 := (iff #260 #1088)
-#1086 := (iff #259 #1085)
-#1083 := (iff #258 #1080)
-#1076 := (implies #476 #1073)
-#1081 := (iff #1076 #1080)
-#1082 := [rewrite]: #1081
-#1077 := (iff #258 #1076)
-#1074 := (iff #257 #1073)
-#1071 := (iff #256 #1068)
-#1064 := (implies #502 #1052)
-#1069 := (iff #1064 #1068)
-#1070 := [rewrite]: #1069
-#1065 := (iff #256 #1064)
-#1062 := (iff #255 #1052)
-#1057 := (implies true #1052)
-#1060 := (iff #1057 #1052)
-#1061 := [rewrite]: #1060
-#1058 := (iff #255 #1057)
-#1055 := (iff #254 #1052)
-#1048 := (implies #505 #1043)
-#1053 := (iff #1048 #1052)
-#1054 := [rewrite]: #1053
-#1049 := (iff #254 #1048)
-#1046 := (iff #253 #1043)
-#1039 := (implies #103 #1034)
-#1044 := (iff #1039 #1043)
-#1045 := [rewrite]: #1044
-#1040 := (iff #253 #1039)
-#1037 := (iff #252 #1034)
-#1030 := (implies #529 #1025)
-#1035 := (iff #1030 #1034)
-#1036 := [rewrite]: #1035
-#1031 := (iff #252 #1030)
-#1028 := (iff #251 #1025)
-#1021 := (implies #555 #1016)
-#1026 := (iff #1021 #1025)
-#1027 := [rewrite]: #1026
-#1022 := (iff #251 #1021)
-#1019 := (iff #250 #1016)
-#1012 := (implies #579 #1009)
-#1017 := (iff #1012 #1016)
-#1018 := [rewrite]: #1017
-#1013 := (iff #250 #1012)
-#1010 := (iff #249 #1009)
-#1007 := (iff #248 #997)
-#1002 := (implies true #997)
-#1005 := (iff #1002 #997)
-#1006 := [rewrite]: #1005
-#1003 := (iff #248 #1002)
-#1000 := (iff #247 #997)
-#994 := (implies #590 #989)
-#998 := (iff #994 #997)
-#999 := [rewrite]: #998
-#995 := (iff #247 #994)
-#992 := (iff #246 #989)
-#732 := (not #729)
-#986 := (implies #732 #981)
-#990 := (iff #986 #989)
-#991 := [rewrite]: #990
-#987 := (iff #246 #986)
-#984 := (iff #245 #981)
-#977 := (implies #175 #972)
-#982 := (iff #977 #981)
-#983 := [rewrite]: #982
-#978 := (iff #245 #977)
-#975 := (iff #244 #972)
-#968 := (implies #743 #963)
-#973 := (iff #968 #972)
-#974 := [rewrite]: #973
-#969 := (iff #244 #968)
-#966 := (iff #243 #963)
-#959 := (implies #181 #954)
-#964 := (iff #959 #963)
-#965 := [rewrite]: #964
-#960 := (iff #243 #959)
-#957 := (iff #242 #954)
-#950 := (implies #757 #945)
-#955 := (iff #950 #954)
-#956 := [rewrite]: #955
-#951 := (iff #242 #950)
-#948 := (iff #241 #945)
-#941 := (implies #771 #938)
-#946 := (iff #941 #945)
-#947 := [rewrite]: #946
-#942 := (iff #241 #941)
-#939 := (iff #240 #938)
-#936 := (iff #239 #933)
-#929 := (implies #197 #926)
-#934 := (iff #929 #933)
-#935 := [rewrite]: #934
-#930 := (iff #239 #929)
-#927 := (iff #238 #926)
-#924 := (iff #237 #921)
-#917 := (implies #786 #914)
-#922 := (iff #917 #921)
-#923 := [rewrite]: #922
-#918 := (iff #237 #917)
-#915 := (iff #236 #914)
-#912 := (iff #235 #909)
-#905 := (implies #789 #902)
-#910 := (iff #905 #909)
-#911 := [rewrite]: #910
-#906 := (iff #235 #905)
-#903 := (iff #234 #902)
-#900 := (iff #233 #897)
-#893 := (implies #205 #890)
-#898 := (iff #893 #897)
-#899 := [rewrite]: #898
-#894 := (iff #233 #893)
-#891 := (iff #232 #890)
-#888 := (iff #231 #885)
-#881 := (implies #809 #878)
-#886 := (iff #881 #885)
-#887 := [rewrite]: #886
-#882 := (iff #231 #881)
-#879 := (iff #230 #878)
-#876 := (iff #229 #873)
-#869 := (implies #835 #859)
-#874 := (iff #869 #873)
-#875 := [rewrite]: #874
-#870 := (iff #229 #869)
-#867 := (iff #228 #859)
-#862 := (and #859 true)
-#865 := (iff #862 #859)
-#866 := [rewrite]: #865
-#863 := (iff #228 #862)
-#860 := (iff #227 #859)
-#857 := (iff #226 #854)
-#850 := (implies #220 #847)
-#855 := (iff #850 #854)
-#856 := [rewrite]: #855
-#851 := (iff #226 #850)
-#848 := (iff #225 #847)
-#845 := (iff #224 #844)
-#842 := (iff #223 #841)
-#839 := (iff #222 #838)
-#821 := (= #215 #820)
-#822 := [rewrite]: #821
-#840 := [monotonicity #822]: #839
-#775 := (iff #199 #774)
-#776 := [rewrite]: #775
-#843 := [monotonicity #776 #840]: #842
-#846 := [monotonicity #843]: #845
-#849 := [quant-intro #846]: #848
-#852 := [monotonicity #849]: #851
-#858 := [trans #852 #856]: #857
-#861 := [quant-intro #858]: #860
-#864 := [monotonicity #861]: #863
-#868 := [trans #864 #866]: #867
-#836 := (iff #218 #835)
-#833 := (iff #217 #830)
-#826 := (implies #815 #823)
-#831 := (iff #826 #830)
-#832 := [rewrite]: #831
-#827 := (iff #217 #826)
-#824 := (iff #216 #823)
-#825 := [monotonicity #822]: #824
-#818 := (iff #214 #815)
-#812 := (and #774 #83)
-#816 := (iff #812 #815)
-#817 := [rewrite]: #816
-#813 := (iff #214 #812)
-#814 := [monotonicity #776]: #813
-#819 := [trans #814 #817]: #818
-#828 := [monotonicity #819 #825]: #827
-#834 := [trans #828 #832]: #833
-#837 := [quant-intro #834]: #836
-#871 := [monotonicity #837 #868]: #870
-#877 := [trans #871 #875]: #876
-#880 := [monotonicity #837 #877]: #879
-#810 := (iff #213 #809)
-#807 := (iff #212 #804)
-#800 := (implies #797 #211)
-#805 := (iff #800 #804)
-#806 := [rewrite]: #805
-#801 := (iff #212 #800)
-#798 := (iff #209 #797)
-#795 := (iff #208 #794)
-#796 := [rewrite]: #795
-#792 := (iff #206 #780)
-#793 := [monotonicity #776]: #792
-#799 := [monotonicity #793 #796]: #798
-#802 := [monotonicity #799]: #801
-#808 := [trans #802 #806]: #807
-#811 := [quant-intro #808]: #810
-#883 := [monotonicity #811 #880]: #882
-#889 := [trans #883 #887]: #888
-#892 := [monotonicity #811 #889]: #891
-#895 := [monotonicity #892]: #894
-#901 := [trans #895 #899]: #900
-#904 := [monotonicity #901]: #903
-#790 := (iff #203 #789)
-#791 := [rewrite]: #790
-#907 := [monotonicity #791 #904]: #906
-#913 := [trans #907 #911]: #912
-#916 := [monotonicity #791 #913]: #915
-#787 := (iff #201 #786)
-#784 := (iff #200 #781)
-#777 := (implies #774 #760)
-#782 := (iff #777 #781)
-#783 := [rewrite]: #782
-#778 := (iff #200 #777)
-#761 := (iff #193 #760)
-#762 := [rewrite]: #761
-#779 := [monotonicity #776 #762]: #778
-#785 := [trans #779 #783]: #784
-#788 := [quant-intro #785]: #787
-#919 := [monotonicity #788 #916]: #918
-#925 := [trans #919 #923]: #924
-#928 := [monotonicity #788 #925]: #927
-#931 := [monotonicity #928]: #930
-#937 := [trans #931 #935]: #936
-#940 := [monotonicity #937]: #939
-#772 := (iff #195 #771)
-#769 := (iff #194 #766)
-#763 := (implies #192 #760)
-#767 := (iff #763 #766)
-#768 := [rewrite]: #767
-#764 := (iff #194 #763)
-#765 := [monotonicity #762]: #764
-#770 := [trans #765 #768]: #769
-#773 := [quant-intro #770]: #772
-#943 := [monotonicity #773 #940]: #942
-#949 := [trans #943 #947]: #948
-#758 := (iff #191 #757)
-#755 := (iff #190 #752)
-#749 := (implies #187 #746)
-#753 := (iff #749 #752)
-#754 := [rewrite]: #753
-#750 := (iff #190 #749)
-#747 := (iff #189 #746)
-#748 := [rewrite]: #747
-#751 := [monotonicity #748]: #750
-#756 := [trans #751 #754]: #755
-#759 := [quant-intro #756]: #758
-#952 := [monotonicity #759 #949]: #951
-#958 := [trans #952 #956]: #957
-#961 := [monotonicity #958]: #960
-#967 := [trans #961 #965]: #966
-#744 := (iff #178 #743)
-#741 := (iff #177 #738)
-#735 := (implies #511 #176)
-#739 := (iff #735 #738)
-#740 := [rewrite]: #739
-#736 := (iff #177 #735)
-#512 := (iff #107 #511)
-#509 := (iff #106 #508)
-#510 := [rewrite]: #509
-#513 := [monotonicity #510]: #512
-#737 := [monotonicity #513]: #736
-#742 := [trans #737 #740]: #741
-#745 := [quant-intro #742]: #744
-#970 := [monotonicity #745 #967]: #969
-#976 := [trans #970 #974]: #975
-#979 := [monotonicity #976]: #978
-#985 := [trans #979 #983]: #984
-#733 := (iff #173 #732)
-#730 := (iff #172 #729)
-#731 := [rewrite]: #730
-#734 := [monotonicity #731]: #733
-#988 := [monotonicity #734 #985]: #987
-#993 := [trans #988 #991]: #992
-#591 := (iff #130 #590)
-#588 := (iff #129 #585)
-#582 := (and #511 #120)
-#586 := (iff #582 #585)
-#587 := [rewrite]: #586
-#583 := (iff #129 #582)
-#584 := [monotonicity #513]: #583
-#589 := [trans #584 #587]: #588
-#592 := [quant-intro #589]: #591
-#996 := [monotonicity #592 #993]: #995
-#1001 := [trans #996 #999]: #1000
-#1004 := [monotonicity #1001]: #1003
-#1008 := [trans #1004 #1006]: #1007
-#727 := (iff #169 #717)
-#722 := (implies true #717)
-#725 := (iff #722 #717)
-#726 := [rewrite]: #725
-#723 := (iff #169 #722)
-#720 := (iff #168 #717)
-#714 := (implies #593 #709)
-#718 := (iff #714 #717)
-#719 := [rewrite]: #718
-#715 := (iff #168 #714)
-#712 := (iff #167 #709)
-#705 := (implies #596 #700)
-#710 := (iff #705 #709)
-#711 := [rewrite]: #710
-#706 := (iff #167 #705)
-#703 := (iff #166 #700)
-#696 := (implies #136 #691)
-#701 := (iff #696 #700)
-#702 := [rewrite]: #701
-#697 := (iff #166 #696)
-#694 := (iff #165 #691)
-#687 := (implies #599 #682)
-#692 := (iff #687 #691)
-#693 := [rewrite]: #692
-#688 := (iff #165 #687)
-#685 := (iff #164 #682)
-#678 := (implies #141 #675)
-#683 := (iff #678 #682)
-#684 := [rewrite]: #683
-#679 := (iff #164 #678)
-#676 := (iff #163 #675)
-#673 := (iff #162 #670)
-#666 := (implies #623 #663)
-#671 := (iff #666 #670)
-#672 := [rewrite]: #671
-#667 := (iff #162 #666)
-#664 := (iff #161 #663)
-#661 := (iff #160 #658)
-#654 := (implies #641 #644)
-#659 := (iff #654 #658)
-#660 := [rewrite]: #659
-#655 := (iff #160 #654)
-#652 := (iff #159 #644)
-#647 := (and #644 true)
-#650 := (iff #647 #644)
-#651 := [rewrite]: #650
-#648 := (iff #159 #647)
-#645 := (iff #158 #644)
-#646 := [rewrite]: #645
-#649 := [monotonicity #646]: #648
-#653 := [trans #649 #651]: #652
-#642 := (iff #156 #641)
-#639 := (iff #155 #636)
-#632 := (implies #626 #629)
-#637 := (iff #632 #636)
-#638 := [rewrite]: #637
-#633 := (iff #155 #632)
-#630 := (iff #154 #629)
-#603 := (= #147 #602)
-#604 := [rewrite]: #603
-#631 := [monotonicity #604]: #630
-#627 := (iff #153 #626)
-#628 := [rewrite]: #627
-#634 := [monotonicity #628 #631]: #633
-#640 := [trans #634 #638]: #639
-#643 := [quant-intro #640]: #642
-#656 := [monotonicity #643 #653]: #655
-#662 := [trans #656 #660]: #661
-#665 := [monotonicity #643 #662]: #664
-#624 := (iff #152 #623)
-#621 := (iff #151 #618)
-#614 := (implies #144 #611)
-#619 := (iff #614 #618)
-#620 := [rewrite]: #619
-#615 := (iff #151 #614)
-#612 := (iff #150 #611)
-#609 := (iff #149 #608)
-#606 := (iff #148 #605)
-#607 := [monotonicity #604]: #606
-#610 := [monotonicity #607]: #609
-#613 := [quant-intro #610]: #612
-#616 := [monotonicity #613]: #615
-#622 := [trans #616 #620]: #621
-#625 := [quant-intro #622]: #624
-#668 := [monotonicity #625 #665]: #667
-#674 := [trans #668 #672]: #673
-#677 := [monotonicity #625 #674]: #676
-#680 := [monotonicity #677]: #679
-#686 := [trans #680 #684]: #685
-#600 := (iff #138 #599)
-#601 := [rewrite]: #600
-#689 := [monotonicity #601 #686]: #688
-#695 := [trans #689 #693]: #694
-#698 := [monotonicity #695]: #697
-#704 := [trans #698 #702]: #703
-#597 := (iff #133 #596)
-#598 := [rewrite]: #597
-#707 := [monotonicity #598 #704]: #706
-#713 := [trans #707 #711]: #712
-#594 := (iff #131 #593)
-#595 := [monotonicity #592]: #594
-#716 := [monotonicity #595 #713]: #715
-#721 := [trans #716 #719]: #720
-#724 := [monotonicity #721]: #723
-#728 := [trans #724 #726]: #727
-#1011 := [monotonicity #728 #1008]: #1010
-#580 := (iff #128 #579)
-#577 := (iff #127 #574)
-#570 := (implies #121 #567)
-#575 := (iff #570 #574)
-#576 := [rewrite]: #575
-#571 := (iff #127 #570)
-#568 := (iff #126 #567)
-#565 := (iff #125 #564)
-#562 := (iff #124 #561)
-#559 := (iff #123 #558)
-#541 := (= #116 #540)
-#542 := [rewrite]: #541
-#560 := [monotonicity #542]: #559
-#563 := [monotonicity #510 #560]: #562
-#566 := [monotonicity #563]: #565
-#569 := [quant-intro #566]: #568
-#572 := [monotonicity #569]: #571
-#578 := [trans #572 #576]: #577
-#581 := [quant-intro #578]: #580
-#1014 := [monotonicity #581 #1011]: #1013
-#1020 := [trans #1014 #1018]: #1019
-#556 := (iff #119 #555)
-#553 := (iff #118 #550)
-#546 := (implies #535 #543)
-#551 := (iff #546 #550)
-#552 := [rewrite]: #551
-#547 := (iff #118 #546)
-#544 := (iff #117 #543)
-#545 := [monotonicity #542]: #544
-#538 := (iff #115 #535)
-#532 := (and #508 #83)
-#536 := (iff #532 #535)
-#537 := [rewrite]: #536
-#533 := (iff #115 #532)
-#534 := [monotonicity #510]: #533
-#539 := [trans #534 #537]: #538
-#548 := [monotonicity #539 #545]: #547
-#554 := [trans #548 #552]: #553
-#557 := [quant-intro #554]: #556
-#1023 := [monotonicity #557 #1020]: #1022
-#1029 := [trans #1023 #1027]: #1028
-#530 := (iff #114 #529)
-#527 := (iff #113 #524)
-#520 := (implies #517 #112)
-#525 := (iff #520 #524)
-#526 := [rewrite]: #525
-#521 := (iff #113 #520)
-#518 := (iff #110 #517)
-#515 := (iff #109 #514)
-#516 := [rewrite]: #515
-#519 := [monotonicity #513 #516]: #518
-#522 := [monotonicity #519]: #521
-#528 := [trans #522 #526]: #527
-#531 := [quant-intro #528]: #530
-#1032 := [monotonicity #531 #1029]: #1031
-#1038 := [trans #1032 #1036]: #1037
-#1041 := [monotonicity #1038]: #1040
-#1047 := [trans #1041 #1045]: #1046
-#506 := (iff #100 #505)
-#507 := [rewrite]: #506
-#1050 := [monotonicity #507 #1047]: #1049
-#1056 := [trans #1050 #1054]: #1055
-#1059 := [monotonicity #1056]: #1058
-#1063 := [trans #1059 #1061]: #1062
-#503 := (iff #97 #502)
-#500 := (iff #96 #497)
-#493 := (implies #90 #490)
-#498 := (iff #493 #497)
-#499 := [rewrite]: #498
-#494 := (iff #96 #493)
-#491 := (iff #95 #490)
-#488 := (iff #94 #487)
-#485 := (iff #93 #482)
-#479 := (and #429 #92)
-#483 := (iff #479 #482)
-#484 := [rewrite]: #483
-#480 := (iff #93 #479)
-#430 := (iff #67 #429)
-#431 := [rewrite]: #430
-#481 := [monotonicity #431]: #480
-#486 := [trans #481 #484]: #485
-#489 := [monotonicity #486]: #488
-#492 := [quant-intro #489]: #491
-#495 := [monotonicity #492]: #494
-#501 := [trans #495 #499]: #500
-#504 := [quant-intro #501]: #503
-#1066 := [monotonicity #504 #1063]: #1065
-#1072 := [trans #1066 #1070]: #1071
-#1075 := [monotonicity #504 #1072]: #1074
-#477 := (iff #88 #476)
-#474 := (iff #87 #471)
-#467 := (implies #462 #86)
-#472 := (iff #467 #471)
-#473 := [rewrite]: #472
-#468 := (iff #87 #467)
-#465 := (iff #84 #462)
-#459 := (and #429 #83)
-#463 := (iff #459 #462)
-#464 := [rewrite]: #463
-#460 := (iff #84 #459)
-#461 := [monotonicity #431]: #460
-#466 := [trans #461 #464]: #465
-#469 := [monotonicity #466]: #468
-#475 := [trans #469 #473]: #474
-#478 := [quant-intro #475]: #477
-#1078 := [monotonicity #478 #1075]: #1077
-#1084 := [trans #1078 #1082]: #1083
-#1087 := [monotonicity #478 #1084]: #1086
-#457 := (iff #80 #456)
-#454 := (iff #79 #451)
-#447 := (implies #444 #78)
-#452 := (iff #447 #451)
-#453 := [rewrite]: #452
-#448 := (iff #79 #447)
-#445 := (iff #76 #444)
-#442 := (iff #75 #441)
-#443 := [rewrite]: #442
-#433 := (iff #68 #432)
-#434 := [monotonicity #431]: #433
-#446 := [monotonicity #434 #443]: #445
-#449 := [monotonicity #446]: #448
-#455 := [trans #449 #453]: #454
-#458 := [quant-intro #455]: #457
-#1090 := [monotonicity #458 #1087]: #1089
-#1096 := [trans #1090 #1094]: #1095
-#1099 := [monotonicity #458 #1096]: #1098
-#1102 := [monotonicity #1099]: #1101
-#1108 := [trans #1102 #1106]: #1107
-#1111 := [monotonicity #1108]: #1110
-#439 := (iff #71 #438)
-#440 := [rewrite]: #439
-#1114 := [monotonicity #440 #1111]: #1113
-#1120 := [trans #1114 #1118]: #1119
-#1123 := [monotonicity #440 #1120]: #1122
-#436 := (iff #69 #435)
-#437 := [quant-intro #434]: #436
-#1126 := [monotonicity #437 #1123]: #1125
-#1132 := [trans #1126 #1130]: #1131
-#427 := (iff #65 #426)
-#424 := (iff #64 #421)
-#418 := (implies #62 #415)
-#422 := (iff #418 #421)
-#423 := [rewrite]: #422
-#419 := (iff #64 #418)
-#416 := (iff #63 #415)
-#417 := [rewrite]: #416
-#420 := [monotonicity #417]: #419
-#425 := [trans #420 #423]: #424
-#428 := [quant-intro #425]: #427
-#1135 := [monotonicity #428 #1132]: #1134
-#1141 := [trans #1135 #1139]: #1140
-#413 := (iff #61 #412)
-#410 := (iff #60 #407)
-#404 := (implies #57 #400)
-#408 := (iff #404 #407)
-#409 := [rewrite]: #408
-#405 := (iff #60 #404)
-#402 := (iff #59 #400)
-#403 := [rewrite]: #402
-#406 := [monotonicity #403]: #405
-#411 := [trans #406 #409]: #410
-#414 := [quant-intro #411]: #413
-#1144 := [monotonicity #414 #1141]: #1143
-#1150 := [trans #1144 #1148]: #1149
-#1153 := [monotonicity #1150]: #1152
-#1157 := [trans #1153 #1155]: #1156
-#1160 := [monotonicity #1157]: #1159
-#1799 := [trans #1160 #1797]: #1798
-#399 := [asserted]: #270
