src/HOL/Boogie/Examples/Boogie_Dijkstra.certs

updated SMT certificates

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)
#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
#19476 := (+ f3 #19047)
#19477 := (<= #19476 0::Int)
#34297 := (not #19477)
decl f24 :: (-> S2 Int)
#2315 := (f24 ?v0!20)
#2316 := (* -1::Int #2315)
#2326 := (+ f3 #2316)
#2327 := (<= #2326 0::Int)
#2328 := (not #2327)
#12 := (:var 0 S2)
#2318 := (f5 #12 ?v0!20)
#4422 := (pattern #2318)
#189 := (f24 #12)
#4362 := (pattern #189)
decl f23 :: S4
#180 := f23
#199 := (f8 f23 #12)
#4388 := (pattern #199)
#2319 := (f4 #2318)
#2918 := (+ #2316 #2319)
#2919 := (+ #189 #2918)
#2922 := (= #2919 0::Int)
#3484 := (not #2922)
#2317 := (+ #189 #2316)
#2322 := (>= #2317 0::Int)
#775 := (= f1 #199)
#781 := (not #775)
#3485 := (or #781 #2322 #3484)
#4423 := (forall (vars (?v1 S2)) (:pat #4388 #4362 #4422) #3485)
#4428 := (not #4423)
#11 := (:var 1 S2)
#82 := (f5 #12 #11)
#4217 := (pattern #82)
#211 := (f24 #11)
#1471 := (* -1::Int #211)
#1472 := (+ #189 #1471)
#83 := (f4 #82)
#1502 := (+ #83 #1472)
#1500 := (>= #1502 0::Int)
#1199 := (* -1::Int #83)
#1202 := (+ f3 #1199)
#1203 := (<= #1202 0::Int)
#3476 := (or #781 #1203 #1500)
#4414 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4217) #3476)
#4419 := (not #4414)
decl f10 :: S2
#56 := f10
#2894 := (= f10 ?v0!20)
#4431 := (or #2327 #2894 #4419 #4428)
#4434 := (not #4431)
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)
#4179 := (pattern #47)
#51 := (f8 #43 #12)
#388 := (= f1 #51)
#385 := (= f1 #45)
#49 := (= #12 #44)
#391 := (ite #49 #385 #388)
#381 := (= f1 #47)
#394 := (iff #381 #391)
#4180 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) (:pat #4179) #394)
#397 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) #394)
#4183 := (iff #397 #4180)
#4181 := (iff #394 #394)
#4182 := [refl]: #4181
#4184 := [quant-intro #4182]: #4183
#1822 := (~ #397 #397)
#1850 := (~ #394 #394)
#1851 := [refl]: #1850
#1823 := [nnf-pos #1851]: #1822
#52 := (= #51 f1)
#50 := (= #45 f1)
#53 := (ite #49 #50 #52)
#48 := (= #47 f1)
#54 := (iff #48 #53)
#55 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1) (?v3 S2)) #54)
#398 := (iff #55 #397)
#395 := (iff #54 #394)
#392 := (iff #53 #391)
#389 := (iff #52 #388)
#390 := [rewrite]: #389
#386 := (iff #50 #385)
#387 := [rewrite]: #386
#393 := [monotonicity #387 #390]: #392
#383 := (iff #48 #381)
#384 := [rewrite]: #383
#396 := [monotonicity #384 #393]: #395
#399 := [quant-intro #396]: #398
#380 := [asserted]: #55
#402 := [mp #380 #399]: #397
#1852 := [mp~ #402 #1823]: #397
#4185 := [mp #1852 #4184]: #4180
#6350 := (not #4180)
#22066 := (or #6350 #13585)
#13584 := (iff #13583 #13581)
#22070 := (or #6350 #13584)
#22072 := (iff #22070 #22066)
#22073 := (iff #22066 #22066)
#22074 := [rewrite]: #22073
#13586 := (iff #13584 #13585)
#13587 := [rewrite]: #13586
#22067 := [monotonicity #13587]: #22072
#22076 := [trans #22067 #22074]: #22072
#22071 := [quant-inst #105 #6633 #5797 #2283]: #22070
#22077 := [mp #22071 #22076]: #22066
#23294 := [unit-resolution #22077 #4185]: #13585
#23299 := (= #2297 #13582)
#23295 := (= #13582 #2297)
#10524 := (= #8578 f23)
#6551 := (= #181 f23)
#182 := (= f23 #181)
#4437 := (or #3459 #4434)
#4440 := (not #4437)
#4405 := (pattern #189 #211)
#1470 := (>= #1472 0::Int)
#208 := (f8 f23 #11)
#795 := (= f1 #208)
#3416 := (not #795)
#3431 := (or #775 #3416 #1470)
#4406 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4405) #3431)
#4411 := (not #4406)
#4443 := (or #4411 #4440)
#4446 := (not #4443)
decl ?v1!16 :: S2
#2256 := ?v1!16
#2260 := (f24 ?v1!16)
#2854 := (* -1::Int #2260)
decl ?v0!17 :: S2
#2257 := ?v0!17
#2258 := (f24 ?v0!17)
#2855 := (+ #2258 #2854)
#2856 := (<= #2855 0::Int)
#2265 := (f8 f23 ?v1!16)
#2266 := (= f1 #2265)
#2263 := (f8 f23 ?v0!17)
#2264 := (= f1 #2263)
#3393 := (not #2264)
#3408 := (or #3393 #2266 #2856)
#3413 := (not #3408)
#4449 := (or #3413 #4446)
#4452 := (not #4449)
#1461 := (>= #189 0::Int)
#4397 := (forall (vars (?v0 S2)) (:pat #4362) #1461)
#4402 := (not #4397)
#4455 := (or #4402 #4452)
#4458 := (not #4455)
decl ?v0!15 :: S2
#2241 := ?v0!15
#2242 := (f24 ?v0!15)
#2243 := (>= #2242 0::Int)
#2244 := (not #2243)
#4461 := (or #2244 #4458)
#4464 := (not #4461)
#203 := (f24 f10)
#204 := (= #203 0::Int)
#1458 := (not #204)
#4467 := (or #1458 #4464)
#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
#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
#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
#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
#2108 := ?v0!11
decl ?v1!10 :: S2
#2107 := ?v1!10
#2113 := (f5 ?v1!10 ?v0!11)
#2114 := (f4 #2113)
#2121 := (* -1::Int #2114)
decl f19 :: S5
#138 := f19
#2111 := (f13 f19 ?v1!10)
#2117 := (* -1::Int #2111)
#2773 := (+ #2117 #2121)
#2109 := (f13 f19 ?v0!11)
#2774 := (+ #2109 #2773)
#2775 := (<= #2774 0::Int)
#2122 := (+ f3 #2121)
#2123 := (<= #2122 0::Int)
#2118 := (+ f3 #2117)
#2119 := (<= #2118 0::Int)
#3329 := (or #2119 #2123 #2775)
#3334 := (not #3329)
#146 := (f13 f19 #11)
#1323 := (* -1::Int #146)
#143 := (f13 f19 #12)
#1324 := (+ #143 #1323)
#1330 := (+ #83 #1324)
#1353 := (>= #1330 0::Int)
#1310 := (* -1::Int #143)
#1311 := (+ f3 #1310)
#1312 := (<= #1311 0::Int)
#3297 := (or #1203 #1312 #1353)
#4316 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4217) #3297)
#4321 := (not #4316)
#158 := (f13 f19 f10)
#159 := (= #158 0::Int)
#4324 := (or #159 #4321)
#4327 := (not #4324)
#4330 := (or #4327 #3334)
#4333 := (not #4330)
#4292 := (pattern #143)
decl ?v1!9 :: (-> S2 S2)
#2084 := (?v1!9 #12)
#2087 := (f5 #2084 #12)
#2088 := (f4 #2087)
#2743 := (* -1::Int #2088)
#2085 := (f13 f19 #2084)
#2726 := (* -1::Int #2085)
#2744 := (+ #2726 #2743)
#2745 := (+ #143 #2744)
#2746 := (= #2745 0::Int)
#3267 := (not #2746)
#2727 := (+ #143 #2726)
#2728 := (<= #2727 0::Int)
#3268 := (or #2728 #3267)
#3269 := (not #3268)
#57 := (= #12 f10)
#3275 := (or #57 #1312 #3269)
#4308 := (forall (vars (?v0 S2)) (:pat #4292) #3275)
#4313 := (not #4308)
#4336 := (or #4313 #4333)
#4339 := (not #4336)
decl ?v0!8 :: S2
#2044 := ?v0!8
#2048 := (f5 #12 ?v0!8)
#4293 := (pattern #2048)
#2049 := (f4 #2048)
#2045 := (f13 f19 ?v0!8)
#2046 := (* -1::Int #2045)
#2696 := (+ #2046 #2049)
#2697 := (+ #143 #2696)
#2700 := (= #2697 0::Int)
#3231 := (not #2700)
#2047 := (+ #143 #2046)
#2052 := (>= #2047 0::Int)
#3232 := (or #2052 #3231)
#4294 := (forall (vars (?v1 S2)) (:pat #4292 #4293) #3232)
#4299 := (not #4294)
#2672 := (= f10 ?v0!8)
#2056 := (+ f3 #2046)
#2057 := (<= #2056 0::Int)
#4302 := (or #2057 #2672 #4299)
#4305 := (not #4302)
#4342 := (or #4305 #4339)
#4345 := (not #4342)
#1265 := (* -1::Int #102)
#1266 := (+ f3 #1265)
#1267 := (<= #1266 0::Int)
#3217 := (or #509 #1267)
#4284 := (forall (vars (?v0 S2)) (:pat #4283 #4241) #3217)
#4289 := (not #4284)
#600 := (= f14 f19)
#691 := (not #600)
decl f16 :: S4
#133 := f16
#597 := (= f15 f16)
#709 := (not #597)
decl f21 :: S5
#141 := f21
decl f20 :: S5
#140 := f20
#142 := (= f20 f21)
#682 := (not #142)
decl f18 :: S2
#136 := f18
decl f17 :: S2
#135 := f17
#137 := (= f17 f18)
#700 := (not #137)
#4348 := (or #700 #682 #709 #691 #4289 #4345)
#4796 := (?v1!7 ?v0!8)
#5111 := (f13 f19 #4796)
#5157 := (* -1::Int #5111)
#4797 := (f13 f14 #4796)
#6353 := (+ #4797 #5157)
#6357 := (<= #6353 0::Int)
#6352 := (= #4797 #5111)
#9885 := (= #5111 #4797)
#139 := (= f19 f14)
#4351 := (not #4348)
#9784 := [hypothesis]: #4351
#4102 := (or #4348 #600)
#4103 := [def-axiom]: #4102
#9853 := [unit-resolution #4103 #9784]: #600
#9854 := [symm #9853]: #139
#9886 := [monotonicity #9854]: #9885
#9783 := [symm #9886]: #6352
#9887 := (not #6352)
#9815 := (or #9887 #6357)
#9719 := [th-lemma arith triangle-eq]: #9815
#9720 := [unit-resolution #9719 #9783]: #6357
#4729 := (f13 f14 ?v0!8)
#4730 := (* -1::Int #4729)
#5068 := (+ #2045 #4730)
#6038 := (<= #5068 0::Int)
#6037 := (= #2045 #4729)
#9773 := (= #4729 #2045)
#10654 := [monotonicity #9853]: #9773
#10651 := [symm #10654]: #6037
#10657 := (not #6037)
#10656 := (or #10657 #6038)
#10658 := [th-lemma arith triangle-eq]: #10656
#10659 := [unit-resolution #10658 #10651]: #6038
#4798 := (* -1::Int #4797)
#4782 := (f5 #4796 ?v0!8)
#4783 := (f4 #4782)
#4784 := (* -1::Int #4783)
#4864 := (+ #4784 #4798)
#4865 := (+ #4729 #4864)
#4951 := (<= #4865 0::Int)
#4868 := (= #4865 0::Int)
#4850 := (not #4868)
#4799 := (+ #4729 #4798)
#4800 := (<= #4799 0::Int)
#4788 := (f8 f15 #4796)
#4789 := (= f1 #4788)
#4790 := (not #4789)
#4855 := (or #4790 #4800 #4850)
#4874 := (not #4855)
#4731 := (+ f3 #4730)
#4732 := (<= #4731 0::Int)
#10943 := (not #4732)
#5109 := (>= #5068 0::Int)
#10709 := (or #10657 #5109)
#10829 := [th-lemma arith triangle-eq]: #10709
#10802 := [unit-resolution #10829 #10651]: #5109
#2058 := (not #2057)
#4104 := (or #4348 #4342)
#4101 := [def-axiom]: #4104
#10253 := [unit-resolution #4101 #9784]: #4342
#3818 := (or #4348 #4284)
#4100 := [def-axiom]: #3818
#10315 := [unit-resolution #4100 #9784]: #4284
#10697 := (or #3329 #4289 #691)
#112 := (f13 f14 #11)
#1279 := (* -1::Int #112)
#1280 := (+ #102 #1279)
#1281 := (+ #83 #1280)
#1676 := (>= #1281 0::Int)
#512 := (not #509)
#3130 := (or #512 #1203 #1676)
#4250 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4217) #3130)
#4509 := (or #4351 #4506)
#4512 := (not #4509)
#2007 := (?v1!7 #12)
#2008 := (f13 f14 #2007)
#2631 := (* -1::Int #2008)
#2646 := (+ #102 #2631)
#2647 := (<= #2646 0::Int)
#2012 := (f5 #2007 #12)
#2013 := (f4 #2012)
#2632 := (* -1::Int #2013)
#2633 := (+ #2631 #2632)
#2634 := (+ #102 #2633)
#2635 := (= #2634 0::Int)
#3201 := (not #2635)
#2016 := (f8 f15 #2007)
#2017 := (= f1 #2016)
#3200 := (not #2017)
#3202 := (or #3200 #3201 #2647)
#3203 := (not #3202)
#3209 := (or #57 #1267 #3203)
#4275 := (forall (vars (?v0 S2)) (:pat #4241) #3209)
#4280 := (not #4275)
decl f11 :: (-> S2 Int)
#58 := (f11 #12)
#4186 := (pattern #58)
decl ?v1!6 :: (-> S2 S2)
#1979 := (?v1!6 #12)
#1983 := (f11 #1979)
#2590 := (* -1::Int #1983)
#1980 := (f5 #1979 #12)
#1981 := (f4 #1980)
#2607 := (* -1::Int #1981)
#2608 := (+ #2607 #2590)
#2609 := (+ #58 #2608)
#2610 := (= #2609 0::Int)
#3173 := (not #2610)
#2591 := (+ #58 #2590)
#2592 := (<= #2591 0::Int)
decl f12 :: S4
#66 := f12
#1989 := (f8 f12 #1979)
#1990 := (= f1 #1989)
#3172 := (not #1990)
#3174 := (or #3172 #2592 #3173)
#3175 := (not #3174)
#1227 := (* -1::Int #58)
#1228 := (+ f3 #1227)
#1229 := (<= #1228 0::Int)
#3181 := (or #57 #1229 #3175)
#4267 := (forall (vars (?v0 S2)) (:pat #4186) #3181)
#4272 := (not #4267)
#109 := (f8 f15 #11)
#4258 := (pattern #106 #109)
#1283 := (>= #1280 0::Int)
#515 := (= f1 #109)
#3138 := (not #515)
#3153 := (or #509 #3138 #1283)
#4259 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4258) #3153)
#4264 := (not #4259)
#4255 := (not #4250)
#1704 := (>= #102 0::Int)
#4242 := (forall (vars (?v0 S2)) (:pat #4241) #1704)
#4247 := (not #4242)
#100 := (f13 f14 f10)
#101 := (= #100 0::Int)
#1715 := (not #101)
#4515 := (or #1715 #4247 #4255 #4264 #4272 #4280 #4512)
#4518 := (not #4515)
decl ?v0!5 :: S2
#1935 := ?v0!5
#1936 := (f5 #12 ?v0!5)
#4226 := (pattern #1936)
#67 := (f8 f12 #12)
#4193 := (pattern #67)