-#1800 := [mp #399 #1799]: #1795
-#1801 := [not-or-elim #1800]: #426
-#1854 := [mp~ #1801 #1824]: #426
-#4191 := [mp #1854 #4190]: #4186
-#4925 := (not #4186)
-#5686 := (or #4925 #2533 #5626)
-#1950 := (= ?v0!5 f10)
-#5627 := (or #1950 #5626)
-#5687 := (or #4925 #5627)
-#5694 := (iff #5687 #5686)
-#5630 := (or #2533 #5626)
-#5689 := (or #4925 #5630)
-#5692 := (iff #5689 #5686)
-#5693 := [rewrite]: #5692
-#5690 := (iff #5687 #5689)
-#5631 := (iff #5627 #5630)
-#2534 := (iff #1950 #2533)
-#2535 := [rewrite]: #2534
-#5632 := [monotonicity #2535]: #5631
-#5691 := [monotonicity #5632]: #5690
-#5695 := [trans #5691 #5693]: #5694
-#5688 := [quant-inst #1934]: #5687
-#5696 := [mp #5688 #5695]: #5686
-#5740 := [unit-resolution #5696 #4191 #5739 #5738]: false
-#5741 := [lemma #5740]: #4234
-#4520 := (or #4237 #4517)
-#4523 := (not #4520)
-#3082 := (or #432 #1197 #1202)
-#4217 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4216) #3082)
-#4222 := (not #4217)
-#4526 := (or #4222 #4523)
-#4529 := (not #4526)
-decl ?v1!3 :: S2
-#1903 := ?v1!3
-#1918 := (f11 ?v1!3)
-decl ?v0!4 :: S2
-#1904 := ?v0!4
-#1915 := (f11 ?v0!4)
-#1916 := (* -1::Int #1915)
-#2514 := (+ #1916 #1918)
-#1905 := (f5 ?v1!3 ?v0!4)
-#1906 := (f4 #1905)
-#2515 := (+ #1906 #2514)
-#2518 := (>= #2515 0::Int)
-#1911 := (f12 ?v1!3)
-#1912 := (= f1 #1911)
-#3045 := (not #1912)
-#1907 := (* -1::Int #1906)
-#1908 := (+ f3 #1907)
-#1909 := (<= #1908 0::Int)
-#3060 := (or #1909 #3045 #2518)
-#3065 := (not #3060)
-#4532 := (or #3065 #4529)
-#4535 := (not #4532)
-#4207 := (pattern #66 #74)
-#2486 := (not #441)
-#3037 := (or #429 #2486 #1177)
-#4208 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4207) #3037)
-#4213 := (not #4208)
-#4538 := (or #4213 #4535)
-#4541 := (not #4538)
-decl ?v1!1 :: S2
-#1876 := ?v1!1
-#1880 := (f11 ?v1!1)
-#2501 := (* -1::Int #1880)
-decl ?v0!2 :: S2
-#1877 := ?v0!2
-#1878 := (f11 ?v0!2)
-#2502 := (+ #1878 #2501)
-#2503 := (<= #2502 0::Int)
-#1885 := (f12 ?v1!1)
-#1886 := (= f1 #1885)
-#1883 := (f12 ?v0!2)
-#1884 := (= f1 #1883)
-#2131 := (not #1884)
-#2304 := (or #2131 #1886 #2503)
-#2021 := (not #2304)
-#4544 := (or #2021 #4541)
-#4547 := (not #4544)
-#4199 := (forall (vars (?v0 S2)) (:pat #4185) #1168)
-#4204 := (not #4199)
-#4550 := (or #4204 #4547)
-#4553 := (not #4550)
-decl ?v0!0 :: S2
-#1861 := ?v0!0
-#1862 := (f11 ?v0!0)
-#1863 := (>= #1862 0::Int)
-#293 := (<= f3 0::Int)
-#294 := (not #293)
-#10 := (< 0::Int f3)
-#295 := (iff #10 #294)
-#296 := [rewrite]: #295
-#290 := [asserted]: #10
-#297 := [mp #290 #296]: #294
-#5160 := (* -1::Int #1862)
-#5161 := (+ f3 #5160)
-#5182 := (<= #5161 0::Int)
-#3882 := (= f3 #1862)
-#4613 := (= f10 ?v0!0)
-#5181 := (not #4613)
-#5246 := (= #1862 0::Int)
-#4859 := (not #5246)
-#1864 := (not #1863)
-#4858 := [hypothesis]: #1864
-#5157 := (or #4859 #1863)
-#5253 := [th-lemma arith triangle-eq]: #5157
-#5254 := [unit-resolution #5253 #4858]: #4859
-#4572 := (forall (vars (?v0 S2)) (:pat #4185) #1772)
-#4575 := (iff #1775 #4572)
-#4573 := (iff #1772 #1772)
-#4574 := [refl]: #4573
-#4576 := [quant-intro #4574]: #4575
-#2226 := (~ #1775 #1775)
-#1993 := (~ #1772 #1772)
-#1994 := [refl]: #1993
-#2227 := [nnf-pos #1994]: #2226
-#1805 := [not-or-elim #1800]: #1775
-#2130 := [mp~ #1805 #2227]: #1775
-#4577 := [mp #2130 #4576]: #4572
-#5440 := (not #4572)
-#5441 := (or #5440 #5181 #5246)
-#3894 := (= ?v0!0 f10)
-#5247 := (not #3894)
-#5248 := (or #5247 #5246)
-#5442 := (or #5440 #5248)
-#5447 := (iff #5442 #5441)
-#5245 := (or #5181 #5246)
-#5444 := (or #5440 #5245)
-#5445 := (iff #5444 #5441)
-#5446 := [rewrite]: #5445
-#5275 := (iff #5442 #5444)
-#5251 := (iff #5248 #5245)
-#5249 := (iff #5247 #5181)
-#4628 := (iff #3894 #4613)
-#4629 := [rewrite]: #4628
-#5250 := [monotonicity #4629]: #5249
-#5252 := [monotonicity #5250]: #5251
-#5439 := [monotonicity #5252]: #5275
-#5448 := [trans #5439 #5446]: #5447
-#5443 := [quant-inst #1861]: #5442
-#3896 := [mp #5443 #5448]: #5441
-#5255 := [unit-resolution #3896 #4577 #5254]: #5181
-#4685 := (or #3882 #4613)
-#4927 := (or #4925 #3882 #4613)
-#4611 := (or #3894 #3882)
-#4928 := (or #4925 #4611)
-#5153 := (iff #4928 #4927)
-#3819 := (or #4925 #4685)
-#5042 := (iff #3819 #4927)
-#5136 := [rewrite]: #5042
-#3829 := (iff #4928 #3819)
-#4688 := (iff #4611 #4685)
-#4610 := (or #4613 #3882)
-#4686 := (iff #4610 #4685)
-#4687 := [rewrite]: #4686
-#4684 := (iff #4611 #4610)
-#4612 := [monotonicity #4629]: #4684
-#4856 := [trans #4612 #4687]: #4688
-#4926 := [monotonicity #4856]: #3829
-#5155 := [trans #4926 #5136]: #5153
-#3914 := [quant-inst #1861]: #4928
-#5156 := [mp #3914 #5155]: #4927
-#5449 := [unit-resolution #5156 #4191]: #4685
-#5509 := [unit-resolution #5449 #5255]: #3882
-#5510 := (not #3882)
-#5511 := (or #5510 #5182)
-#5491 := [th-lemma arith triangle-eq]: #5511
-#5492 := [unit-resolution #5491 #5509]: #5182
-#4857 := (<= #1862 0::Int)
-#5493 := (or #4857 #1863)
-#5494 := [th-lemma arith farkas 1 1]: #5493
-#5495 := [unit-resolution #5494 #4858]: #4857
-#5490 := [th-lemma arith farkas 1 -1 1 #5495 #5492 #297]: false
-#5496 := [lemma #5490]: #1863
-#4556 := (or #1864 #4553)
-#4559 := (not #4556)
-#4562 := (or #1163 #4559)
-#4565 := (not #4562)
-#5587 := [hypothesis]: #1163
-#5579 := (or #5440 #71)
-#3879 := (= f10 f10)
-#5183 := (not #3879)
-#5497 := (or #5183 #71)
-#5580 := (or #5440 #5497)
-#5582 := (iff #5580 #5579)
-#5578 := (iff #5579 #5579)
-#5584 := [rewrite]: #5578
-#5545 := (iff #5497 #71)
-#5541 := (or false #71)
-#5543 := (iff #5541 #71)
-#5544 := [rewrite]: #5543
-#5536 := (iff #5497 #5541)
-#5539 := (iff #5183 false)
-#5500 := (not true)
-#5537 := (iff #5500 false)
-#5538 := [rewrite]: #5537
-#5515 := (iff #5183 #5500)
-#5498 := (iff #3879 true)
-#5499 := [rewrite]: #5498
-#5516 := [monotonicity #5499]: #5515
-#5540 := [trans #5516 #5538]: #5539
-#5542 := [monotonicity #5540]: #5536
-#5546 := [trans #5542 #5544]: #5545
-#5583 := [monotonicity #5546]: #5582
-#5585 := [trans #5583 #5584]: #5582
-#5581 := [quant-inst #56]: #5580
-#5586 := [mp #5581 #5585]: #5579
-#5588 := [unit-resolution #5586 #5587 #4577]: false
-#5593 := [lemma #5588]: #71
-#4568 := (or #1163 #4565)
-#3495 := (forall (vars (?v1 S2)) #3484)
-#3502 := (not #3495)
-#3480 := (forall (vars (?v0 S2) (?v1 S2)) #3475)
-#3501 := (not #3480)
-#3503 := (or #2326 #2893 #3501 #3502)
-#3504 := (not #3503)
-#3509 := (or #3458 #3504)
-#3516 := (not #3509)
-#3435 := (forall (vars (?v0 S2) (?v1 S2)) #3430)
-#3515 := (not #3435)
-#3517 := (or #3515 #3516)
-#3518 := (not #3517)
-#3523 := (or #3412 #3518)
-#3529 := (not #3523)
-#3530 := (or #1466 #3529)
-#3531 := (not #3530)
-#3536 := (or #2243 #3531)
-#3542 := (not #3536)
-#3543 := (or #1457 #3542)
-#3544 := (not #3543)
-#3549 := (or #1457 #3544)
-#3555 := (not #3549)
-#3556 := (or #920 #3555)
-#3557 := (not #3556)
-#3562 := (or #2836 #3557)
-#3568 := (not #3562)
-#3569 := (or #1452 #3568)
-#3570 := (not #3569)
-#3575 := (or #2822 #3570)
-#3583 := (not #3575)
-#3389 := (forall (vars (?v0 S2)) #3384)
-#3582 := (not #3389)
-#3371 := (forall (vars (?v0 S2)) #3368)
-#3581 := (not #3371)
-#3584 := (or #962 #729 #1617 #1621 #2177 #2180 #3581 #3582 #3583)
-#3585 := (not #3584)
-#3301 := (forall (vars (?v0 S2) (?v1 S2)) #3296)
-#3307 := (not #3301)
-#3308 := (or #158 #3307)
-#3309 := (not #3308)
-#3336 := (or #3309 #3333)
-#3343 := (not #3336)
-#3279 := (forall (vars (?v0 S2)) #3274)
-#3342 := (not #3279)
-#3344 := (or #3342 #3343)
-#3345 := (not #3344)
-#3242 := (forall (vars (?v1 S2)) #3231)
-#3248 := (not #3242)
-#3249 := (or #2056 #2671 #3248)
-#3250 := (not #3249)
-#3350 := (or #3250 #3345)
-#3357 := (not #3350)
-#3227 := (forall (vars (?v0 S2)) #3216)
-#3356 := (not #3227)
-#3358 := (or #699 #681 #708 #690 #3356 #3357)
-#3359 := (not #3358)
-#3590 := (or #3359 #3585)
-#3600 := (not #3590)
-#3213 := (forall (vars (?v0 S2)) #3208)
-#3599 := (not #3213)
-#3185 := (forall (vars (?v0 S2)) #3180)
-#3598 := (not #3185)
-#3157 := (forall (vars (?v0 S2) (?v1 S2)) #3152)
-#3597 := (not #3157)
-#3134 := (forall (vars (?v0 S2) (?v1 S2)) #3129)
-#3596 := (not #3134)
-#3601 := (or #1714 #1709 #3596 #3597 #3598 #3599 #3600)
-#3602 := (not #3601)
-#3102 := (forall (vars (?v1 S2)) #3091)
-#3108 := (not #3102)
-#3109 := (or #1948 #2533 #3108)
-#3110 := (not #3109)
-#3607 := (or #3110 #3602)
-#3614 := (not #3607)
-#3087 := (forall (vars (?v0 S2) (?v1 S2)) #3082)
-#3613 := (not #3087)
-#3615 := (or #3613 #3614)
-#3616 := (not #3615)
-#3621 := (or #3065 #3616)
-#3628 := (not #3621)
-#3042 := (forall (vars (?v0 S2) (?v1 S2)) #3037)
-#3627 := (not #3042)
-#3629 := (or #3627 #3628)
-#3630 := (not #3629)
-#3635 := (or #2021 #3630)
-#3641 := (not #3635)
-#3642 := (or #1172 #3641)
-#3643 := (not #3642)
-#3648 := (or #1864 #3643)
-#3654 := (not #3648)
-#3655 := (or #1163 #3654)
-#3656 := (not #3655)
-#3661 := (or #1163 #3656)
-#4569 := (iff #3661 #4568)
-#4566 := (iff #3656 #4565)
-#4563 := (iff #3655 #4562)
-#4560 := (iff #3654 #4559)
-#4557 := (iff #3648 #4556)
-#4554 := (iff #3643 #4553)
-#4551 := (iff #3642 #4550)
-#4548 := (iff #3641 #4547)
-#4545 := (iff #3635 #4544)
-#4542 := (iff #3630 #4541)
-#4539 := (iff #3629 #4538)
-#4536 := (iff #3628 #4535)
-#4533 := (iff #3621 #4532)
-#4530 := (iff #3616 #4529)
-#4527 := (iff #3615 #4526)
-#4524 := (iff #3614 #4523)
-#4521 := (iff #3607 #4520)
-#4518 := (iff #3602 #4517)
-#4515 := (iff #3601 #4514)
-#4512 := (iff #3600 #4511)
-#4509 := (iff #3590 #4508)
-#4506 := (iff #3585 #4505)
-#4503 := (iff #3584 #4502)
-#4500 := (iff #3583 #4499)
-#4497 := (iff #3575 #4496)
-#4494 := (iff #3570 #4493)
-#4491 := (iff #3569 #4490)
-#4488 := (iff #3568 #4487)
-#4485 := (iff #3562 #4484)
-#4482 := (iff #3557 #4481)
-#4479 := (iff #3556 #4478)
-#4476 := (iff #3555 #4475)
-#4473 := (iff #3549 #4472)
-#4470 := (iff #3544 #4469)
-#4467 := (iff #3543 #4466)
-#4464 := (iff #3542 #4463)
-#4461 := (iff #3536 #4460)
-#4458 := (iff #3531 #4457)
-#4455 := (iff #3530 #4454)
-#4452 := (iff #3529 #4451)
-#4449 := (iff #3523 #4448)
-#4446 := (iff #3518 #4445)
-#4443 := (iff #3517 #4442)
-#4440 := (iff #3516 #4439)
-#4437 := (iff #3509 #4436)
-#4434 := (iff #3504 #4433)
-#4431 := (iff #3503 #4430)
-#4428 := (iff #3502 #4427)
-#4425 := (iff #3495 #4422)
-#4423 := (iff #3484 #3484)
-#4424 := [refl]: #4423
-#4426 := [quant-intro #4424]: #4425
-#4429 := [monotonicity #4426]: #4428
-#4419 := (iff #3501 #4418)
-#4416 := (iff #3480 #4413)
-#4414 := (iff #3475 #3475)
-#4415 := [refl]: #4414
-#4417 := [quant-intro #4415]: #4416
-#4420 := [monotonicity #4417]: #4419
-#4432 := [monotonicity #4420 #4429]: #4431
-#4435 := [monotonicity #4432]: #4434
-#4438 := [monotonicity #4435]: #4437
-#4441 := [monotonicity #4438]: #4440
-#4411 := (iff #3515 #4410)
-#4408 := (iff #3435 #4405)
-#4406 := (iff #3430 #3430)
-#4407 := [refl]: #4406
-#4409 := [quant-intro #4407]: #4408
-#4412 := [monotonicity #4409]: #4411
-#4444 := [monotonicity #4412 #4441]: #4443
-#4447 := [monotonicity #4444]: #4446
-#4450 := [monotonicity #4447]: #4449
-#4453 := [monotonicity #4450]: #4452
-#4402 := (iff #1466 #4401)
-#4399 := (iff #1463 #4396)
-#4397 := (iff #1460 #1460)
-#4398 := [refl]: #4397
-#4400 := [quant-intro #4398]: #4399
-#4403 := [monotonicity #4400]: #4402
-#4456 := [monotonicity #4403 #4453]: #4455
-#4459 := [monotonicity #4456]: #4458
-#4462 := [monotonicity #4459]: #4461
-#4465 := [monotonicity #4462]: #4464
-#4468 := [monotonicity #4465]: #4467
-#4471 := [monotonicity #4468]: #4470
-#4474 := [monotonicity #4471]: #4473
-#4477 := [monotonicity #4474]: #4476
-#4394 := (iff #920 #4393)
-#4391 := (iff #786 #4388)
-#4389 := (iff #781 #781)
-#4390 := [refl]: #4389
-#4392 := [quant-intro #4390]: #4391
-#4395 := [monotonicity #4392]: #4394
-#4480 := [monotonicity #4395 #4477]: #4479
-#4483 := [monotonicity #4480]: #4482
-#4486 := [monotonicity #4483]: #4485
-#4489 := [monotonicity #4486]: #4488
-#4385 := (iff #1452 #4384)
-#4382 := (iff #1449 #4379)
-#4380 := (iff #1444 #1444)
-#4381 := [refl]: #4380
-#4383 := [quant-intro #4381]: #4382
-#4386 := [monotonicity #4383]: #4385
-#4492 := [monotonicity #4386 #4489]: #4491
-#4495 := [monotonicity #4492]: #4494
-#4498 := [monotonicity #4495]: #4497
-#4501 := [monotonicity #4498]: #4500
-#4377 := (iff #3582 #4376)
-#4374 := (iff #3389 #4371)
-#4372 := (iff #3384 #3384)
-#4373 := [refl]: #4372
-#4375 := [quant-intro #4373]: #4374
-#4378 := [monotonicity #4375]: #4377
-#4369 := (iff #3581 #4368)
-#4366 := (iff #3371 #4363)
-#4364 := (iff #3368 #3368)
-#4365 := [refl]: #4364
-#4367 := [quant-intro #4365]: #4366
-#4370 := [monotonicity #4367]: #4369
-#4359 := (iff #1617 #4358)
-#4356 := (iff #1614 #4353)
-#4354 := (iff #1609 #1609)
-#4355 := [refl]: #4354
-#4357 := [quant-intro #4355]: #4356
-#4360 := [monotonicity #4357]: #4359
-#4504 := [monotonicity #4360 #4370 #4378 #4501]: #4503
-#4507 := [monotonicity #4504]: #4506
-#4351 := (iff #3359 #4350)
-#4348 := (iff #3358 #4347)
-#4345 := (iff #3357 #4344)
-#4342 := (iff #3350 #4341)
-#4339 := (iff #3345 #4338)
-#4336 := (iff #3344 #4335)
-#4333 := (iff #3343 #4332)
-#4330 := (iff #3336 #4329)
-#4327 := (iff #3309 #4326)
-#4324 := (iff #3308 #4323)
-#4321 := (iff #3307 #4320)
-#4318 := (iff #3301 #4315)
-#4316 := (iff #3296 #3296)
-#4317 := [refl]: #4316
-#4319 := [quant-intro #4317]: #4318
-#4322 := [monotonicity #4319]: #4321
-#4325 := [monotonicity #4322]: #4324
-#4328 := [monotonicity #4325]: #4327
-#4331 := [monotonicity #4328]: #4330
-#4334 := [monotonicity #4331]: #4333
-#4313 := (iff #3342 #4312)
-#4310 := (iff #3279 #4307)
-#4308 := (iff #3274 #3274)
-#4309 := [refl]: #4308
-#4311 := [quant-intro #4309]: #4310
-#4314 := [monotonicity #4311]: #4313
-#4337 := [monotonicity #4314 #4334]: #4336
-#4340 := [monotonicity #4337]: #4339
-#4305 := (iff #3250 #4304)
-#4302 := (iff #3249 #4301)
-#4299 := (iff #3248 #4298)
-#4296 := (iff #3242 #4293)
-#4294 := (iff #3231 #3231)
-#4295 := [refl]: #4294
-#4297 := [quant-intro #4295]: #4296
-#4300 := [monotonicity #4297]: #4299
-#4303 := [monotonicity #4300]: #4302
-#4306 := [monotonicity #4303]: #4305
-#4343 := [monotonicity #4306 #4340]: #4342
-#4346 := [monotonicity #4343]: #4345
-#4289 := (iff #3356 #4288)
-#4286 := (iff #3227 #4283)
-#4284 := (iff #3216 #3216)
-#4285 := [refl]: #4284
-#4287 := [quant-intro #4285]: #4286
-#4290 := [monotonicity #4287]: #4289
-#4349 := [monotonicity #4290 #4346]: #4348
-#4352 := [monotonicity #4349]: #4351
-#4510 := [monotonicity #4352 #4507]: #4509
-#4513 := [monotonicity #4510]: #4512
-#4280 := (iff #3599 #4279)
-#4277 := (iff #3213 #4274)
-#4275 := (iff #3208 #3208)
-#4276 := [refl]: #4275
-#4278 := [quant-intro #4276]: #4277
-#4281 := [monotonicity #4278]: #4280
-#4272 := (iff #3598 #4271)
-#4269 := (iff #3185 #4266)
-#4267 := (iff #3180 #3180)
-#4268 := [refl]: #4267
-#4270 := [quant-intro #4268]: #4269
-#4273 := [monotonicity #4270]: #4272
-#4264 := (iff #3597 #4263)
-#4261 := (iff #3157 #4258)
-#4259 := (iff #3152 #3152)
-#4260 := [refl]: #4259
-#4262 := [quant-intro #4260]: #4261
-#4265 := [monotonicity #4262]: #4264
-#4255 := (iff #3596 #4254)
-#4252 := (iff #3134 #4249)
-#4250 := (iff #3129 #3129)
-#4251 := [refl]: #4250
-#4253 := [quant-intro #4251]: #4252
-#4256 := [monotonicity #4253]: #4255
-#4247 := (iff #1709 #4246)
-#4244 := (iff #1706 #4241)
-#4242 := (iff #1703 #1703)
-#4243 := [refl]: #4242
-#4245 := [quant-intro #4243]: #4244
-#4248 := [monotonicity #4245]: #4247
-#4516 := [monotonicity #4248 #4256 #4265 #4273 #4281 #4513]: #4515
-#4519 := [monotonicity #4516]: #4518
-#4238 := (iff #3110 #4237)
-#4235 := (iff #3109 #4234)
-#4232 := (iff #3108 #4231)
-#4229 := (iff #3102 #4226)
-#4227 := (iff #3091 #3091)
-#4228 := [refl]: #4227
-#4230 := [quant-intro #4228]: #4229
-#4233 := [monotonicity #4230]: #4232
-#4236 := [monotonicity #4233]: #4235
-#4239 := [monotonicity #4236]: #4238
-#4522 := [monotonicity #4239 #4519]: #4521
-#4525 := [monotonicity #4522]: #4524
-#4223 := (iff #3613 #4222)
-#4220 := (iff #3087 #4217)
-#4218 := (iff #3082 #3082)
-#4219 := [refl]: #4218