#1938 := (f11 ?v0!5)
#1939 := (* -1::Int #1938)
#1937 := (f4 #1936)
#2558 := (+ #1937 #1939)
#2559 := (+ #58 #2558)
#2562 := (= #2559 0::Int)
#3091 := (not #2562)
#1943 := (+ #58 #1939)
#1944 := (>= #1943 0::Int)
#430 := (= f1 #67)
#433 := (not #430)
#3092 := (or #433 #1944 #3091)
#4227 := (forall (vars (?v1 S2)) (:pat #4193 #4186 #4226) #3092)
#4232 := (not #4227)
#2534 := (= f10 ?v0!5)
#1948 := (+ f3 #1939)
#1949 := (<= #1948 0::Int)
#4235 := (or #1949 #2534 #4232)
#4238 := (not #4235)
#4521 := (or #4238 #4518)
#4524 := (not #4521)
#78 := (f11 #11)
#1179 := (* -1::Int #78)
#1200 := (+ #1179 #83)
#1201 := (+ #58 #1200)
#1198 := (>= #1201 0::Int)
#3083 := (or #433 #1198 #1203)
#4218 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4217) #3083)
#4223 := (not #4218)
#4527 := (or #4223 #4524)
#4530 := (not #4527)
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)
#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
#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)
#268 := (implies #65 #267)
#60 := (implies #57 #59)
#61 := (forall (vars (?v0 S2)) #60)
#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)
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#1141 := (iff #268 #1138)
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#1125 := (implies #436 #1122)
#1130 := (iff #1125 #1129)
#1131 := [rewrite]: #1130
#1126 := (iff #267 #1125)
#1123 := (iff #266 #1122)
#1120 := (iff #265 #1117)
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#1114 := (iff #265 #1113)
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#1108 := (iff #263 #1105)
#1101 := (implies #74 #1098)
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#1107 := [rewrite]: #1106
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#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
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#1038 := (iff #253 #1035)
#1031 := (implies #530 #1026)
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#1037 := [rewrite]: #1036
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#1029 := (iff #252 #1026)
#1022 := (implies #556 #1017)
#1027 := (iff #1022 #1026)
#1028 := [rewrite]: #1027
#1023 := (iff #252 #1022)
#1020 := (iff #251 #1017)
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#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)
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#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)
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#4261 := [refl]: #4260
#4263 := [quant-intro #4261]: #4262
#4266 := [monotonicity #4263]: #4265
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#4253 := (iff #3135 #4250)
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#4252 := [refl]: #4251
#4254 := [quant-intro #4252]: #4253
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#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)
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#4233 := (iff #3109 #4232)
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#4234 := [monotonicity #4231]: #4233
#4237 := [monotonicity #4234]: #4236
#4240 := [monotonicity #4237]: #4239
#4523 := [monotonicity #4240 #4520]: #4522
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#4222 := [quant-intro #4220]: #4221
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#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
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#2925 := (and #775 #2323 #2922)
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#2931 := (forall (vars (?v1 S2)) #2928)
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#2945 := (or #2891 #2940)
#2948 := (and #1483 #2945)
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#2951 := (or #2864 #2948)
#2954 := (and #1464 #2951)
#2957 := (or #2244 #2954)
#2960 := (and #204 #2957)
#2963 := (or #1458 #2960)
#2966 := (and #787 #2963)
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#2972 := (and #1450 #2969)
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#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)
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#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)
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#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)
#4172 := (pattern #37)
#371 := (= f1 #36)
#38 := (f8 #37 #11)
#367 := (= f1 #38)
#374 := (iff #367 #371)
#4173 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) (:pat #4172) #374)
#377 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) #374)
#4176 := (iff #377 #4173)
#4174 := (iff #374 #374)
#4175 := [refl]: #4174
#4177 := [quant-intro #4175]: #4176
#1820 := (~ #377 #377)
#1847 := (~ #374 #374)
#1848 := [refl]: #1847
#1821 := [nnf-pos #1848]: #1820
#40 := (= #36 f1)
#39 := (= #38 f1)
#41 := (iff #39 #40)
#42 := (forall (vars (?v0 S4) (?v1 S2) (?v2 S1)) #41)
#378 := (iff #42 #377)
#375 := (iff #41 #374)
#372 := (iff #40 #371)
#373 := [rewrite]: #372
#369 := (iff #39 #367)
#370 := [rewrite]: #369
#376 := [monotonicity #370 #373]: #375
#379 := [quant-intro #376]: #378
#366 := [asserted]: #42
#382 := [mp #366 #379]: #377
#1849 := [mp~ #382 #1821]: #377
#4178 := [mp #1849 #4177]: #4173
#5852 := (not #4173)
#5856 := (or #5852 #5798)
#5796 := (= f1 f1)
#5793 := (iff #5798 #5796)
#5909 := (or #5852 #5793)
#5911 := (iff #5909 #5856)
#5915 := (iff #5856 #5856)
#5903 := [rewrite]: #5915
#5850 := (iff #5793 #5798)
#5847 := (iff #5798 true)
#5844 := (iff #5847 #5798)
#5849 := [rewrite]: #5844
#5842 := (iff #5793 #5847)
#5845 := (iff #5796 true)
#5846 := [rewrite]: #5845
#5848 := [monotonicity #5846]: #5842
#5851 := [trans #5848 #5849]: #5850
#5914 := [monotonicity #5851]: #5911
#5916 := [trans #5914 #5903]: #5911
#5910 := [quant-inst #105 #171 #4]: #5909
#5923 := [mp #5910 #5916]: #5856
#6546 := [unit-resolution #5923 #4178]: #5798
#6548 := [symm #6546]: #6547
#16201 := [monotonicity #16510 #6548]: #10522
#16227 := [trans #16201 #14411]: #10524
#23296 := [monotonicity #16227]: #23295
#23314 := [symm #23296]: #23299
#23289 := [hypothesis]: #2298
#23315 := [trans #23289 #23314]: #13583
#22104 := (not #13583)
#22103 := (not #13585)
#22099 := (or #22103 #13581 #22104)
#22105 := [def-axiom]: #22099
#23316 := [unit-resolution #22105 #23315 #23294]: #13581
#8173 := (not #8147)
#8015 := (f13 f14 ?v1!18)
#8190 := (+ #7747 #8015)
#8191 := (+ #2290 #8190)
#8194 := (>= #8191 0::Int)
#23305 := (not #8194)
#8050 := (* -1::Int #8015)
#8051 := (+ #2287 #8050)
#22802 := (>= #8051 0::Int)
#8020 := (= #2287 #8015)
#6858 := (f13 f14 #6633)
#16281 := (= #6858 #2221)
#16269 := (= #2221 #6858)
#13976 := (= ?v0!14 #6633)
#11546 := (f8 f15 ?v0!14)
#11948 := (= f1 #11546)
#13977 := (ite #13976 #5798 #11948)
#13978 := (f8 #8578 ?v0!14)
#13979 := (= f1 #13978)
#13905 := (iff #13977 #13979)
#13931 := (or #6350 #13905)
#13974 := (iff #13979 #13977)
#13932 := (or #6350 #13974)
#13934 := (iff #13932 #13931)
#13935 := (iff #13931 #13931)
#14012 := [rewrite]: #13935
#13930 := (iff #13974 #13905)
#13904 := [rewrite]: #13930
#13929 := [monotonicity #13904]: #13934
#14013 := [trans #13929 #14012]: #13934
#13933 := [quant-inst #105 #6633 #5797 #2216]: #13932
#14008 := [mp #13933 #14013]: #13931
#16192 := [unit-resolution #14008 #4185]: #13905
#16230 := (= #2217 #13978)
#16228 := (= #13978 #2217)
#16229 := [monotonicity #16227]: #16228
#16242 := [symm #16229]: #16230
#16171 := [hypothesis]: #2837
#4095 := (or #2832 #2218)
#4096 := [def-axiom]: #4095
#16198 := [unit-resolution #4096 #16171]: #2218
#16243 := [trans #16198 #16242]: #13979
#14767 := (not #13979)
#14761 := (not #13905)
#15396 := (or #14761 #13977 #14767)
#15397 := [def-axiom]: #15396
#16244 := [unit-resolution #15397 #16243 #16192]: #13977
#12960 := (not #11948)
#15863 := (f5 #6633 ?v0!14)
#15893 := (f7 #15863)
#16428 := (f8 f15 #15893)
#16429 := (= f1 #16428)
#16427 := (not #16429)
#16237 := (iff #16427 #12960)
#16232 := (iff #16429 #11948)
#16200 := (= #16428 #11546)
#16484 := (= #15893 ?v0!14)
#15894 := (= ?v0!14 #15893)
#15908 := (or #6483 #15894)
#15909 := [quant-inst #6633 #2216]: #15908
#16483 := [unit-resolution #15909 #4163]: #15894
#16485 := [symm #16483]: #16484
#16231 := [monotonicity #16485]: #16200
#16235 := [monotonicity #16231]: #16232
#16238 := [monotonicity #16235]: #16237
#12883 := (f5 f22 ?v0!14)
#12885 := (f4 #12883)
#12411 := (* -1::Int #2221)
#12914 := (+ #12411 #12885)
#12958 := (+ #175 #12914)
#12957 := (>= #12958 0::Int)
#13532 := (not #12957)
#12888 := (* -1::Int #12885)
#12884 := (+ f3 #12888)
#12924 := (<= #12884 0::Int)
#12972 := (or #12924 #12957)
#12977 := (not #12972)
#4091 := (not #2826)
#4092 := (or #2832 #4091)
#4097 := [def-axiom]: #4092
#16193 := [unit-resolution #4097 #16171]: #4091
#4012 := (or #4503 #4364)
#4007 := [def-axiom]: #4012
#12183 := [unit-resolution #4007 #12180]: #4364
#13228 := (or #4369 #2826 #12977)
#12889 := (+ #1421 #12888)
#12910 := (+ #2221 #12889)
#12919 := (<= #12910 0::Int)
#12918 := (or #12924 #12919)
#12925 := (not #12918)
#12909 := (or #2222 #12925)
#13245 := (or #4369 #12909)
#13539 := (iff #13245 #13228)
#12979 := (or #2826 #12977)
#13243 := (or #4369 #12979)
#13545 := (iff #13243 #13228)
#13546 := [rewrite]: #13545
#13234 := (iff #13245 #13243)
#12973 := (iff #12909 #12979)
#12952 := (iff #12925 #12977)
#12970 := (iff #12918 #12972)
#12975 := (iff #12919 #12957)
#12923 := (+ #2221 #12888)
#12927 := (+ #1421 #12923)
#12954 := (<= #12927 0::Int)
#12959 := (iff #12954 #12957)
#12974 := [rewrite]: #12959
#12917 := (iff #12919 #12954)
#12953 := (= #12910 #12927)
#12951 := [rewrite]: #12953
#12955 := [monotonicity #12951]: #12917
#12956 := [trans #12955 #12974]: #12975
#12976 := [monotonicity #12956]: #12970
#12978 := [monotonicity #12976]: #12952
#12980 := [monotonicity #2828 #12978]: #12973
#13544 := [monotonicity #12980]: #13234
#13547 := [trans #13544 #13546]: #13539
#13248 := [quant-inst #2216]: #13245
#13543 := [mp #13248 #13547]: #13228
#16270 := [unit-resolution #13543 #12183 #16193]: #12977
#13533 := (or #12972 #13532)
#13611 := [def-axiom]: #13533
#16271 := [unit-resolution #13611 #16270]: #13532
#16584 := (or #16427 #12957)
#15871 := (f4 #15863)
#15935 := (<= #15871 0::Int)
#16419 := (f13 f14 #15893)
#16422 := (* -1::Int #16419)
#16455 := (+ #2221 #16422)
#16465 := (<= #16455 0::Int)
#16454 := (= #2221 #16419)
#16486 := (= #16419 #2221)
#16481 := [monotonicity #16485]: #16486
#16487 := [symm #16481]: #16454
#16488 := (not #16454)
#16489 := (or #16488 #16465)
#16490 := [th-lemma arith triangle-eq]: #16489
#16491 := [unit-resolution #16490 #16487]: #16465
#15424 := [hypothesis]: #13532
#15872 := (* -1::Int #15871)
#16136 := (+ #12885 #15872)
#16143 := (>= #16136 0::Int)
#16133 := (= #12885 #15871)
#16513 := (= #15871 #12885)
#16511 := (= #15863 #12883)
#16512 := [monotonicity #16510]: #16511
#16514 := [monotonicity #16512]: #16513
#16509 := [symm #16514]: #16133
#16515 := (not #16133)
#16516 := (or #16515 #16143)
#16517 := [th-lemma arith triangle-eq]: #16516
#16518 := [unit-resolution #16517 #16509]: #16143
#6879 := (* -1::Int #6858)
#7903 := (+ #175 #6879)
#8012 := (>= #7903 0::Int)
#7909 := (= #175 #6858)
#12821 := (= #6858 #175)
#16519 := [monotonicity #16510]: #12821
#16523 := [symm #16519]: #7909
#12824 := (not #7909)
#12825 := (or #12824 #8012)
#12826 := [th-lemma arith triangle-eq]: #12825
#16524 := [unit-resolution #12826 #16523]: #8012
#16452 := (+ #6858 #16422)
#16453 := (>= #16452 0::Int)
#16522 := [hypothesis]: #16429
#16526 := (or #16427 #16453)
#6860 := (f8 f15 #6633)
#6861 := (= f1 #6860)
#13390 := (not #6861)
#13769 := (or #13768 #13390)
#15494 := (iff #733 #13390)
#15492 := (iff #730 #6861)
#15490 := (iff #6861 #730)
#15488 := (= #6860 #172)
#13757 := [hypothesis]: #6642
#13759 := [symm #13757]: #10520
#13760 := [monotonicity #13759]: #15488
#13765 := [monotonicity #13760]: #15490
#13766 := [symm #13765]: #15492
#13756 := [monotonicity #13766]: #15494
#4021 := (or #4503 #733)
#4016 := [def-axiom]: #4021
#13758 := [unit-resolution #4016 #12180]: #733
#13764 := [mp #13758 #13756]: #13390
#13755 := [hypothesis]: #6861
#13767 := [unit-resolution #13755 #13764]: false
#13774 := [lemma #13767]: #13769
#16525 := [unit-resolution #13774 #13795]: #13390
#3929 := (or #4515 #4259)
#3984 := [def-axiom]: #3929
#13392 := [unit-resolution #3984 #6587]: #4259
#16456 := (or #4264 #6861 #16427 #16453)
#16451 := (or #6861 #16427 #16453)
#16461 := (or #4264 #16451)
#16460 := (iff #16461 #16456)
#16463 := [rewrite]: #16460
#16462 := [quant-inst #15893 #6633]: #16461
#16464 := [mp #16462 #16463]: #16456
#16527 := [unit-resolution #16464 #13392 #16525]: #16526
#16528 := [unit-resolution #16527 #16522]: #16453
#16546 := (not #16465)
#13410 := (not #8012)
#16545 := (not #16453)
#16529 := (not #16143)
#16547 := (or #15935 #16529 #12957 #16545 #13410 #16546)
#16548 := [th-lemma arith assign-bounds 1 1 1 1 1]: #16547
#16549 := [unit-resolution #16548 #16528 #16524 #16518 #15424 #16491]: #15935
#15917 := (not #15935)
#15919 := (or #13976 #15917)
#15 := (f4 #14)
#330 := (<= #15 0::Int)
#331 := (not #330)
#13 := (= #11 #12)
#334 := (or #13 #331)
#4146 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4139) #334)
#337 := (forall (vars (?v0 S2) (?v1 S2)) #334)
#4149 := (iff #337 #4146)
#4147 := (iff #334 #334)
#4148 := [refl]: #4147
#4150 := [quant-intro #4148]: #4149
#1812 := (~ #337 #337)
#1811 := (~ #334 #334)
#1808 := [refl]: #1811
#1813 := [nnf-pos #1808]: #1812
#20 := (< 0::Int #15)
#19 := (not #13)
#21 := (implies #19 #20)
#22 := (forall (vars (?v0 S2) (?v1 S2)) #21)
#340 := (iff #22 #337)
#324 := (or #13 #20)
#327 := (forall (vars (?v0 S2) (?v1 S2)) #324)
#338 := (iff #327 #337)
#335 := (iff #324 #334)
#332 := (iff #20 #331)
#333 := [rewrite]: #332
#336 := [monotonicity #333]: #335
#339 := [quant-intro #336]: #338
#328 := (iff #22 #327)
#325 := (iff #21 #324)
#326 := [rewrite]: #325
#329 := [quant-intro #326]: #328
#341 := [trans #329 #339]: #340
#323 := [asserted]: #22
#342 := [mp #323 #341]: #337
#1809 := [mp~ #342 #1813]: #337
#4151 := [mp #1809 #4150]: #4146
#5423 := (not #4146)
#15916 := (or #5423 #13976 #15917)
#15910 := (= #6633 ?v0!14)
#15918 := (or #15910 #15917)
#15922 := (or #5423 #15918)
#15938 := (iff #15922 #15916)
#15924 := (or #5423 #15919)
#15939 := (iff #15924 #15916)
#15940 := [rewrite]: #15939
#15925 := (iff #15922 #15924)
#15920 := (iff #15918 #15919)
#15898 := (iff #15910 #13976)
#15899 := [rewrite]: #15898
#15921 := [monotonicity #15899]: #15920
#15926 := [monotonicity #15921]: #15925
#15941 := [trans #15926 #15940]: #15938
#15923 := [quant-inst #6633 #2216]: #15922
#15942 := [mp #15923 #15941]: #15916
#16544 := [unit-resolution #15942 #4151]: #15919
#16550 := [unit-resolution #16544 #16549]: #13976
#15911 := (= #15871 0::Int)
#16579 := (not #15911)
#15936 := (>= #15871 0::Int)
#16551 := (not #15936)
#16552 := (or #16551 #16529 #12957 #16545 #13410 #16546)
#16553 := [th-lemma arith assign-bounds 1 -1 1 1 -1]: #16552
#16554 := [unit-resolution #16553 #16528 #16524 #16518 #15424 #16491]: #16551
#16580 := (or #16579 #15936)
#16581 := [th-lemma arith triangle-eq]: #16580
#16582 := [unit-resolution #16581 #16554]: #16579
#14015 := (not #13976)
#15902 := (or #14015 #15911)
#16 := (= #15 0::Int)
#314 := (or #19 #16)
#4140 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4139) #314)
#317 := (forall (vars (?v0 S2) (?v1 S2)) #314)
#4143 := (iff #317 #4140)
#4141 := (iff #314 #314)
#4142 := [refl]: #4141
#4144 := [quant-intro #4142]: #4143
#1836 := (~ #317 #317)
#1834 := (~ #314 #314)
#1835 := [refl]: #1834
#1837 := [nnf-pos #1835]: #1836
#17 := (implies #13 #16)
#18 := (forall (vars (?v0 S2) (?v1 S2)) #17)
#320 := (iff #18 #317)
#293 := (= 0::Int #15)
#304 := (or #19 #293)
#309 := (forall (vars (?v0 S2) (?v1 S2)) #304)
#318 := (iff #309 #317)
#315 := (iff #304 #314)
#312 := (iff #293 #16)
#313 := [rewrite]: #312
#316 := [monotonicity #313]: #315
#319 := [quant-intro #316]: #318
#310 := (iff #18 #309)
#307 := (iff #17 #304)
#301 := (implies #13 #293)
#305 := (iff #301 #304)
#306 := [rewrite]: #305
#302 := (iff #17 #301)
#299 := (iff #16 #293)
#300 := [rewrite]: #299
#303 := [monotonicity #300]: #302
#308 := [trans #303 #306]: #307
#311 := [quant-intro #308]: #310
#321 := [trans #311 #319]: #320
#292 := [asserted]: #18
#322 := [mp #292 #321]: #317
#1810 := [mp~ #322 #1837]: #317
#4145 := [mp #1810 #4144]: #4140
#5404 := (not #4140)
#15904 := (or #5404 #14015 #15911)
#15914 := (not #15910)
#15915 := (or #15914 #15911)
#15905 := (or #5404 #15915)
#15932 := (iff #15905 #15904)
#15907 := (or #5404 #15902)
#15930 := (iff #15907 #15904)
#15931 := [rewrite]: #15930
#15928 := (iff #15905 #15907)
#15897 := (iff #15915 #15902)
#15900 := (iff #15914 #14015)
#15901 := [monotonicity #15899]: #15900
#15903 := [monotonicity #15901]: #15897
#15929 := [monotonicity #15903]: #15928
#15933 := [trans #15929 #15931]: #15932
#15906 := [quant-inst #6633 #2216]: #15905
#15934 := [mp #15906 #15933]: #15904
#16583 := [unit-resolution #15934 #4145]: #15902
#16578 := [unit-resolution #16583 #16582 #16550]: false
#16585 := [lemma #16578]: #16584
#16246 := [unit-resolution #16585 #16271]: #16427
#16239 := [mp #16246 #16238]: #12960
#14014 := (not #13977)
#14082 := (or #14014 #13976 #11948)
#14083 := [def-axiom]: #14082
#16240 := [unit-resolution #14083 #16239 #16244]: #13976
#16275 := [monotonicity #16240]: #16269
#16278 := [symm #16275]: #16281
#16297 := (= #2220 #6858)
#14771 := (= #2220 #175)
#6119 := (f24 f22)
#16276 := (= #6119 #175)
#6120 := (= #175 #6119)
#6108 := (f4 #6107)
#6127 := (>= #6108 0::Int)
#6111 := (* -1::Int #6108)
#6115 := (+ f3 #6111)
#6116 := (<= #6115 0::Int)
#6132 := (or #6116 #6127)
#6641 := (= #6108 0::Int)
#14106 := (not #6641)
#12532 := [hypothesis]: #14106
#12874 := (or #5404 #6641)
#6327 := (= f22 f22)
#6647 := (not #6327)
#6650 := (or #6647 #6641)
#12896 := (or #5404 #6650)
#13528 := (iff #12896 #12874)
#13607 := (iff #12874 #12874)
#13608 := [rewrite]: #13607
#6692 := (iff #6650 #6641)
#6704 := (or false #6641)
#6708 := (iff #6704 #6641)
#6709 := [rewrite]: #6708
#6706 := (iff #6650 #6704)
#6658 := (iff #6647 false)
#6651 := (iff #6647 #3871)
#6333 := (iff #6327 true)
#6334 := [rewrite]: #6333
#6657 := [monotonicity #6334]: #6651
#6703 := [trans #6657 #3862]: #6658
#6707 := [monotonicity #6703]: #6706
#6693 := [trans #6707 #6709]: #6692
#13526 := [monotonicity #6693]: #13528
#13661 := [trans #13526 #13608]: #13528
#12880 := [quant-inst #171 #171]: #12896
#13751 := [mp #12880 #13661]: #12874
#12426 := [unit-resolution #13751 #4145 #12532]: false
#12190 := [lemma #12426]: #6641
#16194 := (or #14106 #6127)
#16166 := [th-lemma arith triangle-eq]: #16194
#16169 := [unit-resolution #16166 #12190]: #6127
#6370 := (not #6127)
#6355 := (or #6132 #6370)
#6356 := [def-axiom]: #6355
#16195 := [unit-resolution #6356 #16169]: #6132
#6135 := (not #6132)
#6138 := (or #6120 #6135)
#6282 := (or #4369 #6120 #6135)
#6112 := (+ #1421 #6111)
#6113 := (+ #175 #6112)
#6114 := (<= #6113 0::Int)
#6117 := (or #6116 #6114)
#6118 := (not #6117)
#6121 := (or #6120 #6118)
#6289 := (or #4369 #6121)
#6365 := (iff #6289 #6282)
#6325 := (or #4369 #6138)
#6362 := (iff #6325 #6282)
#6363 := [rewrite]: #6362
#6360 := (iff #6289 #6325)
#6139 := (iff #6121 #6138)
#6136 := (iff #6118 #6135)
#6133 := (iff #6117 #6132)
#6130 := (iff #6114 #6127)
#6124 := (<= #6111 0::Int)
#6128 := (iff #6124 #6127)
#6129 := [rewrite]: #6128
#6125 := (iff #6114 #6124)
#6122 := (= #6113 #6111)
#6123 := [rewrite]: #6122
#6126 := [monotonicity #6123]: #6125
#6131 := [trans #6126 #6129]: #6130
#6134 := [monotonicity #6131]: #6133
#6137 := [monotonicity #6134]: #6136
#6140 := [monotonicity #6137]: #6139
#6361 := [monotonicity #6140]: #6360
#6326 := [trans #6361 #6363]: #6365
#6324 := [quant-inst #171]: #6289
#6366 := [mp #6324 #6326]: #6282
#16196 := [unit-resolution #6366 #12183]: #6138
#16197 := [unit-resolution #16196 #16195]: #6120
#16279 := [symm #16197]: #16276
#14379 := (= #2220 #6119)
#6789 := (f24 #6633)
#15473 := (= #6789 #6119)
#16274 := [monotonicity #16510]: #15473
#16199 := (= #2220 #6789)
#16273 := [monotonicity #16240]: #16199
#16282 := [trans #16273 #16274]: #14379
#16291 := [trans #16282 #16279]: #14771
#16298 := [trans #16291 #16523]: #16297
#16299 := [trans #16298 #16278]: #2826
#16285 := [unit-resolution #16193 #16299]: false
#16290 := [lemma #16285]: #2832
#3987 := (or #4503 #4497)
#3988 := [def-axiom]: #3987
#14163 := [unit-resolution #3988 #12180]: #4497
#11130 := (f5 f22 ?v0!13)
#11133 := (f4 #11130)
#11305 := (+ #2200 #11133)
#11302 := (+ #175 #11305)
#11707 := (>= #11302 0::Int)
#11263 := (= #11302 0::Int)
#11186 := (* -1::Int #11133)
#11215 := (+ f3 #11186)
#11269 := (<= #11215 0::Int)
#12311 := (not #11269)
#11201 := (+ #2816 #11133)
#11206 := (+ #175 #11201)
#11195 := (>= #11206 0::Int)
#12033 := (or #11195 #11269)
#10743 := (not #12033)
#11606 := (= #2199 #2201)
#12673 := (not #11606)
#12526 := [hypothesis]: #2823
#11506 := (or #12673 #2818)
#12181 := [th-lemma arith triangle-eq]: #11506
#12182 := [unit-resolution #12181 #12526]: #12673
#12297 := (or #4369 #11606 #10743)
#11235 := (+ #1421 #11186)
#11236 := (+ #2201 #11235)
#11214 := (<= #11236 0::Int)
#11708 := (or #11269 #11214)
#11683 := (not #11708)
#11616 := (= #2201 #2199)
#11617 := (or #11616 #11683)
#12257 := (or #4369 #11617)
#12299 := (iff #12257 #12297)
#11871 := (or #11606 #10743)
#12301 := (or #4369 #11871)
#12342 := (iff #12301 #12297)
#12348 := [rewrite]: #12342
#12303 := (iff #12257 #12301)
#12204 := (iff #11617 #11871)
#12253 := (iff #11683 #10743)
#9994 := (iff #11708 #12033)
#11702 := (or #11269 #11195)
#12034 := (iff #11702 #12033)
#11922 := [rewrite]: #12034
#11924 := (iff #11708 #11702)
#11218 := (iff #11214 #11195)
#11191 := (+ #2201 #11186)
#11270 := (+ #1421 #11191)
#9774 := (<= #11270 0::Int)
#11304 := (iff #9774 #11195)
#11325 := [rewrite]: #11304
#10652 := (iff #11214 #9774)
#11303 := (= #11236 #11270)
#9768 := [rewrite]: #11303
#10653 := [monotonicity #9768]: #10652
#11326 := [trans #10653 #11325]: #11218
#11949 := [monotonicity #11326]: #11924
#11854 := [trans #11949 #11922]: #9994
#12198 := [monotonicity #11854]: #12253
#11611 := (iff #11616 #11606)
#11923 := [rewrite]: #11611
#12197 := [monotonicity #11923 #12198]: #12204
#12283 := [monotonicity #12197]: #12303