-#4221 := [quant-intro #4219]: #4220
-#4224 := [monotonicity #4221]: #4223
-#4528 := [monotonicity #4224 #4525]: #4527
-#4531 := [monotonicity #4528]: #4530
-#4534 := [monotonicity #4531]: #4533
-#4537 := [monotonicity #4534]: #4536
-#4214 := (iff #3627 #4213)
-#4211 := (iff #3042 #4208)
-#4209 := (iff #3037 #3037)
-#4210 := [refl]: #4209
-#4212 := [quant-intro #4210]: #4211
-#4215 := [monotonicity #4212]: #4214
-#4540 := [monotonicity #4215 #4537]: #4539
-#4543 := [monotonicity #4540]: #4542
-#4546 := [monotonicity #4543]: #4545
-#4549 := [monotonicity #4546]: #4548
-#4205 := (iff #1172 #4204)
-#4202 := (iff #1169 #4199)
-#4200 := (iff #1168 #1168)
-#4201 := [refl]: #4200
-#4203 := [quant-intro #4201]: #4202
-#4206 := [monotonicity #4203]: #4205
-#4552 := [monotonicity #4206 #4549]: #4551
-#4555 := [monotonicity #4552]: #4554
-#4558 := [monotonicity #4555]: #4557
-#4561 := [monotonicity #4558]: #4560
-#4564 := [monotonicity #4561]: #4563
-#4567 := [monotonicity #4564]: #4566
-#4570 := [monotonicity #4567]: #4569
-#2322 := (not #2321)
-#2924 := (and #774 #2322 #2921)
-#2927 := (not #2924)
-#2930 := (forall (vars (?v1 S2)) #2927)
-#2896 := (not #2893)
-#2327 := (not #2326)
-#2939 := (and #1506 #2327 #2896 #2930)
-#2295 := (not #2294)
-#2866 := (and #2295 #2297)
-#2869 := (not #2866)
-#2887 := (or #2869 #2882)
-#2890 := (not #2887)
-#2944 := (or #2890 #2939)
-#2947 := (and #1482 #2944)
-#2266 := (not #2265)
-#2841 := (and #2263 #2266)
-#2844 := (not #2841)
-#2860 := (or #2844 #2855)
-#2863 := (not #2860)
-#2950 := (or #2863 #2947)
-#2953 := (and #1463 #2950)
-#2956 := (or #2243 #2953)
-#2959 := (and #203 #2956)
-#2962 := (or #1457 #2959)
-#2965 := (and #786 #2962)
-#2968 := (or #2836 #2965)
-#2971 := (and #1449 #2968)
-#2974 := (or #2822 #2971)
-#2181 := (not #2180)
-#2178 := (not #2177)
-#2980 := (and #181 #732 #1438 #1596 #1614 #1622 #2178 #2181 #2974)
-#2123 := (not #2122)
-#2119 := (not #2118)
-#2759 := (and #2119 #2123)
-#2762 := (not #2759)
-#2779 := (or #2762 #2774)
-#2782 := (not #2779)
-#2132 := (not #158)
-#2142 := (and #2132 #1358)
-#2788 := (or #2142 #2782)
-#2732 := (not #2727)
-#2750 := (and #2732 #2745)
-#2753 := (or #1318 #2750)
-#2756 := (forall (vars (?v0 S2)) #2753)
-#2793 := (and #2756 #2788)
-#2052 := (not #2051)
-#2702 := (and #2052 #2699)
-#2705 := (not #2702)
-#2708 := (forall (vars (?v1 S2)) #2705)
-#2674 := (not #2671)
-#2057 := (not #2056)
-#2714 := (and #2057 #2674 #2708)
-#2796 := (or #2714 #2793)
-#2158 := (not #1386)
-#2161 := (forall (vars (?v0 S2)) #2158)
-#2802 := (and #136 #141 #596 #599 #2161 #2796)
-#2985 := (or #2802 #2980)
-#2651 := (not #2646)
-#2654 := (and #2016 #2634 #2651)
-#2657 := (or #1273 #2654)
-#2660 := (forall (vars (?v0 S2)) #2657)
-#2596 := (not #2591)
-#2614 := (and #1989 #2596 #2609)
-#2617 := (or #1235 #2614)
-#2620 := (forall (vars (?v0 S2)) #2617)
-#2991 := (and #100 #1681 #1697 #1706 #2620 #2660 #2985)
-#1944 := (not #1943)
-#2564 := (and #429 #1944 #2561)
-#2567 := (not #2564)
-#2570 := (forall (vars (?v1 S2)) #2567)
-#2576 := (and #1949 #2536 #2570)
-#2996 := (or #2576 #2991)
-#2999 := (and #1220 #2996)
-#1910 := (not #1909)
-#2521 := (and #1910 #1912)
-#2524 := (not #2521)
-#2527 := (or #2518 #2524)
-#2530 := (not #2527)
-#3002 := (or #2530 #2999)
-#3005 := (and #1189 #3002)
-#1887 := (not #1886)
-#2489 := (and #1884 #1887)
-#2492 := (not #2489)
-#2508 := (or #2492 #2503)
-#2511 := (not #2508)
-#3008 := (or #2511 #3005)
-#3011 := (and #1169 #3008)
-#3014 := (or #1864 #3011)
-#3017 := (and #71 #3014)
-#3020 := (or #1163 #3017)
-#3662 := (iff #3020 #3661)
-#3659 := (iff #3017 #3656)
-#3651 := (and #71 #3648)
-#3657 := (iff #3651 #3656)
-#3658 := [rewrite]: #3657
-#3652 := (iff #3017 #3651)
-#3649 := (iff #3014 #3648)
-#3646 := (iff #3011 #3643)
-#3638 := (and #1169 #3635)
-#3644 := (iff #3638 #3643)
-#3645 := [rewrite]: #3644
-#3639 := (iff #3011 #3638)
-#3636 := (iff #3008 #3635)
-#3633 := (iff #3005 #3630)
-#3624 := (and #3042 #3621)
-#3631 := (iff #3624 #3630)
-#3632 := [rewrite]: #3631
-#3625 := (iff #3005 #3624)
-#3622 := (iff #3002 #3621)
-#3619 := (iff #2999 #3616)
-#3610 := (and #3087 #3607)
-#3617 := (iff #3610 #3616)
-#3618 := [rewrite]: #3617
-#3611 := (iff #2999 #3610)
-#3608 := (iff #2996 #3607)
-#3605 := (iff #2991 #3602)
-#3593 := (and #100 #3134 #3157 #1706 #3185 #3213 #3590)
-#3603 := (iff #3593 #3602)
-#3604 := [rewrite]: #3603
-#3594 := (iff #2991 #3593)
-#3591 := (iff #2985 #3590)
-#3588 := (iff #2980 #3585)
-#3578 := (and #181 #732 #3371 #3389 #1614 #1622 #2178 #2181 #3575)
-#3586 := (iff #3578 #3585)
-#3587 := [rewrite]: #3586
-#3579 := (iff #2980 #3578)
-#3576 := (iff #2974 #3575)
-#3573 := (iff #2971 #3570)
-#3565 := (and #1449 #3562)
-#3571 := (iff #3565 #3570)
-#3572 := [rewrite]: #3571
-#3566 := (iff #2971 #3565)
-#3563 := (iff #2968 #3562)
-#3560 := (iff #2965 #3557)
-#3552 := (and #786 #3549)
-#3558 := (iff #3552 #3557)
-#3559 := [rewrite]: #3558
-#3553 := (iff #2965 #3552)
-#3550 := (iff #2962 #3549)
-#3547 := (iff #2959 #3544)
-#3539 := (and #203 #3536)
-#3545 := (iff #3539 #3544)
-#3546 := [rewrite]: #3545
-#3540 := (iff #2959 #3539)
-#3537 := (iff #2956 #3536)
-#3534 := (iff #2953 #3531)
-#3526 := (and #1463 #3523)
-#3532 := (iff #3526 #3531)
-#3533 := [rewrite]: #3532
-#3527 := (iff #2953 #3526)
-#3524 := (iff #2950 #3523)
-#3521 := (iff #2947 #3518)
-#3512 := (and #3435 #3509)
-#3519 := (iff #3512 #3518)
-#3520 := [rewrite]: #3519
-#3513 := (iff #2947 #3512)
-#3510 := (iff #2944 #3509)
-#3507 := (iff #2939 #3504)
-#3498 := (and #3480 #2327 #2896 #3495)
-#3505 := (iff #3498 #3504)
-#3506 := [rewrite]: #3505
-#3499 := (iff #2939 #3498)
-#3496 := (iff #2930 #3495)
-#3493 := (iff #2927 #3484)
-#3485 := (not #3484)
-#3488 := (not #3485)
-#3491 := (iff #3488 #3484)
-#3492 := [rewrite]: #3491
-#3489 := (iff #2927 #3488)
-#3486 := (iff #2924 #3485)
-#3487 := [rewrite]: #3486
-#3490 := [monotonicity #3487]: #3489
-#3494 := [trans #3490 #3492]: #3493
-#3497 := [quant-intro #3494]: #3496
-#3481 := (iff #1506 #3480)
-#3478 := (iff #1503 #3475)
-#3461 := (or #780 #1202)
-#3472 := (or #3461 #1499)
-#3476 := (iff #3472 #3475)
-#3477 := [rewrite]: #3476
-#3473 := (iff #1503 #3472)
-#3470 := (iff #1496 #3461)
-#3462 := (not #3461)
-#3465 := (not #3462)
-#3468 := (iff #3465 #3461)
-#3469 := [rewrite]: #3468
-#3466 := (iff #1496 #3465)
-#3463 := (iff #1491 #3462)
-#3464 := [rewrite]: #3463
-#3467 := [monotonicity #3464]: #3466
-#3471 := [trans #3467 #3469]: #3470
-#3474 := [monotonicity #3471]: #3473
-#3479 := [trans #3474 #3477]: #3478
-#3482 := [quant-intro #3479]: #3481
-#3500 := [monotonicity #3482 #3497]: #3499
-#3508 := [trans #3500 #3506]: #3507
-#3459 := (iff #2890 #3458)
-#3456 := (iff #2887 #3453)
-#3439 := (or #2294 #3438)
-#3450 := (or #3439 #2882)
-#3454 := (iff #3450 #3453)
-#3455 := [rewrite]: #3454
-#3451 := (iff #2887 #3450)
-#3448 := (iff #2869 #3439)
-#3440 := (not #3439)
-#3443 := (not #3440)
-#3446 := (iff #3443 #3439)
-#3447 := [rewrite]: #3446
-#3444 := (iff #2869 #3443)
-#3441 := (iff #2866 #3440)
-#3442 := [rewrite]: #3441
-#3445 := [monotonicity #3442]: #3444
-#3449 := [trans #3445 #3447]: #3448
-#3452 := [monotonicity #3449]: #3451
-#3457 := [trans #3452 #3455]: #3456
-#3460 := [monotonicity #3457]: #3459
-#3511 := [monotonicity #3460 #3508]: #3510
-#3436 := (iff #1482 #3435)
-#3433 := (iff #1477 #3430)
-#3416 := (or #774 #3415)
-#3427 := (or #3416 #1469)
-#3431 := (iff #3427 #3430)
-#3432 := [rewrite]: #3431
-#3428 := (iff #1477 #3427)
-#3425 := (iff #803 #3416)
-#3417 := (not #3416)
-#3420 := (not #3417)
-#3423 := (iff #3420 #3416)
-#3424 := [rewrite]: #3423
-#3421 := (iff #803 #3420)
-#3418 := (iff #797 #3417)
-#3419 := [rewrite]: #3418
-#3422 := [monotonicity #3419]: #3421
-#3426 := [trans #3422 #3424]: #3425
-#3429 := [monotonicity #3426]: #3428
-#3434 := [trans #3429 #3432]: #3433
-#3437 := [quant-intro #3434]: #3436
-#3514 := [monotonicity #3437 #3511]: #3513
-#3522 := [trans #3514 #3520]: #3521
-#3413 := (iff #2863 #3412)
-#3410 := (iff #2860 #3407)
-#3393 := (or #3392 #2265)
-#3404 := (or #3393 #2855)
-#3408 := (iff #3404 #3407)
-#3409 := [rewrite]: #3408
-#3405 := (iff #2860 #3404)
-#3402 := (iff #2844 #3393)
-#3394 := (not #3393)
-#3397 := (not #3394)
-#3400 := (iff #3397 #3393)
-#3401 := [rewrite]: #3400
-#3398 := (iff #2844 #3397)
-#3395 := (iff #2841 #3394)
-#3396 := [rewrite]: #3395
-#3399 := [monotonicity #3396]: #3398
-#3403 := [trans #3399 #3401]: #3402
-#3406 := [monotonicity #3403]: #3405
-#3411 := [trans #3406 #3409]: #3410
-#3414 := [monotonicity #3411]: #3413
-#3525 := [monotonicity #3414 #3522]: #3524
-#3528 := [monotonicity #3525]: #3527
-#3535 := [trans #3528 #3533]: #3534
-#3538 := [monotonicity #3535]: #3537
-#3541 := [monotonicity #3538]: #3540
-#3548 := [trans #3541 #3546]: #3547
-#3551 := [monotonicity #3548]: #3550
-#3554 := [monotonicity #3551]: #3553
-#3561 := [trans #3554 #3559]: #3560
-#3564 := [monotonicity #3561]: #3563
-#3567 := [monotonicity #3564]: #3566
-#3574 := [trans #3567 #3572]: #3573
-#3577 := [monotonicity #3574]: #3576
-#3390 := (iff #1596 #3389)
-#3387 := (iff #1593 #3384)
-#3381 := (or #3364 #1590)
-#3385 := (iff #3381 #3384)
-#3386 := [rewrite]: #3385
-#3382 := (iff #1593 #3381)
-#3379 := (iff #1585 #3364)
-#3374 := (not #3365)
-#3377 := (iff #3374 #3364)
-#3378 := [rewrite]: #3377
-#3375 := (iff #1585 #3374)
-#3366 := (iff #1427 #3365)
-#3367 := [rewrite]: #3366
-#3376 := [monotonicity #3367]: #3375
-#3380 := [trans #3376 #3378]: #3379
-#3383 := [monotonicity #3380]: #3382
-#3388 := [trans #3383 #3386]: #3387
-#3391 := [quant-intro #3388]: #3390
-#3372 := (iff #1438 #3371)
-#3369 := (iff #1433 #3368)
-#3370 := [monotonicity #3367]: #3369
-#3373 := [quant-intro #3370]: #3372
-#3580 := [monotonicity #3373 #3391 #3577]: #3579
-#3589 := [trans #3580 #3587]: #3588
-#3362 := (iff #2802 #3359)
-#3353 := (and #136 #141 #596 #599 #3227 #3350)
-#3360 := (iff #3353 #3359)
-#3361 := [rewrite]: #3360
-#3354 := (iff #2802 #3353)
-#3351 := (iff #2796 #3350)
-#3348 := (iff #2793 #3345)
-#3339 := (and #3279 #3336)
-#3346 := (iff #3339 #3345)
-#3347 := [rewrite]: #3346
-#3340 := (iff #2793 #3339)
-#3337 := (iff #2788 #3336)
-#3334 := (iff #2782 #3333)
-#3331 := (iff #2779 #3328)
-#3314 := (or #2118 #2122)
-#3325 := (or #3314 #2774)
-#3329 := (iff #3325 #3328)
-#3330 := [rewrite]: #3329
-#3326 := (iff #2779 #3325)
-#3323 := (iff #2762 #3314)
-#3315 := (not #3314)
-#3318 := (not #3315)
-#3321 := (iff #3318 #3314)
-#3322 := [rewrite]: #3321
-#3319 := (iff #2762 #3318)
-#3316 := (iff #2759 #3315)
-#3317 := [rewrite]: #3316
-#3320 := [monotonicity #3317]: #3319
-#3324 := [trans #3320 #3322]: #3323
-#3327 := [monotonicity #3324]: #3326
-#3332 := [trans #3327 #3330]: #3331
-#3335 := [monotonicity #3332]: #3334
-#3312 := (iff #2142 #3309)
-#3304 := (and #2132 #3301)
-#3310 := (iff #3304 #3309)
-#3311 := [rewrite]: #3310
-#3305 := (iff #2142 #3304)
-#3302 := (iff #1358 #3301)
-#3299 := (iff #1355 #3296)
-#3282 := (or #1202 #1311)
-#3293 := (or #3282 #1352)
-#3297 := (iff #3293 #3296)
-#3298 := [rewrite]: #3297
-#3294 := (iff #1355 #3293)
-#3291 := (iff #1349 #3282)
-#3283 := (not #3282)
-#3286 := (not #3283)
-#3289 := (iff #3286 #3282)
-#3290 := [rewrite]: #3289
-#3287 := (iff #1349 #3286)
-#3284 := (iff #1346 #3283)
-#3285 := [rewrite]: #3284
-#3288 := [monotonicity #3285]: #3287
-#3292 := [trans #3288 #3290]: #3291
-#3295 := [monotonicity #3292]: #3294
-#3300 := [trans #3295 #3298]: #3299
-#3303 := [quant-intro #3300]: #3302
-#3306 := [monotonicity #3303]: #3305
-#3313 := [trans #3306 #3311]: #3312
-#3338 := [monotonicity #3313 #3335]: #3337
-#3280 := (iff #2756 #3279)
-#3277 := (iff #2753 #3274)
-#3255 := (or #57 #1311)
-#3271 := (or #3255 #3268)
-#3275 := (iff #3271 #3274)
-#3276 := [rewrite]: #3275
-#3272 := (iff #2753 #3271)
-#3269 := (iff #2750 #3268)
-#3270 := [rewrite]: #3269
-#3264 := (iff #1318 #3255)
-#3256 := (not #3255)
-#3259 := (not #3256)
-#3262 := (iff #3259 #3255)
-#3263 := [rewrite]: #3262
-#3260 := (iff #1318 #3259)
-#3257 := (iff #1315 #3256)
-#3258 := [rewrite]: #3257
-#3261 := [monotonicity #3258]: #3260
-#3265 := [trans #3261 #3263]: #3264
-#3273 := [monotonicity #3265 #3270]: #3272
-#3278 := [trans #3273 #3276]: #3277
-#3281 := [quant-intro #3278]: #3280
-#3341 := [monotonicity #3281 #3338]: #3340
-#3349 := [trans #3341 #3347]: #3348
-#3253 := (iff #2714 #3250)
-#3245 := (and #2057 #2674 #3242)
-#3251 := (iff #3245 #3250)
-#3252 := [rewrite]: #3251
-#3246 := (iff #2714 #3245)
-#3243 := (iff #2708 #3242)
-#3240 := (iff #2705 #3231)
-#3232 := (not #3231)
-#3235 := (not #3232)
-#3238 := (iff #3235 #3231)
-#3239 := [rewrite]: #3238
-#3236 := (iff #2705 #3235)
-#3233 := (iff #2702 #3232)
-#3234 := [rewrite]: #3233
-#3237 := [monotonicity #3234]: #3236
-#3241 := [trans #3237 #3239]: #3240
-#3244 := [quant-intro #3241]: #3243
-#3247 := [monotonicity #3244]: #3246
-#3254 := [trans #3247 #3252]: #3253
-#3352 := [monotonicity #3254 #3349]: #3351
-#3228 := (iff #2161 #3227)
-#3225 := (iff #2158 #3216)
-#3217 := (not #3216)
-#3220 := (not #3217)
-#3223 := (iff #3220 #3216)
-#3224 := [rewrite]: #3223
-#3221 := (iff #2158 #3220)
-#3218 := (iff #1386 #3217)
-#3219 := [rewrite]: #3218
-#3222 := [monotonicity #3219]: #3221
-#3226 := [trans #3222 #3224]: #3225
-#3229 := [quant-intro #3226]: #3228
-#3355 := [monotonicity #3229 #3352]: #3354
-#3363 := [trans #3355 #3361]: #3362
-#3592 := [monotonicity #3363 #3589]: #3591
-#3214 := (iff #2660 #3213)
-#3211 := (iff #2657 #3208)
-#3188 := (or #57 #1266)
-#3205 := (or #3188 #3202)
-#3209 := (iff #3205 #3208)
-#3210 := [rewrite]: #3209
-#3206 := (iff #2657 #3205)
-#3203 := (iff #2654 #3202)
-#3204 := [rewrite]: #3203
-#3197 := (iff #1273 #3188)
-#3189 := (not #3188)
-#3192 := (not #3189)
-#3195 := (iff #3192 #3188)
-#3196 := [rewrite]: #3195
-#3193 := (iff #1273 #3192)
-#3190 := (iff #1270 #3189)
-#3191 := [rewrite]: #3190
-#3194 := [monotonicity #3191]: #3193
-#3198 := [trans #3194 #3196]: #3197
-#3207 := [monotonicity #3198 #3204]: #3206
-#3212 := [trans #3207 #3210]: #3211
-#3215 := [quant-intro #3212]: #3214
-#3186 := (iff #2620 #3185)
-#3183 := (iff #2617 #3180)
-#3160 := (or #57 #1228)
-#3177 := (or #3160 #3174)
-#3181 := (iff #3177 #3180)
-#3182 := [rewrite]: #3181
-#3178 := (iff #2617 #3177)
-#3175 := (iff #2614 #3174)
-#3176 := [rewrite]: #3175
-#3169 := (iff #1235 #3160)
-#3161 := (not #3160)
-#3164 := (not #3161)
-#3167 := (iff #3164 #3160)
-#3168 := [rewrite]: #3167
-#3165 := (iff #1235 #3164)
-#3162 := (iff #1232 #3161)
-#3163 := [rewrite]: #3162
-#3166 := [monotonicity #3163]: #3165
-#3170 := [trans #3166 #3168]: #3169
-#3179 := [monotonicity #3170 #3176]: #3178
-#3184 := [trans #3179 #3182]: #3183
-#3187 := [quant-intro #3184]: #3186
-#3158 := (iff #1697 #3157)
-#3155 := (iff #1692 #3152)
-#3138 := (or #508 #3137)
-#3149 := (or #3138 #1282)
-#3153 := (iff #3149 #3152)
-#3154 := [rewrite]: #3153
-#3150 := (iff #1692 #3149)
-#3147 := (iff #523 #3138)
-#3139 := (not #3138)
-#3142 := (not #3139)
-#3145 := (iff #3142 #3138)
-#3146 := [rewrite]: #3145
-#3143 := (iff #523 #3142)
-#3140 := (iff #517 #3139)
-#3141 := [rewrite]: #3140
-#3144 := [monotonicity #3141]: #3143
-#3148 := [trans #3144 #3146]: #3147
-#3151 := [monotonicity #3148]: #3150
-#3156 := [trans #3151 #3154]: #3155
-#3159 := [quant-intro #3156]: #3158
-#3135 := (iff #1681 #3134)
-#3132 := (iff #1678 #3129)
-#3115 := (or #511 #1202)
-#3126 := (or #3115 #1675)
-#3130 := (iff #3126 #3129)
-#3131 := [rewrite]: #3130
-#3127 := (iff #1678 #3126)
-#3124 := (iff #1672 #3115)
-#3116 := (not #3115)
-#3119 := (not #3116)
-#3122 := (iff #3119 #3115)
-#3123 := [rewrite]: #3122
-#3120 := (iff #1672 #3119)
-#3117 := (iff #1667 #3116)
-#3118 := [rewrite]: #3117
-#3121 := [monotonicity #3118]: #3120
-#3125 := [trans #3121 #3123]: #3124
-#3128 := [monotonicity #3125]: #3127
-#3133 := [trans #3128 #3131]: #3132
-#3136 := [quant-intro #3133]: #3135
-#3595 := [monotonicity #3136 #3159 #3187 #3215 #3592]: #3594
-#3606 := [trans #3595 #3604]: #3605
-#3113 := (iff #2576 #3110)