#12349 := [trans #12283 #12348]: #12299
#12295 := [quant-inst #2198]: #12257
#12305 := [mp #12295 #12349]: #12297
#12192 := [unit-resolution #12305 #12183 #12182]: #10743
#12339 := (or #12033 #12311)
#12392 := [def-axiom]: #12339
#12678 := [unit-resolution #12392 #12192]: #12311
#12347 := (not #11195)
#12314 := (or #12033 #12347)
#12329 := [def-axiom]: #12314
#12413 := [unit-resolution #12329 #12192]: #12347
#11408 := (or #11195 #11263 #11269)
#4013 := (or #4503 #4372)
#3986 := [def-axiom]: #4013
#12414 := [unit-resolution #3986 #12180]: #4372
#11620 := (or #4377 #11195 #11263 #11269)
#11135 := (+ #11133 #2200)
#11098 := (+ #175 #11135)
#11120 := (= #11098 0::Int)
#11202 := (or #11269 #11214 #11120)
#11586 := (or #4377 #11202)
#11674 := (iff #11586 #11620)
#11621 := (or #4377 #11408)
#11781 := (iff #11621 #11620)
#11785 := [rewrite]: #11781
#11650 := (iff #11586 #11621)
#11402 := (iff #11202 #11408)
#11328 := (or #11269 #11195 #11263)
#11412 := (iff #11328 #11408)
#11467 := [rewrite]: #11412
#11380 := (iff #11202 #11328)
#11239 := (iff #11120 #11263)
#11301 := (= #11098 #11302)
#11299 := [rewrite]: #11301
#11264 := [monotonicity #11299]: #11239
#11262 := [monotonicity #11326 #11264]: #11380
#11619 := [trans #11262 #11467]: #11402
#11784 := [monotonicity #11619]: #11650
#11737 := [trans #11784 #11785]: #11674
#11585 := [quant-inst #2198]: #11586
#11672 := [mp #11585 #11737]: #11620
#12415 := [unit-resolution #11672 #12414]: #11408
#12405 := [unit-resolution #12415 #12413 #12678]: #11263
#12036 := (not #11263)
#12542 := (or #12036 #11707)
#12499 := [th-lemma arith triangle-eq]: #12542
#12543 := [unit-resolution #12499 #12405]: #11707
#12312 := (>= #2817 0::Int)
#12431 := (or #12312 #2818)
#12530 := [th-lemma arith farkas 1 1]: #12431
#11405 := [unit-resolution #12530 #12526]: #12312
#12529 := [th-lemma arith farkas 1 -1 1 #11405 #12413 #12543]: false
#11320 := [lemma #12529]: #2818
#4017 := (or #4500 #2823 #4494)
#4018 := [def-axiom]: #4017
#14172 := [unit-resolution #4018 #11320 #14163]: #4494
#4032 := (or #4491 #4485)
#4033 := [def-axiom]: #4032
#21229 := [unit-resolution #4033 #14172]: #4485
#4028 := (or #4488 #2837 #4482)
#4029 := [def-axiom]: #4028
#21233 := [unit-resolution #4029 #21229]: #4485
#21234 := [unit-resolution #21233 #16290]: #4482
#4038 := (or #4479 #4389)
#4040 := [def-axiom]: #4038
#21235 := [unit-resolution #4040 #21234]: #4389
#22059 := (or #4394 #3439 #8020)
#8016 := (= #8015 #2287)
#8019 := (or #8016 #3439)
#22060 := (or #4394 #8019)
#22065 := (iff #22060 #22059)
#8026 := (or #3439 #8020)
#22029 := (or #4394 #8026)
#22063 := (iff #22029 #22059)
#22064 := [rewrite]: #22063
#22061 := (iff #22060 #22029)
#8029 := (iff #8019 #8026)
#8023 := (or #8020 #3439)
#8027 := (iff #8023 #8026)
#8028 := [rewrite]: #8027
#8024 := (iff #8019 #8023)
#8021 := (iff #8016 #8020)
#8022 := [rewrite]: #8021
#8025 := [monotonicity #8022]: #8024
#8030 := [trans #8025 #8028]: #8029
#22062 := [monotonicity #8030]: #22061
#22068 := [trans #22062 #22064]: #22065
#22058 := [quant-inst #2283]: #22060
#22069 := [mp #22058 #22068]: #22059
#23317 := [unit-resolution #22069 #21235 #23289]: #8020
#23318 := (not #8020)
#23319 := (or #23318 #22802)
#23320 := [th-lemma arith triangle-eq]: #23319
#23321 := [unit-resolution #23320 #23317]: #22802
#23303 := [hypothesis]: #4090
#7748 := (+ #2285 #7747)
#7749 := (<= #7748 0::Int)
#4030 := (or #4491 #4380)
#4031 := [def-axiom]: #4030
#16406 := [unit-resolution #4031 #14172]: #4380
#22553 := (or #4385 #7749)
#7739 := (+ #7706 #2286)
#7740 := (>= #7739 0::Int)
#22554 := (or #4385 #7740)
#22578 := (iff #22554 #22553)
#22580 := (iff #22553 #22553)
#22581 := [rewrite]: #22580
#7752 := (iff #7740 #7749)
#7741 := (+ #2286 #7706)
#7744 := (>= #7741 0::Int)
#7750 := (iff #7744 #7749)
#7751 := [rewrite]: #7750
#7745 := (iff #7740 #7744)
#7742 := (= #7739 #7741)
#7743 := [rewrite]: #7742
#7746 := [monotonicity #7743]: #7745
#7753 := [trans #7746 #7751]: #7752
#22579 := [monotonicity #7753]: #22578
#22576 := [trans #22579 #22581]: #22578
#22577 := [quant-inst #2284]: #22554
#22582 := [mp #22577 #22576]: #22553
#23304 := [unit-resolution #22582 #16406]: #7749
#23307 := (not #7749)
#23306 := (not #22802)
#23285 := (or #23305 #2883 #23306 #23307)
#23286 := [th-lemma arith assign-bounds 1 1 -1]: #23285
#23284 := [unit-resolution #23286 #23304 #23303 #23321]: #23305
#23287 := (or #8173 #8194)
#23352 := [hypothesis]: #2296
#22714 := (or #4255 #2295 #8173 #8194)
#8186 := (+ #8015 #7747)
#8187 := (+ #2290 #8186)
#8188 := (>= #8187 0::Int)
#8189 := (or #8173 #2295 #8188)
#22715 := (or #4255 #8189)
#22739 := (iff #22715 #22714)
#8200 := (or #2295 #8173 #8194)
#22720 := (or #4255 #8200)
#22722 := (iff #22720 #22714)
#22723 := [rewrite]: #22722
#22713 := (iff #22715 #22720)
#8203 := (iff #8189 #8200)
#8197 := (or #8173 #2295 #8194)
#8201 := (iff #8197 #8200)
#8202 := [rewrite]: #8201
#8198 := (iff #8189 #8197)
#8195 := (iff #8188 #8194)
#8192 := (= #8187 #8191)
#8193 := [rewrite]: #8192
#8196 := [monotonicity #8193]: #8195
#8199 := [monotonicity #8196]: #8198
#8204 := [trans #8199 #8202]: #8203
#22721 := [monotonicity #8204]: #22713
#22740 := [trans #22721 #22723]: #22739
#22719 := [quant-inst #2284 #2283]: #22715
#22738 := [mp #22719 #22740]: #22714
#23288 := [unit-resolution #22738 #9283 #23352]: #23287
#23290 := [unit-resolution #23288 #23284]: #8173
#22091 := (not #13581)
#22094 := (or #22091 #13580 #8147)
#22095 := [def-axiom]: #22094
#23291 := [unit-resolution #22095 #23290 #23316]: #13580
#23293 := [trans #23291 #16510]: #23292
#22436 := [monotonicity #23293]: #22435
#22437 := [monotonicity #22436]: #23160
#22438 := (not #23160)
#22440 := (or #22438 #23171)
#22434 := [th-lemma arith triangle-eq]: #22440
#22442 := [unit-resolution #22434 #22437]: #23171
decl f6 :: (-> S3 S2)
#8254 := (f6 #2289)
#8989 := (f13 f14 #8254)
#9003 := (* -1::Int #8989)
#23119 := (+ #8015 #9003)
#23122 := (>= #23119 0::Int)
#23118 := (= #8015 #8989)
#22446 := (= #8989 #8015)
#22444 := (= #8254 ?v1!18)
#8255 := (= ?v1!18 #8254)
#23 := (f6 #14)
#344 := (= #11 #23)
#4152 := (forall (vars (?v0 S2) (?v1 S2)) (:pat #4139) #344)
#347 := (forall (vars (?v0 S2) (?v1 S2)) #344)
#4155 := (iff #347 #4152)
#4153 := (iff #344 #344)
#4154 := [refl]: #4153
#4156 := [quant-intro #4154]: #4155
#1814 := (~ #347 #347)
#1838 := (~ #344 #344)
#1839 := [refl]: #1838
#1815 := [nnf-pos #1839]: #1814
#24 := (= #23 #11)
#25 := (forall (vars (?v0 S2) (?v1 S2)) #24)
#348 := (iff #25 #347)
#345 := (iff #24 #344)
#346 := [rewrite]: #345
#349 := [quant-intro #346]: #348
#343 := [asserted]: #25
#352 := [mp #343 #349]: #347
#1840 := [mp~ #352 #1815]: #347
#4157 := [mp #1840 #4156]: #4152
#6486 := (not #4152)
#22889 := (or #6486 #8255)
#22890 := [quant-inst #2283 #2284]: #22889
#22443 := [unit-resolution #22890 #4157]: #8255
#22445 := [symm #22443]: #22444
#22512 := [monotonicity #22445]: #22446
#22591 := [symm #22512]: #23118
#22511 := (not #23118)
#22592 := (or #22511 #23122)
#22599 := [th-lemma arith triangle-eq]: #22592
#22600 := [unit-resolution #22599 #22591]: #23122
#9004 := (+ #175 #9003)
#9005 := (<= #9004 0::Int)
#8994 := (f8 f15 #8254)
#8995 := (= f1 #8994)
#23333 := (not #8995)
#23334 := (iff #8173 #23333)
#23332 := (iff #8147 #8995)
#23330 := (iff #8995 #8147)
#23328 := (= #8994 #8146)
#23329 := [monotonicity #22445]: #23328
#23331 := [monotonicity #23329]: #23330
#23313 := [symm #23331]: #23332
#23335 := [monotonicity #23313]: #23334
#23336 := [mp #23290 #23335]: #23333
#9010 := (or #8995 #9005)
#4022 := (or #4503 #4354)
#4008 := [def-axiom]: #4022
#23337 := [unit-resolution #4008 #12180]: #4354
#22808 := (or #4359 #8995 #9005)
#8990 := (+ #8989 #1421)
#8993 := (>= #8990 0::Int)
#8996 := (or #8995 #8993)
#22937 := (or #4359 #8996)
#22977 := (iff #22937 #22808)
#22944 := (or #4359 #9010)
#22947 := (iff #22944 #22808)
#22976 := [rewrite]: #22947
#22945 := (iff #22937 #22944)
#9011 := (iff #8996 #9010)
#9008 := (iff #8993 #9005)
#8997 := (+ #1421 #8989)
#9000 := (>= #8997 0::Int)
#9006 := (iff #9000 #9005)
#9007 := [rewrite]: #9006
#9001 := (iff #8993 #9000)
#8998 := (= #8990 #8997)
#8999 := [rewrite]: #8998
#9002 := [monotonicity #8999]: #9001
#9009 := [trans #9002 #9007]: #9008
#9012 := [monotonicity #9009]: #9011
#22946 := [monotonicity #9012]: #22945
#22978 := [trans #22946 #22976]: #22977
#22943 := [quant-inst #8254]: #22937
#22979 := [mp #22943 #22978]: #22808
#23344 := [unit-resolution #22979 #23337]: #9010
#23345 := [unit-resolution #23344 #23336]: #9005
#23346 := (not #23122)
#23343 := (not #9005)
#23356 := (not #23171)
#23347 := (or #22698 #23307 #23356 #2883 #23343 #23346 #23306)
#23348 := [th-lemma arith assign-bounds -1 1 1 -1 1 1]: #23347
#23341 := [unit-resolution #23348 #23304 #23303 #23321 #23345 #22600 #22442]: #22698
#7772 := (+ f3 #7768)
#7773 := (<= #7772 0::Int)
#22711 := (not #7773)
#23357 := (or #22711 #23356 #2295)
#23353 := [hypothesis]: #7773
#23354 := [hypothesis]: #23171
#23355 := [th-lemma arith farkas 1 -1 1 #23354 #23353 #23352]: false
#23358 := [lemma #23355]: #23357
#23342 := [unit-resolution #23358 #22442 #23352]: #22711
#7789 := (+ #2286 #7764)
#7790 := (+ #175 #7789)
#7793 := (= #7790 0::Int)
#23360 := (not #7793)
#22682 := (>= #7790 0::Int)
#23349 := (not #22682)
#23350 := (or #23349 #23356 #2883 #23343 #23346 #23306)
#23351 := [th-lemma arith assign-bounds 1 1 -1 1 1]: #23350
#23359 := [unit-resolution #23351 #23321 #23303 #23345 #22600 #22442]: #23349
#23361 := (or #23360 #22682)
#23362 := [th-lemma arith triangle-eq]: #23361
#23363 := [unit-resolution #23362 #23359]: #23360
#7796 := (or #7773 #7784 #7793)
#22583 := (or #4377 #7773 #7784 #7793)
#7765 := (+ #7764 #2286)
#7766 := (+ #175 #7765)
#7767 := (= #7766 0::Int)
#7769 := (+ #1421 #7768)
#7770 := (+ #7706 #7769)
#7771 := (<= #7770 0::Int)
#7774 := (or #7773 #7771 #7767)
#22584 := (or #4377 #7774)
#22597 := (iff #22584 #22583)
#22586 := (or #4377 #7796)
#22593 := (iff #22586 #22583)
#22596 := [rewrite]: #22593
#22594 := (iff #22584 #22586)
#7797 := (iff #7774 #7796)
#7794 := (iff #7767 #7793)
#7791 := (= #7766 #7790)
#7792 := [rewrite]: #7791
#7795 := [monotonicity #7792]: #7794
#7787 := (iff #7771 #7784)
#7775 := (+ #7706 #7768)
#7776 := (+ #1421 #7775)
#7779 := (<= #7776 0::Int)
#7785 := (iff #7779 #7784)
#7786 := [rewrite]: #7785
#7780 := (iff #7771 #7779)
#7777 := (= #7770 #7776)
#7778 := [rewrite]: #7777
#7781 := [monotonicity #7778]: #7780
#7788 := [trans #7781 #7786]: #7787
#7798 := [monotonicity #7788 #7795]: #7797
#22595 := [monotonicity #7798]: #22594
#22598 := [trans #22595 #22596]: #22597
#22585 := [quant-inst #2284]: #22584
#22683 := [mp #22585 #22598]: #22583
#23364 := [unit-resolution #22683 #12414]: #7796
#23365 := [unit-resolution #23364 #23363 #23342 #23341]: false
#23367 := [lemma #23365]: #23366
#26248 := [unit-resolution #23367 #24467 #26253 #26260]: false
#26288 := [lemma #26248]: #3454
#6943 := (f13 f14 ?v0!15)
#7164 := (>= #6943 0::Int)
#4002 := (or #4515 #4242)
#3998 := [def-axiom]: #4002
#6588 := [unit-resolution #3998 #6587]: #4242
#7167 := (or #4247 #7164)
#7168 := [quant-inst #2241]: #7167