-#3105 := (and #1949 #2536 #3102)
-#3111 := (iff #3105 #3110)
-#3112 := [rewrite]: #3111
-#3106 := (iff #2576 #3105)
-#3103 := (iff #2570 #3102)
-#3100 := (iff #2567 #3091)
-#3092 := (not #3091)
-#3095 := (not #3092)
-#3098 := (iff #3095 #3091)
-#3099 := [rewrite]: #3098
-#3096 := (iff #2567 #3095)
-#3093 := (iff #2564 #3092)
-#3094 := [rewrite]: #3093
-#3097 := [monotonicity #3094]: #3096
-#3101 := [trans #3097 #3099]: #3100
-#3104 := [quant-intro #3101]: #3103
-#3107 := [monotonicity #3104]: #3106
-#3114 := [trans #3107 #3112]: #3113
-#3609 := [monotonicity #3114 #3606]: #3608
-#3088 := (iff #1220 #3087)
-#3085 := (iff #1217 #3082)
-#3068 := (or #432 #1202)
-#3079 := (or #1197 #3068)
-#3083 := (iff #3079 #3082)
-#3084 := [rewrite]: #3083
-#3080 := (iff #1217 #3079)
-#3077 := (iff #1214 #3068)
-#3069 := (not #3068)
-#3072 := (not #3069)
-#3075 := (iff #3072 #3068)
-#3076 := [rewrite]: #3075
-#3073 := (iff #1214 #3072)
-#3070 := (iff #1209 #3069)
-#3071 := [rewrite]: #3070
-#3074 := [monotonicity #3071]: #3073
-#3078 := [trans #3074 #3076]: #3077
-#3081 := [monotonicity #3078]: #3080
-#3086 := [trans #3081 #3084]: #3085
-#3089 := [quant-intro #3086]: #3088
-#3612 := [monotonicity #3089 #3609]: #3611
-#3620 := [trans #3612 #3618]: #3619
-#3066 := (iff #2530 #3065)
-#3063 := (iff #2527 #3060)
-#3046 := (or #1909 #3045)
-#3057 := (or #2518 #3046)
-#3061 := (iff #3057 #3060)
-#3062 := [rewrite]: #3061
-#3058 := (iff #2527 #3057)
-#3055 := (iff #2524 #3046)
-#3047 := (not #3046)
-#3050 := (not #3047)
-#3053 := (iff #3050 #3046)
-#3054 := [rewrite]: #3053
-#3051 := (iff #2524 #3050)
-#3048 := (iff #2521 #3047)
-#3049 := [rewrite]: #3048
-#3052 := [monotonicity #3049]: #3051
-#3056 := [trans #3052 #3054]: #3055
-#3059 := [monotonicity #3056]: #3058
-#3064 := [trans #3059 #3062]: #3063
-#3067 := [monotonicity #3064]: #3066
-#3623 := [monotonicity #3067 #3620]: #3622
-#3043 := (iff #1189 #3042)
-#3040 := (iff #1184 #3037)
-#3023 := (or #429 #2486)
-#3034 := (or #3023 #1177)
-#3038 := (iff #3034 #3037)
-#3039 := [rewrite]: #3038
-#3035 := (iff #1184 #3034)
-#3032 := (iff #450 #3023)
-#3024 := (not #3023)
-#3027 := (not #3024)
-#3030 := (iff #3027 #3023)
-#3031 := [rewrite]: #3030
-#3028 := (iff #450 #3027)
-#3025 := (iff #444 #3024)
-#3026 := [rewrite]: #3025
-#3029 := [monotonicity #3026]: #3028
-#3033 := [trans #3029 #3031]: #3032
-#3036 := [monotonicity #3033]: #3035
-#3041 := [trans #3036 #3039]: #3040
-#3044 := [quant-intro #3041]: #3043
-#3626 := [monotonicity #3044 #3623]: #3625
-#3634 := [trans #3626 #3632]: #3633
-#2246 := (iff #2511 #2021)
-#1868 := (iff #2508 #2304)
-#1894 := (or #2131 #1886)
-#2274 := (or #1894 #2503)
-#2305 := (iff #2274 #2304)
-#1867 := [rewrite]: #2305
-#2185 := (iff #2508 #2274)
-#2096 := (iff #2492 #1894)
-#1831 := (not #1894)
-#2206 := (not #1831)
-#1926 := (iff #2206 #1894)
-#2095 := [rewrite]: #1926
-#2207 := (iff #2492 #2206)
-#1832 := (iff #2489 #1831)
-#1895 := [rewrite]: #1832
-#1925 := [monotonicity #1895]: #2207
-#2273 := [trans #1925 #2095]: #2096
-#2186 := [monotonicity #2273]: #2185
-#2020 := [trans #2186 #1867]: #1868
-#2247 := [monotonicity #2020]: #2246
-#3637 := [monotonicity #2247 #3634]: #3636
-#3640 := [monotonicity #3637]: #3639
-#3647 := [trans #3640 #3645]: #3646
-#3650 := [monotonicity #3647]: #3649
-#3653 := [monotonicity #3650]: #3652
-#3660 := [trans #3653 #3658]: #3659
-#3663 := [monotonicity #3660]: #3662
-#2319 := (+ #2318 #2316)
-#2320 := (= #2319 0::Int)
-#2323 := (and #774 #2322 #2320)
-#2340 := (not #2323)
-#2343 := (forall (vars (?v1 S2)) #2340)
-#2328 := (= ?v0!20 f10)
-#2329 := (not #2328)
-#2330 := (and #2329 #2327)
-#2331 := (not #2330)
-#2337 := (not #2331)
-#2347 := (and #2337 #2343)
-#2352 := (and #1506 #2347)
-#2285 := (* -1::Int #2284)
-#2287 := (+ #2286 #2285)
-#2290 := (+ #2289 #2287)
-#2291 := (>= #2290 0::Int)
-#2298 := (and #2297 #2295)
-#2299 := (not #2298)
-#2300 := (or #2299 #2291)
-#2301 := (not #2300)
-#2356 := (or #2301 #2352)
-#2360 := (and #1482 #2356)
-#2258 := (* -1::Int #2257)
-#2260 := (+ #2259 #2258)
-#2261 := (>= #2260 0::Int)
-#2267 := (and #2266 #2263)
-#2268 := (not #2267)
-#2269 := (or #2268 #2261)
-#2270 := (not #2269)
-#2364 := (or #2270 #2360)
-#2368 := (and #1463 #2364)
-#2372 := (or #2243 #2368)
-#2237 := (not #1457)
-#2376 := (and #2237 #2372)
-#2380 := (or #1457 #2376)
-#2384 := (and #786 #2380)
-#2221 := (= #2220 #2219)
-#2222 := (or #2221 #2218)
-#2223 := (not #2222)
-#2388 := (or #2223 #2384)
-#2392 := (and #1449 #2388)
-#2199 := (* -1::Int #2198)
-#2201 := (+ #2200 #2199)
-#2202 := (>= #2201 0::Int)
-#2203 := (not #2202)
-#2396 := (or #2203 #2392)
-#2182 := (and #2181 #2178)
-#2168 := (not #962)
-#2416 := (and #2168 #732 #2182 #1438 #2396 #1596 #1614 #1622)
-#2109 := (* -1::Int #2108)
-#2111 := (+ #2110 #2109)
-#2114 := (+ #2113 #2111)
-#2115 := (>= #2114 0::Int)
-#2124 := (and #2123 #2119)
-#2125 := (not #2124)
-#2126 := (or #2125 #2115)
-#2127 := (not #2126)
-#2146 := (or #2127 #2142)
-#2085 := (+ #2084 #1309)
-#2088 := (+ #2087 #2085)
-#2089 := (= #2088 0::Int)
-#2090 := (>= #2085 0::Int)
-#2091 := (not #2090)
-#2092 := (and #2091 #2089)
-#2097 := (or #1318 #2092)
-#2100 := (forall (vars (?v0 S2)) #2097)
-#2150 := (and #2100 #2146)
-#2049 := (+ #2048 #2046)
-#2050 := (= #2049 0::Int)
-#2053 := (and #2052 #2050)
-#2069 := (not #2053)
-#2072 := (forall (vars (?v1 S2)) #2069)
-#2058 := (= ?v0!8 f10)
-#2059 := (not #2058)
-#2060 := (and #2059 #2057)
-#2061 := (not #2060)
-#2066 := (not #2061)
-#2076 := (and #2066 #2072)
-#2154 := (or #2076 #2150)
-#2040 := (not #690)
-#2037 := (not #708)
-#2034 := (not #681)
-#2031 := (not #699)
-#2164 := (and #2031 #2034 #2037 #2040 #2154 #2161)
-#2420 := (or #2164 #2416)
-#2008 := (+ #2007 #1264)
-#2009 := (>= #2008 0::Int)
-#2010 := (not #2009)
-#2013 := (+ #2012 #2008)
-#2014 := (= #2013 0::Int)
-#2017 := (and #2016 #2014 #2010)
-#2022 := (or #1273 #2017)
-#2025 := (forall (vars (?v0 S2)) #2022)
-#1981 := (+ #1226 #1980)
-#1983 := (+ #1982 #1981)
-#1984 := (= #1983 0::Int)
-#1985 := (+ #1982 #1226)
-#1986 := (>= #1985 0::Int)
-#1987 := (not #1986)
-#1990 := (and #1989 #1987 #1984)
-#1995 := (or #1235 #1990)
-#1998 := (forall (vars (?v0 S2)) #1995)
-#1973 := (not #1714)
-#2445 := (and #1973 #1998 #2025 #2420 #1681 #1697 #1706)
-#1939 := (+ #1938 #1936)
-#1940 := (+ #58 #1939)
-#1941 := (= #1940 0::Int)
-#1945 := (and #429 #1944 #1941)
-#1961 := (not #1945)
-#1964 := (forall (vars (?v1 S2)) #1961)
-#1951 := (not #1950)
-#1952 := (and #1951 #1949)
-#1953 := (not #1952)
-#1958 := (not #1953)
-#1968 := (and #1958 #1964)
-#2449 := (or #1968 #2445)
-#2453 := (and #1220 #2449)
-#1913 := (and #1912 #1910)
-#1914 := (not #1913)
-#1917 := (+ #1916 #1906)
-#1919 := (+ #1918 #1917)
-#1920 := (>= #1919 0::Int)
-#1921 := (or #1920 #1914)
-#1922 := (not #1921)
-#2457 := (or #1922 #2453)
-#2461 := (and #1189 #2457)
-#1879 := (* -1::Int #1878)
-#1881 := (+ #1880 #1879)
-#1882 := (>= #1881 0::Int)
-#1888 := (and #1887 #1884)
-#1889 := (not #1888)
-#1890 := (or #1889 #1882)
-#1891 := (not #1890)
-#2465 := (or #1891 #2461)
-#2469 := (and #1169 #2465)
-#2473 := (or #1864 #2469)
-#1827 := (not #1163)
-#2477 := (and #1827 #2473)
-#2481 := (or #1163 #2477)
-#3021 := (iff #2481 #3020)
-#3018 := (iff #2477 #3017)
-#3015 := (iff #2473 #3014)
-#3012 := (iff #2469 #3011)
-#3009 := (iff #2465 #3008)
-#3006 := (iff #2461 #3005)
-#3003 := (iff #2457 #3002)
-#3000 := (iff #2453 #2999)
-#2997 := (iff #2449 #2996)
-#2994 := (iff #2445 #2991)
-#2988 := (and #100 #2620 #2660 #2985 #1681 #1697 #1706)
-#2992 := (iff #2988 #2991)
-#2993 := [rewrite]: #2992
-#2989 := (iff #2445 #2988)
-#2986 := (iff #2420 #2985)
-#2983 := (iff #2416 #2980)
-#2977 := (and #181 #732 #2182 #1438 #2974 #1596 #1614 #1622)
-#2981 := (iff #2977 #2980)
-#2982 := [rewrite]: #2981
-#2978 := (iff #2416 #2977)
-#2975 := (iff #2396 #2974)
-#2972 := (iff #2392 #2971)
-#2969 := (iff #2388 #2968)
-#2966 := (iff #2384 #2965)
-#2963 := (iff #2380 #2962)
-#2960 := (iff #2376 #2959)
-#2957 := (iff #2372 #2956)
-#2954 := (iff #2368 #2953)
-#2951 := (iff #2364 #2950)
-#2948 := (iff #2360 #2947)
-#2945 := (iff #2356 #2944)
-#2942 := (iff #2352 #2939)
-#2902 := (and #2327 #2896)
-#2933 := (and #2902 #2930)
-#2936 := (and #1506 #2933)
-#2940 := (iff #2936 #2939)
-#2941 := [rewrite]: #2940
-#2937 := (iff #2352 #2936)
-#2934 := (iff #2347 #2933)
-#2931 := (iff #2343 #2930)
-#2928 := (iff #2340 #2927)
-#2925 := (iff #2323 #2924)
-#2922 := (iff #2320 #2921)
-#2919 := (= #2319 #2918)
-#2920 := [rewrite]: #2919
-#2923 := [monotonicity #2920]: #2922
-#2926 := [monotonicity #2923]: #2925
-#2929 := [monotonicity #2926]: #2928
-#2932 := [quant-intro #2929]: #2931
-#2915 := (iff #2337 #2902)
-#2907 := (not #2902)
-#2910 := (not #2907)
-#2913 := (iff #2910 #2902)
-#2914 := [rewrite]: #2913
-#2911 := (iff #2337 #2910)
-#2908 := (iff #2331 #2907)
-#2905 := (iff #2330 #2902)
-#2899 := (and #2896 #2327)
-#2903 := (iff #2899 #2902)
-#2904 := [rewrite]: #2903
-#2900 := (iff #2330 #2899)
-#2897 := (iff #2329 #2896)
-#2894 := (iff #2328 #2893)
-#2895 := [rewrite]: #2894
-#2898 := [monotonicity #2895]: #2897
-#2901 := [monotonicity #2898]: #2900
-#2906 := [trans #2901 #2904]: #2905
-#2909 := [monotonicity #2906]: #2908
-#2912 := [monotonicity #2909]: #2911
-#2916 := [trans #2912 #2914]: #2915
-#2935 := [monotonicity #2916 #2932]: #2934
-#2938 := [monotonicity #2935]: #2937
-#2943 := [trans #2938 #2941]: #2942
-#2891 := (iff #2301 #2890)
-#2888 := (iff #2300 #2887)
-#2885 := (iff #2291 #2882)
-#2872 := (+ #2286 #2289)
-#2873 := (+ #2285 #2872)
-#2876 := (>= #2873 0::Int)
-#2883 := (iff #2876 #2882)
-#2884 := [rewrite]: #2883
-#2877 := (iff #2291 #2876)
-#2874 := (= #2290 #2873)
-#2875 := [rewrite]: #2874
-#2878 := [monotonicity #2875]: #2877
-#2886 := [trans #2878 #2884]: #2885
-#2870 := (iff #2299 #2869)
-#2867 := (iff #2298 #2866)
-#2868 := [rewrite]: #2867
-#2871 := [monotonicity #2868]: #2870
-#2889 := [monotonicity #2871 #2886]: #2888
-#2892 := [monotonicity #2889]: #2891
-#2946 := [monotonicity #2892 #2943]: #2945
-#2949 := [monotonicity #2946]: #2948
-#2864 := (iff #2270 #2863)
-#2861 := (iff #2269 #2860)
-#2858 := (iff #2261 #2855)
-#2847 := (+ #2258 #2259)
-#2850 := (>= #2847 0::Int)
-#2856 := (iff #2850 #2855)
-#2857 := [rewrite]: #2856
-#2851 := (iff #2261 #2850)
-#2848 := (= #2260 #2847)
-#2849 := [rewrite]: #2848
-#2852 := [monotonicity #2849]: #2851
-#2859 := [trans #2852 #2857]: #2858
-#2845 := (iff #2268 #2844)
-#2842 := (iff #2267 #2841)
-#2843 := [rewrite]: #2842
-#2846 := [monotonicity #2843]: #2845
-#2862 := [monotonicity #2846 #2859]: #2861
-#2865 := [monotonicity #2862]: #2864
-#2952 := [monotonicity #2865 #2949]: #2951
-#2955 := [monotonicity #2952]: #2954
-#2958 := [monotonicity #2955]: #2957
-#2839 := (iff #2237 #203)
-#2840 := [rewrite]: #2839
-#2961 := [monotonicity #2840 #2958]: #2960
-#2964 := [monotonicity #2961]: #2963
-#2967 := [monotonicity #2964]: #2966
-#2837 := (iff #2223 #2836)
-#2834 := (iff #2222 #2831)
-#2828 := (or #2825 #2218)
-#2832 := (iff #2828 #2831)
-#2833 := [rewrite]: #2832
-#2829 := (iff #2222 #2828)
-#2826 := (iff #2221 #2825)
-#2827 := [rewrite]: #2826
-#2830 := [monotonicity #2827]: #2829
-#2835 := [trans #2830 #2833]: #2834
-#2838 := [monotonicity #2835]: #2837
-#2970 := [monotonicity #2838 #2967]: #2969
-#2973 := [monotonicity #2970]: #2972
-#2823 := (iff #2203 #2822)
-#2820 := (iff #2202 #2817)
-#2809 := (+ #2199 #2200)
-#2812 := (>= #2809 0::Int)
-#2818 := (iff #2812 #2817)
-#2819 := [rewrite]: #2818
-#2813 := (iff #2202 #2812)
-#2810 := (= #2201 #2809)
-#2811 := [rewrite]: #2810
-#2814 := [monotonicity #2811]: #2813
-#2821 := [trans #2814 #2819]: #2820
-#2824 := [monotonicity #2821]: #2823
-#2976 := [monotonicity #2824 #2973]: #2975
-#2807 := (iff #2168 #181)
-#2808 := [rewrite]: #2807
-#2979 := [monotonicity #2808 #2976]: #2978
-#2984 := [trans #2979 #2982]: #2983
-#2805 := (iff #2164 #2802)
-#2799 := (and #136 #141 #596 #599 #2796 #2161)
-#2803 := (iff #2799 #2802)
-#2804 := [rewrite]: #2803
-#2800 := (iff #2164 #2799)
-#2797 := (iff #2154 #2796)
-#2794 := (iff #2150 #2793)
-#2791 := (iff #2146 #2788)
-#2785 := (or #2782 #2142)
-#2789 := (iff #2785 #2788)
-#2790 := [rewrite]: #2789
-#2786 := (iff #2146 #2785)
-#2783 := (iff #2127 #2782)
-#2780 := (iff #2126 #2779)
-#2777 := (iff #2115 #2774)
-#2765 := (+ #2110 #2113)
-#2766 := (+ #2109 #2765)
-#2769 := (>= #2766 0::Int)
-#2775 := (iff #2769 #2774)
-#2776 := [rewrite]: #2775
-#2770 := (iff #2115 #2769)
-#2767 := (= #2114 #2766)
-#2768 := [rewrite]: #2767
-#2771 := [monotonicity #2768]: #2770
-#2778 := [trans #2771 #2776]: #2777
-#2763 := (iff #2125 #2762)
-#2760 := (iff #2124 #2759)
-#2761 := [rewrite]: #2760
-#2764 := [monotonicity #2761]: #2763
-#2781 := [monotonicity #2764 #2778]: #2780
-#2784 := [monotonicity #2781]: #2783
-#2787 := [monotonicity #2784]: #2786
-#2792 := [trans #2787 #2790]: #2791
-#2757 := (iff #2100 #2756)
-#2754 := (iff #2097 #2753)
-#2751 := (iff #2092 #2750)
-#2748 := (iff #2089 #2745)
-#2735 := (+ #2084 #2087)
-#2736 := (+ #1309 #2735)
-#2739 := (= #2736 0::Int)
-#2746 := (iff #2739 #2745)
-#2747 := [rewrite]: #2746
-#2740 := (iff #2089 #2739)
-#2737 := (= #2088 #2736)
-#2738 := [rewrite]: #2737
-#2741 := [monotonicity #2738]: #2740
-#2749 := [trans #2741 #2747]: #2748
-#2733 := (iff #2091 #2732)
-#2730 := (iff #2090 #2727)
-#2719 := (+ #1309 #2084)
-#2722 := (>= #2719 0::Int)
-#2728 := (iff #2722 #2727)
-#2729 := [rewrite]: #2728
-#2723 := (iff #2090 #2722)
-#2720 := (= #2085 #2719)
-#2721 := [rewrite]: #2720
-#2724 := [monotonicity #2721]: #2723
-#2731 := [trans #2724 #2729]: #2730
-#2734 := [monotonicity #2731]: #2733
-#2752 := [monotonicity #2734 #2749]: #2751
-#2755 := [monotonicity #2752]: #2754
-#2758 := [quant-intro #2755]: #2757
-#2795 := [monotonicity #2758 #2792]: #2794
-#2717 := (iff #2076 #2714)
-#2680 := (and #2057 #2674)
-#2711 := (and #2680 #2708)
-#2715 := (iff #2711 #2714)
-#2716 := [rewrite]: #2715
-#2712 := (iff #2076 #2711)
-#2709 := (iff #2072 #2708)
-#2706 := (iff #2069 #2705)
-#2703 := (iff #2053 #2702)
-#2700 := (iff #2050 #2699)
-#2697 := (= #2049 #2696)
-#2698 := [rewrite]: #2697
-#2701 := [monotonicity #2698]: #2700
-#2704 := [monotonicity #2701]: #2703
-#2707 := [monotonicity #2704]: #2706
-#2710 := [quant-intro #2707]: #2709
-#2693 := (iff #2066 #2680)
-#2685 := (not #2680)
-#2688 := (not #2685)
-#2691 := (iff #2688 #2680)
-#2692 := [rewrite]: #2691
-#2689 := (iff #2066 #2688)
-#2686 := (iff #2061 #2685)
-#2683 := (iff #2060 #2680)
-#2677 := (and #2674 #2057)
-#2681 := (iff #2677 #2680)
-#2682 := [rewrite]: #2681
-#2678 := (iff #2060 #2677)
-#2675 := (iff #2059 #2674)
-#2672 := (iff #2058 #2671)
-#2673 := [rewrite]: #2672
-#2676 := [monotonicity #2673]: #2675
-#2679 := [monotonicity #2676]: #2678
-#2684 := [trans #2679 #2682]: #2683
-#2687 := [monotonicity #2684]: #2686
-#2690 := [monotonicity #2687]: #2689
-#2694 := [trans #2690 #2692]: #2693
-#2713 := [monotonicity #2694 #2710]: #2712
-#2718 := [trans #2713 #2716]: #2717
-#2798 := [monotonicity #2718 #2795]: #2797
-#2669 := (iff #2040 #599)
-#2670 := [rewrite]: #2669
-#2667 := (iff #2037 #596)
-#2668 := [rewrite]: #2667
-#2665 := (iff #2034 #141)
-#2666 := [rewrite]: #2665
-#2663 := (iff #2031 #136)
-#2664 := [rewrite]: #2663
-#2801 := [monotonicity #2664 #2666 #2668 #2670 #2798]: #2800
-#2806 := [trans #2801 #2804]: #2805
-#2987 := [monotonicity #2806 #2984]: #2986
-#2661 := (iff #2025 #2660)
-#2658 := (iff #2022 #2657)
-#2655 := (iff #2017 #2654)
-#2652 := (iff #2010 #2651)
-#2649 := (iff #2009 #2646)
-#2639 := (+ #1264 #2007)
-#2642 := (>= #2639 0::Int)
-#2647 := (iff #2642 #2646)
-#2648 := [rewrite]: #2647
-#2643 := (iff #2009 #2642)
-#2640 := (= #2008 #2639)
-#2641 := [rewrite]: #2640
-#2644 := [monotonicity #2641]: #2643
-#2650 := [trans #2644 #2648]: #2649
-#2653 := [monotonicity #2650]: #2652
-#2637 := (iff #2014 #2634)
-#2623 := (+ #2007 #2012)
-#2624 := (+ #1264 #2623)
-#2627 := (= #2624 0::Int)
-#2635 := (iff #2627 #2634)
-#2636 := [rewrite]: #2635
-#2628 := (iff #2014 #2627)
-#2625 := (= #2013 #2624)
-#2626 := [rewrite]: #2625
-#2629 := [monotonicity #2626]: #2628
-#2638 := [trans #2629 #2636]: #2637
-#2656 := [monotonicity #2638 #2653]: #2655
-#2659 := [monotonicity #2656]: #2658
-#2662 := [quant-intro #2659]: #2661
-#2621 := (iff #1998 #2620)
-#2618 := (iff #1995 #2617)
-#2615 := (iff #1990 #2614)
-#2612 := (iff #1984 #2609)
-#2599 := (+ #1980 #1982)
-#2600 := (+ #1226 #2599)
-#2603 := (= #2600 0::Int)
-#2610 := (iff #2603 #2609)
-#2611 := [rewrite]: #2610
-#2604 := (iff #1984 #2603)
-#2601 := (= #1983 #2600)
-#2602 := [rewrite]: #2601
-#2605 := [monotonicity #2602]: #2604
-#2613 := [trans #2605 #2611]: #2612
-#2597 := (iff #1987 #2596)
-#2594 := (iff #1986 #2591)
-#2583 := (+ #1226 #1982)
-#2586 := (>= #2583 0::Int)
-#2592 := (iff #2586 #2591)
-#2593 := [rewrite]: #2592
-#2587 := (iff #1986 #2586)
-#2584 := (= #1985 #2583)
-#2585 := [rewrite]: #2584
-#2588 := [monotonicity #2585]: #2587
-#2595 := [trans #2588 #2593]: #2594
-#2598 := [monotonicity #2595]: #2597
-#2616 := [monotonicity #2598 #2613]: #2615
-#2619 := [monotonicity #2616]: #2618
-#2622 := [quant-intro #2619]: #2621
-#2581 := (iff #1973 #100)
-#2582 := [rewrite]: #2581
-#2990 := [monotonicity #2582 #2622 #2662 #2987]: #2989
-#2995 := [trans #2990 #2993]: #2994
-#2579 := (iff #1968 #2576)
-#2542 := (and #1949 #2536)
-#2573 := (and #2542 #2570)
-#2577 := (iff #2573 #2576)
-#2578 := [rewrite]: #2577
-#2574 := (iff #1968 #2573)
-#2571 := (iff #1964 #2570)
-#2568 := (iff #1961 #2567)
-#2565 := (iff #1945 #2564)
-#2562 := (iff #1941 #2561)
-#2559 := (= #1940 #2558)
-#2560 := [rewrite]: #2559
-#2563 := [monotonicity #2560]: #2562
-#2566 := [monotonicity #2563]: #2565
-#2569 := [monotonicity #2566]: #2568
-#2572 := [quant-intro #2569]: #2571
-#2555 := (iff #1958 #2542)
-#2547 := (not #2542)
-#2550 := (not #2547)
-#2553 := (iff #2550 #2542)
-#2554 := [rewrite]: #2553
-#2551 := (iff #1958 #2550)
-#2548 := (iff #1953 #2547)
-#2545 := (iff #1952 #2542)
-#2539 := (and #2536 #1949)
-#2543 := (iff #2539 #2542)
-#2544 := [rewrite]: #2543
-#2540 := (iff #1952 #2539)
-#2537 := (iff #1951 #2536)
-#2538 := [monotonicity #2535]: #2537
-#2541 := [monotonicity #2538]: #2540
-#2546 := [trans #2541 #2544]: #2545
-#2549 := [monotonicity #2546]: #2548
-#2552 := [monotonicity #2549]: #2551
-#2556 := [trans #2552 #2554]: #2555
-#2575 := [monotonicity #2556 #2572]: #2574
-#2580 := [trans #2575 #2578]: #2579
-#2998 := [monotonicity #2580 #2995]: #2997
-#3001 := [monotonicity #2998]: #3000
-#2531 := (iff #1922 #2530)
-#2528 := (iff #1921 #2527)
-#2525 := (iff #1914 #2524)
-#2522 := (iff #1913 #2521)
-#2523 := [rewrite]: #2522
-#2526 := [monotonicity #2523]: #2525
-#2519 := (iff #1920 #2518)
-#2516 := (= #1919 #2515)
-#2517 := [rewrite]: #2516
-#2520 := [monotonicity #2517]: #2519
-#2529 := [monotonicity #2520 #2526]: #2528
-#2532 := [monotonicity #2529]: #2531
-#3004 := [monotonicity #2532 #3001]: #3003
-#3007 := [monotonicity #3004]: #3006
-#2512 := (iff #1891 #2511)
-#2509 := (iff #1890 #2508)
-#2506 := (iff #1882 #2503)
-#2495 := (+ #1879 #1880)
-#2498 := (>= #2495 0::Int)
-#2504 := (iff #2498 #2503)
-#2505 := [rewrite]: #2504
-#2499 := (iff #1882 #2498)
-#2496 := (= #1881 #2495)
-#2497 := [rewrite]: #2496
-#2500 := [monotonicity #2497]: #2499
-#2507 := [trans #2500 #2505]: #2506
-#2493 := (iff #1889 #2492)
-#2490 := (iff #1888 #2489)
-#2491 := [rewrite]: #2490
-#2494 := [monotonicity #2491]: #2493
-#2510 := [monotonicity #2494 #2507]: #2509
-#2513 := [monotonicity #2510]: #2512
-#3010 := [monotonicity #2513 #3007]: #3009
-#3013 := [monotonicity #3010]: #3012
-#3016 := [monotonicity #3013]: #3015
-#2487 := (iff #1827 #71)
-#2488 := [rewrite]: #2487
-#3019 := [monotonicity #2488 #3016]: #3018
-#3022 := [monotonicity #3019]: #3021
-#1803 := (not #1767)
-#2482 := (~ #1803 #2481)
-#2478 := (not #1764)
-#2479 := (~ #2478 #2477)
-#2474 := (not #1761)
-#2475 := (~ #2474 #2473)
-#2470 := (not #1758)
-#2471 := (~ #2470 #2469)
-#2466 := (not #1755)
-#2467 := (~ #2466 #2465)
-#2462 := (not #1752)
-#2463 := (~ #2462 #2461)
-#2458 := (not #1749)
-#2459 := (~ #2458 #2457)
-#2454 := (not #1746)
-#2455 := (~ #2454 #2453)
-#2450 := (not #1743)
-#2451 := (~ #2450 #2449)
-#2446 := (not #1738)
-#2447 := (~ #2446 #2445)
-#2442 := (not #1709)
-#2443 := (~ #2442 #1706)
-#2440 := (~ #1706 #1706)
-#2438 := (~ #1703 #1703)
-#2439 := [refl]: #2438
-#2441 := [nnf-pos #2439]: #2440
-#2444 := [nnf-neg #2441]: #2443
-#2435 := (not #1700)
-#2436 := (~ #2435 #1697)
-#2433 := (~ #1697 #1697)
-#2431 := (~ #1692 #1692)
-#2432 := [refl]: #2431
-#2434 := [nnf-pos #2432]: #2433
-#2437 := [nnf-neg #2434]: #2436
-#2428 := (not #1684)
-#2429 := (~ #2428 #1681)
-#2426 := (~ #1681 #1681)
-#2424 := (~ #1678 #1678)
-#2425 := [refl]: #2424
-#2427 := [nnf-pos #2425]: #2426
-#2430 := [nnf-neg #2427]: #2429
-#2421 := (not #1661)
-#2422 := (~ #2421 #2420)
-#2417 := (not #1656)
-#2418 := (~ #2417 #2416)
-#2414 := (~ #1622 #1622)
-#2415 := [refl]: #2414
-#2411 := (not #1617)
-#2412 := (~ #2411 #1614)
-#2409 := (~ #1614 #1614)
-#2407 := (~ #1609 #1609)
-#2408 := [refl]: #2407
-#2410 := [nnf-pos #2408]: #2409
-#2413 := [nnf-neg #2410]: #2412
-#2404 := (not #1599)
-#2405 := (~ #2404 #1596)
-#2402 := (~ #1596 #1596)
-#2400 := (~ #1593 #1593)
-#2401 := [refl]: #2400
-#2403 := [nnf-pos #2401]: #2402
-#2406 := [nnf-neg #2403]: #2405
-#2397 := (not #1582)
-#2398 := (~ #2397 #2396)
-#2393 := (not #1579)
-#2394 := (~ #2393 #2392)
-#2389 := (not #1576)
-#2390 := (~ #2389 #2388)
-#2385 := (not #1573)
-#2386 := (~ #2385 #2384)
-#2381 := (not #1570)
-#2382 := (~ #2381 #2380)
-#2377 := (not #1567)
-#2378 := (~ #2377 #2376)
-#2373 := (not #1564)
-#2374 := (~ #2373 #2372)
-#2369 := (not #1561)
-#2370 := (~ #2369 #2368)
-#2365 := (not #1558)
-#2366 := (~ #2365 #2364)
-#2361 := (not #1555)
-#2362 := (~ #2361 #2360)
-#2357 := (not #1552)
-#2358 := (~ #2357 #2356)
-#2353 := (not #1549)
-#2354 := (~ #2353 #2352)
-#2334 := (not #1546)
-#2350 := (~ #2334 #2347)
-#2324 := (exists (vars (?v1 S2)) #2323)
-#2332 := (or #2331 #2324)
-#2333 := (not #2332)
-#2348 := (~ #2333 #2347)
-#2344 := (not #2324)
-#2345 := (~ #2344 #2343)
-#2341 := (~ #2340 #2340)
-#2342 := [refl]: #2341
-#2346 := [nnf-neg #2342]: #2345
-#2338 := (~ #2337 #2337)
-#2339 := [refl]: #2338
-#2349 := [nnf-neg #2339 #2346]: #2348
-#2335 := (~ #2334 #2333)
-#2336 := [sk]: #2335
-#2351 := [trans #2336 #2349]: #2350
-#2310 := (not #1509)
-#2311 := (~ #2310 #1506)
-#2308 := (~ #1506 #1506)
-#2306 := (~ #1503 #1503)
-#2307 := [refl]: #2306
-#2309 := [nnf-pos #2307]: #2308
-#2312 := [nnf-neg #2309]: #2311
-#2355 := [nnf-neg #2312 #2351]: #2354
-#2302 := (~ #1509 #2301)
-#2303 := [sk]: #2302
-#2359 := [nnf-neg #2303 #2355]: #2358
-#2279 := (not #1485)
-#2280 := (~ #2279 #1482)
-#2277 := (~ #1482 #1482)
-#2275 := (~ #1477 #1477)
-#2276 := [refl]: #2275
-#2278 := [nnf-pos #2276]: #2277
-#2281 := [nnf-neg #2278]: #2280
-#2363 := [nnf-neg #2281 #2359]: #2362
-#2271 := (~ #1485 #2270)
-#2272 := [sk]: #2271
-#2367 := [nnf-neg #2272 #2363]: #2366
-#2252 := (not #1466)
-#2253 := (~ #2252 #1463)
-#2250 := (~ #1463 #1463)
-#2248 := (~ #1460 #1460)
-#2249 := [refl]: #2248
-#2251 := [nnf-pos #2249]: #2250
-#2254 := [nnf-neg #2251]: #2253
-#2371 := [nnf-neg #2254 #2367]: #2370
-#2244 := (~ #1466 #2243)
-#2245 := [sk]: #2244
-#2375 := [nnf-neg #2245 #2371]: #2374
-#2238 := (~ #2237 #2237)
-#2239 := [refl]: #2238
-#2379 := [nnf-neg #2239 #2375]: #2378
-#2235 := (~ #1457 #1457)
-#2236 := [refl]: #2235
-#2383 := [nnf-neg #2236 #2379]: #2382
-#2232 := (not #920)
-#2233 := (~ #2232 #786)
-#2230 := (~ #786 #786)
-#2228 := (~ #781 #781)
-#2229 := [refl]: #2228
-#2231 := [nnf-pos #2229]: #2230
-#2234 := [nnf-neg #2231]: #2233
-#2387 := [nnf-neg #2234 #2383]: #2386
-#2224 := (~ #920 #2223)
-#2225 := [sk]: #2224
-#2391 := [nnf-neg #2225 #2387]: #2390
-#2212 := (not #1452)
-#2213 := (~ #2212 #1449)
-#2210 := (~ #1449 #1449)
-#2208 := (~ #1444 #1444)
-#2209 := [refl]: #2208
-#2211 := [nnf-pos #2209]: #2210
-#2214 := [nnf-neg #2211]: #2213
-#2395 := [nnf-neg #2214 #2391]: #2394
-#2204 := (~ #1452 #2203)
-#2205 := [sk]: #2204
-#2399 := [nnf-neg #2205 #2395]: #2398
-#2194 := (not #1441)
-#2195 := (~ #2194 #1438)
-#2192 := (~ #1438 #1438)
-#2190 := (~ #1433 #1433)
-#2191 := [refl]: #2190
-#2193 := [nnf-pos #2191]: #2192
-#2196 := [nnf-neg #2193]: #2195
-#2187 := (not #1632)
-#2188 := (~ #2187 #2182)
-#2183 := (~ #1391 #2182)
-#2184 := [sk]: #2183
-#2189 := [nnf-neg #2184]: #2188
-#2171 := (~ #732 #732)
-#2172 := [refl]: #2171
-#2169 := (~ #2168 #2168)
-#2170 := [refl]: #2169
-#2419 := [nnf-neg #2170 #2172 #2189 #2196 #2399 #2406 #2413 #2415]: #2418
-#2165 := (not #1409)
-#2166 := (~ #2165 #2164)
-#2162 := (~ #1632 #2161)
-#2159 := (~ #2158 #2158)
-#2160 := [refl]: #2159
-#2163 := [nnf-neg #2160]: #2162
-#2155 := (not #1380)
-#2156 := (~ #2155 #2154)
-#2151 := (not #1377)
-#2152 := (~ #2151 #2150)
-#2147 := (not #1374)
-#2148 := (~ #2147 #2146)
-#2143 := (not #1369)
-#2144 := (~ #2143 #2142)
-#2139 := (not #1361)
-#2140 := (~ #2139 #1358)
-#2137 := (~ #1358 #1358)
-#2135 := (~ #1355 #1355)
-#2136 := [refl]: #2135
-#2138 := [nnf-pos #2136]: #2137
-#2141 := [nnf-neg #2138]: #2140
-#2133 := (~ #2132 #2132)
-#2134 := [refl]: #2133
-#2145 := [nnf-neg #2134 #2141]: #2144
-#2128 := (~ #1361 #2127)
-#2129 := [sk]: #2128
-#2149 := [nnf-neg #2129 #2145]: #2148
-#2103 := (not #1343)
-#2104 := (~ #2103 #2100)
-#2101 := (~ #1340 #2100)
-#2098 := (~ #1337 #2097)
-#2093 := (~ #1334 #2092)
-#2094 := [sk]: #2093
-#2081 := (~ #1318 #1318)
-#2082 := [refl]: #2081
-#2099 := [monotonicity #2082 #2094]: #2098
-#2102 := [nnf-pos #2099]: #2101
-#2105 := [nnf-neg #2102]: #2104
-#2153 := [nnf-neg #2105 #2149]: #2152
-#2079 := (~ #1343 #2076)
-#2054 := (exists (vars (?v1 S2)) #2053)
-#2062 := (or #2061 #2054)
-#2063 := (not #2062)
-#2077 := (~ #2063 #2076)
-#2073 := (not #2054)
-#2074 := (~ #2073 #2072)
-#2070 := (~ #2069 #2069)
-#2071 := [refl]: #2070
-#2075 := [nnf-neg #2071]: #2074
-#2067 := (~ #2066 #2066)
-#2068 := [refl]: #2067
-#2078 := [nnf-neg #2068 #2075]: #2077
-#2064 := (~ #1343 #2063)
-#2065 := [sk]: #2064
-#2080 := [trans #2065 #2078]: #2079
-#2157 := [nnf-neg #2080 #2153]: #2156
-#2041 := (~ #2040 #2040)
-#2042 := [refl]: #2041
-#2038 := (~ #2037 #2037)
-#2039 := [refl]: #2038
-#2035 := (~ #2034 #2034)
-#2036 := [refl]: #2035
-#2032 := (~ #2031 #2031)
-#2033 := [refl]: #2032
-#2167 := [nnf-neg #2033 #2036 #2039 #2042 #2157 #2163]: #2166
-#2423 := [nnf-neg #2167 #2419]: #2422
-#2028 := (not #1306)
-#2029 := (~ #2028 #2025)
-#2026 := (~ #1303 #2025)
-#2023 := (~ #1300 #2022)
-#2018 := (~ #1297 #2017)
-#2019 := [sk]: #2018
-#2004 := (~ #1273 #1273)
-#2005 := [refl]: #2004
-#2024 := [monotonicity #2005 #2019]: #2023
-#2027 := [nnf-pos #2024]: #2026
-#2030 := [nnf-neg #2027]: #2029
-#2001 := (not #1717)
-#2002 := (~ #2001 #1998)
-#1999 := (~ #1261 #1998)
-#1996 := (~ #1258 #1995)
-#1991 := (~ #1255 #1990)
-#1992 := [sk]: #1991
-#1976 := (~ #1235 #1235)
-#1977 := [refl]: #1976
-#1997 := [monotonicity #1977 #1992]: #1996
-#2000 := [nnf-pos #1997]: #1999
-#2003 := [nnf-neg #2000]: #2002
-#1974 := (~ #1973 #1973)
-#1975 := [refl]: #1974
-#2448 := [nnf-neg #1975 #2003 #2030 #2423 #2430 #2437 #2444]: #2447
-#1971 := (~ #1717 #1968)
-#1946 := (exists (vars (?v1 S2)) #1945)
-#1954 := (or #1953 #1946)
-#1955 := (not #1954)
-#1969 := (~ #1955 #1968)
-#1965 := (not #1946)
-#1966 := (~ #1965 #1964)
-#1962 := (~ #1961 #1961)
-#1963 := [refl]: #1962
-#1967 := [nnf-neg #1963]: #1966
-#1959 := (~ #1958 #1958)
-#1960 := [refl]: #1959
-#1970 := [nnf-neg #1960 #1967]: #1969
-#1956 := (~ #1717 #1955)
-#1957 := [sk]: #1956
-#1972 := [trans #1957 #1970]: #1971
-#2452 := [nnf-neg #1972 #2448]: #2451
-#1931 := (not #1223)
-#1932 := (~ #1931 #1220)
-#1929 := (~ #1220 #1220)
-#1927 := (~ #1217 #1217)
-#1928 := [refl]: #1927
-#1930 := [nnf-pos #1928]: #1929
-#1933 := [nnf-neg #1930]: #1932
-#2456 := [nnf-neg #1933 #2452]: #2455
-#1923 := (~ #1223 #1922)
-#1924 := [sk]: #1923
-#2460 := [nnf-neg #1924 #2456]: #2459
-#1900 := (not #1192)
-#1901 := (~ #1900 #1189)
-#1898 := (~ #1189 #1189)
-#1896 := (~ #1184 #1184)
-#1897 := [refl]: #1896
-#1899 := [nnf-pos #1897]: #1898
-#1902 := [nnf-neg #1899]: #1901
-#2464 := [nnf-neg #1902 #2460]: #2463
-#1892 := (~ #1192 #1891)
-#1893 := [sk]: #1892
-#2468 := [nnf-neg #1893 #2464]: #2467
-#1873 := (not #1172)
-#1874 := (~ #1873 #1169)
-#1871 := (~ #1169 #1169)
-#1869 := (~ #1168 #1168)
-#1870 := [refl]: #1869
-#1872 := [nnf-pos #1870]: #1871
-#1875 := [nnf-neg #1872]: #1874
-#2472 := [nnf-neg #1875 #2468]: #2471
-#1865 := (~ #1172 #1864)
-#1866 := [sk]: #1865
-#2476 := [nnf-neg #1866 #2472]: #2475
-#1828 := (~ #1827 #1827)
-#1860 := [refl]: #1828
-#2480 := [nnf-neg #1860 #2476]: #2479
-#1858 := (~ #1163 #1163)
-#1859 := [refl]: #1858
-#2483 := [nnf-neg #1859 #2480]: #2482
-#1804 := [not-or-elim #1800]: #1803
-#2484 := [mp~ #1804 #2483]: #2481
-#2485 := [mp #2484 #3022]: #3020
-#3664 := [mp #2485 #3663]: #3661
-#4571 := [mp #3664 #4570]: #4568
-#6438 := [unit-resolution #4571 #5593]: #4565
-#3910 := (or #4562 #4556)
-#3911 := [def-axiom]: #3910
-#6439 := [unit-resolution #3911 #6438]: #4556
-#3905 := (or #4559 #1864 #4553)
-#3906 := [def-axiom]: #3905
-#6440 := [unit-resolution #3906 #6439 #5496]: #4553
-#3929 := (or #4550 #4544)
-#3930 := [def-axiom]: #3929
-#6441 := [unit-resolution #3930 #6440]: #4544
-#6443 := (or #4547 #4541)
-#5503 := [hypothesis]: #1884
-#4193 := (forall (vars (?v0 S2)) (:pat #4192) #432)
-#4196 := (iff #435 #4193)
-#4194 := (iff #432 #432)
-#4195 := [refl]: #4194
-#4197 := [quant-intro #4195]: #4196
-#1825 := (~ #435 #435)
-#1855 := (~ #432 #432)
-#1856 := [refl]: #1855
-#1826 := [nnf-pos #1856]: #1825
-#1802 := [not-or-elim #1800]: #435
-#1857 := [mp~ #1802 #1826]: #435
-#4198 := [mp #1857 #4197]: #4193
-#5505 := (not #4193)
-#5506 := (or #5505 #2131)
-#5507 := [quant-inst #1877]: #5506
-#5504 := [unit-resolution #5507 #4198 #5503]: false
-#5508 := [lemma #5504]: #2131
-#3722 := (or #2304 #1884)
-#3809 := [def-axiom]: #3722
-#6442 := [unit-resolution #3809 #5508]: #2304
-#3923 := (or #4547 #2021 #4541)
-#3925 := [def-axiom]: #3923
-#6444 := [unit-resolution #3925 #6442]: #6443
-#6445 := [unit-resolution #6444 #6441]: #4541
-#3950 := (or #4538 #4532)
-#3951 := [def-axiom]: #3950
-#6446 := [unit-resolution #3951 #6445]: #4532
-#5865 := [hypothesis]: #1912
-#5721 := (or #5505 #3045)
-#5722 := [quant-inst #1903]: #5721
-#5866 := [unit-resolution #5722 #4198 #5865]: false
-#5874 := [lemma #5866]: #3045
-#3812 := (or #3060 #1912)
-#3816 := [def-axiom]: #3812
-#6447 := [unit-resolution #3816 #5874]: #3060
-#3946 := (or #4535 #3065 #4529)
-#3947 := [def-axiom]: #3946
-#6448 := [unit-resolution #3947 #6447 #6446]: #4529
-#3960 := (or #4526 #4520)
-#3981 := [def-axiom]: #3960
-#6449 := [unit-resolution #3981 #6448]: #4520
-#3968 := (or #4523 #4237 #4517)
-#3969 := [def-axiom]: #3968
-#6450 := [unit-resolution #3969 #6449 #5741]: #4517
-#5134 := (or #4514 #4505)
-#4689 := (?v1!7 ?v0!8)
-#4690 := (f13 f14 #4689)
-#4672 := (* -1::Int #4690)
-#4622 := (f13 f14 ?v0!8)
-#4673 := (+ #4622 #4672)
-#4674 := (<= #4673 0::Int)
-#5029 := [hypothesis]: #4502
-#5035 := [hypothesis]: #4517
-#3990 := (or #4514 #4508)
-#3958 := [def-axiom]: #3990
-#5036 := [unit-resolution #3958 #5035]: #4508
-#3995 := (or #4511 #4350 #4505)
-#3996 := [def-axiom]: #3995
-#5037 := [unit-resolution #3996 #5036 #5029]: #4350
-#4103 := (or #4347 #4341)
-#4100 := [def-axiom]: #4103
-#5038 := [unit-resolution #4100 #5037]: #4341
-#3999 := (or #4514 #100)
-#4000 := [def-axiom]: #3999
-#5039 := [unit-resolution #4000 #5035]: #100
-#5079 := (= #157 #99)
-#4101 := (or #4347 #599)
-#4102 := [def-axiom]: #4101
-#5054 := [unit-resolution #4102 #5037]: #599
-#5055 := [symm #5054]: #138
-#5080 := [monotonicity #5055]: #5079
-#5081 := [trans #5080 #5039]: #158
-#4113 := (or #4323 #2132)
-#3776 := [def-axiom]: #4113
-#5082 := [unit-resolution #3776 #5081]: #4323
-#4002 := (or #4514 #4249)