#7188 := [unit-resolution #7168 #6588]: #7164
#6977 := (* -1::Int #6943)
#6978 := (+ #2242 #6977)
#7187 := (>= #6978 0::Int)
#6946 := (= #2242 #6943)
#7412 := [hypothesis]: #2244
#18221 := (or #6946 #2243)
#6239 := (>= #175 0::Int)
#6242 := (or #4247 #6239)
#6243 := [quant-inst #171]: #6242
#6589 := [unit-resolution #6243 #6588]: #6239
#16828 := (f5 #6633 ?v0!15)
#16895 := (f4 #16828)
#16790 := (* -1::Int #16895)
#6993 := (f5 f22 ?v0!15)
#6994 := (f4 #6993)
#18188 := (+ #6994 #16790)
#18308 := (>= #18188 0::Int)
#18312 := (= #6994 #16895)
#15755 := (= #16895 #6994)
#15886 := (= #16828 #6993)
#15887 := [monotonicity #16510]: #15886
#16048 := [monotonicity #15887]: #15755
#16041 := [symm #16048]: #18312
#16042 := (not #18312)
#16024 := (or #16042 #18308)
#16031 := [th-lemma arith triangle-eq]: #16024
#16320 := [unit-resolution #16031 #16041]: #18308
#18195 := (>= #16895 0::Int)
#18023 := (<= #16895 0::Int)
#18224 := (not #18023)
#23823 := (= ?v0!15 #6633)
#17264 := (not #23823)
#7075 := (f8 f15 ?v0!15)
#7076 := (= f1 #7075)
#23824 := (ite #23823 #5798 #7076)
#17239 := (not #23824)
#23833 := (f8 #8578 ?v0!15)
#23834 := (= f1 #23833)
#23836 := (iff #23824 #23834)
#17065 := (or #6350 #23836)
#23835 := (iff #23834 #23824)
#17066 := (or #6350 #23835)
#17067 := (iff #17066 #17065)
#17263 := (iff #17065 #17065)
#17261 := [rewrite]: #17263
#23837 := (iff #23835 #23836)
#23838 := [rewrite]: #23837
#17258 := [monotonicity #23838]: #17067
#17249 := [trans #17258 #17261]: #17067
#16990 := [quant-inst #105 #6633 #5797 #2241]: #17066
#17061 := [mp #16990 #17249]: #17065
#16612 := [unit-resolution #17061 #4185]: #23836
#17325 := (not #23834)
#6940 := (f8 f23 ?v0!15)
#6941 := (= f1 #6940)
#6942 := (not #6941)
#17255 := (iff #6942 #17325)
#16789 := (iff #6941 #23834)
#16751 := (iff #23834 #6941)
#16958 := (= #23833 #6940)
#16959 := [monotonicity #16227]: #16958
#16788 := [monotonicity #16959]: #16751
#16787 := [symm #16788]: #16789
#17269 := [monotonicity #16787]: #17255
#7399 := (not #6946)
#7400 := [hypothesis]: #7399
#6952 := (or #6942 #6946)
#6957 := (or #4394 #6942 #6946)
#6944 := (= #6943 #2242)
#6945 := (or #6944 #6942)
#6958 := (or #4394 #6945)
#6965 := (iff #6958 #6957)
#6960 := (or #4394 #6952)
#6963 := (iff #6960 #6957)
#6964 := [rewrite]: #6963
#6961 := (iff #6958 #6960)
#6955 := (iff #6945 #6952)
#6949 := (or #6946 #6942)
#6953 := (iff #6949 #6952)
#6954 := [rewrite]: #6953
#6950 := (iff #6945 #6949)
#6947 := (iff #6944 #6946)
#6948 := [rewrite]: #6947
#6951 := [monotonicity #6948]: #6950
#6956 := [trans #6951 #6954]: #6955
#6962 := [monotonicity #6956]: #6961
#6966 := [trans #6962 #6964]: #6965
#6959 := [quant-inst #2241]: #6958
#6967 := [mp #6959 #6966]: #6957
#15581 := [unit-resolution #6967 #21235]: #6952
#15927 := [unit-resolution #15581 #7400]: #6942
#17322 := [mp #15927 #17269]: #17325
#17267 := (not #23836)
#17291 := (or #17267 #17239 #23834)
#17356 := [def-axiom]: #17291
#17689 := [unit-resolution #17356 #17322 #16612]: #17239
#17695 := (or #23824 #17264)
#6364 := (not #5798)
#17260 := (or #23824 #17264 #6364)
#17268 := [def-axiom]: #17260
#17696 := [unit-resolution #17268 #6546]: #17695
#17668 := [unit-resolution #17696 #17689]: #17264
#18219 := (or #18224 #23823)
#18191 := (or #5423 #18224 #23823)
#17755 := (= #6633 ?v0!15)
#18196 := (or #17755 #18224)
#18162 := (or #5423 #18196)
#18309 := (iff #18162 #18191)
#18194 := (or #5423 #18219)
#18220 := (iff #18194 #18191)
#18193 := [rewrite]: #18220
#18190 := (iff #18162 #18194)
#18189 := (iff #18196 #18219)
#18226 := (or #23823 #18224)
#18253 := (iff #18226 #18219)
#18225 := [rewrite]: #18253
#18227 := (iff #18196 #18226)
#17925 := (iff #17755 #23823)
#17895 := [rewrite]: #17925
#18223 := [monotonicity #17895]: #18227
#18161 := [trans #18223 #18225]: #18189
#18186 := [monotonicity #18161]: #18190
#18304 := [trans #18186 #18193]: #18309
#18192 := [quant-inst #6633 #2241]: #18162
#18306 := [mp #18192 #18304]: #18191
#17678 := [unit-resolution #18306 #4151]: #18219
#17690 := [unit-resolution #17678 #17668]: #18224
#17694 := (or #18195 #18023)
#17688 := [th-lemma arith farkas 1 1]: #17694
#17680 := [unit-resolution #17688 #17690]: #18195
#6968 := (* -1::Int #2242)
#7019 := (+ #6968 #6994)
#7020 := (+ #175 #7019)
#7040 := (<= #7020 0::Int)
#7023 := (= #7020 0::Int)
#6998 := (* -1::Int #6994)
#7002 := (+ f3 #6998)
#7003 := (<= #7002 0::Int)
#7065 := (not #7003)
#7012 := (+ #6977 #6994)
#7013 := (+ #175 #7012)
#7014 := (>= #7013 0::Int)
#7045 := (or #7003 #7014)
#7048 := (not #7045)
#7051 := (or #6946 #7048)
#7054 := (or #4369 #6946 #7048)
#6999 := (+ #1421 #6998)
#7000 := (+ #6943 #6999)
#7001 := (<= #7000 0::Int)
#7042 := (or #7003 #7001)
#7043 := (not #7042)
#7044 := (or #6944 #7043)
#7055 := (or #4369 #7044)
#7062 := (iff #7055 #7054)
#7057 := (or #4369 #7051)
#7060 := (iff #7057 #7054)
#7061 := [rewrite]: #7060
#7058 := (iff #7055 #7057)
#7052 := (iff #7044 #7051)
#7049 := (iff #7043 #7048)
#7046 := (iff #7042 #7045)
#7017 := (iff #7001 #7014)
#7005 := (+ #6943 #6998)
#7006 := (+ #1421 #7005)
#7009 := (<= #7006 0::Int)
#7015 := (iff #7009 #7014)
#7016 := [rewrite]: #7015
#7010 := (iff #7001 #7009)
#7007 := (= #7000 #7006)
#7008 := [rewrite]: #7007
#7011 := [monotonicity #7008]: #7010
#7018 := [trans #7011 #7016]: #7017
#7047 := [monotonicity #7018]: #7046
#7050 := [monotonicity #7047]: #7049
#7053 := [monotonicity #6948 #7050]: #7052
#7059 := [monotonicity #7053]: #7058
#7063 := [trans #7059 #7061]: #7062
#7056 := [quant-inst #2241]: #7055
#7064 := [mp #7056 #7063]: #7054
#17697 := [unit-resolution #7064 #12183]: #7051
#17687 := [unit-resolution #17697 #7400]: #7048
#7066 := (or #7045 #7065)
#7067 := [def-axiom]: #7066
#17704 := [unit-resolution #7067 #17687]: #7065
#7068 := (not #7014)
#7069 := (or #7045 #7068)
#7070 := [def-axiom]: #7069
#17686 := [unit-resolution #7070 #17687]: #7068
#7026 := (or #7003 #7014 #7023)
#7029 := (or #4377 #7003 #7014 #7023)
#6995 := (+ #6994 #6968)
#6996 := (+ #175 #6995)
#6997 := (= #6996 0::Int)
#7004 := (or #7003 #7001 #6997)
#7030 := (or #4377 #7004)
#7037 := (iff #7030 #7029)
#7032 := (or #4377 #7026)
#7035 := (iff #7032 #7029)
#7036 := [rewrite]: #7035
#7033 := (iff #7030 #7032)
#7027 := (iff #7004 #7026)
#7024 := (iff #6997 #7023)
#7021 := (= #6996 #7020)
#7022 := [rewrite]: #7021
#7025 := [monotonicity #7022]: #7024
#7028 := [monotonicity #7018 #7025]: #7027
#7034 := [monotonicity #7028]: #7033
#7038 := [trans #7034 #7036]: #7037
#7031 := [quant-inst #2241]: #7030
#7039 := [mp #7031 #7038]: #7029
#17703 := [unit-resolution #7039 #12414]: #7026
#17707 := [unit-resolution #17703 #17686 #17704]: #7023
#7408 := (not #7023)
#7409 := (or #7408 #7040)
#7410 := [th-lemma arith triangle-eq]: #7409
#18024 := [unit-resolution #7410 #17707]: #7040
#18025 := [th-lemma arith farkas 1 1 1 1 1 #7412 #18024 #17680 #16320 #6589]: false
#18222 := [lemma #18025]: #18221
#17240 := [unit-resolution #18222 #7412]: #6946
#7190 := (or #7399 #7187)
#7193 := [th-lemma arith triangle-eq]: #7190
#17265 := [unit-resolution #7193 #17240]: #7187
#17092 := [th-lemma arith farkas -1 1 1 #7412 #17265 #7188]: false
#17248 := [lemma #17092]: #2243
#4041 := (or #4479 #4473)
#4042 := [def-axiom]: #4041
#23385 := [unit-resolution #4042 #21234]: #4473
#6294 := (= #100 #203)
#23388 := (iff #6294 #204)
#23387 := [commutativity]: #1456
#23386 := (iff #6294 #790)
#23381 := [monotonicity #6590]: #23386
#23389 := [trans #23381 #23387]: #23388
#16723 := (or #6294 #4394)
#6595 := (or #6294 #963 #4394 #4369)
#6246 := (f5 f22 f10)
#6253 := (f4 #6246)
#6521 := (<= #6253 0::Int)
#6523 := (not #6521)
#6200 := (= f10 f22)
#6431 := (not #6200)
#4579 := (f8 f15 f10)
#4580 := (= f1 #4579)
#6414 := (ite #6200 #5798 #4580)
#6430 := (not #6414)
#6329 := (f9 f15 f22 #5797)
#6415 := (f8 #6329 f10)
#6416 := (= f1 #6415)
#6418 := (iff #6414 #6416)
#6421 := (or #6350 #6418)
#6417 := (iff #6416 #6414)
#6422 := (or #6350 #6417)
#6424 := (iff #6422 #6421)
#6426 := (iff #6421 #6421)
#6427 := [rewrite]: #6426
#6419 := (iff #6417 #6418)
#6420 := [rewrite]: #6419
#6425 := [monotonicity #6420]: #6424
#6428 := [trans #6425 #6427]: #6424
#6423 := [quant-inst #105 #171 #5797 #56]: #6422
#6429 := [mp #6423 #6428]: #6421
#6539 := [unit-resolution #6429 #4185]: #6418
#6441 := (not #6416)
#6379 := (f8 f23 f10)
#6380 := (= f1 #6379)
#6383 := (not #6380)
#6561 := (iff #6383 #6441)
#6559 := (iff #6380 #6416)
#6557 := (iff #6416 #6380)
#6555 := (= #6415 #6379)
#6553 := (= #6329 f23)
#6545 := [hypothesis]: #182
#6552 := [symm #6545]: #6551
#6549 := (= #6329 #181)
#6550 := [monotonicity #6548]: #6549
#6554 := [trans #6550 #6552]: #6553
#6556 := [monotonicity #6554]: #6555
#6558 := [monotonicity #6556]: #6557
#6560 := [symm #6558]: #6559
#6562 := [monotonicity #6560]: #6561
#6540 := (not #6294)
#6541 := [hypothesis]: #6540
#6384 := (or #6294 #6383)
#6542 := [hypothesis]: #4389
#6387 := (or #4394 #6294 #6383)
#6388 := (or #4394 #6384)
#6390 := (iff #6388 #6387)
#6391 := [rewrite]: #6390
#6389 := [quant-inst #56]: #6388
#6392 := [mp #6389 #6391]: #6387
#6543 := [unit-resolution #6392 #6542]: #6384
#6544 := [unit-resolution #6543 #6541]: #6383
#6563 := [mp #6544 #6562]: #6441
#6440 := (not #6418)
#6444 := (or #6440 #6430 #6416)
#6445 := [def-axiom]: #6444
#6564 := [unit-resolution #6445 #6563 #6539]: #6430
#6565 := (or #6414 #6431)
#6436 := (or #6414 #6431 #6364)
#6437 := [def-axiom]: #6436
#6566 := [unit-resolution #6437 #6546]: #6565
#6567 := [unit-resolution #6566 #6564]: #6431
#6525 := (or #6200 #6523)
#6528 := (or #5423 #6200 #6523)
#6198 := (= f22 f10)
#6524 := (or #6198 #6523)
#6529 := (or #5423 #6524)
#6536 := (iff #6529 #6528)
#6531 := (or #5423 #6525)
#6534 := (iff #6531 #6528)
#6535 := [rewrite]: #6534
#6532 := (iff #6529 #6531)
#6526 := (iff #6524 #6525)
#6201 := (iff #6198 #6200)
#6202 := [rewrite]: #6201
#6527 := [monotonicity #6202]: #6526
#6533 := [monotonicity #6527]: #6532
#6537 := [trans #6533 #6535]: #6536
#6530 := [quant-inst #171 #56]: #6529
#6538 := [mp #6530 #6537]: #6528
#6568 := [unit-resolution #6538 #4151]: #6525
#6569 := [unit-resolution #6568 #6567]: #6523
#6257 := (* -1::Int #6253)
#6258 := (+ #1421 #6257)
#6259 := (+ #100 #6258)
#6260 := (<= #6259 0::Int)
#6319 := (not #6260)
#6261 := (+ f3 #6257)
#6262 := (<= #6261 0::Int)
#6296 := (or #6260 #6262)
#6299 := (not #6296)
#6302 := (or #6294 #6299)
#6570 := [hypothesis]: #4364
#6305 := (or #4369 #6294 #6299)
#6292 := (or #6262 #6260)
#6293 := (not #6292)
#6295 := (or #6294 #6293)
#6306 := (or #4369 #6295)
#6313 := (iff #6306 #6305)
#6308 := (or #4369 #6302)
#6311 := (iff #6308 #6305)
#6312 := [rewrite]: #6311
#6309 := (iff #6306 #6308)
#6303 := (iff #6295 #6302)
#6300 := (iff #6293 #6299)
#6297 := (iff #6292 #6296)
#6298 := [rewrite]: #6297
#6301 := [monotonicity #6298]: #6300
#6304 := [monotonicity #6301]: #6303
#6310 := [monotonicity #6304]: #6309
#6314 := [trans #6310 #6312]: #6313
#6307 := [quant-inst #56]: #6306
#6315 := [mp #6307 #6314]: #6305
#6571 := [unit-resolution #6315 #6570]: #6302
#6572 := [unit-resolution #6571 #6541]: #6299
#6320 := (or #6296 #6319)
#6321 := [def-axiom]: #6320
#6573 := [unit-resolution #6321 #6572]: #6319