-#3982 := [def-axiom]: #4002
-#5083 := [unit-resolution #3982 #5035]: #4249
-#3817 := (or #4347 #4283)
-#4099 := [def-axiom]: #3817
-#5078 := [unit-resolution #4099 #5037]: #4283
-#4919 := (or #3328 #4288 #4254 #690)
-#4892 := [hypothesis]: #3333
-#4116 := (or #3328 #2119)
-#4117 := [def-axiom]: #4116
-#4893 := [unit-resolution #4117 #4892]: #2119
-#4691 := (f13 f14 ?v1!10)
-#4692 := (* -1::Int #4691)
-#4693 := (+ f3 #4692)
-#4694 := (<= #4693 0::Int)
-#4695 := (f8 f15 ?v1!10)
-#4696 := (= f1 #4695)
-#4767 := (not #4696)
-#3804 := (f13 f14 ?v0!11)
-#3805 := (* -1::Int #3804)
-#4769 := (+ #3805 #4691)
-#4770 := (+ #2113 #4769)
-#4773 := (>= #4770 0::Int)
-#4902 := (not #4773)
-#4876 := (+ #2110 #4692)
-#4878 := (>= #4876 0::Int)
-#4875 := (= #2110 #4691)
-#4880 := (= #4691 #2110)
-#4879 := [hypothesis]: #599
-#4881 := [monotonicity #4879]: #4880
-#4882 := [symm #4881]: #4875
-#4883 := (not #4875)
-#4884 := (or #4883 #4878)
-#4885 := [th-lemma arith triangle-eq]: #4884
-#4886 := [unit-resolution #4885 #4882]: #4878
-#4114 := (not #2774)
-#4120 := (or #3328 #4114)
-#3758 := [def-axiom]: #4120
-#4887 := [unit-resolution #3758 #4892]: #4114
-#4865 := (+ #2108 #3805)
-#4873 := (<= #4865 0::Int)
-#4864 := (= #2108 #3804)
-#4890 := (= #3804 #2108)
-#4891 := [monotonicity #4879]: #4890
-#4894 := [symm #4891]: #4864
-#4895 := (not #4864)
-#4896 := (or #4895 #4873)
-#4907 := [th-lemma arith triangle-eq]: #4896
-#4908 := [unit-resolution #4907 #4894]: #4873
-#4904 := (not #4878)
-#4903 := (not #4873)
-#4905 := (or #4902 #4903 #2774 #4904)
-#4897 := [hypothesis]: #4878
-#4898 := [hypothesis]: #4114
-#4899 := [hypothesis]: #4873
-#4900 := [hypothesis]: #4773
-#4901 := [th-lemma arith farkas 1 -1 1 1 #4900 #4899 #4898 #4897]: false
-#4906 := [lemma #4901]: #4905
-#4909 := [unit-resolution #4906 #4908 #4887 #4886]: #4902
-#4912 := (or #4767 #4773)
-#4118 := (or #3328 #2123)
-#4119 := [def-axiom]: #4118
-#4910 := [unit-resolution #4119 #4892]: #2123
-#4911 := [hypothesis]: #4249
-#4784 := (or #4254 #2122 #4767 #4773)
-#4762 := (+ #4691 #3805)
-#4763 := (+ #2113 #4762)
-#4766 := (>= #4763 0::Int)
-#4768 := (or #4767 #2122 #4766)
-#4785 := (or #4254 #4768)
-#4792 := (iff #4785 #4784)
-#4779 := (or #2122 #4767 #4773)
-#4787 := (or #4254 #4779)
-#4790 := (iff #4787 #4784)
-#4791 := [rewrite]: #4790
-#4788 := (iff #4785 #4787)
-#4782 := (iff #4768 #4779)
-#4776 := (or #4767 #2122 #4773)
-#4780 := (iff #4776 #4779)
-#4781 := [rewrite]: #4780
-#4777 := (iff #4768 #4776)
-#4774 := (iff #4766 #4773)
-#4771 := (= #4763 #4770)
-#4772 := [rewrite]: #4771
-#4775 := [monotonicity #4772]: #4774
-#4778 := [monotonicity #4775]: #4777
-#4783 := [trans #4778 #4781]: #4782
-#4789 := [monotonicity #4783]: #4788
-#4793 := [trans #4789 #4791]: #4792
-#4786 := [quant-inst #2107 #2106]: #4785
-#4794 := [mp #4786 #4793]: #4784
-#4913 := [unit-resolution #4794 #4911 #4910]: #4912
-#4914 := [unit-resolution #4913 #4909]: #4767
-#4698 := (or #4694 #4696)
-#4915 := [hypothesis]: #4283
-#4701 := (or #4288 #4694 #4696)
-#4697 := (or #4696 #4694)
-#4702 := (or #4288 #4697)
-#4709 := (iff #4702 #4701)
-#4704 := (or #4288 #4698)
-#4707 := (iff #4704 #4701)
-#4708 := [rewrite]: #4707
-#4705 := (iff #4702 #4704)
-#4699 := (iff #4697 #4698)
-#4700 := [rewrite]: #4699
-#4706 := [monotonicity #4700]: #4705
-#4710 := [trans #4706 #4708]: #4709
-#4703 := [quant-inst #2106]: #4702
-#4711 := [mp #4703 #4710]: #4701
-#4916 := [unit-resolution #4711 #4915]: #4698
-#4917 := [unit-resolution #4916 #4914]: #4694
-#4918 := [th-lemma arith farkas 1 -1 1 #4886 #4917 #4893]: false
-#4920 := [lemma #4918]: #4919
-#5084 := [unit-resolution #4920 #5078 #5083 #5054]: #3328
-#4125 := (or #4332 #4326 #3333)
-#4111 := [def-axiom]: #4125
-#5085 := [unit-resolution #4111 #5084 #5082]: #4332
-#3835 := (or #4335 #4329)
-#3836 := [def-axiom]: #3835
-#5086 := [unit-resolution #3836 #5085]: #4335
-#4105 := (or #4344 #4304 #4338)
-#4109 := [def-axiom]: #4105
-#5087 := [unit-resolution #4109 #5086 #5038]: #4304
-#4137 := (or #4301 #2057)
-#4127 := [def-axiom]: #4137
-#5088 := [unit-resolution #4127 #5087]: #2057
-#4128 := (or #4301 #4293)
-#3788 := [def-axiom]: #4128
-#5115 := [unit-resolution #3788 #5087]: #4293
-#3787 := (or #4301 #2674)
-#3792 := [def-axiom]: #3787
-#5116 := [unit-resolution #3792 #5087]: #2674
-#3989 := (or #4514 #4274)
-#3984 := [def-axiom]: #3989
-#5117 := [unit-resolution #3984 #5035]: #4274
-#5033 := (or #4674 #4279 #2671 #4298 #690 #2056)
-#4675 := (f5 #4689 ?v0!8)
-#4676 := (f4 #4675)
-#4671 := (* -1::Int #4676)
-#4757 := (+ #4671 #4672)
-#4758 := (+ #4622 #4757)
-#4740 := (= #4758 0::Int)
-#4743 := (not #4740)
-#5676 := [hypothesis]: #4293
-#4852 := (not #4674)
-#5671 := [hypothesis]: #4852
-#5684 := (or #4743 #4298 #4674 #690)
-#4938 := (f13 f19 #4689)
-#4951 := (* -1::Int #4938)
-#4965 := (+ #4671 #4951)
-#4966 := (+ #2044 #4965)
-#4990 := (>= #4966 0::Int)
-#5185 := (+ #4690 #4951)
-#5187 := (>= #5185 0::Int)
-#5184 := (= #4690 #4938)
-#5634 := (= #4938 #4690)
-#5633 := [symm #4879]: #138
-#5635 := [monotonicity #5633]: #5634
-#5636 := [symm #5635]: #5184
-#5637 := (not #5184)
-#5638 := (or #5637 #5187)
-#5639 := [th-lemma arith triangle-eq]: #5638
-#5640 := [unit-resolution #5639 #5636]: #5187
-#4623 := (* -1::Int #4622)
-#4934 := (+ #2044 #4623)
-#4936 := (>= #4934 0::Int)
-#4933 := (= #2044 #4622)
-#5641 := (= #4622 #2044)
-#5642 := [monotonicity #4879]: #5641
-#5643 := [symm #5642]: #4933
-#5644 := (not #4933)
-#5645 := (or #5644 #4936)
-#5646 := [th-lemma arith triangle-eq]: #5645
-#5647 := [unit-resolution #5646 #5643]: #4936
-#4851 := (>= #4758 0::Int)
-#5648 := [hypothesis]: #4740
-#5649 := (or #4743 #4851)
-#5650 := [th-lemma arith triangle-eq]: #5649
-#5651 := [unit-resolution #5650 #5648]: #4851
-#5652 := (not #5187)
-#5405 := (not #4936)
-#5403 := (not #4851)
-#5653 := (or #4990 #5403 #5405 #5652)
-#5654 := [th-lemma arith assign-bounds -1 -1 -1]: #5653
-#5655 := [unit-resolution #5654 #5651 #5647 #5640]: #4990
-#4989 := (<= #4966 0::Int)
-#5186 := (<= #5185 0::Int)
-#5656 := (or #5637 #5186)
-#5657 := [th-lemma arith triangle-eq]: #5656
-#5658 := [unit-resolution #5657 #5636]: #5186
-#4935 := (<= #4934 0::Int)
-#5659 := (or #5644 #4935)
-#5660 := [th-lemma arith triangle-eq]: #5659
-#5661 := [unit-resolution #5660 #5643]: #4935
-#4850 := (<= #4758 0::Int)
-#5662 := (or #4743 #4850)
-#5663 := [th-lemma arith triangle-eq]: #5662
-#5664 := [unit-resolution #5663 #5648]: #4850
-#5667 := (not #5186)
-#5666 := (not #4935)
-#5665 := (not #4850)
-#5668 := (or #4989 #5665 #5666 #5667)
-#5669 := [th-lemma arith assign-bounds -1 -1 -1]: #5668
-#5670 := [unit-resolution #5669 #5664 #5661 #5658]: #4989
-#4967 := (= #4966 0::Int)
-#4972 := (not #4967)
-#4952 := (+ #2044 #4951)
-#4953 := (<= #4952 0::Int)
-#5672 := (not #4953)
-#5673 := (or #5672 #5405 #4674 #5652)
-#5674 := [th-lemma arith assign-bounds -1 -1 -1]: #5673
-#5675 := [unit-resolution #5674 #5640 #5671 #5647]: #5672
-#4975 := (or #4953 #4972)
-#4978 := (or #4298 #4953 #4972)
-#4937 := (+ #2045 #4676)
-#4939 := (+ #4938 #4937)
-#4940 := (= #4939 0::Int)
-#4941 := (not #4940)
-#4942 := (+ #4938 #2045)
-#4943 := (>= #4942 0::Int)
-#4944 := (or #4943 #4941)
-#4979 := (or #4298 #4944)
-#4986 := (iff #4979 #4978)
-#4981 := (or #4298 #4975)
-#4984 := (iff #4981 #4978)
-#4985 := [rewrite]: #4984
-#4982 := (iff #4979 #4981)
-#4976 := (iff #4944 #4975)
-#4973 := (iff #4941 #4972)
-#4970 := (iff #4940 #4967)
-#4958 := (+ #4676 #4938)
-#4959 := (+ #2045 #4958)
-#4962 := (= #4959 0::Int)
-#4968 := (iff #4962 #4967)
-#4969 := [rewrite]: #4968
-#4963 := (iff #4940 #4962)
-#4960 := (= #4939 #4959)
-#4961 := [rewrite]: #4960
-#4964 := [monotonicity #4961]: #4963
-#4971 := [trans #4964 #4969]: #4970
-#4974 := [monotonicity #4971]: #4973
-#4956 := (iff #4943 #4953)
-#4945 := (+ #2045 #4938)
-#4948 := (>= #4945 0::Int)
-#4954 := (iff #4948 #4953)
-#4955 := [rewrite]: #4954
-#4949 := (iff #4943 #4948)
-#4946 := (= #4942 #4945)
-#4947 := [rewrite]: #4946
-#4950 := [monotonicity #4947]: #4949
-#4957 := [trans #4950 #4955]: #4956
-#4977 := [monotonicity #4957 #4974]: #4976
-#4983 := [monotonicity #4977]: #4982
-#4987 := [trans #4983 #4985]: #4986
-#4980 := [quant-inst #4689]: #4979
-#4988 := [mp #4980 #4987]: #4978
-#5677 := [unit-resolution #4988 #5676]: #4975
-#5678 := [unit-resolution #5677 #5675]: #4972
-#5680 := (not #4990)
-#5679 := (not #4989)
-#5681 := (or #4967 #5679 #5680)
-#5682 := [th-lemma arith triangle-eq]: #5681
-#5683 := [unit-resolution #5682 #5678 #5670 #5655]: false
-#5685 := [lemma #5683]: #5684
-#5043 := [unit-resolution #5685 #5671 #5676 #4879]: #4743
-#4681 := (f8 f15 #4689)
-#4752 := (= f1 #4681)
-#4753 := (not #4752)
-#4748 := (or #4674 #4743 #4753)
-#4822 := (not #4748)
-#4624 := (+ f3 #4623)
-#4604 := (<= #4624 0::Int)
-#5044 := (not #4604)
-#5298 := [hypothesis]: #2057
-#5045 := (or #5044 #2056 #5405)
-#5046 := [th-lemma arith assign-bounds -1 -1]: #5045
-#5047 := [unit-resolution #5046 #5298 #5647]: #5044
-#5050 := (or #4604 #4822)
-#5048 := [hypothesis]: #2674
-#5049 := [hypothesis]: #4274
-#4827 := (or #4279 #2671 #4604 #4822)
-#4677 := (+ #4672 #4671)
-#4678 := (+ #4622 #4677)
-#4679 := (= #4678 0::Int)
-#4680 := (not #4679)
-#4754 := (or #4753 #4680 #4674)
-#4755 := (not #4754)
-#4756 := (or #2058 #4604 #4755)
-#4828 := (or #4279 #4756)
-#4841 := (iff #4828 #4827)
-#4825 := (or #2671 #4604 #4822)
-#4830 := (or #4279 #4825)
-#4837 := (iff #4830 #4827)
-#4840 := [rewrite]: #4837
-#4835 := (iff #4828 #4830)
-#4820 := (iff #4756 #4825)
-#4823 := (iff #4755 #4822)
-#4765 := (iff #4754 #4748)
-#4745 := (or #4753 #4743 #4674)
-#4749 := (iff #4745 #4748)
-#4764 := [rewrite]: #4749
-#4746 := (iff #4754 #4745)
-#4744 := (iff #4680 #4743)
-#4741 := (iff #4679 #4740)
-#4759 := (= #4678 #4758)
-#4760 := [rewrite]: #4759
-#4742 := [monotonicity #4760]: #4741
-#4739 := [monotonicity #4742]: #4744
-#4747 := [monotonicity #4739]: #4746
-#4821 := [trans #4747 #4764]: #4765
-#4824 := [monotonicity #4821]: #4823
-#4826 := [monotonicity #2673 #4824]: #4820
-#4836 := [monotonicity #4826]: #4835
-#4842 := [trans #4836 #4840]: #4841
-#4829 := [quant-inst #2043]: #4828
-#4848 := [mp #4829 #4842]: #4827
-#5030 := [unit-resolution #4848 #5049 #5048]: #5050
-#5031 := [unit-resolution #5030 #5047]: #4822
-#4849 := (or #4748 #4740)
-#4855 := [def-axiom]: #4849
-#5032 := [unit-resolution #4855 #5031 #5043]: false
-#5034 := [lemma #5032]: #5033
-#5118 := [unit-resolution #5034 #5117 #5116 #5115 #5054 #5088]: #4674
-#5119 := [monotonicity #5054]: #5641
-#5114 := [symm #5119]: #4933
-#5120 := [unit-resolution #5646 #5114]: #4936
-#5121 := [unit-resolution #5046 #5088 #5120]: #5044
-#5122 := [unit-resolution #4848 #5117 #5116]: #5050
-#5123 := [unit-resolution #5122 #5121]: #4822
-#4853 := (or #4748 #4852)
-#4854 := [def-axiom]: #4853
-#5124 := [unit-resolution #4854 #5123 #5118]: false
-#5135 := [lemma #5124]: #5134
-#6451 := [unit-resolution #5135 #6450]: #4505
-#4018 := (or #4502 #181)
-#4019 := [def-axiom]: #4018
-#8689 := [unit-resolution #4019 #6451]: #181
-#8696 := [symm #8689]: #8695
-#8693 := (= #7238 #180)
-#8691 := (= #5830 f1)
+#269 := (implies #61 #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)
+#772 := (forall (vars (?v0 S2)) #767)
+#945 := (not #772)
+#946 := (or #945 #939)
+#747 := (= #186 #189)
+#753 := (or #193 #747)
+#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)
+#1493 := (iff #1489 #1492)
+#1494 := [rewrite]: #1493
+#1490 := (iff #816 #1489)
+#1205 := (iff #84 #1204)
+#1206 := [rewrite]: #1205
+#1491 := [monotonicity #1206]: #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)
+#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
+#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)
+#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)
+#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)
+#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)
+#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)
+#768 := (iff #764 #767)
+#769 := [rewrite]: #768
+#765 := (iff #195 #764)
+#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)
+#754 := (iff #750 #753)
+#755 := [rewrite]: #754
+#751 := (iff #191 #750)
+#748 := (iff #190 #747)
+#749 := [rewrite]: #748
+#752 := [monotonicity #749]: #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)
+#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)
+#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)
+#423 := (iff #419 #422)
+#424 := [rewrite]: #423
+#420 := (iff #64 #419)
+#417 := (iff #63 #416)
+#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)
+#4560 := (not #4557)
+#4563 := (or #1164 #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)
+#4564 := (iff #3656 #4563)
+#4561 := (iff #3655 #4560)
+#4558 := (iff #3649 #4557)
+#4555 := (iff #3644 #4554)
+#4552 := (iff #3643 #4551)
+#4549 := (iff #3642 #4548)
+#4546 := (iff #3636 #4545)
+#4543 := (iff #3631 #4542)
+#4540 := (iff #3630 #4539)
+#4537 := (iff #3629 #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)
+#4492 := (iff #3570 #4491)
+#4489 := (iff #3569 #4488)
+#4486 := (iff #3563 #4485)
+#4483 := (iff #3558 #4482)
+#4480 := (iff #3557 #4479)
+#4477 := (iff #3556 #4476)
+#4474 := (iff #3550 #4473)
+#4471 := (iff #3545 #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)
+#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
+#4448 := [monotonicity #4445]: #4447
+#4451 := [monotonicity #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
+#4460 := [monotonicity #4457]: #4459
+#4463 := [monotonicity #4460]: #4462
+#4466 := [monotonicity #4463]: #4465
+#4469 := [monotonicity #4466]: #4468
+#4472 := [monotonicity #4469]: #4471
+#4475 := [monotonicity #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
+#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
+#4496 := [monotonicity #4493]: #4495
+#4499 := [monotonicity #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
+#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
+#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
+#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
+#4544 := [monotonicity #4541]: #4543
+#4547 := [monotonicity #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
+#4556 := [monotonicity #4553]: #4555
+#4559 := [monotonicity #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)
+#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)
+#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
+#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)
+#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)
+#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)
+#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)
+#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)
+#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)
+#2958 := (iff #2373 #2957)
+#2955 := (iff #2369 #2954)
+#2952 := (iff #2365 #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
+#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)
+#2905 := [rewrite]: #2904
+#2901 := (iff #2331 #2900)
+#2898 := (iff #2330 #2897)
+#2895 := (iff #2329 #2894)
+#2896 := [rewrite]: #2895
+#2899 := [monotonicity #2896]: #2898
+#2902 := [monotonicity #2899]: #2901
+#2907 := [trans #2902 #2905]: #2906
+#2910 := [monotonicity #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
+#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
+#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
+#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)
+#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)
+#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
+#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
+#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)
+#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)
+#2480 := (~ #2479 #2478)
+#2475 := (not #1762)
+#2476 := (~ #2475 #2474)
+#2471 := (not #1759)
+#2472 := (~ #2471 #2470)
+#2467 := (not #1756)
+#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)
+#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)
+#2399 := (~ #2398 #2397)