#4597 := (<= #100 0::Int)
#6591 := (or #1715 #4597)
#6592 := [th-lemma arith triangle-eq]: #6591
#6593 := [unit-resolution #6592 #6590]: #4597
#6594 := [th-lemma arith farkas 1 1 1 1 #6593 #6589 #6573 #6569]: false
#6596 := [lemma #6594]: #6595
#16991 := [unit-resolution #6596 #12183 #14384]: #16723
#16994 := [unit-resolution #16991 #21235]: #6294
#23390 := [mp #16994 #23389]: #204
#4051 := (or #4476 #1458 #4470)
#4037 := [def-axiom]: #4051
#23376 := [unit-resolution #4037 #23390 #23385]: #4470
#4060 := (or #4467 #4461)
#4044 := [def-axiom]: #4060
#23407 := [unit-resolution #4044 #23376]: #4461
#4057 := (or #4464 #2244 #4458)
#4058 := [def-axiom]: #4057
#23408 := [unit-resolution #4058 #23407]: #4461
#23406 := [unit-resolution #23408 #17248]: #4458
#4052 := (or #4455 #4449)
#4054 := [def-axiom]: #4052
#23409 := [unit-resolution #4054 #23406]: #4449
#23423 := (or #4452 #4446)
#12871 := (or #3408 #6861 #4369 #4377 #4359 #963 #4385)
#7870 := (f13 f14 ?v1!16)
#7887 := (* -1::Int #7870)
#8417 := (+ #175 #7887)
#8418 := (<= #8417 0::Int)
#7241 := (f8 f15 ?v1!16)
#7242 := (= f1 #7241)
#12265 := (not #7242)
#8636 := (= ?v1!16 #6633)
#8577 := (ite #8636 #5798 #7242)
#11216 := (not #8577)
#8579 := (f8 #8578 ?v1!16)
#8580 := (= f1 #8579)
#8576 := (iff #8577 #8580)
#11651 := (or #6350 #8576)
#8581 := (iff #8580 #8577)
#12234 := (or #6350 #8581)
#11795 := (iff #12234 #11651)
#11187 := (iff #11651 #11651)
#10865 := [rewrite]: #11187
#8582 := (iff #8581 #8576)
#8583 := [rewrite]: #8582
#11748 := [monotonicity #8583]: #11795
#11059 := [trans #11748 #10865]: #11795
#12235 := [quant-inst #105 #6633 #5797 #2256]: #12234
#11040 := [mp #12235 #11059]: #11651
#12698 := [unit-resolution #11040 #4185]: #8576
#12268 := (not #8580)
#12787 := (iff #2267 #12268)
#12733 := (iff #2266 #8580)
#12731 := (iff #8580 #2266)
#12705 := (= #8579 #2265)
#10519 := [unit-resolution #6646 #4163]: #6642
#10521 := [symm #10519]: #10520
#10523 := [monotonicity #10521 #6548]: #10522
#10525 := [trans #10523 #6552]: #10524
#12730 := [monotonicity #10525]: #12705
#12732 := [monotonicity #12730]: #12731
#12735 := [symm #12732]: #12733
#12788 := [monotonicity #12735]: #12787
#12727 := [hypothesis]: #3413
#3941 := (or #3408 #2267)
#3942 := [def-axiom]: #3941
#12717 := [unit-resolution #3942 #12727]: #2267
#12789 := [mp #12717 #12788]: #12268
#12267 := (not #8576)
#12274 := (or #12267 #11216 #8580)
#12275 := [def-axiom]: #12274
#12784 := [unit-resolution #12275 #12789 #12698]: #11216
#11129 := (not #8636)
#12785 := (or #8577 #11129)
#12196 := (or #8577 #11129 #6364)
#12086 := [def-axiom]: #12196
#12831 := [unit-resolution #12086 #6546]: #12785
#12832 := [unit-resolution #12831 #12784]: #11129
#12260 := (or #8577 #8636 #12265)
#12266 := [def-axiom]: #12260
#12827 := [unit-resolution #12266 #12832 #12784]: #12265
#8423 := (or #7242 #8418)
#12833 := [hypothesis]: #4354
#12401 := (or #4359 #7242 #8418)
#8388 := (+ #7870 #1421)
#8389 := (>= #8388 0::Int)
#8392 := (or #7242 #8389)
#12402 := (or #4359 #8392)
#12444 := (iff #12402 #12401)
#12423 := (or #4359 #8423)
#12443 := (iff #12423 #12401)
#12437 := [rewrite]: #12443
#12427 := (iff #12402 #12423)
#8424 := (iff #8392 #8423)
#8421 := (iff #8389 #8418)
#8393 := (+ #1421 #7870)
#8396 := (>= #8393 0::Int)
#8419 := (iff #8396 #8418)
#8420 := [rewrite]: #8419
#8397 := (iff #8389 #8396)
#8394 := (= #8388 #8393)
#8395 := [rewrite]: #8394
#8387 := [monotonicity #8395]: #8397
#8422 := [trans #8387 #8420]: #8421
#8425 := [monotonicity #8422]: #8424
#12440 := [monotonicity #8425]: #12427
#12446 := [trans #12440 #12437]: #12444
#12403 := [quant-inst #2256]: #12402
#12447 := [mp #12403 #12446]: #12401
#12834 := [unit-resolution #12447 #12833]: #8423
#12835 := [unit-resolution #12834 #12827]: #8418
#4084 := (not #2856)
#4085 := (or #3408 #4084)
#4086 := [def-axiom]: #4085
#12836 := [unit-resolution #4086 #12727]: #4084
#7250 := (f13 f14 ?v0!17)
#7648 := (* -1::Int #7250)
#7649 := (+ #2258 #7648)
#7650 := (<= #7649 0::Int)
#12837 := [hypothesis]: #4380
#12330 := (or #4385 #7650)
#7632 := (+ #7250 #2259)
#7633 := (>= #7632 0::Int)
#12331 := (or #4385 #7633)
#12292 := (iff #12331 #12330)
#12315 := (iff #12330 #12330)
#12316 := [rewrite]: #12315
#7647 := (iff #7633 #7650)
#7630 := (+ #2259 #7250)
#7637 := (>= #7630 0::Int)
#7651 := (iff #7637 #7650)
#7646 := [rewrite]: #7651
#7638 := (iff #7633 #7637)
#7635 := (= #7632 #7630)
#7636 := [rewrite]: #7635
#7639 := [monotonicity #7636]: #7638
#7652 := [trans #7639 #7646]: #7647
#12306 := [monotonicity #7652]: #12292
#12317 := [trans #12306 #12316]: #12292
#12333 := [quant-inst #2257]: #12331
#12291 := [mp #12333 #12317]: #12330
#12853 := [unit-resolution #12291 #12837]: #7650
#12822 := [monotonicity #10521]: #12821
#12823 := [symm #12822]: #7909
#12807 := [unit-resolution #12826 #12823]: #8012
#12699 := (+ #6858 #7648)
#12700 := (>= #12699 0::Int)
#13391 := [hypothesis]: #13390
#7513 := (f8 f15 ?v0!17)
#7514 := (= f1 #7513)
#8847 := (= ?v0!17 #6633)
#8848 := (ite #8847 #5798 #7514)
#8838 := (f8 #8578 ?v0!17)
#8868 := (= f1 #8838)
#9021 := (iff #8848 #8868)
#12208 := (or #6350 #9021)
#8869 := (iff #8868 #8848)
#12261 := (or #6350 #8869)
#12263 := (iff #12261 #12208)
#12272 := (iff #12208 #12208)
#12270 := [rewrite]: #12272
#9022 := (iff #8869 #9021)
#9075 := [rewrite]: #9022
#12264 := [monotonicity #9075]: #12263
#12271 := [trans #12264 #12270]: #12263
#12262 := [quant-inst #105 #6633 #5797 #2257]: #12261
#12273 := [mp #12262 #12271]: #12208
#12854 := [unit-resolution #12273 #4185]: #9021
#12860 := (= #2263 #8838)
#12856 := (= #8838 #2263)
#12857 := [monotonicity #10525]: #12856
#12861 := [symm #12857]: #12860
#4099 := (or #3408 #2264)
#3940 := [def-axiom]: #4099
#12855 := [unit-resolution #3940 #12727]: #2264
#12841 := [trans #12855 #12861]: #8868
#12300 := (not #8868)
#12285 := (not #9021)
#12286 := (or #12285 #8848 #12300)
#12287 := [def-axiom]: #12286
#12842 := [unit-resolution #12287 #12841 #12854]: #8848
#12296 := (not #8847)
#12706 := (= #2258 #6119)
#12815 := (not #12706)
#6160 := (* -1::Int #6119)
#12725 := (+ #2258 #6160)
#12726 := (<= #12725 0::Int)
#12539 := (not #12726)
#6371 := (+ #175 #6160)
#6372 := (>= #6371 0::Int)
#6377 := (or #4385 #6372)
#6378 := [quant-inst #171]: #6377
#12843 := [unit-resolution #6378 #12837]: #6372
#7888 := (+ #2260 #7887)
#9433 := (>= #7888 0::Int)
#8060 := (= #2260 #7870)
#7911 := (f5 f22 ?v1!16)
#7913 := (f4 #7911)
#7974 := (+ #7887 #7913)
#7969 := (+ #175 #7974)
#7975 := (>= #7969 0::Int)
#7938 := (* -1::Int #7913)
#7935 := (+ f3 #7938)
#7941 := (<= #7935 0::Int)
#8062 := (or #7941 #7975)
#7405 := [hypothesis]: #4372
#7979 := (+ #2854 #7913)
#8004 := (+ #175 #7979)
#8008 := (= #8004 0::Int)
#11151 := (not #8008)
#9352 := (<= #8004 0::Int)
#13412 := (not #9352)
#13411 := (not #7650)
#12258 := (not #8848)
#9988 := (not #6372)
#12829 := (or #13412 #2856 #9988 #12258 #6861 #13411 #8636)
#12813 := (= ?v0!17 f22)
#13372 := [hypothesis]: #8848
#12302 := (not #7514)
#12801 := (not #12700)
#11160 := (f5 #6633 ?v1!16)
#11161 := (f4 #11160)
#11162 := (* -1::Int #11161)
#10312 := (+ #7913 #11162)
#10316 := (>= #10312 0::Int)
#8672 := (= #7913 #11161)
#12791 := (= #11161 #7913)
#12786 := (= #11160 #7911)
#12790 := [monotonicity #10521]: #12786
#12792 := [monotonicity #12790]: #12791
#12793 := [symm #12792]: #8672
#12794 := (not #8672)
#12805 := (or #12794 #10316)
#12808 := [th-lemma arith triangle-eq]: #12805
#12809 := [unit-resolution #12808 #12793]: #10316
#11204 := (<= #11161 0::Int)
#11207 := (not #11204)
#12819 := [hypothesis]: #11129
#12416 := (or #5423 #8636 #11207)
#11203 := (= #6633 ?v1!16)
#11208 := (or #11203 #11207)
#12417 := (or #5423 #11208)
#12583 := (iff #12417 #12416)
#11211 := (or #8636 #11207)
#12522 := (or #5423 #11211)
#12564 := (iff #12522 #12416)
#12582 := [rewrite]: #12564
#12575 := (iff #12417 #12522)
#11212 := (iff #11208 #11211)
#11209 := (iff #11203 #8636)
#11210 := [rewrite]: #11209
#11213 := [monotonicity #11210]: #11212
#12563 := [monotonicity #11213]: #12575
#12584 := [trans #12563 #12582]: #12583
#12500 := [quant-inst #6633 #2256]: #12417
#12670 := [mp #12500 #12584]: #12416
#12820 := [unit-resolution #12670 #4151 #12819]: #11207
#13399 := [hypothesis]: #4084
#13400 := [hypothesis]: #7650
#13398 := [hypothesis]: #9352
#13413 := (not #10316)
#12802 := (or #12801 #13410 #13411 #2856 #13412 #11204 #13413)
#12800 := [hypothesis]: #12700
#13396 := [hypothesis]: #10316
#13397 := [hypothesis]: #11207
#13408 := [hypothesis]: #8012
#12795 := [th-lemma arith farkas 1 1 1 1 1 1 1 #13408 #13400 #13399 #13398 #13397 #13396 #12800]: false
#12803 := [lemma #12795]: #12802
#12810 := [unit-resolution #12803 #13398 #13400 #13399 #12807 #12820 #12809]: #12801
#12799 := (or #12302 #6861 #12700)
#12796 := [hypothesis]: #12801
#12797 := [hypothesis]: #7514
#12704 := (or #4264 #6861 #12302 #12700)
#12701 := (or #6861 #12302 #12700)
#12707 := (or #4264 #12701)
#12709 := (iff #12707 #12704)
#12723 := [rewrite]: #12709
#12708 := [quant-inst #2257 #6633]: #12707
#12724 := [mp #12708 #12723]: #12704
#12798 := [unit-resolution #12724 #13392 #13391 #12797 #12796]: false
#12804 := [lemma #12798]: #12799
#12811 := [unit-resolution #12804 #12810 #13391]: #12302
#12298 := (or #12258 #8847 #7514)
#12281 := [def-axiom]: #12298
#12812 := [unit-resolution #12281 #12811 #13372]: #8847
#12806 := [trans #12812 #10521]: #12813
#12814 := [monotonicity #12806]: #12706
#12816 := (or #12815 #12726)
#12817 := [th-lemma arith triangle-eq]: #12816
#12818 := [unit-resolution #12817 #12814]: #12726
#9977 := [hypothesis]: #6372
#12828 := [th-lemma arith farkas 1 1 1 1 1 1 #13399 #13398 #12820 #12809 #9977 #12818]: false
#12830 := [lemma #12828]: #12829
#12844 := [unit-resolution #12830 #12836 #12843 #12842 #13391 #12853 #12832]: #13412
#12845 := (or #11151 #9352)
#12840 := [th-lemma arith triangle-eq]: #12845
#12846 := [unit-resolution #12840 #12844]: #11151
#11158 := (or #8062 #8008 #4377)
#11152 := [hypothesis]: #11151
#9434 := (not #7941)
#8065 := (not #8062)
#11153 := [hypothesis]: #8065
#9435 := (or #8062 #9434)
#9436 := [def-axiom]: #9435
#11154 := [unit-resolution #9436 #11153]: #9434
#9431 := (not #7975)
#9437 := (or #8062 #9431)
#9438 := [def-axiom]: #9437
#11155 := [unit-resolution #9438 #11153]: #9431
#8010 := (or #7941 #7975 #8008)
#9319 := (or #4377 #7941 #7975 #8008)
#7936 := (+ #7913 #2854)
#7912 := (+ #175 #7936)
#7937 := (= #7912 0::Int)
#7939 := (+ #1421 #7938)
#7902 := (+ #7870 #7939)
#7940 := (<= #7902 0::Int)
#7942 := (or #7941 #7940 #7937)
#9320 := (or #4377 #7942)
#9349 := (iff #9320 #9319)
#9345 := (or #4377 #8010)
#9347 := (iff #9345 #9319)
#9348 := [rewrite]: #9347
#9317 := (iff #9320 #9345)
#8006 := (iff #7942 #8010)
#8003 := (iff #7937 #8008)
#8005 := (= #7912 #8004)
#8007 := [rewrite]: #8005
#8009 := [monotonicity #8007]: #8003
#7977 := (iff #7940 #7975)
#7899 := (+ #7870 #7938)
#7943 := (+ #1421 #7899)
#7970 := (<= #7943 0::Int)
#7976 := (iff #7970 #7975)
#7972 := [rewrite]: #7976
#7971 := (iff #7940 #7970)
#7944 := (= #7902 #7943)
#7945 := [rewrite]: #7944
#7973 := [monotonicity #7945]: #7971
#7978 := [trans #7973 #7972]: #7977
#8011 := [monotonicity #7978 #8009]: #8006
#9346 := [monotonicity #8011]: #9317
#9344 := [trans #9346 #9348]: #9349
#9321 := [quant-inst #2256]: #9320
#9351 := [mp #9321 #9344]: #9319
#11156 := [unit-resolution #9351 #7405]: #8010
#11157 := [unit-resolution #11156 #11155 #11154 #11152]: false
#11159 := [lemma #11157]: #11158
#12847 := [unit-resolution #11159 #12846 #7405]: #8062
#8106 := (or #8060 #8065)
#12385 := (or #4369 #8060 #8065)
#8040 := (or #7941 #7940)
#8041 := (not #8040)
#8058 := (= #7870 #2260)
#8059 := (or #8058 #8041)
#12386 := (or #4369 #8059)
#12352 := (iff #12386 #12385)
#12387 := (or #4369 #8106)
#12372 := (iff #12387 #12385)
#12351 := [rewrite]: #12372
#12371 := (iff #12386 #12387)
#8107 := (iff #8059 #8106)
#8103 := (iff #8041 #8065)
#8063 := (iff #8040 #8062)
#8064 := [monotonicity #7978]: #8063
#8104 := [monotonicity #8064]: #8103
#8061 := (iff #8058 #8060)
#8057 := [rewrite]: #8061
#8102 := [monotonicity #8057 #8104]: #8107
#12365 := [monotonicity #8102]: #12371
#12370 := [trans #12365 #12351]: #12352
#12382 := [quant-inst #2256]: #12386
#12354 := [mp #12382 #12370]: #12385
#12848 := [unit-resolution #12354 #6570]: #8106
#12849 := [unit-resolution #12848 #12847]: #8060
#12850 := (not #8060)
#12864 := (or #12850 #9433)
#12865 := [th-lemma arith triangle-eq]: #12864
#12863 := [unit-resolution #12865 #12849]: #9433
#12541 := (not #8418)
#12540 := (not #9433)
#12674 := (or #12539 #12540 #2856 #9988 #12541)
#12251 := [hypothesis]: #8418
#12289 := [hypothesis]: #12726
#12537 := [hypothesis]: #9433
#12538 := [th-lemma arith farkas -1 1 -1 -1 1 #12537 #12289 #13399 #9977 #12251]: false
#12675 := [lemma #12538]: #12674
#12866 := [unit-resolution #12675 #12863 #12836 #12843 #12835]: #12539
#12867 := [unit-resolution #12817 #12866]: #12815
#12358 := (or #12296 #12706)
#12553 := [hypothesis]: #8847
#12554 := [trans #12553 #10521]: #12813
#12555 := [monotonicity #12554]: #12706
#12531 := [hypothesis]: #12815
#12290 := [unit-resolution #12531 #12555]: false
#12404 := [lemma #12290]: #12358
#12868 := [unit-resolution #12404 #12867]: #12296
#12869 := [unit-resolution #12281 #12868 #12842]: #7514
#12862 := [unit-resolution #12804 #12869 #13391]: #12700
#12870 := [th-lemma arith farkas -1 -1 -1 1 -1 1 #12863 #12862 #12807 #12853 #12836 #12835]: false
#12872 := [lemma #12870]: #12871
#23410 := [unit-resolution #12872 #16525 #12183 #12414 #23337 #14384 #16406]: #3408
#4074 := (or #4452 #3413 #4446)
#4061 := [def-axiom]: #4074
#23424 := [unit-resolution #4061 #23410]: #23423
#23425 := [unit-resolution #23424 #23409]: #4446
#3968 := (or #4443 #4437)
#3976 := [def-axiom]: #3968
#35870 := [unit-resolution #3976 #23425]: #4437
#3957 := (or #4440 #3459 #4434)
#3972 := [def-axiom]: #3957
#35975 := [unit-resolution #3972 #35870]: #4437
#35977 := [unit-resolution #35975 #26288]: #4434
#4076 := (or #4431 #2328)
#4078 := [def-axiom]: #4076
#35978 := [unit-resolution #4078 #35977]: #2328
#19048 := (+ #2315 #19047)
#33257 := (>= #19048 0::Int)
#19017 := (= #2315 #19006)
#3963 := (or #4431 #4423)
#3964 := [def-axiom]: #3963
#35976 := [unit-resolution #3964 #35977]: #4423
#36283 := (or #19017 #4428)
#6796 := (* -1::Int #6789)
#18972 := (+ #2315 #6796)
#19255 := (<= #18972 0::Int)
#36252 := (not #19255)
#19240 := (f5 #6633 ?v0!20)
#19241 := (f4 #19240)
#35004 := (<= #19241 0::Int)
#35006 := (not #35004)
#23778 := (= ?v0!20 #6633)
#34700 := (not #23778)
#19430 := (f8 f15 ?v0!20)
#19431 := (= f1 #19430)
#23779 := (ite #23778 #5798 #19431)
#34699 := (not #23779)
#23780 := (f8 #8578 ?v0!20)
#23781 := (= f1 #23780)
#23783 := (iff #23779 #23781)
#34667 := (or #6350 #23783)
#23782 := (iff #23781 #23779)
#34662 := (or #6350 #23782)
#34669 := (iff #34662 #34667)
#34671 := (iff #34667 #34667)
#34672 := [rewrite]: #34671
#23784 := (iff #23782 #23783)
#23785 := [rewrite]: #23784
#34670 := [monotonicity #23785]: #34669
#34697 := [trans #34670 #34672]: #34669
#34668 := [quant-inst #105 #6633 #5797 #2314]: #34662
#34698 := [mp #34668 #34697]: #34667
#35187 := [unit-resolution #34698 #4185]: #23783
#34715 := (not #23781)
#7379 := (f8 f23 ?v0!20)
#7380 := (= f1 #7379)
#7658 := (not #7380)
#35308 := (iff #7658 #34715)
#35196 := (iff #7380 #23781)
#35194 := (iff #23781 #7380)
#35192 := (= #23780 #7379)
#35193 := [monotonicity #16227]: #35192
#35195 := [monotonicity #35193]: #35194
#35197 := [symm #35195]: #35196
#35309 := [monotonicity #35197]: #35308
#35188 := (not #19017)
#35189 := [hypothesis]: #35188
#19023 := (or #7658 #19017)
#33213 := (or #4394 #7658 #19017)
#19013 := (= #19006 #2315)
#19016 := (or #19013 #7658)
#33201 := (or #4394 #19016)
#33255 := (iff #33201 #33213)
#33218 := (or #4394 #19023)
#33250 := (iff #33218 #33213)
#33247 := [rewrite]: #33250
#33251 := (iff #33201 #33218)
#19026 := (iff #19016 #19023)
#19020 := (or #19017 #7658)
#19024 := (iff #19020 #19023)
#19025 := [rewrite]: #19024
#19021 := (iff #19016 #19020)
#19018 := (iff #19013 #19017)
#19019 := [rewrite]: #19018
#19022 := [monotonicity #19019]: #19021
#19027 := [trans #19022 #19025]: #19026
#33252 := [monotonicity #19027]: #33251
#33254 := [trans #33252 #33247]: #33255
#33219 := [quant-inst #2314]: #33201
#33256 := [mp #33219 #33254]: #33213
#35190 := [unit-resolution #33256 #21235]: #19023
#35191 := [unit-resolution #35190 #35189]: #7658
#35310 := [mp #35191 #35309]: #34715
#34712 := (not #23783)
#34735 := (or #34712 #34699 #23781)
#34736 := [def-axiom]: #34735
#35317 := [unit-resolution #34736 #35310 #35187]: #34699
#35318 := (or #23779 #34700)
#34704 := (or #23779 #34700 #6364)
#34705 := [def-axiom]: #34704
#35319 := [unit-resolution #34705 #6546]: #35318
#35320 := [unit-resolution #35319 #35317]: #34700
#35008 := (or #23778 #35006)
#35035 := (or #5423 #23778 #35006)
#34947 := (= #6633 ?v0!20)
#35007 := (or #34947 #35006)
#35036 := (or #5423 #35007)
#35042 := (iff #35036 #35035)
#35032 := (or #5423 #35008)
#35040 := (iff #35032 #35035)
#35041 := [rewrite]: #35040
#35038 := (iff #35036 #35032)
#35033 := (iff #35007 #35008)
#34952 := (iff #34947 #23778)
#34977 := [rewrite]: #34952
#35034 := [monotonicity #34977]: #35033
#35039 := [monotonicity #35034]: #35038
#35067 := [trans #35039 #35041]: #35042
#35037 := [quant-inst #6633 #2314]: #35036
#35068 := [mp #35037 #35067]: #35035
#35321 := [unit-resolution #35068 #4151]: #35008
#35322 := [unit-resolution #35321 #35320]: #35006
#19267 := (* -1::Int #19241)
#19063 := (f5 f22 ?v0!20)
#19064 := (f4 #19063)
#32479 := (+ #19064 #19267)
#32087 := (>= #32479 0::Int)
#32478 := (= #19064 #19241)
#35325 := (= #19241 #19064)
#35323 := (= #19240 #19063)
#35324 := [monotonicity #16510]: #35323
#35326 := [monotonicity #35324]: #35325
#35412 := [symm #35326]: #32478
#35413 := (not #32478)
#35420 := (or #35413 #32087)
#35421 := [th-lemma arith triangle-eq]: #35420
#35623 := [unit-resolution #35421 #35412]: #32087
#21232 := [unit-resolution #6378 #16406]: #6372
#6821 := (+ #6119 #6796)
#13529 := (>= #6821 0::Int)
#6795 := (= #6119 #6789)
#20632 := [symm #16274]: #6795
#15476 := (not #6795)
#25674 := (or #15476 #13529)
#25675 := [th-lemma arith triangle-eq]: #25674
#25676 := [unit-resolution #25675 #20632]: #13529
#19089 := (+ #2316 #19064)
#19090 := (+ #175 #19089)
#33287 := (<= #19090 0::Int)
#19093 := (= #19090 0::Int)
#19068 := (* -1::Int #19064)
#19072 := (+ f3 #19068)
#19073 := (<= #19072 0::Int)
#33290 := (not #19073)
#19082 := (+ #19047 #19064)
#19083 := (+ #175 #19082)
#19084 := (>= #19083 0::Int)
#19115 := (or #19073 #19084)
#19118 := (not #19115)
#19121 := (or #19017 #19118)
#33272 := (or #4369 #19017 #19118)
#19069 := (+ #1421 #19068)
#19070 := (+ #19006 #19069)
#19071 := (<= #19070 0::Int)
#19112 := (or #19073 #19071)
#19113 := (not #19112)
#19114 := (or #19013 #19113)
#33275 := (or #4369 #19114)
#33281 := (iff #33275 #33272)
#33276 := (or #4369 #19121)
#33265 := (iff #33276 #33272)
#33278 := [rewrite]: #33265
#33264 := (iff #33275 #33276)
#19122 := (iff #19114 #19121)
#19119 := (iff #19113 #19118)
#19116 := (iff #19112 #19115)
#19087 := (iff #19071 #19084)
#19075 := (+ #19006 #19068)
#19076 := (+ #1421 #19075)
#19079 := (<= #19076 0::Int)
#19085 := (iff #19079 #19084)
#19086 := [rewrite]: #19085
#19080 := (iff #19071 #19079)
#19077 := (= #19070 #19076)
#19078 := [rewrite]: #19077
#19081 := [monotonicity #19078]: #19080
#19088 := [trans #19081 #19086]: #19087
#19117 := [monotonicity #19088]: #19116
#19120 := [monotonicity #19117]: #19119
#19123 := [monotonicity #19019 #19120]: #19122
#33277 := [monotonicity #19123]: #33264
#33279 := [trans #33277 #33278]: #33281
#33271 := [quant-inst #2314]: #33275
#33289 := [mp #33271 #33279]: #33272
#35624 := [unit-resolution #33289 #12183]: #19121
#35636 := [unit-resolution #35624 #35189]: #19118
#33291 := (or #19115 #33290)
#33286 := [def-axiom]: #33291
#35637 := [unit-resolution #33286 #35636]: #33290
#33293 := (not #19084)
#33294 := (or #19115 #33293)
#33284 := [def-axiom]: #33294
#35718 := [unit-resolution #33284 #35636]: #33293
#19096 := (or #19073 #19084 #19093)
#33268 := (or #4377 #19073 #19084 #19093)
#19065 := (+ #19064 #2316)
#19066 := (+ #175 #19065)
#19067 := (= #19066 0::Int)
#19074 := (or #19073 #19071 #19067)
#33266 := (or #4377 #19074)
#33285 := (iff #33266 #33268)
#33204 := (or #4377 #19096)
#33282 := (iff #33204 #33268)
#33283 := [rewrite]: #33282
#33270 := (iff #33266 #33204)
#19097 := (iff #19074 #19096)
#19094 := (iff #19067 #19093)
#19091 := (= #19066 #19090)
#19092 := [rewrite]: #19091
#19095 := [monotonicity #19092]: #19094
#19098 := [monotonicity #19088 #19095]: #19097
#33280 := [monotonicity #19098]: #33270
#33288 := [trans #33280 #33283]: #33285
#33269 := [quant-inst #2314]: #33266
#33273 := [mp #33269 #33288]: #33268
#35787 := [unit-resolution #33273 #12414]: #19096
#35788 := [unit-resolution #35787 #35718 #35637]: #19093
#36221 := (not #19093)
#36222 := (or #36221 #33287)
#36225 := [th-lemma arith triangle-eq]: #36222
#36226 := [unit-resolution #36225 #35788]: #33287
#36255 := (not #32087)
#36254 := (not #13529)
#36253 := (not #33287)
#36256 := (or #36252 #36253 #36254 #9988 #35004 #36255)
#36257 := [th-lemma arith assign-bounds 1 -1 -1 -1 -1]: #36256
#36258 := [unit-resolution #36257 #36226 #25676 #21232 #35623 #35322]: #36252
#19268 := (+ #6796 #19267)
#19269 := (+ #2315 #19268)
#19270 := (= #19269 0::Int)
#33442 := (>= #19269 0::Int)
#36259 := (or #33442 #36253 #36254 #9988 #36255)
#36260 := [th-lemma arith assign-bounds 1 -1 -1 -1]: #36259
#36261 := [unit-resolution #36260 #36226 #25676 #21232 #35623]: #33442
#33446 := (<= #19269 0::Int)
#32475 := (<= #32479 0::Int)
#36262 := (or #35413 #32475)
#36263 := [th-lemma arith triangle-eq]: #36262
#36264 := [unit-resolution #36263 #35412]: #32475
#6405 := (<= #6371 0::Int)
#25670 := (not #6120)
#25671 := (or #25670 #6405)
#25672 := [th-lemma arith triangle-eq]: #25671
#25673 := [unit-resolution #25672 #16197]: #6405
#6822 := (<= #6821 0::Int)
#15477 := (or #15476 #6822)
#15478 := [th-lemma arith triangle-eq]: #15477
#20633 := [unit-resolution #15478 #20632]: #6822
#33274 := (>= #19090 0::Int)
#36265 := (or #36221 #33274)
#36266 := [th-lemma arith triangle-eq]: #36265
#36267 := [unit-resolution #36266 #35788]: #33274