+#2394 := (not #1580)
+#2395 := (~ #2394 #2393)
+#2390 := (not #1577)
+#2391 := (~ #2390 #2389)
+#2386 := (not #1574)
+#2387 := (~ #2386 #2385)
+#2382 := (not #1571)
+#2383 := (~ #2382 #2381)
+#2378 := (not #1568)
+#2379 := (~ #2378 #2377)
+#2374 := (not #1565)
+#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)
+#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
+#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)
+#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)
-#4171 := (pattern #37)
-#370 := (= f1 #36)
+#4172 := (pattern #37)
+#371 := (= f1 #36)
 #38 := (f8 #37 #11)
-#366 := (= f1 #38)
-#373 := (iff #366 #370)
-#4172 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) (:pat #4171) #373)
-#376 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) #373)
-#4175 := (iff #376 #4172)
-#4173 := (iff #373 #373)
-#4174 := [refl]: #4173
-#4176 := [quant-intro #4174]: #4175
-#1819 := (~ #376 #376)
-#1846 := (~ #373 #373)
-#1847 := [refl]: #1846
-#1820 := [nnf-pos #1847]: #1819
+#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)
-#377 := (iff #42 #376)
-#374 := (iff #41 #373)
-#371 := (iff #40 #370)
-#372 := [rewrite]: #371
-#368 := (iff #39 #366)
-#369 := [rewrite]: #368
-#375 := [monotonicity #369 #372]: #374
-#378 := [quant-intro #375]: #377
-#365 := [asserted]: #42
-#381 := [mp #365 #378]: #376
-#1848 := [mp~ #381 #1820]: #376
-#4177 := [mp #1848 #4176]: #4172
-#5855 := (not #4172)
-#5850 := (or #5855 #5831)
-#5829 := (= f1 f1)
-#5837 := (iff #5831 #5829)
-#5856 := (or #5855 #5837)
-#5858 := (iff #5856 #5850)
-#5860 := (iff #5850 #5850)
-#5867 := [rewrite]: #5860
-#5853 := (iff #5837 #5831)
-#5842 := (iff #5831 true)
-#5851 := (iff #5842 #5831)
-#5852 := [rewrite]: #5851
-#5843 := (iff #5837 #5842)
-#5838 := (iff #5829 true)
-#5841 := [rewrite]: #5838
-#5849 := [monotonicity #5841]: #5843
-#5854 := [trans #5849 #5852]: #5853
-#5859 := [monotonicity #5854]: #5858
-#5869 := [trans #5859 #5867]: #5858
-#5857 := [quant-inst #104 #170 #4]: #5856
-#5870 := [mp #5857 #5869]: #5850
-#8690 := [unit-resolution #5870 #4177]: #5831
-#8692 := [symm #8690]: #8691
-#7564 := (= #6386 f22)
-#6387 := (= f22 #6386)
-#14 := (f5 #11 #12)
-#4138 := (pattern #14)
-#23 := (f6 #14)
-#343 := (= #11 #23)
-#4151 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4138) #343)
-#346 := (forall (vars (?v0 S2) (?v1 S2)) #343)
-#4154 := (iff #346 #4151)
-#4152 := (iff #343 #343)
-#4153 := [refl]: #4152
-#4155 := [quant-intro #4153]: #4154
-#1813 := (~ #346 #346)
-#1837 := (~ #343 #343)
-#1838 := [refl]: #1837
-#1814 := [nnf-pos #1838]: #1813
-#24 := (= #23 #11)
-#25 := (forall (vars (?v0 S2) (?v1 S2)) #24)
-#347 := (iff #25 #346)
-#344 := (iff #24 #343)
-#345 := [rewrite]: #344
-#348 := [quant-intro #345]: #347
-#342 := [asserted]: #25
-#351 := [mp #342 #348]: #346
-#1839 := [mp~ #351 #1814]: #346
-#4156 := [mp #1839 #4155]: #4151
-#6389 := (not #4151)
-#6571 := (or #6389 #6387)
-#6572 := [quant-inst #170 #56]: #6571
-#7563 := [unit-resolution #6572 #4156]: #6387
-#7565 := [symm #7563]: #7564
-#8694 := [monotonicity #7565 #8692]: #8693
-#8698 := [trans #8694 #8696]: #8697
-#23017 := [monotonicity #8698]: #23000
-#23006 := [monotonicity #23017]: #23020
-#22998 := [symm #23006]: #22987
-#23007 := [monotonicity #22998]: #22994
-#19081 := (f24 #14273)
-#19098 := (* -1::Int #19081)
-#14278 := (f5 #14273 ?v0!20)
-#14279 := (f4 #14278)
-#14280 := (* -1::Int #14279)
-#19309 := (+ #14280 #19098)
-#19310 := (+ #2314 #19309)
-#19311 := (= #19310 0::Int)
-#10493 := (>= #19310 0::Int)
-#14274 := (f13 f14 #14273)
-#19099 := (+ #14274 #19098)
-#19100 := (>= #19099 0::Int)
-#3986 := (or #4502 #4496)
-#3987 := [def-axiom]: #3986
-#8746 := [unit-resolution #3987 #6451]: #4496
-#6803 := (f5 f22 ?v0!13)
-#6804 := (f4 #6803)
-#6829 := (+ #2199 #6804)
-#6830 := (+ #174 #6829)
-#6851 := (>= #6830 0::Int)
-#6833 := (= #6830 0::Int)
-#6808 := (* -1::Int #6804)
-#6812 := (+ f3 #6808)
-#6813 := (<= #6812 0::Int)
-#6880 := (not #6813)
-#6822 := (+ #2815 #6804)
-#6823 := (+ #174 #6822)
-#6824 := (>= #6823 0::Int)
-#6859 := (or #6813 #6824)
-#6862 := (not #6859)
-#6856 := (= #2198 #2200)
-#6981 := (not #6856)
-#6980 := [hypothesis]: #2822
-#6984 := (or #6981 #2817)
-#6985 := [th-lemma arith triangle-eq]: #6984
-#6986 := [unit-resolution #6985 #6980]: #6981
-#4011 := (or #4502 #4363)
-#4006 := [def-axiom]: #4011
-#6477 := [unit-resolution #4006 #6451]: #4363
-#6868 := (or #4368 #6856 #6862)
-#6809 := (+ #1420 #6808)
-#6810 := (+ #2200 #6809)
-#6811 := (<= #6810 0::Int)
-#6852 := (or #6813 #6811)
-#6853 := (not #6852)
-#6854 := (= #2200 #2198)
-#6855 := (or #6854 #6853)
-#6869 := (or #4368 #6855)
-#6876 := (iff #6869 #6868)
-#6865 := (or #6856 #6862)
-#6871 := (or #4368 #6865)
-#6874 := (iff #6871 #6868)
-#6875 := [rewrite]: #6874
-#6872 := (iff #6869 #6871)
-#6866 := (iff #6855 #6865)
-#6863 := (iff #6853 #6862)
-#6860 := (iff #6852 #6859)
-#6827 := (iff #6811 #6824)
-#6815 := (+ #2200 #6808)
-#6816 := (+ #1420 #6815)
-#6819 := (<= #6816 0::Int)
-#6825 := (iff #6819 #6824)
-#6826 := [rewrite]: #6825
-#6820 := (iff #6811 #6819)
-#6817 := (= #6810 #6816)
-#6818 := [rewrite]: #6817
-#6821 := [monotonicity #6818]: #6820
-#6828 := [trans #6821 #6826]: #6827
-#6861 := [monotonicity #6828]: #6860
-#6864 := [monotonicity #6861]: #6863
-#6857 := (iff #6854 #6856)
-#6858 := [rewrite]: #6857
-#6867 := [monotonicity #6858 #6864]: #6866
-#6873 := [monotonicity #6867]: #6872
-#6877 := [trans #6873 #6875]: #6876
-#6870 := [quant-inst #2197]: #6869
-#6878 := [mp #6870 #6877]: #6868
-#6987 := [unit-resolution #6878 #6477 #6986]: #6862
-#6881 := (or #6859 #6880)
-#6882 := [def-axiom]: #6881
-#6988 := [unit-resolution #6882 #6987]: #6880
-#6883 := (not #6824)
-#6884 := (or #6859 #6883)
-#6885 := [def-axiom]: #6884
-#6989 := [unit-resolution #6885 #6987]: #6883
-#6836 := (or #6813 #6824 #6833)
-#4012 := (or #4502 #4371)
-#3985 := [def-axiom]: #4012
-#6291 := [unit-resolution #3985 #6451]: #4371
-#6839 := (or #4376 #6813 #6824 #6833)
-#6805 := (+ #6804 #2199)
-#6806 := (+ #174 #6805)
-#6807 := (= #6806 0::Int)
-#6814 := (or #6813 #6811 #6807)
-#6840 := (or #4376 #6814)
-#6847 := (iff #6840 #6839)
-#6842 := (or #4376 #6836)
-#6845 := (iff #6842 #6839)
-#6846 := [rewrite]: #6845
-#6843 := (iff #6840 #6842)
-#6837 := (iff #6814 #6836)
-#6834 := (iff #6807 #6833)
-#6831 := (= #6806 #6830)
-#6832 := [rewrite]: #6831
-#6835 := [monotonicity #6832]: #6834
-#6838 := [monotonicity #6828 #6835]: #6837
-#6844 := [monotonicity #6838]: #6843
-#6848 := [trans #6844 #6846]: #6847
-#6841 := [quant-inst #2197]: #6840
-#6849 := [mp #6841 #6848]: #6839
-#6990 := [unit-resolution #6849 #6291]: #6836
-#6991 := [unit-resolution #6990 #6989 #6988]: #6833
-#6992 := (not #6833)
-#6993 := (or #6992 #6851)
-#6994 := [th-lemma arith triangle-eq]: #6993
-#6995 := [unit-resolution #6994 #6991]: #6851
-#6879 := (>= #2816 0::Int)
-#6996 := (or #6879 #2817)
-#6997 := [th-lemma arith farkas 1 1]: #6996
-#6998 := [unit-resolution #6997 #6980]: #6879
-#6999 := [th-lemma arith farkas 1 -1 1 #6998 #6989 #6995]: false
-#7000 := [lemma #6999]: #2817
-#4016 := (or #4499 #2822 #4493)
-#4017 := [def-axiom]: #4016
-#8738 := [unit-resolution #4017 #7000 #8746]: #4493
-#4029 := (or #4490 #4379)
-#4030 := [def-axiom]: #4029
-#10275 := [unit-resolution #4030 #8738]: #4379
-#15705 := (or #4384 #19100)
-#14698 := [quant-inst #14273]: #15705
-#29722 := [unit-resolution #14698 #10275]: #19100
-#14275 := (* -1::Int #14274)
-#14281 := (+ #14275 #14280)
-#14282 := (+ #14126 #14281)
-#8606 := (>= #14282 0::Int)
-#14283 := (= #14282 0::Int)
-#14287 := (not #14286)
-#14284 := (not #14283)
-#14276 := (+ #14126 #14275)
-#14277 := (<= #14276 0::Int)
-#14293 := (or #14277 #14284 #14287)
-#14296 := (not #14293)
-#14290 := (+ f3 #14143)
-#14291 := (<= #14290 0::Int)
-#22561 := (not #14291)
-#22543 := [hypothesis]: #19137
-#22806 := (or #22561 #22448)
-#12390 := (f5 f22 ?v0!19)
-#12391 := (f4 #12390)
-#12416 := (+ #2285 #12391)
-#12417 := (+ #174 #12416)
-#11416 := (>= #12417 0::Int)
-#12420 := (= #12417 0::Int)
-#12395 := (* -1::Int #12391)
-#12399 := (+ f3 #12395)
-#12400 := (<= #12399 0::Int)
-#11456 := (not #12400)
-#14158 := [hypothesis]: #3458
-#4081 := (or #3453 #2295)
-#4087 := [def-axiom]: #4081
-#14196 := [unit-resolution #4087 #14158]: #2295
-#14021 := (+ #2289 #12395)
-#14056 := (>= #14021 0::Int)
-#14020 := (= #2289 #12391)
-#14155 := (= #2288 #12390)
-#14153 := (= ?v1!18 f22)
-#11849 := (= ?v1!18 #6386)
-#11847 := (f8 f15 ?v1!18)
-#11848 := (= f1 #11847)
-#11850 := (ite #11849 #5831 #11848)
-#11851 := (f8 #7238 ?v1!18)
-#11852 := (= f1 #11851)
-#11854 := (iff #11850 #11852)
-#12005 := (or #6238 #11854)
-#11853 := (iff #11852 #11850)
-#12035 := (or #6238 #11853)
-#12030 := (iff #12035 #12005)
-#12106 := (iff #12005 #12005)
-#12107 := [rewrite]: #12106
-#11855 := (iff #11853 #11854)
-#11856 := [rewrite]: #11855
-#12104 := [monotonicity #11856]: #12030
-#12105 := [trans #12104 #12107]: #12030
-#12036 := [quant-inst #104 #6386 #5830 #2282]: #12035
-#12037 := [mp #12036 #12105]: #12005
-#14197 := [unit-resolution #12037 #4184]: #11854
-#14201 := (= #2296 #11851)
-#14198 := (= #11851 #2296)
-#14199 := [monotonicity #8698]: #14198
-#14243 := [symm #14199]: #14201
-#4088 := (or #3453 #2297)
-#4082 := [def-axiom]: #4088
-#14152 := [unit-resolution #4082 #14158]: #2297
-#14225 := [trans #14152 #14243]: #11852
-#12133 := (not #11852)
-#12138 := (not #11854)
-#12187 := (or #12138 #11850 #12133)
-#12137 := [def-axiom]: #12187
-#14226 := [unit-resolution #12137 #14225 #14197]: #11850
-#11874 := (not #11848)
-#12339 := (f13 f14 ?v0!19)
-#12374 := (* -1::Int #12339)
-#11822 := (f13 f14 ?v1!18)
-#12470 := (+ #11822 #12374)
-#12471 := (+ #2289 #12470)
-#12472 := (>= #12471 0::Int)
-#15882 := (not #12472)
-#4089 := (not #2882)
-#3918 := (or #3453 #4089)
-#3920 := [def-axiom]: #3918
-#14107 := [unit-resolution #3920 #14158]: #4089
-#12051 := (* -1::Int #11822)
-#12052 := (+ #2286 #12051)
-#12288 := (>= #12052 0::Int)
-#11825 := (= #2286 #11822)
-#6404 := (f13 f14 #6386)
-#8791 := (= #6404 #2220)
-#8808 := (= #2220 #6404)
-#7234 := (= ?v0!14 #6386)
-#7064 := (f8 f15 ?v0!14)
-#7065 := (= f1 #7064)
-#7235 := (ite #7234 #5831 #7065)
-#7239 := (f8 #7238 ?v0!14)
-#7240 := (= f1 #7239)
-#7242 := (iff #7235 #7240)
-#7258 := (or #6238 #7242)
-#7241 := (iff #7240 #7235)
-#7262 := (or #6238 #7241)
-#7261 := (iff #7262 #7258)
-#7267 := (iff #7258 #7258)
-#7268 := [rewrite]: #7267
-#7243 := (iff #7241 #7242)
-#7244 := [rewrite]: #7243
-#7266 := [monotonicity #7244]: #7261
-#7273 := [trans #7266 #7268]: #7261
-#7265 := [quant-inst #104 #6386 #5830 #2215]: #7262
-#7274 := [mp #7265 #7273]: #7258
-#7818 := [unit-resolution #7274 #4184]: #7242
-#7657 := (= #2216 #7239)
-#7793 := (= #7239 #2216)
-#7820 := [monotonicity #8698]: #7793
-#7658 := [symm #7820]: #7657
-#7693 := [hypothesis]: #2836
-#4094 := (or #2831 #2217)
-#4095 := [def-axiom]: #4094
-#7819 := [unit-resolution #4095 #7693]: #2217
-#7659 := [trans #7819 #7658]: #7240
-#7320 := (not #7240)
-#7324 := (not #7242)
-#7325 := (or #7324 #7235 #7320)
-#7336 := [def-axiom]: #7325
-#7660 := [unit-resolution #7336 #7659 #7818]: #7235
-#7093 := (f5 f22 ?v0!14)
-#7094 := (f4 #7093)
-#7046 := (* -1::Int #2220)
-#7111 := (+ #7046 #7094)
-#7112 := (+ #174 #7111)
-#7113 := (>= #7112 0::Int)
-#7082 := (not #7113)
-#7095 := (* -1::Int #7094)
-#7099 := (+ f3 #7095)
-#7100 := (<= #7099 0::Int)
-#7118 := (or #7100 #7113)
-#7121 := (not #7118)
-#4090 := (not #2825)
-#4091 := (or #2831 #4090)
-#4096 := [def-axiom]: #4091
-#7694 := [unit-resolution #4096 #7693]: #4090
-#6455 := (or #4368 #2825 #7121)
-#7096 := (+ #1420 #7095)
-#7097 := (+ #2220 #7096)
-#7098 := (<= #7097 0::Int)
-#7101 := (or #7100 #7098)
-#7102 := (not #7101)
-#7103 := (or #2221 #7102)
-#6460 := (or #4368 #7103)
-#7131 := (iff #6460 #6455)
-#7124 := (or #2825 #7121)
-#6462 := (or #4368 #7124)
-#7129 := (iff #6462 #6455)
-#7130 := [rewrite]: #7129
-#6463 := (iff #6460 #6462)
-#7125 := (iff #7103 #7124)
-#7122 := (iff #7102 #7121)
-#7119 := (iff #7101 #7118)
-#7116 := (iff #7098 #7113)
-#7104 := (+ #2220 #7095)
-#7105 := (+ #1420 #7104)
-#7108 := (<= #7105 0::Int)
-#7114 := (iff #7108 #7113)
-#7115 := [rewrite]: #7114
-#7109 := (iff #7098 #7108)
-#7106 := (= #7097 #7105)
-#7107 := [rewrite]: #7106
-#7110 := [monotonicity #7107]: #7109
-#7117 := [trans #7110 #7115]: #7116
-#7120 := [monotonicity #7117]: #7119
-#7123 := [monotonicity #7120]: #7122
-#7126 := [monotonicity #2827 #7123]: #7125
-#7128 := [monotonicity #7126]: #6463
-#7144 := [trans #7128 #7130]: #7131
-#6461 := [quant-inst #2215]: #6460
-#7132 := [mp #6461 #7144]: #6455
-#7661 := [unit-resolution #7132 #6477 #7694]: #7121
-#7090 := (or #7118 #7082)
-#7091 := [def-axiom]: #7090
-#7656 := [unit-resolution #7091 #7661]: #7082
-#7246 := (not #7235)
-#8732 := (or #7234 #7113 #7246)
-decl f7 :: (-> S3 S2)
-#7276 := (f5 #6386 ?v0!14)
-#7316 := (f7 #7276)
-#7666 := (f13 f14 #7316)
-#7695 := (* -1::Int #7666)
-#7696 := (+ #6404 #7695)
-#7697 := (>= #7696 0::Int)
-#7692 := (f8 f15 #7316)
-#7665 := (= f1 #7692)
-#7797 := (= #7064 #7692)
-#7786 := (= #7692 #7064)
-#7776 := (= #7316 ?v0!14)
-#7317 := (= ?v0!14 #7316)
-#26 := (f7 #14)
-#350 := (= #12 #26)
-#4157 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4138) #350)
-#354 := (forall (vars (?v0 S2) (?v1 S2)) #350)
-#4160 := (iff #354 #4157)
-#4158 := (iff #350 #350)
-#4159 := [refl]: #4158
-#4161 := [quant-intro #4159]: #4160
-#1815 := (~ #354 #354)
-#1840 := (~ #350 #350)
-#1841 := [refl]: #1840
-#1816 := [nnf-pos #1841]: #1815
-#27 := (= #26 #12)
-#28 := (forall (vars (?v0 S2) (?v1 S2)) #27)
-#355 := (iff #28 #354)
-#352 := (iff #27 #350)
-#353 := [rewrite]: #352
-#356 := [quant-intro #353]: #355
-#349 := [asserted]: #28
-#359 := [mp #349 #356]: #354
-#1842 := [mp~ #359 #1816]: #354
-#4162 := [mp #1842 #4161]: #4157
-#5129 := (not #4157)
-#7448 := (or #5129 #7317)
-#7479 := [quant-inst #6386 #2215]: #7448
-#7785 := [unit-resolution #7479 #4162]: #7317
-#7707 := [symm #7785]: #7776
-#7794 := [monotonicity #7707]: #7786
-#7984 := [symm #7794]: #7797
-#7708 := [hypothesis]: #7235
-#7255 := (not #7234)
-#7783 := [hypothesis]: #7255
-#7272 := (or #7246 #7234 #7065)
-#7245 := [def-axiom]: #7272
-#7784 := [unit-resolution #7245 #7783 #7708]: #7065
-#7985 := [trans #7784 #7984]: #7665
-#7698 := (not #7665)
-#8065 := (or #7698 #7697)
-#6407 := (f8 f15 #6386)
-#6402 := (= f1 #6407)
-#7988 := (not #6402)
-#7871 := (iff #732 #7988)
-#7824 := (iff #729 #6402)
-#7983 := (iff #6402 #729)
-#7989 := (= #6407 #171)
-#8060 := [monotonicity #7565]: #7989
-#7823 := [monotonicity #8060]: #7983
-#7825 := [symm #7823]: #7824
-#8068 := [monotonicity #7825]: #7871
-#4020 := (or #4502 #732)
-#4015 := [def-axiom]: #4020
-#7986 := [unit-resolution #4015 #6451]: #732
-#8069 := [mp #7986 #8068]: #7988
-#3928 := (or #4514 #4258)
-#3983 := [def-axiom]: #3928
-#7878 := [unit-resolution #3983 #6450]: #4258
-#7702 := (or #4263 #6402 #7698 #7697)
-#7699 := (or #6402 #7698 #7697)
-#7712 := (or #4263 #7699)
-#7711 := (iff #7712 #7702)
-#7778 := [rewrite]: #7711
-#7777 := [quant-inst #7316 #6386]: #7712
-#7779 := [mp #7777 #7778]: #7702
-#8070 := [unit-resolution #7779 #7878 #8069]: #8065
-#8066 := [unit-resolution #8070 #7985]: #7697
-#8133 := [hypothesis]: #7082
-#7277 := (f4 #7276)
-#7278 := (* -1::Int #7277)
-#7616 := (+ #7094 #7278)
-#7632 := (>= #7616 0::Int)
-#7615 := (= #7094 #7277)
-#7873 := (= #7277 #7094)
-#8134 := (= #7276 #7093)
-#8414 := [monotonicity #7565]: #8134
-#8135 := [monotonicity #8414]: #7873
-#8147 := [symm #8135]: #7615
-#8146 := (not #7615)
-#8629 := (or #8146 #7632)
-#7870 := [th-lemma arith triangle-eq]: #8629
-#8667 := [unit-resolution #7870 #8147]: #7632
-#7459 := (>= #7277 0::Int)
-#7346 := (<= #7277 0::Int)
-#7348 := (not #7346)
-#7350 := (or #7234 #7348)
+#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)
-#329 := (<= #15 0::Int)
-#330 := (not #329)
+#330 := (<= #15 0::Int)
+#331 := (not #330)
 #13 := (= #11 #12)
-#333 := (or #13 #330)
-#4145 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4138) #333)
-#336 := (forall (vars (?v0 S2) (?v1 S2)) #333)
-#4148 := (iff #336 #4145)
-#4146 := (iff #333 #333)
-#4147 := [refl]: #4146
-#4149 := [quant-intro #4147]: #4148
-#1811 := (~ #336 #336)
-#1810 := (~ #333 #333)
-#1807 := [refl]: #1810
-#1812 := [nnf-pos #1807]: #1811
+#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)
-#339 := (iff #22 #336)
-#323 := (or #13 #20)
-#326 := (forall (vars (?v0 S2) (?v1 S2)) #323)
-#337 := (iff #326 #336)
-#334 := (iff #323 #333)
-#331 := (iff #20 #330)
-#332 := [rewrite]: #331
-#335 := [monotonicity #332]: #334
-#338 := [quant-intro #335]: #337
-#327 := (iff #22 #326)
-#324 := (iff #21 #323)
-#325 := [rewrite]: #324
-#328 := [quant-intro #325]: #327
-#340 := [trans #328 #338]: #339
-#322 := [asserted]: #22
-#341 := [mp #322 #340]: #336
-#1808 := [mp~ #341 #1812]: #336
-#4150 := [mp #1808 #4149]: #4145
-#6420 := (not #4145)
-#7437 := (or #6420 #7234 #7348)
-#7322 := (= #6386 ?v0!14)
-#7349 := (or #7322 #7348)
-#7441 := (or #6420 #7349)
-#7532 := (iff #7441 #7437)
-#7445 := (or #6420 #7350)
-#7526 := (iff #7445 #7437)
-#7531 := [rewrite]: #7526
-#7446 := (iff #7441 #7445)
-#7351 := (iff #7349 #7350)
-#7328 := (iff #7322 #7234)
-#7329 := [rewrite]: #7328
-#7352 := [monotonicity #7329]: #7351
-#7525 := [monotonicity #7352]: #7446
-#7523 := [trans #7525 #7531]: #7532
-#7442 := [quant-inst #6386 #2215]: #7441
-#7524 := [mp #7442 #7523]: #7437
-#8625 := [unit-resolution #7524 #4150]: #7350
-#8630 := [unit-resolution #8625 #7783]: #7348
-#8631 := (or #7459 #7346)
-#7957 := [th-lemma arith farkas 1 1]: #8631
-#8132 := [unit-resolution #7957 #8630]: #7459
-#7781 := (+ #2220 #7695)
-#7821 := (<= #7781 0::Int)
-#7782 := (= #2220 #7666)
-#8155 := (= #7666 #2220)
-#8650 := [monotonicity #7707]: #8155
-#8413 := [symm #8650]: #7782
-#8160 := (not #7782)
-#8167 := (or #8160 #7821)
-#8168 := [th-lemma arith triangle-eq]: #8167
-#8537 := [unit-resolution #8168 #8413]: #7821
-#6414 := (* -1::Int #6404)
-#6751 := (+ #174 #6414)
-#6759 := (>= #6751 0::Int)
-#6382 := (= #174 #6404)
-#8807 := [monotonicity #7563]: #6382
-#8151 := (not #6382)
-#8148 := (or #8151 #6759)
-#8182 := [th-lemma arith triangle-eq]: #8148
-#8183 := [unit-resolution #8182 #8807]: #6759
-#8724 := [th-lemma arith farkas 1 1 1 1 -1 1 #8183 #8537 #8132 #8667 #8133 #8066]: false
-#8733 := [lemma #8724]: #8732
-#7662 := [unit-resolution #8733 #7656 #7660]: #7234
-#7795 := [monotonicity #7662]: #8808
-#8736 := [symm #7795]: #8791
-#8813 := (= #2219 #6404)
-#7796 := (= #6404 #174)
-#8734 := [monotonicity #7565]: #7796
-#8735 := [symm #8734]: #6382
-#8811 := (= #2219 #174)
-#5955 := (f24 f22)
-#8792 := (= #5955 #174)
-#5956 := (= #174 #5955)
-#5943 := (f5 f22 f22)
-#5944 := (f4 #5943)
-#5963 := (>= #5944 0::Int)
-#5947 := (* -1::Int #5944)
-#5951 := (+ f3 #5947)
-#5952 := (<= #5951 0::Int)
-#5968 := (or #5952 #5963)
-#7494 := (f5 #6386 #6386)
-#7495 := (f4 #7494)
-#7496 := (* -1::Int #7495)
-#7560 := (+ #5944 #7496)
-#7562 := (>= #7560 0::Int)
-#7559 := (= #5944 #7495)
-#7568 := (= #5943 #7494)
-#7566 := (= #7494 #5943)
-#7567 := [monotonicity #7565 #7565]: #7566
-#7569 := [symm #7567]: #7568
-#7570 := [monotonicity #7569]: #7559
-#7571 := (not #7559)
-#7572 := (or #7571 #7562)
-#7573 := [th-lemma arith triangle-eq]: #7572
-#7574 := [unit-resolution #7573 #7570]: #7562
-#7505 := (>= #7495 0::Int)
-#7533 := (= #7495 0::Int)
+#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)
-#313 := (or #19 #16)
-#4139 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4138) #313)
-#316 := (forall (vars (?v0 S2) (?v1 S2)) #313)
-#4142 := (iff #316 #4139)
-#4140 := (iff #313 #313)
-#4141 := [refl]: #4140
-#4143 := [quant-intro #4141]: #4142
-#1835 := (~ #316 #316)
-#1833 := (~ #313 #313)
-#1834 := [refl]: #1833
-#1836 := [nnf-pos #1834]: #1835
+#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)
-#319 := (iff #18 #316)
-#292 := (= 0::Int #15)
-#303 := (or #19 #292)
-#308 := (forall (vars (?v0 S2) (?v1 S2)) #303)
-#317 := (iff #308 #316)
-#314 := (iff #303 #313)
-#311 := (iff #292 #16)
-#312 := [rewrite]: #311
-#315 := [monotonicity #312]: #314
-#318 := [quant-intro #315]: #317
-#309 := (iff #18 #308)
-#306 := (iff #17 #303)
-#300 := (implies #13 #292)
-#304 := (iff #300 #303)
-#305 := [rewrite]: #304
-#301 := (iff #17 #300)
-#298 := (iff #16 #292)
-#299 := [rewrite]: #298
-#302 := [monotonicity #299]: #301
-#307 := [trans #302 #305]: #306
-#310 := [quant-intro #307]: #309
-#320 := [trans #310 #318]: #319
-#291 := [asserted]: #18
-#321 := [mp #291 #320]: #316
-#1809 := [mp~ #321 #1836]: #316
-#4144 := [mp #1809 #4143]: #4139
-#6380 := (not #4139)
-#7549 := (or #6380 #7533)
-#7364 := (= #6386 #6386)
-#7534 := (not #7364)
-#7537 := (or #7534 #7533)
-#7550 := (or #6380 #7537)
-#7552 := (iff #7550 #7549)
-#7554 := (iff #7549 #7549)
-#7555 := [rewrite]: #7554
-#7547 := (iff #7537 #7533)
-#7542 := (or false #7533)
-#7545 := (iff #7542 #7533)
-#7546 := [rewrite]: #7545
-#7543 := (iff #7537 #7542)
-#7540 := (iff #7534 false)
-#7538 := (iff #7534 #5500)
-#7369 := (iff #7364 true)
-#7370 := [rewrite]: #7369
-#7539 := [monotonicity #7370]: #7538
-#7541 := [trans #7539 #5538]: #7540
-#7544 := [monotonicity #7541]: #7543
-#7548 := [trans #7544 #7546]: #7547
-#7553 := [monotonicity #7548]: #7552
-#7556 := [trans #7553 #7555]: #7552
-#7551 := [quant-inst #6386 #6386]: #7550
-#7557 := [mp #7551 #7556]: #7549
-#7575 := [unit-resolution #7557 #4144]: #7533
-#7576 := (not #7533)
-#7577 := (or #7576 #7505)
-#7578 := [th-lemma arith triangle-eq]: #7577
-#7579 := [unit-resolution #7578 #7575]: #7505
-#5991 := (not #5963)
-#7580 := [hypothesis]: #5991
-#7581 := [th-lemma arith farkas -1 1 1 #7580 #7579 #7574]: false
-#7582 := [lemma #7581]: #5963
-#5992 := (or #5968 #5991)
-#5993 := [def-axiom]: #5992
-#8785 := [unit-resolution #5993 #7582]: #5968
-#5971 := (not #5968)
-#5974 := (or #5956 #5971)
-#5977 := (or #4368 #5956 #5971)
-#5948 := (+ #1420 #5947)
-#5949 := (+ #174 #5948)
-#5950 := (<= #5949 0::Int)
-#5953 := (or #5952 #5950)
-#5954 := (not #5953)
-#5957 := (or #5956 #5954)
-#5978 := (or #4368 #5957)
-#5985 := (iff #5978 #5977)
-#5980 := (or #4368 #5974)
-#5983 := (iff #5980 #5977)
-#5984 := [rewrite]: #5983
-#5981 := (iff #5978 #5980)
-#5975 := (iff #5957 #5974)
-#5972 := (iff #5954 #5971)
-#5969 := (iff #5953 #5968)
-#5966 := (iff #5950 #5963)
-#5960 := (<= #5947 0::Int)
-#5964 := (iff #5960 #5963)
-#5965 := [rewrite]: #5964
-#5961 := (iff #5950 #5960)
-#5958 := (= #5949 #5947)
-#5959 := [rewrite]: #5958
-#5962 := [monotonicity #5959]: #5961
-#5967 := [trans #5962 #5965]: #5966
-#5970 := [monotonicity #5967]: #5969
-#5973 := [monotonicity #5970]: #5972
-#5976 := [monotonicity #5973]: #5975
-#5982 := [monotonicity #5976]: #5981
-#5986 := [trans #5982 #5984]: #5985
-#5979 := [quant-inst #170]: #5978
-#5987 := [mp #5979 #5986]: #5977
-#8793 := [unit-resolution #5987 #6477]: #5974
-#8794 := [unit-resolution #8793 #8785]: #5956
-#8806 := [symm #8794]: #8792
-#8795 := (= #2219 #5955)
-#8788 := (= ?v0!14 f22)
-#7663 := [trans #7662 #7565]: #8788
-#7981 := [monotonicity #7663]: #8795
-#8725 := [trans #7981 #8806]: #8811
-#8173 := [trans #8725 #8735]: #8813
-#8678 := [trans #8173 #8736]: #2825
-#7979 := [unit-resolution #7694 #8678]: false
-#8048 := [lemma #7979]: #2831
-#4031 := (or #4490 #4484)
-#4032 := [def-axiom]: #4031
-#8651 := [unit-resolution #4032 #8738]: #4484
-#4027 := (or #4487 #2836 #4481)
-#4028 := [def-axiom]: #4027
-#8737 := [unit-resolution #4028 #8651]: #4484
-#8043 := [unit-resolution #8737 #8048]: #4481
-#4037 := (or #4478 #4388)
-#4039 := [def-axiom]: #4037
-#8044 := [unit-resolution #4039 #8043]: #4388
-#11868 := (or #4393 #3438 #11825)
-#11823 := (= #11822 #2286)
-#11824 := (or #11823 #3438)
-#11883 := (or #4393 #11824)
-#11839 := (iff #11883 #11868)
-#11831 := (or #3438 #11825)
-#11930 := (or #4393 #11831)
-#11783 := (iff #11930 #11868)
-#11840 := [rewrite]: #11783
-#11837 := (iff #11883 #11930)
-#11834 := (iff #11824 #11831)
-#11828 := (or #11825 #3438)
-#11832 := (iff #11828 #11831)
-#11833 := [rewrite]: #11832
-#11829 := (iff #11824 #11828)
-#11826 := (iff #11823 #11825)
-#11827 := [rewrite]: #11826
-#11830 := [monotonicity #11827]: #11829
-#11835 := [trans #11830 #11833]: #11834
-#11838 := [monotonicity #11835]: #11837
-#11799 := [trans #11838 #11840]: #11839
-#11903 := [quant-inst #2282]: #11883
-#11841 := [mp #11903 #11799]: #11868
-#14128 := [unit-resolution #11841 #8044 #14152]: #11825
-#14123 := (not #11825)
-#14129 := (or #14123 #12288)
-#14127 := [th-lemma arith triangle-eq]: #14129
-#14130 := [unit-resolution #14127 #14128]: #12288
-#15883 := (not #12288)
-#15884 := (or #15882 #15883 #2882)
-#15862 := [hypothesis]: #4089
-#15863 := [hypothesis]: #12288
-#12524 := (f7 #2288)
-#12647 := (f13 f14 #12524)
-#12661 := (* -1::Int #12647)
-#12311 := (+ #12339 #12661)
-#12316 := (>= #12311 0::Int)
-#12295 := (= #12339 #12647)
-#12525 := (= ?v0!19 #12524)
-#12287 := (or #5129 #12525)
-#12294 := [quant-inst #2282 #2283]: #12287
-#15864 := [unit-resolution #12294 #4162]: #12525
-#15865 := [monotonicity #15864]: #12295
-#15866 := (not #12295)
-#15867 := (or #15866 #12316)
-#15868 := [th-lemma arith triangle-eq]: #15867
-#15869 := [unit-resolution #15868 #15865]: #12316
-#15870 := [hypothesis]: #12472
-#12979 := (f24 #12524)
-#12996 := (* -1::Int #12979)
-#12997 := (+ #12647 #12996)
-#12998 := (>= #12997 0::Int)
-#12522 := (or #4384 #12998)
-#12541 := [quant-inst #12524]: #12522
-#15871 := [unit-resolution #12541 #10275]: #12998
-#13229 := (+ #2284 #12996)
-#13230 := (<= #13229 0::Int)
-#13224 := (= #2284 #12979)
-#15874 := (= #12979 #2284)
-#15872 := (= #12524 ?v0!19)
-#15873 := [symm #15864]: #15872
-#15875 := [monotonicity #15873]: #15874
-#15876 := [symm #15875]: #13224
-#15877 := (not #13224)
-#15878 := (or #15877 #13230)
-#15879 := [th-lemma arith triangle-eq]: #15878
-#15880 := [unit-resolution #15879 #15876]: #13230
-#15881 := [th-lemma arith farkas -1 1 1 1 1 1 #15880 #15871 #15870 #15869 #15863 #15862]: false
-#15885 := [lemma #15881]: #15884
-#14106 := [unit-resolution #15885 #14130 #14107]: #15882
-#14132 := (or #11874 #12472)
-#14131 := [unit-resolution #3982 #6450]: #4249
-#12193 := (or #4254 #2294 #11874 #12472)
-#12473 := (or #11874 #2294 #12472)
-#12255 := (or #4254 #12473)
-#12219 := (iff #12255 #12193)
-#12474 := (or #2294 #11874 #12472)
-#12259 := (or #4254 #12474)
-#12134 := (iff #12259 #12193)
-#12194 := [rewrite]: #12134
-#12279 := (iff #12255 #12259)
-#12475 := (iff #12473 #12474)
-#12476 := [rewrite]: #12475
-#12280 := [monotonicity #12476]: #12279
-#12220 := [trans #12280 #12194]: #12219
-#12258 := [quant-inst #2283 #2282]: #12255
-#12215 := [mp #12258 #12220]: #12193
-#14135 := [unit-resolution #12215 #14131 #14196]: #14132
-#14151 := [unit-resolution #14135 #14106]: #11874
-#12108 := (not #11850)
-#12130 := (or #12108 #11849 #11848)
-#12131 := [def-axiom]: #12130
-#14134 := [unit-resolution #12131 #14151 #14226]: #11849
-#14154 := [trans #14134 #7565]: #14153
-#14156 := [monotonicity #14154]: #14155
-#14150 := [monotonicity #14156]: #14020
-#14157 := (not #14020)
-#14231 := (or #14157 #14056)
-#14203 := [th-lemma arith triangle-eq]: #14231
-#14229 := [unit-resolution #14203 #14150]: #14056
-#15334 := (not #14056)
-#15340 := (or #11456 #15334 #2294)
-#15336 := [hypothesis]: #2295
-#15337 := [hypothesis]: #14056
-#15338 := [hypothesis]: #12400
-#15339 := [th-lemma arith farkas -1 1 1 #15338 #15337 #15336]: false
-#15341 := [lemma #15339]: #15340
-#14204 := [unit-resolution #15341 #14229 #14196]: #11456
-#12409 := (+ #12374 #12391)
-#12410 := (+ #174 #12409)
-#12411 := (>= #12410 0::Int)
-#11381 := (not #12411)
-#12526 := (f6 #2288)
-#12547 := (f13 f14 #12526)
-#12565 := (* -1::Int #12547)
-#15720 := (+ #6404 #12565)
-#14007 := (<= #15720 0::Int)
-#13983 := (= #6404 #12547)
-#14240 := (= #12547 #6404)
-#12777 := (= #12526 #6386)
-#14238 := (= #12526 ?v1!18)
-#12527 := (= ?v1!18 #12526)
-#12285 := (or #6389 #12527)
-#12296 := [quant-inst #2282 #2283]: #12285
-#14515 := [unit-resolution #12296 #4156]: #12527
-#14239 := [symm #14515]: #14238
-#14230 := [trans #14239 #14134]: #12777
-#14241 := [monotonicity #14230]: #14240
-#14242 := [symm #14241]: #13983
-#14202 := (not #13983)
-#14224 := (or #14202 #14007)
-#14234 := [th-lemma arith triangle-eq]: #14224
-#14263 := [unit-resolution #14234 #14242]: #14007
-#14478 := (not #14007)
-#14523 := (or #11381 #15334 #2882 #15883 #14478)
-#12375 := (+ #2284 #12374)
-#12376 := (<= #12375 0::Int)
-#11370 := (or #4384 #12376)
-#12366 := (+ #12339 #2285)
-#12367 := (>= #12366 0::Int)
-#11369 := (or #4384 #12367)
-#11352 := (iff #11369 #11370)
-#11356 := (iff #11370 #11370)
-#11363 := [rewrite]: #11356
-#12379 := (iff #12367 #12376)
-#12368 := (+ #2285 #12339)
-#12371 := (>= #12368 0::Int)
-#12377 := (iff #12371 #12376)
-#12378 := [rewrite]: #12377
-#12372 := (iff #12367 #12371)
-#12369 := (= #12366 #12368)
-#12370 := [rewrite]: #12369
-#12373 := [monotonicity #12370]: #12372
-#12380 := [trans #12373 #12378]: #12379
-#11355 := [monotonicity #12380]: #11352
-#11365 := [trans #11355 #11363]: #11352
-#11354 := [quant-inst #2283]: #11369
-#11366 := [mp #11354 #11365]: #11370
-#14491 := [unit-resolution #11366 #10275]: #12376
-#12321 := (+ #11822 #12565)
-#12328 := (>= #12321 0::Int)
-#12320 := (= #11822 #12547)
-#14518 := [monotonicity #14515]: #12320
-#14519 := (not #12320)
-#14532 := (or #14519 #12328)
-#14533 := [th-lemma arith triangle-eq]: #14532
-#14559 := [unit-resolution #14533 #14518]: #12328
-#6512 := (<= #6751 0::Int)
-#14565 := (or #8151 #6512)
-#14566 := [th-lemma arith triangle-eq]: #14565
-#14567 := [unit-resolution #14566 #8807]: #6512
-#14568 := [hypothesis]: #14007
-#14479 := [hypothesis]: #12411
-#14522 := [th-lemma arith farkas -1 -1 -1 -1 1 1 -1 1 #15337 #14479 #15862 #15863 #14568 #14567 #14559 #14491]: false
-#14524 := [lemma #14522]: #14523
-#14264 := [unit-resolution #14524 #14229 #14107 #14130 #14263]: #11381
-#12423 := (or #12400 #12411 #12420)
-#11389 := (or #4376 #12400 #12411 #12420)
-#12392 := (+ #12391 #2285)
-#12393 := (+ #174 #12392)
-#12394 := (= #12393 0::Int)
-#12396 := (+ #1420 #12395)
-#12397 := (+ #12339 #12396)
-#12398 := (<= #12397 0::Int)
-#12401 := (or #12400 #12398 #12394)
-#11357 := (or #4376 #12401)
-#11458 := (iff #11357 #11389)
-#11390 := (or #4376 #12423)
-#11391 := (iff #11390 #11389)
-#11392 := [rewrite]: #11391
-#11364 := (iff #11357 #11390)
-#12424 := (iff #12401 #12423)
-#12421 := (iff #12394 #12420)
-#12418 := (= #12393 #12417)
-#12419 := [rewrite]: #12418
-#12422 := [monotonicity #12419]: #12421
-#12414 := (iff #12398 #12411)
-#12402 := (+ #12339 #12395)
-#12403 := (+ #1420 #12402)
-#12406 := (<= #12403 0::Int)
-#12412 := (iff #12406 #12411)
-#12413 := [rewrite]: #12412
-#12407 := (iff #12398 #12406)
-#12404 := (= #12397 #12403)
-#12405 := [rewrite]: #12404
-#12408 := [monotonicity #12405]: #12407
-#12415 := [trans #12408 #12413]: #12414
-#12425 := [monotonicity #12415 #12422]: #12424
-#11383 := [monotonicity #12425]: #11364
-#11459 := [trans #11383 #11392]: #11458
-#11404 := [quant-inst #2283]: #11357
-#11457 := [mp #11404 #11459]: #11389
-#14265 := [unit-resolution #11457 #6291]: #12423
-#14266 := [unit-resolution #14265 #14264 #14204]: #12420
-#14268 := (not #12420)
-#14319 := (or #14268 #11416)
-#14320 := [th-lemma arith triangle-eq]: #14319
-#14321 := [unit-resolution #14320 #14266]: #11416
-#14267 := [th-lemma arith farkas 1 1 1 -1 -1 1 1 #14229 #14107 #14130 #14263 #14567 #14559 #14321]: false
-#14262 := [lemma #14267]: #3453
-#4040 := (or #4478 #4472)
-#4041 := [def-axiom]: #4040
-#13724 := [unit-resolution #4041 #8043]: #4472
-#13668 := (or #4475 #4469)
-#5880 := (= #99 #202)
-#13485 := (iff #5880 #203)
-#13484 := [commutativity]: #1455
-#13287 := (iff #5880 #789)
-#6483 := [unit-resolution #4000 #6450]: #100
-#13293 := [monotonicity #6483]: #13287
-#13489 := [trans #13293 #13484]: #13485
-#5756 := (f4 #5873)
-#5811 := (* -1::Int #5756)