#36270 := (not #32475)
#9167 := (not #6405)
#36269 := (not #6822)
#36268 := (not #33274)
#36271 := (or #33446 #36268 #36269 #9167 #36270)
#36272 := [th-lemma arith assign-bounds 1 -1 -1 -1]: #36271
#36273 := [unit-resolution #36272 #36267 #20633 #25673 #36264]: #33446
#36275 := (not #33442)
#36274 := (not #33446)
#36276 := (or #19270 #36274 #36275)
#36277 := [th-lemma arith triangle-eq]: #36276
#36278 := [unit-resolution #36277 #36273 #36261]: #19270
#19275 := (not #19270)
#36280 := (or #19255 #19275)
#12408 := (f8 f23 #6633)
#12409 := (= f1 #12408)
#15483 := (= #5797 #12408)
#15481 := (= #12408 #5797)
#23255 := [monotonicity #14384 #16510]: #15481
#23382 := [symm #23255]: #15483
#23383 := [trans #6546 #23382]: #12409
#36279 := [hypothesis]: #4423
#12293 := (not #12409)
#33458 := (or #4428 #12293 #19255 #19275)
#19242 := (+ #2316 #19241)
#19243 := (+ #6789 #19242)
#19244 := (= #19243 0::Int)
#19245 := (not #19244)
#19246 := (+ #6789 #2316)
#19247 := (>= #19246 0::Int)
#19248 := (or #12293 #19247 #19245)
#20120 := (or #4428 #19248)
#33444 := (iff #20120 #33458)
#19278 := (or #12293 #19255 #19275)
#17209 := (or #4428 #19278)
#22024 := (iff #17209 #33458)
#33443 := [rewrite]: #22024
#18500 := (iff #20120 #17209)
#19279 := (iff #19248 #19278)
#19276 := (iff #19245 #19275)
#19273 := (iff #19244 #19270)
#19260 := (+ #6789 #19241)
#19261 := (+ #2316 #19260)
#19264 := (= #19261 0::Int)
#19271 := (iff #19264 #19270)
#19272 := [rewrite]: #19271
#19265 := (iff #19244 #19264)
#19262 := (= #19243 #19261)
#19263 := [rewrite]: #19262
#19266 := [monotonicity #19263]: #19265
#19274 := [trans #19266 #19272]: #19273
#19277 := [monotonicity #19274]: #19276
#19258 := (iff #19247 #19255)
#19249 := (+ #2316 #6789)
#19252 := (>= #19249 0::Int)
#19256 := (iff #19252 #19255)
#19257 := [rewrite]: #19256
#19253 := (iff #19247 #19252)
#19250 := (= #19246 #19249)
#19251 := [rewrite]: #19250
#19254 := [monotonicity #19251]: #19253
#19259 := [trans #19254 #19257]: #19258
#19280 := [monotonicity #19259 #19277]: #19279
#17218 := [monotonicity #19280]: #18500
#33445 := [trans #17218 #33443]: #33444
#20081 := [quant-inst #6633]: #20120
#33440 := [mp #20081 #33445]: #33458
#36281 := [unit-resolution #33440 #36279 #23383]: #36280
#36282 := [unit-resolution #36281 #36278 #36258]: false
#36284 := [lemma #36282]: #36283
#35973 := [unit-resolution #36284 #35976]: #19017
#36033 := (or #35188 #33257)
#33585 := [th-lemma arith triangle-eq]: #36033
#33590 := [unit-resolution #33585 #35973]: #33257
#34298 := (not #33257)
#34299 := (or #34297 #34298 #2327)
#34287 := [hypothesis]: #2328
#34288 := [hypothesis]: #33257
#34295 := [hypothesis]: #19477
#34296 := [th-lemma arith farkas -1 1 1 #34295 #34288 #34287]: false
#34300 := [lemma #34296]: #34299
#33591 := [unit-resolution #34300 #33590 #35978]: #34297
#4079 := (or #4431 #2897)
#4077 := [def-axiom]: #4079
#33599 := [unit-resolution #4077 #35977]: #2897
#24658 := (or #4280 #2894 #19477 #19482)
#19474 := (or #19473 #19470 #19463)
#19475 := (not #19474)
#19478 := (or #2329 #19477 #19475)
#24511 := (or #4280 #19478)
#24684 := (iff #24511 #24658)
#19485 := (or #2894 #19477 #19482)
#24685 := (or #4280 #19485)
#24577 := (iff #24685 #24658)
#24665 := [rewrite]: #24577
#24709 := (iff #24511 #24685)
#19486 := (iff #19478 #19485)
#19483 := (iff #19475 #19482)
#19480 := (iff #19474 #19479)
#19481 := [rewrite]: #19480
#19484 := [monotonicity #19481]: #19483
#19487 := [monotonicity #2896 #19484]: #19486
#24712 := [monotonicity #19487]: #24709
#24867 := [trans #24712 #24665]: #24684
#24578 := [quant-inst #2314]: #24511
#24900 := [mp #24578 #24867]: #24658
#36032 := [unit-resolution #24900 #9365 #33599 #33591]: #19482
#25017 := (or #19479 #24892)
#25018 := [def-axiom]: #25017
#32517 := [unit-resolution #25018 #36032]: #24892
#33452 := (<= #19468 0::Int)
#24899 := (or #19479 #19469)
#25016 := [def-axiom]: #24899
#42938 := [unit-resolution #25016 #36032]: #19469
#32527 := (or #19470 #33452)
#32534 := [th-lemma arith triangle-eq]: #32527
#32533 := [unit-resolution #32534 #42938]: #33452
#34394 := (f24 #19459)
#34411 := (* -1::Int #34394)
#34572 := (+ #19466 #34411)
#34573 := (+ #2315 #34572)
#28077 := (>= #34573 0::Int)
#34412 := (+ #19460 #34411)
#34413 := (>= #34412 0::Int)
#27942 := (or #4385 #34413)
#27748 := [quant-inst #19459]: #27942
#42937 := [unit-resolution #27748 #16406]: #34413
#24897 := (>= #19468 0::Int)
#42947 := (or #19470 #24897)
#42948 := [th-lemma arith triangle-eq]: #42947
#42949 := [unit-resolution #42948 #42938]: #24897
#42950 := (not #28077)
#42951 := [hypothesis]: #42950
#42952 := [th-lemma arith farkas -1 1 1 1 #42951 #42949 #33590 #42937]: false
#42953 := [lemma #42952]: #28077
#34605 := (+ #2315 #34411)
#34606 := (<= #34605 0::Int)
#34616 := (= #34573 0::Int)
#32567 := (or #34616 #42950)
#34574 := (<= #34573 0::Int)
#34562 := (+ f3 #19466)
#34563 := (<= #34562 0::Int)
#36818 := (not #34563)
#34556 := (>= #19460 0::Int)
#28036 := (or #4247 #34556)
#28035 := [quant-inst #19459]: #28036
#32369 := [unit-resolution #28035 #6588]: #34556
#32485 := (not #34556)
#36820 := (not #24897)
#32536 := (or #36818 #36820 #2327 #32485 #34298)
#32520 := [th-lemma arith assign-bounds -1 -1 -1 -1]: #32536
#32532 := [unit-resolution #32520 #33590 #32369 #42949 #35978]: #36818
#34391 := (f8 f23 #19459)
#34392 := (= f1 #34391)
#34709 := (f6 #19464)
#34766 := (f8 f23 #34709)
#34767 := (= f1 #34766)
#32529 := (iff #34767 #34392)
#32541 := (iff #34392 #34767)
#32537 := (= #34391 #34766)
#34710 := (= #19459 #34709)
#28153 := (or #6486 #34710)
#28142 := [quant-inst #19459 #2314]: #28153
#33589 := [unit-resolution #28142 #4157]: #34710
#32530 := [monotonicity #33589]: #32537
#32544 := [monotonicity #32530]: #32541
#32543 := [symm #32544]: #32529
#35609 := (f8 #8578 #34709)
#38823 := (= #35609 #34766)
#38819 := (= #34766 #35609)
#38817 := (= f23 #8578)
#38815 := (= #181 #8578)
#38816 := [symm #16201]: #38815
#38818 := [trans #14384 #38816]: #38817
#38820 := [monotonicity #38818]: #38819
#38824 := [symm #38820]: #38823
#35571 := (= f1 #35609)
#36662 := (f8 f15 #34709)
#36663 := (= f1 #36662)
#35595 := (= #6633 #34709)
#35602 := (ite #35595 #5798 #36663)
#35693 := (iff #35571 #35602)
#38791 := (or #6350 #35693)
#35615 := (= #34709 #6633)
#35690 := (ite #35615 #5798 #36663)
#35610 := (iff #35571 #35690)
#38792 := (or #6350 #35610)
#38794 := (iff #38792 #38791)
#38796 := (iff #38791 #38791)
#38797 := [rewrite]: #38796
#35694 := (iff #35610 #35693)
#35613 := (iff #35690 #35602)
#35593 := (iff #35615 #35595)
#35596 := [rewrite]: #35593
#35614 := [monotonicity #35596]: #35613
#35695 := [monotonicity #35614]: #35694
#38795 := [monotonicity #35695]: #38794
#38798 := [trans #38795 #38797]: #38794
#38793 := [quant-inst #105 #6633 #5797 #34709]: #38792
#38799 := [mp #38793 #38798]: #38791
#38811 := [unit-resolution #38799 #4185]: #35693
#38800 := (not #35693)
#38812 := (or #38800 #35571)
#35728 := (not #35602)
#35930 := [hypothesis]: #35728
#35729 := (not #35595)
#35933 := (or #35602 #35729)
#35778 := (or #35602 #35729 #6364)
#35779 := [def-axiom]: #35778
#35974 := [unit-resolution #35779 #6546]: #35933
#35929 := [unit-resolution #35974 #35930]: #35729
#33617 := (or #35602 #35595)
#33612 := (= #19471 #36662)
#33598 := (= #36662 #19471)
#33601 := (= #34709 #19459)
#33603 := [symm #33589]: #33601
#33605 := [monotonicity #33603]: #33598
#33616 := [symm #33605]: #33612
#24901 := (or #19479 #19472)
#24888 := [def-axiom]: #24901
#33600 := [unit-resolution #24888 #36032]: #19472
#33604 := [trans #33600 #33616]: #36663
#36664 := (not #36663)
#35781 := (or #35602 #35595 #36664)
#35843 := [def-axiom]: #35781
#33670 := [unit-resolution #35843 #33604]: #33617
#33816 := [unit-resolution #33670 #35929 #35930]: false
#33830 := [lemma #33816]: #35602
#38801 := (or #38800 #35571 #35728)
#38802 := [def-axiom]: #38801
#38813 := [unit-resolution #38802 #33830]: #38812
#38814 := [unit-resolution #38813 #38811]: #35571
#38825 := [trans #38814 #38824]: #34767
#34768 := (not #34767)
#38810 := [hypothesis]: #34768
#38826 := [unit-resolution #38810 #38825]: false
#38827 := [lemma #38826]: #34767
#32542 := [mp #38827 #32543]: #34392
#34393 := (not #34392)
#34579 := (or #34393 #34563 #34574)
#4080 := (or #4431 #4414)
#3962 := [def-axiom]: #4080
#32539 := [unit-resolution #3962 #35977]: #4414
#28044 := (or #4419 #34393 #34563 #34574)
#34557 := (+ #34394 #2316)
#34558 := (+ #19465 #34557)
#34561 := (>= #34558 0::Int)
#34564 := (or #34393 #34563 #34561)
#28042 := (or #4419 #34564)
#28080 := (iff #28042 #28044)
#28054 := (or #4419 #34579)
#28079 := (iff #28054 #28044)
#28066 := [rewrite]: #28079
#28073 := (iff #28042 #28054)
#34580 := (iff #34564 #34579)
#34577 := (iff #34561 #34574)
#34565 := (+ #19465 #34394)
#34566 := (+ #2316 #34565)
#34569 := (>= #34566 0::Int)
#34575 := (iff #34569 #34574)
#34576 := [rewrite]: #34575
#34570 := (iff #34561 #34569)
#34567 := (= #34558 #34566)
#34568 := [rewrite]: #34567
#34571 := [monotonicity #34568]: #34570
#34578 := [trans #34571 #34576]: #34577
#34581 := [monotonicity #34578]: #34580
#28074 := [monotonicity #34581]: #28073
#28070 := [trans #28074 #28066]: #28080
#28075 := [quant-inst #2314 #19459]: #28042
#28083 := [mp #28075 #28070]: #28044
#32553 := [unit-resolution #28083 #32539]: #34579
#32574 := [unit-resolution #32553 #32542 #32532]: #34574
#32559 := (not #34574)
#32572 := (or #34616 #32559 #42950)
#32585 := [th-lemma arith triangle-eq]: #32572
#32581 := [unit-resolution #32585 #32574]: #32567
#32595 := [unit-resolution #32581 #42953]: #34616
#34621 := (not #34616)
#32578 := (or #34606 #34621)
#34624 := (or #34393 #34606 #34621)
#28089 := (or #4428 #34393 #34606 #34621)
#34593 := (+ #2316 #19465)
#34594 := (+ #34394 #34593)
#34595 := (= #34594 0::Int)
#34596 := (not #34595)
#34597 := (>= #34557 0::Int)
#34598 := (or #34393 #34597 #34596)
#28088 := (or #4428 #34598)
#28092 := (iff #28088 #28089)
#28091 := (or #4428 #34624)
#28094 := (iff #28091 #28089)
#28062 := [rewrite]: #28094
#28085 := (iff #28088 #28091)
#34625 := (iff #34598 #34624)
#34622 := (iff #34596 #34621)
#34619 := (iff #34595 #34616)
#34613 := (= #34566 0::Int)
#34617 := (iff #34613 #34616)
#34618 := [rewrite]: #34617
#34614 := (iff #34595 #34613)
#34611 := (= #34594 #34566)
#34612 := [rewrite]: #34611
#34615 := [monotonicity #34612]: #34614
#34620 := [trans #34615 #34618]: #34619
#34623 := [monotonicity #34620]: #34622
#34609 := (iff #34597 #34606)
#34599 := (+ #2316 #34394)
#34602 := (>= #34599 0::Int)
#34607 := (iff #34602 #34606)
#34608 := [rewrite]: #34607
#34603 := (iff #34597 #34602)
#34600 := (= #34557 #34599)
#34601 := [rewrite]: #34600
#34604 := [monotonicity #34601]: #34603
#34610 := [trans #34604 #34608]: #34609
#34626 := [monotonicity #34610 #34623]: #34625
#28090 := [monotonicity #34626]: #28085
#28093 := [trans #28090 #28062]: #28092
#28087 := [quant-inst #19459]: #28088
#28057 := [mp #28087 #28093]: #28089
#32590 := [unit-resolution #28057 #35976]: #34624
#32592 := [unit-resolution #32590 #32542]: #32578
#32584 := [unit-resolution #32592 #32595]: #34606
[th-lemma arith farkas -1 1 -1 1 #32584 #42953 #32533 #32517]: false
unsat